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/*
* Copyright (c) 2006-2021, RT-Thread Development Team
*
* SPDX-License-Identifier: Apache-2.0
*
* Change Logs:
* Date Author Notes
*/
#include <math.h>
/*
* COPYRIGHT: See COPYING in the top level directory
* PROJECT: ReactOS CRT
* FILE: lib/crt/math/cos.c
* PURPOSE: Generic C Implementation of cos
* PROGRAMMER: Timo Kreuzer ([email protected])
*/
#define PRECISION 9
static double cos_off_tbl[] = {0.0, -M_PI/2., 0, -M_PI/2.};
static double cos_sign_tbl[] = {1,-1,-1,1};
static double sin_off_tbl[] = {0.0, -M_PI/2., 0, -M_PI/2.};
static double sin_sign_tbl[] = {1,-1,-1,1};
double sin(double x)
{
int quadrant;
double x2, result;
/* Calculate the quadrant */
quadrant = x * (2./M_PI);
/* Get offset inside quadrant */
x = x - quadrant * (M_PI/2.);
/* Normalize quadrant to [0..3] */
quadrant = (quadrant - 1) & 0x3;
/* Fixup value for the generic function */
x += sin_off_tbl[quadrant];
/* Calculate the negative of the square of x */
x2 = - (x * x);
/* This is an unrolled taylor series using <PRECISION> iterations
* Example with 4 iterations:
* result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
* To save multiplications and to keep the precision high, it's performed
* like this:
* result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
*/
/* Start with 0, compiler will optimize this away */
result = 0;
#if (PRECISION >= 10)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
result *= x2;
#endif
#if (PRECISION >= 9)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
result *= x2;
#endif
#if (PRECISION >= 8)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
result *= x2;
#endif
#if (PRECISION >= 7)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
result *= x2;
#endif
#if (PRECISION >= 6)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
result *= x2;
#endif
#if (PRECISION >= 5)
result += 1./(1.*2*3*4*5*6*7*8*9*10);
result *= x2;
#endif
result += 1./(1.*2*3*4*5*6*7*8);
result *= x2;
result += 1./(1.*2*3*4*5*6);
result *= x2;
result += 1./(1.*2*3*4);
result *= x2;
result += 1./(1.*2);
result *= x2;
result += 1;
/* Apply correct sign */
result *= sin_sign_tbl[quadrant];
return result;
}
double cos(double x)
{
int quadrant;
double x2, result;
/* Calculate the quadrant */
quadrant = x * (2./M_PI);
/* Get offset inside quadrant */
x = x - quadrant * (M_PI/2.);
/* Normalize quadrant to [0..3] */
quadrant = quadrant & 0x3;
/* Fixup value for the generic function */
x += cos_off_tbl[quadrant];
/* Calculate the negative of the square of x */
x2 = - (x * x);
/* This is an unrolled taylor series using <PRECISION> iterations
* Example with 4 iterations:
* result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
* To save multiplications and to keep the precision high, it's performed
* like this:
* result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
*/
/* Start with 0, compiler will optimize this away */
result = 0;
#if (PRECISION >= 10)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
result *= x2;
#endif
#if (PRECISION >= 9)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
result *= x2;
#endif
#if (PRECISION >= 8)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
result *= x2;
#endif
#if (PRECISION >= 7)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
result *= x2;
#endif
#if (PRECISION >= 6)
result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
result *= x2;
#endif
#if (PRECISION >= 5)
result += 1./(1.*2*3*4*5*6*7*8*9*10);
result *= x2;
#endif
result += 1./(1.*2*3*4*5*6*7*8);
result *= x2;
result += 1./(1.*2*3*4*5*6);
result *= x2;
result += 1./(1.*2*3*4);
result *= x2;
result += 1./(1.*2);
result *= x2;
result += 1;
/* Apply correct sign */
result *= cos_sign_tbl[quadrant];
return result;
}
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