mirror of
https://github.com/autc04/Retro68.git
synced 2024-12-11 03:52:59 +00:00
119 lines
2.6 KiB
C
119 lines
2.6 KiB
C
|
|
/* @(#)s_cbrt.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* 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.
|
|
* ====================================================
|
|
*
|
|
*/
|
|
|
|
/*
|
|
FUNCTION
|
|
<<cbrt>>, <<cbrtf>>---cube root
|
|
|
|
INDEX
|
|
cbrt
|
|
INDEX
|
|
cbrtf
|
|
|
|
SYNOPSIS
|
|
#include <math.h>
|
|
double cbrt(double <[x]>);
|
|
float cbrtf(float <[x]>);
|
|
|
|
DESCRIPTION
|
|
<<cbrt>> computes the cube root of the argument.
|
|
|
|
RETURNS
|
|
The cube root is returned.
|
|
|
|
PORTABILITY
|
|
<<cbrt>> is in System V release 4. <<cbrtf>> is an extension.
|
|
*/
|
|
|
|
#include "fdlibm.h"
|
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
|
/* cbrt(x)
|
|
* Return cube root of x
|
|
*/
|
|
#ifdef __STDC__
|
|
static const __uint32_t
|
|
#else
|
|
static __uint32_t
|
|
#endif
|
|
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
|
|
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
|
|
|
|
#ifdef __STDC__
|
|
static const double
|
|
#else
|
|
static double
|
|
#endif
|
|
C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
|
|
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
|
|
E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
|
|
F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
|
|
G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
|
|
|
|
#ifdef __STDC__
|
|
double cbrt(double x)
|
|
#else
|
|
double cbrt(x)
|
|
double x;
|
|
#endif
|
|
{
|
|
__int32_t hx;
|
|
double r,s,t=0.0,w;
|
|
__uint32_t sign;
|
|
__uint32_t high,low;
|
|
|
|
GET_HIGH_WORD(hx,x);
|
|
sign=hx&0x80000000; /* sign= sign(x) */
|
|
hx ^=sign;
|
|
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
|
|
GET_LOW_WORD(low,x);
|
|
if((hx|low)==0)
|
|
return(x); /* cbrt(0) is itself */
|
|
|
|
SET_HIGH_WORD(x,hx); /* x <- |x| */
|
|
/* rough cbrt to 5 bits */
|
|
if(hx<0x00100000) /* subnormal number */
|
|
{SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
|
|
t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
|
|
}
|
|
else
|
|
SET_HIGH_WORD(t,hx/3+B1);
|
|
|
|
|
|
/* new cbrt to 23 bits, may be implemented in single precision */
|
|
r=t*t/x;
|
|
s=C+r*t;
|
|
t*=G+F/(s+E+D/s);
|
|
|
|
/* chopped to 20 bits and make it larger than cbrt(x) */
|
|
GET_HIGH_WORD(high,t);
|
|
INSERT_WORDS(t,high+0x00000001,0);
|
|
|
|
|
|
/* one step newton iteration to 53 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-s is exact */
|
|
t=t+t*r;
|
|
|
|
/* retore the sign bit */
|
|
GET_HIGH_WORD(high,t);
|
|
SET_HIGH_WORD(t,high|sign);
|
|
return(t);
|
|
}
|
|
|
|
#endif /* _DOUBLE_IS_32BITS */
|