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[] = "$Id: s_cbrt.c,v 1.6 1994/08/18 23:06:25 jtc 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 #ifdef __STDC__ 24 static const u_int32_t 25 #else 26 static u_int32_t 27 #endif 28 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 29 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 30 31 #ifdef __STDC__ 32 static const double 33 #else 34 static double 35 #endif 36 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 37 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 38 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 39 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 40 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 41 42 #ifdef __STDC__ 43 double cbrt(double x) 44 #else 45 double cbrt(x) 46 double x; 47 #endif 48 { 49 int32_t hx; 50 double r,s,t=0.0,w; 51 u_int32_t sign; 52 u_int32_t high,low; 53 54 GET_HIGH_WORD(hx,x); 55 sign=hx&0x80000000; /* sign= sign(x) */ 56 hx ^=sign; 57 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ 58 GET_LOW_WORD(low,x); 59 if((hx|low)==0) 60 return(x); /* cbrt(0) is itself */ 61 62 SET_HIGH_WORD(x,hx); /* x <- |x| */ 63 /* rough cbrt to 5 bits */ 64 if(hx<0x00100000) /* subnormal number */ 65 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ 66 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); 67 } 68 else 69 SET_HIGH_WORD(t,hx/3+B1); 70 71 72 /* new cbrt to 23 bits, may be implemented in single precision */ 73 r=t*t/x; 74 s=C+r*t; 75 t*=G+F/(s+E+D/s); 76 77 /* chopped to 20 bits and make it larger than cbrt(x) */ 78 GET_HIGH_WORD(high,t); 79 INSERT_WORDS(t,high+0x00000001,0); 80 81 82 /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 83 s=t*t; /* t*t is exact */ 84 r=x/s; 85 w=t+t; 86 r=(r-t)/(w+r); /* r-s is exact */ 87 t=t+t*r; 88 89 /* retore the sign bit */ 90 GET_HIGH_WORD(high,t); 91 SET_HIGH_WORD(t,high|sign); 92 return(t); 93 } 94