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/* 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
*/
#include <math.h>
static float CBRT2 = 1.25992104989487316477;
static float CBRT4 = 1.58740105196819947475;
float frexpf(float, int *), ldexpf(float, int);
float cbrtf( float xx )
{
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 = 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);
}
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