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#include <sys/cdefs.h> 14#if defined(LIBM_SCCS) && !defined(lint) 15__RCSID("$NetBSD: s_cbrt.c,v 1.12 2013/11/19 19:24:34 joerg Exp $"); 16#endif 17 18#include "namespace.h" 19#include "math.h" 20#include "math_private.h" 21 22#ifndef __HAVE_LONG_DOUBLE 23__strong_alias(_cbrtl, cbrt) 24__weak_alias(cbrtl, _cbrtl) 25#endif 26 27/* cbrt(x) 28 * Return cube root of x 29 */ 30static const u_int32_t 31 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 32 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 33 34static const double 35C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 36D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 37E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 38F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 39G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 40 41double 42cbrt(double x) 43{ 44 int32_t hx; 45 double r,s,t=0.0,w; 46 u_int32_t sign; 47 u_int32_t high,low; 48 49 GET_HIGH_WORD(hx,x); 50 sign=hx&0x80000000; /* sign= sign(x) */ 51 hx ^=sign; 52 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ 53 GET_LOW_WORD(low,x); 54 if((hx|low)==0) 55 return(x); /* cbrt(0) is itself */ 56 57 SET_HIGH_WORD(x,hx); /* x <- |x| */ 58 /* rough cbrt to 5 bits */ 59 if(hx<0x00100000) /* subnormal number */ 60 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ 61 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); 62 } 63 else 64 SET_HIGH_WORD(t,hx/3+B1); 65 66 67 /* new cbrt to 23 bits, may be implemented in single precision */ 68 r=t*t/x; 69 s=C+r*t; 70 t*=G+F/(s+E+D/s); 71 72 /* chopped to 20 bits and make it larger than cbrt(x) */ 73 GET_HIGH_WORD(high,t); 74 INSERT_WORDS(t,high+0x00000001,0); 75 76 77 /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 78 s=t*t; /* t*t is exact */ 79 r=x/s; 80 w=t+t; 81 r=(r-t)/(w+r); /* r-s is exact */ 82 t=t+t*r; 83 84 /* retore the sign bit */ 85 GET_HIGH_WORD(high,t); 86 SET_HIGH_WORD(t,high|sign); 87 return(t); 88} 89