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/* s_cbrtf.c -- float version of s_cbrt.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef lint
static char rcsid[] = "$FreeBSD$";
#endif
#include "math.h"
#include "math_private.h"
/* cbrtf(x)
* Return cube root of x
*/
static const unsigned
B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
float
cbrtf(float x)
{
double r,T;
float t;
int32_t hx;
u_int32_t sign;
u_int32_t high;
GET_FLOAT_WORD(hx,x);
sign=hx&0x80000000; /* sign= sign(x) */
hx ^=sign;
if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
/* rough cbrt to 5 bits */
if(hx<0x00800000) { /* zero or subnormal? */
if(hx==0)
return(x); /* cbrt(+-0) is itself */
SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
t*=x;
GET_FLOAT_WORD(high,t);
SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
} else
SET_FLOAT_WORD(t,sign|(hx/3+B1));
/*
* First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
* double precision so that its terms can be arranged for efficiency
* without causing overflow or underflow.
*/
T=t;
r=T*T*T;
T=T*((double)x+x+r)/(x+r+r);
/*
* Second step Newton iteration to 47 bits. In double precision for
* efficiency and accuracy.
*/
r=T*T*T;
T=T*((double)x+x+r)/(x+r+r);
/* rounding to 24 bits is perfect in round-to-nearest mode */
return(T);
}
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