s_cbrt.c revision 97413
12116Sjkh/* @(#)s_cbrt.c 5.1 93/09/24 */ 22116Sjkh/* 32116Sjkh * ==================================================== 42116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 52116Sjkh * 62116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 72116Sjkh * Permission to use, copy, modify, and distribute this 88870Srgrimes * software is freely granted, provided that this notice 92116Sjkh * is preserved. 102116Sjkh * ==================================================== 112116Sjkh */ 122116Sjkh 132116Sjkh#ifndef lint 1450476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/s_cbrt.c 97413 2002-05-28 18:15:04Z alfred $"; 152116Sjkh#endif 162116Sjkh 172116Sjkh#include "math.h" 182116Sjkh#include "math_private.h" 192116Sjkh 202116Sjkh/* cbrt(x) 212116Sjkh * Return cube root of x 222116Sjkh */ 232116Sjkhstatic const u_int32_t 242116Sjkh B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 252116Sjkh B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 262116Sjkh 272116Sjkhstatic const double 282116SjkhC = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 292116SjkhD = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 302116SjkhE = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 312116SjkhF = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 322116SjkhG = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 332116Sjkh 3497413Salfreddouble 3597413Salfredcbrt(double x) 362116Sjkh{ 372116Sjkh int32_t hx; 382116Sjkh double r,s,t=0.0,w; 392116Sjkh u_int32_t sign; 402116Sjkh u_int32_t high,low; 412116Sjkh 422116Sjkh GET_HIGH_WORD(hx,x); 432116Sjkh sign=hx&0x80000000; /* sign= sign(x) */ 442116Sjkh hx ^=sign; 452116Sjkh if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ 462116Sjkh GET_LOW_WORD(low,x); 478870Srgrimes if((hx|low)==0) 482116Sjkh return(x); /* cbrt(0) is itself */ 492116Sjkh 502116Sjkh SET_HIGH_WORD(x,hx); /* x <- |x| */ 512116Sjkh /* rough cbrt to 5 bits */ 522116Sjkh if(hx<0x00100000) /* subnormal number */ 532116Sjkh {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ 542116Sjkh t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); 552116Sjkh } 562116Sjkh else 572116Sjkh SET_HIGH_WORD(t,hx/3+B1); 582116Sjkh 592116Sjkh 602116Sjkh /* new cbrt to 23 bits, may be implemented in single precision */ 612116Sjkh r=t*t/x; 622116Sjkh s=C+r*t; 638870Srgrimes t*=G+F/(s+E+D/s); 642116Sjkh 658870Srgrimes /* chopped to 20 bits and make it larger than cbrt(x) */ 662116Sjkh GET_HIGH_WORD(high,t); 672116Sjkh INSERT_WORDS(t,high+0x00000001,0); 682116Sjkh 692116Sjkh 702116Sjkh /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 712116Sjkh s=t*t; /* t*t is exact */ 722116Sjkh r=x/s; 732116Sjkh w=t+t; 742116Sjkh r=(r-t)/(w+r); /* r-s is exact */ 752116Sjkh t=t+t*r; 762116Sjkh 772116Sjkh /* retore the sign bit */ 782116Sjkh GET_HIGH_WORD(high,t); 792116Sjkh SET_HIGH_WORD(t,high|sign); 802116Sjkh return(t); 812116Sjkh} 82