0,0 → 1,123 |
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/* @(#)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 |
|
ANSI_SYNOPSIS |
#include <math.h> |
double cbrt(double <[x]>); |
float cbrtf(float <[x]>); |
|
TRAD_SYNOPSIS |
#include <math.h> |
double cbrt(<[x]>); |
float cbrtf(<[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. |
*/ |
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#include "fdlibm.h" |
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#ifndef _DOUBLE_IS_32BITS |
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/* 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); |
} |
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#endif /* _DOUBLE_IS_32BITS */ |