170 lines
4.2 KiB
C
170 lines
4.2 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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#define M_PI 3.141592653589793238462643
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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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