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Libm: add 32-bit variant of fmod() function.

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This commit is contained in:
Serge Vakulenko
2015-11-06 20:40:45 -08:00
parent c46bd3c1e9
commit 03ed62db5d
1 changed files with 201 additions and 70 deletions
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271
src/libm/fmod.c
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@@ -12,7 +12,7 @@ typedef union {
/*
* Get two 32 bit ints from a double.
*/
#define EXTRACT_WORDS(high,low,d) {\
#define UNPACK_DOUBLE(high,low,d) {\
union64_t u = {0}; \
u.value = d; \
high = u.uns.hi; \
@@ -22,116 +22,247 @@ typedef union {
/*
* Set a double from two 32 bit ints.
*/
#define INSERT_WORDS(d,high,low) { \
#define PACK_DOUBLE(d,high,low) { \
union64_t u = {0}; \
u.uns.hi = high; \
u.uns.lo = low; \
d = u.value; \
}
typedef union {
float value;
uint32_t word;
} union32_t;
/*
* Get two 32 bit ints from a double.
*/
#define UNPACK_FLOAT(w,f) {\
union32_t u = {0}; \
u.value = f; \
w = u.word; \
}
/*
* Set a double from two 32 bit ints.
*/
#define PACK_FLOAT(f,w) { \
union32_t u = {0}; \
u.word = w; \
f = u.value; \
}
static const double one = 1.0, Zero[] = {0.0, -0.0,};
double fmod(double x, double y)
{
int32_t n=0,hx=0,hy=0,hz=0,ix=0,iy=0,sx=0,i=0;
uint32_t lx=0,ly=0,lz=0;
int32_t n=0, hx=0, hy=0, hz=0, ix=0, iy=0, sx=0, i=0;
EXTRACT_WORDS(hx,lx,x);
EXTRACT_WORDS(hy,ly,y);
sx = hx&0x80000000; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
if (sizeof(float) == sizeof(double)) {
/*
* Double is 32-bit.
*/
UNPACK_FLOAT(hx,x);
UNPACK_FLOAT(hy,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[(uint32_t)sx>>31]; /* |x|=|y| return x*0*/
/* 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[(uint32_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;
}
/* determine ix = ilogb(x) */
if(hx<0x00100000) { /* subnormal x */
if(hx==0) {
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
/* fix point fmod */
n = ix - iy;
while (n--) {
hz = hx - hy;
if (hz < 0) {
hx = hx + hx;
} else {
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
if (hz == 0) /* return sign(x)*0 */
return Zero[(uint32_t)sx >> 31];
hx = hz + hz;
}
} else ix = (hx>>20)-1023;
}
hz = hx - hy;
if (hz >= 0) {
hx = hz;
}
/* determine iy = ilogb(y) */
if(hy<0x00100000) { /* subnormal y */
/* convert back to floating value and restore the sign */
if (hx == 0) /* return sign(x)*0 */
return Zero[(uint32_t)sx >> 31];
while (hx < 0x00800000) { /* normalize x */
hx = hx + hx;
iy -= 1;
}
if (iy >= -126) { /* normalize output */
hx = (hx - 0x00800000) | ((iy + 127) << 23);
PACK_FLOAT(x, hx | sx);
} else { /* subnormal output */
n = -126 - iy;
hx >>= n;
PACK_FLOAT(x, hx | sx);
x *= one; /* create necessary signal */
}
} else {
/*
* Double is 64-bit.
*/
uint32_t lx=0, ly=0, lz=0;
UNPACK_DOUBLE(hx, lx, x);
UNPACK_DOUBLE(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[(uint32_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;
for (iy = -1043, i=ly; i>0; i<<=1)
iy -= 1;
} else {
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
for (iy = -1022,i=(hy<<11); i>0; i<<=1)
iy -= 1;
}
} else iy = (hy>>20)-1023;
} 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));
/* 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);
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));
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);
hy = ly << (n - 32);
ly = 0;
}
}
/* fix point fmod */
/* 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[(uint32_t)sx>>31];
hx = hz+hz+(lz>>31); lx = lz+lz;
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[(uint32_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;}
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[(uint32_t)sx>>31];
while(hx<0x00100000) { /* normalize x */
hx = hx+hx+(lx>>31); lx = lx+lx;
/* convert back to floating value and restore the sign */
if ((hx | lx) == 0) /* return sign(x)*0 */
return Zero[(uint32_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 */
if (iy >= -1022) { /* normalize output */
hx = (hx - 0x00100000) | ((iy + 1023) << 20);
PACK_DOUBLE(x, hx | sx, lx);
} else { /* subnormal output */
n = -1022 - iy;
if(n<=20) {
lx = (lx>>n)|((uint32_t)hx<<(32-n));
if (n <= 20) {
lx = (lx >> n) | ((uint32_t)hx << (32 - n));
hx >>= n;
} else if (n<=31) {
lx = (hx<<(32-n))|(lx>>n); hx = sx;
} else if (n <= 31) {
lx = (hx << (32 - n)) | (lx >> n);
hx = sx;
} else {
lx = hx>>(n-32); hx = sx;
lx = hx >> (n - 32);
hx = sx;
}
INSERT_WORDS(x,hx|sx,lx);
x *= one; /* create necessary signal */
PACK_DOUBLE(x, hx | sx, lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
return x; /* exact output */
}