Patchwork New generic cosf

login
register
mail settings
Submitter Paul Clarke
Date Dec. 5, 2017, 8:45 p.m.
Message ID <72875dc7-0d21-17e6-3802-4cca20b62371@us.ibm.com>
Download mbox | patch
Permalink /patch/24748/
State New
Headers show

Comments

Paul Clarke - Dec. 5, 2017, 8:45 p.m.
From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
From: "Paul A. Clarke" <pc@us.ibm.com>
Date: Tue, 5 Dec 2017 09:32:56 -0600
Subject: [PATCH] New generic cosf

The same logic used in s_cosf.S version for x86 and powerpc
is used to create a generic s_cosf.c, so there is no performance
improvement in x86_64 and powerpc64.

-- 8< --
For s390, this is the improvement noted.

With patch:
  "cosf": {
   "": {
    "duration": 1.00479e+10,
    "iterations": 1.53856e+08,
    "max": 900.645,
    "min": 4.264,
    "mean": 65.3074
   }
  }
Without patch:
  "cosf": {
   "": {
    "duration": 9.93841e+09,
    "iterations": 4.63972e+08,
    "max": 1010.9,
    "min": 6.593,
    "mean": 21.4203
   }
  }

Tested on s390x, x86_64 and powerpc64le and powerpc32.

I include below a diff with recent generic s_sinf.c, as it is more
instructive than a diff with existing s_cosf.c.  There are a fair number
of cosmetic changes, a few hard differences because it's a different
computation, and adoption of changes from recent patches deemed acceptable.
--
1c1
< /* Compute sine of argument.
---
> /* Compute cosine of argument.
24,25c24,25
< #ifndef SINF
< # define SINF_FUNC __sinf
---
> #ifndef COSF
> # define COSF_FUNC __cosf
27c27
< # define SINF_FUNC SINF
---
> # define COSF_FUNC COSF
44,46c44,46
< /* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
< static const double SS0 = -0x1.555555543d49dp-3;
< static const double SS1 =  0x1.110f475cec8c5p-7;
---
> /* Chebyshev constants for cos, range 2^-27 - 2^-5.  */
> static const double CC0 = -0x1.fffffff5cc6fdp-2;
> static const double CC1 =  0x1.55514b178dac5p-5;
52d51
< static const double SMALL = 0x1p-50; /* 2^-50.  */
78c77
< static const int ones[] = { +1, -1 };
---
> static const double ones[] = { +1, -1 };
80c79
< /* Compute the sine value using Chebyshev polynomials where
---
> /* Compute the cosine value using Chebyshev polynomials where
85,86c84
<    SIGNBIT is used to add the correct sign after the Chebyshev
<    polynomial is computed.  */
---
>    the sign of the result.  */
88,89c86
< reduced (const double theta, const unsigned long int n,
< 	 const unsigned long int signbit)
---
> reduced (double theta, unsigned int n)
91c88
<   double sx;
---
>   double sign, cx;
93,95c90
<   /* We are operating on |x|, so we need to add back the original
<      signbit for sinf.  */
<   int sign;
---
>
97c92,94
<   sign = ones[((n >> 2) & 1) ^ signbit];
---
>   n += 2;
>   sign = ones[(n >> 2) & 1];
>
101c98
<       /* Here sinf() is calculated using sin Chebyshev polynomial:
---
>       /* Here cosf() is calculated using sin Chebyshev polynomial:
103,107c100,104
<       sx = S3 + theta2 * S4;     /* S3+x^2*S4.  */
<       sx = S2 + theta2 * sx;     /* S2+x^2*(S3+x^2*S4).  */
<       sx = S1 + theta2 * sx;     /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */
<       sx = S0 + theta2 * sx;     /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */
<       sx = theta + theta * theta2 * sx;
---
>       cx = S3 + theta2 * S4;
>       cx = S2 + theta2 * cx;
>       cx = S1 + theta2 * cx;
>       cx = S0 + theta2 * cx;
>       cx = theta + theta * theta2 * cx;
111c108
<      /* Here sinf() is calculated using cos Chebyshev polynomial:
---
>      /* Here cosf() is calculated using cos Chebyshev polynomial:
113,117c110,114
<       sx = C3 + theta2 * C4;     /* C3+x^2*C4.  */
<       sx = C2 + theta2 * sx;     /* C2+x^2*(C3+x^2*C4).  */
<       sx = C1 + theta2 * sx;     /* C1+x^2*(C2+x^2*(C3+x^2*C4)).  */
<       sx = C0 + theta2 * sx;     /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))).  */
<       sx = 1.0 + theta2 * sx;
---
>       cx = C3 + theta2 * C4;
>       cx = C2 + theta2 * cx;
>       cx = C1 + theta2 * cx;
>       cx = C0 + theta2 * cx;
>       cx = 1. + theta2 * cx;
119,121c116
<
<   /* Add in the signbit and assign the result.  */
<   return sign * sx;
---
>   return sign * cx;
125c120
< SINF_FUNC (float x)
---
> COSF_FUNC (float x)
127d121
<   double cx;
130,131c124
<   /* If |x|< Pi/4.  */
<   if (abstheta < M_PI_4)
---
>   if (isless (abstheta, M_PI_4))
133c126,127
<       if (abstheta >= 0x1p-5) /* |x| >= 2^-5.  */
---
>       double cx;
>       if (abstheta >= 0x1p-5)
136,142c130,136
< 	  /* Chebyshev polynomial of the form for sin
< 	     x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
< 	  cx = S3 + theta2 * S4;
< 	  cx = S2 + theta2 * cx;
< 	  cx = S1 + theta2 * cx;
< 	  cx = S0 + theta2 * cx;
< 	  cx = theta + theta * theta2 * cx;
---
> 	  /* Chebyshev polynomial of the form for cos:
> 	   * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))).  */
> 	  cx = C3 + theta2 * C4;
> 	  cx = C2 + theta2 * cx;
> 	  cx = C1 + theta2 * cx;
> 	  cx = C0 + theta2 * cx;
> 	  cx = 1. + theta2 * cx;
145c139
<       else if (abstheta >= 0x1p-27)     /* |x| >= 2^-27.  */
---
>       else if (abstheta >= 0x1p-27)
148c142
< 	     for sin: x+x^3*(SS0+x^2*SS1).  */
---
> 	   * 1 + x^2 (CC0 + x^3 * CC1).  */
150,151c144,145
< 	  cx = SS0 + theta2 * SS1;
< 	  cx = theta + theta * theta2 * cx;
---
> 	  cx = CC0 + theta * theta2 * CC1;
> 	  cx = 1.0 + theta2 * cx;
156,160c150,151
< 	  /* Handle some special cases.  */
< 	  if (theta)
< 	    return theta - (theta * SMALL);
< 	  else
< 	    return theta;
---
> 	  /* For small enough |theta|, this is close enough.  */
> 	  return 1.0 - abstheta;
163c154
<   else                          /* |x| >= Pi/4.  */
---
>   else /* |theta| >= Pi/4.  */
165,166c156
<       unsigned long int signbit = (x < 0);
<       if (abstheta < 9 * M_PI_4)        /* |x| < 9*Pi/4.  */
---
>       if (isless (abstheta, 9 * M_PI_4))
172c162
< 	  unsigned long int n = (abstheta * inv_PI_4) + 1;
---
> 	  unsigned int n = (abstheta * inv_PI_4) + 1;
174c164
< 	  return reduced (theta, n, signbit);
---
> 	  return reduced (theta, n);
178c168
< 	  if (abstheta < 0x1p+23)     /* |x| < 2^23.  */
---
> 	  if (abstheta < 0x1p+23)
180,181c170,171
< 	      unsigned long int n = __floor (abstheta * inv_PI_4) + 1.0;
< 	      double x = __floor (n / 2.0);
---
> 	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
> 	      double x = n / 2.0;
184c174
< 	      return reduced (theta, n, signbit);
---
> 	      return reduced (theta, n);
186c176
< 	  else                  /* |x| >= 2^23.  */
---
> 	  else /* |theta| >= 2^23.  */
191,192c181,182
< 	      exponent
< 	        = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
---
> 	      exponent = (exponent >> FLOAT_EXPONENT_SHIFT)
> 			 - FLOAT_EXPONENT_BIAS;
212c202
< 	          return reduced (e, l + 1, signbit);
---
> 		  return reduced (e, l + 1);
222c212
< 		      return reduced (e, l + 1, signbit);
---
> 		      return reduced (e, l + 1);
229c219
< 		      return reduced (e, l + 1, signbit);
---
> 		      return reduced (e, l + 1);
237d226
< 	  /* High word of x.  */
239,240c228,229
< 	  /* Sin(Inf or NaN) is NaN.  */
< 	  if (ix == 0x7f800000)
---
> 	  /* cos(Inf or NaN) is NaN.  */
> 	  if (ix == 0x7f800000) /* Inf.  */
247,248c236,237
< #ifndef SINF
< libm_alias_float (__sin, sin)
---
> #ifndef COSF
> libm_alias_float (__cos, cos)
-- 8< --

2017-12-05  Paul A. Clarke  <pc@us.ibm.com>

	* sysdeps/ieee754/flt-32/s_cosf.c: New implementation.
---
 sysdeps/ieee754/flt-32/s_cosf.c | 254 +++++++++++++++++++++++++++++++++-------
 1 file changed, 214 insertions(+), 40 deletions(-)
H.J. Lu - Dec. 5, 2017, 8:49 p.m.
On Tue, Dec 5, 2017 at 12:45 PM, Paul Clarke <pc@us.ibm.com> wrote:
> From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
> From: "Paul A. Clarke" <pc@us.ibm.com>
> Date: Tue, 5 Dec 2017 09:32:56 -0600
> Subject: [PATCH] New generic cosf
>
> The same logic used in s_cosf.S version for x86 and powerpc
> is used to create a generic s_cosf.c, so there is no performance
> improvement in x86_64 and powerpc64.
>
> -- 8< --
> For s390, this is the improvement noted.
>
> With patch:
>   "cosf": {
>    "": {
>     "duration": 1.00479e+10,
>     "iterations": 1.53856e+08,
>     "max": 900.645,
>     "min": 4.264,
>     "mean": 65.3074
>    }
>   }
> Without patch:
>   "cosf": {
>    "": {
>     "duration": 9.93841e+09,
>     "iterations": 4.63972e+08,
>     "max": 1010.9,
>     "min": 6.593,
>     "mean": 21.4203
>    }
>   }
>
> Tested on s390x, x86_64 and powerpc64le and powerpc32.
>
> I include below a diff with recent generic s_sinf.c, as it is more
> instructive than a diff with existing s_cosf.c.  There are a fair number
> of cosmetic changes, a few hard differences because it's a different
> computation, and adoption of changes from recent patches deemed acceptable.

1. Please use the current s_sinf.c.
2. Please use "diff -up".
Joseph Myers - Dec. 5, 2017, 9 p.m.
On Tue, 5 Dec 2017, Paul Clarke wrote:

> +	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
> +	      double x = n / 2.0;

I'd expect adding integer 1 and dividing by integer 2, as in the current 
sinf version, unless there's some reason that's incorrect in this case.
Matt Turner - Dec. 6, 2017, 1:11 a.m.
On Tue, Dec 5, 2017 at 12:45 PM, Paul Clarke <pc@us.ibm.com> wrote:
> From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
> From: "Paul A. Clarke" <pc@us.ibm.com>
> Date: Tue, 5 Dec 2017 09:32:56 -0600
> Subject: [PATCH] New generic cosf
>
> The same logic used in s_cosf.S version for x86 and powerpc
> is used to create a generic s_cosf.c, so there is no performance
> improvement in x86_64 and powerpc64.
>
> -- 8< --
> For s390, this is the improvement noted.
>
> With patch:
>   "cosf": {
>    "": {
>     "duration": 1.00479e+10,
>     "iterations": 1.53856e+08,
>     "max": 900.645,
>     "min": 4.264,
>     "mean": 65.3074
>    }
>   }
> Without patch:
>   "cosf": {
>    "": {
>     "duration": 9.93841e+09,
>     "iterations": 4.63972e+08,
>     "max": 1010.9,
>     "min": 6.593,
>     "mean": 21.4203
>    }
>   }

Did I misunderstand, or did the mean time increase with the patch?
Paul Clarke - Dec. 6, 2017, 1:08 p.m.
On 12/05/2017 07:11 PM, Matt Turner wrote:
> On Tue, Dec 5, 2017 at 12:45 PM, Paul Clarke <pc@us.ibm.com> wrote:
>> The same logic used in s_cosf.S version for x86 and powerpc
>> is used to create a generic s_cosf.c, so there is no performance
>> improvement in x86_64 and powerpc64.
>>
>> -- 8< --
>> For s390, this is the improvement noted.
>>
>> With patch:
>>   "cosf": {
>>    "": {
>>     "duration": 1.00479e+10,
>>     "iterations": 1.53856e+08,
>>     "max": 900.645,
>>     "min": 4.264,
>>     "mean": 65.3074
>>    }
>>   }
>> Without patch:
>>   "cosf": {
>>    "": {
>>     "duration": 9.93841e+09,
>>     "iterations": 4.63972e+08,
>>     "max": 1010.9,
>>     "min": 6.593,
>>     "mean": 21.4203
>>    }
>>   }
> 
> Did I misunderstand, or did the mean time increase with the patch?

Sigh. It's not you. I was trying to mimic Raji's patch, but confused her "with/without" with what I'd normally use "before/after".  I'll rectify in V2.

PC

Patch

diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c
index 5ed0bca..301b36e 100644
--- a/sysdeps/ieee754/flt-32/s_cosf.c
+++ b/sysdeps/ieee754/flt-32/s_cosf.c
@@ -1,21 +1,20 @@ 
-/* s_cosf.c -- float version of s_cos.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
-#endif
+/* Compute cosine of argument.
+   Copyright (C) 2017 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
 
 #include <errno.h>
 #include <math.h>
@@ -28,35 +27,210 @@  static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
 # define COSF_FUNC COSF
 #endif
 
-float COSF_FUNC(float x)
+/* Chebyshev constants for cos, range -PI/4 - PI/4.  */
+static const double C0 = -0x1.ffffffffe98aep-2;
+static const double C1 =  0x1.55555545c50c7p-5;
+static const double C2 = -0x1.6c16b348b6874p-10;
+static const double C3 =  0x1.a00eb9ac43ccp-16;
+static const double C4 = -0x1.23c97dd8844d7p-22;
+
+/* Chebyshev constants for sin, range -PI/4 - PI/4.  */
+static const double S0 = -0x1.5555555551cd9p-3;
+static const double S1 =  0x1.1111110c2688bp-7;
+static const double S2 = -0x1.a019f8b4bd1f9p-13;
+static const double S3 =  0x1.71d7264e6b5b4p-19;
+static const double S4 = -0x1.a947e1674b58ap-26;
+
+/* Chebyshev constants for cos, range 2^-27 - 2^-5.  */
+static const double CC0 = -0x1.fffffff5cc6fdp-2;
+static const double CC1 =  0x1.55514b178dac5p-5;
+
+/* PI/2 with 98 bits of accuracy.  */
+static const double PI_2_hi = -0x1.921fb544p+0;
+static const double PI_2_lo = -0x1.0b4611a626332p-34;
+
+static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI.  */
+
+#define FLOAT_EXPONENT_SHIFT 23
+#define FLOAT_EXPONENT_BIAS 127
+
+static const double pio2_table[] = {
+  0 * M_PI_2,
+  1 * M_PI_2,
+  2 * M_PI_2,
+  3 * M_PI_2,
+  4 * M_PI_2,
+  5 * M_PI_2
+};
+
+static const double invpio4_table[] = {
+  0x0p+0,
+  0x1.45f306cp+0,
+  0x1.c9c882ap-28,
+  0x1.4fe13a8p-58,
+  0x1.f47d4dp-85,
+  0x1.bb81b6cp-112,
+  0x1.4acc9ep-142,
+  0x1.0e4107cp-169
+};
+
+static const double ones[] = { +1, -1 };
+
+/* Compute the cosine value using Chebyshev polynomials where
+   THETA is the range reduced absolute value of the input
+   and it is less than Pi/4,
+   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
+   whether a sine or cosine approximation is more accurate and
+   the sign of the result.  */
+static inline float
+reduced (double theta, unsigned int n)
 {
-	float y[2],z=0.0;
-	int32_t n,ix;
+  double sign, cx;
+  const double theta2 = theta * theta;
 
-	GET_FLOAT_WORD(ix,x);
+  /* Determine positive or negative primary interval.  */
+  n += 2;
+  sign = ones[(n >> 2) & 1];
 
-    /* |x| ~< pi/4 */
-	ix &= 0x7fffffff;
-	if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
+  /* Are we in the primary interval of sin or cos?  */
+  if ((n & 2) == 0)
+    {
+      /* Here cosf() is calculated using sin Chebyshev polynomial:
+	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
+      cx = S3 + theta2 * S4;
+      cx = S2 + theta2 * cx;
+      cx = S1 + theta2 * cx;
+      cx = S0 + theta2 * cx;
+      cx = theta + theta * theta2 * cx;
+    }
+  else
+    {
+     /* Here cosf() is calculated using cos Chebyshev polynomial:
+	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
+      cx = C3 + theta2 * C4;
+      cx = C2 + theta2 * cx;
+      cx = C1 + theta2 * cx;
+      cx = C0 + theta2 * cx;
+      cx = 1. + theta2 * cx;
+    }
+  return sign * cx;
+}
 
-    /* cos(Inf or NaN) is NaN */
-	else if (ix>=0x7f800000) {
-	  if (ix == 0x7f800000)
-	    __set_errno (EDOM);
-	  return x-x;
+float
+COSF_FUNC (float x)
+{
+  double theta = x;
+  double abstheta = fabs (theta);
+  if (isless (abstheta, M_PI_4))
+    {
+      double cx;
+      if (abstheta >= 0x1p-5)
+	{
+	  const double theta2 = theta * theta;
+	  /* Chebyshev polynomial of the form for cos:
+	   * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))).  */
+	  cx = C3 + theta2 * C4;
+	  cx = C2 + theta2 * cx;
+	  cx = C1 + theta2 * cx;
+	  cx = C0 + theta2 * cx;
+	  cx = 1. + theta2 * cx;
+	  return cx;
 	}
-
-    /* argument reduction needed */
-	else {
-	    n = __ieee754_rem_pio2f(x,y);
-	    switch(n&3) {
-		case 0: return  __kernel_cosf(y[0],y[1]);
-		case 1: return -__kernel_sinf(y[0],y[1],1);
-		case 2: return -__kernel_cosf(y[0],y[1]);
-		default:
-		        return  __kernel_sinf(y[0],y[1],1);
+      else if (abstheta >= 0x1p-27)
+	{
+	  /* A simpler Chebyshev approximation is close enough for this range:
+	   * 1 + x^2 (CC0 + x^3 * CC1).  */
+	  const double theta2 = theta * theta;
+	  cx = CC0 + theta * theta2 * CC1;
+	  cx = 1.0 + theta2 * cx;
+	  return cx;
+	}
+      else
+	{
+	  /* For small enough |theta|, this is close enough.  */
+	  return 1.0 - abstheta;
+	}
+    }
+  else /* |theta| >= Pi/4.  */
+    {
+      if (isless (abstheta, 9 * M_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];
+	  return reduced (theta, n);
+	}
+      else if (isless (abstheta, INFINITY))
+	{
+	  if (abstheta < 0x1p+23)
+	    {
+	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
+	      double x = n / 2.0;
+	      theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+	      /* Argument reduction needed.  */
+	      return reduced (theta, n);
+	    }
+	  else /* |theta| >= 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;
+		  return reduced (e, l + 1);
+		}
+	      else
+		{
+		  e += b;
+		  e += c;
+		  e += d;
+		  if (e <= 1.0)
+		    {
+		      e *= M_PI_4;
+		      return reduced (e, l + 1);
+		    }
+		  else
+		    {
+		      l++;
+		      e -= 2.0;
+		      e *= M_PI_4;
+		      return reduced (e, l + 1);
+		    }
+		}
 	    }
 	}
+      else
+	{
+	  int32_t ix;
+	  GET_FLOAT_WORD (ix, abstheta);
+	  /* cos(Inf or NaN) is NaN.  */
+	  if (ix == 0x7f800000) /* Inf.  */
+	    __set_errno (EDOM);
+	  return x - x;
+	}
+    }
 }
 
 #ifndef COSF