| |
| /* |
| * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| #include "fdlibm.h" |
| |
| /* cbrt(x) |
| * Return cube root of x |
| */ |
| #ifdef __STDC__ |
| static const unsigned |
| #else |
| static unsigned |
| #endif |
| B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
| B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
| |
| #ifdef __STDC__ |
| static const double |
| #else |
| static double |
| #endif |
| 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 */ |
| |
| #ifdef __STDC__ |
| double cbrt(double x) |
| #else |
| double cbrt(x) |
| double x; |
| #endif |
| { |
| 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); |
| } |
