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cbrt.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 <math.h>
#include "cephes_mconf.h"

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

#ifndef __MINGW32__
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
#endif

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

#ifdef __MINGW32__
      if (!isfinite (x) || x == 0)
            return x;
#else
#ifdef NANS
      if (isnan(x))
            return x;
#endif
#ifdef INFINITIES
      if (!isfinite(x))
            return x;
#endif
      if (x == 0)
            return (x);
#endif /* __MINGW32__ */

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

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

      /* Approximate cube root of number between .5 and 1,
       * peak relative error = 9.2e-6
       */
      x = (((-1.3466110473359520655053e-1  * x
            + 5.4664601366395524503440e-1) * x
            - 9.5438224771509446525043e-1) * x
            + 1.1399983354717293273738e0 ) * x
            + 4.0238979564544752126924e-1;

      /* 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;
      }
      /* argument less than 1 */
      else
      {
            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 = ldexp(x, e);

      /* Newton iteration */
      x -= ( x - (z/(x*x)) )*0.33333333333333333333;
#ifdef DEC
      x -= ( x - (z/(x*x)) )/3.0;
#else
      x -= ( x - (z/(x*x)) )*0.33333333333333333333;
#endif

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

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