text: /*							cbrtf.c
   *
   *	Cube root
   *
   *
   *
   * SYNOPSIS:
   *
   * float x, y, cephes_cbrtf();
   *
   * y = cephes_cbrtf( 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 to converge to an accurate result.
   *
   *
   *
   * ACCURACY:
   *
   *                      Relative error:
   * arithmetic   domain     # trials      peak         rms
   *    IEEE      0,1e38      100000      7.6e-8      2.7e-8
   *
   */
  /*							cbrt.c  */
  
  /*
  Cephes Math Library Release 2.2:  June, 1992
  Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
  Direct inquiries to 30 Frost Street, Cambridge, MA 02140
  */
  
  
  #include "mconf.h"
  
  static float CBRT2 = 1.25992104989487316477;
  static float CBRT4 = 1.58740105196819947475;
  
  
  #ifdef ANSIC
  float cephes_frexpf(float, int *), cephes_ldexpf(float, int);
  
  float cephes_cbrtf( float xx )
  #else
  float cephes_frexpf(), cephes_ldexpf();
  
  float cephes_cbrtf(xx)
  double xx;
  #endif
  {
  int e, rem, sign;
  float x, z;
  
  x = xx;
  if( x == 0 )
  	return( 0.0 );
  if( x > 0 )
  	sign = 1;
  else
  	{
  	sign = -1;
  	x = -x;
  	}
  
  z = x;
  /* extract power of 2, leaving
   * mantissa between 0.5 and 1
   */
  x = cephes_frexpf( x, &e );
  
  /* Approximate cube root of number between .5 and 1,
   * peak relative error = 9.2e-6
   */
  x = (((-0.13466110473359520655053f  * x
        + 0.54664601366395524503440f ) * x
        - 0.95438224771509446525043f ) * x
        + 1.1399983354717293273738f  ) * x
        + 0.40238979564544752126924f;
  
  /* 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 = cephes_ldexpf( x, e );
  
  /* Newton iteration */
  x -= ( x - (z/(x*x)) ) * 0.333333333333f;
  
  if( sign < 0 )
  	x = -x;
  return(x);
  }
  