148 lines
2.6 KiB
C
148 lines
2.6 KiB
C
/* cbrtf.c
|
||
*
|
||
* Cube root
|
||
*
|
||
*
|
||
*
|
||
* SYNOPSIS:
|
||
*
|
||
* float x, y, cbrtf();
|
||
*
|
||
* y = 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
|
||
*/
|
||
|
||
/*
|
||
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 float CBRT2 = 1.25992104989487316477;
|
||
static const float CBRT4 = 1.58740105196819947475;
|
||
|
||
#ifndef __MINGW32__
|
||
#ifdef ANSIC
|
||
float frexpf(float, int *), ldexpf(float, int);
|
||
|
||
float cbrtf( float xx )
|
||
#else
|
||
float frexpf(), ldexpf();
|
||
|
||
float cbrtf(xx)
|
||
double xx;
|
||
#endif
|
||
{
|
||
int e, rem, sign;
|
||
float x, z;
|
||
|
||
x = xx;
|
||
|
||
#else /* __MINGW32__ */
|
||
float cbrtf (float x)
|
||
{
|
||
int e, rem, sign;
|
||
float z;
|
||
#endif /* __MINGW32__ */
|
||
|
||
#ifdef __MINGW32__
|
||
if (!isfinite (x) || x == 0.0F )
|
||
return x;
|
||
#else
|
||
if( x == 0 )
|
||
return( 0.0 );
|
||
#endif
|
||
if( x > 0 )
|
||
sign = 1;
|
||
else
|
||
{
|
||
sign = -1;
|
||
x = -x;
|
||
}
|
||
|
||
z = x;
|
||
/* extract power of 2, leaving
|
||
* mantissa between 0.5 and 1
|
||
*/
|
||
x = frexpf( x, &e );
|
||
|
||
/* Approximate cube root of number between .5 and 1,
|
||
* peak relative error = 9.2e-6
|
||
*/
|
||
x = (((-0.13466110473359520655053 * x
|
||
+ 0.54664601366395524503440 ) * x
|
||
- 0.95438224771509446525043 ) * x
|
||
+ 1.1399983354717293273738 ) * x
|
||
+ 0.40238979564544752126924;
|
||
|
||
/* 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 = ldexpf( x, e );
|
||
|
||
/* Newton iteration */
|
||
x -= ( x - (z/(x*x)) ) * 0.333333333333;
|
||
|
||
if( sign < 0 )
|
||
x = -x;
|
||
return(x);
|
||
}
|