sysdeps/powerpc/fpu/e_sqrtf.c

   1 /* Single-precision floating point square root.
   2    Copyright (C) 1997, 2003, 2004, 2008 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
  28 static const float almost_half = 0.50000006;    /* 0.5 + 2^-24 */
  29 static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 };
  30 static const ieee_float_shape_type a_inf = {.word = 0x7f800000 };
  31 static const float two48 = 281474976710656.0;
  32 static const float twom24 = 5.9604644775390625e-8;
  33 extern const float __t_sqrt[1024];
  34
  35 /* The method is based on a description in
  36    Computation of elementary functions on the IBM RISC System/6000 processor,
  37    P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
  38    Basically, it consists of two interleaved Newton-Rhapson approximations,
  39    one to find the actual square root, and one to find its reciprocal
  40    without the expense of a division operation.   The tricky bit here
  41    is the use of the POWER/PowerPC multiply-add operation to get the
  42    required accuracy with high speed.
  43
  44    The argument reduction works by a combination of table lookup to
  45    obtain the initial guesses, and some careful modification of the
  46    generated guesses (which mostly runs on the integer unit, while the
  47    Newton-Rhapson is running on the FPU).  */
  48
  49 #ifdef __STDC__
  50 float
  51 __slow_ieee754_sqrtf (float x)
  52 #else
  53 float
  54 __slow_ieee754_sqrtf (x)
  55      float x;
  56 #endif
  57 {
  58   const float inf = a_inf.value;
  59
  60   if (x > 0)
  61     {
  62       if (x != inf)
  63         {
  64           /* Variables named starting with 's' exist in the
  65              argument-reduced space, so that 2 > sx >= 0.5,
  66              1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
  67              Variables named ending with 'i' are integer versions of
  68              floating-point values.  */
  69           float sx;             /* The value of which we're trying to find the square
  70                                    root.  */
  71           float sg, g;          /* Guess of the square root of x.  */
  72           float sd, d;          /* Difference between the square of the guess and x.  */
  73           float sy;             /* Estimate of 1/2g (overestimated by 1ulp).  */
  74           float sy2;            /* 2*sy */
  75           float e;              /* Difference between y*g and 1/2 (note that e==se).  */
  76           float shx;            /* == sx * fsg */
  77           float fsg;            /* sg*fsg == g.  */
  78           fenv_t fe;            /* Saved floating-point environment (stores rounding
  79                                    mode and whether the inexact exception is
  80                                    enabled).  */
  81           uint32_t xi, sxi, fsgi;
  82           const float *t_sqrt;
  83
  84           GET_FLOAT_WORD (xi, x);
  85           fe = fegetenv_register ();
  86           relax_fenv_state ();
  87           sxi = (xi & 0x3fffffff) | 0x3f000000;
  88           SET_FLOAT_WORD (sx, sxi);
  89           t_sqrt = __t_sqrt + (xi >> (23 - 8 - 1) & 0x3fe);
  90           sg = t_sqrt[0];
  91           sy = t_sqrt[1];
  92
  93           /* Here we have three Newton-Rhapson iterations each of a
  94              division and a square root and the remainder of the
  95              argument reduction, all interleaved.   */
  96           sd = -(sg * sg - sx);
  97           fsgi = (xi + 0x40000000) >> 1 & 0x7f800000;
  98           sy2 = sy + sy;
  99           sg = sy * sd + sg;    /* 16-bit approximation to sqrt(sx). */
 100           e = -(sy * sg - almost_half);
 101           SET_FLOAT_WORD (fsg, fsgi);
 102           sd = -(sg * sg - sx);
 103           sy = sy + e * sy2;
 104           if ((xi & 0x7f800000) == 0)
 105             goto denorm;
 106           shx = sx * fsg;
 107           sg = sg + sy * sd;    /* 32-bit approximation to sqrt(sx),
 108                                    but perhaps rounded incorrectly.  */
 109           sy2 = sy + sy;
 110           g = sg * fsg;
 111           e = -(sy * sg - almost_half);
 112           d = -(g * sg - shx);
 113           sy = sy + e * sy2;
 114           fesetenv_register (fe);
 115           return g + sy * d;
 116         denorm:
 117           /* For denormalised numbers, we normalise, calculate the
 118              square root, and return an adjusted result.  */
 119           fesetenv_register (fe);
 120           return __slow_ieee754_sqrtf (x * two48) * twom24;
 121         }
 122     }
 123   else if (x < 0)
 124     {
 125       /* For some reason, some PowerPC32 processors don't implement
 126          FE_INVALID_SQRT.  */
 127 #ifdef FE_INVALID_SQRT
 128       feraiseexcept (FE_INVALID_SQRT);
 129
 130       fenv_union_t u = { .fenv = fegetenv_register () };
 131       if ((u.l[1] & FE_INVALID) == 0)
 132 #endif
 133         feraiseexcept (FE_INVALID);
 134       x = a_nan.value;
 135     }
 136   return f_washf (x);
 137 }
 138
 139
 140 #ifdef __STDC__
 141 float
 142 __ieee754_sqrtf (float x)
 143 #else
 144 float
 145 __ieee754_sqrtf (x)
 146      float x;
 147 #endif
 148 {
 149   double z;
 150
 151   /* If the CPU is 64-bit we can use the optional FP instructions.  */
 152   if (__CPU_HAS_FSQRT)
 153     {
 154       /* Volatile is required to prevent the compiler from moving the
 155          fsqrt instruction above the branch.  */
 156       __asm __volatile ("       fsqrts  %0,%1\n"
 157                                 :"=f" (z):"f" (x));
 158     }
 159   else
 160     z = __slow_ieee754_sqrtf (x);
 161
 162   return z;
 163 }