ref: 53aac62a54ebbcc1781c0000d3e2384ed038c7bb
dir: /libmath/fdlibm/s_cbrt.c/
/* derived from /netlib/fdlibm */ /* @(#)s_cbrt.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ #include "fdlibm.h" /* cbrt(x) * Return cube root of x */ static const unsigned B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ static const double C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ double cbrt(double x) { int hx; double r,s,t=0.0,w; unsigned sign; hx = __HI(x); /* high word of x */ sign=hx&0x80000000; /* sign= sign(x) */ hx ^=sign; if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ if((hx|__LO(x))==0) return(x); /* cbrt(0) is itself */ __HI(x) = hx; /* x <- |x| */ /* rough cbrt to 5 bits */ if(hx<0x00100000) /* subnormal number */ {__HI(t)=0x43500000; /* set t= 2**54 */ t*=x; __HI(t)=__HI(t)/3+B2; } else __HI(t)=hx/3+B1; /* new cbrt to 23 bits, may be implemented in single precision */ r=t*t/x; s=C+r*t; t*=G+F/(s+E+D/s); /* chopped to 20 bits and make it larger than cbrt(x) */ __LO(t)=0; __HI(t)+=0x00000001; /* one step newton iteration to 53 bits with error less than 0.667 ulps */ s=t*t; /* t*t is exact */ r=x/s; w=t+t; r=(r-t)/(w+r); /* r-s is exact */ t=t+t*r; /* retore the sign bit */ __HI(t) |= sign; return(t); }