include/elf.h: sync with GNU C library
[uclibc-ng.git] / libm / s_cbrt.c
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1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
12 #include "math.h"
13 #include "math_private.h"
15 /* cbrt(x)
16 * Return cube root of x
18 static const u_int32_t
19 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
20 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
22 static const double
23 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
24 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
25 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
26 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
27 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
29 double cbrt(double x)
31 int32_t hx;
32 double r,s,t=0.0,w;
33 u_int32_t sign;
34 u_int32_t high,low;
36 GET_HIGH_WORD(hx,x);
37 sign=hx&0x80000000; /* sign= sign(x) */
38 hx ^=sign;
39 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
40 GET_LOW_WORD(low,x);
41 if((hx|low)==0)
42 return(x); /* cbrt(0) is itself */
44 SET_HIGH_WORD(x,hx); /* x <- |x| */
45 /* rough cbrt to 5 bits */
46 if(hx<0x00100000) /* subnormal number */
47 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
48 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
50 else
51 SET_HIGH_WORD(t,hx/3+B1);
54 /* new cbrt to 23 bits, may be implemented in single precision */
55 r=t*t/x;
56 s=C+r*t;
57 t*=G+F/(s+E+D/s);
59 /* chopped to 20 bits and make it larger than cbrt(x) */
60 GET_HIGH_WORD(high,t);
61 INSERT_WORDS(t,high+0x00000001,0);
64 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
65 s=t*t; /* t*t is exact */
66 r=x/s;
67 w=t+t;
68 r=(r-t)/(w+r); /* r-s is exact */
69 t=t+t*r;
71 /* retore the sign bit */
72 GET_HIGH_WORD(high,t);
73 SET_HIGH_WORD(t,high|sign);
74 return(t);
76 libm_hidden_def(cbrt)