From: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
To: "libc-alpha@sourceware.org" <libc-alpha@sourceware.org>
Cc: nd <nd@arm.com>
Subject: [PATCH 7/7] sin/cos slow paths: refactor sincos implementation
Date: Wed, 21 Mar 2018 17:57:00 -0000 [thread overview]
Message-ID: <DB6PR0801MB2053216804EA0B8989EF9F7E83AA0@DB6PR0801MB2053.eurprd08.prod.outlook.com> (raw)
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.
ChangeLog:
2018-03-20 Wilco Dijkstra <wdijkstr@arm.com>
* 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.
--
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index e4a2153bb8d010d72d898c0d08e9253f4173f51d..2fde7713ee340aa8e3ce143db7254d0b57f1ab5d 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 4335ecbba3c9894e61c087ac970b392fa73abfab..c7460371e44a02c99522f265efa7e5e66a121b1e 100644
--- a/sysdeps/ieee754/dbl-64/s_sincos.c
+++ b/sysdeps/ieee754/dbl-64/s_sincos.c
@@ -23,9 +23,7 @@
#include <math_private.h>
#include <libm-alias-double.h>
-#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))
next reply other threads:[~2018-03-21 17:57 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-03-21 17:57 Wilco Dijkstra [this message]
2018-03-22 22:37 ` Joseph Myers
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