118 lines
2.4 KiB
Lua
118 lines
2.4 KiB
Lua
-- 3e Essais de faire des fonctions trigos qui manque dans NodeMCU
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-- source pour arctan,arcsin et arccos: http://mathonweb.com/help_ebook/html/algorithms.htm
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-- source pour sin&cos: https://www.esp8266.com/viewtopic.php?p=64415#
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-- source pour arcsin&arctan: http://www.electronicwings.com/nodemcu/magnetometer-hmc5883l-interfacing-with-nodemcu
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print("\ntrigo3.lua zf180819.1745 \n")
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pi = 3.14159265358979323846
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function zsin(x)
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local p=-x*x*x local f=6 local r=x+p/f
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for j=1,60 do
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p=-p*x*x f=f*2*(j+1)*(j+j+3) r=r+p/f
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end
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return r
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end
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function zcos(x)
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return zsin(math.pi/2-x)
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end
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function ztan(x)
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return zsin(x)/zcos(x)
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end
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function zatan(x)
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local y=1 local z
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if x<0 then
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y=-1 x=y*x
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end
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if x<1 then
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z=zzatan(x)
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else
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z=pi/2-zatan(1/x)
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end
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return y*z
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end
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function zzatan(x)
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return x-x^3/3+x^5/5-x^7/7
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end
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--[[
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--print("On voit que l'arc sinus est précis au 1/2% prêt !")
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a=0.9
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print("théorique tan("..a.."): "..math.tan(a))
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print("calculée tan("..a.."): "..ztan(a))
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b=math.tan(a)
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print("théorique atan("..b.."): "..math.atan(b))
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print("calculée atan("..b.."): "..zatan(b)..", "..pi/2-zatan(1/b))
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--print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
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]]
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--[[
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print("On voit que l'arc sinus est précis au 1/2% prêt !")
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print("sin(3.14/2): "..sin(3.14/2))
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print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
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]]
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--[[
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function arcsin(value)
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local val = value
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local sum = value
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if(value == nil) then
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return 0
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end
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-- as per equation it needs infinite iterations to reach upto 100% accuracy
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-- but due to technical limitations we are using
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-- only 10000 iterations to acquire reliable accuracy
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for i = 1,10000, 2 do
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val = (val*(value*value)*(i*i)) / ((i+1)*(i+2))
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sum = sum + val;
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end
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return sum
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end
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function arctan(value)
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if(value == nil) then
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return 0
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end
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local _value = value/math.sqrt((value*value)+1)
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return arcsin(_value)
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end
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function atan2(y, x)
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if(x == nil or y == nil) then
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return 0
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end
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if(x > 0) then
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return arctan(y/x)
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end
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if(x < 0 and 0 <= y) then
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return arctan(y/x) + pi
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end
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if(x < 0 and y < 0) then
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return arctan(y/x) - pi
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end
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if(x == 0 and y > 0) then
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return pi/2
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end
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if(x == 0 and y < 0) then
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return -pi/2
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end
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if(x == 0 and y == 0) then
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return 0
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end
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return 0
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end
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]]
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