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glibc  2.9
Functions | Variables
e_sqrt.c File Reference
#include <math.h>
#include <math_private.h>
#include <fenv_libc.h>
#include <inttypes.h>
#include <sysdep.h>
#include <ldsodefs.h>

Go to the source code of this file.

Functions

double __slow_ieee754_sqrt (double x)
double __ieee754_sqrt (double x)

Variables

static const double almost_half = 0.5000000000000001
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
const float __t_sqrt [1024]

Function Documentation

double __ieee754_sqrt ( double  x)

Definition at line 168 of file e_sqrt.c.

{
  double z;

  /* If the CPU is 64-bit we can use the optional FP instructions.  */
  if (__CPU_HAS_FSQRT)
    {
      /* 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;
}

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double __slow_ieee754_sqrt ( double  x)

Definition at line 54 of file e_sqrt.c.

{
  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);

      fenv_union_t u = { .fenv = fegetenv_register () };
      if ((u.l[1] & FE_INVALID) == 0)
#endif
       feraiseexcept (FE_INVALID);
      x = a_nan.value;
    }
  return f_wash (x);
}

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Variable Documentation

const float __t_sqrt[1024]

Definition at line 1 of file t_sqrt.c.

const ieee_float_shape_type a_inf = {.word = 0x7f800000 } [static]

Definition at line 30 of file e_sqrt.c.

const ieee_float_shape_type a_nan = {.word = 0x7fc00000 } [static]

Definition at line 29 of file e_sqrt.c.

const double almost_half = 0.5000000000000001 [static]

Definition at line 28 of file e_sqrt.c.

const float two108 = 3.245185536584267269e+32 [static]

Definition at line 31 of file e_sqrt.c.

const float twom54 = 5.551115123125782702e-17 [static]

Definition at line 32 of file e_sqrt.c.