New generic sincosf

This implementation is based on generic s_sinf.c and s_cosf.c.
Tested on s390x, powerpc64le and powerpc32.

1 files changed, 129 insertions, 43 deletions

diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c
index 4946a6eb54..c376d205bd 100644
--- a/sysdeps/ieee754/flt-32/s_sincosf.c
+++ b/sysdeps/ieee754/flt-32/s_sincosf.c
@@ -1,7 +1,6 @@
 /* Compute sine and cosine of argument.
-   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+   Copyright (C) 2017 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
-   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
    The GNU C Library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
@@ -19,9 +18,9 @@
 
 #include <errno.h>
 #include <math.h>
-
 #include <math_private.h>
 #include <libm-alias-float.h>
+#include "s_sincosf.h"
 
 #ifndef SINCOSF
 # define SINCOSF_FUNC __sincosf
@@ -32,50 +31,137 @@
 void
 SINCOSF_FUNC (float x, float *sinx, float *cosx)
 {
-  int32_t ix;
-
-  /* High word of x. */
-  GET_FLOAT_WORD (ix, x);
-
-  /* |x| ~< pi/4 */
-  ix &= 0x7fffffff;
-  if (ix <= 0x3f490fd8)
-    {
-      *sinx = __kernel_sinf (x, 0.0, 0);
-      *cosx = __kernel_cosf (x, 0.0);
-    }
-  else if (ix>=0x7f800000)
+  double cx;
+  double theta = x;
+  double abstheta = fabs (theta);
+  /* If |x|< Pi/4.  */
+  if (isless (abstheta, M_PI_4))
     {
-      /* sin(Inf or NaN) is NaN */
-      *sinx = *cosx = x - x;
-      if (ix == 0x7f800000)
-	__set_errno (EDOM);
+      if (abstheta >= 0x1p-5) /* |x| >= 2^-5.  */
+	{
+	  const double theta2 = theta * theta;
+	  /* Chebyshev polynomial of the form for sin and cos.  */
+	  cx = C3 + theta2 * C4;
+	  cx = C2 + theta2 * cx;
+	  cx = C1 + theta2 * cx;
+	  cx = C0 + theta2 * cx;
+	  cx = 1.0 + theta2 * cx;
+	  *cosx = cx;
+	  cx = S3 + theta2 * S4;
+	  cx = S2 + theta2 * cx;
+	  cx = S1 + theta2 * cx;
+	  cx = S0 + theta2 * cx;
+	  cx = theta + theta * theta2 * cx;
+	  *sinx = cx;
+	}
+      else if (abstheta >= 0x1p-27)     /* |x| >= 2^-27.  */
+	{
+	  /* A simpler Chebyshev approximation is close enough for this range:
+	     for sin: x+x^3*(SS0+x^2*SS1)
+	     for cos: 1.0+x^2*(CC0+x^3*CC1).  */
+	  const double theta2 = theta * theta;
+	  cx = CC0 + theta * theta2 * CC1;
+	  cx = 1.0 + theta2 * cx;
+	  *cosx = cx;
+	  cx = SS0 + theta2 * SS1;
+	  cx = theta + theta * theta2 * cx;
+	  *sinx = cx;
+	}
+      else
+	{
+	  /* Handle some special cases.  */
+	  if (theta)
+	    *sinx = theta - (theta * SMALL);
+	  else
+	    *sinx = theta;
+	  *cosx = 1.0 - abstheta;
+	}
     }
-  else
+  else                          /* |x| >= Pi/4.  */
     {
-      /* Argument reduction needed.  */
-      float y[2];
-      int n;
-
-      n = __ieee754_rem_pio2f (x, y);
-      switch (n & 3)
+      unsigned int signbit = isless (x, 0);
+      if (isless (abstheta, 9 * M_PI_4))        /* |x| < 9*Pi/4.  */
+	{
+	  /* There are cases where FE_UPWARD rounding mode can
+	     produce a result of abstheta * inv_PI_4 == 9,
+	     where abstheta < 9pi/4, so the domain for
+	     pio2_table must go to 5 (9 / 2 + 1).  */
+	  unsigned int n = (abstheta * inv_PI_4) + 1;
+	  theta = abstheta - pio2_table[n / 2];
+	  *sinx = reduced_sin (theta, n, signbit);
+	  *cosx = reduced_cos (theta, n);
+	}
+      else if (isless (abstheta, INFINITY))
+	{
+	  if (abstheta < 0x1p+23)     /* |x| < 2^23.  */
+	    {
+	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
+	      double x = n / 2;
+	      theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
+	      /* Argument reduction needed.  */
+	      *sinx = reduced_sin (theta, n, signbit);
+	      *cosx = reduced_cos (theta, n);
+	    }
+	  else                  /* |x| >= 2^23.  */
+	    {
+	      x = fabsf (x);
+	      int exponent;
+	      GET_FLOAT_WORD (exponent, x);
+	      exponent
+	        = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+	      exponent += 3;
+	      exponent /= 28;
+	      double a = invpio4_table[exponent] * x;
+	      double b = invpio4_table[exponent + 1] * x;
+	      double c = invpio4_table[exponent + 2] * x;
+	      double d = invpio4_table[exponent + 3] * x;
+	      uint64_t l = a;
+	      l &= ~0x7;
+	      a -= l;
+	      double e = a + b;
+	      l = e;
+	      e = a - l;
+	      if (l & 1)
+	        {
+	          e -= 1.0;
+	          e += b;
+	          e += c;
+	          e += d;
+	          e *= M_PI_4;
+		  *sinx = reduced_sin (e, l + 1, signbit);
+		  *cosx = reduced_cos (e, l + 1);
+	        }
+	      else
+		{
+		  e += b;
+		  e += c;
+		  e += d;
+		  if (e <= 1.0)
+		    {
+		      e *= M_PI_4;
+		      *sinx = reduced_sin (e, l + 1, signbit);
+		      *cosx = reduced_cos (e, l + 1);
+		    }
+		  else
+		    {
+		      l++;
+		      e -= 2.0;
+		      e *= M_PI_4;
+		      *sinx = reduced_sin (e, l + 1, signbit);
+		      *cosx = reduced_cos (e, l + 1);
+		    }
+		}
+	    }
+	}
+      else
 	{
-	case 0:
-	  *sinx = __kernel_sinf (y[0], y[1], 1);
-	  *cosx = __kernel_cosf (y[0], y[1]);
-	  break;
-	case 1:
-	  *sinx = __kernel_cosf (y[0], y[1]);
-	  *cosx = -__kernel_sinf (y[0], y[1], 1);
-	  break;
-	case 2:
-	  *sinx = -__kernel_sinf (y[0], y[1], 1);
-	  *cosx = -__kernel_cosf (y[0], y[1]);
-	  break;
-	default:
-	  *sinx = -__kernel_cosf (y[0], y[1]);
-	  *cosx = __kernel_sinf (y[0], y[1], 1);
-	  break;
+	  int32_t ix;
+	  /* High word of x.  */
+	  GET_FLOAT_WORD (ix, abstheta);
+	  /* sin/cos(Inf or NaN) is NaN.  */
+	  *sinx = *cosx = x - x;
+	  if (ix == 0x7f800000)
+	    __set_errno (EDOM);
 	}
     }
 }