261 lines
4.9 KiB
C
261 lines
4.9 KiB
C
#include <math.h>
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/*
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* COPYRIGHT: See COPYING in the top level directory
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* PROJECT: ReactOS CRT
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* FILE: lib/crt/math/cos.c
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* PURPOSE: Generic C Implementation of cos
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* PROGRAMMER: Timo Kreuzer (timo.kreuzer@reactos.org)
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*/
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#define PRECISION 9
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static double cos_off_tbl[] = {0.0, -M_PI/2., 0, -M_PI/2.};
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static double cos_sign_tbl[] = {1,-1,-1,1};
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static double sin_off_tbl[] = {0.0, -M_PI/2., 0, -M_PI/2.};
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static double sin_sign_tbl[] = {1,-1,-1,1};
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double sin(double x)
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{
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int quadrant;
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double x2, result;
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/* Calculate the quadrant */
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quadrant = x * (2./M_PI);
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/* Get offset inside quadrant */
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x = x - quadrant * (M_PI/2.);
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/* Normalize quadrant to [0..3] */
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quadrant = (quadrant - 1) & 0x3;
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/* Fixup value for the generic function */
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x += sin_off_tbl[quadrant];
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/* Calculate the negative of the square of x */
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x2 = - (x * x);
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/* This is an unrolled taylor series using <PRECISION> iterations
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* Example with 4 iterations:
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* result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
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* To save multiplications and to keep the precision high, it's performed
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* like this:
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* result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
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*/
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/* Start with 0, compiler will optimize this away */
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result = 0;
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#if (PRECISION >= 10)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
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result *= x2;
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#endif
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#if (PRECISION >= 9)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
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result *= x2;
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#endif
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#if (PRECISION >= 8)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
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result *= x2;
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#endif
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#if (PRECISION >= 7)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
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result *= x2;
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#endif
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#if (PRECISION >= 6)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
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result *= x2;
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#endif
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#if (PRECISION >= 5)
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result += 1./(1.*2*3*4*5*6*7*8*9*10);
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result *= x2;
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#endif
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result += 1./(1.*2*3*4*5*6*7*8);
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result *= x2;
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result += 1./(1.*2*3*4*5*6);
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result *= x2;
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result += 1./(1.*2*3*4);
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result *= x2;
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result += 1./(1.*2);
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result *= x2;
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result += 1;
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/* Apply correct sign */
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result *= sin_sign_tbl[quadrant];
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return result;
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}
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double cos(double x)
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{
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int quadrant;
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double x2, result;
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/* Calculate the quadrant */
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quadrant = x * (2./M_PI);
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/* Get offset inside quadrant */
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x = x - quadrant * (M_PI/2.);
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/* Normalize quadrant to [0..3] */
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quadrant = quadrant & 0x3;
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/* Fixup value for the generic function */
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x += cos_off_tbl[quadrant];
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/* Calculate the negative of the square of x */
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x2 = - (x * x);
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/* This is an unrolled taylor series using <PRECISION> iterations
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* Example with 4 iterations:
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* result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
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* To save multiplications and to keep the precision high, it's performed
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* like this:
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* result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
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*/
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/* Start with 0, compiler will optimize this away */
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result = 0;
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#if (PRECISION >= 10)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
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result *= x2;
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#endif
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#if (PRECISION >= 9)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
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result *= x2;
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#endif
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#if (PRECISION >= 8)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
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result *= x2;
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#endif
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#if (PRECISION >= 7)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
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result *= x2;
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#endif
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#if (PRECISION >= 6)
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result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
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result *= x2;
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#endif
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#if (PRECISION >= 5)
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result += 1./(1.*2*3*4*5*6*7*8*9*10);
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result *= x2;
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#endif
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result += 1./(1.*2*3*4*5*6*7*8);
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result *= x2;
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result += 1./(1.*2*3*4*5*6);
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result *= x2;
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result += 1./(1.*2*3*4);
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result *= x2;
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result += 1./(1.*2);
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result *= x2;
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result += 1;
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/* Apply correct sign */
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result *= cos_sign_tbl[quadrant];
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return result;
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}
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static const int N = 100;
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double coef(int n)
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{
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double t;
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if (n == 0)
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{
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return 0;
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}
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t = 1.0/n;
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if (n%2 == 0)
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{
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t = -t;
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}
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return t;
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}
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double horner(double x)
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{
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double u = coef(N);
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int i;
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for(i=N-1; i>=0; i--)
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{
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u = u*x + coef(i);
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}
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return u;
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}
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double sqrt(double b)
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{
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double x = 1;
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int step = 0;
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while ((x*x-b<-0.000000000000001 || x*x-b>0.000000000000001) && step<50)
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{
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x = (b/x+x)/2.0;
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step++;
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}
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return x;
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}
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double ln(double x)
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{
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int i;
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if (x > 1.5)
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{
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for(i=0; x>1.25; i++)
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{
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x = sqrt(x);
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}
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return (1<<i)*horner(x-1);
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}
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else if (x<0.7 && x>0)
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{
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for(i=0; x<0.7; i++)
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{
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x = sqrt(x);
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}
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return (1<<i)*horner(x-1);
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}
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else if(x > 0)
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{
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return horner(x-1);
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}
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}
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double exp(double x)
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{
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double sum = 1;
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int i;
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for(i=N; i>0; i--)
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{
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sum /= i;
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sum *= x;
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sum += 1;
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}
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return sum;
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}
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double pow(double m, double n)
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{
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return exp(n*ln(m));
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}
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