/* $Id: cbrt.c,v 1.1 2003/04/15 03:20:17 cher Exp $ */

/* This file is taken from Cephes math library */

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

#include "cephes.h"
#include "mconf.h"

#include <math.h>

/*							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
 *
 */

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

double cephes_cbrt(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;
  } 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 = 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);
}

/*
 * Local variables:
 *  compile-command: "make -C .."
 * End:
 */