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cbrtf.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 float CBRT2 = 1.25992104989487316477;
static const float CBRT4 = 1.58740105196819947475;

float cbrtf (float x)
{
      int e, rem, sign;
      float z;
      if (!isfinite (x) || x == 0.0F)
            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 = frexpf(x, &e);

      /* Approximate cube root of number between .5 and 1,
       * peak relative error = 9.2e-6
       */
      x = (((-0.13466110473359520655053  * x
            + 0.54664601366395524503440 ) * x
            - 0.95438224771509446525043 ) * x
            + 1.1399983354717293273738  ) * x
            + 0.40238979564544752126924;

      /* 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 /= CBRT2;
            else if (rem == 2)
                  x /= CBRT4;
            e = -e;
      }

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

      /* Newton iteration */
      x -= ( x - (z/(x*x)) ) * 0.333333333333;

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

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