CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/cbrt.c

/*							cbrt.c
 *
 *	Cube root
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, cbrt();
 *
 * y = cbrt( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the cube root of the argument, which may be negative.
 *
 * Range reduction involves determining the power of 2 of
 * the argument.  A polynomial of degree 2 applied to the
 * mantissa, and multiplication by the cube root of 1, 2, or 4
 * approximates the root to within about 0.1%.  Then Newton's
 * iteration is used three times to converge to an accurate
 * result.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC        -10,10     200000      1.8e-17     6.2e-18
 *    IEEE       0,1e308     30000      1.5e-16     5.0e-17
 *
 */
/*							cbrt.c  */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1991, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

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

#ifdef ANSIPROT
extern double frexp(double, int *);
extern double ldexp(double, int);
extern int isnan(double);
extern int isfinite(double);
#else
double frexp(), ldexp();
int isnan(), isfinite();
#endif

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

#ifdef NANS
  if (isnan(x))
    return x;
#endif
#ifdef INFINITIES
  if (!isfinite(x))
    return x;
#endif
  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 = 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);
}