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https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
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Add in sincos(), an efficient method of computing the sine and cosine of an angle together
This commit is contained in:
Elliot Saba
parent
29af332f36
commit
0cf89fad5d
4 changed files with 388 additions and 44 deletions
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@ -28,9 +28,9 @@ $(CUR_SRCS) = \
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s_nexttowardf.c s_remquo.c s_remquof.c \
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s_rint.c s_rintf.c s_round.c s_roundf.c s_roundl.c \
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s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \
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s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \
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s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \
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s_cpow.c s_cpowf.c s_cpowl.c \
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s_signgam.c s_significand.c s_significandf.c s_sin.c s_sincos.c \
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s_sinf.c s_sincosf.c s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c \
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s_trunc.c s_truncf.c s_cpow.c s_cpowf.c s_cpowl.c \
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w_cabs.c w_cabsf.c w_drem.c w_dremf.c
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ifneq ($(OS), WINNT)
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@ -47,7 +47,7 @@ $(CUR_SRCS) += e_acosl.c e_asinl.c e_atan2l.c e_fmodl.c \
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s_csqrtl.c s_floorl.c s_fmal.c \
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s_frexpl.c s_logbl.c s_nexttoward.c \
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s_remquol.c \
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s_sinl.c s_tanl.c s_truncl.c w_cabsl.c \
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s_sinl.c s_sincosl.c s_tanl.c s_truncl.c w_cabsl.c \
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s_nextafterl.c s_rintl.c s_scalbnl.c
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# s_cbrtl.c
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151
src/s_sincos.c
Normal file
151
src/s_sincos.c
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@ -0,0 +1,151 @@
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/* @(#)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.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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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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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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printf( "bleh?\n");
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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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__weak_reference(sincos, sincosl);
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#endif
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162
src/s_sincosf.c
Normal file
162
src/s_sincosf.c
Normal file
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@ -0,0 +1,162 @@
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/* s_sincosf.c -- float version of s_sincos.c
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*
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* Copyright (C) 2013 Elliot Saba
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* Developed at the University of Washington
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*
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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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#include <float.h>
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#include "openlibm.h"
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//#define INLINE_KERNEL_COSDF
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//#define INLINE_KERNEL_SINDF
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//#define INLINE_REM_PIO2F
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#include "math_private.h"
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//#include "e_rem_pio2f.c"
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//#include "k_cosf.c"
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//#include "k_sinf.c"
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/* Constants used in shortcircuits in sincosf */
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static const double
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sc1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
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sc2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
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sc3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
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sc4pio2 = 4*M_PI_2, /* 0x401921FB, 0x54442D18 */
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/* Constants used in polynomial approximation of sin/cos */
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one = 1.0,
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S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
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S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */
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S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */
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S4 = 0x16cd878c3b46a7.0p-71, /* 0.0000027183114939898219064 */
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C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */
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C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */
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C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */
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C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */
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void
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__kernel_sincosdf( double x, float * s, float * c )
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{
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double r, w, z, v;
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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 = C2+z*C3;
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double k_c = ((one+z*C0) + w*C1) + (w*z)*r;
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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 = S3+z*S4;
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v = z*x;
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double k_s = (x + v*(S1+z*S2)) + v*w*r;
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*c = k_c;
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*s = k_s;
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}
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void
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sincosf(float x, float * s, float * c) {
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// Worst approximation of sin and cos NA
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*s = x;
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*c = x;
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double y;
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float k_c, k_s;
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int32_t n, hx, ix;
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GET_FLOAT_WORD(hx,x);
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ix = hx & 0x7fffffff;
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if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
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if(ix<0x39800000) { /* |x| < 2**-12 */
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/* Check if x is exactly zero */
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if(((int)x)==0) {
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*s = x;
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*c = 1.0f;
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return;
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}
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}
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__kernel_sincosdf(x, s, c);
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return;
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}
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/* |x| ~<= 5*pi/4 */
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if (ix<=0x407b53d1) {
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/* |x| ~<= 3pi/4 */
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if(ix<=0x4016cbe3) {
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if(hx>0) {
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__kernel_sincosdf( sc1pio2 - x, c, s );
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}
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else {
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__kernel_sincosdf( sc1pio2 + x, c, &k_s );
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*s = -k_s;
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}
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} else {
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if(hx>0) {
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__kernel_sincosdf( sc2pio2 - x, s, &k_c );
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*c = -k_c;
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} else {
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__kernel_sincosdf( -sc2pio2 - x, s, &k_c );
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*c = -k_c;
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}
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}
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return;
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}
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/* |x| ~<= 9*pi/4 */
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if(ix<=0x40e231d5) {
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/* |x| ~> 7*pi/4 */
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if(ix<=0x40afeddf) {
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if(hx>0) {
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__kernel_sincosdf( x - sc3pio2, c, &k_s );
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*s = -k_s;
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} else {
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__kernel_sincosdf( x + sc3pio2, &k_c, s );
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*c = -k_c;
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}
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}
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else {
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if( hx > 0 ) {
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__kernel_sincosdf( x - sc4pio2, s, c );
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} else {
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__kernel_sincosdf( x + sc4pio2, s, c );
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}
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}
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return;
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}
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/* cos(Inf or NaN) is NaN */
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else if(ix>=0x7f800000) {
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*c = *s = x-x;
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} else {
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/* general argument reduction needed */
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n = __ieee754_rem_pio2f(x,&y);
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switch(n&3) {
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case 0:
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__kernel_sincosdf( y, s, c );
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break;
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case 1:
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__kernel_sincosdf( -y, c, s );
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break;
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case 2:
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__kernel_sincosdf( -y, s, &k_c);
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*c = -k_c;
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break;
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default:
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__kernel_sincosdf( -y, &k_c, &k_s );
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*c = -k_c;
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*s = -k_s;
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break;
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}
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}
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}
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31
src/s_sincosl.c
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31
src/s_sincosl.c
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/* s_sincosl.c -- long double version of s_sincos.c
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*
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* Copyright (C) 2013 Elliot Saba
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* Developed at the University of Washington
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*
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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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#include <float.h>
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#include "openlibm.h"
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#include "math_private.h"
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#if LDBL_MANT_DIG == 64
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#include "../ld80/e_rem_pio2l.h"
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#elif LDBL_MANT_DIG == 113
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#include "../ld128/e_rem_pio2l.h"
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#else
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#error "Unsupported long double format"
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#endif
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void
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sincosl( long double x, long double * s, long double * c )
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{
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*s = cosl( x );
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*c = sinl( x );
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}
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