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cbrtl.c

/**
 * This file has no copyright assigned and is placed in the Public Domain.
 * This file is part of the w64 mingw-runtime package.
 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
 */
#include "cephes_mconf.h"

static const long double CBRT2  = 1.2599210498948731647672L;
static const long double CBRT4  = 1.5874010519681994747517L;
static const long double CBRT2I = 0.79370052598409973737585L;
static const long double CBRT4I = 0.62996052494743658238361L;

extern long double ldexpl(long double,int);

long double cbrtl(long double x)
{
      int e, rem, sign;
      long double z;

      if (!isfinite (x) || x == 0.0L)
            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)) )*0.3333333333333333333333L;
      x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;

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

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