sysdeps/powerpc/fpu/e_sqrtf.c

   1 /* Single-precision floating point square root.
   2    Copyright (C) 1997, 2003, 2004 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, write to the Free
  17    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  18    02111-1307 USA.  */
  19
  20 #include <math.h>
  21 #include <math_private.h>
  22 #include <fenv_libc.h>
  23 #include <inttypes.h>
  24
  25 #include <sysdep.h>
  26 #include <ldsodefs.h>
  27 #include <dl-procinfo.h>
  28
  29 static const float almost_half = 0.50000006;    /* 0.5 + 2^-24 */
  30 static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 };
  31 static const ieee_float_shape_type a_inf = {.word = 0x7f800000 };
  32 static const float two48 = 281474976710656.0;
  33 static const float twom24 = 5.9604644775390625e-8;
  34 extern const float __t_sqrt[1024];
  35
  36 /* The method is based on a description in
  37    Computation of elementary functions on the IBM RISC System/6000 processor,
  38    P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
  39    Basically, it consists of two interleaved Newton-Rhapson approximations,
  40    one to find the actual square root, and one to find its reciprocal
  41    without the expense of a division operation.   The tricky bit here
  42    is the use of the POWER/PowerPC multiply-add operation to get the
  43    required accuracy with high speed.
  44
  45    The argument reduction works by a combination of table lookup to
  46    obtain the initial guesses, and some careful modification of the
  47    generated guesses (which mostly runs on the integer unit, while the
  48    Newton-Rhapson is running on the FPU).  */
  49
  50 #ifdef __STDC__
  51 float
  52 __slow_ieee754_sqrtf (float x)
  53 #else
  54 float
  55 __slow_ieee754_sqrtf (x)
  56      float x;
  57 #endif
  58 {
  59   const float inf = a_inf.value;
  60
  61   if (x > 0)
  62     {
  63       if (x != inf)
  64         {
  65           /* Variables named starting with 's' exist in the
  66              argument-reduced space, so that 2 > sx >= 0.5,
  67              1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
  68              Variables named ending with 'i' are integer versions of
  69              floating-point values.  */
  70           float sx;             /* The value of which we're trying to find the square
  71                                    root.  */
  72           float sg, g;          /* Guess of the square root of x.  */
  73           float sd, d;          /* Difference between the square of the guess and x.  */
  74           float sy;             /* Estimate of 1/2g (overestimated by 1ulp).  */
  75           float sy2;            /* 2*sy */
  76           float e;              /* Difference between y*g and 1/2 (note that e==se).  */
  77           float shx;            /* == sx * fsg */
  78           float fsg;            /* sg*fsg == g.  */
  79           fenv_t fe;            /* Saved floating-point environment (stores rounding
  80                                    mode and whether the inexact exception is
  81                                    enabled).  */
  82           uint32_t xi, sxi, fsgi;
  83           const float *t_sqrt;
  84
  85           GET_FLOAT_WORD (xi, x);
  86           fe = fegetenv_register ();
  87           relax_fenv_state ();
  88           sxi = (xi & 0x3fffffff) | 0x3f000000;
  89           SET_FLOAT_WORD (sx, sxi);
  90           t_sqrt = __t_sqrt + (xi >> (23 - 8 - 1) & 0x3fe);
  91           sg = t_sqrt[0];
  92           sy = t_sqrt[1];
  93
  94           /* Here we have three Newton-Rhapson iterations each of a
  95              division and a square root and the remainder of the
  96              argument reduction, all interleaved.   */
  97           sd = -(sg * sg - sx);
  98           fsgi = (xi + 0x40000000) >> 1 & 0x7f800000;
  99           sy2 = sy + sy;
 100           sg = sy * sd + sg;    /* 16-bit approximation to sqrt(sx). */
 101           e = -(sy * sg - almost_half);
 102           SET_FLOAT_WORD (fsg, fsgi);
 103           sd = -(sg * sg - sx);
 104           sy = sy + e * sy2;
 105           if ((xi & 0x7f800000) == 0)
 106             goto denorm;
 107           shx = sx * fsg;
 108           sg = sg + sy * sd;    /* 32-bit approximation to sqrt(sx),
 109                                    but perhaps rounded incorrectly.  */
 110           sy2 = sy + sy;
 111           g = sg * fsg;
 112           e = -(sy * sg - almost_half);
 113           d = -(g * sg - shx);
 114           sy = sy + e * sy2;
 115           fesetenv_register (fe);
 116           return g + sy * d;
 117         denorm:
 118           /* For denormalised numbers, we normalise, calculate the
 119              square root, and return an adjusted result.  */
 120           fesetenv_register (fe);
 121           return __slow_ieee754_sqrtf (x * two48) * twom24;
 122         }
 123     }
 124   else if (x < 0)
 125     {
 126       /* For some reason, some PowerPC32 processors don't implement
 127          FE_INVALID_SQRT.  */
 128 #ifdef FE_INVALID_SQRT
 129       feraiseexcept (FE_INVALID_SQRT);
 130       if (!fetestexcept (FE_INVALID))
 131 #endif
 132         feraiseexcept (FE_INVALID);
 133       x = a_nan.value;
 134     }
 135   return f_washf (x);
 136 }
 137
 138
 139 #ifdef __STDC__
 140 float
 141 __ieee754_sqrtf (float x)
 142 #else
 143 float
 144 __ieee754_sqrtf (x)
 145      float x;
 146 #endif
 147 {
 148   double z;
 149
 150   /* If the CPU is 64-bit we can use the optional FP instructions we.  */
 151   if ((GLRO (dl_hwcap) & PPC_FEATURE_64) != 0)
 152     {
 153       /* Volatile is required to prevent the compiler from moving the
 154          fsqrt instruction above the branch.  */
 155       __asm __volatile ("       fsqrts  %0,%1\n"
 156                                 :"=f" (z):"f" (x));
 157     }
 158   else
 159     z = __slow_ieee754_sqrtf (x);
 160
 161   return z;
 162 }