Full switch to clang/ELF. Drop ack. Simplify.
There is important information about booting non-ack images in docs/UPDATING. ack/aout-format images can't be built any more, and booting clang/ELF-format ones is a little different. Updating to the new boot monitor is recommended. Changes in this commit: . drop boot monitor -> allowing dropping ack support . facility to copy ELF boot files to /boot so that old boot monitor can still boot fairly easily, see UPDATING . no more ack-format libraries -> single-case libraries . some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases . drop several ack toolchain commands, but not all support commands (e.g. aal is gone but acksize is not yet). . a few libc files moved to netbsd libc dir . new /bin/date as minix date used code in libc/ . test compile fix . harmonize includes . /usr/lib is no longer special: without ack, /usr/lib plays no kind of special bootstrapping role any more and bootstrapping is done exclusively through packages, so releases depend even less on the state of the machine making them now. . rename nbsd_lib* to lib* . reduce mtree
This commit is contained in:
Ben Gras
@@ -0,0 +1,104 @@
|
||||
/* @(#)e_acos.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
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||||
__RCSID("$NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_acos(x)
|
||||
* Method :
|
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* acos(x) = pi/2 - asin(x)
|
||||
* acos(-x) = pi/2 + asin(x)
|
||||
* For |x|<=0.5
|
||||
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
|
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* For x>0.5
|
||||
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
|
||||
* = 2asin(sqrt((1-x)/2))
|
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* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
|
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* = 2f + (2c + 2s*z*R(z))
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* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
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* for f so that f+c ~ sqrt(z).
|
||||
* For x<-0.5
|
||||
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
|
||||
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
* Function needed: __ieee754_sqrt
|
||||
*/
|
||||
|
||||
#include "math.h"
|
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#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
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pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
double
|
||||
__ieee754_acos(double x)
|
||||
{
|
||||
double z,p,q,r,w,s,c,df;
|
||||
int32_t hx,ix;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3ff00000) { /* |x| >= 1 */
|
||||
u_int32_t lx;
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
|
||||
}
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3fe00000) { /* |x| < 0.5 */
|
||||
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = __ieee754_sqrt(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - 2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
z = (one-x)*0.5;
|
||||
s = __ieee754_sqrt(z);
|
||||
df = s;
|
||||
SET_LOW_WORD(df,0);
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return 2.0*(df+w);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,82 @@
|
||||
/* e_acosf.c -- float version of e_acos.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_acosf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
|
||||
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
|
||||
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
|
||||
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
|
||||
pS3 = -4.0055535734e-02, /* 0xbd241146 */
|
||||
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
|
||||
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
|
||||
qS1 = -2.4033949375e+00, /* 0xc019d139 */
|
||||
qS2 = 2.0209457874e+00, /* 0x4001572d */
|
||||
qS3 = -6.8828397989e-01, /* 0xbf303361 */
|
||||
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
|
||||
|
||||
float
|
||||
__ieee754_acosf(float x)
|
||||
{
|
||||
float z,p,q,r,w,s,c,df;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix==0x3f800000) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
|
||||
} else if(ix>0x3f800000) { /* |x| >= 1 */
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3f000000) { /* |x| < 0.5 */
|
||||
if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*(float)0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = __ieee754_sqrtf(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - (float)2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
int32_t idf;
|
||||
z = (one-x)*(float)0.5;
|
||||
s = __ieee754_sqrtf(z);
|
||||
df = s;
|
||||
GET_FLOAT_WORD(idf,df);
|
||||
SET_FLOAT_WORD(df,idf&0xfffff000);
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return (float)2.0*(df+w);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,62 @@
|
||||
/* @(#)e_acosh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_acosh(x)
|
||||
* Method :
|
||||
* Based on
|
||||
* acosh(x) = log [ x + sqrt(x*x-1) ]
|
||||
* we have
|
||||
* acosh(x) := log(x)+ln2, if x is large; else
|
||||
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
|
||||
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
|
||||
*
|
||||
* Special cases:
|
||||
* acosh(x) is NaN with signal if x<1.
|
||||
* acosh(NaN) is NaN without signal.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one = 1.0,
|
||||
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
||||
|
||||
double
|
||||
__ieee754_acosh(double x)
|
||||
{
|
||||
double t;
|
||||
int32_t hx;
|
||||
u_int32_t lx;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
if(hx<0x3ff00000) { /* x < 1 */
|
||||
return (x-x)/(x-x);
|
||||
} else if(hx >=0x41b00000) { /* x > 2**28 */
|
||||
if(hx >=0x7ff00000) { /* x is inf of NaN */
|
||||
return x+x;
|
||||
} else
|
||||
return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
|
||||
} else if(((hx-0x3ff00000)|lx)==0) {
|
||||
return 0.0; /* acosh(1) = 0 */
|
||||
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
||||
t=x*x;
|
||||
return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
|
||||
} else { /* 1<x<2 */
|
||||
t = x-one;
|
||||
return log1p(t+sqrt(2.0*t+t*t));
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,50 @@
|
||||
/* e_acoshf.c -- float version of e_acosh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_acoshf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
ln2 = 6.9314718246e-01; /* 0x3f317218 */
|
||||
|
||||
float
|
||||
__ieee754_acoshf(float x)
|
||||
{
|
||||
float t;
|
||||
int32_t hx;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
if(hx<0x3f800000) { /* x < 1 */
|
||||
return (x-x)/(x-x);
|
||||
} else if(hx >=0x4d800000) { /* x > 2**28 */
|
||||
if(hx >=0x7f800000) { /* x is inf of NaN */
|
||||
return x+x;
|
||||
} else
|
||||
return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */
|
||||
} else if (hx==0x3f800000) {
|
||||
return 0.0; /* acosh(1) = 0 */
|
||||
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
||||
t=x*x;
|
||||
return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one)));
|
||||
} else { /* 1<x<2 */
|
||||
t = x-one;
|
||||
return log1pf(t+sqrtf((float)2.0*t+t*t));
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,115 @@
|
||||
/* @(#)e_asin.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_asin(x)
|
||||
* Method :
|
||||
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
|
||||
* we approximate asin(x) on [0,0.5] by
|
||||
* asin(x) = x + x*x^2*R(x^2)
|
||||
* where
|
||||
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
|
||||
* and its remez error is bounded by
|
||||
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
|
||||
*
|
||||
* For x in [0.5,1]
|
||||
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
|
||||
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
|
||||
* then for x>0.98
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
|
||||
* For x<=0.98, let pio4_hi = pio2_hi/2, then
|
||||
* f = hi part of s;
|
||||
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
|
||||
* and
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
|
||||
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
huge = 1.000e+300,
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
double
|
||||
__ieee754_asin(double x)
|
||||
{
|
||||
double t,w,p,q,c,r,s;
|
||||
int32_t hx,ix;
|
||||
|
||||
t = 0;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>= 0x3ff00000) { /* |x|>= 1 */
|
||||
u_int32_t lx;
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((ix-0x3ff00000)|lx)==0)
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3fe00000) { /* |x|<0.5 */
|
||||
if(ix<0x3e400000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
} else
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabs(x);
|
||||
t = w*0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = __ieee754_sqrt(t);
|
||||
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
|
||||
w = p/q;
|
||||
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
|
||||
} else {
|
||||
w = s;
|
||||
SET_LOW_WORD(w,0);
|
||||
c = (t-w*w)/(s+w);
|
||||
r = p/q;
|
||||
p = 2.0*s*r-(pio2_lo-2.0*c);
|
||||
q = pio4_hi-2.0*w;
|
||||
t = pio4_hi-(p-q);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
@@ -0,0 +1,87 @@
|
||||
/* e_asinf.c -- float version of e_asin.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_asinf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
huge = 1.000e+30,
|
||||
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
|
||||
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
|
||||
pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
|
||||
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
|
||||
pS3 = -4.0055535734e-02, /* 0xbd241146 */
|
||||
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
|
||||
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
|
||||
qS1 = -2.4033949375e+00, /* 0xc019d139 */
|
||||
qS2 = 2.0209457874e+00, /* 0x4001572d */
|
||||
qS3 = -6.8828397989e-01, /* 0xbf303361 */
|
||||
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
|
||||
|
||||
float
|
||||
__ieee754_asinf(float x)
|
||||
{
|
||||
float t,w,p,q,c,r,s;
|
||||
int32_t hx,ix;
|
||||
|
||||
t = 0;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix==0x3f800000) {
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
} else if(ix> 0x3f800000) { /* |x|>= 1 */
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3f000000) { /* |x|<0.5 */
|
||||
if(ix<0x32000000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
} else
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabsf(x);
|
||||
t = w*(float)0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = __ieee754_sqrtf(t);
|
||||
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
|
||||
w = p/q;
|
||||
t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
|
||||
} else {
|
||||
int32_t iw;
|
||||
w = s;
|
||||
GET_FLOAT_WORD(iw,w);
|
||||
SET_FLOAT_WORD(w,iw&0xfffff000);
|
||||
c = (t-w*w)/(s+w);
|
||||
r = p/q;
|
||||
p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
|
||||
q = pio4_hi-(float)2.0*w;
|
||||
t = pio4_hi-(p-q);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
@@ -0,0 +1,123 @@
|
||||
/* @(#)e_atan2.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_atan2(y,x)
|
||||
* Method :
|
||||
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
|
||||
* 2. Reduce x to positive by (if x and y are unexceptional):
|
||||
* ARG (x+iy) = arctan(y/x) ... if x > 0,
|
||||
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
|
||||
*
|
||||
* Special cases:
|
||||
*
|
||||
* ATAN2((anything), NaN ) is NaN;
|
||||
* ATAN2(NAN , (anything) ) is NaN;
|
||||
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
|
||||
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
|
||||
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
|
||||
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
|
||||
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
|
||||
* ATAN2(+-INF,+INF ) is +-pi/4 ;
|
||||
* ATAN2(+-INF,-INF ) is +-3pi/4;
|
||||
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
tiny = 1.0e-300,
|
||||
zero = 0.0,
|
||||
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
|
||||
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
|
||||
|
||||
double
|
||||
__ieee754_atan2(double y, double x)
|
||||
{
|
||||
double z;
|
||||
int32_t k,m,hx,hy,ix,iy;
|
||||
u_int32_t lx,ly;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
EXTRACT_WORDS(hy,ly,y);
|
||||
iy = hy&0x7fffffff;
|
||||
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
|
||||
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
|
||||
return x+y;
|
||||
if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
|
||||
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if((iy|ly)==0) {
|
||||
switch(m) {
|
||||
case 0:
|
||||
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
||||
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
||||
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* when x is INF */
|
||||
if(ix==0x7ff00000) {
|
||||
if(iy==0x7ff00000) {
|
||||
switch(m) {
|
||||
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
||||
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
||||
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
||||
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
||||
}
|
||||
} else {
|
||||
switch(m) {
|
||||
case 0: return zero ; /* atan(+...,+INF) */
|
||||
case 1: return -zero ; /* atan(-...,+INF) */
|
||||
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
||||
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* compute y/x */
|
||||
k = (iy-ix)>>20;
|
||||
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
|
||||
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
||||
else z=atan(fabs(y/x)); /* safe to do y/x */
|
||||
switch (m) {
|
||||
case 0: return z ; /* atan(+,+) */
|
||||
case 1: {
|
||||
u_int32_t zh;
|
||||
GET_HIGH_WORD(zh,z);
|
||||
SET_HIGH_WORD(z,zh ^ 0x80000000);
|
||||
}
|
||||
return z ; /* atan(-,+) */
|
||||
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
||||
default: /* case 3 */
|
||||
return (z-pi_lo)-pi;/* atan(-,-) */
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,98 @@
|
||||
/* e_atan2f.c -- float version of e_atan2.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_atan2f.c,v 1.7 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
tiny = 1.0e-30,
|
||||
zero = 0.0,
|
||||
pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
|
||||
pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pi_lo = 1.5099578832e-07; /* 0x34222168 */
|
||||
|
||||
float
|
||||
__ieee754_atan2f(float y, float x)
|
||||
{
|
||||
float z;
|
||||
int32_t k,m,hx,hy,ix,iy;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
iy = hy&0x7fffffff;
|
||||
if((ix>0x7f800000)||
|
||||
(iy>0x7f800000)) /* x or y is NaN */
|
||||
return x+y;
|
||||
if(hx==0x3f800000) return atanf(y); /* x=1.0 */
|
||||
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if(iy==0) {
|
||||
switch(m) {
|
||||
case 0:
|
||||
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
||||
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
||||
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* when x is INF */
|
||||
if(ix==0x7f800000) {
|
||||
if(iy==0x7f800000) {
|
||||
switch(m) {
|
||||
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
||||
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
||||
case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
||||
case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
||||
}
|
||||
} else {
|
||||
switch(m) {
|
||||
case 0: return zero ; /* atan(+...,+INF) */
|
||||
case 1: return -zero ; /* atan(-...,+INF) */
|
||||
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
||||
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* compute y/x */
|
||||
k = (iy-ix)>>23;
|
||||
if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
|
||||
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
||||
else z=atanf(fabsf(y/x)); /* safe to do y/x */
|
||||
switch (m) {
|
||||
case 0: return z ; /* atan(+,+) */
|
||||
case 1: {
|
||||
u_int32_t zh;
|
||||
GET_FLOAT_WORD(zh,z);
|
||||
SET_FLOAT_WORD(z,zh ^ 0x80000000);
|
||||
}
|
||||
return z ; /* atan(-,+) */
|
||||
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
||||
default: /* case 3 */
|
||||
return (z-pi_lo)-pi;/* atan(-,-) */
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,63 @@
|
||||
/* @(#)e_atanh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_atanh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_atanh(x)
|
||||
* Method :
|
||||
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
|
||||
* 2.For x>=0.5
|
||||
* 1 2x x
|
||||
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
|
||||
* 2 1 - x 1 - x
|
||||
*
|
||||
* For x<0.5
|
||||
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
|
||||
*
|
||||
* Special cases:
|
||||
* atanh(x) is NaN if |x| > 1 with signal;
|
||||
* atanh(NaN) is that NaN with no signal;
|
||||
* atanh(+-1) is +-INF with signal.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double one = 1.0, huge = 1e300;
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
double
|
||||
__ieee754_atanh(double x)
|
||||
{
|
||||
double t;
|
||||
int32_t hx,ix;
|
||||
u_int32_t lx;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
|
||||
return (x-x)/(x-x);
|
||||
if(ix==0x3ff00000)
|
||||
return x/zero;
|
||||
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
|
||||
SET_HIGH_WORD(x,ix);
|
||||
if(ix<0x3fe00000) { /* x < 0.5 */
|
||||
t = x+x;
|
||||
t = 0.5*log1p(t+t*x/(one-x));
|
||||
} else
|
||||
t = 0.5*log1p((x+x)/(one-x));
|
||||
if(hx>=0) return t; else return -t;
|
||||
}
|
||||
@@ -0,0 +1,47 @@
|
||||
/* e_atanhf.c -- float version of e_atanh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_atanhf.c,v 1.7 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float one = 1.0, huge = 1e30;
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_atanhf(float x)
|
||||
{
|
||||
float t;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if (ix>0x3f800000) /* |x|>1 */
|
||||
return (x-x)/(x-x);
|
||||
if(ix==0x3f800000)
|
||||
return x/zero;
|
||||
if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */
|
||||
SET_FLOAT_WORD(x,ix);
|
||||
if(ix<0x3f000000) { /* x < 0.5 */
|
||||
t = x+x;
|
||||
t = (float)0.5*log1pf(t+t*x/(one-x));
|
||||
} else
|
||||
t = (float)0.5*log1pf((x+x)/(one-x));
|
||||
if(hx>=0) return t; else return -t;
|
||||
}
|
||||
@@ -0,0 +1,86 @@
|
||||
/* @(#)e_cosh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_cosh(x)
|
||||
* Method :
|
||||
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
|
||||
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
|
||||
* 2.
|
||||
* [ exp(x) - 1 ]^2
|
||||
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
|
||||
* 2*exp(x)
|
||||
*
|
||||
* exp(x) + 1/exp(x)
|
||||
* ln2/2 <= x <= 22 : cosh(x) := -------------------
|
||||
* 2
|
||||
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : cosh(x) := huge*huge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* cosh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only cosh(0)=1 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double one = 1.0, half=0.5, huge = 1.0e300;
|
||||
|
||||
double
|
||||
__ieee754_cosh(double x)
|
||||
{
|
||||
double t,w;
|
||||
int32_t ix;
|
||||
u_int32_t lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
|
||||
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
|
||||
if(ix<0x3fd62e43) {
|
||||
t = expm1(fabs(x));
|
||||
w = one+t;
|
||||
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
|
||||
return one+(t*t)/(w+w);
|
||||
}
|
||||
|
||||
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
|
||||
if (ix < 0x40360000) {
|
||||
t = __ieee754_exp(fabs(x));
|
||||
return half*t+half/t;
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
|
||||
if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
GET_LOW_WORD(lx,x);
|
||||
if (ix<0x408633CE ||
|
||||
((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
|
||||
w = __ieee754_exp(half*fabs(x));
|
||||
t = half*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, cosh(x) overflow */
|
||||
return huge*huge;
|
||||
}
|
||||
@@ -0,0 +1,65 @@
|
||||
/* e_coshf.c -- float version of e_cosh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_coshf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e30;
|
||||
static const float one = 1.0, half=0.5;
|
||||
|
||||
float
|
||||
__ieee754_coshf(float x)
|
||||
{
|
||||
float t,w;
|
||||
int32_t ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7f800000) return x*x;
|
||||
|
||||
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
|
||||
if(ix<0x3eb17218) {
|
||||
t = expm1f(fabsf(x));
|
||||
w = one+t;
|
||||
if (ix<0x24000000) return w; /* cosh(tiny) = 1 */
|
||||
return one+(t*t)/(w+w);
|
||||
}
|
||||
|
||||
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
|
||||
if (ix < 0x41b00000) {
|
||||
t = __ieee754_expf(fabsf(x));
|
||||
return half*t+half/t;
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
|
||||
if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
if (ix<=0x42b2d4fc) {
|
||||
w = __ieee754_expf(half*fabsf(x));
|
||||
t = half*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, cosh(x) overflow */
|
||||
return huge*huge;
|
||||
}
|
||||
@@ -0,0 +1,162 @@
|
||||
/* @(#)e_exp.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_exp.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_exp(x)
|
||||
* Returns the exponential of x.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2.
|
||||
*
|
||||
* Here r will be represented as r = hi-lo for better
|
||||
* accuracy.
|
||||
*
|
||||
* 2. Approximation of exp(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Write
|
||||
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
|
||||
* We use a special Reme algorithm on [0,0.34658] to generate
|
||||
* a polynomial of degree 5 to approximate R. The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-59. In
|
||||
* other words,
|
||||
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
|
||||
* (where z=r*r, and the values of P1 to P5 are listed below)
|
||||
* and
|
||||
* | 5 | -59
|
||||
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
|
||||
* | |
|
||||
* The computation of exp(r) thus becomes
|
||||
* 2*r
|
||||
* exp(r) = 1 + -------
|
||||
* R - r
|
||||
* r*R1(r)
|
||||
* = 1 + r + ----------- (for better accuracy)
|
||||
* 2 - R1(r)
|
||||
* where
|
||||
* 2 4 10
|
||||
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
|
||||
*
|
||||
* 3. Scale back to obtain exp(x):
|
||||
* From step 1, we have
|
||||
* exp(x) = 2^k * exp(r)
|
||||
*
|
||||
* Special cases:
|
||||
* exp(INF) is INF, exp(NaN) is NaN;
|
||||
* exp(-INF) is 0, and
|
||||
* for finite argument, only exp(0)=1 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then exp(x) overflow
|
||||
* if x < -7.45133219101941108420e+02 then exp(x) underflow
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
huge = 1.0e+300,
|
||||
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
|
||||
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
|
||||
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
|
||||
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
|
||||
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
|
||||
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
|
||||
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
|
||||
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
|
||||
|
||||
|
||||
double
|
||||
__ieee754_exp(double x) /* default IEEE double exp */
|
||||
{
|
||||
double y,hi,lo,c,t;
|
||||
int32_t k,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
hi = lo = 0;
|
||||
k = 0;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
|
||||
if(hx>=0x7ff00000) {
|
||||
u_int32_t lx;
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((hx&0xfffff)|lx)!=0)
|
||||
return x+x; /* NaN */
|
||||
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
}
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom1000*twom1000; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = invln2*x+halF[xsb];
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
if(k==0) return one-((x*c)/(c-2.0)-x);
|
||||
else y = one-((lo-(x*c)/(2.0-c))-hi);
|
||||
if(k >= -1021) {
|
||||
u_int32_t hy;
|
||||
GET_HIGH_WORD(hy,y);
|
||||
SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
u_int32_t hy;
|
||||
GET_HIGH_WORD(hy,y);
|
||||
SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
|
||||
return y*twom1000;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,99 @@
|
||||
/* e_expf.c -- float version of e_exp.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e+30;
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
|
||||
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
|
||||
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
|
||||
ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
|
||||
-6.9313812256e-01,}, /* 0xbf317180 */
|
||||
ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
-9.0580006145e-06,}, /* 0xb717f7d1 */
|
||||
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
|
||||
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
||||
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
||||
P5 = 4.1381369442e-08; /* 0x3331bb4c */
|
||||
|
||||
float
|
||||
__ieee754_expf(float x) /* default IEEE double exp */
|
||||
{
|
||||
float y,hi,lo,c,t;
|
||||
int32_t k,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
hi = lo = 0;
|
||||
k = 0;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
||||
if(hx>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx==0x7f800000)
|
||||
return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom100*twom100; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = invln2*x+halF[xsb];
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if(hx < 0x31800000) { /* when |x|<2**-28 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
|
||||
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
|
||||
if(k >= -125) {
|
||||
u_int32_t hy;
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
u_int32_t hy;
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
|
||||
return y*twom100;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,133 @@
|
||||
/* @(#)e_fmod.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_fmod.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_fmod(x,y)
|
||||
* Return x mod y in exact arithmetic
|
||||
* Method: shift and subtract
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
|
||||
double
|
||||
__ieee754_fmod(double x, double y)
|
||||
{
|
||||
int32_t n,hx,hy,hz,ix,iy,sx,i;
|
||||
u_int32_t lx,ly,lz;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
EXTRACT_WORDS(hy,ly,y);
|
||||
sx = hx&0x80000000; /* sign of x */
|
||||
hx ^=sx; /* |x| */
|
||||
hy &= 0x7fffffff; /* |y| */
|
||||
|
||||
/* purge off exception values */
|
||||
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
|
||||
((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
|
||||
return (x*y)/(x*y);
|
||||
if(hx<=hy) {
|
||||
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
|
||||
if(lx==ly)
|
||||
return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
|
||||
}
|
||||
|
||||
/* determine ix = ilogb(x) */
|
||||
if(hx<0x00100000) { /* subnormal x */
|
||||
if(hx==0) {
|
||||
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
|
||||
} else {
|
||||
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
|
||||
}
|
||||
} else ix = (hx>>20)-1023;
|
||||
|
||||
/* determine iy = ilogb(y) */
|
||||
if(hy<0x00100000) { /* subnormal y */
|
||||
if(hy==0) {
|
||||
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
|
||||
} else {
|
||||
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
|
||||
}
|
||||
} else iy = (hy>>20)-1023;
|
||||
|
||||
/* set up {hx,lx}, {hy,ly} and align y to x */
|
||||
if(ix >= -1022)
|
||||
hx = 0x00100000|(0x000fffff&hx);
|
||||
else { /* subnormal x, shift x to normal */
|
||||
n = -1022-ix;
|
||||
if(n<=31) {
|
||||
hx = (hx<<n)|(lx>>(32-n));
|
||||
lx <<= n;
|
||||
} else {
|
||||
hx = lx<<(n-32);
|
||||
lx = 0;
|
||||
}
|
||||
}
|
||||
if(iy >= -1022)
|
||||
hy = 0x00100000|(0x000fffff&hy);
|
||||
else { /* subnormal y, shift y to normal */
|
||||
n = -1022-iy;
|
||||
if(n<=31) {
|
||||
hy = (hy<<n)|(ly>>(32-n));
|
||||
ly <<= n;
|
||||
} else {
|
||||
hy = ly<<(n-32);
|
||||
ly = 0;
|
||||
}
|
||||
}
|
||||
|
||||
/* fix point fmod */
|
||||
n = ix - iy;
|
||||
while(n--) {
|
||||
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
||||
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
|
||||
else {
|
||||
if((hz|lz)==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
hx = hz+hz+(lz>>31); lx = lz+lz;
|
||||
}
|
||||
}
|
||||
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
||||
if(hz>=0) {hx=hz;lx=lz;}
|
||||
|
||||
/* convert back to floating value and restore the sign */
|
||||
if((hx|lx)==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
while(hx<0x00100000) { /* normalize x */
|
||||
hx = hx+hx+(lx>>31); lx = lx+lx;
|
||||
iy -= 1;
|
||||
}
|
||||
if(iy>= -1022) { /* normalize output */
|
||||
hx = ((hx-0x00100000)|((iy+1023)<<20));
|
||||
INSERT_WORDS(x,hx|sx,lx);
|
||||
} else { /* subnormal output */
|
||||
n = -1022 - iy;
|
||||
if(n<=20) {
|
||||
lx = (lx>>n)|((u_int32_t)hx<<(32-n));
|
||||
hx >>= n;
|
||||
} else if (n<=31) {
|
||||
lx = (hx<<(32-n))|(lx>>n); hx = sx;
|
||||
} else {
|
||||
lx = hx>>(n-32); hx = sx;
|
||||
}
|
||||
INSERT_WORDS(x,hx|sx,lx);
|
||||
x *= one; /* create necessary signal */
|
||||
}
|
||||
return x; /* exact output */
|
||||
}
|
||||
@@ -0,0 +1,106 @@
|
||||
/* e_fmodf.c -- float version of e_fmod.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_fmodf.c,v 1.7 2002/05/26 22:01:49 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_fmodf(x,y)
|
||||
* Return x mod y in exact arithmetic
|
||||
* Method: shift and subtract
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
|
||||
float
|
||||
__ieee754_fmodf(float x, float y)
|
||||
{
|
||||
int32_t n,hx,hy,hz,ix,iy,sx,i;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
sx = hx&0x80000000; /* sign of x */
|
||||
hx ^=sx; /* |x| */
|
||||
hy &= 0x7fffffff; /* |y| */
|
||||
|
||||
/* purge off exception values */
|
||||
if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */
|
||||
(hy>0x7f800000)) /* or y is NaN */
|
||||
return (x*y)/(x*y);
|
||||
if(hx<hy) return x; /* |x|<|y| return x */
|
||||
if(hx==hy)
|
||||
return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
|
||||
|
||||
/* determine ix = ilogb(x) */
|
||||
if(hx<0x00800000) { /* subnormal x */
|
||||
for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
|
||||
} else ix = (hx>>23)-127;
|
||||
|
||||
/* determine iy = ilogb(y) */
|
||||
if(hy<0x00800000) { /* subnormal y */
|
||||
for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
|
||||
} else iy = (hy>>23)-127;
|
||||
|
||||
/* set up {hx,lx}, {hy,ly} and align y to x */
|
||||
if(ix >= -126)
|
||||
hx = 0x00800000|(0x007fffff&hx);
|
||||
else { /* subnormal x, shift x to normal */
|
||||
n = -126-ix;
|
||||
hx = hx<<n;
|
||||
}
|
||||
if(iy >= -126)
|
||||
hy = 0x00800000|(0x007fffff&hy);
|
||||
else { /* subnormal y, shift y to normal */
|
||||
n = -126-iy;
|
||||
hy = hy<<n;
|
||||
}
|
||||
|
||||
/* fix point fmod */
|
||||
n = ix - iy;
|
||||
while(n--) {
|
||||
hz=hx-hy;
|
||||
if(hz<0){hx = hx+hx;}
|
||||
else {
|
||||
if(hz==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
hx = hz+hz;
|
||||
}
|
||||
}
|
||||
hz=hx-hy;
|
||||
if(hz>=0) {hx=hz;}
|
||||
|
||||
/* convert back to floating value and restore the sign */
|
||||
if(hx==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
while(hx<0x00800000) { /* normalize x */
|
||||
hx = hx+hx;
|
||||
iy -= 1;
|
||||
}
|
||||
if(iy>= -126) { /* normalize output */
|
||||
hx = ((hx-0x00800000)|((iy+127)<<23));
|
||||
SET_FLOAT_WORD(x,hx|sx);
|
||||
} else { /* subnormal output */
|
||||
n = -126 - iy;
|
||||
hx >>= n;
|
||||
SET_FLOAT_WORD(x,hx|sx);
|
||||
x *= one; /* create necessary signal */
|
||||
}
|
||||
return x; /* exact output */
|
||||
}
|
||||
@@ -0,0 +1,125 @@
|
||||
/* @(#)e_hypot.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_hypot(x,y)
|
||||
*
|
||||
* Method :
|
||||
* If (assume round-to-nearest) z=x*x+y*y
|
||||
* has error less than sqrt(2)/2 ulp, than
|
||||
* sqrt(z) has error less than 1 ulp (exercise).
|
||||
*
|
||||
* So, compute sqrt(x*x+y*y) with some care as
|
||||
* follows to get the error below 1 ulp:
|
||||
*
|
||||
* Assume x>y>0;
|
||||
* (if possible, set rounding to round-to-nearest)
|
||||
* 1. if x > 2y use
|
||||
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
|
||||
* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
|
||||
* 2. if x <= 2y use
|
||||
* t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
|
||||
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
|
||||
* yy1= y with lower 32 bits chopped, y2 = y-yy1.
|
||||
*
|
||||
* NOTE: scaling may be necessary if some argument is too
|
||||
* large or too tiny
|
||||
*
|
||||
* Special cases:
|
||||
* hypot(x,y) is INF if x or y is +INF or -INF; else
|
||||
* hypot(x,y) is NAN if x or y is NAN.
|
||||
*
|
||||
* Accuracy:
|
||||
* hypot(x,y) returns sqrt(x^2+y^2) with error less
|
||||
* than 1 ulps (units in the last place)
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
double
|
||||
__ieee754_hypot(double x, double y)
|
||||
{
|
||||
double a=x,b=y,t1,t2,yy1,y2,w;
|
||||
int32_t j,k,ha,hb;
|
||||
|
||||
GET_HIGH_WORD(ha,x);
|
||||
ha &= 0x7fffffff;
|
||||
GET_HIGH_WORD(hb,y);
|
||||
hb &= 0x7fffffff;
|
||||
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
|
||||
SET_HIGH_WORD(a,ha); /* a <- |a| */
|
||||
SET_HIGH_WORD(b,hb); /* b <- |b| */
|
||||
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
|
||||
k=0;
|
||||
if(ha > 0x5f300000) { /* a>2**500 */
|
||||
if(ha >= 0x7ff00000) { /* Inf or NaN */
|
||||
u_int32_t low;
|
||||
w = a+b; /* for sNaN */
|
||||
GET_LOW_WORD(low,a);
|
||||
if(((ha&0xfffff)|low)==0) w = a;
|
||||
GET_LOW_WORD(low,b);
|
||||
if(((hb^0x7ff00000)|low)==0) w = b;
|
||||
return w;
|
||||
}
|
||||
/* scale a and b by 2**-600 */
|
||||
ha -= 0x25800000; hb -= 0x25800000; k += 600;
|
||||
SET_HIGH_WORD(a,ha);
|
||||
SET_HIGH_WORD(b,hb);
|
||||
}
|
||||
if(hb < 0x20b00000) { /* b < 2**-500 */
|
||||
if(hb <= 0x000fffff) { /* subnormal b or 0 */
|
||||
u_int32_t low;
|
||||
GET_LOW_WORD(low,b);
|
||||
if((hb|low)==0) return a;
|
||||
t1=0;
|
||||
SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
|
||||
b *= t1;
|
||||
a *= t1;
|
||||
k -= 1022;
|
||||
} else { /* scale a and b by 2^600 */
|
||||
ha += 0x25800000; /* a *= 2^600 */
|
||||
hb += 0x25800000; /* b *= 2^600 */
|
||||
k -= 600;
|
||||
SET_HIGH_WORD(a,ha);
|
||||
SET_HIGH_WORD(b,hb);
|
||||
}
|
||||
}
|
||||
/* medium size a and b */
|
||||
w = a-b;
|
||||
if (w>b) {
|
||||
t1 = 0;
|
||||
SET_HIGH_WORD(t1,ha);
|
||||
t2 = a-t1;
|
||||
w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
|
||||
} else {
|
||||
a = a+a;
|
||||
yy1 = 0;
|
||||
SET_HIGH_WORD(yy1,hb);
|
||||
y2 = b - yy1;
|
||||
t1 = 0;
|
||||
SET_HIGH_WORD(t1,ha+0x00100000);
|
||||
t2 = a - t1;
|
||||
w = __ieee754_sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
|
||||
}
|
||||
if(k!=0) {
|
||||
u_int32_t high;
|
||||
t1 = 1.0;
|
||||
GET_HIGH_WORD(high,t1);
|
||||
SET_HIGH_WORD(t1,high+(k<<20));
|
||||
return t1*w;
|
||||
} else return w;
|
||||
}
|
||||
@@ -0,0 +1,84 @@
|
||||
/* e_hypotf.c -- float version of e_hypot.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_hypotf.c,v 1.9 2008/04/25 22:21:53 christos Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
__ieee754_hypotf(float x, float y)
|
||||
{
|
||||
float a=x,b=y,t1,t2,yy1,y2,w;
|
||||
int32_t j,k,ha,hb;
|
||||
|
||||
GET_FLOAT_WORD(ha,x);
|
||||
ha &= 0x7fffffff;
|
||||
GET_FLOAT_WORD(hb,y);
|
||||
hb &= 0x7fffffff;
|
||||
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
|
||||
SET_FLOAT_WORD(a,ha); /* a <- |a| */
|
||||
SET_FLOAT_WORD(b,hb); /* b <- |b| */
|
||||
if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
|
||||
k=0;
|
||||
if(ha > 0x58800000) { /* a>2**50 */
|
||||
if(ha >= 0x7f800000) { /* Inf or NaN */
|
||||
w = a+b; /* for sNaN */
|
||||
if(ha == 0x7f800000) w = a;
|
||||
if(hb == 0x7f800000) w = b;
|
||||
return w;
|
||||
}
|
||||
/* scale a and b by 2**-60 */
|
||||
ha -= 0x5d800000; hb -= 0x5d800000; k += 60;
|
||||
SET_FLOAT_WORD(a,ha);
|
||||
SET_FLOAT_WORD(b,hb);
|
||||
}
|
||||
if(hb < 0x26800000) { /* b < 2**-50 */
|
||||
if(hb <= 0x007fffff) { /* subnormal b or 0 */
|
||||
if(hb==0) return a;
|
||||
SET_FLOAT_WORD(t1,0x3f000000); /* t1=2^126 */
|
||||
b *= t1;
|
||||
a *= t1;
|
||||
k -= 126;
|
||||
} else { /* scale a and b by 2^60 */
|
||||
ha += 0x5d800000; /* a *= 2^60 */
|
||||
hb += 0x5d800000; /* b *= 2^60 */
|
||||
k -= 60;
|
||||
SET_FLOAT_WORD(a,ha);
|
||||
SET_FLOAT_WORD(b,hb);
|
||||
}
|
||||
}
|
||||
/* medium size a and b */
|
||||
w = a-b;
|
||||
if (w>b) {
|
||||
SET_FLOAT_WORD(t1,ha&0xfffff000);
|
||||
t2 = a-t1;
|
||||
w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
|
||||
} else {
|
||||
a = a+a;
|
||||
SET_FLOAT_WORD(yy1,hb&0xfffff000);
|
||||
y2 = b - yy1;
|
||||
SET_FLOAT_WORD(t1,ha+0x00800000);
|
||||
t2 = a - t1;
|
||||
w = __ieee754_sqrtf(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
|
||||
}
|
||||
if(k!=0) {
|
||||
SET_FLOAT_WORD(t1,0x3f800000+(k<<23));
|
||||
return t1*w;
|
||||
} else return w;
|
||||
}
|
||||
@@ -0,0 +1,389 @@
|
||||
/* @(#)e_j0.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_j0.c,v 1.12 2007/08/20 16:01:38 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_j0(x), __ieee754_y0(x)
|
||||
* Bessel function of the first and second kinds of order zero.
|
||||
* Method -- j0(x):
|
||||
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
|
||||
* 2. Reduce x to |x| since j0(x)=j0(-x), and
|
||||
* for x in (0,2)
|
||||
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
|
||||
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
|
||||
* for x in (2,inf)
|
||||
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
|
||||
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
|
||||
* as follow:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (cos(x) + sin(x))
|
||||
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* (To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.)
|
||||
*
|
||||
* 3 Special cases
|
||||
* j0(nan)= nan
|
||||
* j0(0) = 1
|
||||
* j0(inf) = 0
|
||||
*
|
||||
* Method -- y0(x):
|
||||
* 1. For x<2.
|
||||
* Since
|
||||
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
|
||||
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
|
||||
* We use the following function to approximate y0,
|
||||
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
|
||||
* where
|
||||
* U(z) = u00 + u01*z + ... + u06*z^6
|
||||
* V(z) = 1 + v01*z + ... + v04*z^4
|
||||
* with absolute approximation error bounded by 2**-72.
|
||||
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
|
||||
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
|
||||
* 2. For x>=2.
|
||||
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
|
||||
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
|
||||
* by the method mentioned above.
|
||||
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static double pzero(double), qzero(double);
|
||||
|
||||
static const double
|
||||
huge = 1e300,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/* R0/S0 on [0, 2.00] */
|
||||
R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
|
||||
R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
|
||||
R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
|
||||
R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
|
||||
S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
|
||||
S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
|
||||
S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
|
||||
S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
double
|
||||
__ieee754_j0(double x)
|
||||
{
|
||||
double z, s,c,ss,cc,r,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return one/(x*x);
|
||||
x = fabs(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = sin(x);
|
||||
c = cos(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = -cos(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);
|
||||
else {
|
||||
u = pzero(x); v = qzero(x);
|
||||
z = invsqrtpi*(u*cc-v*ss)/sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<0x3f200000) { /* |x| < 2**-13 */
|
||||
if(huge+x>one) { /* raise inexact if x != 0 */
|
||||
if(ix<0x3e400000) return one; /* |x|<2**-27 */
|
||||
else return one - 0.25*x*x;
|
||||
}
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(R02+z*(R03+z*(R04+z*R05)));
|
||||
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
|
||||
if(ix < 0x3FF00000) { /* |x| < 1.00 */
|
||||
return one + z*(-0.25+(r/s));
|
||||
} else {
|
||||
u = 0.5*x;
|
||||
return((one+u)*(one-u)+z*(r/s));
|
||||
}
|
||||
}
|
||||
|
||||
static const double
|
||||
u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
|
||||
u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
|
||||
u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
|
||||
u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
|
||||
u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
|
||||
u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
|
||||
u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
|
||||
v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
|
||||
v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
|
||||
v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
|
||||
v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
|
||||
|
||||
double
|
||||
__ieee754_y0(double x)
|
||||
{
|
||||
double z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix,lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
|
||||
if(ix>=0x7ff00000) return one/(x+x*x);
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
|
||||
* where x0 = x-pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) + cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
s = sin(x);
|
||||
c = cos(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = -cos(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
|
||||
else {
|
||||
u = pzero(x); v = qzero(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x3e400000) { /* x < 2**-27 */
|
||||
return(u00 + tpi*__ieee754_log(x));
|
||||
}
|
||||
z = x*x;
|
||||
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
|
||||
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
|
||||
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
|
||||
}
|
||||
|
||||
/* The asymptotic expansions of pzero is
|
||||
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
|
||||
* For x >= 2, We approximate pzero by
|
||||
* pzero(x) = 1 + (R/S)
|
||||
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
|
||||
* S = 1 + pS0*s^2 + ... + pS4*s^10
|
||||
* and
|
||||
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
|
||||
*/
|
||||
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
-7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
|
||||
-8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
|
||||
-2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
|
||||
-2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
|
||||
-5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
|
||||
};
|
||||
static const double pS8[5] = {
|
||||
1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
|
||||
3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
|
||||
4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
|
||||
1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
|
||||
4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
|
||||
};
|
||||
|
||||
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
-1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
|
||||
-7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
|
||||
-4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
|
||||
-6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
|
||||
-3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
|
||||
-3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
|
||||
};
|
||||
static const double pS5[5] = {
|
||||
6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
|
||||
1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
|
||||
5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
|
||||
9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
|
||||
2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
|
||||
};
|
||||
|
||||
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
-2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
|
||||
-7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
|
||||
-2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
|
||||
-2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
|
||||
-5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
|
||||
-3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
|
||||
};
|
||||
static const double pS3[5] = {
|
||||
3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
|
||||
3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
|
||||
1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
|
||||
1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
|
||||
1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
|
||||
};
|
||||
|
||||
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
-8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
|
||||
-7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
|
||||
-1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
|
||||
-7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
|
||||
-1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
|
||||
-3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
|
||||
};
|
||||
static const double pS2[5] = {
|
||||
2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
|
||||
1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
|
||||
2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
|
||||
1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
|
||||
1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
|
||||
};
|
||||
|
||||
static double
|
||||
pzero(double x)
|
||||
{
|
||||
const double *p,*q;
|
||||
double z,r,s;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = pR8; q= pS8;}
|
||||
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
|
||||
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
|
||||
else if(ix>=0x40000000){p = pR2; q= pS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qzero is
|
||||
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pzero by
|
||||
* qzero(x) = s*(-1.25 + (R/S))
|
||||
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
|
||||
* S = 1 + qS0*s^2 + ... + qS5*s^12
|
||||
* and
|
||||
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
|
||||
*/
|
||||
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
|
||||
1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
|
||||
5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
|
||||
8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
|
||||
3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
|
||||
};
|
||||
static const double qS8[6] = {
|
||||
1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
|
||||
8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
|
||||
1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
|
||||
8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
|
||||
8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
|
||||
-3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
|
||||
};
|
||||
|
||||
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
|
||||
7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
|
||||
5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
|
||||
1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
|
||||
1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
|
||||
1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
|
||||
};
|
||||
static const double qS5[6] = {
|
||||
8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
|
||||
2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
|
||||
1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
|
||||
5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
|
||||
3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
|
||||
-5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
|
||||
};
|
||||
|
||||
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
|
||||
7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
|
||||
3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
|
||||
4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
|
||||
1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
|
||||
1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
|
||||
};
|
||||
static const double qS3[6] = {
|
||||
4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
|
||||
7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
|
||||
3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
|
||||
6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
|
||||
2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
|
||||
-1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
|
||||
};
|
||||
|
||||
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
|
||||
7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
|
||||
1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
|
||||
1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
|
||||
3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
|
||||
1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
|
||||
};
|
||||
static const double qS2[6] = {
|
||||
3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
|
||||
2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
|
||||
8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
|
||||
8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
|
||||
2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
|
||||
-5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
|
||||
};
|
||||
|
||||
static double
|
||||
qzero(double x)
|
||||
{
|
||||
const double *p,*q;
|
||||
double s,r,z;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = qR8; q= qS8;}
|
||||
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
|
||||
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
|
||||
else if(ix>=0x40000000){p = qR2; q= qS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (-.125 + r/s)/x;
|
||||
}
|
||||
@@ -0,0 +1,352 @@
|
||||
/* e_j0f.c -- float version of e_j0.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_j0f.c,v 1.10 2007/08/20 16:01:38 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static float pzerof(float), qzerof(float);
|
||||
|
||||
static const float
|
||||
huge = 1e30,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
|
||||
tpi = 6.3661974669e-01, /* 0x3f22f983 */
|
||||
/* R0/S0 on [0, 2.00] */
|
||||
R02 = 1.5625000000e-02, /* 0x3c800000 */
|
||||
R03 = -1.8997929874e-04, /* 0xb947352e */
|
||||
R04 = 1.8295404516e-06, /* 0x35f58e88 */
|
||||
R05 = -4.6183270541e-09, /* 0xb19eaf3c */
|
||||
S01 = 1.5619102865e-02, /* 0x3c7fe744 */
|
||||
S02 = 1.1692678527e-04, /* 0x38f53697 */
|
||||
S03 = 5.1354652442e-07, /* 0x3509daa6 */
|
||||
S04 = 1.1661400734e-09; /* 0x30a045e8 */
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_j0f(float x)
|
||||
{
|
||||
float z, s,c,ss,cc,r,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return one/(x*x);
|
||||
x = fabsf(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = sinf(x);
|
||||
c = cosf(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
if(ix<0x7f000000) { /* make sure x+x not overflow */
|
||||
z = -cosf(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
#ifdef DEAD_CODE
|
||||
if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
|
||||
else
|
||||
#endif
|
||||
{
|
||||
u = pzerof(x); v = qzerof(x);
|
||||
z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<0x39000000) { /* |x| < 2**-13 */
|
||||
if(huge+x>one) { /* raise inexact if x != 0 */
|
||||
if(ix<0x32000000) return one; /* |x|<2**-27 */
|
||||
else return one - (float)0.25*x*x;
|
||||
}
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(R02+z*(R03+z*(R04+z*R05)));
|
||||
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
|
||||
if(ix < 0x3F800000) { /* |x| < 1.00 */
|
||||
return one + z*((float)-0.25+(r/s));
|
||||
} else {
|
||||
u = (float)0.5*x;
|
||||
return((one+u)*(one-u)+z*(r/s));
|
||||
}
|
||||
}
|
||||
|
||||
static const float
|
||||
u00 = -7.3804296553e-02, /* 0xbd9726b5 */
|
||||
u01 = 1.7666645348e-01, /* 0x3e34e80d */
|
||||
u02 = -1.3818567619e-02, /* 0xbc626746 */
|
||||
u03 = 3.4745343146e-04, /* 0x39b62a69 */
|
||||
u04 = -3.8140706238e-06, /* 0xb67ff53c */
|
||||
u05 = 1.9559013964e-08, /* 0x32a802ba */
|
||||
u06 = -3.9820518410e-11, /* 0xae2f21eb */
|
||||
v01 = 1.2730483897e-02, /* 0x3c509385 */
|
||||
v02 = 7.6006865129e-05, /* 0x389f65e0 */
|
||||
v03 = 2.5915085189e-07, /* 0x348b216c */
|
||||
v04 = 4.4111031494e-10; /* 0x2ff280c2 */
|
||||
|
||||
float
|
||||
__ieee754_y0f(float x)
|
||||
{
|
||||
float z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
|
||||
if(ix>=0x7f800000) return one/(x+x*x);
|
||||
if(ix==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
|
||||
* where x0 = x-pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) + cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
s = sinf(x);
|
||||
c = cosf(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix<0x7f000000) { /* make sure x+x not overflow */
|
||||
z = -cosf(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
#ifdef DEAD_CODE
|
||||
if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
|
||||
else
|
||||
#endif
|
||||
{
|
||||
u = pzerof(x); v = qzerof(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x32000000) { /* x < 2**-27 */
|
||||
return(u00 + tpi*__ieee754_logf(x));
|
||||
}
|
||||
z = x*x;
|
||||
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
|
||||
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
|
||||
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
|
||||
}
|
||||
|
||||
/* The asymptotic expansions of pzero is
|
||||
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
|
||||
* For x >= 2, We approximate pzero by
|
||||
* pzero(x) = 1 + (R/S)
|
||||
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
|
||||
* S = 1 + pS0*s^2 + ... + pS4*s^10
|
||||
* and
|
||||
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
|
||||
*/
|
||||
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
-7.0312500000e-02, /* 0xbd900000 */
|
||||
-8.0816707611e+00, /* 0xc1014e86 */
|
||||
-2.5706311035e+02, /* 0xc3808814 */
|
||||
-2.4852163086e+03, /* 0xc51b5376 */
|
||||
-5.2530439453e+03, /* 0xc5a4285a */
|
||||
};
|
||||
static const float pS8[5] = {
|
||||
1.1653436279e+02, /* 0x42e91198 */
|
||||
3.8337448730e+03, /* 0x456f9beb */
|
||||
4.0597855469e+04, /* 0x471e95db */
|
||||
1.1675296875e+05, /* 0x47e4087c */
|
||||
4.7627726562e+04, /* 0x473a0bba */
|
||||
};
|
||||
static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
-1.1412546255e-11, /* 0xad48c58a */
|
||||
-7.0312492549e-02, /* 0xbd8fffff */
|
||||
-4.1596107483e+00, /* 0xc0851b88 */
|
||||
-6.7674766541e+01, /* 0xc287597b */
|
||||
-3.3123129272e+02, /* 0xc3a59d9b */
|
||||
-3.4643338013e+02, /* 0xc3ad3779 */
|
||||
};
|
||||
static const float pS5[5] = {
|
||||
6.0753936768e+01, /* 0x42730408 */
|
||||
1.0512523193e+03, /* 0x44836813 */
|
||||
5.9789707031e+03, /* 0x45bad7c4 */
|
||||
9.6254453125e+03, /* 0x461665c8 */
|
||||
2.4060581055e+03, /* 0x451660ee */
|
||||
};
|
||||
|
||||
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
-2.5470459075e-09, /* 0xb12f081b */
|
||||
-7.0311963558e-02, /* 0xbd8fffb8 */
|
||||
-2.4090321064e+00, /* 0xc01a2d95 */
|
||||
-2.1965976715e+01, /* 0xc1afba52 */
|
||||
-5.8079170227e+01, /* 0xc2685112 */
|
||||
-3.1447946548e+01, /* 0xc1fb9565 */
|
||||
};
|
||||
static const float pS3[5] = {
|
||||
3.5856033325e+01, /* 0x420f6c94 */
|
||||
3.6151397705e+02, /* 0x43b4c1ca */
|
||||
1.1936077881e+03, /* 0x44953373 */
|
||||
1.1279968262e+03, /* 0x448cffe6 */
|
||||
1.7358093262e+02, /* 0x432d94b8 */
|
||||
};
|
||||
|
||||
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
-8.8753431271e-08, /* 0xb3be98b7 */
|
||||
-7.0303097367e-02, /* 0xbd8ffb12 */
|
||||
-1.4507384300e+00, /* 0xbfb9b1cc */
|
||||
-7.6356959343e+00, /* 0xc0f4579f */
|
||||
-1.1193166733e+01, /* 0xc1331736 */
|
||||
-3.2336456776e+00, /* 0xc04ef40d */
|
||||
};
|
||||
static const float pS2[5] = {
|
||||
2.2220300674e+01, /* 0x41b1c32d */
|
||||
1.3620678711e+02, /* 0x430834f0 */
|
||||
2.7047027588e+02, /* 0x43873c32 */
|
||||
1.5387539673e+02, /* 0x4319e01a */
|
||||
1.4657617569e+01, /* 0x416a859a */
|
||||
};
|
||||
|
||||
static float
|
||||
pzerof(float x)
|
||||
{
|
||||
const float *p,*q;
|
||||
float z,r,s;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x41000000) {p = pR8; q= pS8;}
|
||||
else if(ix>=0x40f71c58){p = pR5; q= pS5;}
|
||||
else if(ix>=0x4036db68){p = pR3; q= pS3;}
|
||||
else if(ix>=0x40000000){p = pR2; q= pS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qzero is
|
||||
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pzero by
|
||||
* qzero(x) = s*(-1.25 + (R/S))
|
||||
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
|
||||
* S = 1 + qS0*s^2 + ... + qS5*s^12
|
||||
* and
|
||||
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
|
||||
*/
|
||||
static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
7.3242187500e-02, /* 0x3d960000 */
|
||||
1.1768206596e+01, /* 0x413c4a93 */
|
||||
5.5767340088e+02, /* 0x440b6b19 */
|
||||
8.8591972656e+03, /* 0x460a6cca */
|
||||
3.7014625000e+04, /* 0x471096a0 */
|
||||
};
|
||||
static const float qS8[6] = {
|
||||
1.6377603149e+02, /* 0x4323c6aa */
|
||||
8.0983447266e+03, /* 0x45fd12c2 */
|
||||
1.4253829688e+05, /* 0x480b3293 */
|
||||
8.0330925000e+05, /* 0x49441ed4 */
|
||||
8.4050156250e+05, /* 0x494d3359 */
|
||||
-3.4389928125e+05, /* 0xc8a7eb69 */
|
||||
};
|
||||
|
||||
static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
1.8408595828e-11, /* 0x2da1ec79 */
|
||||
7.3242180049e-02, /* 0x3d95ffff */
|
||||
5.8356351852e+00, /* 0x40babd86 */
|
||||
1.3511157227e+02, /* 0x43071c90 */
|
||||
1.0272437744e+03, /* 0x448067cd */
|
||||
1.9899779053e+03, /* 0x44f8bf4b */
|
||||
};
|
||||
static const float qS5[6] = {
|
||||
8.2776611328e+01, /* 0x42a58da0 */
|
||||
2.0778142090e+03, /* 0x4501dd07 */
|
||||
1.8847289062e+04, /* 0x46933e94 */
|
||||
5.6751113281e+04, /* 0x475daf1d */
|
||||
3.5976753906e+04, /* 0x470c88c1 */
|
||||
-5.3543427734e+03, /* 0xc5a752be */
|
||||
};
|
||||
|
||||
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
4.3774099900e-09, /* 0x3196681b */
|
||||
7.3241114616e-02, /* 0x3d95ff70 */
|
||||
3.3442313671e+00, /* 0x405607e3 */
|
||||
4.2621845245e+01, /* 0x422a7cc5 */
|
||||
1.7080809021e+02, /* 0x432acedf */
|
||||
1.6673394775e+02, /* 0x4326bbe4 */
|
||||
};
|
||||
static const float qS3[6] = {
|
||||
4.8758872986e+01, /* 0x42430916 */
|
||||
7.0968920898e+02, /* 0x44316c1c */
|
||||
3.7041481934e+03, /* 0x4567825f */
|
||||
6.4604252930e+03, /* 0x45c9e367 */
|
||||
2.5163337402e+03, /* 0x451d4557 */
|
||||
-1.4924745178e+02, /* 0xc3153f59 */
|
||||
};
|
||||
|
||||
static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
1.5044444979e-07, /* 0x342189db */
|
||||
7.3223426938e-02, /* 0x3d95f62a */
|
||||
1.9981917143e+00, /* 0x3fffc4bf */
|
||||
1.4495602608e+01, /* 0x4167edfd */
|
||||
3.1666231155e+01, /* 0x41fd5471 */
|
||||
1.6252708435e+01, /* 0x4182058c */
|
||||
};
|
||||
static const float qS2[6] = {
|
||||
3.0365585327e+01, /* 0x41f2ecb8 */
|
||||
2.6934811401e+02, /* 0x4386ac8f */
|
||||
8.4478375244e+02, /* 0x44533229 */
|
||||
8.8293585205e+02, /* 0x445cbbe5 */
|
||||
2.1266638184e+02, /* 0x4354aa98 */
|
||||
-5.3109550476e+00, /* 0xc0a9f358 */
|
||||
};
|
||||
|
||||
static float
|
||||
qzerof(float x)
|
||||
{
|
||||
const float *p,*q;
|
||||
float s,r,z;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x41000000) {p = qR8; q= qS8;}
|
||||
else if(ix>=0x40f71c58){p = qR5; q= qS5;}
|
||||
else if(ix>=0x4036db68){p = qR3; q= qS3;}
|
||||
else if(ix>=0x40000000){p = qR2; q= qS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (-(float).125 + r/s)/x;
|
||||
}
|
||||
@@ -0,0 +1,384 @@
|
||||
/* @(#)e_j1.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_j1.c,v 1.12 2007/08/20 16:01:38 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_j1(x), __ieee754_y1(x)
|
||||
* Bessel function of the first and second kinds of order zero.
|
||||
* Method -- j1(x):
|
||||
* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
|
||||
* 2. Reduce x to |x| since j1(x)=-j1(-x), and
|
||||
* for x in (0,2)
|
||||
* j1(x) = x/2 + x*z*R0/S0, where z = x*x;
|
||||
* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
|
||||
* for x in (2,inf)
|
||||
* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
|
||||
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
|
||||
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
|
||||
* as follow:
|
||||
* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (sin(x) + cos(x))
|
||||
* (To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.)
|
||||
*
|
||||
* 3 Special cases
|
||||
* j1(nan)= nan
|
||||
* j1(0) = 0
|
||||
* j1(inf) = 0
|
||||
*
|
||||
* Method -- y1(x):
|
||||
* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
|
||||
* 2. For x<2.
|
||||
* Since
|
||||
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
|
||||
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
|
||||
* We use the following function to approximate y1,
|
||||
* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
|
||||
* where for x in [0,2] (abs err less than 2**-65.89)
|
||||
* U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
|
||||
* V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
|
||||
* Note: For tiny x, 1/x dominate y1 and hence
|
||||
* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
|
||||
* 3. For x>=2.
|
||||
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
|
||||
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
|
||||
* by method mentioned above.
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static double pone(double), qone(double);
|
||||
|
||||
static const double
|
||||
huge = 1e300,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/* R0/S0 on [0,2] */
|
||||
r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
|
||||
r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
|
||||
r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
|
||||
r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
|
||||
s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
|
||||
s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
|
||||
s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
|
||||
s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
|
||||
s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
double
|
||||
__ieee754_j1(double x)
|
||||
{
|
||||
double z, s,c,ss,cc,r,u,v,y;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return one/x;
|
||||
y = fabs(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = sin(y);
|
||||
c = cos(y);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7fe00000) { /* make sure y+y not overflow */
|
||||
z = cos(y+y);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
|
||||
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
|
||||
else {
|
||||
u = pone(y); v = qone(y);
|
||||
z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
|
||||
}
|
||||
if(hx<0) return -z;
|
||||
else return z;
|
||||
}
|
||||
if(ix<0x3e400000) { /* |x|<2**-27 */
|
||||
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(r00+z*(r01+z*(r02+z*r03)));
|
||||
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
|
||||
r *= x;
|
||||
return(x*0.5+r/s);
|
||||
}
|
||||
|
||||
static const double U0[5] = {
|
||||
-1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
|
||||
5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
|
||||
-1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
|
||||
2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
|
||||
-9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
|
||||
};
|
||||
static const double V0[5] = {
|
||||
1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
|
||||
2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
|
||||
1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
|
||||
6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
|
||||
1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
|
||||
};
|
||||
|
||||
double
|
||||
__ieee754_y1(double x)
|
||||
{
|
||||
double z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix,lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
|
||||
if(ix>=0x7ff00000) return one/(x+x*x);
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = sin(x);
|
||||
c = cos(x);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = cos(x+x);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
|
||||
* where x0 = x-3pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (cos(x) + sin(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
|
||||
else {
|
||||
u = pone(x); v = qone(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x3c900000) { /* x < 2**-54 */
|
||||
return(-tpi/x);
|
||||
}
|
||||
z = x*x;
|
||||
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
|
||||
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
|
||||
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
|
||||
}
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of pone is
|
||||
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* pone(x) = 1 + (R/S)
|
||||
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
|
||||
* S = 1 + ps0*s^2 + ... + ps4*s^10
|
||||
* and
|
||||
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
|
||||
*/
|
||||
|
||||
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
|
||||
1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
|
||||
4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
|
||||
3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
|
||||
7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
|
||||
};
|
||||
static const double ps8[5] = {
|
||||
1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
|
||||
3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
|
||||
3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
|
||||
9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
|
||||
3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
|
||||
};
|
||||
|
||||
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
|
||||
1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
|
||||
6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
|
||||
1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
|
||||
5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
|
||||
5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
|
||||
};
|
||||
static const double ps5[5] = {
|
||||
5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
|
||||
9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
|
||||
5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
|
||||
7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
|
||||
1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
|
||||
};
|
||||
|
||||
static const double pr3[6] = {
|
||||
3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
|
||||
1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
|
||||
3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
|
||||
3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
|
||||
9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
|
||||
4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
|
||||
};
|
||||
static const double ps3[5] = {
|
||||
3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
|
||||
3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
|
||||
1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
|
||||
8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
|
||||
1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
|
||||
};
|
||||
|
||||
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
|
||||
1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
|
||||
2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
|
||||
1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
|
||||
1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
|
||||
5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
|
||||
};
|
||||
static const double ps2[5] = {
|
||||
2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
|
||||
1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
|
||||
2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
|
||||
1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
|
||||
8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
|
||||
};
|
||||
|
||||
static double
|
||||
pone(double x)
|
||||
{
|
||||
const double *p,*q;
|
||||
double z,r,s;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = pr8; q= ps8;}
|
||||
else if(ix>=0x40122E8B){p = pr5; q= ps5;}
|
||||
else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
|
||||
else if(ix>=0x40000000){p = pr2; q= ps2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qone is
|
||||
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* qone(x) = s*(0.375 + (R/S))
|
||||
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
|
||||
* S = 1 + qs1*s^2 + ... + qs6*s^12
|
||||
* and
|
||||
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
|
||||
*/
|
||||
|
||||
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
-1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
|
||||
-1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
|
||||
-7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
|
||||
-1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
|
||||
-4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
|
||||
};
|
||||
static const double qs8[6] = {
|
||||
1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
|
||||
7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
|
||||
1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
|
||||
7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
|
||||
6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
|
||||
-2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
|
||||
};
|
||||
|
||||
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
-2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
|
||||
-1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
|
||||
-8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
|
||||
-1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
|
||||
-1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
|
||||
-2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
|
||||
};
|
||||
static const double qs5[6] = {
|
||||
8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
|
||||
1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
|
||||
1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
|
||||
4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
|
||||
2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
|
||||
-4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
|
||||
};
|
||||
|
||||
static const double qr3[6] = {
|
||||
-5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
|
||||
-1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
|
||||
-4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
|
||||
-5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
|
||||
-2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
|
||||
-2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
|
||||
};
|
||||
static const double qs3[6] = {
|
||||
4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
|
||||
6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
|
||||
3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
|
||||
5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
|
||||
1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
|
||||
-1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
|
||||
};
|
||||
|
||||
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
-1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
|
||||
-1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
|
||||
-2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
|
||||
-1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
|
||||
-4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
|
||||
-2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
|
||||
};
|
||||
static const double qs2[6] = {
|
||||
2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
|
||||
2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
|
||||
7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
|
||||
7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
|
||||
1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
|
||||
-4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
|
||||
};
|
||||
|
||||
static double
|
||||
qone(double x)
|
||||
{
|
||||
const double *p,*q;
|
||||
double s,r,z;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = qr8; q= qs8;}
|
||||
else if(ix>=0x40122E8B){p = qr5; q= qs5;}
|
||||
else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
|
||||
else if(ix>=0x40000000){p = qr2; q= qs2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (.375 + r/s)/x;
|
||||
}
|
||||
@@ -0,0 +1,349 @@
|
||||
/* e_j1f.c -- float version of e_j1.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_j1f.c,v 1.11 2007/08/20 16:01:38 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static float ponef(float), qonef(float);
|
||||
|
||||
static const float
|
||||
huge = 1e30,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
|
||||
tpi = 6.3661974669e-01, /* 0x3f22f983 */
|
||||
/* R0/S0 on [0,2] */
|
||||
r00 = -6.2500000000e-02, /* 0xbd800000 */
|
||||
r01 = 1.4070566976e-03, /* 0x3ab86cfd */
|
||||
r02 = -1.5995563444e-05, /* 0xb7862e36 */
|
||||
r03 = 4.9672799207e-08, /* 0x335557d2 */
|
||||
s01 = 1.9153760746e-02, /* 0x3c9ce859 */
|
||||
s02 = 1.8594678841e-04, /* 0x3942fab6 */
|
||||
s03 = 1.1771846857e-06, /* 0x359dffc2 */
|
||||
s04 = 5.0463624390e-09, /* 0x31ad6446 */
|
||||
s05 = 1.2354227016e-11; /* 0x2d59567e */
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_j1f(float x)
|
||||
{
|
||||
float z, s,c,ss,cc,r,u,v,y;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return one/x;
|
||||
y = fabsf(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = sinf(y);
|
||||
c = cosf(y);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7f000000) { /* make sure y+y not overflow */
|
||||
z = cosf(y+y);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
|
||||
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
|
||||
*/
|
||||
#ifdef DEAD_CODE
|
||||
if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y);
|
||||
else
|
||||
#endif
|
||||
{
|
||||
u = ponef(y); v = qonef(y);
|
||||
z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
|
||||
}
|
||||
if(hx<0) return -z;
|
||||
else return z;
|
||||
}
|
||||
if(ix<0x32000000) { /* |x|<2**-27 */
|
||||
if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(r00+z*(r01+z*(r02+z*r03)));
|
||||
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
|
||||
r *= x;
|
||||
return(x*(float)0.5+r/s);
|
||||
}
|
||||
|
||||
static const float U0[5] = {
|
||||
-1.9605709612e-01, /* 0xbe48c331 */
|
||||
5.0443872809e-02, /* 0x3d4e9e3c */
|
||||
-1.9125689287e-03, /* 0xbafaaf2a */
|
||||
2.3525259166e-05, /* 0x37c5581c */
|
||||
-9.1909917899e-08, /* 0xb3c56003 */
|
||||
};
|
||||
static const float V0[5] = {
|
||||
1.9916731864e-02, /* 0x3ca3286a */
|
||||
2.0255257550e-04, /* 0x3954644b */
|
||||
1.3560879779e-06, /* 0x35b602d4 */
|
||||
6.2274145840e-09, /* 0x31d5f8eb */
|
||||
1.6655924903e-11, /* 0x2d9281cf */
|
||||
};
|
||||
|
||||
float
|
||||
__ieee754_y1f(float x)
|
||||
{
|
||||
float z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
|
||||
if(ix>=0x7f800000) return one/(x+x*x);
|
||||
if(ix==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = sinf(x);
|
||||
c = cosf(x);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7f000000) { /* make sure x+x not overflow */
|
||||
z = cosf(x+x);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
|
||||
* where x0 = x-3pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (cos(x) + sin(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x);
|
||||
else {
|
||||
u = ponef(x); v = qonef(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x24800000) { /* x < 2**-54 */
|
||||
return(-tpi/x);
|
||||
}
|
||||
z = x*x;
|
||||
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
|
||||
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
|
||||
return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
|
||||
}
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of pone is
|
||||
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* pone(x) = 1 + (R/S)
|
||||
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
|
||||
* S = 1 + ps0*s^2 + ... + ps4*s^10
|
||||
* and
|
||||
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
|
||||
*/
|
||||
|
||||
static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
1.1718750000e-01, /* 0x3df00000 */
|
||||
1.3239480972e+01, /* 0x4153d4ea */
|
||||
4.1205184937e+02, /* 0x43ce06a3 */
|
||||
3.8747453613e+03, /* 0x45722bed */
|
||||
7.9144794922e+03, /* 0x45f753d6 */
|
||||
};
|
||||
static const float ps8[5] = {
|
||||
1.1420736694e+02, /* 0x42e46a2c */
|
||||
3.6509309082e+03, /* 0x45642ee5 */
|
||||
3.6956207031e+04, /* 0x47105c35 */
|
||||
9.7602796875e+04, /* 0x47bea166 */
|
||||
3.0804271484e+04, /* 0x46f0a88b */
|
||||
};
|
||||
|
||||
static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
1.3199052094e-11, /* 0x2d68333f */
|
||||
1.1718749255e-01, /* 0x3defffff */
|
||||
6.8027510643e+00, /* 0x40d9b023 */
|
||||
1.0830818176e+02, /* 0x42d89dca */
|
||||
5.1763616943e+02, /* 0x440168b7 */
|
||||
5.2871520996e+02, /* 0x44042dc6 */
|
||||
};
|
||||
static const float ps5[5] = {
|
||||
5.9280597687e+01, /* 0x426d1f55 */
|
||||
9.9140142822e+02, /* 0x4477d9b1 */
|
||||
5.3532670898e+03, /* 0x45a74a23 */
|
||||
7.8446904297e+03, /* 0x45f52586 */
|
||||
1.5040468750e+03, /* 0x44bc0180 */
|
||||
};
|
||||
|
||||
static const float pr3[6] = {
|
||||
3.0250391081e-09, /* 0x314fe10d */
|
||||
1.1718686670e-01, /* 0x3defffab */
|
||||
3.9329774380e+00, /* 0x407bb5e7 */
|
||||
3.5119403839e+01, /* 0x420c7a45 */
|
||||
9.1055007935e+01, /* 0x42b61c2a */
|
||||
4.8559066772e+01, /* 0x42423c7c */
|
||||
};
|
||||
static const float ps3[5] = {
|
||||
3.4791309357e+01, /* 0x420b2a4d */
|
||||
3.3676245117e+02, /* 0x43a86198 */
|
||||
1.0468714600e+03, /* 0x4482dbe3 */
|
||||
8.9081134033e+02, /* 0x445eb3ed */
|
||||
1.0378793335e+02, /* 0x42cf936c */
|
||||
};
|
||||
|
||||
static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
1.0771083225e-07, /* 0x33e74ea8 */
|
||||
1.1717621982e-01, /* 0x3deffa16 */
|
||||
2.3685150146e+00, /* 0x401795c0 */
|
||||
1.2242610931e+01, /* 0x4143e1bc */
|
||||
1.7693971634e+01, /* 0x418d8d41 */
|
||||
5.0735230446e+00, /* 0x40a25a4d */
|
||||
};
|
||||
static const float ps2[5] = {
|
||||
2.1436485291e+01, /* 0x41ab7dec */
|
||||
1.2529022980e+02, /* 0x42fa9499 */
|
||||
2.3227647400e+02, /* 0x436846c7 */
|
||||
1.1767937469e+02, /* 0x42eb5bd7 */
|
||||
8.3646392822e+00, /* 0x4105d590 */
|
||||
};
|
||||
|
||||
static float
|
||||
ponef(float x)
|
||||
{
|
||||
const float *p,*q;
|
||||
float z,r,s;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x41000000) {p = pr8; q= ps8;}
|
||||
else if(ix>=0x40f71c58){p = pr5; q= ps5;}
|
||||
else if(ix>=0x4036db68){p = pr3; q= ps3;}
|
||||
else if(ix>=0x40000000){p = pr2; q= ps2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qone is
|
||||
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* qone(x) = s*(0.375 + (R/S))
|
||||
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
|
||||
* S = 1 + qs1*s^2 + ... + qs6*s^12
|
||||
* and
|
||||
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
|
||||
*/
|
||||
|
||||
static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
-1.0253906250e-01, /* 0xbdd20000 */
|
||||
-1.6271753311e+01, /* 0xc1822c8d */
|
||||
-7.5960174561e+02, /* 0xc43de683 */
|
||||
-1.1849806641e+04, /* 0xc639273a */
|
||||
-4.8438511719e+04, /* 0xc73d3683 */
|
||||
};
|
||||
static const float qs8[6] = {
|
||||
1.6139537048e+02, /* 0x43216537 */
|
||||
7.8253862305e+03, /* 0x45f48b17 */
|
||||
1.3387534375e+05, /* 0x4802bcd6 */
|
||||
7.1965775000e+05, /* 0x492fb29c */
|
||||
6.6660125000e+05, /* 0x4922be94 */
|
||||
-2.9449025000e+05, /* 0xc88fcb48 */
|
||||
};
|
||||
|
||||
static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
-2.0897993405e-11, /* 0xadb7d219 */
|
||||
-1.0253904760e-01, /* 0xbdd1fffe */
|
||||
-8.0564479828e+00, /* 0xc100e736 */
|
||||
-1.8366960144e+02, /* 0xc337ab6b */
|
||||
-1.3731937256e+03, /* 0xc4aba633 */
|
||||
-2.6124443359e+03, /* 0xc523471c */
|
||||
};
|
||||
static const float qs5[6] = {
|
||||
8.1276550293e+01, /* 0x42a28d98 */
|
||||
1.9917987061e+03, /* 0x44f8f98f */
|
||||
1.7468484375e+04, /* 0x468878f8 */
|
||||
4.9851425781e+04, /* 0x4742bb6d */
|
||||
2.7948074219e+04, /* 0x46da5826 */
|
||||
-4.7191835938e+03, /* 0xc5937978 */
|
||||
};
|
||||
|
||||
static const float qr3[6] = { /* for x in [4.5454,2.8570]=1/[0.22001,0.3499] */
|
||||
-5.0783124372e-09, /* 0xb1ae7d4f */
|
||||
-1.0253783315e-01, /* 0xbdd1ff5b */
|
||||
-4.6101160049e+00, /* 0xc0938612 */
|
||||
-5.7847221375e+01, /* 0xc267638e */
|
||||
-2.2824453735e+02, /* 0xc3643e9a */
|
||||
-2.1921012878e+02, /* 0xc35b35cb */
|
||||
};
|
||||
static const float qs3[6] = {
|
||||
4.7665153503e+01, /* 0x423ea91e */
|
||||
6.7386511230e+02, /* 0x4428775e */
|
||||
3.3801528320e+03, /* 0x45534272 */
|
||||
5.5477290039e+03, /* 0x45ad5dd5 */
|
||||
1.9031191406e+03, /* 0x44ede3d0 */
|
||||
-1.3520118713e+02, /* 0xc3073381 */
|
||||
};
|
||||
|
||||
static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
-1.7838172539e-07, /* 0xb43f8932 */
|
||||
-1.0251704603e-01, /* 0xbdd1f475 */
|
||||
-2.7522056103e+00, /* 0xc0302423 */
|
||||
-1.9663616180e+01, /* 0xc19d4f16 */
|
||||
-4.2325313568e+01, /* 0xc2294d1f */
|
||||
-2.1371921539e+01, /* 0xc1aaf9b2 */
|
||||
};
|
||||
static const float qs2[6] = {
|
||||
2.9533363342e+01, /* 0x41ec4454 */
|
||||
2.5298155212e+02, /* 0x437cfb47 */
|
||||
7.5750280762e+02, /* 0x443d602e */
|
||||
7.3939318848e+02, /* 0x4438d92a */
|
||||
1.5594900513e+02, /* 0x431bf2f2 */
|
||||
-4.9594988823e+00, /* 0xc09eb437 */
|
||||
};
|
||||
|
||||
static float
|
||||
qonef(float x)
|
||||
{
|
||||
const float *p,*q;
|
||||
float s,r,z;
|
||||
int32_t ix;
|
||||
|
||||
p = q = 0;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
/* [inf, 8] (8 41000000) */
|
||||
if(ix>=0x41000000) {p = qr8; q= qs8;}
|
||||
/* [8, 4.5454] (4.5454 409173eb) */
|
||||
else if(ix>=0x409173eb){p = qr5; q= qs5;}
|
||||
/* [4.5454, 2.8570] (2.8570 4036d917) */
|
||||
else if(ix>=0x4036d917){p = qr3; q= qs3;}
|
||||
/* [2.8570, 2] (2 40000000) */
|
||||
else if(ix>=0x40000000){p = qr2; q= qs2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return ((float).375 + r/s)/x;
|
||||
}
|
||||
@@ -0,0 +1,274 @@
|
||||
/* @(#)e_jn.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_jn.c,v 1.14 2010/11/29 15:10:06 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_jn(n, x), __ieee754_yn(n, x)
|
||||
* floating point Bessel's function of the 1st and 2nd kind
|
||||
* of order n
|
||||
*
|
||||
* Special cases:
|
||||
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
|
||||
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
|
||||
* Note 2. About jn(n,x), yn(n,x)
|
||||
* For n=0, j0(x) is called,
|
||||
* for n=1, j1(x) is called,
|
||||
* for n<x, forward recursion us used starting
|
||||
* from values of j0(x) and j1(x).
|
||||
* for n>x, a continued fraction approximation to
|
||||
* j(n,x)/j(n-1,x) is evaluated and then backward
|
||||
* recursion is used starting from a supposed value
|
||||
* for j(n,x). The resulting value of j(0,x) is
|
||||
* compared with the actual value to correct the
|
||||
* supposed value of j(n,x).
|
||||
*
|
||||
* yn(n,x) is similar in all respects, except
|
||||
* that forward recursion is used for all
|
||||
* values of n>1.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
|
||||
|
||||
static const double zero = 0.00000000000000000000e+00;
|
||||
|
||||
double
|
||||
__ieee754_jn(int n, double x)
|
||||
{
|
||||
int32_t i,hx,ix,lx, sgn;
|
||||
double a, b, temp, di;
|
||||
double z, w;
|
||||
|
||||
temp = 0;
|
||||
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
|
||||
* Thus, J(-n,x) = J(n,-x)
|
||||
*/
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if J(n,NaN) is NaN */
|
||||
if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
x = -x;
|
||||
hx ^= 0x80000000;
|
||||
}
|
||||
if(n==0) return(__ieee754_j0(x));
|
||||
if(n==1) return(__ieee754_j1(x));
|
||||
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
|
||||
x = fabs(x);
|
||||
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
|
||||
b = zero;
|
||||
else if((double)n<=x) {
|
||||
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
|
||||
if(ix>=0x52D00000) { /* x > 2**302 */
|
||||
/* (x >> n**2)
|
||||
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Let s=sin(x), c=cos(x),
|
||||
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
|
||||
*
|
||||
* n sin(xn)*sqt2 cos(xn)*sqt2
|
||||
* ----------------------------------
|
||||
* 0 s-c c+s
|
||||
* 1 -s-c -c+s
|
||||
* 2 -s+c -c-s
|
||||
* 3 s+c c-s
|
||||
*/
|
||||
switch(n&3) {
|
||||
case 0: temp = cos(x)+sin(x); break;
|
||||
case 1: temp = -cos(x)+sin(x); break;
|
||||
case 2: temp = -cos(x)-sin(x); break;
|
||||
case 3: temp = cos(x)-sin(x); break;
|
||||
}
|
||||
b = invsqrtpi*temp/sqrt(x);
|
||||
} else {
|
||||
a = __ieee754_j0(x);
|
||||
b = __ieee754_j1(x);
|
||||
for(i=1;i<n;i++){
|
||||
temp = b;
|
||||
b = b*((double)(i+i)/x) - a; /* avoid underflow */
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if(ix<0x3e100000) { /* x < 2**-29 */
|
||||
/* x is tiny, return the first Taylor expansion of J(n,x)
|
||||
* J(n,x) = 1/n!*(x/2)^n - ...
|
||||
*/
|
||||
if(n>33) /* underflow */
|
||||
b = zero;
|
||||
else {
|
||||
temp = x*0.5; b = temp;
|
||||
for (a=one,i=2;i<=n;i++) {
|
||||
a *= (double)i; /* a = n! */
|
||||
b *= temp; /* b = (x/2)^n */
|
||||
}
|
||||
b = b/a;
|
||||
}
|
||||
} else {
|
||||
/* use backward recurrence */
|
||||
/* x x^2 x^2
|
||||
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
|
||||
* 2n - 2(n+1) - 2(n+2)
|
||||
*
|
||||
* 1 1 1
|
||||
* (for large x) = ---- ------ ------ .....
|
||||
* 2n 2(n+1) 2(n+2)
|
||||
* -- - ------ - ------ -
|
||||
* x x x
|
||||
*
|
||||
* Let w = 2n/x and h=2/x, then the above quotient
|
||||
* is equal to the continued fraction:
|
||||
* 1
|
||||
* = -----------------------
|
||||
* 1
|
||||
* w - -----------------
|
||||
* 1
|
||||
* w+h - ---------
|
||||
* w+2h - ...
|
||||
*
|
||||
* To determine how many terms needed, let
|
||||
* Q(0) = w, Q(1) = w(w+h) - 1,
|
||||
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
|
||||
* When Q(k) > 1e4 good for single
|
||||
* When Q(k) > 1e9 good for double
|
||||
* When Q(k) > 1e17 good for quadruple
|
||||
*/
|
||||
/* determine k */
|
||||
double t,v;
|
||||
double q0,q1,h,tmp; int32_t k,m;
|
||||
w = (n+n)/(double)x; h = 2.0/(double)x;
|
||||
q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
|
||||
while(q1<1.0e9) {
|
||||
k += 1; z += h;
|
||||
tmp = z*q1 - q0;
|
||||
q0 = q1;
|
||||
q1 = tmp;
|
||||
}
|
||||
m = n+n;
|
||||
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
|
||||
a = t;
|
||||
b = one;
|
||||
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
|
||||
* Hence, if n*(log(2n/x)) > ...
|
||||
* single 8.8722839355e+01
|
||||
* double 7.09782712893383973096e+02
|
||||
* long double 1.1356523406294143949491931077970765006170e+04
|
||||
* then recurrent value may overflow and the result is
|
||||
* likely underflow to zero
|
||||
*/
|
||||
tmp = n;
|
||||
v = two/x;
|
||||
tmp = tmp*__ieee754_log(fabs(v*tmp));
|
||||
if(tmp<7.09782712893383973096e+02) {
|
||||
for(i=n-1,di=(double)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
}
|
||||
} else {
|
||||
for(i=n-1,di=(double)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
/* scale b to avoid spurious overflow */
|
||||
if(b>1e100) {
|
||||
a /= b;
|
||||
t /= b;
|
||||
b = one;
|
||||
}
|
||||
}
|
||||
}
|
||||
z = __ieee754_j0(x);
|
||||
w = __ieee754_j1(x);
|
||||
if (fabs(z) >= fabs(w))
|
||||
b = (t*z/b);
|
||||
else
|
||||
b = (t*w/a);
|
||||
}
|
||||
}
|
||||
if(sgn==1) return -b; else return b;
|
||||
}
|
||||
|
||||
double
|
||||
__ieee754_yn(int n, double x)
|
||||
{
|
||||
int32_t i,hx,ix,lx;
|
||||
int32_t sign;
|
||||
double a, b, temp;
|
||||
|
||||
temp = 0;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y(n,NaN) is NaN */
|
||||
if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
sign = 1;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
sign = 1 - ((n&1)<<1);
|
||||
}
|
||||
if(n==0) return(__ieee754_y0(x));
|
||||
if(n==1) return(sign*__ieee754_y1(x));
|
||||
if(ix==0x7ff00000) return zero;
|
||||
if(ix>=0x52D00000) { /* x > 2**302 */
|
||||
/* (x >> n**2)
|
||||
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Let s=sin(x), c=cos(x),
|
||||
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
|
||||
*
|
||||
* n sin(xn)*sqt2 cos(xn)*sqt2
|
||||
* ----------------------------------
|
||||
* 0 s-c c+s
|
||||
* 1 -s-c -c+s
|
||||
* 2 -s+c -c-s
|
||||
* 3 s+c c-s
|
||||
*/
|
||||
switch(n&3) {
|
||||
case 0: temp = sin(x)-cos(x); break;
|
||||
case 1: temp = -sin(x)-cos(x); break;
|
||||
case 2: temp = -sin(x)+cos(x); break;
|
||||
case 3: temp = sin(x)+cos(x); break;
|
||||
}
|
||||
b = invsqrtpi*temp/sqrt(x);
|
||||
} else {
|
||||
u_int32_t high;
|
||||
a = __ieee754_y0(x);
|
||||
b = __ieee754_y1(x);
|
||||
/* quit if b is -inf */
|
||||
GET_HIGH_WORD(high,b);
|
||||
for(i=1;i<n&&high!=0xfff00000;i++){
|
||||
temp = b;
|
||||
b = ((double)(i+i)/x)*b - a;
|
||||
GET_HIGH_WORD(high,b);
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
if(sign>0) return b; else return -b;
|
||||
}
|
||||
@@ -0,0 +1,204 @@
|
||||
/* e_jnf.c -- float version of e_jn.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_jnf.c,v 1.11 2010/11/29 15:10:06 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
#if 0
|
||||
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
|
||||
#endif
|
||||
two = 2.0000000000e+00, /* 0x40000000 */
|
||||
one = 1.0000000000e+00; /* 0x3F800000 */
|
||||
|
||||
static const float zero = 0.0000000000e+00;
|
||||
|
||||
float
|
||||
__ieee754_jnf(int n, float x)
|
||||
{
|
||||
int32_t i,hx,ix, sgn;
|
||||
float a, b, temp, di;
|
||||
float z, w;
|
||||
|
||||
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
|
||||
* Thus, J(-n,x) = J(n,-x)
|
||||
*/
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if J(n,NaN) is NaN */
|
||||
if(ix>0x7f800000) return x+x;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
x = -x;
|
||||
hx ^= 0x80000000;
|
||||
}
|
||||
if(n==0) return(__ieee754_j0f(x));
|
||||
if(n==1) return(__ieee754_j1f(x));
|
||||
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
|
||||
x = fabsf(x);
|
||||
if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */
|
||||
b = zero;
|
||||
else if((float)n<=x) {
|
||||
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
|
||||
a = __ieee754_j0f(x);
|
||||
b = __ieee754_j1f(x);
|
||||
for(i=1;i<n;i++){
|
||||
temp = b;
|
||||
b = b*((float)(i+i)/x) - a; /* avoid underflow */
|
||||
a = temp;
|
||||
}
|
||||
} else {
|
||||
if(ix<0x30800000) { /* x < 2**-29 */
|
||||
/* x is tiny, return the first Taylor expansion of J(n,x)
|
||||
* J(n,x) = 1/n!*(x/2)^n - ...
|
||||
*/
|
||||
if(n>33) /* underflow */
|
||||
b = zero;
|
||||
else {
|
||||
temp = x*(float)0.5; b = temp;
|
||||
for (a=one,i=2;i<=n;i++) {
|
||||
a *= (float)i; /* a = n! */
|
||||
b *= temp; /* b = (x/2)^n */
|
||||
}
|
||||
b = b/a;
|
||||
}
|
||||
} else {
|
||||
/* use backward recurrence */
|
||||
/* x x^2 x^2
|
||||
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
|
||||
* 2n - 2(n+1) - 2(n+2)
|
||||
*
|
||||
* 1 1 1
|
||||
* (for large x) = ---- ------ ------ .....
|
||||
* 2n 2(n+1) 2(n+2)
|
||||
* -- - ------ - ------ -
|
||||
* x x x
|
||||
*
|
||||
* Let w = 2n/x and h=2/x, then the above quotient
|
||||
* is equal to the continued fraction:
|
||||
* 1
|
||||
* = -----------------------
|
||||
* 1
|
||||
* w - -----------------
|
||||
* 1
|
||||
* w+h - ---------
|
||||
* w+2h - ...
|
||||
*
|
||||
* To determine how many terms needed, let
|
||||
* Q(0) = w, Q(1) = w(w+h) - 1,
|
||||
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
|
||||
* When Q(k) > 1e4 good for single
|
||||
* When Q(k) > 1e9 good for double
|
||||
* When Q(k) > 1e17 good for quadruple
|
||||
*/
|
||||
/* determine k */
|
||||
float t,v;
|
||||
float q0,q1,h,tmp; int32_t k,m;
|
||||
w = (n+n)/(float)x; h = (float)2.0/(float)x;
|
||||
q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1;
|
||||
while(q1<(float)1.0e9) {
|
||||
k += 1; z += h;
|
||||
tmp = z*q1 - q0;
|
||||
q0 = q1;
|
||||
q1 = tmp;
|
||||
}
|
||||
m = n+n;
|
||||
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
|
||||
a = t;
|
||||
b = one;
|
||||
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
|
||||
* Hence, if n*(log(2n/x)) > ...
|
||||
* single 8.8722839355e+01
|
||||
* double 7.09782712893383973096e+02
|
||||
* long double 1.1356523406294143949491931077970765006170e+04
|
||||
* then recurrent value may overflow and the result is
|
||||
* likely underflow to zero
|
||||
*/
|
||||
tmp = n;
|
||||
v = two/x;
|
||||
tmp = tmp*__ieee754_logf(fabsf(v*tmp));
|
||||
if(tmp<(float)8.8721679688e+01) {
|
||||
for(i=n-1,di=(float)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
}
|
||||
} else {
|
||||
for(i=n-1,di=(float)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
/* scale b to avoid spurious overflow */
|
||||
if(b>(float)1e10) {
|
||||
a /= b;
|
||||
t /= b;
|
||||
b = one;
|
||||
}
|
||||
}
|
||||
}
|
||||
z = __ieee754_j0f(x);
|
||||
w = __ieee754_j1f(x);
|
||||
if (fabsf(z) >= fabsf(w))
|
||||
b = (t*z/b);
|
||||
else
|
||||
b = (t*w/a);
|
||||
}
|
||||
}
|
||||
if(sgn==1) return -b; else return b;
|
||||
}
|
||||
|
||||
float
|
||||
__ieee754_ynf(int n, float x)
|
||||
{
|
||||
int32_t i,hx,ix,ib;
|
||||
int32_t sign;
|
||||
float a, b, temp;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y(n,NaN) is NaN */
|
||||
if(ix>0x7f800000) return x+x;
|
||||
if(ix==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
sign = 1;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
sign = 1 - ((n&1)<<1);
|
||||
}
|
||||
if(n==0) return(__ieee754_y0f(x));
|
||||
if(n==1) return(sign*__ieee754_y1f(x));
|
||||
if(ix==0x7f800000) return zero;
|
||||
|
||||
a = __ieee754_y0f(x);
|
||||
b = __ieee754_y1f(x);
|
||||
/* quit if b is -inf */
|
||||
GET_FLOAT_WORD(ib,b);
|
||||
for(i=1;i<n&&(uint32_t)ib!=0xff800000;i++){
|
||||
temp = b;
|
||||
b = ((float)(i+i)/x)*b - a;
|
||||
GET_FLOAT_WORD(ib,b);
|
||||
a = temp;
|
||||
}
|
||||
if(sign>0) return b; else return -b;
|
||||
}
|
||||
@@ -0,0 +1,298 @@
|
||||
/* @(#)er_lgamma.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_lgamma_r.c,v 1.10 2002/05/26 22:01:51 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_lgamma_r(x, signgamp)
|
||||
* Reentrant version of the logarithm of the Gamma function
|
||||
* with user provide pointer for the sign of Gamma(x).
|
||||
*
|
||||
* Method:
|
||||
* 1. Argument Reduction for 0 < x <= 8
|
||||
* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
|
||||
* reduce x to a number in [1.5,2.5] by
|
||||
* lgamma(1+s) = log(s) + lgamma(s)
|
||||
* for example,
|
||||
* lgamma(7.3) = log(6.3) + lgamma(6.3)
|
||||
* = log(6.3*5.3) + lgamma(5.3)
|
||||
* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
|
||||
* 2. Polynomial approximation of lgamma around its
|
||||
* minimun ymin=1.461632144968362245 to maintain monotonicity.
|
||||
* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
|
||||
* Let z = x-ymin;
|
||||
* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
|
||||
* where
|
||||
* poly(z) is a 14 degree polynomial.
|
||||
* 2. Rational approximation in the primary interval [2,3]
|
||||
* We use the following approximation:
|
||||
* s = x-2.0;
|
||||
* lgamma(x) = 0.5*s + s*P(s)/Q(s)
|
||||
* with accuracy
|
||||
* |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
|
||||
* Our algorithms are based on the following observation
|
||||
*
|
||||
* zeta(2)-1 2 zeta(3)-1 3
|
||||
* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
|
||||
* 2 3
|
||||
*
|
||||
* where Euler = 0.5771... is the Euler constant, which is very
|
||||
* close to 0.5.
|
||||
*
|
||||
* 3. For x>=8, we have
|
||||
* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
|
||||
* (better formula:
|
||||
* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
|
||||
* Let z = 1/x, then we approximation
|
||||
* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
|
||||
* by
|
||||
* 3 5 11
|
||||
* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
|
||||
* where
|
||||
* |w - f(z)| < 2**-58.74
|
||||
*
|
||||
* 4. For negative x, since (G is gamma function)
|
||||
* -x*G(-x)*G(x) = pi/sin(pi*x),
|
||||
* we have
|
||||
* G(x) = pi/(sin(pi*x)*(-x)*G(-x))
|
||||
* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
|
||||
* Hence, for x<0, signgam = sign(sin(pi*x)) and
|
||||
* lgamma(x) = log(|Gamma(x)|)
|
||||
* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
|
||||
* Note: one should avoid compute pi*(-x) directly in the
|
||||
* computation of sin(pi*(-x)).
|
||||
*
|
||||
* 5. Special Cases
|
||||
* lgamma(2+s) ~ s*(1-Euler) for tiny s
|
||||
* lgamma(1)=lgamma(2)=0
|
||||
* lgamma(x) ~ -log(x) for tiny x
|
||||
* lgamma(0) = lgamma(inf) = inf
|
||||
* lgamma(-integer) = +-inf
|
||||
*
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
|
||||
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
|
||||
a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
|
||||
a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
|
||||
a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
|
||||
a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
|
||||
a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
|
||||
a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
|
||||
a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
|
||||
a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
|
||||
a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
|
||||
a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
|
||||
a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
|
||||
tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
|
||||
tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
|
||||
/* tt = -(tail of tf) */
|
||||
tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
|
||||
t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
|
||||
t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
|
||||
t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
|
||||
t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
|
||||
t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
|
||||
t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
|
||||
t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
|
||||
t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
|
||||
t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
|
||||
t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
|
||||
t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
|
||||
t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
|
||||
t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
|
||||
t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
|
||||
t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
|
||||
u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
|
||||
u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
|
||||
u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
|
||||
u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
|
||||
u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
|
||||
v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
|
||||
v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
|
||||
v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
|
||||
v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
|
||||
v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
|
||||
s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
|
||||
s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
|
||||
s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
|
||||
s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
|
||||
s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
|
||||
s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
|
||||
r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
|
||||
r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
|
||||
r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
|
||||
r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
|
||||
r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
|
||||
r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
|
||||
w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
|
||||
w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
|
||||
w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
|
||||
w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
|
||||
w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
|
||||
w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
|
||||
w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
|
||||
|
||||
static const double zero= 0.00000000000000000000e+00;
|
||||
|
||||
static
|
||||
double sin_pi(double x)
|
||||
{
|
||||
double y,z;
|
||||
int n,ix;
|
||||
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
|
||||
y = -x; /* x is assume negative */
|
||||
|
||||
/*
|
||||
* argument reduction, make sure inexact flag not raised if input
|
||||
* is an integer
|
||||
*/
|
||||
z = floor(y);
|
||||
if(z!=y) { /* inexact anyway */
|
||||
y *= 0.5;
|
||||
y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */
|
||||
n = (int) (y*4.0);
|
||||
} else {
|
||||
if(ix>=0x43400000) {
|
||||
y = zero; n = 0; /* y must be even */
|
||||
} else {
|
||||
if(ix<0x43300000) z = y+two52; /* exact */
|
||||
GET_LOW_WORD(n,z);
|
||||
n &= 1;
|
||||
y = n;
|
||||
n<<= 2;
|
||||
}
|
||||
}
|
||||
switch (n) {
|
||||
case 0: y = __kernel_sin(pi*y,zero,0); break;
|
||||
case 1:
|
||||
case 2: y = __kernel_cos(pi*(0.5-y),zero); break;
|
||||
case 3:
|
||||
case 4: y = __kernel_sin(pi*(one-y),zero,0); break;
|
||||
case 5:
|
||||
case 6: y = -__kernel_cos(pi*(y-1.5),zero); break;
|
||||
default: y = __kernel_sin(pi*(y-2.0),zero,0); break;
|
||||
}
|
||||
return -y;
|
||||
}
|
||||
|
||||
|
||||
double
|
||||
__ieee754_lgamma_r(double x, int *signgamp)
|
||||
{
|
||||
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
|
||||
int i,hx,lx,ix;
|
||||
|
||||
nadj = 0;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
if((ix|lx)==0) return one/zero;
|
||||
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_log(-x);
|
||||
} else return -__ieee754_log(x);
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
|
||||
return one/zero;
|
||||
t = sin_pi(x);
|
||||
if(t==zero) return one/zero; /* -integer */
|
||||
nadj = __ieee754_log(pi/fabs(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_log(x);
|
||||
if(ix>=0x3FE76944) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-0.5*y + p1/p2);
|
||||
}
|
||||
}
|
||||
else if(ix<0x40200000) { /* x < 8.0 */
|
||||
i = (int)x;
|
||||
t = zero;
|
||||
y = x-(double)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+2.0); /* FALLTHRU */
|
||||
r += __ieee754_log(z); break;
|
||||
}
|
||||
/* 8.0 <= x < 2**58 */
|
||||
} else if (ix < 0x43900000) {
|
||||
t = __ieee754_log(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x*(__ieee754_log(x)-one);
|
||||
if(hx<0) r = nadj - r;
|
||||
return r;
|
||||
}
|
||||
@@ -0,0 +1,234 @@
|
||||
/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_lgammaf_r.c,v 1.6 2002/05/26 22:01:51 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
two23= 8.3886080000e+06, /* 0x4b000000 */
|
||||
half= 5.0000000000e-01, /* 0x3f000000 */
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
pi = 3.1415927410e+00, /* 0x40490fdb */
|
||||
a0 = 7.7215664089e-02, /* 0x3d9e233f */
|
||||
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
|
||||
a2 = 6.7352302372e-02, /* 0x3d89f001 */
|
||||
a3 = 2.0580807701e-02, /* 0x3ca89915 */
|
||||
a4 = 7.3855509982e-03, /* 0x3bf2027e */
|
||||
a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
|
||||
a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
|
||||
a7 = 5.1006977446e-04, /* 0x3a05b634 */
|
||||
a8 = 2.2086278477e-04, /* 0x39679767 */
|
||||
a9 = 1.0801156895e-04, /* 0x38e28445 */
|
||||
a10 = 2.5214456400e-05, /* 0x37d383a2 */
|
||||
a11 = 4.4864096708e-05, /* 0x383c2c75 */
|
||||
tc = 1.4616321325e+00, /* 0x3fbb16c3 */
|
||||
tf = -1.2148628384e-01, /* 0xbdf8cdcd */
|
||||
/* tt = -(tail of tf) */
|
||||
tt = 6.6971006518e-09, /* 0x31e61c52 */
|
||||
t0 = 4.8383611441e-01, /* 0x3ef7b95e */
|
||||
t1 = -1.4758771658e-01, /* 0xbe17213c */
|
||||
t2 = 6.4624942839e-02, /* 0x3d845a15 */
|
||||
t3 = -3.2788541168e-02, /* 0xbd064d47 */
|
||||
t4 = 1.7970675603e-02, /* 0x3c93373d */
|
||||
t5 = -1.0314224288e-02, /* 0xbc28fcfe */
|
||||
t6 = 6.1005386524e-03, /* 0x3bc7e707 */
|
||||
t7 = -3.6845202558e-03, /* 0xbb7177fe */
|
||||
t8 = 2.2596477065e-03, /* 0x3b141699 */
|
||||
t9 = -1.4034647029e-03, /* 0xbab7f476 */
|
||||
t10 = 8.8108185446e-04, /* 0x3a66f867 */
|
||||
t11 = -5.3859531181e-04, /* 0xba0d3085 */
|
||||
t12 = 3.1563205994e-04, /* 0x39a57b6b */
|
||||
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
|
||||
t14 = 3.3552918467e-04, /* 0x39afe9f7 */
|
||||
u0 = -7.7215664089e-02, /* 0xbd9e233f */
|
||||
u1 = 6.3282704353e-01, /* 0x3f2200f4 */
|
||||
u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
|
||||
u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
|
||||
u4 = 2.2896373272e-01, /* 0x3e6a7578 */
|
||||
u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
|
||||
v1 = 2.4559779167e+00, /* 0x401d2ebe */
|
||||
v2 = 2.1284897327e+00, /* 0x4008392d */
|
||||
v3 = 7.6928514242e-01, /* 0x3f44efdf */
|
||||
v4 = 1.0422264785e-01, /* 0x3dd572af */
|
||||
v5 = 3.2170924824e-03, /* 0x3b52d5db */
|
||||
s0 = -7.7215664089e-02, /* 0xbd9e233f */
|
||||
s1 = 2.1498242021e-01, /* 0x3e5c245a */
|
||||
s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
|
||||
s3 = 1.4635047317e-01, /* 0x3e15dce6 */
|
||||
s4 = 2.6642270386e-02, /* 0x3cda40e4 */
|
||||
s5 = 1.8402845599e-03, /* 0x3af135b4 */
|
||||
s6 = 3.1947532989e-05, /* 0x3805ff67 */
|
||||
r1 = 1.3920053244e+00, /* 0x3fb22d3b */
|
||||
r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
|
||||
r3 = 1.7193385959e-01, /* 0x3e300f6e */
|
||||
r4 = 1.8645919859e-02, /* 0x3c98bf54 */
|
||||
r5 = 7.7794247773e-04, /* 0x3a4beed6 */
|
||||
r6 = 7.3266842264e-06, /* 0x36f5d7bd */
|
||||
w0 = 4.1893854737e-01, /* 0x3ed67f1d */
|
||||
w1 = 8.3333335817e-02, /* 0x3daaaaab */
|
||||
w2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
w3 = 7.9365057172e-04, /* 0x3a500cfd */
|
||||
w4 = -5.9518753551e-04, /* 0xba1c065c */
|
||||
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
|
||||
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
|
||||
|
||||
static const float zero= 0.0000000000e+00;
|
||||
|
||||
static float
|
||||
sin_pif(float x)
|
||||
{
|
||||
float y,z;
|
||||
int n,ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
|
||||
y = -x; /* x is assume negative */
|
||||
|
||||
/*
|
||||
* argument reduction, make sure inexact flag not raised if input
|
||||
* is an integer
|
||||
*/
|
||||
z = floorf(y);
|
||||
if(z!=y) { /* inexact anyway */
|
||||
y *= (float)0.5;
|
||||
y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
|
||||
n = (int) (y*(float)4.0);
|
||||
} else {
|
||||
if(ix>=0x4b800000) {
|
||||
y = zero; n = 0; /* y must be even */
|
||||
} else {
|
||||
if(ix<0x4b000000) z = y+two23; /* exact */
|
||||
GET_FLOAT_WORD(n,z);
|
||||
n &= 1;
|
||||
y = n;
|
||||
n<<= 2;
|
||||
}
|
||||
}
|
||||
switch (n) {
|
||||
case 0: y = __kernel_sinf(pi*y,zero,0); break;
|
||||
case 1:
|
||||
case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
|
||||
case 3:
|
||||
case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
|
||||
case 5:
|
||||
case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
|
||||
default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
|
||||
}
|
||||
return -y;
|
||||
}
|
||||
|
||||
|
||||
float
|
||||
__ieee754_lgammaf_r(float x, int *signgamp)
|
||||
{
|
||||
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
|
||||
int i,hx,ix;
|
||||
|
||||
nadj = 0;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return x*x;
|
||||
if(ix==0) return one/zero;
|
||||
if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_logf(-x);
|
||||
} else return -__ieee754_logf(x);
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
|
||||
return one/zero;
|
||||
t = sin_pif(x);
|
||||
if(t==zero) return one/zero; /* -integer */
|
||||
nadj = __ieee754_logf(pi/fabsf(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if (ix==0x3f800000||ix==0x40000000) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_logf(x);
|
||||
if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-(float)0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-(float)0.5*y + p1/p2);
|
||||
}
|
||||
}
|
||||
else if(ix<0x41000000) { /* x < 8.0 */
|
||||
i = (int)x;
|
||||
t = zero;
|
||||
y = x-(float)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+(float)6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+(float)5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+(float)4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+(float)3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+(float)2.0); /* FALLTHRU */
|
||||
r += __ieee754_logf(z); break;
|
||||
}
|
||||
/* 8.0 <= x < 2**58 */
|
||||
} else if (ix < 0x5c800000) {
|
||||
t = __ieee754_logf(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x*(__ieee754_logf(x)-one);
|
||||
if(hx<0) r = nadj - r;
|
||||
return r;
|
||||
}
|
||||
@@ -0,0 +1,136 @@
|
||||
/* @(#)e_log.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_log(x)
|
||||
* Return the logrithm of x
|
||||
*
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* 2. Approximation of log(1+f).
|
||||
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
||||
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
||||
* = 2s + s*R
|
||||
* We use a special Reme algorithm on [0,0.1716] to generate
|
||||
* a polynomial of degree 14 to approximate R The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-58.45. In
|
||||
* other words,
|
||||
* 2 4 6 8 10 12 14
|
||||
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
|
||||
* (the values of Lg1 to Lg7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lg1*s +...+Lg7*s - R(z) | <= 2
|
||||
* | |
|
||||
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
||||
* In order to guarantee error in log below 1ulp, we compute log
|
||||
* by
|
||||
* log(1+f) = f - s*(f - R) (if f is not too large)
|
||||
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
|
||||
*
|
||||
* 3. Finally, log(x) = k*ln2 + log(1+f).
|
||||
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
|
||||
* Here ln2 is split into two floating point number:
|
||||
* ln2_hi + ln2_lo,
|
||||
* where n*ln2_hi is always exact for |n| < 2000.
|
||||
*
|
||||
* Special cases:
|
||||
* log(x) is NaN with signal if x < 0 (including -INF) ;
|
||||
* log(+INF) is +INF; log(0) is -INF with signal;
|
||||
* log(NaN) is that NaN with no signal.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
|
||||
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
|
||||
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
||||
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
||||
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
||||
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
||||
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
||||
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
||||
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
double
|
||||
__ieee754_log(double x)
|
||||
{
|
||||
double hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,hx,i,j;
|
||||
u_int32_t lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx+0x95f64)&0x100000;
|
||||
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
|
||||
k += (i>>20);
|
||||
f = x-1.0;
|
||||
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
|
||||
if(f==zero) { if(k==0) return zero; else {dk=(double)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;}
|
||||
}
|
||||
R = f*f*(0.5-0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(double)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/(2.0+f);
|
||||
dk = (double)k;
|
||||
z = s*s;
|
||||
i = hx-0x6147a;
|
||||
w = z*z;
|
||||
j = 0x6b851-hx;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=0.5*f*f;
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
|
||||
} else {
|
||||
if(k==0) return f-s*(f-R); else
|
||||
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,87 @@
|
||||
/* @(#)e_log10.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_log10(x)
|
||||
* Return the base 10 logarithm of x
|
||||
*
|
||||
* Method :
|
||||
* Let log10_2hi = leading 40 bits of log10(2) and
|
||||
* log10_2lo = log10(2) - log10_2hi,
|
||||
* ivln10 = 1/log(10) rounded.
|
||||
* Then
|
||||
* n = ilogb(x),
|
||||
* if(n<0) n = n+1;
|
||||
* x = scalbn(x,-n);
|
||||
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
|
||||
*
|
||||
* Note 1:
|
||||
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
|
||||
* mode must set to Round-to-Nearest.
|
||||
* Note 2:
|
||||
* [1/log(10)] rounded to 53 bits has error .198 ulps;
|
||||
* log10 is monotonic at all binary break points.
|
||||
*
|
||||
* Special cases:
|
||||
* log10(x) is NaN with signal if x < 0;
|
||||
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
|
||||
* log10(NaN) is that NaN with no signal;
|
||||
* log10(10**N) = N for N=0,1,...,22.
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following constants.
|
||||
* The decimal values may be used, provided that the compiler will convert
|
||||
* from decimal to binary accurately enough to produce the hexadecimal values
|
||||
* shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
||||
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
|
||||
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
|
||||
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
double
|
||||
__ieee754_log10(double x)
|
||||
{
|
||||
double y,z;
|
||||
int32_t i,k,hx;
|
||||
u_int32_t lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
i = ((u_int32_t)k&0x80000000)>>31;
|
||||
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
|
||||
y = (double)(k+i);
|
||||
SET_HIGH_WORD(x,hx);
|
||||
z = y*log10_2lo + ivln10*__ieee754_log(x);
|
||||
return z+y*log10_2hi;
|
||||
}
|
||||
@@ -0,0 +1,56 @@
|
||||
/* e_log10f.c -- float version of e_log10.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_log10f.c,v 1.8 2002/05/26 22:01:51 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
two25 = 3.3554432000e+07, /* 0x4c000000 */
|
||||
ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
|
||||
log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
|
||||
log10_2lo = 7.9034151668e-07; /* 0x355427db */
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_log10f(float x)
|
||||
{
|
||||
float y,z;
|
||||
int32_t i,k,hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00800000) { /* x < 2**-126 */
|
||||
if ((hx&0x7fffffff)==0)
|
||||
return -two25/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 25; x *= two25; /* subnormal number, scale up x */
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7f800000) return x+x;
|
||||
k += (hx>>23)-127;
|
||||
i = ((u_int32_t)k&0x80000000)>>31;
|
||||
hx = (hx&0x007fffff)|((0x7f-i)<<23);
|
||||
y = (float)(k+i);
|
||||
SET_FLOAT_WORD(x,hx);
|
||||
z = y*log10_2lo + ivln10*__ieee754_logf(x);
|
||||
return z+y*log10_2hi;
|
||||
}
|
||||
@@ -0,0 +1,80 @@
|
||||
|
||||
/* @(#)e_log.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
ln2 = 0.6931471805599452862268,
|
||||
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
|
||||
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
||||
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
||||
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
||||
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
||||
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
||||
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
||||
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
double
|
||||
__ieee754_log2(double x)
|
||||
{
|
||||
double hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,hx,i,j;
|
||||
u_int32_t lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx+0x95f64)&0x100000;
|
||||
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
|
||||
k += (i>>20);
|
||||
f = x-1.0;
|
||||
dk = (double)k;
|
||||
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
|
||||
if (f==zero)
|
||||
return (dk);
|
||||
R = f*f*(0.5-0.33333333333333333*f);
|
||||
return (dk-(R-f)/ln2);
|
||||
}
|
||||
s = f/(2.0+f);
|
||||
z = s*s;
|
||||
i = hx-0x6147a;
|
||||
w = z*z;
|
||||
j = 0x6b851-hx;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=0.5*f*f;
|
||||
return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
|
||||
} else
|
||||
return (dk-((s*(f-R))-f)/ln2);
|
||||
}
|
||||
@@ -0,0 +1,81 @@
|
||||
/* e_logf.c -- float version of e_log.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_log2f.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
ln2 = 0.6931471805599452862268,
|
||||
two25 = 3.355443200e+07, /* 0x4c000000 */
|
||||
Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
|
||||
Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
|
||||
Lg3 = 2.8571429849e-01, /* 3E924925 */
|
||||
Lg4 = 2.2222198546e-01, /* 3E638E29 */
|
||||
Lg5 = 1.8183572590e-01, /* 3E3A3325 */
|
||||
Lg6 = 1.5313838422e-01, /* 3E1CD04F */
|
||||
Lg7 = 1.4798198640e-01; /* 3E178897 */
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_log2f(float x)
|
||||
{
|
||||
float hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,ix,i,j;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
k=0;
|
||||
if (ix < 0x00800000) { /* x < 2**-126 */
|
||||
if ((ix&0x7fffffff)==0)
|
||||
return -two25/zero; /* log(+-0)=-inf */
|
||||
if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 25; x *= two25; /* subnormal number, scale up x */
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
}
|
||||
if (ix >= 0x7f800000) return x+x;
|
||||
k += (ix>>23)-127;
|
||||
ix &= 0x007fffff;
|
||||
i = (ix+(0x95f64<<3))&0x800000;
|
||||
SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
|
||||
k += (i>>23);
|
||||
dk = (float)k;
|
||||
f = x-(float)1.0;
|
||||
if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
|
||||
if (f==zero)
|
||||
return (dk);
|
||||
R = f*f*((float)0.5-(float)0.33333333333333333*f);
|
||||
return (dk-(R-f)/ln2);
|
||||
}
|
||||
s = f/((float)2.0+f);
|
||||
z = s*s;
|
||||
i = ix-(0x6147a<<3);
|
||||
w = z*z;
|
||||
j = (0x6b851<<3)-ix;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=(float)0.5*f*f;
|
||||
return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
|
||||
} else
|
||||
return (dk-((s*(f-R))-f)/ln2);
|
||||
}
|
||||
@@ -0,0 +1,87 @@
|
||||
/* e_logf.c -- float version of e_log.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_logf.c,v 1.8 2002/05/26 22:01:51 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
two25 = 3.355443200e+07, /* 0x4c000000 */
|
||||
Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
|
||||
Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
|
||||
Lg3 = 2.8571429849e-01, /* 3E924925 */
|
||||
Lg4 = 2.2222198546e-01, /* 3E638E29 */
|
||||
Lg5 = 1.8183572590e-01, /* 3E3A3325 */
|
||||
Lg6 = 1.5313838422e-01, /* 3E1CD04F */
|
||||
Lg7 = 1.4798198640e-01; /* 3E178897 */
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
float
|
||||
__ieee754_logf(float x)
|
||||
{
|
||||
float hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,ix,i,j;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
k=0;
|
||||
if (ix < 0x00800000) { /* x < 2**-126 */
|
||||
if ((ix&0x7fffffff)==0)
|
||||
return -two25/zero; /* log(+-0)=-inf */
|
||||
if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 25; x *= two25; /* subnormal number, scale up x */
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
}
|
||||
if (ix >= 0x7f800000) return x+x;
|
||||
k += (ix>>23)-127;
|
||||
ix &= 0x007fffff;
|
||||
i = (ix+(0x95f64<<3))&0x800000;
|
||||
SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
|
||||
k += (i>>23);
|
||||
f = x-(float)1.0;
|
||||
if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
|
||||
if(f==zero) { if(k==0) return zero; else {dk=(float)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;}
|
||||
}
|
||||
R = f*f*((float)0.5-(float)0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(float)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/((float)2.0+f);
|
||||
dk = (float)k;
|
||||
z = s*s;
|
||||
i = ix-(0x6147a<<3);
|
||||
w = z*z;
|
||||
j = (0x6b851<<3)-ix;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=(float)0.5*f*f;
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
|
||||
} else {
|
||||
if(k==0) return f-s*(f-R); else
|
||||
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,303 @@
|
||||
/* @(#)e_pow.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_pow.c,v 1.16 2010/04/23 19:17:07 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_pow(x,y) return x**y
|
||||
*
|
||||
* n
|
||||
* Method: Let x = 2 * (1+f)
|
||||
* 1. Compute and return log2(x) in two pieces:
|
||||
* log2(x) = w1 + w2,
|
||||
* where w1 has 53-24 = 29 bit trailing zeros.
|
||||
* 2. Perform y*log2(x) = n+y' by simulating multi-precision
|
||||
* arithmetic, where |y'|<=0.5.
|
||||
* 3. Return x**y = 2**n*exp(y'*log2)
|
||||
*
|
||||
* Special cases:
|
||||
* 1. (anything) ** 0 is 1
|
||||
* 2. (anything) ** 1 is itself
|
||||
* 3. (anything) ** NAN is NAN
|
||||
* 4. NAN ** (anything except 0) is NAN
|
||||
* 5. +-(|x| > 1) ** +INF is +INF
|
||||
* 6. +-(|x| > 1) ** -INF is +0
|
||||
* 7. +-(|x| < 1) ** +INF is +0
|
||||
* 8. +-(|x| < 1) ** -INF is +INF
|
||||
* 9. +-1 ** +-INF is NAN
|
||||
* 10. +0 ** (+anything except 0, NAN) is +0
|
||||
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
||||
* 12. +0 ** (-anything except 0, NAN) is +INF
|
||||
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
||||
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
||||
* 15. +INF ** (+anything except 0,NAN) is +INF
|
||||
* 16. +INF ** (-anything except 0,NAN) is +0
|
||||
* 17. -INF ** (anything) = -0 ** (-anything)
|
||||
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
||||
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
||||
*
|
||||
* Accuracy:
|
||||
* pow(x,y) returns x**y nearly rounded. In particular
|
||||
* pow(integer,integer)
|
||||
* always returns the correct integer provided it is
|
||||
* representable.
|
||||
*
|
||||
* Constants :
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
|
||||
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
|
||||
huge = 1.0e300,
|
||||
tiny = 1.0e-300,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
|
||||
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
|
||||
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
|
||||
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
|
||||
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
|
||||
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
|
||||
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
|
||||
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
|
||||
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
|
||||
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
|
||||
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
|
||||
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
|
||||
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
|
||||
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
|
||||
|
||||
double
|
||||
__ieee754_pow(double x, double y)
|
||||
{
|
||||
double z,ax,z_h,z_l,p_h,p_l;
|
||||
double yy1,t1,t2,r,s,t,u,v,w;
|
||||
int32_t i,j,k,yisint,n;
|
||||
int32_t hx,hy,ix,iy;
|
||||
u_int32_t lx,ly;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
EXTRACT_WORDS(hy,ly,y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if((iy|ly)==0) return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
|
||||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
|
||||
return x+y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx<0) {
|
||||
if(iy>=0x43400000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3ff00000) {
|
||||
k = (iy>>20)-0x3ff; /* exponent */
|
||||
if(k>20) {
|
||||
j = ly>>(52-k);
|
||||
if((uint32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
|
||||
} else if(ly==0) {
|
||||
j = iy>>(20-k);
|
||||
if((j<<(20-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if(ly==0) {
|
||||
if (iy==0x7ff00000) { /* y is +-inf */
|
||||
if(((ix-0x3ff00000)|lx)==0)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3ff00000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3fe00000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return __ieee754_sqrt(x);
|
||||
}
|
||||
}
|
||||
|
||||
ax = fabs(x);
|
||||
/* special value of x */
|
||||
if(lx==0) {
|
||||
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3ff00000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
n = (hx>>31)+1;
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if((n|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x41e00000) { /* if |y| > 2**31 */
|
||||
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
|
||||
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
|
||||
if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = ax-one; /* t has 20 trailing zeros */
|
||||
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
|
||||
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
SET_LOW_WORD(t1,0);
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
double ss,s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00100000)
|
||||
{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
|
||||
n += ((ix)>>20)-0x3ff;
|
||||
j = ix&0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3ff00000; /* normalize ix */
|
||||
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00100000;}
|
||||
SET_HIGH_WORD(ax,ix);
|
||||
|
||||
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one/(ax+bp[k]);
|
||||
ss = u*v;
|
||||
s_h = ss;
|
||||
SET_LOW_WORD(s_h,0);
|
||||
/* t_h=ax+bp[k] High */
|
||||
t_h = zero;
|
||||
SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
|
||||
t_l = ax - (t_h-bp[k]);
|
||||
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = ss*ss;
|
||||
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
||||
r += s_l*(s_h+ss);
|
||||
s2 = s_h*s_h;
|
||||
t_h = 3.0+s2+r;
|
||||
SET_LOW_WORD(t_h,0);
|
||||
t_l = r-((t_h-3.0)-s2);
|
||||
/* u+v = ss*(1+...) */
|
||||
u = s_h*t_h;
|
||||
v = s_l*t_h+t_l*ss;
|
||||
/* 2/(3log2)*(ss+...) */
|
||||
p_h = u+v;
|
||||
SET_LOW_WORD(p_h,0);
|
||||
p_l = v-(p_h-u);
|
||||
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
||||
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (double)n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
SET_LOW_WORD(t1,0);
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
|
||||
yy1 = y;
|
||||
SET_LOW_WORD(yy1,0);
|
||||
p_l = (y-yy1)*t1+y*t2;
|
||||
p_h = yy1*t1;
|
||||
z = p_l+p_h;
|
||||
EXTRACT_WORDS(j,i,z);
|
||||
if (j>=0x40900000) { /* z >= 1024 */
|
||||
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
|
||||
return s*huge*huge; /* overflow */
|
||||
else {
|
||||
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
||||
}
|
||||
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
|
||||
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
|
||||
return s*tiny*tiny; /* underflow */
|
||||
else {
|
||||
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>20)-0x3ff;
|
||||
n = 0;
|
||||
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00100000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
|
||||
t = zero;
|
||||
SET_HIGH_WORD(t,n&~(0x000fffff>>k));
|
||||
n = ((n&0x000fffff)|0x00100000)>>(20-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
SET_LOW_WORD(t,0);
|
||||
u = t*lg2_h;
|
||||
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
||||
z = u+v;
|
||||
w = v-(z-u);
|
||||
t = z*z;
|
||||
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
r = (z*t1)/(t1-two)-(w+z*w);
|
||||
z = one-(r-z);
|
||||
GET_HIGH_WORD(j,z);
|
||||
j += (n<<20);
|
||||
if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
|
||||
else SET_HIGH_WORD(z,j);
|
||||
return s*z;
|
||||
}
|
||||
@@ -0,0 +1,247 @@
|
||||
/* e_powf.c -- float version of e_pow.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_powf.c,v 1.15 2010/04/23 19:17:07 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e+30, tiny = 1.0e-30;
|
||||
|
||||
static const float
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
||||
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two24 = 16777216.0, /* 0x4b800000 */
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 6.0000002384e-01, /* 0x3f19999a */
|
||||
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
|
||||
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
|
||||
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
|
||||
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
|
||||
L6 = 2.0697501302e-01, /* 0x3e53f142 */
|
||||
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
||||
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
||||
P5 = 4.1381369442e-08, /* 0x3331bb4c */
|
||||
lg2 = 6.9314718246e-01, /* 0x3f317218 */
|
||||
lg2_h = 6.93145752e-01, /* 0x3f317200 */
|
||||
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
|
||||
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
|
||||
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
|
||||
cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
|
||||
cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
|
||||
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
|
||||
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
|
||||
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
|
||||
|
||||
float
|
||||
__ieee754_powf(float x, float y)
|
||||
{
|
||||
float z,ax,z_h,z_l,p_h,p_l;
|
||||
float yy1,t1,t2,r,s,t,u,v,w;
|
||||
int32_t i,j,k,yisint,n;
|
||||
int32_t hx,hy,ix,iy,is;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if(iy==0) return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if(ix > 0x7f800000 ||
|
||||
iy > 0x7f800000)
|
||||
return x+y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx<0) {
|
||||
if(iy>=0x4b800000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3f800000) {
|
||||
k = (iy>>23)-0x7f; /* exponent */
|
||||
j = iy>>(23-k);
|
||||
if((j<<(23-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if (iy==0x7f800000) { /* y is +-inf */
|
||||
if (ix==0x3f800000)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3f800000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3f000000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return __ieee754_sqrtf(x);
|
||||
}
|
||||
|
||||
ax = fabsf(x);
|
||||
/* special value of x */
|
||||
if(ix==0x7f800000||ix==0||ix==0x3f800000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3f800000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x4d000000) { /* if |y| > 2**27 */
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = ax-one; /* t has 20 trailing zeros */
|
||||
w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
|
||||
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
GET_FLOAT_WORD(is,t1);
|
||||
SET_FLOAT_WORD(t1,is&0xfffff000);
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
float s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00800000)
|
||||
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
|
||||
n += ((ix)>>23)-0x7f;
|
||||
j = ix&0x007fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3f800000; /* normalize ix */
|
||||
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00800000;}
|
||||
SET_FLOAT_WORD(ax,ix);
|
||||
|
||||
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one/(ax+bp[k]);
|
||||
s = u*v;
|
||||
s_h = s;
|
||||
GET_FLOAT_WORD(is,s_h);
|
||||
SET_FLOAT_WORD(s_h,is&0xfffff000);
|
||||
/* t_h=ax+bp[k] High */
|
||||
SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
|
||||
t_l = ax - (t_h-bp[k]);
|
||||
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = s*s;
|
||||
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
||||
r += s_l*(s_h+s);
|
||||
s2 = s_h*s_h;
|
||||
t_h = (float)3.0+s2+r;
|
||||
GET_FLOAT_WORD(is,t_h);
|
||||
SET_FLOAT_WORD(t_h,is&0xfffff000);
|
||||
t_l = r-((t_h-(float)3.0)-s2);
|
||||
/* u+v = s*(1+...) */
|
||||
u = s_h*t_h;
|
||||
v = s_l*t_h+t_l*s;
|
||||
/* 2/(3log2)*(s+...) */
|
||||
p_h = u+v;
|
||||
GET_FLOAT_WORD(is,p_h);
|
||||
SET_FLOAT_WORD(p_h,is&0xfffff000);
|
||||
p_l = v-(p_h-u);
|
||||
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
||||
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (float)n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
GET_FLOAT_WORD(is,t1);
|
||||
SET_FLOAT_WORD(t1,is&0xfffff000);
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
|
||||
s = -one; /* (-ve)**(odd int) */
|
||||
|
||||
/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
|
||||
GET_FLOAT_WORD(is,y);
|
||||
SET_FLOAT_WORD(yy1,is&0xfffff000);
|
||||
p_l = (y-yy1)*t1+y*t2;
|
||||
p_h = yy1*t1;
|
||||
z = p_l+p_h;
|
||||
GET_FLOAT_WORD(j,z);
|
||||
if (j>0x43000000) /* if z > 128 */
|
||||
return s*huge*huge; /* overflow */
|
||||
else if (j==0x43000000) { /* if z == 128 */
|
||||
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
||||
}
|
||||
else if ((uint32_t)j==0xc3160000){ /* z == -150 */
|
||||
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
||||
}
|
||||
else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
|
||||
return s*tiny*tiny; /* underflow */
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>23)-0x7f;
|
||||
n = 0;
|
||||
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00800000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
|
||||
SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
|
||||
n = ((n&0x007fffff)|0x00800000)>>(23-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
GET_FLOAT_WORD(is,t);
|
||||
SET_FLOAT_WORD(t,is&0xfffff000);
|
||||
u = t*lg2_h;
|
||||
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
||||
z = u+v;
|
||||
w = v-(z-u);
|
||||
t = z*z;
|
||||
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
r = (z*t1)/(t1-two)-(w+z*w);
|
||||
z = one-(r-z);
|
||||
GET_FLOAT_WORD(j,z);
|
||||
j += (n<<23);
|
||||
if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */
|
||||
else SET_FLOAT_WORD(z,j);
|
||||
return s*z;
|
||||
}
|
||||
@@ -0,0 +1,169 @@
|
||||
/* @(#)e_rem_pio2.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_rem_pio2(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
||||
* use __kernel_rem_pio2()
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/*
|
||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
||||
*/
|
||||
static const int32_t two_over_pi[] = {
|
||||
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
||||
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
||||
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
||||
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
||||
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
||||
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
||||
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
||||
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
||||
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
||||
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
||||
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
||||
};
|
||||
|
||||
static const int32_t npio2_hw[] = {
|
||||
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
|
||||
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
|
||||
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
|
||||
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
|
||||
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
|
||||
0x404858EB, 0x404921FB,
|
||||
};
|
||||
|
||||
/*
|
||||
* invpio2: 53 bits of 2/pi
|
||||
* pio2_1: first 33 bit of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
* pio2_2: second 33 bit of pi/2
|
||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
||||
* pio2_3: third 33 bit of pi/2
|
||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
||||
*/
|
||||
|
||||
static const double
|
||||
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
|
||||
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
|
||||
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
|
||||
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
|
||||
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
|
||||
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
|
||||
|
||||
int32_t
|
||||
__ieee754_rem_pio2(double x, double *y)
|
||||
{
|
||||
double z,w,t,r,fn;
|
||||
double tx[3];
|
||||
int32_t e0,i,j,nx,n,ix,hx;
|
||||
u_int32_t low;
|
||||
|
||||
z = 0;
|
||||
GET_HIGH_WORD(hx,x); /* high word of x */
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
|
||||
{y[0] = x; y[1] = 0; return 0;}
|
||||
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
|
||||
if(hx>0) {
|
||||
z = x - pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z - pio2_1t;
|
||||
y[1] = (z-y[0])-pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z -= pio2_2;
|
||||
y[0] = z - pio2_2t;
|
||||
y[1] = (z-y[0])-pio2_2t;
|
||||
}
|
||||
return 1;
|
||||
} else { /* negative x */
|
||||
z = x + pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z + pio2_1t;
|
||||
y[1] = (z-y[0])+pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z += pio2_2;
|
||||
y[0] = z + pio2_2t;
|
||||
y[1] = (z-y[0])+pio2_2t;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
}
|
||||
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
|
||||
t = fabs(x);
|
||||
n = (int32_t) (t*invpio2+half);
|
||||
fn = (double)n;
|
||||
r = t-fn*pio2_1;
|
||||
w = fn*pio2_1t; /* 1st round good to 85 bit */
|
||||
if(n<32&&ix!=npio2_hw[n-1]) {
|
||||
y[0] = r-w; /* quick check no cancellation */
|
||||
} else {
|
||||
u_int32_t high;
|
||||
j = ix>>20;
|
||||
y[0] = r-w;
|
||||
GET_HIGH_WORD(high,y[0]);
|
||||
i = j-((high>>20)&0x7ff);
|
||||
if(i>16) { /* 2nd iteration needed, good to 118 */
|
||||
t = r;
|
||||
w = fn*pio2_2;
|
||||
r = t-w;
|
||||
w = fn*pio2_2t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
GET_HIGH_WORD(high,y[0]);
|
||||
i = j-((high>>20)&0x7ff);
|
||||
if(i>49) { /* 3rd iteration need, 151 bits acc */
|
||||
t = r; /* will cover all possible cases */
|
||||
w = fn*pio2_3;
|
||||
r = t-w;
|
||||
w = fn*pio2_3t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
}
|
||||
}
|
||||
}
|
||||
y[1] = (r-y[0])-w;
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
else return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7ff00000) { /* x is inf or NaN */
|
||||
y[0]=y[1]=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(x)-23) */
|
||||
GET_LOW_WORD(low,x);
|
||||
SET_LOW_WORD(z,low);
|
||||
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
|
||||
SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
|
||||
for(i=0;i<2;i++) {
|
||||
tx[i] = (double)((int32_t)(z));
|
||||
z = (z-tx[i])*two24;
|
||||
}
|
||||
tx[2] = z;
|
||||
nx = 3;
|
||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
||||
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
return n;
|
||||
}
|
||||
@@ -0,0 +1,181 @@
|
||||
/* e_rem_pio2f.c -- float version of e_rem_pio2.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_rem_pio2f.c,v 1.9 2009/01/19 06:00:30 lukem Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_rem_pio2f(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
||||
* use __kernel_rem_pio2f()
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/*
|
||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
||||
*/
|
||||
static const int32_t two_over_pi[] = {
|
||||
0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
|
||||
0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
|
||||
0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
|
||||
0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
|
||||
0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
|
||||
0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
|
||||
0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
|
||||
0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
|
||||
0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
|
||||
0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
|
||||
0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
|
||||
0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
|
||||
0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
|
||||
0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
|
||||
0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
|
||||
0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
|
||||
0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
|
||||
0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
|
||||
0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
|
||||
0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
|
||||
0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
|
||||
0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
|
||||
};
|
||||
|
||||
/* This array is like the one in e_rem_pio2.c, but the numbers are
|
||||
single precision and the last 8 bits are forced to 0. */
|
||||
static const int32_t npio2_hw[] = {
|
||||
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
|
||||
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
|
||||
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
|
||||
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
|
||||
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
|
||||
0x4242c700, 0x42490f00
|
||||
};
|
||||
|
||||
/*
|
||||
* invpio2: 24 bits of 2/pi
|
||||
* pio2_1: first 17 bit of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
* pio2_2: second 17 bit of pi/2
|
||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
||||
* pio2_3: third 17 bit of pi/2
|
||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
||||
*/
|
||||
|
||||
static const float
|
||||
zero = 0.0000000000e+00, /* 0x00000000 */
|
||||
half = 5.0000000000e-01, /* 0x3f000000 */
|
||||
two8 = 2.5600000000e+02, /* 0x43800000 */
|
||||
invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
|
||||
pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
|
||||
pio2_1t = 1.0804334124e-05, /* 0x37354443 */
|
||||
pio2_2 = 1.0804273188e-05, /* 0x37354400 */
|
||||
pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
|
||||
pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
|
||||
pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
|
||||
|
||||
int32_t
|
||||
__ieee754_rem_pio2f(float x, float *y)
|
||||
{
|
||||
float z,w,t,r,fn;
|
||||
float tx[3];
|
||||
int32_t e0,i,j,nx,n,ix,hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
|
||||
{y[0] = x; y[1] = 0; return 0;}
|
||||
if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
|
||||
if(hx>0) {
|
||||
z = x - pio2_1;
|
||||
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
|
||||
y[0] = z - pio2_1t;
|
||||
y[1] = (z-y[0])-pio2_1t;
|
||||
} else { /* near pi/2, use 24+24+24 bit pi */
|
||||
z -= pio2_2;
|
||||
y[0] = z - pio2_2t;
|
||||
y[1] = (z-y[0])-pio2_2t;
|
||||
}
|
||||
return 1;
|
||||
} else { /* negative x */
|
||||
z = x + pio2_1;
|
||||
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
|
||||
y[0] = z + pio2_1t;
|
||||
y[1] = (z-y[0])+pio2_1t;
|
||||
} else { /* near pi/2, use 24+24+24 bit pi */
|
||||
z += pio2_2;
|
||||
y[0] = z + pio2_2t;
|
||||
y[1] = (z-y[0])+pio2_2t;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
}
|
||||
if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
|
||||
t = fabsf(x);
|
||||
n = (int32_t) (t*invpio2+half);
|
||||
fn = (float)n;
|
||||
r = t-fn*pio2_1;
|
||||
w = fn*pio2_1t; /* 1st round good to 40 bit */
|
||||
if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) {
|
||||
y[0] = r-w; /* quick check no cancellation */
|
||||
} else {
|
||||
u_int32_t high;
|
||||
j = ix>>23;
|
||||
y[0] = r-w;
|
||||
GET_FLOAT_WORD(high,y[0]);
|
||||
i = j-((high>>23)&0xff);
|
||||
if(i>8) { /* 2nd iteration needed, good to 57 */
|
||||
t = r;
|
||||
w = fn*pio2_2;
|
||||
r = t-w;
|
||||
w = fn*pio2_2t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
GET_FLOAT_WORD(high,y[0]);
|
||||
i = j-((high>>23)&0xff);
|
||||
if(i>25) { /* 3rd iteration need, 74 bits acc */
|
||||
t = r; /* will cover all possible cases */
|
||||
w = fn*pio2_3;
|
||||
r = t-w;
|
||||
w = fn*pio2_3t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
}
|
||||
}
|
||||
}
|
||||
y[1] = (r-y[0])-w;
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
else return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7f800000) { /* x is inf or NaN */
|
||||
y[0]=y[1]=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(x)-7) */
|
||||
e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */
|
||||
SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
|
||||
for(i=0;i<2;i++) {
|
||||
tx[i] = (float)((int32_t)(z));
|
||||
z = (z-tx[i])*two8;
|
||||
}
|
||||
tx[2] = z;
|
||||
nx = 3;
|
||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
||||
n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
return n;
|
||||
}
|
||||
@@ -0,0 +1,73 @@
|
||||
/* @(#)e_remainder.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_remainder.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_remainder(x,p)
|
||||
* Return :
|
||||
* returns x REM p = x - [x/p]*p as if in infinite
|
||||
* precise arithmetic, where [x/p] is the (infinite bit)
|
||||
* integer nearest x/p (in half way case choose the even one).
|
||||
* Method :
|
||||
* Based on fmod() return x-[x/p]chopped*p exactlp.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double zero = 0.0;
|
||||
|
||||
|
||||
double
|
||||
__ieee754_remainder(double x, double p)
|
||||
{
|
||||
int32_t hx,hp;
|
||||
u_int32_t sx,lx,lp;
|
||||
double p_half;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
EXTRACT_WORDS(hp,lp,p);
|
||||
sx = hx&0x80000000;
|
||||
hp &= 0x7fffffff;
|
||||
hx &= 0x7fffffff;
|
||||
|
||||
/* purge off exception values */
|
||||
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
|
||||
if((hx>=0x7ff00000)|| /* x not finite */
|
||||
((hp>=0x7ff00000)&& /* p is NaN */
|
||||
(((hp-0x7ff00000)|lp)!=0)))
|
||||
return (x*p)/(x*p);
|
||||
|
||||
|
||||
if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
|
||||
if (((hx-hp)|(lx-lp))==0) return zero*x;
|
||||
x = fabs(x);
|
||||
p = fabs(p);
|
||||
if (hp<0x00200000) {
|
||||
if(x+x>p) {
|
||||
x-=p;
|
||||
if(x+x>=p) x -= p;
|
||||
}
|
||||
} else {
|
||||
p_half = 0.5*p;
|
||||
if(x>p_half) {
|
||||
x-=p;
|
||||
if(x>=p_half) x -= p;
|
||||
}
|
||||
}
|
||||
GET_HIGH_WORD(hx,x);
|
||||
SET_HIGH_WORD(x,hx^sx);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,66 @@
|
||||
/* e_remainderf.c -- float version of e_remainder.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_remainderf.c,v 1.7 2002/05/26 22:01:52 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float zero = 0.0;
|
||||
|
||||
|
||||
float
|
||||
__ieee754_remainderf(float x, float p)
|
||||
{
|
||||
int32_t hx,hp;
|
||||
u_int32_t sx;
|
||||
float p_half;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hp,p);
|
||||
sx = hx&0x80000000;
|
||||
hp &= 0x7fffffff;
|
||||
hx &= 0x7fffffff;
|
||||
|
||||
/* purge off exception values */
|
||||
if(hp==0) return (x*p)/(x*p); /* p = 0 */
|
||||
if((hx>=0x7f800000)|| /* x not finite */
|
||||
((hp>0x7f800000))) /* p is NaN */
|
||||
return (x*p)/(x*p);
|
||||
|
||||
|
||||
if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */
|
||||
if ((hx-hp)==0) return zero*x;
|
||||
x = fabsf(x);
|
||||
p = fabsf(p);
|
||||
if (hp<0x01000000) {
|
||||
if(x+x>p) {
|
||||
x-=p;
|
||||
if(x+x>=p) x -= p;
|
||||
}
|
||||
} else {
|
||||
p_half = (float)0.5*p;
|
||||
if(x>p_half) {
|
||||
x-=p;
|
||||
if(x>=p_half) x -= p;
|
||||
}
|
||||
}
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
SET_FLOAT_WORD(x,hx^sx);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,49 @@
|
||||
/* @(#)e_scalb.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_scalb.c,v 1.10 2010/04/23 19:17:07 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_scalb(x, fn) is provide for
|
||||
* passing various standard test suite. One
|
||||
* should use scalbn() instead.
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef _SCALB_INT
|
||||
double
|
||||
__ieee754_scalb(double x, int fn)
|
||||
#else
|
||||
double
|
||||
__ieee754_scalb(double x, double fn)
|
||||
#endif
|
||||
{
|
||||
#ifdef _SCALB_INT
|
||||
return scalbn(x,fn);
|
||||
#else
|
||||
if (isnan(x)||isnan(fn)) return x*fn;
|
||||
if (!finite(fn)) {
|
||||
if(fn>0.0) return x*fn;
|
||||
else return x/(-fn);
|
||||
}
|
||||
if (rint(fn)!=fn) return (fn-fn)/(fn-fn);
|
||||
if ( fn > 65000.0) return scalbn(x, 65000);
|
||||
if (-fn > 65000.0) return scalbn(x,-65000);
|
||||
return scalbn(x,(int)fn);
|
||||
#endif
|
||||
}
|
||||
@@ -0,0 +1,46 @@
|
||||
/* e_scalbf.c -- float version of e_scalb.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_scalbf.c,v 1.7 2010/04/23 19:17:07 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef _SCALB_INT
|
||||
float
|
||||
__ieee754_scalbf(float x, int fn)
|
||||
#else
|
||||
float
|
||||
__ieee754_scalbf(float x, float fn)
|
||||
#endif
|
||||
{
|
||||
#ifdef _SCALB_INT
|
||||
return scalbnf(x,fn);
|
||||
#else
|
||||
if (isnanf(x)||isnanf(fn)) return x*fn;
|
||||
if (!finitef(fn)) {
|
||||
if(fn>(float)0.0) return x*fn;
|
||||
else return x/(-fn);
|
||||
}
|
||||
if (rintf(fn)!=fn) return (fn-fn)/(fn-fn);
|
||||
if ( fn > (float)65000.0) return scalbnf(x, 65000);
|
||||
if (-fn > (float)65000.0) return scalbnf(x,-65000);
|
||||
return scalbnf(x,(int)fn);
|
||||
#endif
|
||||
}
|
||||
@@ -0,0 +1,79 @@
|
||||
/* @(#)e_sinh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_sinh(x)
|
||||
* Method :
|
||||
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
||||
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : sinh(x) := x*shuge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinh(0)=0 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double one = 1.0, shuge = 1.0e307;
|
||||
|
||||
double
|
||||
__ieee754_sinh(double x)
|
||||
{
|
||||
double t,w,h;
|
||||
int32_t ix,jx;
|
||||
u_int32_t lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
GET_HIGH_WORD(jx,x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) return x+x;
|
||||
|
||||
h = 0.5;
|
||||
if (jx<0) h = -h;
|
||||
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x40360000) { /* |x|<22 */
|
||||
if (ix<0x3e300000) /* |x|<2**-28 */
|
||||
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
|
||||
t = expm1(fabs(x));
|
||||
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
|
||||
return h*(t+t/(t+one));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
GET_LOW_WORD(lx,x);
|
||||
if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
|
||||
w = __ieee754_exp(0.5*fabs(x));
|
||||
t = h*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*shuge;
|
||||
}
|
||||
@@ -0,0 +1,61 @@
|
||||
/* e_sinhf.c -- float version of e_sinh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_sinhf.c,v 1.7 2002/05/26 22:01:52 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float one = 1.0, shuge = 1.0e37;
|
||||
|
||||
float
|
||||
__ieee754_sinhf(float x)
|
||||
{
|
||||
float t,w,h;
|
||||
int32_t ix,jx;
|
||||
|
||||
GET_FLOAT_WORD(jx,x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7f800000) return x+x;
|
||||
|
||||
h = 0.5;
|
||||
if (jx<0) h = -h;
|
||||
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x41b00000) { /* |x|<22 */
|
||||
if (ix<0x31800000) /* |x|<2**-28 */
|
||||
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
|
||||
t = expm1f(fabsf(x));
|
||||
if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
|
||||
return h*(t+t/(t+one));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x42b17180) return h*__ieee754_expf(fabsf(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
if (ix<=0x42b2d4fc) {
|
||||
w = __ieee754_expf((float)0.5*fabsf(x));
|
||||
t = h*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*shuge;
|
||||
}
|
||||
@@ -0,0 +1,446 @@
|
||||
/* @(#)e_sqrt.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_sqrt.c,v 1.13 2009/02/16 01:19:34 lukem Exp $");
|
||||
#endif
|
||||
|
||||
/* __ieee754_sqrt(x)
|
||||
* Return correctly rounded sqrt.
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebric manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods : see the appended file at the end of the program below.
|
||||
*---------------
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double one = 1.0, tiny=1.0e-300;
|
||||
|
||||
double
|
||||
__ieee754_sqrt(double x)
|
||||
{
|
||||
double z;
|
||||
int32_t sign = (int)0x80000000;
|
||||
int32_t ix0,s0,q,m,t,i;
|
||||
u_int32_t r,t1,s1,ix1,q1;
|
||||
|
||||
EXTRACT_WORDS(ix0,ix1,x);
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix0&0x7ff00000)==0x7ff00000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix0<=0) {
|
||||
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix0<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0>>20);
|
||||
if(m==0) { /* subnormal x */
|
||||
while(ix0==0) {
|
||||
m -= 21;
|
||||
ix0 |= (ix1>>11); ix1 <<= 21;
|
||||
}
|
||||
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
|
||||
m -= i-1;
|
||||
ix0 |= (ix1>>(32-i));
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0&0x000fffff)|0x00100000;
|
||||
if(m&1){ /* odd m, double x to make it even */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s0+r;
|
||||
if(t<=ix0) {
|
||||
s0 = t+r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
r = sign;
|
||||
while(r!=0) {
|
||||
t1 = s1+r;
|
||||
t = s0;
|
||||
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
|
||||
s1 = t1+r;
|
||||
if(((t1&sign)==(u_int32_t)sign)&&(s1&sign)==0) s0 += 1;
|
||||
ix0 -= t;
|
||||
if (ix1 < t1) ix0 -= 1;
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if((ix0|ix1)!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
|
||||
else if (z>one) {
|
||||
if (q1==(u_int32_t)0xfffffffe) q+=1;
|
||||
q1+=2;
|
||||
} else
|
||||
q1 += (q1&1);
|
||||
}
|
||||
}
|
||||
ix0 = (q>>1)+0x3fe00000;
|
||||
ix1 = q1>>1;
|
||||
if ((q&1)==1) ix1 |= sign;
|
||||
ix0 += (m <<20);
|
||||
INSERT_WORDS(z,ix0,ix1);
|
||||
return z;
|
||||
}
|
||||
|
||||
/*
|
||||
Other methods (use floating-point arithmetic)
|
||||
-------------
|
||||
(This is a copy of a drafted paper by Prof W. Kahan
|
||||
and K.C. Ng, written in May, 1986)
|
||||
|
||||
Two algorithms are given here to implement sqrt(x)
|
||||
(IEEE double precision arithmetic) in software.
|
||||
Both supply sqrt(x) correctly rounded. The first algorithm (in
|
||||
Section A) uses newton iterations and involves four divisions.
|
||||
The second one uses reciproot iterations to avoid division, but
|
||||
requires more multiplications. Both algorithms need the ability
|
||||
to chop results of arithmetic operations instead of round them,
|
||||
and the INEXACT flag to indicate when an arithmetic operation
|
||||
is executed exactly with no roundoff error, all part of the
|
||||
standard (IEEE 754-1985). The ability to perform shift, add,
|
||||
subtract and logical AND operations upon 32-bit words is needed
|
||||
too, though not part of the standard.
|
||||
|
||||
A. sqrt(x) by Newton Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
|
||||
1 11 52 ...widths
|
||||
------------------------------------------------------
|
||||
x: |s| e | f |
|
||||
------------------------------------------------------
|
||||
msb lsb msb lsb ...order
|
||||
|
||||
|
||||
------------------------ ------------------------
|
||||
x0: |s| e | f1 | x1: | f2 |
|
||||
------------------------ ------------------------
|
||||
|
||||
By performing shifts and subtracts on x0 and x1 (both regarded
|
||||
as integers), we obtain an 8-bit approximation of sqrt(x) as
|
||||
follows.
|
||||
|
||||
k := (x0>>1) + 0x1ff80000;
|
||||
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
|
||||
Here k is a 32-bit integer and T1[] is an integer array containing
|
||||
correction terms. Now magically the floating value of y (y's
|
||||
leading 32-bit word is y0, the value of its trailing word is 0)
|
||||
approximates sqrt(x) to almost 8-bit.
|
||||
|
||||
Value of T1:
|
||||
static int T1[32]= {
|
||||
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
|
||||
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
|
||||
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
|
||||
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Heron's rule three times to y, we have y approximates
|
||||
sqrt(x) to within 1 ulp (Unit in the Last Place):
|
||||
|
||||
y := (y+x/y)/2 ... almost 17 sig. bits
|
||||
y := (y+x/y)/2 ... almost 35 sig. bits
|
||||
y := y-(y-x/y)/2 ... within 1 ulp
|
||||
|
||||
|
||||
Remark 1.
|
||||
Another way to improve y to within 1 ulp is:
|
||||
|
||||
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
|
||||
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
|
||||
|
||||
2
|
||||
(x-y )*y
|
||||
y := y + 2* ---------- ...within 1 ulp
|
||||
2
|
||||
3y + x
|
||||
|
||||
|
||||
This formula has one division fewer than the one above; however,
|
||||
it requires more multiplications and additions. Also x must be
|
||||
scaled in advance to avoid spurious overflow in evaluating the
|
||||
expression 3y*y+x. Hence it is not recommended uless division
|
||||
is slow. If division is very slow, then one should use the
|
||||
reciproot algorithm given in section B.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
I := FALSE; ... reset INEXACT flag I
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
z := x/y; ... chopped quotient, possibly inexact
|
||||
If(not I) then { ... if the quotient is exact
|
||||
if(z=y) {
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
} else {
|
||||
z := z - ulp; ... special rounding
|
||||
}
|
||||
}
|
||||
i := TRUE; ... sqrt(x) is inexact
|
||||
If (r=RN) then z=z+ulp ... rounded-to-nearest
|
||||
If (r=RP) then { ... round-toward-+inf
|
||||
y = y+ulp; z=z+ulp;
|
||||
}
|
||||
y := y+z; ... chopped sum
|
||||
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
|
||||
(4) Special cases
|
||||
|
||||
Square root of +inf, +-0, or NaN is itself;
|
||||
Square root of a negative number is NaN with invalid signal.
|
||||
|
||||
|
||||
B. sqrt(x) by Reciproot Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
(see section A). By performing shifs and subtracts on x0 and y0,
|
||||
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
|
||||
|
||||
k := 0x5fe80000 - (x0>>1);
|
||||
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
|
||||
|
||||
Here k is a 32-bit integer and T2[] is an integer array
|
||||
containing correction terms. Now magically the floating
|
||||
value of y (y's leading 32-bit word is y0, the value of
|
||||
its trailing word y1 is set to zero) approximates 1/sqrt(x)
|
||||
to almost 7.8-bit.
|
||||
|
||||
Value of T2:
|
||||
static int T2[64]= {
|
||||
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
|
||||
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
|
||||
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
|
||||
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
|
||||
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
|
||||
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
|
||||
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
|
||||
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Reciproot iteration three times to y and multiply the
|
||||
result by x to get an approximation z that matches sqrt(x)
|
||||
to about 1 ulp. To be exact, we will have
|
||||
-1ulp < sqrt(x)-z<1.0625ulp.
|
||||
|
||||
... set rounding mode to Round-to-nearest
|
||||
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
|
||||
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
|
||||
... special arrangement for better accuracy
|
||||
z := x*y ... 29 bits to sqrt(x), with z*y<1
|
||||
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
|
||||
|
||||
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
|
||||
(a) the term z*y in the final iteration is always less than 1;
|
||||
(b) the error in the final result is biased upward so that
|
||||
-1 ulp < sqrt(x) - z < 1.0625 ulp
|
||||
instead of |sqrt(x)-z|<1.03125ulp.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
switch(r) {
|
||||
case RN: ... round-to-nearest
|
||||
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
break;
|
||||
case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
R:=RP; ... reset rounding mod to round-to-+inf
|
||||
if(x<z*z ... rounded up) z = z - ulp; else
|
||||
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
break;
|
||||
case RP: ... round-to-+inf
|
||||
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
if(x>z*z ...chopped) z = z+ulp;
|
||||
break;
|
||||
}
|
||||
|
||||
Remark 3. The above comparisons can be done in fixed point. For
|
||||
example, to compare x and w=z*z chopped, it suffices to compare
|
||||
x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
two's complement integers.
|
||||
|
||||
...Is z an exact square root?
|
||||
To determine whether z is an exact square root of x, let z1 be the
|
||||
trailing part of z, and also let x0 and x1 be the leading and
|
||||
trailing parts of x.
|
||||
|
||||
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
I := 1; ... Raise Inexact flag: z is not exact
|
||||
else {
|
||||
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
fraction bits
|
||||
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
}
|
||||
R:= r ... restore rounded mode
|
||||
return sqrt(x):=z.
|
||||
|
||||
If multiplication is cheaper than the foregoing red tape, the
|
||||
Inexact flag can be evaluated by
|
||||
|
||||
I := i;
|
||||
I := (z*z!=x) or I.
|
||||
|
||||
Note that z*z can overwrite I; this value must be sensed if it is
|
||||
True.
|
||||
|
||||
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
zero.
|
||||
|
||||
--------------------
|
||||
z1: | f2 |
|
||||
--------------------
|
||||
bit 31 bit 0
|
||||
|
||||
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
or even of logb(x) have the following relations:
|
||||
|
||||
-------------------------------------------------
|
||||
bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
-------------------------------------------------
|
||||
00 00 odd and even
|
||||
01 01 even
|
||||
10 10 odd
|
||||
10 00 even
|
||||
11 01 even
|
||||
-------------------------------------------------
|
||||
|
||||
(4) Special cases (see (4) of Section A).
|
||||
|
||||
*/
|
||||
|
||||
@@ -0,0 +1,90 @@
|
||||
/* e_sqrtf.c -- float version of e_sqrt.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: e_sqrtf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float one = 1.0, tiny=1.0e-30;
|
||||
|
||||
float
|
||||
__ieee754_sqrtf(float x)
|
||||
{
|
||||
float z;
|
||||
int32_t sign = (int)0x80000000;
|
||||
int32_t ix,s,q,m,t,i;
|
||||
u_int32_t r;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix&0x7f800000)==0x7f800000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix<=0) {
|
||||
if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix>>23);
|
||||
if(m==0) { /* subnormal x */
|
||||
for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
|
||||
m -= i-1;
|
||||
}
|
||||
m -= 127; /* unbias exponent */
|
||||
ix = (ix&0x007fffff)|0x00800000;
|
||||
if(m&1) /* odd m, double x to make it even */
|
||||
ix += ix;
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix += ix;
|
||||
q = s = 0; /* q = sqrt(x) */
|
||||
r = 0x01000000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s+r;
|
||||
if(t<=ix) {
|
||||
s = t+r;
|
||||
ix -= t;
|
||||
q += r;
|
||||
}
|
||||
ix += ix;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if(ix!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (z>one)
|
||||
q += 2;
|
||||
else
|
||||
q += (q&1);
|
||||
}
|
||||
}
|
||||
ix = (q>>1)+0x3f000000;
|
||||
ix += (m <<23);
|
||||
SET_FLOAT_WORD(z,ix);
|
||||
return z;
|
||||
}
|
||||
@@ -0,0 +1,89 @@
|
||||
/* @(#)k_cos.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __kernel_cos( x, y )
|
||||
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
|
||||
* 3. cos(x) is approximated by a polynomial of degree 14 on
|
||||
* [0,pi/4]
|
||||
* 4 14
|
||||
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
|
||||
* where the remez error is
|
||||
*
|
||||
* | 2 4 6 8 10 12 14 | -58
|
||||
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
|
||||
* | |
|
||||
*
|
||||
* 4 6 8 10 12 14
|
||||
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
|
||||
* cos(x) = 1 - x*x/2 + r
|
||||
* since cos(x+y) ~ cos(x) - sin(x)*y
|
||||
* ~ cos(x) - x*y,
|
||||
* a correction term is necessary in cos(x) and hence
|
||||
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
|
||||
* For better accuracy when x > 0.3, let qx = |x|/4 with
|
||||
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
|
||||
* Then
|
||||
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
|
||||
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
|
||||
* magnitude of the latter is at least a quarter of x*x/2,
|
||||
* thus, reducing the rounding error in the subtraction.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
|
||||
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
|
||||
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
|
||||
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
|
||||
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
|
||||
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
|
||||
|
||||
double
|
||||
__kernel_cos(double x, double y)
|
||||
{
|
||||
double a,hz,z,r,qx;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
||||
if(ix<0x3e400000) { /* if x < 2**27 */
|
||||
if(((int)x)==0) return one; /* generate inexact */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||
if(ix < 0x3FD33333) /* if |x| < 0.3 */
|
||||
return one - (0.5*z - (z*r - x*y));
|
||||
else {
|
||||
if(ix > 0x3fe90000) { /* x > 0.78125 */
|
||||
qx = 0.28125;
|
||||
} else {
|
||||
INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
|
||||
}
|
||||
hz = 0.5*z-qx;
|
||||
a = one-qx;
|
||||
return a - (hz - (z*r-x*y));
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,57 @@
|
||||
/* k_cosf.c -- float version of k_cos.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_cosf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
C1 = 4.1666667908e-02, /* 0x3d2aaaab */
|
||||
C2 = -1.3888889225e-03, /* 0xbab60b61 */
|
||||
C3 = 2.4801587642e-05, /* 0x37d00d01 */
|
||||
C4 = -2.7557314297e-07, /* 0xb493f27c */
|
||||
C5 = 2.0875723372e-09, /* 0x310f74f6 */
|
||||
C6 = -1.1359647598e-11; /* 0xad47d74e */
|
||||
|
||||
float
|
||||
__kernel_cosf(float x, float y)
|
||||
{
|
||||
float a,hz,z,r,qx;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
||||
if(ix<0x32000000) { /* if x < 2**27 */
|
||||
if(((int)x)==0) return one; /* generate inexact */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||
if(ix < 0x3e99999a) /* if |x| < 0.3 */
|
||||
return one - ((float)0.5*z - (z*r - x*y));
|
||||
else {
|
||||
if(ix > 0x3f480000) { /* x > 0.78125 */
|
||||
qx = (float)0.28125;
|
||||
} else {
|
||||
SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
|
||||
}
|
||||
hz = (float)0.5*z-qx;
|
||||
a = one-qx;
|
||||
return a - (hz - (z*r-x*y));
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,306 @@
|
||||
/* @(#)k_rem_pio2.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_rem_pio2.c,v 1.12 2010/04/23 19:17:07 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
* double x[],y[]; int e0,nx,prec; int ipio2[];
|
||||
*
|
||||
* __kernel_rem_pio2 return the last three digits of N with
|
||||
* y = x - N*pi/2
|
||||
* so that |y| < pi/2.
|
||||
*
|
||||
* The method is to compute the integer (mod 8) and fraction parts of
|
||||
* (2/pi)*x without doing the full multiplication. In general we
|
||||
* skip the part of the product that are known to be a huge integer (
|
||||
* more accurately, = 0 mod 8 ). Thus the number of operations are
|
||||
* independent of the exponent of the input.
|
||||
*
|
||||
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
|
||||
*
|
||||
* Input parameters:
|
||||
* x[] The input value (must be positive) is broken into nx
|
||||
* pieces of 24-bit integers in double precision format.
|
||||
* x[i] will be the i-th 24 bit of x. The scaled exponent
|
||||
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
|
||||
* match x's up to 24 bits.
|
||||
*
|
||||
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
|
||||
* e0 = ilogb(z)-23
|
||||
* z = scalbn(z,-e0)
|
||||
* for i = 0,1,2
|
||||
* x[i] = floor(z)
|
||||
* z = (z-x[i])*2**24
|
||||
*
|
||||
*
|
||||
* y[] output result in an array of double precision numbers.
|
||||
* The dimension of y[] is:
|
||||
* 24-bit precision 1
|
||||
* 53-bit precision 2
|
||||
* 64-bit precision 2
|
||||
* 113-bit precision 3
|
||||
* The actual value is the sum of them. Thus for 113-bit
|
||||
* precison, one may have to do something like:
|
||||
*
|
||||
* long double t,w,r_head, r_tail;
|
||||
* t = (long double)y[2] + (long double)y[1];
|
||||
* w = (long double)y[0];
|
||||
* r_head = t+w;
|
||||
* r_tail = w - (r_head - t);
|
||||
*
|
||||
* e0 The exponent of x[0]
|
||||
*
|
||||
* nx dimension of x[]
|
||||
*
|
||||
* prec an integer indicating the precision:
|
||||
* 0 24 bits (single)
|
||||
* 1 53 bits (double)
|
||||
* 2 64 bits (extended)
|
||||
* 3 113 bits (quad)
|
||||
*
|
||||
* ipio2[]
|
||||
* integer array, contains the (24*i)-th to (24*i+23)-th
|
||||
* bit of 2/pi after binary point. The corresponding
|
||||
* floating value is
|
||||
*
|
||||
* ipio2[i] * 2^(-24(i+1)).
|
||||
*
|
||||
* External function:
|
||||
* double scalbn(), floor();
|
||||
*
|
||||
*
|
||||
* Here is the description of some local variables:
|
||||
*
|
||||
* jk jk+1 is the initial number of terms of ipio2[] needed
|
||||
* in the computation. The recommended value is 2,3,4,
|
||||
* 6 for single, double, extended,and quad.
|
||||
*
|
||||
* jz local integer variable indicating the number of
|
||||
* terms of ipio2[] used.
|
||||
*
|
||||
* jx nx - 1
|
||||
*
|
||||
* jv index for pointing to the suitable ipio2[] for the
|
||||
* computation. In general, we want
|
||||
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
|
||||
* is an integer. Thus
|
||||
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
|
||||
* Hence jv = max(0,(e0-3)/24).
|
||||
*
|
||||
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
|
||||
*
|
||||
* q[] double array with integral value, representing the
|
||||
* 24-bits chunk of the product of x and 2/pi.
|
||||
*
|
||||
* q0 the corresponding exponent of q[0]. Note that the
|
||||
* exponent for q[i] would be q0-24*i.
|
||||
*
|
||||
* PIo2[] double precision array, obtained by cutting pi/2
|
||||
* into 24 bits chunks.
|
||||
*
|
||||
* f[] ipio2[] in floating point
|
||||
*
|
||||
* iq[] integer array by breaking up q[] in 24-bits chunk.
|
||||
*
|
||||
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
|
||||
*
|
||||
* ih integer. If >0 it indicates q[] is >= 0.5, hence
|
||||
* it also indicates the *sign* of the result.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
/*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
|
||||
|
||||
static const double PIo2[] = {
|
||||
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
||||
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
||||
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
||||
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
|
||||
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
||||
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
||||
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
||||
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
||||
};
|
||||
|
||||
static const double
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
|
||||
|
||||
int
|
||||
__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
|
||||
{
|
||||
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||
double z,fw,f[20],fq[20],q[20];
|
||||
|
||||
/* initialize jk*/
|
||||
jk = init_jk[prec];
|
||||
jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
jx = nx-1;
|
||||
jv = (e0-3)/24; if(jv<0) jv=0;
|
||||
q0 = e0-24*(jv+1);
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
j = jv-jx; m = jx+jk;
|
||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
|
||||
|
||||
jz = jk;
|
||||
recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (double)((int32_t)(twon24* z));
|
||||
iq[i] = (int32_t)(z-two24*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = scalbn(z,q0); /* actual value of z */
|
||||
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
||||
n = (int32_t) z;
|
||||
z -= (double)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(24-q0)); n += i;
|
||||
iq[jz-1] -= i<<(24-q0);
|
||||
ih = iq[jz-1]>>(23-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>23;
|
||||
else if(z>=0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x1000000- j;
|
||||
}
|
||||
} else iq[i] = 0xffffff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7fffff; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3fffff; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= scalbn(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (double) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==0.0) {
|
||||
jz -= 1; q0 -= 24;
|
||||
while(iq[jz]==0) { jz--; q0-=24;}
|
||||
} else { /* break z into 24-bit if necessary */
|
||||
z = scalbn(z,-q0);
|
||||
if(z>=two24) {
|
||||
fw = (double)((int32_t)(twon24*z));
|
||||
iq[jz] = (int32_t)(z-two24*fw);
|
||||
jz += 1; q0 += 24;
|
||||
iq[jz] = (int32_t) fw;
|
||||
} else iq[jz] = (int32_t) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = scalbn(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(double)iq[i]; fw*=twon24;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
@@ -0,0 +1,199 @@
|
||||
/* k_rem_pio2f.c -- float version of k_rem_pio2.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_rem_pio2f.c,v 1.8 2010/04/23 19:17:07 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* In the float version, the input parameter x contains 8 bit
|
||||
integers, not 24 bit integers. 113 bit precision is not supported. */
|
||||
|
||||
static const int init_jk[] = {4,7,9}; /* initial value for jk */
|
||||
|
||||
static const float PIo2[] = {
|
||||
1.5703125000e+00, /* 0x3fc90000 */
|
||||
4.5776367188e-04, /* 0x39f00000 */
|
||||
2.5987625122e-05, /* 0x37da0000 */
|
||||
7.5437128544e-08, /* 0x33a20000 */
|
||||
6.0026650317e-11, /* 0x2e840000 */
|
||||
7.3896444519e-13, /* 0x2b500000 */
|
||||
5.3845816694e-15, /* 0x27c20000 */
|
||||
5.6378512969e-18, /* 0x22d00000 */
|
||||
8.3009228831e-20, /* 0x1fc40000 */
|
||||
3.2756352257e-22, /* 0x1bc60000 */
|
||||
6.3331015649e-25, /* 0x17440000 */
|
||||
};
|
||||
|
||||
static const float
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two8 = 2.5600000000e+02, /* 0x43800000 */
|
||||
twon8 = 3.9062500000e-03; /* 0x3b800000 */
|
||||
|
||||
int
|
||||
__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
|
||||
{
|
||||
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||
float z,fw,f[20],fq[20],q[20];
|
||||
|
||||
/* initialize jk*/
|
||||
jk = init_jk[prec];
|
||||
jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
jx = nx-1;
|
||||
jv = (e0-3)/8; if(jv<0) jv=0;
|
||||
q0 = e0-8*(jv+1);
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
j = jv-jx; m = jx+jk;
|
||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
|
||||
|
||||
jz = jk;
|
||||
recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (float)((int32_t)(twon8* z));
|
||||
iq[i] = (int32_t)(z-two8*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = scalbnf(z,q0); /* actual value of z */
|
||||
z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
|
||||
n = (int32_t) z;
|
||||
z -= (float)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(8-q0)); n += i;
|
||||
iq[jz-1] -= i<<(8-q0);
|
||||
ih = iq[jz-1]>>(7-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>8;
|
||||
else if(z>=(float)0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x100- j;
|
||||
}
|
||||
} else iq[i] = 0xff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7f; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3f; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= scalbnf(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (float) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==(float)0.0) {
|
||||
jz -= 1; q0 -= 8;
|
||||
while(iq[jz]==0) { jz--; q0-=8;}
|
||||
} else { /* break z into 8-bit if necessary */
|
||||
z = scalbnf(z,-q0);
|
||||
if(z>=two8) {
|
||||
fw = (float)((int32_t)(twon8*z));
|
||||
iq[jz] = (int32_t)(z-two8*fw);
|
||||
jz += 1; q0 += 8;
|
||||
iq[jz] = (int32_t) fw;
|
||||
} else iq[jz] = (int32_t) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = scalbnf(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(float)iq[i]; fw*=twon8;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
@@ -0,0 +1,72 @@
|
||||
/* @(#)k_sin.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* __kernel_sin( x, y, iy)
|
||||
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
|
||||
* 3. sin(x) is approximated by a polynomial of degree 13 on
|
||||
* [0,pi/4]
|
||||
* 3 13
|
||||
* sin(x) ~ x + S1*x + ... + S6*x
|
||||
* where
|
||||
*
|
||||
* |sin(x) 2 4 6 8 10 12 | -58
|
||||
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
|
||||
* | x |
|
||||
*
|
||||
* 4. sin(x+y) = sin(x) + sin'(x')*y
|
||||
* ~ sin(x) + (1-x*x/2)*y
|
||||
* For better accuracy, let
|
||||
* 3 2 2 2 2
|
||||
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
|
||||
* then 3 2
|
||||
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
|
||||
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
|
||||
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
|
||||
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
|
||||
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
|
||||
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
|
||||
|
||||
double
|
||||
__kernel_sin(double x, double y, int iy)
|
||||
{
|
||||
double z,r,v;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* high word of x */
|
||||
if(ix<0x3e400000) /* |x| < 2**-27 */
|
||||
{if((int)x==0) return x;} /* generate inexact */
|
||||
z = x*x;
|
||||
v = z*x;
|
||||
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
||||
if(iy==0) return x+v*(S1+z*r);
|
||||
else return x-((z*(half*y-v*r)-y)-v*S1);
|
||||
}
|
||||
@@ -0,0 +1,47 @@
|
||||
/* k_sinf.c -- float version of k_sin.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_sinf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
half = 5.0000000000e-01,/* 0x3f000000 */
|
||||
S1 = -1.6666667163e-01, /* 0xbe2aaaab */
|
||||
S2 = 8.3333337680e-03, /* 0x3c088889 */
|
||||
S3 = -1.9841270114e-04, /* 0xb9500d01 */
|
||||
S4 = 2.7557314297e-06, /* 0x3638ef1b */
|
||||
S5 = -2.5050759689e-08, /* 0xb2d72f34 */
|
||||
S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */
|
||||
|
||||
float
|
||||
__kernel_sinf(float x, float y, int iy)
|
||||
{
|
||||
float z,r,v;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* high word of x */
|
||||
if(ix<0x32000000) /* |x| < 2**-27 */
|
||||
{if((int)x==0) return x;} /* generate inexact */
|
||||
z = x*x;
|
||||
v = z*x;
|
||||
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
||||
if(iy==0) return x+v*(S1+z*r);
|
||||
else return x-((z*(half*y-v*r)-y)-v*S1);
|
||||
}
|
||||
@@ -0,0 +1,815 @@
|
||||
/* @(#)k_standard.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_standard.c,v 1.16 2010/09/01 10:44:28 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
#include <errno.h>
|
||||
|
||||
#ifndef _USE_WRITE
|
||||
#include <stdio.h> /* fputs(), stderr */
|
||||
#define WRITE2(u,v) fputs(u, stderr)
|
||||
#else /* !defined(_USE_WRITE) */
|
||||
#include <unistd.h> /* write */
|
||||
#define WRITE2(u,v) write(2, u, v)
|
||||
#undef fflush
|
||||
#endif /* !defined(_USE_WRITE) */
|
||||
|
||||
static const double zero = 0.0; /* used as const */
|
||||
|
||||
/*
|
||||
* Standard conformance (non-IEEE) on exception cases.
|
||||
* Mapping:
|
||||
* 1 -- acos(|x|>1)
|
||||
* 2 -- asin(|x|>1)
|
||||
* 3 -- atan2(+-0,+-0)
|
||||
* 4 -- hypot overflow
|
||||
* 5 -- cosh overflow
|
||||
* 6 -- exp overflow
|
||||
* 7 -- exp underflow
|
||||
* 8 -- y0(0)
|
||||
* 9 -- y0(-ve)
|
||||
* 10-- y1(0)
|
||||
* 11-- y1(-ve)
|
||||
* 12-- yn(0)
|
||||
* 13-- yn(-ve)
|
||||
* 14-- lgamma(finite) overflow
|
||||
* 15-- lgamma(-integer)
|
||||
* 16-- log(0)
|
||||
* 17-- log(x<0)
|
||||
* 18-- log10(0)
|
||||
* 19-- log10(x<0)
|
||||
* 20-- pow(0.0,0.0)
|
||||
* 21-- pow(x,y) overflow
|
||||
* 22-- pow(x,y) underflow
|
||||
* 23-- pow(0,negative)
|
||||
* 24-- pow(neg,non-integral)
|
||||
* 25-- sinh(finite) overflow
|
||||
* 26-- sqrt(negative)
|
||||
* 27-- fmod(x,0)
|
||||
* 28-- remainder(x,0)
|
||||
* 29-- acosh(x<1)
|
||||
* 30-- atanh(|x|>1)
|
||||
* 31-- atanh(|x|=1)
|
||||
* 32-- scalb overflow
|
||||
* 33-- scalb underflow
|
||||
* 34-- j0(|x|>X_TLOSS)
|
||||
* 35-- y0(x>X_TLOSS)
|
||||
* 36-- j1(|x|>X_TLOSS)
|
||||
* 37-- y1(x>X_TLOSS)
|
||||
* 38-- jn(|x|>X_TLOSS, n)
|
||||
* 39-- yn(x>X_TLOSS, n)
|
||||
* 40-- gamma(finite) overflow
|
||||
* 41-- gamma(-integer)
|
||||
* 42-- pow(NaN,0.0)
|
||||
* 48-- log2(0)
|
||||
* 49-- log2(x<0)
|
||||
*/
|
||||
|
||||
|
||||
double
|
||||
__kernel_standard(double x, double y, int type)
|
||||
{
|
||||
struct exception exc;
|
||||
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
|
||||
#define HUGE_VAL inf
|
||||
double inf = 0.0;
|
||||
|
||||
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
|
||||
#endif
|
||||
|
||||
#ifdef _USE_WRITE
|
||||
(void) fflush(stdout);
|
||||
#endif
|
||||
exc.arg1 = x;
|
||||
exc.arg2 = y;
|
||||
switch(type) {
|
||||
case 1:
|
||||
case 101:
|
||||
/* acos(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "acos" : "acosf";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_) {
|
||||
exc.retval = zero/zero;
|
||||
errno = EDOM;
|
||||
} else if (!matherr(&exc)) {
|
||||
if(_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("acos: DOMAIN error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 2:
|
||||
case 102:
|
||||
/* asin(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "asin" : "asinf";
|
||||
exc.retval = zero;
|
||||
if(_LIB_VERSION == _POSIX_) {
|
||||
exc.retval = zero/zero;
|
||||
errno = EDOM;
|
||||
} else if (!matherr(&exc)) {
|
||||
if(_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("asin: DOMAIN error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 3:
|
||||
case 103:
|
||||
/* atan2(+-0,+-0) */
|
||||
exc.arg1 = y;
|
||||
exc.arg2 = x;
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "atan2" : "atan2f";
|
||||
exc.retval = zero;
|
||||
if(_LIB_VERSION == _POSIX_) {
|
||||
exc.retval = copysign(signbit(y) ? M_PI : zero, x);
|
||||
} else if (!matherr(&exc)) {
|
||||
if(_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("atan2: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 4:
|
||||
case 104:
|
||||
/* hypot(finite,finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "hypot" : "hypotf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 5:
|
||||
case 105:
|
||||
/* cosh(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "cosh" : "coshf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 6:
|
||||
case 106:
|
||||
/* exp(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "exp" : "expf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 7:
|
||||
case 107:
|
||||
/* exp(finite) underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = type < 100 ? "exp" : "expf";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 8:
|
||||
case 108:
|
||||
/* y0(0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = type < 100 ? "y0" : "y0f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y0: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 9:
|
||||
case 109:
|
||||
/* y0(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "y0" : "y0f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y0: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 10:
|
||||
case 110:
|
||||
/* y1(0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = type < 100 ? "y1" : "y1f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y1: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 11:
|
||||
case 111:
|
||||
/* y1(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "y1" : "y1f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("y1: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 12:
|
||||
case 112:
|
||||
/* yn(n,0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = type < 100 ? "yn" : "ynf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("yn: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 13:
|
||||
case 113:
|
||||
/* yn(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "yn" : "ynf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("yn: DOMAIN error\n", 17);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 14:
|
||||
case 114:
|
||||
/* lgamma(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "lgamma" : "lgammaf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 15:
|
||||
case 115:
|
||||
/* lgamma(-integer) or lgamma(0) */
|
||||
exc.type = SING;
|
||||
exc.name = type < 100 ? "lgamma" : "lgammaf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("lgamma: SING error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 16:
|
||||
case 116:
|
||||
/* log(0) */
|
||||
exc.type = SING;
|
||||
exc.name = type < 100 ? "log" : "logf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log: SING error\n", 16);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 17:
|
||||
case 117:
|
||||
/* log(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "log" : "logf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log: DOMAIN error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 18:
|
||||
case 118:
|
||||
/* log10(0) */
|
||||
exc.type = SING;
|
||||
exc.name = type < 100 ? "log10" : "log10f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log10: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 19:
|
||||
case 119:
|
||||
/* log10(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "log10" : "log10f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log10: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 20:
|
||||
case 120:
|
||||
/* pow(0.0,0.0) */
|
||||
/* error only if _LIB_VERSION == _SVID_ */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "pow" : "powf";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
|
||||
else if (!matherr(&exc)) {
|
||||
(void) WRITE2("pow(0,0): DOMAIN error\n", 23);
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 21:
|
||||
case 121:
|
||||
/* pow(x,y) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "pow" : "powf";
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
exc.retval = HUGE;
|
||||
y *= 0.5;
|
||||
if(x<zero&&rint(y)!=y) exc.retval = -HUGE;
|
||||
} else {
|
||||
exc.retval = HUGE_VAL;
|
||||
y *= 0.5;
|
||||
if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL;
|
||||
}
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 22:
|
||||
case 122:
|
||||
/* pow(x,y) underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = type < 100 ? "pow" : "powf";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 23:
|
||||
case 123:
|
||||
/* 0**neg */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "pow" : "powf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 24:
|
||||
case 124:
|
||||
/* neg**non-integral */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "pow" : "powf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = zero/zero; /* X/Open allow NaN */
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 25:
|
||||
case 125:
|
||||
/* sinh(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "sinh" : "sinhf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = ( (x>zero) ? HUGE : -HUGE);
|
||||
else
|
||||
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 26:
|
||||
case 126:
|
||||
/* sqrt(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "sqrt" : "sqrtf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("sqrt: DOMAIN error\n", 19);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 27:
|
||||
case 127:
|
||||
/* fmod(x,0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "fmod" : "fmodf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = x;
|
||||
else
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("fmod: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 28:
|
||||
case 128:
|
||||
/* remainder(x,0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "remainder" : "remainderf";
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("remainder: DOMAIN error\n", 24);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 29:
|
||||
case 129:
|
||||
/* acosh(x<1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "acosh" : "acoshf";
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("acosh: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 30:
|
||||
case 130:
|
||||
/* atanh(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "atanh" : "atanhf";
|
||||
exc.retval = zero/zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("atanh: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 31:
|
||||
case 131:
|
||||
/* atanh(|x|=1) */
|
||||
exc.type = SING;
|
||||
exc.name = type < 100 ? "atanh" : "atanhf";
|
||||
exc.retval = x/zero; /* sign(x)*inf */
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("atanh: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 32:
|
||||
case 132:
|
||||
/* scalb overflow; SVID also returns +-HUGE_VAL */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "scalb" : "scalbf";
|
||||
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 33:
|
||||
case 133:
|
||||
/* scalb underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = type < 100 ? "scalb" : "scalbf";
|
||||
exc.retval = copysign(zero,x);
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 34:
|
||||
case 134:
|
||||
/* j0(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = type < 100 ? "j0" : "j0f";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 35:
|
||||
case 135:
|
||||
/* y0(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = type < 100 ? "y0" : "y0f";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 36:
|
||||
case 136:
|
||||
/* j1(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = type < 100 ? "j1" : "j1f";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 37:
|
||||
case 137:
|
||||
/* y1(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = type < 100 ? "y1" : "y1f";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 38:
|
||||
case 138:
|
||||
/* jn(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = type < 100 ? "jn" : "jnf";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 39:
|
||||
case 139:
|
||||
/* yn(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = type < 100 ? "yn" : "ynf";
|
||||
exc.retval = zero;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2(exc.name, 2);
|
||||
(void) WRITE2(": TLOSS error\n", 14);
|
||||
}
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 40:
|
||||
case 140:
|
||||
/* gamma(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = type < 100 ? "gamma" : "gammaf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
break;
|
||||
case 41:
|
||||
case 141:
|
||||
/* gamma(-integer) or gamma(0) */
|
||||
exc.type = SING;
|
||||
exc.name = type < 100 ? "gamma" : "gammaf";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("gamma: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 42:
|
||||
case 142:
|
||||
/* pow(NaN,0.0) */
|
||||
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "pow" : "powf";
|
||||
exc.retval = x;
|
||||
if (_LIB_VERSION == _IEEE_ ||
|
||||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 48:
|
||||
case 148:
|
||||
/* log2(0) */
|
||||
exc.type = SING;
|
||||
exc.name = type < 100 ? "log2" : "log2f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log2: SING error\n", 18);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
case 49:
|
||||
case 149:
|
||||
/* log2(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = type < 100 ? "log2" : "log2f";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
(void) WRITE2("log2: DOMAIN error\n", 20);
|
||||
}
|
||||
errno = EDOM;
|
||||
}
|
||||
break;
|
||||
}
|
||||
return exc.retval;
|
||||
}
|
||||
@@ -0,0 +1,156 @@
|
||||
/* @(#)k_tan.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_tan.c,v 1.12 2004/07/22 18:24:09 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/* __kernel_tan( x, y, k )
|
||||
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
* Input k indicates whether tan (if k=1) or
|
||||
* -1/tan (if k= -1) is returned.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
|
||||
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
|
||||
* [0,0.67434]
|
||||
* 3 27
|
||||
* tan(x) ~ x + T1*x + ... + T13*x
|
||||
* where
|
||||
*
|
||||
* |tan(x) 2 4 26 | -59.2
|
||||
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
|
||||
* | x |
|
||||
*
|
||||
* Note: tan(x+y) = tan(x) + tan'(x)*y
|
||||
* ~ tan(x) + (1+x*x)*y
|
||||
* Therefore, for better accuracy in computing tan(x+y), let
|
||||
* 3 2 2 2 2
|
||||
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
|
||||
* then
|
||||
* 3 2
|
||||
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
|
||||
*
|
||||
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
|
||||
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
|
||||
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double xxx[] = {
|
||||
3.33333333333334091986e-01, /* 3FD55555, 55555563 */
|
||||
1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
|
||||
5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
|
||||
2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
|
||||
8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
|
||||
3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
|
||||
1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
|
||||
5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
|
||||
2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
|
||||
7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
|
||||
7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
|
||||
-1.85586374855275456654e-05, /* BEF375CB, DB605373 */
|
||||
2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
|
||||
/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
|
||||
/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
|
||||
/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
|
||||
};
|
||||
#define one xxx[13]
|
||||
#define pio4 xxx[14]
|
||||
#define pio4lo xxx[15]
|
||||
#define T xxx
|
||||
|
||||
double
|
||||
__kernel_tan(double x, double y, int iy)
|
||||
{
|
||||
double z, r, v, w, s;
|
||||
int32_t ix, hx;
|
||||
|
||||
GET_HIGH_WORD(hx, x); /* high word of x */
|
||||
ix = hx & 0x7fffffff; /* high word of |x| */
|
||||
if (ix < 0x3e300000) { /* x < 2**-28 */
|
||||
if ((int) x == 0) { /* generate inexact */
|
||||
u_int32_t low;
|
||||
GET_LOW_WORD(low, x);
|
||||
if(((ix | low) | (iy + 1)) == 0)
|
||||
return one / fabs(x);
|
||||
else {
|
||||
if (iy == 1)
|
||||
return x;
|
||||
else { /* compute -1 / (x+y) carefully */
|
||||
double a, t;
|
||||
|
||||
z = w = x + y;
|
||||
SET_LOW_WORD(z, 0);
|
||||
v = y - (z - x);
|
||||
t = a = -one / w;
|
||||
SET_LOW_WORD(t, 0);
|
||||
s = one + t * z;
|
||||
return t + a * (s + t * v);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
|
||||
if (hx < 0) {
|
||||
x = -x;
|
||||
y = -y;
|
||||
}
|
||||
z = pio4 - x;
|
||||
w = pio4lo - y;
|
||||
x = z + w;
|
||||
y = 0.0;
|
||||
}
|
||||
z = x * x;
|
||||
w = z * z;
|
||||
/*
|
||||
* Break x^5*(T[1]+x^2*T[2]+...) into
|
||||
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
||||
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
||||
*/
|
||||
r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
|
||||
w * T[11]))));
|
||||
v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
|
||||
w * T[12])))));
|
||||
s = z * x;
|
||||
r = y + z * (s * (r + v) + y);
|
||||
r += T[0] * s;
|
||||
w = x + r;
|
||||
if (ix >= 0x3FE59428) {
|
||||
v = (double) iy;
|
||||
return (double) (1 - ((hx >> 30) & 2)) *
|
||||
(v - 2.0 * (x - (w * w / (w + v) - r)));
|
||||
}
|
||||
if (iy == 1)
|
||||
return w;
|
||||
else {
|
||||
/*
|
||||
* if allow error up to 2 ulp, simply return
|
||||
* -1.0 / (x+r) here
|
||||
*/
|
||||
/* compute -1.0 / (x+r) accurately */
|
||||
double a, t;
|
||||
z = w;
|
||||
SET_LOW_WORD(z, 0);
|
||||
v = r - (z - x); /* z+v = r+x */
|
||||
t = a = -1.0 / w; /* a = -1.0/w */
|
||||
SET_LOW_WORD(t, 0);
|
||||
s = 1.0 + t * z;
|
||||
return t + a * (s + t * v);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,94 @@
|
||||
/* k_tanf.c -- float version of k_tan.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: k_tanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
pio4 = 7.8539812565e-01, /* 0x3f490fda */
|
||||
pio4lo= 3.7748947079e-08, /* 0x33222168 */
|
||||
T[] = {
|
||||
3.3333334327e-01, /* 0x3eaaaaab */
|
||||
1.3333334029e-01, /* 0x3e088889 */
|
||||
5.3968254477e-02, /* 0x3d5d0dd1 */
|
||||
2.1869488060e-02, /* 0x3cb327a4 */
|
||||
8.8632395491e-03, /* 0x3c11371f */
|
||||
3.5920790397e-03, /* 0x3b6b6916 */
|
||||
1.4562094584e-03, /* 0x3abede48 */
|
||||
5.8804126456e-04, /* 0x3a1a26c8 */
|
||||
2.4646313977e-04, /* 0x398137b9 */
|
||||
7.8179444245e-05, /* 0x38a3f445 */
|
||||
7.1407252108e-05, /* 0x3895c07a */
|
||||
-1.8558637748e-05, /* 0xb79bae5f */
|
||||
2.5907305826e-05, /* 0x37d95384 */
|
||||
};
|
||||
|
||||
float
|
||||
__kernel_tanf(float x, float y, int iy)
|
||||
{
|
||||
float z,r,v,w,s;
|
||||
int32_t ix,hx;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff; /* high word of |x| */
|
||||
if(ix<0x31800000) /* x < 2**-28 */
|
||||
{if((int)x==0) { /* generate inexact */
|
||||
if((ix|(iy+1))==0) return one/fabsf(x);
|
||||
else return (iy==1)? x: -one/x;
|
||||
}
|
||||
}
|
||||
if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
|
||||
if(hx<0) {x = -x; y = -y;}
|
||||
z = pio4-x;
|
||||
w = pio4lo-y;
|
||||
x = z+w; y = 0.0;
|
||||
}
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* Break x^5*(T[1]+x^2*T[2]+...) into
|
||||
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
||||
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
||||
*/
|
||||
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
|
||||
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
|
||||
s = z*x;
|
||||
r = y + z*(s*(r+v)+y);
|
||||
r += T[0]*s;
|
||||
w = x+r;
|
||||
if(ix>=0x3f2ca140) {
|
||||
v = (float)iy;
|
||||
return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
|
||||
}
|
||||
if(iy==1) return w;
|
||||
else { /* if allow error up to 2 ulp,
|
||||
simply return -1.0/(x+r) here */
|
||||
/* compute -1.0/(x+r) accurately */
|
||||
float a,t;
|
||||
int32_t i;
|
||||
z = w;
|
||||
GET_FLOAT_WORD(i,z);
|
||||
SET_FLOAT_WORD(z,i&0xfffff000);
|
||||
v = r-(z - x); /* z+v = r+x */
|
||||
t = a = -(float)1.0/w; /* a = -1.0/w */
|
||||
GET_FLOAT_WORD(i,t);
|
||||
SET_FLOAT_WORD(t,i&0xfffff000);
|
||||
s = (float)1.0+t*z;
|
||||
return t+a*(s+t*v);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,13 @@
|
||||
/* $NetBSD: llrint.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */
|
||||
|
||||
/*
|
||||
* Written by Matthias Drochner <drochner@NetBSD.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#define LRINTNAME llrint
|
||||
#define RESTYPE long long int
|
||||
#define RESTYPE_MIN LLONG_MIN
|
||||
#define RESTYPE_MAX LLONG_MAX
|
||||
|
||||
#include "lrint.c"
|
||||
@@ -0,0 +1,13 @@
|
||||
/* $NetBSD: llrintf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */
|
||||
|
||||
/*
|
||||
* Written by Matthias Drochner <drochner@NetBSD.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#define LRINTNAME llrintf
|
||||
#define RESTYPE long long int
|
||||
#define RESTYPE_MIN LLONG_MIN
|
||||
#define RESTYPE_MAX LLONG_MAX
|
||||
|
||||
#include "lrintf.c"
|
||||
@@ -0,0 +1,13 @@
|
||||
/* $NetBSD: llround.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */
|
||||
|
||||
/*
|
||||
* Written by Matthias Drochner <drochner@NetBSD.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#define LROUNDNAME llround
|
||||
#define RESTYPE long long int
|
||||
#define RESTYPE_MIN LLONG_MIN
|
||||
#define RESTYPE_MAX LLONG_MAX
|
||||
|
||||
#include "lround.c"
|
||||
@@ -0,0 +1,13 @@
|
||||
/* $NetBSD: llroundf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */
|
||||
|
||||
/*
|
||||
* Written by Matthias Drochner <drochner@NetBSD.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#define LROUNDNAME llroundf
|
||||
#define RESTYPE long long int
|
||||
#define RESTYPE_MIN LLONG_MIN
|
||||
#define RESTYPE_MAX LLONG_MAX
|
||||
|
||||
#include "lroundf.c"
|
||||
@@ -0,0 +1,92 @@
|
||||
/* $NetBSD: lrint.c,v 1.4 2008/04/26 23:49:50 christos Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 2004
|
||||
* Matthias Drochner. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <math.h>
|
||||
#include <sys/ieee754.h>
|
||||
#include <machine/limits.h>
|
||||
#include "math_private.h"
|
||||
|
||||
#ifndef LRINTNAME
|
||||
#define LRINTNAME lrint
|
||||
#define RESTYPE long int
|
||||
#define RESTYPE_MIN LONG_MIN
|
||||
#define RESTYPE_MAX LONG_MAX
|
||||
#endif
|
||||
|
||||
#define RESTYPE_BITS (sizeof(RESTYPE) * 8)
|
||||
|
||||
static const double
|
||||
TWO52[2]={
|
||||
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
|
||||
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
|
||||
};
|
||||
|
||||
RESTYPE
|
||||
LRINTNAME(double x)
|
||||
{
|
||||
u_int32_t i0, i1;
|
||||
int e, s, shift;
|
||||
RESTYPE res;
|
||||
|
||||
GET_HIGH_WORD(i0, x);
|
||||
e = i0 >> 20;
|
||||
s = (uint32_t)e >> DBL_EXPBITS;
|
||||
e = (e & 0x7ff) - DBL_EXP_BIAS;
|
||||
|
||||
/* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */
|
||||
if (e < -1)
|
||||
return (0);
|
||||
/* 1.0 x 2^31 (or 2^63) is already too large */
|
||||
if (e >= (int)RESTYPE_BITS - 1)
|
||||
return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */
|
||||
|
||||
/* >= 2^52 is already an exact integer */
|
||||
if (e < DBL_FRACBITS) {
|
||||
/* round, using current direction */
|
||||
x += TWO52[s];
|
||||
x -= TWO52[s];
|
||||
}
|
||||
|
||||
EXTRACT_WORDS(i0, i1, x);
|
||||
e = ((i0 >> 20) & 0x7ff) - DBL_EXP_BIAS;
|
||||
i0 &= 0xfffff;
|
||||
i0 |= (1 << 20);
|
||||
|
||||
shift = e - DBL_FRACBITS;
|
||||
if (shift >=0)
|
||||
res = (shift < 32 ? (RESTYPE)i1 << shift : 0);
|
||||
else
|
||||
res = (shift > -32 ? i1 >> -shift : 0);
|
||||
shift += 32;
|
||||
if (shift >=0)
|
||||
res |= (shift < 32 ? (RESTYPE)i0 << shift : 0);
|
||||
else
|
||||
res |= (shift > -32 ? i0 >> -shift : 0);
|
||||
|
||||
return (s ? -res : res);
|
||||
}
|
||||
@@ -0,0 +1,91 @@
|
||||
/* $NetBSD: lrintf.c,v 1.5 2008/04/26 23:49:50 christos Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 2004
|
||||
* Matthias Drochner. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <math.h>
|
||||
#include <sys/ieee754.h>
|
||||
#include <machine/limits.h>
|
||||
#include "math_private.h"
|
||||
|
||||
#ifndef LRINTNAME
|
||||
#define LRINTNAME lrintf
|
||||
#define RESTYPE long int
|
||||
#define RESTYPE_MIN LONG_MIN
|
||||
#define RESTYPE_MAX LONG_MAX
|
||||
#endif
|
||||
|
||||
#define RESTYPE_BITS (sizeof(RESTYPE) * 8)
|
||||
|
||||
static const float
|
||||
TWO23[2]={
|
||||
8.3886080000e+06, /* 0x4b000000 */
|
||||
-8.3886080000e+06, /* 0xcb000000 */
|
||||
};
|
||||
|
||||
RESTYPE
|
||||
LRINTNAME(float x)
|
||||
{
|
||||
u_int32_t i0;
|
||||
int e, s, shift;
|
||||
RESTYPE res;
|
||||
#ifdef __i386__ /* XXX gcc4 will omit the rounding otherwise */
|
||||
volatile
|
||||
#endif
|
||||
float w;
|
||||
|
||||
GET_FLOAT_WORD(i0, x);
|
||||
e = i0 >> SNG_FRACBITS;
|
||||
s = (uint32_t)e >> SNG_EXPBITS;
|
||||
e = (e & 0xff) - SNG_EXP_BIAS;
|
||||
|
||||
/* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */
|
||||
if (e < -1)
|
||||
return (0);
|
||||
/* 1.0 x 2^31 (or 2^63) is already too large */
|
||||
if (e >= (int)RESTYPE_BITS - 1)
|
||||
return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */
|
||||
|
||||
/* >= 2^23 is already an exact integer */
|
||||
if (e < SNG_FRACBITS) {
|
||||
/* round, using current direction */
|
||||
w = TWO23[s] + x;
|
||||
x = w - TWO23[s];
|
||||
}
|
||||
|
||||
GET_FLOAT_WORD(i0, x);
|
||||
e = ((i0 >> SNG_FRACBITS) & 0xff) - SNG_EXP_BIAS;
|
||||
i0 &= 0x7fffff;
|
||||
i0 |= (1 << SNG_FRACBITS);
|
||||
|
||||
shift = e - SNG_FRACBITS;
|
||||
if (shift >=0)
|
||||
res = (shift < 32 ? (RESTYPE)i0 << shift : 0);
|
||||
else
|
||||
res = (shift > -32 ? i0 >> -shift : 0);
|
||||
|
||||
return (s ? -res : res);
|
||||
}
|
||||
@@ -0,0 +1,85 @@
|
||||
/* $NetBSD: lround.c,v 1.3 2008/04/26 23:49:50 christos Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 2004
|
||||
* Matthias Drochner. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <math.h>
|
||||
#include <sys/ieee754.h>
|
||||
#include <machine/limits.h>
|
||||
#include "math_private.h"
|
||||
|
||||
#ifndef LROUNDNAME
|
||||
#define LROUNDNAME lround
|
||||
#define RESTYPE long int
|
||||
#define RESTYPE_MIN LONG_MIN
|
||||
#define RESTYPE_MAX LONG_MAX
|
||||
#endif
|
||||
|
||||
#define RESTYPE_BITS (sizeof(RESTYPE) * 8)
|
||||
|
||||
RESTYPE
|
||||
LROUNDNAME(double x)
|
||||
{
|
||||
u_int32_t i0, i1;
|
||||
int e, s, shift;
|
||||
RESTYPE res;
|
||||
|
||||
GET_HIGH_WORD(i0, x);
|
||||
e = i0 >> 20;
|
||||
s = (uint32_t)e >> DBL_EXPBITS;
|
||||
e = (e & 0x7ff) - DBL_EXP_BIAS;
|
||||
|
||||
/* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */
|
||||
if (e < -1)
|
||||
return (0);
|
||||
/* 1.0 x 2^31 (or 2^63) is already too large */
|
||||
if (e >= (int)RESTYPE_BITS - 1)
|
||||
return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */
|
||||
|
||||
/* >= 2^52 is already an exact integer */
|
||||
if (e < DBL_FRACBITS) {
|
||||
/* add 0.5, extraction below will truncate */
|
||||
x += (s ? -0.5 : 0.5);
|
||||
}
|
||||
|
||||
EXTRACT_WORDS(i0, i1, x);
|
||||
e = ((i0 >> 20) & 0x7ff) - DBL_EXP_BIAS;
|
||||
i0 &= 0xfffff;
|
||||
i0 |= (1 << 20);
|
||||
|
||||
shift = e - DBL_FRACBITS;
|
||||
if (shift >=0)
|
||||
res = (shift < 32 ? (RESTYPE)i1 << shift : 0);
|
||||
else
|
||||
res = (shift > -32 ? i1 >> -shift : 0);
|
||||
shift += 32;
|
||||
if (shift >=0)
|
||||
res |= (shift < 32 ? (RESTYPE)i0 << shift : 0);
|
||||
else
|
||||
res |= (shift > -32 ? i0 >> -shift : 0);
|
||||
|
||||
return (s ? -res : res);
|
||||
}
|
||||
@@ -0,0 +1,80 @@
|
||||
/* $NetBSD: lroundf.c,v 1.3 2008/04/26 23:49:50 christos Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 2004
|
||||
* Matthias Drochner. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <math.h>
|
||||
#include <sys/ieee754.h>
|
||||
#include <machine/limits.h>
|
||||
#include "math_private.h"
|
||||
|
||||
#ifndef LROUNDNAME
|
||||
#define LROUNDNAME lroundf
|
||||
#define RESTYPE long int
|
||||
#define RESTYPE_MIN LONG_MIN
|
||||
#define RESTYPE_MAX LONG_MAX
|
||||
#endif
|
||||
|
||||
#define RESTYPE_BITS (sizeof(RESTYPE) * 8)
|
||||
|
||||
RESTYPE
|
||||
LROUNDNAME(float x)
|
||||
{
|
||||
u_int32_t i0;
|
||||
int e, s, shift;
|
||||
RESTYPE res;
|
||||
|
||||
GET_FLOAT_WORD(i0, x);
|
||||
e = i0 >> SNG_FRACBITS;
|
||||
s = (uint32_t)e >> SNG_EXPBITS;
|
||||
e = (e & 0xff) - SNG_EXP_BIAS;
|
||||
|
||||
/* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */
|
||||
if (e < -1)
|
||||
return (0);
|
||||
/* 1.0 x 2^31 (or 2^63) is already too large */
|
||||
if (e >= (int)RESTYPE_BITS - 1)
|
||||
return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */
|
||||
|
||||
/* >= 2^23 is already an exact integer */
|
||||
if (e < SNG_FRACBITS) {
|
||||
/* add 0.5, extraction below will truncate */
|
||||
x += (s ? -0.5 : 0.5);
|
||||
}
|
||||
|
||||
GET_FLOAT_WORD(i0, x);
|
||||
e = ((i0 >> SNG_FRACBITS) & 0xff) - SNG_EXP_BIAS;
|
||||
i0 &= 0x7fffff;
|
||||
i0 |= (1 << SNG_FRACBITS);
|
||||
|
||||
shift = e - SNG_FRACBITS;
|
||||
if (shift >=0)
|
||||
res = (shift < 32 ? (RESTYPE)i0 << shift : 0);
|
||||
else
|
||||
res = (shift > -32 ? i0 >> -shift : 0);
|
||||
|
||||
return (s ? -res : res);
|
||||
}
|
||||
@@ -0,0 +1,278 @@
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* from: @(#)fdlibm.h 5.1 93/09/24
|
||||
* $NetBSD: math_private.h,v 1.16 2010/09/16 20:39:50 drochner Exp $
|
||||
*/
|
||||
|
||||
#ifndef _MATH_PRIVATE_H_
|
||||
#define _MATH_PRIVATE_H_
|
||||
|
||||
#include <sys/types.h>
|
||||
|
||||
/* The original fdlibm code used statements like:
|
||||
n0 = ((*(int*)&one)>>29)^1; * index of high word *
|
||||
ix0 = *(n0+(int*)&x); * high word of x *
|
||||
ix1 = *((1-n0)+(int*)&x); * low word of x *
|
||||
to dig two 32 bit words out of the 64 bit IEEE floating point
|
||||
value. That is non-ANSI, and, moreover, the gcc instruction
|
||||
scheduler gets it wrong. We instead use the following macros.
|
||||
Unlike the original code, we determine the endianness at compile
|
||||
time, not at run time; I don't see much benefit to selecting
|
||||
endianness at run time. */
|
||||
|
||||
/* A union which permits us to convert between a double and two 32 bit
|
||||
ints. */
|
||||
|
||||
/*
|
||||
* The ARM ports are little endian except for the FPA word order which is
|
||||
* big endian.
|
||||
*/
|
||||
|
||||
#if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__))
|
||||
|
||||
typedef union
|
||||
{
|
||||
double value;
|
||||
struct
|
||||
{
|
||||
u_int32_t msw;
|
||||
u_int32_t lsw;
|
||||
} parts;
|
||||
} ieee_double_shape_type;
|
||||
|
||||
#endif
|
||||
|
||||
#if (BYTE_ORDER == LITTLE_ENDIAN) && \
|
||||
!(defined(__arm__) && !defined(__VFP_FP__))
|
||||
|
||||
typedef union
|
||||
{
|
||||
double value;
|
||||
struct
|
||||
{
|
||||
u_int32_t lsw;
|
||||
u_int32_t msw;
|
||||
} parts;
|
||||
} ieee_double_shape_type;
|
||||
|
||||
#endif
|
||||
|
||||
/* Get two 32 bit ints from a double. */
|
||||
|
||||
#define EXTRACT_WORDS(ix0,ix1,d) \
|
||||
do { \
|
||||
ieee_double_shape_type ew_u; \
|
||||
ew_u.value = (d); \
|
||||
(ix0) = ew_u.parts.msw; \
|
||||
(ix1) = ew_u.parts.lsw; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* Get the more significant 32 bit int from a double. */
|
||||
|
||||
#define GET_HIGH_WORD(i,d) \
|
||||
do { \
|
||||
ieee_double_shape_type gh_u; \
|
||||
gh_u.value = (d); \
|
||||
(i) = gh_u.parts.msw; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* Get the less significant 32 bit int from a double. */
|
||||
|
||||
#define GET_LOW_WORD(i,d) \
|
||||
do { \
|
||||
ieee_double_shape_type gl_u; \
|
||||
gl_u.value = (d); \
|
||||
(i) = gl_u.parts.lsw; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* Set a double from two 32 bit ints. */
|
||||
|
||||
#define INSERT_WORDS(d,ix0,ix1) \
|
||||
do { \
|
||||
ieee_double_shape_type iw_u; \
|
||||
iw_u.parts.msw = (ix0); \
|
||||
iw_u.parts.lsw = (ix1); \
|
||||
(d) = iw_u.value; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* Set the more significant 32 bits of a double from an int. */
|
||||
|
||||
#define SET_HIGH_WORD(d,v) \
|
||||
do { \
|
||||
ieee_double_shape_type sh_u; \
|
||||
sh_u.value = (d); \
|
||||
sh_u.parts.msw = (v); \
|
||||
(d) = sh_u.value; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* Set the less significant 32 bits of a double from an int. */
|
||||
|
||||
#define SET_LOW_WORD(d,v) \
|
||||
do { \
|
||||
ieee_double_shape_type sl_u; \
|
||||
sl_u.value = (d); \
|
||||
sl_u.parts.lsw = (v); \
|
||||
(d) = sl_u.value; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* A union which permits us to convert between a float and a 32 bit
|
||||
int. */
|
||||
|
||||
typedef union
|
||||
{
|
||||
float value;
|
||||
u_int32_t word;
|
||||
} ieee_float_shape_type;
|
||||
|
||||
/* Get a 32 bit int from a float. */
|
||||
|
||||
#define GET_FLOAT_WORD(i,d) \
|
||||
do { \
|
||||
ieee_float_shape_type gf_u; \
|
||||
gf_u.value = (d); \
|
||||
(i) = gf_u.word; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/* Set a float from a 32 bit int. */
|
||||
|
||||
#define SET_FLOAT_WORD(d,i) \
|
||||
do { \
|
||||
ieee_float_shape_type sf_u; \
|
||||
sf_u.word = (i); \
|
||||
(d) = sf_u.value; \
|
||||
} while (/*CONSTCOND*/0)
|
||||
|
||||
/*
|
||||
* Attempt to get strict C99 semantics for assignment with non-C99 compilers.
|
||||
*/
|
||||
#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
|
||||
#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
|
||||
#else
|
||||
#define STRICT_ASSIGN(type, lval, rval) do { \
|
||||
volatile type __lval; \
|
||||
\
|
||||
if (sizeof(type) >= sizeof(double)) \
|
||||
(lval) = (rval); \
|
||||
else { \
|
||||
__lval = (rval); \
|
||||
(lval) = __lval; \
|
||||
} \
|
||||
} while (/*CONSTCOND*/0)
|
||||
#endif
|
||||
|
||||
#ifdef _COMPLEX_H
|
||||
|
||||
/*
|
||||
* Quoting from ISO/IEC 9899:TC2:
|
||||
*
|
||||
* 6.2.5.13 Types
|
||||
* Each complex type has the same representation and alignment requirements as
|
||||
* an array type containing exactly two elements of the corresponding real type;
|
||||
* the first element is equal to the real part, and the second element to the
|
||||
* imaginary part, of the complex number.
|
||||
*/
|
||||
typedef union {
|
||||
float complex z;
|
||||
float parts[2];
|
||||
} float_complex;
|
||||
|
||||
typedef union {
|
||||
double complex z;
|
||||
double parts[2];
|
||||
} double_complex;
|
||||
|
||||
typedef union {
|
||||
long double complex z;
|
||||
long double parts[2];
|
||||
} long_double_complex;
|
||||
|
||||
#define REAL_PART(z) ((z).parts[0])
|
||||
#define IMAG_PART(z) ((z).parts[1])
|
||||
|
||||
#endif /* _COMPLEX_H */
|
||||
|
||||
/* ieee style elementary functions */
|
||||
extern double __ieee754_sqrt __P((double));
|
||||
extern double __ieee754_acos __P((double));
|
||||
extern double __ieee754_acosh __P((double));
|
||||
extern double __ieee754_log __P((double));
|
||||
extern double __ieee754_atanh __P((double));
|
||||
extern double __ieee754_asin __P((double));
|
||||
extern double __ieee754_atan2 __P((double,double));
|
||||
extern double __ieee754_exp __P((double));
|
||||
extern double __ieee754_cosh __P((double));
|
||||
extern double __ieee754_fmod __P((double,double));
|
||||
extern double __ieee754_pow __P((double,double));
|
||||
extern double __ieee754_lgamma_r __P((double,int *));
|
||||
extern double __ieee754_gamma_r __P((double,int *));
|
||||
extern double __ieee754_lgamma __P((double));
|
||||
extern double __ieee754_gamma __P((double));
|
||||
extern double __ieee754_log10 __P((double));
|
||||
extern double __ieee754_log2 __P((double));
|
||||
extern double __ieee754_sinh __P((double));
|
||||
extern double __ieee754_hypot __P((double,double));
|
||||
extern double __ieee754_j0 __P((double));
|
||||
extern double __ieee754_j1 __P((double));
|
||||
extern double __ieee754_y0 __P((double));
|
||||
extern double __ieee754_y1 __P((double));
|
||||
extern double __ieee754_jn __P((int,double));
|
||||
extern double __ieee754_yn __P((int,double));
|
||||
extern double __ieee754_remainder __P((double,double));
|
||||
extern int __ieee754_rem_pio2 __P((double,double*));
|
||||
extern double __ieee754_scalb __P((double,double));
|
||||
|
||||
/* fdlibm kernel function */
|
||||
extern double __kernel_standard __P((double,double,int));
|
||||
extern double __kernel_sin __P((double,double,int));
|
||||
extern double __kernel_cos __P((double,double));
|
||||
extern double __kernel_tan __P((double,double,int));
|
||||
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));
|
||||
|
||||
|
||||
/* ieee style elementary float functions */
|
||||
extern float __ieee754_sqrtf __P((float));
|
||||
extern float __ieee754_acosf __P((float));
|
||||
extern float __ieee754_acoshf __P((float));
|
||||
extern float __ieee754_logf __P((float));
|
||||
extern float __ieee754_atanhf __P((float));
|
||||
extern float __ieee754_asinf __P((float));
|
||||
extern float __ieee754_atan2f __P((float,float));
|
||||
extern float __ieee754_expf __P((float));
|
||||
extern float __ieee754_coshf __P((float));
|
||||
extern float __ieee754_fmodf __P((float,float));
|
||||
extern float __ieee754_powf __P((float,float));
|
||||
extern float __ieee754_lgammaf_r __P((float,int *));
|
||||
extern float __ieee754_gammaf_r __P((float,int *));
|
||||
extern float __ieee754_lgammaf __P((float));
|
||||
extern float __ieee754_gammaf __P((float));
|
||||
extern float __ieee754_log10f __P((float));
|
||||
extern float __ieee754_log2f __P((float));
|
||||
extern float __ieee754_sinhf __P((float));
|
||||
extern float __ieee754_hypotf __P((float,float));
|
||||
extern float __ieee754_j0f __P((float));
|
||||
extern float __ieee754_j1f __P((float));
|
||||
extern float __ieee754_y0f __P((float));
|
||||
extern float __ieee754_y1f __P((float));
|
||||
extern float __ieee754_jnf __P((int,float));
|
||||
extern float __ieee754_ynf __P((int,float));
|
||||
extern float __ieee754_remainderf __P((float,float));
|
||||
extern int __ieee754_rem_pio2f __P((float,float*));
|
||||
extern float __ieee754_scalbf __P((float,float));
|
||||
|
||||
/* float versions of fdlibm kernel functions */
|
||||
extern float __kernel_sinf __P((float,float,int));
|
||||
extern float __kernel_cosf __P((float,float));
|
||||
extern float __kernel_tanf __P((float,float,int));
|
||||
extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*));
|
||||
|
||||
#endif /* _MATH_PRIVATE_H_ */
|
||||
@@ -0,0 +1,34 @@
|
||||
/* $NetBSD: namespace.h,v 1.3 2010/04/23 19:17:07 drochner Exp $ */
|
||||
|
||||
#define atan2 _atan2
|
||||
#define atan2f _atan2f
|
||||
#define hypot _hypot
|
||||
#define hypotf _hypotf
|
||||
|
||||
#define exp _exp
|
||||
#define expf _expf
|
||||
#define log _log
|
||||
#define logf _logf
|
||||
|
||||
#if 0 /* not yet - need to review use in machdep code first */
|
||||
#define sin _sin
|
||||
#define sinf _sinf
|
||||
#define cos _cos
|
||||
#define cosf _cosf
|
||||
#define finite _finite
|
||||
#define finitef _finitef
|
||||
#endif /* notyet */
|
||||
#define sinh _sinh
|
||||
#define sinhf _sinhf
|
||||
#define cosh _cosh
|
||||
#define coshf _coshf
|
||||
#define asin _asin
|
||||
#define asinf _asinf
|
||||
|
||||
#define casin _casin
|
||||
#define casinf _casinf
|
||||
#define catan _catan
|
||||
#define catanf _catanf
|
||||
|
||||
#define scalbn _scalbn
|
||||
#define scalbnf _scalbnf
|
||||
@@ -0,0 +1,58 @@
|
||||
/* @(#)s_asinh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_asinh.c,v 1.12 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* asinh(x)
|
||||
* Method :
|
||||
* Based on
|
||||
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
|
||||
* we have
|
||||
* asinh(x) := x if 1+x*x=1,
|
||||
* := sign(x)*(log(x)+ln2)) for large |x|, else
|
||||
* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
|
||||
* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
huge= 1.00000000000000000000e+300;
|
||||
|
||||
double
|
||||
asinh(double x)
|
||||
{
|
||||
double t,w;
|
||||
int32_t hx,ix;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
|
||||
if(ix< 0x3e300000) { /* |x|<2**-28 */
|
||||
if(huge+x>one) return x; /* return x inexact except 0 */
|
||||
}
|
||||
if(ix>0x41b00000) { /* |x| > 2**28 */
|
||||
w = __ieee754_log(fabs(x))+ln2;
|
||||
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
|
||||
t = fabs(x);
|
||||
w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
|
||||
} else { /* 2.0 > |x| > 2**-28 */
|
||||
t = x*x;
|
||||
w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
|
||||
}
|
||||
if(hx>0) return w; else return -w;
|
||||
}
|
||||
@@ -0,0 +1,50 @@
|
||||
/* s_asinhf.c -- float version of s_asinh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_asinhf.c,v 1.8 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
ln2 = 6.9314718246e-01, /* 0x3f317218 */
|
||||
huge= 1.0000000000e+30;
|
||||
|
||||
float
|
||||
asinhf(float x)
|
||||
{
|
||||
float t,w;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return x+x; /* x is inf or NaN */
|
||||
if(ix< 0x31800000) { /* |x|<2**-28 */
|
||||
if(huge+x>one) return x; /* return x inexact except 0 */
|
||||
}
|
||||
if(ix>0x4d800000) { /* |x| > 2**28 */
|
||||
w = __ieee754_logf(fabsf(x))+ln2;
|
||||
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
|
||||
t = fabsf(x);
|
||||
w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t));
|
||||
} else { /* 2.0 > |x| > 2**-28 */
|
||||
t = x*x;
|
||||
w =log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t)));
|
||||
}
|
||||
if(hx>0) return w; else return -w;
|
||||
}
|
||||
@@ -0,0 +1,120 @@
|
||||
/* @(#)s_atan.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* atan(x)
|
||||
* Method
|
||||
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
||||
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
||||
* is further reduced to one of the following intervals and the
|
||||
* arctangent of t is evaluated by the corresponding formula:
|
||||
*
|
||||
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
||||
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
||||
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
||||
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
||||
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double atanhi[] = {
|
||||
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||||
};
|
||||
|
||||
static const double atanlo[] = {
|
||||
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||||
};
|
||||
|
||||
static const double aT[] = {
|
||||
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
||||
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
||||
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
||||
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
||||
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
||||
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
||||
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
||||
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
||||
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
||||
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
||||
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
||||
};
|
||||
|
||||
static const double
|
||||
one = 1.0,
|
||||
huge = 1.0e300;
|
||||
|
||||
double
|
||||
atan(double x)
|
||||
{
|
||||
double w,s1,s2,z;
|
||||
int32_t ix,hx,id;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x44100000) { /* if |x| >= 2^66 */
|
||||
u_int32_t low;
|
||||
GET_LOW_WORD(low,x);
|
||||
if(ix>0x7ff00000||
|
||||
(ix==0x7ff00000&&(low!=0)))
|
||||
return x+x; /* NaN */
|
||||
if(hx>0) return atanhi[3]+atanlo[3];
|
||||
else return -atanhi[3]-atanlo[3];
|
||||
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
|
||||
if (ix < 0x3e200000) { /* |x| < 2^-29 */
|
||||
if(huge+x>one) return x; /* raise inexact */
|
||||
}
|
||||
id = -1;
|
||||
} else {
|
||||
x = fabs(x);
|
||||
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
|
||||
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
|
||||
id = 0; x = (2.0*x-one)/(2.0+x);
|
||||
} else { /* 11/16<=|x|< 19/16 */
|
||||
id = 1; x = (x-one)/(x+one);
|
||||
}
|
||||
} else {
|
||||
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
||||
id = 2; x = (x-1.5)/(one+1.5*x);
|
||||
} else { /* 2.4375 <= |x| < 2^66 */
|
||||
id = 3; x = -1.0/x;
|
||||
}
|
||||
}}
|
||||
/* end of argument reduction */
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
||||
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||||
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||||
if (id<0) return x - x*(s1+s2);
|
||||
else {
|
||||
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
||||
return (hx<0)? -z:z;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,100 @@
|
||||
/* s_atanf.c -- float version of s_atan.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float atanhi[] = {
|
||||
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
|
||||
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
|
||||
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
|
||||
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
|
||||
};
|
||||
|
||||
static const float atanlo[] = {
|
||||
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
|
||||
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
|
||||
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
|
||||
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
|
||||
};
|
||||
|
||||
static const float aT[] = {
|
||||
3.3333334327e-01, /* 0x3eaaaaaa */
|
||||
-2.0000000298e-01, /* 0xbe4ccccd */
|
||||
1.4285714924e-01, /* 0x3e124925 */
|
||||
-1.1111110449e-01, /* 0xbde38e38 */
|
||||
9.0908870101e-02, /* 0x3dba2e6e */
|
||||
-7.6918758452e-02, /* 0xbd9d8795 */
|
||||
6.6610731184e-02, /* 0x3d886b35 */
|
||||
-5.8335702866e-02, /* 0xbd6ef16b */
|
||||
4.9768779427e-02, /* 0x3d4bda59 */
|
||||
-3.6531571299e-02, /* 0xbd15a221 */
|
||||
1.6285819933e-02, /* 0x3c8569d7 */
|
||||
};
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
huge = 1.0e30;
|
||||
|
||||
float
|
||||
atanf(float x)
|
||||
{
|
||||
float w,s1,s2,z;
|
||||
int32_t ix,hx,id;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x50800000) { /* if |x| >= 2^34 */
|
||||
if(ix>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx>0) return atanhi[3]+atanlo[3];
|
||||
else return -atanhi[3]-atanlo[3];
|
||||
} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
|
||||
if (ix < 0x31000000) { /* |x| < 2^-29 */
|
||||
if(huge+x>one) return x; /* raise inexact */
|
||||
}
|
||||
id = -1;
|
||||
} else {
|
||||
x = fabsf(x);
|
||||
if (ix < 0x3f980000) { /* |x| < 1.1875 */
|
||||
if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
|
||||
id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
|
||||
} else { /* 11/16<=|x|< 19/16 */
|
||||
id = 1; x = (x-one)/(x+one);
|
||||
}
|
||||
} else {
|
||||
if (ix < 0x401c0000) { /* |x| < 2.4375 */
|
||||
id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
|
||||
} else { /* 2.4375 <= |x| < 2^66 */
|
||||
id = 3; x = -(float)1.0/x;
|
||||
}
|
||||
}}
|
||||
/* end of argument reduction */
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
||||
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||||
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||||
if (id<0) return x - x*(s1+s2);
|
||||
else {
|
||||
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
||||
return (hx<0)? -z:z;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,82 @@
|
||||
/* @(#)s_cbrt.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_cbrt.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* cbrt(x)
|
||||
* Return cube root of x
|
||||
*/
|
||||
static const u_int32_t
|
||||
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
|
||||
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
|
||||
|
||||
static const double
|
||||
C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
|
||||
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
|
||||
E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
|
||||
F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
|
||||
G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
|
||||
|
||||
double
|
||||
cbrt(double x)
|
||||
{
|
||||
int32_t hx;
|
||||
double r,s,t=0.0,w;
|
||||
u_int32_t sign;
|
||||
u_int32_t high,low;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
sign=hx&0x80000000; /* sign= sign(x) */
|
||||
hx ^=sign;
|
||||
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
|
||||
GET_LOW_WORD(low,x);
|
||||
if((hx|low)==0)
|
||||
return(x); /* cbrt(0) is itself */
|
||||
|
||||
SET_HIGH_WORD(x,hx); /* x <- |x| */
|
||||
/* rough cbrt to 5 bits */
|
||||
if(hx<0x00100000) /* subnormal number */
|
||||
{SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
|
||||
t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
|
||||
}
|
||||
else
|
||||
SET_HIGH_WORD(t,hx/3+B1);
|
||||
|
||||
|
||||
/* new cbrt to 23 bits, may be implemented in single precision */
|
||||
r=t*t/x;
|
||||
s=C+r*t;
|
||||
t*=G+F/(s+E+D/s);
|
||||
|
||||
/* chopped to 20 bits and make it larger than cbrt(x) */
|
||||
GET_HIGH_WORD(high,t);
|
||||
INSERT_WORDS(t,high+0x00000001,0);
|
||||
|
||||
|
||||
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
|
||||
s=t*t; /* t*t is exact */
|
||||
r=x/s;
|
||||
w=t+t;
|
||||
r=(r-t)/(w+r); /* r-s is exact */
|
||||
t=t+t*r;
|
||||
|
||||
/* retore the sign bit */
|
||||
GET_HIGH_WORD(high,t);
|
||||
SET_HIGH_WORD(t,high|sign);
|
||||
return(t);
|
||||
}
|
||||
@@ -0,0 +1,72 @@
|
||||
/* s_cbrtf.c -- float version of s_cbrt.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_cbrtf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* cbrtf(x)
|
||||
* Return cube root of x
|
||||
*/
|
||||
static const unsigned
|
||||
B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
|
||||
B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
|
||||
|
||||
static const float
|
||||
C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
|
||||
D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
|
||||
E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
|
||||
F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
|
||||
G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
|
||||
|
||||
float
|
||||
cbrtf(float x)
|
||||
{
|
||||
float r,s,t;
|
||||
int32_t hx;
|
||||
u_int32_t sign;
|
||||
u_int32_t high;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
sign=hx&0x80000000; /* sign= sign(x) */
|
||||
hx ^=sign;
|
||||
if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
|
||||
if(hx==0)
|
||||
return(x); /* cbrt(0) is itself */
|
||||
|
||||
SET_FLOAT_WORD(x,hx); /* x <- |x| */
|
||||
/* rough cbrt to 5 bits */
|
||||
if(hx<0x00800000) /* subnormal number */
|
||||
{SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
|
||||
t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
|
||||
}
|
||||
else
|
||||
SET_FLOAT_WORD(t,hx/3+B1);
|
||||
|
||||
|
||||
/* new cbrt to 23 bits */
|
||||
r=t*t/x;
|
||||
s=C+r*t;
|
||||
t*=G+F/(s+E+D/s);
|
||||
|
||||
/* retore the sign bit */
|
||||
GET_FLOAT_WORD(high,t);
|
||||
SET_FLOAT_WORD(t,high|sign);
|
||||
return(t);
|
||||
}
|
||||
@@ -0,0 +1,73 @@
|
||||
/* @(#)s_ceil.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_ceil.c,v 1.13 2009/02/16 01:22:18 lukem Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* ceil(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to ceil(x).
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double huge = 1.0e300;
|
||||
|
||||
double
|
||||
ceil(double x)
|
||||
{
|
||||
int32_t i0,i1,jj0;
|
||||
u_int32_t i,j;
|
||||
EXTRACT_WORDS(i0,i1,x);
|
||||
jj0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(jj0<20) {
|
||||
if(jj0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0<0) {i0=0x80000000;i1=0;}
|
||||
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
|
||||
}
|
||||
} else {
|
||||
i = (0x000fffff)>>jj0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0>0) i0 += (0x00100000)>>jj0;
|
||||
i0 &= (~i); i1=0;
|
||||
}
|
||||
}
|
||||
} else if (jj0>51) {
|
||||
if(jj0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((u_int32_t)(0xffffffff))>>(jj0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0>0) {
|
||||
if(jj0==20) i0+=1;
|
||||
else {
|
||||
j = i1 + (1<<(52-jj0));
|
||||
if(j<(u_int32_t)i1) i0+=1; /* got a carry */
|
||||
i1 = j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
INSERT_WORDS(x,i0,i1);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,54 @@
|
||||
/* s_ceilf.c -- float version of s_ceil.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_ceilf.c,v 1.8 2008/04/25 22:21:53 christos Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e30;
|
||||
|
||||
float
|
||||
ceilf(float x)
|
||||
{
|
||||
int32_t i0,jj0;
|
||||
u_int32_t i;
|
||||
|
||||
GET_FLOAT_WORD(i0,x);
|
||||
jj0 = ((i0>>23)&0xff)-0x7f;
|
||||
if(jj0<23) {
|
||||
if(jj0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0<0) {i0=0x80000000;}
|
||||
else if(i0!=0) { i0=0x3f800000;}
|
||||
}
|
||||
} else {
|
||||
i = (0x007fffff)>>jj0;
|
||||
if((i0&i)==0) return x; /* x is integral */
|
||||
if(huge+x>(float)0.0) { /* raise inexact flag */
|
||||
if(i0>0) i0 += (0x00800000)>>jj0;
|
||||
i0 &= (~i);
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if(jj0==0x80) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
}
|
||||
SET_FLOAT_WORD(x,i0);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,35 @@
|
||||
/* @(#)s_copysign.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_copysign.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* copysign(double x, double y)
|
||||
* copysign(x,y) returns a value with the magnitude of x and
|
||||
* with the sign bit of y.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
double
|
||||
copysign(double x, double y)
|
||||
{
|
||||
u_int32_t hx,hy;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
GET_HIGH_WORD(hy,y);
|
||||
SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000));
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,38 @@
|
||||
/* s_copysignf.c -- float version of s_copysign.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_copysignf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* copysignf(float x, float y)
|
||||
* copysignf(x,y) returns a value with the magnitude of x and
|
||||
* with the sign bit of y.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
copysignf(float x, float y)
|
||||
{
|
||||
u_int32_t ix,iy;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
GET_FLOAT_WORD(iy,y);
|
||||
SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000));
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,51 @@
|
||||
/* $NetBSD: s_copysignl.c,v 1.2 2010/09/17 20:39:39 christos Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 2010 The NetBSD Foundation, Inc.
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
|
||||
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
||||
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
|
||||
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
* POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_copysignl.c,v 1.2 2010/09/17 20:39:39 christos Exp $");
|
||||
|
||||
#include <math.h>
|
||||
#include <machine/ieee.h>
|
||||
|
||||
/*
|
||||
* copysignl(long double x, long double y)
|
||||
* This function returns a value with the magnitude of x and the sign of y.
|
||||
*/
|
||||
#ifdef EXT_EXP_INFNAN
|
||||
long double
|
||||
copysignl(long double x, long double y)
|
||||
{
|
||||
union ieee_ext_u ux, uy;
|
||||
|
||||
ux.extu_ld = x;
|
||||
uy.extu_ld = y;
|
||||
|
||||
ux.extu_ext.ext_sign = uy.extu_ext.ext_sign;
|
||||
|
||||
return (ux.extu_ld);
|
||||
}
|
||||
#endif
|
||||
@@ -0,0 +1,86 @@
|
||||
/* @(#)s_cos.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_cos.c,v 1.11 2007/08/20 16:01:39 drochner Exp $");
|
||||
#endif
|
||||
|
||||
/* cos(x)
|
||||
* Return cosine function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_sin ... sine function on [-pi/4,pi/4]
|
||||
* __kernel_cos ... cosine function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#if 0 /* notyet */
|
||||
#ifdef __weak_alias
|
||||
__weak_alias(cos, _cos)
|
||||
#endif
|
||||
#endif
|
||||
|
||||
double
|
||||
cos(double x)
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int32_t n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
GET_HIGH_WORD(ix,x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
|
||||
|
||||
/* cos(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_cos(y[0],y[1]);
|
||||
case 1: return -__kernel_sin(y[0],y[1],1);
|
||||
case 2: return -__kernel_cos(y[0],y[1]);
|
||||
default:
|
||||
return __kernel_sin(y[0],y[1],1);
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,61 @@
|
||||
/* s_cosf.c -- float version of s_cos.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_cosf.c,v 1.9 2007/08/20 16:01:39 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "namespace.h"
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#if 0 /* notyet */
|
||||
#ifdef __weak_alias
|
||||
__weak_alias(cosf, _cosf)
|
||||
#endif
|
||||
#endif
|
||||
|
||||
#if 0
|
||||
static const float one=1.0;
|
||||
#endif
|
||||
|
||||
float
|
||||
cosf(float x)
|
||||
{
|
||||
float y[2],z=0.0;
|
||||
int32_t n,ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
|
||||
|
||||
/* cos(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7f800000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2f(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_cosf(y[0],y[1]);
|
||||
case 1: return -__kernel_sinf(y[0],y[1],1);
|
||||
case 2: return -__kernel_cosf(y[0],y[1]);
|
||||
default:
|
||||
return __kernel_sinf(y[0],y[1],1);
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,303 @@
|
||||
/* @(#)s_erf.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_erf.c,v 1.11 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* double erf(double x)
|
||||
* double erfc(double x)
|
||||
* x
|
||||
* 2 |\
|
||||
* erf(x) = --------- | exp(-t*t)dt
|
||||
* sqrt(pi) \|
|
||||
* 0
|
||||
*
|
||||
* erfc(x) = 1-erf(x)
|
||||
* Note that
|
||||
* erf(-x) = -erf(x)
|
||||
* erfc(-x) = 2 - erfc(x)
|
||||
*
|
||||
* Method:
|
||||
* 1. For |x| in [0, 0.84375]
|
||||
* erf(x) = x + x*R(x^2)
|
||||
* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
|
||||
* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
|
||||
* where R = P/Q where P is an odd poly of degree 8 and
|
||||
* Q is an odd poly of degree 10.
|
||||
* -57.90
|
||||
* | R - (erf(x)-x)/x | <= 2
|
||||
*
|
||||
*
|
||||
* Remark. The formula is derived by noting
|
||||
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
|
||||
* and that
|
||||
* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
|
||||
* is close to one. The interval is chosen because the fix
|
||||
* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
|
||||
* near 0.6174), and by some experiment, 0.84375 is chosen to
|
||||
* guarantee the error is less than one ulp for erf.
|
||||
*
|
||||
* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
|
||||
* c = 0.84506291151 rounded to single (24 bits)
|
||||
* erf(x) = sign(x) * (c + P1(s)/Q1(s))
|
||||
* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
|
||||
* 1+(c+P1(s)/Q1(s)) if x < 0
|
||||
* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
|
||||
* Remark: here we use the taylor series expansion at x=1.
|
||||
* erf(1+s) = erf(1) + s*Poly(s)
|
||||
* = 0.845.. + P1(s)/Q1(s)
|
||||
* That is, we use rational approximation to approximate
|
||||
* erf(1+s) - (c = (single)0.84506291151)
|
||||
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
|
||||
* where
|
||||
* P1(s) = degree 6 poly in s
|
||||
* Q1(s) = degree 6 poly in s
|
||||
*
|
||||
* 3. For x in [1.25,1/0.35(~2.857143)],
|
||||
* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
|
||||
* erf(x) = 1 - erfc(x)
|
||||
* where
|
||||
* R1(z) = degree 7 poly in z, (z=1/x^2)
|
||||
* S1(z) = degree 8 poly in z
|
||||
*
|
||||
* 4. For x in [1/0.35,28]
|
||||
* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
|
||||
* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
|
||||
* = 2.0 - tiny (if x <= -6)
|
||||
* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
|
||||
* erf(x) = sign(x)*(1.0 - tiny)
|
||||
* where
|
||||
* R2(z) = degree 6 poly in z, (z=1/x^2)
|
||||
* S2(z) = degree 7 poly in z
|
||||
*
|
||||
* Note1:
|
||||
* To compute exp(-x*x-0.5625+R/S), let s be a single
|
||||
* precision number and s := x; then
|
||||
* -x*x = -s*s + (s-x)*(s+x)
|
||||
* exp(-x*x-0.5626+R/S) =
|
||||
* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
|
||||
* Note2:
|
||||
* Here 4 and 5 make use of the asymptotic series
|
||||
* exp(-x*x)
|
||||
* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
|
||||
* x*sqrt(pi)
|
||||
* We use rational approximation to approximate
|
||||
* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
|
||||
* Here is the error bound for R1/S1 and R2/S2
|
||||
* |R1/S1 - f(x)| < 2**(-62.57)
|
||||
* |R2/S2 - f(x)| < 2**(-61.52)
|
||||
*
|
||||
* 5. For inf > x >= 28
|
||||
* erf(x) = sign(x) *(1 - tiny) (raise inexact)
|
||||
* erfc(x) = tiny*tiny (raise underflow) if x > 0
|
||||
* = 2 - tiny if x<0
|
||||
*
|
||||
* 7. Special case:
|
||||
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
|
||||
* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
|
||||
* erfc/erf(NaN) is NaN
|
||||
*/
|
||||
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
tiny = 1e-300,
|
||||
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
|
||||
/* c = (float)0.84506291151 */
|
||||
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
|
||||
/*
|
||||
* Coefficients for approximation to erf on [0,0.84375]
|
||||
*/
|
||||
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
|
||||
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
|
||||
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
|
||||
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
|
||||
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
|
||||
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
|
||||
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
|
||||
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
|
||||
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
|
||||
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
|
||||
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
|
||||
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
|
||||
/*
|
||||
* Coefficients for approximation to erf in [0.84375,1.25]
|
||||
*/
|
||||
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
|
||||
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
|
||||
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
|
||||
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
|
||||
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
|
||||
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
|
||||
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
|
||||
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
|
||||
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
|
||||
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
|
||||
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
|
||||
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
|
||||
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1.25,1/0.35]
|
||||
*/
|
||||
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
|
||||
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
|
||||
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
|
||||
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
|
||||
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
|
||||
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
|
||||
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
|
||||
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
|
||||
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
|
||||
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
|
||||
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
|
||||
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
|
||||
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
|
||||
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
|
||||
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
|
||||
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1/.35,28]
|
||||
*/
|
||||
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
|
||||
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
|
||||
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
|
||||
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
|
||||
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
|
||||
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
|
||||
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
|
||||
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
|
||||
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
|
||||
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
|
||||
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
|
||||
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
|
||||
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
|
||||
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
|
||||
|
||||
double
|
||||
erf(double x)
|
||||
{
|
||||
int32_t hx,ix,i;
|
||||
double R,S,P,Q,s,y,z,r;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) { /* erf(nan)=nan */
|
||||
i = ((u_int32_t)hx>>31)<<1;
|
||||
return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */
|
||||
}
|
||||
|
||||
if(ix < 0x3feb0000) { /* |x|<0.84375 */
|
||||
if(ix < 0x3e300000) { /* |x|<2**-28 */
|
||||
if (ix < 0x00800000)
|
||||
return 0.125*(8.0*x+efx8*x); /*avoid underflow */
|
||||
return x + efx*x;
|
||||
}
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
return x + x*y;
|
||||
}
|
||||
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabs(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
|
||||
}
|
||||
if (ix >= 0x40180000) { /* inf>|x|>=6 */
|
||||
if(hx>=0) return one-tiny; else return tiny-one;
|
||||
}
|
||||
x = fabs(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/0.35 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
z = x;
|
||||
SET_LOW_WORD(z,0);
|
||||
r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S);
|
||||
if(hx>=0) return one-r/x; else return r/x-one;
|
||||
}
|
||||
|
||||
double
|
||||
erfc(double x)
|
||||
{
|
||||
int32_t hx,ix;
|
||||
double R,S,P,Q,s,y,z,r;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) { /* erfc(nan)=nan */
|
||||
/* erfc(+-inf)=0,2 */
|
||||
return (double)(((u_int32_t)hx>>31)<<1)+one/x;
|
||||
}
|
||||
|
||||
if(ix < 0x3feb0000) { /* |x|<0.84375 */
|
||||
if(ix < 0x3c700000) /* |x|<2**-56 */
|
||||
return one-x;
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
if(hx < 0x3fd00000) { /* x<1/4 */
|
||||
return one-(x+x*y);
|
||||
} else {
|
||||
r = x*y;
|
||||
r += (x-half);
|
||||
return half - r ;
|
||||
}
|
||||
}
|
||||
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabs(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) {
|
||||
z = one-erx; return z - P/Q;
|
||||
} else {
|
||||
z = erx+P/Q; return one+z;
|
||||
}
|
||||
}
|
||||
if (ix < 0x403c0000) { /* |x|<28 */
|
||||
x = fabs(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/.35 ~ 2.857143 */
|
||||
if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
z = x;
|
||||
SET_LOW_WORD(z,0);
|
||||
r = __ieee754_exp(-z*z-0.5625)*
|
||||
__ieee754_exp((z-x)*(z+x)+R/S);
|
||||
if(hx>0) return r/x; else return two-r/x;
|
||||
} else {
|
||||
if(hx>0) return tiny*tiny; else return two-tiny;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,212 @@
|
||||
/* s_erff.c -- float version of s_erf.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_erff.c,v 1.7 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
tiny = 1e-30,
|
||||
half= 5.0000000000e-01, /* 0x3F000000 */
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
two = 2.0000000000e+00, /* 0x40000000 */
|
||||
/* c = (subfloat)0.84506291151 */
|
||||
erx = 8.4506291151e-01, /* 0x3f58560b */
|
||||
/*
|
||||
* Coefficients for approximation to erf on [0,0.84375]
|
||||
*/
|
||||
efx = 1.2837916613e-01, /* 0x3e0375d4 */
|
||||
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
|
||||
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
|
||||
pp1 = -3.2504209876e-01, /* 0xbea66beb */
|
||||
pp2 = -2.8481749818e-02, /* 0xbce9528f */
|
||||
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
|
||||
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
|
||||
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
|
||||
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
|
||||
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
|
||||
qq4 = 1.3249473704e-04, /* 0x390aee49 */
|
||||
qq5 = -3.9602282413e-06, /* 0xb684e21a */
|
||||
/*
|
||||
* Coefficients for approximation to erf in [0.84375,1.25]
|
||||
*/
|
||||
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
|
||||
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
|
||||
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
|
||||
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
|
||||
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
|
||||
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
|
||||
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
|
||||
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
|
||||
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
|
||||
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
|
||||
qa4 = 1.2617121637e-01, /* 0x3e013307 */
|
||||
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
|
||||
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1.25,1/0.35]
|
||||
*/
|
||||
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
|
||||
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
|
||||
ra2 = -1.0558626175e+01, /* 0xc128f022 */
|
||||
ra3 = -6.2375331879e+01, /* 0xc2798057 */
|
||||
ra4 = -1.6239666748e+02, /* 0xc322658c */
|
||||
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
|
||||
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
|
||||
ra7 = -9.8143291473e+00, /* 0xc11d077e */
|
||||
sa1 = 1.9651271820e+01, /* 0x419d35ce */
|
||||
sa2 = 1.3765776062e+02, /* 0x4309a863 */
|
||||
sa3 = 4.3456588745e+02, /* 0x43d9486f */
|
||||
sa4 = 6.4538726807e+02, /* 0x442158c9 */
|
||||
sa5 = 4.2900814819e+02, /* 0x43d6810b */
|
||||
sa6 = 1.0863500214e+02, /* 0x42d9451f */
|
||||
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
|
||||
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1/.35,28]
|
||||
*/
|
||||
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
|
||||
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
|
||||
rb2 = -1.7757955551e+01, /* 0xc18e104b */
|
||||
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
|
||||
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
|
||||
rb5 = -1.0250950928e+03, /* 0xc480230b */
|
||||
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
|
||||
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
|
||||
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
|
||||
sb3 = 1.5367296143e+03, /* 0x44c01759 */
|
||||
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
|
||||
sb5 = 2.5530502930e+03, /* 0x451f90ce */
|
||||
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
|
||||
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
|
||||
|
||||
float
|
||||
erff(float x)
|
||||
{
|
||||
int32_t hx,ix,i;
|
||||
float R,S,P,Q,s,y,z,r;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) { /* erf(nan)=nan */
|
||||
i = ((u_int32_t)hx>>31)<<1;
|
||||
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
|
||||
}
|
||||
|
||||
if(ix < 0x3f580000) { /* |x|<0.84375 */
|
||||
if(ix < 0x31800000) { /* |x|<2**-28 */
|
||||
if (ix < 0x04000000)
|
||||
/*avoid underflow */
|
||||
return (float)0.125*((float)8.0*x+efx8*x);
|
||||
return x + efx*x;
|
||||
}
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
return x + x*y;
|
||||
}
|
||||
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabsf(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
|
||||
}
|
||||
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
|
||||
if(hx>=0) return one-tiny; else return tiny-one;
|
||||
}
|
||||
x = fabsf(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/0.35 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
SET_FLOAT_WORD(z,ix&0xfffff000);
|
||||
r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
|
||||
if(hx>=0) return one-r/x; else return r/x-one;
|
||||
}
|
||||
|
||||
float
|
||||
erfcf(float x)
|
||||
{
|
||||
int32_t hx,ix;
|
||||
float R,S,P,Q,s,y,z,r;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) { /* erfc(nan)=nan */
|
||||
/* erfc(+-inf)=0,2 */
|
||||
return (float)(((u_int32_t)hx>>31)<<1)+one/x;
|
||||
}
|
||||
|
||||
if(ix < 0x3f580000) { /* |x|<0.84375 */
|
||||
if(ix < 0x23800000) /* |x|<2**-56 */
|
||||
return one-x;
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
if(hx < 0x3e800000) { /* x<1/4 */
|
||||
return one-(x+x*y);
|
||||
} else {
|
||||
r = x*y;
|
||||
r += (x-half);
|
||||
return half - r ;
|
||||
}
|
||||
}
|
||||
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabsf(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) {
|
||||
z = one-erx; return z - P/Q;
|
||||
} else {
|
||||
z = erx+P/Q; return one+z;
|
||||
}
|
||||
}
|
||||
if (ix < 0x41e00000) { /* |x|<28 */
|
||||
x = fabsf(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/.35 ~ 2.857143 */
|
||||
if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
SET_FLOAT_WORD(z,ix&0xfffff000);
|
||||
r = __ieee754_expf(-z*z-(float)0.5625)*
|
||||
__ieee754_expf((z-x)*(z+x)+R/S);
|
||||
if(hx>0) return r/x; else return two-r/x;
|
||||
} else {
|
||||
if(hx>0) return tiny*tiny; else return two-tiny;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,401 @@
|
||||
/*-
|
||||
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_exp2.c,v 1.2 2010/01/11 23:38:24 christos Exp $");
|
||||
#ifdef __FBSDID
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2.c,v 1.7 2008/02/22 02:27:34 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 8
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
|
||||
static const double
|
||||
huge = 0x1p1000,
|
||||
redux = 0x1.8p52 / TBLSIZE,
|
||||
P1 = 0x1.62e42fefa39efp-1,
|
||||
P2 = 0x1.ebfbdff82c575p-3,
|
||||
P3 = 0x1.c6b08d704a0a6p-5,
|
||||
P4 = 0x1.3b2ab88f70400p-7,
|
||||
P5 = 0x1.5d88003875c74p-10;
|
||||
|
||||
static volatile double twom1000 = 0x1p-1000;
|
||||
|
||||
static const double tbl[TBLSIZE * 2] = {
|
||||
/* exp2(z + eps) eps */
|
||||
0x1.6a09e667f3d5dp-1, 0x1.9880p-44,
|
||||
0x1.6b052fa751744p-1, 0x1.8000p-50,
|
||||
0x1.6c012750bd9fep-1, -0x1.8780p-45,
|
||||
0x1.6cfdcddd476bfp-1, 0x1.ec00p-46,
|
||||
0x1.6dfb23c651a29p-1, -0x1.8000p-50,
|
||||
0x1.6ef9298593ae3p-1, -0x1.c000p-52,
|
||||
0x1.6ff7df9519386p-1, -0x1.fd80p-45,
|
||||
0x1.70f7466f42da3p-1, -0x1.c880p-45,
|
||||
0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46,
|
||||
0x1.72f8286eacf05p-1, -0x1.8300p-44,
|
||||
0x1.73f9a48a58152p-1, -0x1.0c00p-47,
|
||||
0x1.74fbd35d7ccfcp-1, 0x1.f880p-45,
|
||||
0x1.75feb564267f1p-1, 0x1.3e00p-47,
|
||||
0x1.77024b1ab6d48p-1, -0x1.7d00p-45,
|
||||
0x1.780694fde5d38p-1, -0x1.d000p-50,
|
||||
0x1.790b938ac1d00p-1, 0x1.3000p-49,
|
||||
0x1.7a11473eb0178p-1, -0x1.d000p-49,
|
||||
0x1.7b17b0976d060p-1, 0x1.0400p-45,
|
||||
0x1.7c1ed0130c133p-1, 0x1.0000p-53,
|
||||
0x1.7d26a62ff8636p-1, -0x1.6900p-45,
|
||||
0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47,
|
||||
0x1.7f3878491c3e8p-1, -0x1.4580p-45,
|
||||
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|
||||
0x1.671c1c708328ep+0, -0x1.7200p-44,
|
||||
0x1.68155d44ca97ep+0, 0x1.6800p-49,
|
||||
0x1.690f4b19e9471p+0, -0x1.9780p-45,
|
||||
};
|
||||
|
||||
/*
|
||||
* exp2(x): compute the base 2 exponential of x
|
||||
*
|
||||
* Accuracy: Peak error < 0.503 ulp for normalized results.
|
||||
*
|
||||
* Method: (accurate tables)
|
||||
*
|
||||
* Reduce x:
|
||||
* x = 2**k + y, for integer k and |y| <= 1/2.
|
||||
* Thus we have exp2(x) = 2**k * exp2(y).
|
||||
*
|
||||
* Reduce y:
|
||||
* y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE.
|
||||
* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]),
|
||||
* with |z - eps[i]| <= 2**-9 + 2**-39 for the table used.
|
||||
*
|
||||
* We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via
|
||||
* a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61.
|
||||
* The values in exp2t[] and eps[] are chosen such that
|
||||
* exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such
|
||||
* that exp2t[i] is accurate to 2**-64.
|
||||
*
|
||||
* Note that the range of i is +-TBLSIZE/2, so we actually index the tables
|
||||
* by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are
|
||||
* virtual tables, interleaved in the real table tbl[].
|
||||
*
|
||||
* This method is due to Gal, with many details due to Gal and Bachelis:
|
||||
*
|
||||
* Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library
|
||||
* for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991).
|
||||
*/
|
||||
double
|
||||
exp2(double x)
|
||||
{
|
||||
double r, t, twopk, twopkp1000, z;
|
||||
uint32_t hx, ix, lx, i0;
|
||||
int k;
|
||||
|
||||
/* Filter out exceptional cases. */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx & 0x7fffffff; /* high word of |x| */
|
||||
if(ix >= 0x40900000) { /* |x| >= 1024 */
|
||||
if(ix >= 0x7ff00000) {
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0)
|
||||
return (x + x); /* x is NaN or +Inf */
|
||||
else
|
||||
return (0.0); /* x is -Inf */
|
||||
}
|
||||
if(x >= 0x1.0p10)
|
||||
return (huge * huge); /* overflow */
|
||||
if(x <= -0x1.0ccp10)
|
||||
return (twom1000 * twom1000); /* underflow */
|
||||
} else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */
|
||||
return (1.0 + x);
|
||||
}
|
||||
|
||||
/* Reduce x, computing z, i0, and k. */
|
||||
STRICT_ASSIGN(double, t, x + redux);
|
||||
GET_LOW_WORD(i0, t);
|
||||
i0 += TBLSIZE / 2;
|
||||
k = (i0 >> TBLBITS) << 20;
|
||||
i0 = (i0 & (TBLSIZE - 1)) << 1;
|
||||
t -= redux;
|
||||
z = x - t;
|
||||
|
||||
/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
|
||||
t = tbl[i0]; /* exp2t[i0] */
|
||||
z -= tbl[i0 + 1]; /* eps[i0] */
|
||||
if (k >= -1021 << 20)
|
||||
INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
|
||||
else
|
||||
INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0);
|
||||
r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
|
||||
|
||||
/* Scale by 2**(k>>20). */
|
||||
if(k >= -1021 << 20) {
|
||||
if (k == 1024 << 20)
|
||||
return (r * 2.0 * 0x1p1023);
|
||||
return (r * twopk);
|
||||
} else {
|
||||
return (r * twopkp1000 * twom1000);
|
||||
}
|
||||
}
|
||||
|
||||
#ifdef notyet
|
||||
#if (LDBL_MANT_DIG == 53)
|
||||
__weak_reference(exp2, exp2l);
|
||||
#endif
|
||||
#endif
|
||||
@@ -0,0 +1,139 @@
|
||||
/*-
|
||||
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_exp2f.c,v 1.1 2010/01/11 16:28:39 christos Exp $");
|
||||
#ifdef __FBSDID
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#define TBLBITS 4
|
||||
#define TBLSIZE (1 << TBLBITS)
|
||||
|
||||
static const float
|
||||
huge = 0x1p100f,
|
||||
redux = 0x1.8p23f / TBLSIZE,
|
||||
P1 = 0x1.62e430p-1f,
|
||||
P2 = 0x1.ebfbe0p-3f,
|
||||
P3 = 0x1.c6b348p-5f,
|
||||
P4 = 0x1.3b2c9cp-7f;
|
||||
|
||||
static volatile float twom100 = 0x1p-100f;
|
||||
|
||||
static const double exp2ft[TBLSIZE] = {
|
||||
0x1.6a09e667f3bcdp-1,
|
||||
0x1.7a11473eb0187p-1,
|
||||
0x1.8ace5422aa0dbp-1,
|
||||
0x1.9c49182a3f090p-1,
|
||||
0x1.ae89f995ad3adp-1,
|
||||
0x1.c199bdd85529cp-1,
|
||||
0x1.d5818dcfba487p-1,
|
||||
0x1.ea4afa2a490dap-1,
|
||||
0x1.0000000000000p+0,
|
||||
0x1.0b5586cf9890fp+0,
|
||||
0x1.172b83c7d517bp+0,
|
||||
0x1.2387a6e756238p+0,
|
||||
0x1.306fe0a31b715p+0,
|
||||
0x1.3dea64c123422p+0,
|
||||
0x1.4bfdad5362a27p+0,
|
||||
0x1.5ab07dd485429p+0,
|
||||
};
|
||||
|
||||
/*
|
||||
* exp2f(x): compute the base 2 exponential of x
|
||||
*
|
||||
* Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
|
||||
*
|
||||
* Method: (equally-spaced tables)
|
||||
*
|
||||
* Reduce x:
|
||||
* x = 2**k + y, for integer k and |y| <= 1/2.
|
||||
* Thus we have exp2f(x) = 2**k * exp2(y).
|
||||
*
|
||||
* Reduce y:
|
||||
* y = i/TBLSIZE + z for integer i near y * TBLSIZE.
|
||||
* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
|
||||
* with |z| <= 2**-(TBLSIZE+1).
|
||||
*
|
||||
* We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
|
||||
* degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
|
||||
* Using double precision for everything except the reduction makes
|
||||
* roundoff error insignificant and simplifies the scaling step.
|
||||
*
|
||||
* This method is due to Tang, but I do not use his suggested parameters:
|
||||
*
|
||||
* Tang, P. Table-driven Implementation of the Exponential Function
|
||||
* in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
|
||||
*/
|
||||
float
|
||||
exp2f(float x)
|
||||
{
|
||||
double tv, twopk, u, z;
|
||||
float t;
|
||||
uint32_t hx, ix, i0;
|
||||
int32_t k;
|
||||
|
||||
/* Filter out exceptional cases. */
|
||||
GET_FLOAT_WORD(hx, x);
|
||||
ix = hx & 0x7fffffff; /* high word of |x| */
|
||||
if(ix >= 0x43000000) { /* |x| >= 128 */
|
||||
if(ix >= 0x7f800000) {
|
||||
if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
|
||||
return (x + x); /* x is NaN or +Inf */
|
||||
else
|
||||
return (0.0); /* x is -Inf */
|
||||
}
|
||||
if(x >= 0x1.0p7f)
|
||||
return (huge * huge); /* overflow */
|
||||
if(x <= -0x1.2cp7f)
|
||||
return (twom100 * twom100); /* underflow */
|
||||
} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
|
||||
return (1.0f + x);
|
||||
}
|
||||
|
||||
/* Reduce x, computing z, i0, and k. */
|
||||
STRICT_ASSIGN(float, t, x + redux);
|
||||
GET_FLOAT_WORD(i0, t);
|
||||
i0 += TBLSIZE / 2;
|
||||
k = (i0 >> TBLBITS) << 20;
|
||||
i0 &= TBLSIZE - 1;
|
||||
t -= redux;
|
||||
z = x - t;
|
||||
INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
|
||||
|
||||
/* Compute r = exp2(y) = exp2ft[i0] * p(z). */
|
||||
tv = exp2ft[i0];
|
||||
u = tv * z;
|
||||
tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
|
||||
|
||||
/* Scale by 2**(k>>20). */
|
||||
return (tv * twopk);
|
||||
}
|
||||
@@ -0,0 +1,223 @@
|
||||
/* @(#)s_expm1.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_expm1.c,v 1.12 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* expm1(x)
|
||||
* Returns exp(x)-1, the exponential of x minus 1.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
|
||||
*
|
||||
* Here a correction term c will be computed to compensate
|
||||
* the error in r when rounded to a floating-point number.
|
||||
*
|
||||
* 2. Approximating expm1(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Since
|
||||
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
|
||||
* we define R1(r*r) by
|
||||
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
|
||||
* That is,
|
||||
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
|
||||
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
|
||||
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
|
||||
* We use a special Reme algorithm on [0,0.347] to generate
|
||||
* a polynomial of degree 5 in r*r to approximate R1. The
|
||||
* maximum error of this polynomial approximation is bounded
|
||||
* by 2**-61. In other words,
|
||||
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
|
||||
* where Q1 = -1.6666666666666567384E-2,
|
||||
* Q2 = 3.9682539681370365873E-4,
|
||||
* Q3 = -9.9206344733435987357E-6,
|
||||
* Q4 = 2.5051361420808517002E-7,
|
||||
* Q5 = -6.2843505682382617102E-9;
|
||||
* (where z=r*r, and the values of Q1 to Q5 are listed below)
|
||||
* with error bounded by
|
||||
* | 5 | -61
|
||||
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
|
||||
* | |
|
||||
*
|
||||
* expm1(r) = exp(r)-1 is then computed by the following
|
||||
* specific way which minimize the accumulation rounding error:
|
||||
* 2 3
|
||||
* r r [ 3 - (R1 + R1*r/2) ]
|
||||
* expm1(r) = r + --- + --- * [--------------------]
|
||||
* 2 2 [ 6 - r*(3 - R1*r/2) ]
|
||||
*
|
||||
* To compensate the error in the argument reduction, we use
|
||||
* expm1(r+c) = expm1(r) + c + expm1(r)*c
|
||||
* ~ expm1(r) + c + r*c
|
||||
* Thus c+r*c will be added in as the correction terms for
|
||||
* expm1(r+c). Now rearrange the term to avoid optimization
|
||||
* screw up:
|
||||
* ( 2 2 )
|
||||
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
|
||||
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
|
||||
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
|
||||
* ( )
|
||||
*
|
||||
* = r - E
|
||||
* 3. Scale back to obtain expm1(x):
|
||||
* From step 1, we have
|
||||
* expm1(x) = either 2^k*[expm1(r)+1] - 1
|
||||
* = or 2^k*[expm1(r) + (1-2^-k)]
|
||||
* 4. Implementation notes:
|
||||
* (A). To save one multiplication, we scale the coefficient Qi
|
||||
* to Qi*2^i, and replace z by (x^2)/2.
|
||||
* (B). To achieve maximum accuracy, we compute expm1(x) by
|
||||
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
|
||||
* (ii) if k=0, return r-E
|
||||
* (iii) if k=-1, return 0.5*(r-E)-0.5
|
||||
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
|
||||
* else return 1.0+2.0*(r-E);
|
||||
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
|
||||
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
|
||||
* (vii) return 2^k(1-((E+2^-k)-r))
|
||||
*
|
||||
* Special cases:
|
||||
* expm1(INF) is INF, expm1(NaN) is NaN;
|
||||
* expm1(-INF) is -1, and
|
||||
* for finite argument, only expm1(0)=0 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
one = 1.0,
|
||||
huge = 1.0e+300,
|
||||
tiny = 1.0e-300,
|
||||
o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
|
||||
ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
|
||||
invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
|
||||
/* scaled coefficients related to expm1 */
|
||||
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
|
||||
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
|
||||
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
|
||||
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
|
||||
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
|
||||
|
||||
double
|
||||
expm1(double x)
|
||||
{
|
||||
double y,hi,lo,c,t,e,hxs,hfx,r1;
|
||||
int32_t k,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
c = 0;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
xsb = hx&0x80000000; /* sign bit of x */
|
||||
if(xsb==0) y=x; else y= -x; /* y = |x| */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out huge and non-finite argument */
|
||||
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
|
||||
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
|
||||
if(hx>=0x7ff00000) {
|
||||
u_int32_t low;
|
||||
GET_LOW_WORD(low,x);
|
||||
if(((hx&0xfffff)|low)!=0)
|
||||
return x+x; /* NaN */
|
||||
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
|
||||
}
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
}
|
||||
if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
|
||||
if(x+tiny<0.0) /* raise inexact */
|
||||
return tiny-one; /* return -1 */
|
||||
}
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
|
||||
if(xsb==0)
|
||||
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
|
||||
else
|
||||
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
|
||||
} else {
|
||||
k = invln2*x+((xsb==0)?0.5:-0.5);
|
||||
t = k;
|
||||
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
|
||||
lo = t*ln2_lo;
|
||||
}
|
||||
x = hi - lo;
|
||||
c = (hi-x)-lo;
|
||||
}
|
||||
else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
|
||||
t = huge+x; /* return x with inexact flags when x!=0 */
|
||||
return x - (t-(huge+x));
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
hfx = 0.5*x;
|
||||
hxs = x*hfx;
|
||||
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
|
||||
t = 3.0-r1*hfx;
|
||||
e = hxs*((r1-t)/(6.0 - x*t));
|
||||
if(k==0) return x - (x*e-hxs); /* c is 0 */
|
||||
else {
|
||||
e = (x*(e-c)-c);
|
||||
e -= hxs;
|
||||
if(k== -1) return 0.5*(x-e)-0.5;
|
||||
if(k==1) {
|
||||
if(x < -0.25) return -2.0*(e-(x+0.5));
|
||||
else return one+2.0*(x-e);
|
||||
}
|
||||
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
|
||||
u_int32_t high;
|
||||
y = one-(e-x);
|
||||
GET_HIGH_WORD(high,y);
|
||||
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
|
||||
return y-one;
|
||||
}
|
||||
t = one;
|
||||
if(k<20) {
|
||||
u_int32_t high;
|
||||
SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
|
||||
y = t-(e-x);
|
||||
GET_HIGH_WORD(high,y);
|
||||
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
|
||||
} else {
|
||||
u_int32_t high;
|
||||
SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */
|
||||
y = x-(e+t);
|
||||
y += one;
|
||||
GET_HIGH_WORD(high,y);
|
||||
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
|
||||
}
|
||||
}
|
||||
return y;
|
||||
}
|
||||
@@ -0,0 +1,128 @@
|
||||
/* s_expm1f.c -- float version of s_expm1.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_expm1f.c,v 1.10 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e+30, tiny = 1.0e-30;
|
||||
|
||||
static const float
|
||||
one = 1.0,
|
||||
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
|
||||
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
|
||||
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
|
||||
/* scaled coefficients related to expm1 */
|
||||
Q1 = -3.3333335072e-02, /* 0xbd088889 */
|
||||
Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
|
||||
Q3 = -7.9365076090e-05, /* 0xb8a670cd */
|
||||
Q4 = 4.0082177293e-06, /* 0x36867e54 */
|
||||
Q5 = -2.0109921195e-07; /* 0xb457edbb */
|
||||
|
||||
float
|
||||
expm1f(float x)
|
||||
{
|
||||
float y,hi,lo,c,t,e,hxs,hfx,r1;
|
||||
int32_t k,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
c = 0;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
xsb = hx&0x80000000; /* sign bit of x */
|
||||
if(xsb==0) y=x; else y= -x; /* y = |x| */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out huge and non-finite argument */
|
||||
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
|
||||
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
||||
if(hx>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx==0x7f800000)
|
||||
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
}
|
||||
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
|
||||
if(x+tiny<(float)0.0) /* raise inexact */
|
||||
return tiny-one; /* return -1 */
|
||||
}
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
||||
if(xsb==0)
|
||||
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
|
||||
else
|
||||
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
|
||||
} else {
|
||||
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
|
||||
t = k;
|
||||
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
|
||||
lo = t*ln2_lo;
|
||||
}
|
||||
x = hi - lo;
|
||||
c = (hi-x)-lo;
|
||||
}
|
||||
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
|
||||
t = huge+x; /* return x with inexact flags when x!=0 */
|
||||
return x - (t-(huge+x));
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
hfx = (float)0.5*x;
|
||||
hxs = x*hfx;
|
||||
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
|
||||
t = (float)3.0-r1*hfx;
|
||||
e = hxs*((r1-t)/((float)6.0 - x*t));
|
||||
if(k==0) return x - (x*e-hxs); /* c is 0 */
|
||||
else {
|
||||
e = (x*(e-c)-c);
|
||||
e -= hxs;
|
||||
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
|
||||
if(k==1) {
|
||||
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
|
||||
else return one+(float)2.0*(x-e);
|
||||
}
|
||||
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
|
||||
int32_t i;
|
||||
y = one-(e-x);
|
||||
GET_FLOAT_WORD(i,y);
|
||||
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
||||
return y-one;
|
||||
}
|
||||
t = one;
|
||||
if(k<23) {
|
||||
int32_t i;
|
||||
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
|
||||
y = t-(e-x);
|
||||
GET_FLOAT_WORD(i,y);
|
||||
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
||||
} else {
|
||||
int32_t i;
|
||||
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
|
||||
y = x-(e+t);
|
||||
y += one;
|
||||
GET_FLOAT_WORD(i,y);
|
||||
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
||||
}
|
||||
}
|
||||
return y;
|
||||
}
|
||||
@@ -0,0 +1,32 @@
|
||||
/* @(#)s_fabs.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_fabs.c,v 1.10 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* fabs(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
double
|
||||
fabs(double x)
|
||||
{
|
||||
u_int32_t high;
|
||||
GET_HIGH_WORD(high,x);
|
||||
SET_HIGH_WORD(x,high&0x7fffffff);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,35 @@
|
||||
/* s_fabsf.c -- float version of s_fabs.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_fabsf.c,v 1.7 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* fabsf(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
fabsf(float x)
|
||||
{
|
||||
u_int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
SET_FLOAT_WORD(x,ix&0x7fffffff);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,49 @@
|
||||
/* $NetBSD: s_fabsl.c,v 1.2 2010/09/17 20:39:39 christos Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 2010 The NetBSD Foundation, Inc.
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
|
||||
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
||||
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
|
||||
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
* POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fabsl.c,v 1.2 2010/09/17 20:39:39 christos Exp $");
|
||||
|
||||
#include <math.h>
|
||||
#include <machine/ieee.h>
|
||||
|
||||
/*
|
||||
* fabsl(long double x)
|
||||
* This function returns the absolute value of its argumetn x, |x|.
|
||||
*/
|
||||
#ifdef EXT_EXP_INFNAN
|
||||
long double
|
||||
fabsl(long double x)
|
||||
{
|
||||
union ieee_ext_u ux;
|
||||
|
||||
ux.extu_ld = x;
|
||||
ux.extu_ext.ext_sign = 0;
|
||||
|
||||
return (ux.extu_ld);
|
||||
}
|
||||
#endif
|
||||
@@ -0,0 +1,49 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD$");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fdim.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#define DECL(type, fn) \
|
||||
type \
|
||||
fn(type x, type y) \
|
||||
{ \
|
||||
\
|
||||
if (isnan(x)) \
|
||||
return (x); \
|
||||
if (isnan(y)) \
|
||||
return (y); \
|
||||
return (x > y ? x - y : 0.0); \
|
||||
}
|
||||
|
||||
DECL(double, fdim)
|
||||
DECL(float, fdimf)
|
||||
DECL(long double, fdiml)
|
||||
@@ -0,0 +1,32 @@
|
||||
/* @(#)s_finite.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_finite.c,v 1.11 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* finite(x) returns 1 is x is finite, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
int
|
||||
finite(double x)
|
||||
{
|
||||
int32_t hx;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31);
|
||||
}
|
||||
@@ -0,0 +1,35 @@
|
||||
/* s_finitef.c -- float version of s_finite.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_finitef.c,v 1.7 2002/05/26 22:01:55 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* finitef(x) returns 1 is x is finite, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
int
|
||||
finitef(float x)
|
||||
{
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
return (int)((u_int32_t)((ix&0x7fffffff)-0x7f800000)>>31);
|
||||
}
|
||||
@@ -0,0 +1,74 @@
|
||||
/* @(#)s_floor.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_floor.c,v 1.13 2009/02/16 01:27:36 lukem Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* floor(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to floor(x).
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double huge = 1.0e300;
|
||||
|
||||
double
|
||||
floor(double x)
|
||||
{
|
||||
int32_t i0,i1,jj0;
|
||||
u_int32_t i,j;
|
||||
EXTRACT_WORDS(i0,i1,x);
|
||||
jj0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(jj0<20) {
|
||||
if(jj0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0>=0) {i0=i1=0;}
|
||||
else if(((i0&0x7fffffff)|i1)!=0)
|
||||
{ i0=0xbff00000;i1=0;}
|
||||
}
|
||||
} else {
|
||||
i = (0x000fffff)>>jj0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0<0) i0 += (0x00100000)>>jj0;
|
||||
i0 &= (~i); i1=0;
|
||||
}
|
||||
}
|
||||
} else if (jj0>51) {
|
||||
if(jj0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((u_int32_t)(0xffffffff))>>(jj0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0<0) {
|
||||
if(jj0==20) i0+=1;
|
||||
else {
|
||||
j = i1+(1<<(52-jj0));
|
||||
if(j<(u_int32_t)i1) i0 +=1 ; /* got a carry */
|
||||
i1=j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
INSERT_WORDS(x,i0,i1);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,63 @@
|
||||
/* s_floorf.c -- float version of s_floor.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_floorf.c,v 1.8 2008/04/25 22:21:53 christos Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* floorf(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to floorf(x).
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e30;
|
||||
|
||||
float
|
||||
floorf(float x)
|
||||
{
|
||||
int32_t i0,jj0;
|
||||
u_int32_t i;
|
||||
GET_FLOAT_WORD(i0,x);
|
||||
jj0 = ((i0>>23)&0xff)-0x7f;
|
||||
if(jj0<23) {
|
||||
if(jj0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0>=0) {i0=0;}
|
||||
else if((i0&0x7fffffff)!=0)
|
||||
{ i0=0xbf800000;}
|
||||
}
|
||||
} else {
|
||||
i = (0x007fffff)>>jj0;
|
||||
if((i0&i)==0) return x; /* x is integral */
|
||||
if(huge+x>(float)0.0) { /* raise inexact flag */
|
||||
if(i0<0) i0 += (0x00800000)>>jj0;
|
||||
i0 &= (~i);
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if(jj0==0x80) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
}
|
||||
SET_FLOAT_WORD(x,i0);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,58 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fmax.c,v 1.2 2010/03/08 01:05:20 snj Exp $");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fmax.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#include <machine/ieee.h>
|
||||
|
||||
double
|
||||
fmax(double x, double y)
|
||||
{
|
||||
union ieee_double_u u[2];
|
||||
|
||||
u[0].dblu_d = x;
|
||||
u[1].dblu_d = y;
|
||||
|
||||
/* Check for NaNs to avoid raising spurious exceptions. */
|
||||
if (u[0].dblu_dbl.dbl_exp == DBL_EXP_INFNAN &&
|
||||
(u[0].dblu_dbl.dbl_frach | u[0].dblu_dbl.dbl_fracl) != 0)
|
||||
return (y);
|
||||
if (u[1].dblu_dbl.dbl_exp == DBL_EXP_INFNAN &&
|
||||
(u[1].dblu_dbl.dbl_frach | u[1].dblu_dbl.dbl_fracl) != 0)
|
||||
return (x);
|
||||
|
||||
/* Handle comparisons of signed zeroes. */
|
||||
if (u[0].dblu_dbl.dbl_sign != u[1].dblu_dbl.dbl_sign)
|
||||
return (u[u[0].dblu_dbl.dbl_sign].dblu_d);
|
||||
|
||||
return (x > y ? x : y);
|
||||
}
|
||||
@@ -0,0 +1,58 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fmaxf.c,v 1.2 2010/03/08 01:05:20 snj Exp $");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaxf.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#include <machine/ieee.h>
|
||||
|
||||
float
|
||||
fmaxf(float x, float y)
|
||||
{
|
||||
union ieee_single_u u[2];
|
||||
|
||||
u[0].sngu_f = x;
|
||||
u[1].sngu_f = y;
|
||||
|
||||
/* Check for NaNs to avoid raising spurious exceptions. */
|
||||
if (u[0].sngu_sng.sng_exp == SNG_EXP_INFNAN &&
|
||||
u[0].sngu_sng.sng_frac != 0)
|
||||
return (y);
|
||||
if (u[1].sngu_sng.sng_exp == SNG_EXP_INFNAN &&
|
||||
u[1].sngu_sng.sng_frac != 0)
|
||||
return (x);
|
||||
|
||||
/* Handle comparisons of sng_signed zeroes. */
|
||||
if (u[0].sngu_sng.sng_sign != u[1].sngu_sng.sng_sign)
|
||||
return (u[u[0].sngu_sng.sng_sign].sngu_f);
|
||||
|
||||
return (x > y ? x : y);
|
||||
}
|
||||
@@ -0,0 +1,61 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fmaxl.c,v 1.2 2010/03/08 01:05:20 snj Exp $");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaxl.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#include <machine/ieee.h>
|
||||
#ifdef EXT_EXP_INFNAN
|
||||
long double
|
||||
fmaxl(long double x, long double y)
|
||||
{
|
||||
union ieee_ext_u u[2];
|
||||
|
||||
u[0].extu_ld = x;
|
||||
u[0].extu_ext.ext_frach &= ~0x80000000;
|
||||
u[1].extu_ld = y;
|
||||
u[1].extu_ext.ext_frach &= ~0x80000000;
|
||||
|
||||
/* Check for NaNs to avoid raising spurious exceptions. */
|
||||
if (u[0].extu_ext.ext_exp == EXT_EXP_INFNAN &&
|
||||
(u[0].extu_ext.ext_frach | u[0].extu_ext.ext_fracl) != 0)
|
||||
return (y);
|
||||
if (u[1].extu_ext.ext_exp == EXT_EXP_INFNAN &&
|
||||
(u[1].extu_ext.ext_frach | u[1].extu_ext.ext_fracl) != 0)
|
||||
return (x);
|
||||
|
||||
/* Handle comparisons of ext_signed zeroes. */
|
||||
if (u[0].extu_ext.ext_sign != u[1].extu_ext.ext_sign)
|
||||
return (u[0].extu_ext.ext_sign ? y : x);
|
||||
|
||||
return (x > y ? x : y);
|
||||
}
|
||||
#endif
|
||||
@@ -0,0 +1,58 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fmin.c,v 1.1 2009/10/04 22:04:30 christos Exp $");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fmin.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#include <machine/ieee.h>
|
||||
|
||||
double
|
||||
fmin(double x, double y)
|
||||
{
|
||||
union ieee_double_u u[2];
|
||||
|
||||
u[0].dblu_d = x;
|
||||
u[1].dblu_d = y;
|
||||
|
||||
/* Check for NaNs to avoid raising spurious exceptions. */
|
||||
if (u[0].dblu_dbl.dbl_exp == DBL_EXP_INFNAN &&
|
||||
(u[0].dblu_dbl.dbl_frach | u[0].dblu_dbl.dbl_fracl) != 0)
|
||||
return (y);
|
||||
if (u[1].dblu_dbl.dbl_exp == DBL_EXP_INFNAN &&
|
||||
(u[1].dblu_dbl.dbl_frach | u[1].dblu_dbl.dbl_fracl) != 0)
|
||||
return (x);
|
||||
|
||||
/* Handle comparisons of signed zeroes. */
|
||||
if (u[0].dblu_dbl.dbl_sign != u[1].dblu_dbl.dbl_sign)
|
||||
return (u[u[1].dblu_dbl.dbl_sign].dblu_d);
|
||||
|
||||
return (x < y ? x : y);
|
||||
}
|
||||
@@ -0,0 +1,58 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fminf.c,v 1.2 2010/03/08 01:05:20 snj Exp $");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fminf.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#include <machine/ieee.h>
|
||||
|
||||
float
|
||||
fminf(float x, float y)
|
||||
{
|
||||
union ieee_single_u u[2];
|
||||
|
||||
u[0].sngu_f = x;
|
||||
u[1].sngu_f = y;
|
||||
|
||||
/* Check for NaNs to avoid raising spurious exceptions. */
|
||||
if (u[0].sngu_sng.sng_exp == SNG_EXP_INFNAN &&
|
||||
u[0].sngu_sng.sng_frac != 0)
|
||||
return (y);
|
||||
if (u[1].sngu_sng.sng_exp == SNG_EXP_INFNAN &&
|
||||
u[1].sngu_sng.sng_frac != 0)
|
||||
return (x);
|
||||
|
||||
/* Handle comparisons of sng_singed zeroes. */
|
||||
if (u[0].sngu_sng.sng_sign != u[1].sngu_sng.sng_sign)
|
||||
return (u[u[1].sngu_sng.sng_sign].sngu_f);
|
||||
|
||||
return (x < y ? x : y);
|
||||
}
|
||||
@@ -0,0 +1,61 @@
|
||||
/*-
|
||||
* Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
__RCSID("$NetBSD: s_fminl.c,v 1.2 2010/03/08 01:05:20 snj Exp $");
|
||||
#ifdef notdef
|
||||
__FBSDID("$FreeBSD: src/lib/msun/src/s_fminl.c,v 1.1 2004/06/30 07:04:01 das Exp $");
|
||||
#endif
|
||||
|
||||
#include <math.h>
|
||||
|
||||
#include <machine/ieee.h>
|
||||
#ifdef EXT_EXP_INFNAN
|
||||
long double
|
||||
fminl(long double x, long double y)
|
||||
{
|
||||
union ieee_ext_u u[2];
|
||||
|
||||
u[0].extu_ld = x;
|
||||
u[0].extu_ext.ext_frach &= ~0x80000000;
|
||||
u[1].extu_ld = y;
|
||||
u[1].extu_ext.ext_frach &= ~0x80000000;
|
||||
|
||||
/* Check for NaNs to avoid raising spurious exceptions. */
|
||||
if (u[0].extu_ext.ext_exp == EXT_EXP_INFNAN &&
|
||||
(u[0].extu_ext.ext_frach | u[0].extu_ext.ext_fracl) != 0)
|
||||
return (y);
|
||||
if (u[1].extu_ext.ext_exp == EXT_EXP_INFNAN &&
|
||||
(u[1].extu_ext.ext_frach | u[1].extu_ext.ext_fracl) != 0)
|
||||
return (x);
|
||||
|
||||
/* Handle comparisons of ext_signed zeroes. */
|
||||
if (u[0].extu_ext.ext_sign != u[1].extu_ext.ext_sign)
|
||||
return (u[1].extu_ext.ext_sign ? y : x);
|
||||
|
||||
return (x < y ? x : y);
|
||||
}
|
||||
#endif
|
||||
@@ -0,0 +1,52 @@
|
||||
/* @(#)s_frexp.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_frexp.c,v 1.13 2008/09/28 18:54:55 christos Exp $");
|
||||
#endif
|
||||
|
||||
/*
|
||||
* for non-zero x
|
||||
* x = frexp(arg,&exp);
|
||||
* return a double fp quantity x such that 0.5 <= |x| <1.0
|
||||
* and the corresponding binary exponent "exp". That is
|
||||
* arg = x*2^exp.
|
||||
* If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
|
||||
* with *exp=0.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const double
|
||||
two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
|
||||
|
||||
double
|
||||
frexp(double x, int *eptr)
|
||||
{
|
||||
int32_t hx, ix, lx;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
*eptr = 0;
|
||||
if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
|
||||
if (ix<0x00100000) { /* subnormal */
|
||||
x *= two54;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
*eptr = -54;
|
||||
}
|
||||
*eptr += ((uint32_t)ix>>20)-1022;
|
||||
hx = (hx&0x800fffff)|0x3fe00000;
|
||||
SET_HIGH_WORD(x,hx);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,45 @@
|
||||
/* s_frexpf.c -- float version of s_frexp.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_frexpf.c,v 1.10 2007/08/21 20:12:27 drochner Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
two25 = 3.3554432000e+07; /* 0x4c000000 */
|
||||
|
||||
float
|
||||
frexpf(float x, int *eptr)
|
||||
{
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
*eptr = 0;
|
||||
if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */
|
||||
if (ix<0x00800000) { /* subnormal */
|
||||
x *= two25;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
*eptr = -25;
|
||||
}
|
||||
*eptr += (ix>>23)-126;
|
||||
hx = (hx&0x807fffff)|0x3f000000;
|
||||
SET_FLOAT_WORD(x,hx);
|
||||
return x;
|
||||
}
|
||||
@@ -0,0 +1,48 @@
|
||||
/* @(#)s_ilogb.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_ilogb.c,v 1.12 2002/05/26 22:01:56 wiz Exp $");
|
||||
#endif
|
||||
|
||||
/* ilogb(double x)
|
||||
* return the binary exponent of non-zero x
|
||||
* ilogb(0) = 0x80000001
|
||||
* ilogb(inf/NaN) = 0x7fffffff (no signal is raised)
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
int
|
||||
ilogb(double x)
|
||||
{
|
||||
int32_t hx,lx,ix;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
hx &= 0x7fffffff;
|
||||
if(hx<0x00100000) {
|
||||
GET_LOW_WORD(lx,x);
|
||||
if((hx|lx)==0)
|
||||
return 0x80000001; /* ilogb(0) = 0x80000001 */
|
||||
else /* subnormal x */
|
||||
if(hx==0) {
|
||||
for (ix = -1043; lx>0; lx<<=1) ix -=1;
|
||||
} else {
|
||||
for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
|
||||
}
|
||||
return ix;
|
||||
}
|
||||
else if (hx<0x7ff00000) return (hx>>20)-1023;
|
||||
else return 0x7fffffff;
|
||||
}
|
||||
@@ -0,0 +1,40 @@
|
||||
/* s_ilogbf.c -- float version of s_ilogb.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
__RCSID("$NetBSD: s_ilogbf.c,v 1.7 2002/05/26 22:01:56 wiz Exp $");
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
int
|
||||
ilogbf(float x)
|
||||
{
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
hx &= 0x7fffffff;
|
||||
if(hx<0x00800000) {
|
||||
if(hx==0)
|
||||
return 0x80000001; /* ilogb(0) = 0x80000001 */
|
||||
else /* subnormal x */
|
||||
for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1;
|
||||
return ix;
|
||||
}
|
||||
else if (hx<0x7f800000) return (hx>>23)-127;
|
||||
else return 0x7fffffff;
|
||||
}
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user