Output of file : CBRT.C contained in archive : CEPHES22.ZIP
/* 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 0,8 50000 1.8e-17 5.6e-18
* IEEE 0,1e308 30000 1.5e-16 5.0e-17
*
*/
/* cbrt.c */

/*
Cephes Math Library Release 2.1: December, 1988
Copyright 1984, 1987, 1988 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "mconf.h"

#ifdef UNK
static double CBRT2 = 1.25992104989487316477;
static double CBRT4 = 1.58740105196819947475;
#endif

#ifdef DEC
static short CBT2[] = {040241,042427,0146153,0112127};
static short CBT4[] = {040313,027765,024753,070744};
#define CBRT2 *(double *)CBT2
#define CBRT4 *(double *)CBT4
#endif

#ifdef IBMPC
static short CBT2[] = {0x728b,0xf98d,0x28a2,0x3ff4};
static short CBT4[] = {0x6e3d,0xa53d,0x65fe,0x3ff9};
#define CBRT2 *(double *)CBT2
#define CBRT4 *(double *)CBT4
#endif

#ifdef MIEEE
static short CBT2[] = {
0x3ff4,0x28a2,0xf98d,0x728b
};
static short CBT4[] = {
0x3ff9,0x65fe,0xa53d,0x6e3d,
};
#define CBRT2 *(double *)CBT2
#define CBRT4 *(double *)CBT4
#endif

double cbrt(x)
double x;
{
int e, rem, sign;
double z;
double frexp(), ldexp();

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 = frexp( x, &e );

/* Approximate cube root of number between .5 and 1,
* peak relative error = 6.36e-4
*/
x = (-1.9150215751434832257e-1 * x
+ 6.9757045195246484393e-1) * x
+ 4.9329566506409572486e-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 /= CBRT2;
else if( rem == 2 )
x /= CBRT4;
e = -e;
}

/* multiply by power of 2 */
x = ldexp( x, e );

/* Newton iteration */
x -= ( x - (z/(x*x)) )/3.0;
x -= ( x - (z/(x*x)) )/3.0;
x -= ( x - (z/(x*x)) )/3.0;

if( sign < 0 )
x = -x;
return(x);
}

### 3 Responses to “Category : C Source CodeArchive   : CEPHES22.ZIPFilename : CBRT.C”

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