151 lines
4.5 KiB
C
151 lines
4.5 KiB
C
/* @(#)s_sincos.c 5.1 13/07/15 */
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/*
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* ====================================================
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* Copyright (C) 2013 Elliot Saba. All rights reserved.
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*
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* Developed at the University of Washington.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "cdefs-compat.h"
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/* sincos(x, s, c)
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* Several applications need sine and cosine of the same
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* angle x. This function computes both at the same time,
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* and stores the results in *sin and *cos.
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*
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* kernel function:
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* __kernel_sin ... sine function on [-pi/4,pi/4]
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* __kernel_cos ... cose function on [-pi/4,pi/4]
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* __ieee754_rem_pio2 ... argument reduction routine
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*
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* Method.
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* Borrow liberally from s_sin.c and s_cos.c, merging
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* efforts where applicable and returning their values in
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* appropriate variables, thereby slightly reducing the
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* amount of work relative to just calling sin/cos(x)
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* separately
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*
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* Special cases:
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* Let trig be any of sin, cos, or tan.
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* sincos(+-INF, s, c) is NaN, with signals;
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* sincos(NaN, s, c) is that NaN;
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*/
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#include <float.h>
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#include <openlibm_math.h>
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//#define INLINE_REM_PIO2
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#include "math_private.h"
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//#include "e_rem_pio2.c"
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/* Constants used in polynomial approximation of sin/cos */
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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S6 = 1.58969099521155010221e-10, /* 0x3DE5D93A, 0x5ACFD57C */
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C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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static void
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__kernel_sincos( double x, double y, int iy, double * k_s, double * k_c )
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{
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/* Inline calculation of sin/cos, as we can save
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some work, and we will always need to calculate
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both values, no matter the result of switch */
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double z, w, r, v, hz;
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z = x*x;
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w = z*z;
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/* cos-specific computation; equivalent to calling
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__kernel_cos(x,y) and storing in k_c*/
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r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6));
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hz = 0.5*z;
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v = one-hz;
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*k_c = v + (((one-v)-hz) + (z*r-x*y));
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/* sin-specific computation; equivalent to calling
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__kernel_sin(x,y,1) and storing in k_s*/
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r = S2+z*(S3+z*S4) + z*w*(S5+z*S6);
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v = z*x;
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if(iy == 0)
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*k_s = x+v*(S1+z*r);
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else
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*k_s = x-((z*(half*y-v*r)-y)-v*S1);
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}
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OLM_DLLEXPORT void
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sincos(double x, double * s, double * c)
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{
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double y[2];
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int32_t ix;
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/* Store high word of x in ix */
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GET_HIGH_WORD(ix,x);
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/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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if(ix <= 0x3fe921fb) {
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/* Check for small x for sin and cos */
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if(ix<0x3e46a09e) {
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/* Check for exact zero */
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if( (int)x==0 ) {
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*s = x;
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*c = 1.0;
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return;
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}
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}
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/* Call kernel function with 0 extra */
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__kernel_sincos(x,0.0,0, s, c);
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} else if( ix >= 0x7ff00000 ) {
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/* sincos(Inf or NaN) is NaN */
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*s = x-x;
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*c = x-x;
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}
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/*argument reduction needed*/
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else {
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double k_c, k_s;
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/* Calculate remainer, then sub out to kernel */
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int32_t n = __ieee754_rem_pio2(x,y);
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__kernel_sincos( y[0], y[1], 1, &k_s, &k_c );
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/* Figure out permutation of sin/cos outputs to true outputs */
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switch(n&3) {
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case 0:
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*c = k_c;
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*s = k_s;
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break;
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case 1:
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*c = -k_s;
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*s = k_c;
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break;
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case 2:
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*c = -k_c;
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*s = -k_s;
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break;
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default:
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*c = k_s;
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*s = -k_c;
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break;
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}
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}
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}
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#if (LDBL_MANT_DIG == 53)
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openlibm_weak_reference(sincos, sincosl);
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#endif
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