blob: 005505235a0a83f992a8960ce802805af23bf432 [file] [log] [blame]
/**
* This file has no copyright assigned and is placed in the Public Domain.
* This file is part of the mingw-w64 runtime package.
* No warranty is given; refer to the file DISCLAIMER.PD within this package.
*/
#include <math.h>
#include "cephes_mconf.h"
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__
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
#endif
double cbrt(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);
}