163 lines
3.0 KiB
C
163 lines
3.0 KiB
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 2.2: January, 1991
|
||
Copyright 1984, 1991 by Stephen L. Moshier
|
||
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
|
||
*/
|
||
|
||
/*
|
||
Modified for mingwex.a
|
||
2002-07-01 Danny Smith <dannysmith@users.sourceforge.net>
|
||
*/
|
||
#ifdef __MINGW32__
|
||
#include <math.h>
|
||
#include "cephes_mconf.h"
|
||
#else
|
||
#include "mconf.h"
|
||
#endif
|
||
|
||
|
||
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__
|
||
#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
|
||
#endif
|
||
|
||
double cbrt(x)
|
||
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);
|
||
}
|