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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: src/lib/msun/src/s_cbrtf.c,v 1.12 2005/12/13 20:17:23 bde Exp $";
#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 */
static const float
C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
float
cbrtf(float x)
{
float r,s,t,w;
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 */
if(hx==0)
return(x); /* cbrt(0) is itself */
/* rough cbrt to 5 bits */
if(hx<0x00800000) { /* subnormal number */
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));
/* new cbrt to 23 bits */
r=t*t/x;
s=C+r*t;
t*=G+F/(s+E+D/s);
/* chop t to 12 bits and make it larger in magnitude than cbrt(x) */
GET_FLOAT_WORD(high,t);
SET_FLOAT_WORD(t,(high&0xfffff000)+0x00001000);
/* one step Newton iteration to 24 bits with error less than 0.667 ulps */
s=t*t; /* t*t is exact */
r=x/s;
w=t+t;
r=(r-t)/(w+r); /* r-t is exact */
t=t+t*r;
return(t);
}
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