[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.

ChangeLog

@@ -1,3 +1,10 @@
+2018-04-03  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.
+
 2018-04-03  Wilco Dijkstra  <wdijkstr@arm.com>
 
 	* sysdeps/ieee754/dbl-64/s_sin.c (do_sin): Use TAYLOR_SIN for small

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

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))