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glibc  2.9
Functions | Variables
e_sqrtf.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

float __slow_ieee754_sqrtf (float x)
float __ieee754_sqrtf (float x)

Variables

static const float almost_half = 0.50000006
static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 }
static const ieee_float_shape_type a_inf = {.word = 0x7f800000 }
static const float two48 = 281474976710656.0
static const float twom24 = 5.9604644775390625e-8
const float __t_sqrt [1024]

Function Documentation

float __ieee754_sqrtf ( float  x)

Definition at line 145 of file e_sqrtf.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 ("   fsqrts %0,%1\n"
                            :"=f" (z):"f" (x));
    }
  else
    z = __slow_ieee754_sqrtf (x);

  return z;
}

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float __slow_ieee754_sqrtf ( float  x)

Definition at line 54 of file e_sqrtf.c.

{
  const float inf = a_inf.value;

  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.  */
         float sx;          /* The value of which we're trying to find the square
                               root.  */
         float sg, g;              /* Guess of the square root of x.  */
         float sd, d;              /* Difference between the square of the guess and x.  */
         float sy;          /* Estimate of 1/2g (overestimated by 1ulp).  */
         float sy2;         /* 2*sy */
         float e;           /* Difference between y*g and 1/2 (note that e==se).  */
         float shx;         /* == sx * fsg */
         float fsg;         /* sg*fsg == g.  */
         fenv_t fe;         /* Saved floating-point environment (stores rounding
                               mode and whether the inexact exception is
                               enabled).  */
         uint32_t xi, sxi, fsgi;
         const float *t_sqrt;

         GET_FLOAT_WORD (xi, x);
         fe = fegetenv_register ();
         relax_fenv_state ();
         sxi = (xi & 0x3fffffff) | 0x3f000000;
         SET_FLOAT_WORD (sx, sxi);
         t_sqrt = __t_sqrt + (xi >> (23 - 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 = (xi + 0x40000000) >> 1 & 0x7f800000;
         sy2 = sy + sy;
         sg = sy * sd + sg; /* 16-bit approximation to sqrt(sx). */
         e = -(sy * sg - almost_half);
         SET_FLOAT_WORD (fsg, fsgi);
         sd = -(sg * sg - sx);
         sy = sy + e * sy2;
         if ((xi & 0x7f800000) == 0)
           goto denorm;
         shx = sx * fsg;
         sg = sg + sy * sd; /* 32-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_sqrtf (x * two48) * twom24;
       }
    }
  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_washf (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_sqrtf.c.

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

Definition at line 29 of file e_sqrtf.c.

const float almost_half = 0.50000006 [static]

Definition at line 28 of file e_sqrtf.c.

const float two48 = 281474976710656.0 [static]

Definition at line 31 of file e_sqrtf.c.

const float twom24 = 5.9604644775390625e-8 [static]

Definition at line 32 of file e_sqrtf.c.