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-rw-r--r--sysdeps/powerpc/fpu/e_sqrt.c186
1 files changed, 185 insertions, 1 deletions
diff --git a/sysdeps/powerpc/fpu/e_sqrt.c b/sysdeps/powerpc/fpu/e_sqrt.c
index 9416ea60c8..eb9984d0a1 100644
--- a/sysdeps/powerpc/fpu/e_sqrt.c
+++ b/sysdeps/powerpc/fpu/e_sqrt.c
@@ -1 +1,185 @@
-/* __ieee754_sqrt is in w_sqrt.c  */
+/* Double-precision floating point square root.
+   Copyright (C) 1997, 2002, 2003, 2004 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, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <fenv_libc.h>
+#include <inttypes.h>
+
+#include <sysdep.h>
+#include <ldsodefs.h>
+#include <dl-procinfo.h>
+
+static const double almost_half = 0.5000000000000001;	/* 0.5 + 2^-53 */
+static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 };
+static const ieee_float_shape_type a_inf = {.word = 0x7f800000 };
+static const float two108 = 3.245185536584267269e+32;
+static const float twom54 = 5.551115123125782702e-17;
+extern const float __t_sqrt[1024];
+
+/* The method is based on a description in
+   Computation of elementary functions on the IBM RISC System/6000 processor,
+   P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
+   Basically, it consists of two interleaved Newton-Rhapson approximations,
+   one to find the actual square root, and one to find its reciprocal
+   without the expense of a division operation.   The tricky bit here
+   is the use of the POWER/PowerPC multiply-add operation to get the
+   required accuracy with high speed.
+
+   The argument reduction works by a combination of table lookup to
+   obtain the initial guesses, and some careful modification of the
+   generated guesses (which mostly runs on the integer unit, while the
+   Newton-Rhapson is running on the FPU).  */
+
+#ifdef __STDC__
+double
+__slow_ieee754_sqrt (double x)
+#else
+double
+__slow_ieee754_sqrt (x)
+     double x;
+#endif
+{
+  const float inf = a_inf.value;
+
+  if (x > 0)
+    {
+      /* schedule the EXTRACT_WORDS to get separation between the store
+         and the load.  */
+      ieee_double_shape_type ew_u;
+      ieee_double_shape_type iw_u;
+      ew_u.value = (x);
+      if (x != inf)
+	{
+	  /* Variables named starting with 's' exist in the
+	     argument-reduced space, so that 2 > sx >= 0.5,
+	     1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
+	     Variables named ending with 'i' are integer versions of
+	     floating-point values.  */
+	  double sx;	/* The value of which we're trying to find the
+			   square root.  */
+	  double sg, g;	/* Guess of the square root of x.  */
+	  double sd, d;	/* Difference between the square of the guess and x.  */
+	  double sy;	/* Estimate of 1/2g (overestimated by 1ulp).  */
+	  double sy2;	/* 2*sy */
+	  double e;	/* Difference between y*g and 1/2 (se = e * fsy).  */
+	  double shx;	/* == sx * fsg */
+	  double fsg;	/* sg*fsg == g.  */
+	  fenv_t fe;	/* Saved floating-point environment (stores rounding
+			   mode and whether the inexact exception is
+			   enabled).  */
+	  uint32_t xi0, xi1, sxi, fsgi;
+	  const float *t_sqrt;
+
+	  fe = fegetenv_register ();
+	  /* complete the EXTRACT_WORDS (xi0,xi1,x) operation.  */
+	  xi0 = ew_u.parts.msw;
+	  xi1 = ew_u.parts.lsw;
+	  relax_fenv_state ();
+	  sxi = (xi0 & 0x3fffffff) | 0x3fe00000;
+	  /* schedule the INSERT_WORDS (sx, sxi, xi1) to get separation
+	     between the store and the load.  */
+	  iw_u.parts.msw = sxi;
+	  iw_u.parts.lsw = xi1;
+	  t_sqrt = __t_sqrt + (xi0 >> (52 - 32 - 8 - 1) & 0x3fe);
+	  sg = t_sqrt[0];
+	  sy = t_sqrt[1];
+	  /* complete the INSERT_WORDS (sx, sxi, xi1) operation.  */
+	  sx = iw_u.value;
+
+	  /* Here we have three Newton-Rhapson iterations each of a
+	     division and a square root and the remainder of the
+	     argument reduction, all interleaved.   */
+	  sd = -(sg * sg - sx);
+	  fsgi = (xi0 + 0x40000000) >> 1 & 0x7ff00000;
+	  sy2 = sy + sy;
+	  sg = 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);
+	  if ((xi0 & 0x7ff00000) == 0)
+	    goto denorm;
+	  sy = sy + e * sy2;
+	  sg = sg + sy * sd;	/* 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;
+	  shx = sx * fsg;
+	  sg = sg + sy * sd;	/* 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;
+	  fesetenv_register (fe);
+	  return g + sy * d;
+	denorm:
+	  /* For denormalised numbers, we normalise, calculate the
+	     square root, and return an adjusted result.  */
+	  fesetenv_register (fe);
+	  return __slow_ieee754_sqrt (x * two108) * twom54;
+	}
+    }
+  else if (x < 0)
+    {
+      /* For some reason, some PowerPC32 processors don't implement
+         FE_INVALID_SQRT.  */
+#ifdef FE_INVALID_SQRT
+      feraiseexcept (FE_INVALID_SQRT);
+      if (!fetestexcept (FE_INVALID))
+#endif
+	feraiseexcept (FE_INVALID);
+      x = a_nan.value;
+    }
+  return f_wash (x);
+}
+
+#ifdef __STDC__
+double
+__ieee754_sqrt (double x)
+#else
+double
+__ieee754_sqrt (x)
+     double x;
+#endif
+{
+  double z;
+
+  /* If the CPU is 64-bit we can use the optional FP instructions we.  */
+  if ((GLRO (dl_hwcap) & PPC_FEATURE_64) != 0)
+    {
+      /* Volatile is required to prevent the compiler from moving the 
+         fsqrt instruction above the branch.  */
+      __asm __volatile ("	fsqrt	%0,%1\n"
+				:"=f" (z):"f" (x));
+    }
+  else
+    z = __slow_ieee754_sqrt (x);
+
+  return z;
+}