From e88ecbbfe836db5b6da809108759de4ca56be5e7 Mon Sep 17 00:00:00 2001 From: Wilco Dijkstra Date: Tue, 3 Apr 2018 16:49:33 +0100 Subject: [PATCH 7/7] sin/cos slow paths: refactor sincos implementation Refactor the sincos implementation - rather than rely on odd partial inlining of preprocessed portions from sin and cos, explicitly write out the cases. This makes sincos much easier to maintain and provides an additional 16-20% speedup between 0 and 2^27. The overall speedup of sincos is 48% over this range. Between 0 and PI it is 66% faster. * sysdeps/ieee754/dbl-64/s_sin.c (__sin): Cleanup ifdefs. (__cos): Likewise. * sysdeps/ieee754/dbl-64/s_sin.c (__sincos): Refactor using the same logic as sin and cos. --- sysdeps/ieee754/dbl-64/s_sin.c | 29 ++--------------- sysdeps/ieee754/dbl-64/s_sincos.c | 68 ++++++++++++++++++++++++++++----------- 2 files changed, 52 insertions(+), 45 deletions(-) (limited to 'sysdeps/ieee754') diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c index 6e261f24bb..ba1dbe27b6 100644 --- a/sysdeps/ieee754/dbl-64/s_sin.c +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -197,27 +197,17 @@ do_sincos (double a, double da, int4 n) /* An ultimate sin routine. Given an IEEE double machine number x */ /* it computes the correctly rounded (to nearest) value of sin(x) */ /*******************************************************************/ -#ifdef IN_SINCOS -static double -#else +#ifndef IN_SINCOS double SECTION -#endif __sin (double x) { -#ifndef IN_SINCOS double t, a, da; mynumber u; int4 k, m, n; double retval = 0; SET_RESTORE_ROUND_53BIT (FE_TONEAREST); -#else - double xx, t, cor; - mynumber u; - int4 k, m; - double retval = 0; -#endif u.x = x; m = u.i[HIGH_HALF]; @@ -242,7 +232,6 @@ __sin (double x) retval = __copysign (do_cos (t, hp1), x); } /* else if (k < 0x400368fd) */ -#ifndef IN_SINCOS /*-------------------------- 2.426265<|x|< 105414350 ----------------------*/ else if (k < 0x419921FB) { @@ -263,7 +252,6 @@ __sin (double x) __set_errno (EDOM); retval = x / x; } -#endif return retval; } @@ -274,27 +262,17 @@ __sin (double x) /* it computes the correctly rounded (to nearest) value of cos(x) */ /*******************************************************************/ -#ifdef IN_SINCOS -static double -#else double SECTION -#endif __cos (double x) { double y, a, da; mynumber u; -#ifndef IN_SINCOS int4 k, m, n; -#else - int4 k, m; -#endif double retval = 0; -#ifndef IN_SINCOS SET_RESTORE_ROUND_53BIT (FE_TONEAREST); -#endif u.x = x; m = u.i[HIGH_HALF]; @@ -320,8 +298,6 @@ __cos (double x) retval = do_sin (a, da); } /* else if (k < 0x400368fd) */ - -#ifndef IN_SINCOS else if (k < 0x419921FB) { /* 2.426265<|x|< 105414350 */ n = reduce_sincos (x, &a, &da); @@ -341,7 +317,6 @@ __cos (double x) __set_errno (EDOM); retval = x / x; /* |x| > 2^1024 */ } -#endif return retval; } @@ -352,3 +327,5 @@ libm_alias_double (__cos, cos) #ifndef __sin libm_alias_double (__sin, sin) #endif + +#endif diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c index 4335ecbba3..c7460371e4 100644 --- a/sysdeps/ieee754/dbl-64/s_sincos.c +++ b/sysdeps/ieee754/dbl-64/s_sincos.c @@ -23,9 +23,7 @@ #include #include -#define __sin __sin_local -#define __cos __cos_local -#define IN_SINCOS 1 +#define IN_SINCOS #include "s_sin.c" void @@ -37,31 +35,63 @@ __sincos (double x, double *sinx, double *cosx) SET_RESTORE_ROUND_53BIT (FE_TONEAREST); u.x = x; - k = 0x7fffffff & u.i[HIGH_HALF]; + k = u.i[HIGH_HALF] & 0x7fffffff; if (k < 0x400368fd) { - *sinx = __sin_local (x); - *cosx = __cos_local (x); - return; - } - if (k < 0x419921FB) - { - double a, da; - int4 n = reduce_sincos (x, &a, &da); - - *sinx = do_sincos (a, da, n); - *cosx = do_sincos (a, da, n + 1); + double a, da, y; + /* |x| < 2^-27 => cos (x) = 1, sin (x) = x. */ + if (k < 0x3e400000) + { + if (k < 0x3e500000) + math_check_force_underflow (x); + *sinx = x; + *cosx = 1.0; + return; + } + /* |x| < 0.855469. */ + else if (k < 0x3feb6000) + { + *sinx = do_sin (x, 0); + *cosx = do_cos (x, 0); + return; + } + /* |x| < 2.426265. */ + y = hp0 - fabs (x); + a = y + hp1; + da = (y - a) + hp1; + *sinx = __copysign (do_cos (a, da), x); + *cosx = do_sin (a, da); return; } + /* |x| < 2^1024. */ if (k < 0x7ff00000) { - double a, da; - int4 n = __branred (x, &a, &da); + double a, da, xx; + unsigned int n; - *sinx = do_sincos (a, da, n); - *cosx = do_sincos (a, da, n + 1); + /* If |x| < 105414350 use simple range reduction. */ + n = k < 0x419921FB ? reduce_sincos (x, &a, &da) : __branred (x, &a, &da); + n = n & 3; + + if (n == 1 || n == 2) + { + a = -a; + da = -da; + } + + if (n & 1) + { + double *temp = cosx; + cosx = sinx; + sinx = temp; + } + + *sinx = do_sin (a, da); + xx = do_cos (a, da); + *cosx = (n & 2) ? -xx : xx; + return; } if (isinf (x)) -- cgit v1.2.3