Fix powerpc software sqrt (bug 17964) [committed]

[Joseph Myers <joseph at codesourcery dot com>]

As Adhemerval noted in
<https://sourceware.org/ml/libc-alpha/2015-01/msg00451.html>, the
powerpc sqrt implementation for when _ARCH_PPCSQ is not defined is
inaccurate in some cases.

The problem is that this code relies on fused multiply-add, and relies
on the compiler contracting a * b + c to get a fused operation.  But
sysdeps/ieee754/dbl-64/Makefile disables contraction for e_sqrt.c,
because the implementation in that directory relies on *not* having
contracted operations.

While it would be possible to arrange makefiles so that an earlier
sysdeps directory can disable the setting in
sysdeps/ieee754/dbl-64/Makefile, it seems a lot cleaner to make the
dependence on fused operations explicit in the .c file.  GCC 4.6
introduced support for __builtin_fma on powerpc and other
architectures with such instructions, so we can rely on that; this
patch duly makes the code use __builtin_fma for all such fused
operations.

Tested for powerpc32 (hard float).  Committed.

2015-02-12  Joseph Myers  <joseph@codesourcery.com>

	[BZ #17964]
	* sysdeps/powerpc/fpu/e_sqrt.c (__slow_ieee754_sqrt): Use
	__builtin_fma instead of relying on contraction of a * b + c.

diff --git a/sysdeps/powerpc/fpu/e_sqrt.c b/sysdeps/powerpc/fpu/e_sqrt.c
index 0934faa..9b55ef8 100644
--- a/sysdeps/powerpc/fpu/e_sqrt.c
+++ b/sysdeps/powerpc/fpu/e_sqrt.c
@@ -99,38 +99,41 @@ __slow_ieee754_sqrt (double x)
 	  /* Here we have three Newton-Raphson iterations each of a
 	     division and a square root and the remainder of the
 	     argument reduction, all interleaved.   */
-	  sd = -(sg * sg - sx);
+	  sd = -__builtin_fma (sg, sg, -sx);
 	  fsgi = (xi0 + 0x40000000) >> 1 & 0x7ff00000;
 	  sy2 = sy + sy;
-	  sg = sy * sd + sg;	/* 16-bit approximation to sqrt(sx). */
+	  sg = __builtin_fma (sy, sd, sg);	/* 16-bit approximation to
+						   sqrt(sx). */
 
 	  /* schedule the INSERT_WORDS (fsg, fsgi, 0) to get separation
 	     between the store and the load.  */
 	  INSERT_WORDS (fsg, fsgi, 0);
 	  iw_u.parts.msw = fsgi;
 	  iw_u.parts.lsw = (0);
-	  e = -(sy * sg - almost_half);
-	  sd = -(sg * sg - sx);
+	  e = -__builtin_fma (sy, sg, -almost_half);
+	  sd = -__builtin_fma (sg, sg, -sx);
 	  if ((xi0 & 0x7ff00000) == 0)
 	    goto denorm;
-	  sy = sy + e * sy2;
-	  sg = sg + sy * sd;	/* 32-bit approximation to sqrt(sx).  */
+	  sy = __builtin_fma (e, sy2, sy);
+	  sg = __builtin_fma (sy, sd, sg);	/* 32-bit approximation to
+						   sqrt(sx).  */
 	  sy2 = sy + sy;
 	  /* complete the INSERT_WORDS (fsg, fsgi, 0) operation.  */
 	  fsg = iw_u.value;
-	  e = -(sy * sg - almost_half);
-	  sd = -(sg * sg - sx);
-	  sy = sy + e * sy2;
+	  e = -__builtin_fma (sy, sg, -almost_half);
+	  sd = -__builtin_fma (sg, sg, -sx);
+	  sy = __builtin_fma (e, sy2, sy);
 	  shx = sx * fsg;
-	  sg = sg + sy * sd;	/* 64-bit approximation to sqrt(sx),
-				   but perhaps rounded incorrectly.  */
+	  sg = __builtin_fma (sy, sd, sg);	/* 64-bit approximation to
+						   sqrt(sx), but perhaps
+						   rounded incorrectly.  */
 	  sy2 = sy + sy;
 	  g = sg * fsg;
-	  e = -(sy * sg - almost_half);
-	  d = -(g * sg - shx);
-	  sy = sy + e * sy2;
+	  e = -__builtin_fma (sy, sg, -almost_half);
+	  d = -__builtin_fma (g, sg, -shx);
+	  sy = __builtin_fma (e, sy2, sy);
 	  fesetenv_register (fe);
-	  return g + sy * d;
+	  return __builtin_fma (sy, d, g);
 	denorm:
 	  /* For denormalised numbers, we normalise, calculate the
 	     square root, and return an adjusted result.  */

-- 
Joseph S. Myers
joseph@codesourcery.com