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glibc  2.9
Functions | Variables
e_log2l.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

static long double neval (long double x, const long double *p, int n)
static long double deval (long double x, const long double *p, int n)
long double __ieee754_log2l (long double x)

Variables

static const long double P [13]
static const long double Q [12]
static const long double R [6]
static const long double S [6]
static const long double LOG2EA = 4.4269504088896340735992468100189213742664595E-1L
static const long double SQRTH = 7.071067811865475244008443621048490392848359E-1L

Function Documentation

long double __ieee754_log2l ( long double  x)

Definition at line 175 of file e_log2l.c.

{
  long double z;
  long double y;
  int e;
  int64_t hx, lx;

/* Test for domain */
  GET_LDOUBLE_WORDS64 (hx, lx, x);
  if (((hx & 0x7fffffffffffffffLL) | (lx & 0x7fffffffffffffffLL)) == 0)
    return (-1.0L / (x - x));
  if (hx < 0)
    return (x - x) / (x - x);
  if (hx >= 0x7ff0000000000000LL)
    return (x + x);

/* separate mantissa from exponent */

/* Note, frexp is used so that denormal numbers
 * will be handled properly.
 */
  x = __frexpl (x, &e);


/* logarithm using log(x) = z + z**3 P(z)/Q(z),
 * where z = 2(x-1)/x+1)
 */
  if ((e > 2) || (e < -2))
    {
      if (x < SQRTH)
       {                    /* 2( 2x-1 )/( 2x+1 ) */
         e -= 1;
         z = x - 0.5L;
         y = 0.5L * z + 0.5L;
       }
      else
       {                    /*  2 (x-1)/(x+1)   */
         z = x - 0.5L;
         z -= 0.5L;
         y = 0.5L * x + 0.5L;
       }
      x = z / y;
      z = x * x;
      y = x * (z * neval (z, R, 5) / deval (z, S, 5));
      goto done;
    }


/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */

  if (x < SQRTH)
    {
      e -= 1;
      x = 2.0 * x - 1.0L;   /*  2x - 1  */
    }
  else
    {
      x = x - 1.0L;
    }
  z = x * x;
  y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
  y = y - 0.5 * z;

done:

/* Multiply log of fraction by log2(e)
 * and base 2 exponent by 1
 */
  z = y * LOG2EA;
  z += x * LOG2EA;
  z += y;
  z += x;
  z += e;
  return (z);
}

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static long double deval ( long double  x,
const long double *  p,
int  n 
) [static]

Definition at line 158 of file e_log2l.c.

{
  long double y;

  p += n;
  y = x + *p--;
  do
    {
      y = y * x + *p--;
    }
  while (--n > 0);
  return y;
}

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static long double neval ( long double  x,
const long double *  p,
int  n 
) [static]

Definition at line 140 of file e_log2l.c.

{
  long double y;

  p += n;
  y = *p--;
  do
    {
      y = y * x + *p--;
    }
  while (--n > 0);
  return y;
}

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Variable Documentation

const long double LOG2EA = 4.4269504088896340735992468100189213742664595E-1L [static]

Definition at line 132 of file e_log2l.c.

const long double P[13] [static]
Initial value:
{
  1.313572404063446165910279910527789794488E4L,
  7.771154681358524243729929227226708890930E4L,
  2.014652742082537582487669938141683759923E5L,
  3.007007295140399532324943111654767187848E5L,
  2.854829159639697837788887080758954924001E5L,
  1.797628303815655343403735250238293741397E5L,
  7.594356839258970405033155585486712125861E4L,
  2.128857716871515081352991964243375186031E4L,
  3.824952356185897735160588078446136783779E3L,
  4.114517881637811823002128927449878962058E2L,
  2.321125933898420063925789532045674660756E1L,
  4.998469661968096229986658302195402690910E-1L,
  1.538612243596254322971797716843006400388E-6L
}

Definition at line 71 of file e_log2l.c.

const long double Q[12] [static]
Initial value:
{
  3.940717212190338497730839731583397586124E4L,
  2.626900195321832660448791748036714883242E5L,
  7.777690340007566932935753241556479363645E5L,
  1.347518538384329112529391120390701166528E6L,
  1.514882452993549494932585972882995548426E6L,
  1.158019977462989115839826904108208787040E6L,
  6.132189329546557743179177159925690841200E5L,
  2.248234257620569139969141618556349415120E5L,
  5.605842085972455027590989944010492125825E4L,
  9.147150349299596453976674231612674085381E3L,
  9.104928120962988414618126155557301584078E2L,
  4.839208193348159620282142911143429644326E1L

}

Definition at line 87 of file e_log2l.c.

const long double R[6] [static]
Initial value:
{
  1.418134209872192732479751274970992665513E5L,
 -8.977257995689735303686582344659576526998E4L,
  2.048819892795278657810231591630928516206E4L,
 -2.024301798136027039250415126250455056397E3L,
  8.057002716646055371965756206836056074715E1L,
 -8.828896441624934385266096344596648080902E-1L
}

Definition at line 110 of file e_log2l.c.

const long double S[6] [static]
Initial value:
{
  1.701761051846631278975701529965589676574E6L,
 -1.332535117259762928288745111081235577029E6L,
  4.001557694070773974936904547424676279307E5L,
 -5.748542087379434595104154610899551484314E4L,
  3.998526750980007367835804959888064681098E3L,
 -1.186359407982897997337150403816839480438E2L

}

Definition at line 119 of file e_log2l.c.

const long double SQRTH = 7.071067811865475244008443621048490392848359E-1L [static]

Definition at line 134 of file e_log2l.c.