| 1 | /* @(#)s_cbrt.c 5.1 93/09/24 */
|
|---|
| 2 | /*
|
|---|
| 3 | * ====================================================
|
|---|
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|---|
| 5 | *
|
|---|
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business.
|
|---|
| 7 | * Permission to use, copy, modify, and distribute this
|
|---|
| 8 | * software is freely granted, provided that this notice
|
|---|
| 9 | * is preserved.
|
|---|
| 10 | * ====================================================
|
|---|
| 11 | */
|
|---|
| 12 |
|
|---|
| 13 | #ifndef lint
|
|---|
| 14 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
|
|---|
| 15 | #endif
|
|---|
| 16 |
|
|---|
| 17 | #include "math.h"
|
|---|
| 18 | #include "math_private.h"
|
|---|
| 19 |
|
|---|
| 20 | /* cbrt(x)
|
|---|
| 21 | * Return cube root of x
|
|---|
| 22 | */
|
|---|
| 23 | static const u_int32_t
|
|---|
| 24 | B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
|
|---|
| 25 | B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
|
|---|
| 26 |
|
|---|
| 27 | static const double
|
|---|
| 28 | C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
|
|---|
| 29 | D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
|
|---|
| 30 | E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
|
|---|
| 31 | F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
|
|---|
| 32 | G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
|
|---|
| 33 |
|
|---|
| 34 | double
|
|---|
| 35 | cbrt(double x)
|
|---|
| 36 | {
|
|---|
| 37 | int32_t hx;
|
|---|
| 38 | double r,s,t=0.0,w;
|
|---|
| 39 | u_int32_t sign;
|
|---|
| 40 | u_int32_t high,low;
|
|---|
| 41 |
|
|---|
| 42 | GET_HIGH_WORD(hx,x);
|
|---|
| 43 | sign=hx&0x80000000; /* sign= sign(x) */
|
|---|
| 44 | hx ^=sign;
|
|---|
| 45 | if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
|
|---|
| 46 | GET_LOW_WORD(low,x);
|
|---|
| 47 | if((hx|low)==0)
|
|---|
| 48 | return(x); /* cbrt(0) is itself */
|
|---|
| 49 |
|
|---|
| 50 | SET_HIGH_WORD(x,hx); /* x <- |x| */
|
|---|
| 51 | /* rough cbrt to 5 bits */
|
|---|
| 52 | if(hx<0x00100000) /* subnormal number */
|
|---|
| 53 | {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
|
|---|
| 54 | t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
|
|---|
| 55 | }
|
|---|
| 56 | else
|
|---|
| 57 | SET_HIGH_WORD(t,hx/3+B1);
|
|---|
| 58 |
|
|---|
| 59 |
|
|---|
| 60 | /* new cbrt to 23 bits, may be implemented in single precision */
|
|---|
| 61 | r=t*t/x;
|
|---|
| 62 | s=C+r*t;
|
|---|
| 63 | t*=G+F/(s+E+D/s);
|
|---|
| 64 |
|
|---|
| 65 | /* chopped to 20 bits and make it larger than cbrt(x) */
|
|---|
| 66 | GET_HIGH_WORD(high,t);
|
|---|
| 67 | INSERT_WORDS(t,high+0x00000001,0);
|
|---|
| 68 |
|
|---|
| 69 |
|
|---|
| 70 | /* one step newton iteration to 53 bits with error less than 0.667 ulps */
|
|---|
| 71 | s=t*t; /* t*t is exact */
|
|---|
| 72 | r=x/s;
|
|---|
| 73 | w=t+t;
|
|---|
| 74 | r=(r-t)/(w+r); /* r-s is exact */
|
|---|
| 75 | t=t+t*r;
|
|---|
| 76 |
|
|---|
| 77 | /* retore the sign bit */
|
|---|
| 78 | GET_HIGH_WORD(high,t);
|
|---|
| 79 | SET_HIGH_WORD(t,high|sign);
|
|---|
| 80 | return(t);
|
|---|
| 81 | }
|
|---|
