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 1.9 1997/10/09 11:31:07 lukem Exp $"); 16 #endif 17 18 #include "math.h" 19 #include "math_private.h" 20 21 /* cbrt(x) 22 * Return cube root of x 23 */ 24 #ifdef __STDC__ 25 static const u_int32_t 26 #else 27 static u_int32_t 28 #endif 29 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 30 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 31 32 #ifdef __STDC__ 33 static const double 34 #else 35 static double 36 #endif 37 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 38 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 39 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 40 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 41 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 42 43 #ifdef __STDC__ 44 double cbrt(double x) 45 #else 46 double cbrt(x) 47 double x; 48 #endif 49 { 50 int32_t hx; 51 double r,s,t=0.0,w; 52 u_int32_t sign; 53 u_int32_t high,low; 54 55 GET_HIGH_WORD(hx,x); 56 sign=hx&0x80000000; /* sign= sign(x) */ 57 hx ^=sign; 58 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ 59 GET_LOW_WORD(low,x); 60 if((hx|low)==0) 61 return(x); /* cbrt(0) is itself */ 62 63 SET_HIGH_WORD(x,hx); /* x <- |x| */ 64 /* rough cbrt to 5 bits */ 65 if(hx<0x00100000) /* subnormal number */ 66 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ 67 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); 68 } 69 else 70 SET_HIGH_WORD(t,hx/3+B1); 71 72 73 /* new cbrt to 23 bits, may be implemented in single precision */ 74 r=t*t/x; 75 s=C+r*t; 76 t*=G+F/(s+E+D/s); 77 78 /* chopped to 20 bits and make it larger than cbrt(x) */ 79 GET_HIGH_WORD(high,t); 80 INSERT_WORDS(t,high+0x00000001,0); 81 82 83 /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 84 s=t*t; /* t*t is exact */ 85 r=x/s; 86 w=t+t; 87 r=(r-t)/(w+r); /* r-s is exact */ 88 t=t+t*r; 89 90 /* retore the sign bit */ 91 GET_HIGH_WORD(high,t); 92 SET_HIGH_WORD(t,high|sign); 93 return(t); 94 } 95