1 /* derived from /netlib/fdlibm */ 2 3 /* @(#)s_cbrt.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 * 14 */ 15 16 #include "fdlibm.h" 17 18 /* cbrt(x) 19 * Return cube root of x 20 */ 21 static const unsigned 22 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ 23 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ 24 25 static const double 26 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ 27 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ 28 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ 29 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ 30 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ 31 cbrt(double x)32 double cbrt(double x) 33 { 34 int hx; 35 double r,s,t=0.0,w; 36 unsigned sign; 37 38 39 hx = __HI(x); /* high word of x */ 40 sign=hx&0x80000000; /* sign= sign(x) */ 41 hx ^=sign; 42 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ 43 if((hx|__LO(x))==0) 44 return(x); /* cbrt(0) is itself */ 45 46 __HI(x) = hx; /* x <- |x| */ 47 /* rough cbrt to 5 bits */ 48 if(hx<0x00100000) /* subnormal number */ 49 {__HI(t)=0x43500000; /* set t= 2**54 */ 50 t*=x; __HI(t)=__HI(t)/3+B2; 51 } 52 else 53 __HI(t)=hx/3+B1; 54 55 56 /* new cbrt to 23 bits, may be implemented in single precision */ 57 r=t*t/x; 58 s=C+r*t; 59 t*=G+F/(s+E+D/s); 60 61 /* chopped to 20 bits and make it larger than cbrt(x) */ 62 __LO(t)=0; __HI(t)+=0x00000001; 63 64 65 /* one step newton iteration to 53 bits with error less than 0.667 ulps */ 66 s=t*t; /* t*t is exact */ 67 r=x/s; 68 w=t+t; 69 r=(r-t)/(w+r); /* r-s is exact */ 70 t=t+t*r; 71 72 /* retore the sign bit */ 73 __HI(t) |= sign; 74 return(t); 75 } 76