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-rw-r--r--sysdeps/powerpc/w_sqrt.c141
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+/* Single-precision floating point square root.
+   Copyright (C) 1997 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 Library General Public License as
+   published by the Free Software Foundation; either version 2 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
+   Library General Public License for more details.
+
+   You should have received a copy of the GNU Library General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  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>
+
+static const double almost_half = 0.5000000000000001;  /* 0.5 + 2^-53 */
+static const uint32_t a_nan = 0x7fc00000;
+static const uint32_t a_inf = 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).  */
+double
+__sqrt(double x)
+{
+  const float inf = *(const float *)&a_inf;
+  /* x = f_wash(x); *//* This ensures only one exception for SNaN. */
+  if (x > 0)
+    {
+      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();
+	  EXTRACT_WORDS (xi0,xi1,x);
+	  relax_fenv_state();
+	  sxi = xi0 & 0x3fffffff | 0x3fe00000;
+	  INSERT_WORDS (sx, sxi, xi1);
+	  t_sqrt = __t_sqrt + (xi0 >> 52-32-8-1  & 0x3fe);
+	  sg = t_sqrt[0];
+	  sy = t_sqrt[1];
+	  
+	  /* 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). */
+	  INSERT_WORDS (fsg, fsgi, 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;
+	  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 __sqrt(x * two108) * twom54;
+	}
+    }
+  else if (x < 0)
+    {
+#ifdef FE_INVALID_SQRT
+      feraiseexcept (FE_INVALID_SQRT);
+      /* For some reason, some PowerPC processors don't implement
+	 FE_INVALID_SQRT.  I guess no-one ever thought they'd be
+	 used for square roots... :-) */
+      if (!fetestexcept (FE_INVALID))
+#endif
+	feraiseexcept (FE_INVALID);
+#ifndef _IEEE_LIBM
+      if (_LIB_VERSION != _IEEE_)
+	x = __kernel_standard(x,x,26);
+      else
+#endif
+      x = *(const float*)&a_nan;
+    }
+  return f_wash(x);
+}
+
+weak_alias (__sqrt, sqrt)
+/* Strictly, this is wrong, but the only places where _ieee754_sqrt is
+   used will not pass in a negative result.  */
+strong_alias(__sqrt,__ieee754_sqrt)