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glibc  2.9
Functions | Variables
s_cbrtl.c File Reference
#include "math.h"
#include "math_private.h"
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Go to the source code of this file.

Functions

long double __cbrtl (long double x)

Variables

static const long double CBRT2 = 1.259921049894873164767210607278228350570251L
static const long double CBRT4 = 1.587401051968199474751705639272308260391493L
static const long double CBRT2I = 0.7937005259840997373758528196361541301957467L
static const long double CBRT4I = 0.6299605249474365823836053036391141752851257L

Function Documentation

long double __cbrtl ( long double  x)

Definition at line 67 of file s_cbrtl.c.

{
  int e, rem, sign;
  long double z;

  if (!__finitel (x))
    return x + x;

  if (x == 0)
    return (x);

  if (x > 0)
    sign = 1;
  else
    {
      sign = -1;
      x = -x;
    }

  z = x;
 /* extract power of 2, leaving mantissa between 0.5 and 1  */
  x = __frexpl (x, &e);

  /* Approximate cube root of number between .5 and 1,
     peak relative error = 1.2e-6  */
  x = ((((1.3584464340920900529734e-1L * x
         - 6.3986917220457538402318e-1L) * x
        + 1.2875551670318751538055e0L) * x
       - 1.4897083391357284957891e0L) * x
       + 1.3304961236013647092521e0L) * x + 3.7568280825958912391243e-1L;

  /* exponent divided by 3 */
  if (e >= 0)
    {
      rem = e;
      e /= 3;
      rem -= 3 * e;
      if (rem == 1)
       x *= CBRT2;
      else if (rem == 2)
       x *= CBRT4;
    }
  else
    {                       /* argument less than 1 */
      e = -e;
      rem = e;
      e /= 3;
      rem -= 3 * e;
      if (rem == 1)
       x *= CBRT2I;
      else if (rem == 2)
       x *= CBRT4I;
      e = -e;
    }

  /* multiply by power of 2 */
  x = __ldexpl (x, e);

  /* Newton iteration */
  x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
  x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
  x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;

  if (sign < 0)
    x = -x;
  return (x);
}

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Variable Documentation

const long double CBRT2 = 1.259921049894873164767210607278228350570251L [static]

Definition at line 60 of file s_cbrtl.c.

const long double CBRT2I = 0.7937005259840997373758528196361541301957467L [static]

Definition at line 62 of file s_cbrtl.c.

const long double CBRT4 = 1.587401051968199474751705639272308260391493L [static]

Definition at line 61 of file s_cbrtl.c.

const long double CBRT4I = 0.6299605249474365823836053036391141752851257L [static]

Definition at line 63 of file s_cbrtl.c.