sysdeps/powerpc/fpu/e_sqrtf.c

   1 /* Single-precision floating point square root.
   2    Copyright (C) 1997-2014 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, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 #include <math.h>
  20 #include <math_private.h>
  21 #include <fenv_libc.h>
  22 #include <inttypes.h>
  23 #include <stdint.h>
  24 #include <sysdep.h>
  25 #include <ldsodefs.h>
  26
  27 static const float almost_half = 0.50000006;    /* 0.5 + 2^-24 */
  28 static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 };
  29 static const ieee_float_shape_type a_inf = {.word = 0x7f800000 };
  30 static const float two48 = 281474976710656.0;
  31 static const float twom24 = 5.9604644775390625e-8;
  32 extern const float __t_sqrt[1024];
  33
  34 /* The method is based on a description in
  35    Computation of elementary functions on the IBM RISC System/6000 processor,
  36    P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
  37    Basically, it consists of two interleaved Newton-Raphson approximations,
  38    one to find the actual square root, and one to find its reciprocal
  39    without the expense of a division operation.   The tricky bit here
  40    is the use of the POWER/PowerPC multiply-add operation to get the
  41    required accuracy with high speed.
  42
  43    The argument reduction works by a combination of table lookup to
  44    obtain the initial guesses, and some careful modification of the
  45    generated guesses (which mostly runs on the integer unit, while the
  46    Newton-Raphson is running on the FPU).  */
  47
  48 float
  49 __slow_ieee754_sqrtf (float x)
  50 {
  51   const float inf = a_inf.value;
  52
  53   if (x > 0)
  54     {
  55       if (x != inf)
  56         {
  57           /* Variables named starting with 's' exist in the
  58              argument-reduced space, so that 2 > sx >= 0.5,
  59              1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
  60              Variables named ending with 'i' are integer versions of
  61              floating-point values.  */
  62           float sx;             /* The value of which we're trying to find the square
  63                                    root.  */
  64           float sg, g;          /* Guess of the square root of x.  */
  65           float sd, d;          /* Difference between the square of the guess and x.  */
  66           float sy;             /* Estimate of 1/2g (overestimated by 1ulp).  */
  67           float sy2;            /* 2*sy */
  68           float e;              /* Difference between y*g and 1/2 (note that e==se).  */
  69           float shx;            /* == sx * fsg */
  70           float fsg;            /* sg*fsg == g.  */
  71           fenv_t fe;            /* Saved floating-point environment (stores rounding
  72                                    mode and whether the inexact exception is
  73                                    enabled).  */
  74           uint32_t xi, sxi, fsgi;
  75           const float *t_sqrt;
  76
  77           GET_FLOAT_WORD (xi, x);
  78           fe = fegetenv_register ();
  79           relax_fenv_state ();
  80           sxi = (xi & 0x3fffffff) | 0x3f000000;
  81           SET_FLOAT_WORD (sx, sxi);
  82           t_sqrt = __t_sqrt + (xi >> (23 - 8 - 1) & 0x3fe);
  83           sg = t_sqrt[0];
  84           sy = t_sqrt[1];
  85
  86           /* Here we have three Newton-Raphson iterations each of a
  87              division and a square root and the remainder of the
  88              argument reduction, all interleaved.   */
  89           sd = -(sg * sg - sx);
  90           fsgi = (xi + 0x40000000) >> 1 & 0x7f800000;
  91           sy2 = sy + sy;
  92           sg = sy * sd + sg;    /* 16-bit approximation to sqrt(sx). */
  93           e = -(sy * sg - almost_half);
  94           SET_FLOAT_WORD (fsg, fsgi);
  95           sd = -(sg * sg - sx);
  96           sy = sy + e * sy2;
  97           if ((xi & 0x7f800000) == 0)
  98             goto denorm;
  99           shx = sx * fsg;
 100           sg = sg + sy * sd;    /* 32-bit approximation to sqrt(sx),
 101                                    but perhaps rounded incorrectly.  */
 102           sy2 = sy + sy;
 103           g = sg * fsg;
 104           e = -(sy * sg - almost_half);
 105           d = -(g * sg - shx);
 106           sy = sy + e * sy2;
 107           fesetenv_register (fe);
 108           return g + sy * d;
 109         denorm:
 110           /* For denormalised numbers, we normalise, calculate the
 111              square root, and return an adjusted result.  */
 112           fesetenv_register (fe);
 113           return __slow_ieee754_sqrtf (x * two48) * twom24;
 114         }
 115     }
 116   else if (x < 0)
 117     {
 118       /* For some reason, some PowerPC32 processors don't implement
 119          FE_INVALID_SQRT.  */
 120 #ifdef FE_INVALID_SQRT
 121       feraiseexcept (FE_INVALID_SQRT);
 122
 123       fenv_union_t u = { .fenv = fegetenv_register () };
 124       if ((u.l & FE_INVALID) == 0)
 125 #endif
 126         feraiseexcept (FE_INVALID);
 127       x = a_nan.value;
 128     }
 129   return f_washf (x);
 130 }
 131
 132 #undef __ieee754_sqrtf
 133 float
 134 __ieee754_sqrtf (float x)
 135 {
 136   double z;
 137
 138   /* If the CPU is 64-bit we can use the optional FP instructions.  */
 139   if (__CPU_HAS_FSQRT)
 140     {
 141       /* Volatile is required to prevent the compiler from moving the
 142          fsqrt instruction above the branch.  */
 143       __asm __volatile ("       fsqrts  %0,%1\n"
 144                                 :"=f" (z):"f" (x));
 145     }
 146   else
 147     z = __slow_ieee754_sqrtf (x);
 148
 149   return z;
 150 }
 151 strong_alias (__ieee754_sqrtf, __sqrtf_finite)