[glibc/maskray/grte] [PATCH 7/7] sin/cos slow paths: refactor sincos implementation

[Fangrui Song <maskray@sourceware.org>]

https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=2d20ffe431ddd299b50ba250fce43285b9617d31

commit 2d20ffe431ddd299b50ba250fce43285b9617d31
Author: Wilco Dijkstra <wdijkstr@arm.com>
Date:   Tue Apr 3 16:49:33 2018 +0100

    [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.

Diff:
---
 sysdeps/ieee754/dbl-64/s_sin.c    | 29 ++---------------
 sysdeps/ieee754/dbl-64/s_sincos.c | 68 ++++++++++++++++++++++++++++-----------
 2 files changed, 52 insertions(+), 45 deletions(-)

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 <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))