Back to index

glibc  2.9
Defines | Functions
math_private.h File Reference
#include <sysdep.h>
#include <ldsodefs.h>
#include <dl-procinfo.h>
#include <math/math_private.h>
This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Defines

#define __CPU_HAS_FSQRT   ((GLRO(dl_hwcap) & PPC_FEATURE_64) != 0)

Functions

double __slow_ieee754_sqrt (double)
__inline double __ieee754_sqrt (double __x)
float __slow_ieee754_sqrtf (float)
__inline float __ieee754_sqrtf (float __x)

Define Documentation

#define __CPU_HAS_FSQRT   ((GLRO(dl_hwcap) & PPC_FEATURE_64) != 0)

Definition at line 31 of file math_private.h.


Function Documentation

__inline double __ieee754_sqrt ( double  __x)

Definition at line 37 of file math_private.h.

{
  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;
}

Here is the call graph for this function:

__inline float __ieee754_sqrtf ( float  __x)

Definition at line 60 of file math_private.h.

{
  float __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
       fsqrts instruction above the branch.  */
     __asm __volatile (
       "      fsqrts %0,%1\n"
              : "=f" (__z)
              : "f" (__x));
  }
  else
     __z = __slow_ieee754_sqrtf(__x);

  return __z;
}

Here is the call graph for this function:

double __slow_ieee754_sqrt ( double  )

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);
}

Here is the call graph for this function:

Here is the caller graph for this function:

float __slow_ieee754_sqrtf ( float  )

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);
}

Here is the call graph for this function:

Here is the caller graph for this function: