90 lines
3.0 KiB
C#
90 lines
3.0 KiB
C#
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/*
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* Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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static partial class fdlibm
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{
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internal static double cbrt(double x)
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{
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/* cbrt(x)
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* Return cube root of x
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*/
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const int
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B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
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B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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const double
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C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
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D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
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E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
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F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
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G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
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int hx;
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double r,s,t=0.0,w;
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int sign;
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hx = __HI(x); /* high word of x */
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sign=hx&unchecked((int)0x80000000); /* sign= sign(x) */
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hx ^=sign;
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if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
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if((hx|__LO(x))==0)
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return(x); /* cbrt(0) is itself */
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x = __HI(x, hx); /* x <- |x| */
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/* rough cbrt to 5 bits */
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if(hx<0x00100000) /* subnormal number */
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{t = __HI(t, 0x43500000); /* set t= 2**54 */
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t*=x; t = __HI(t, __HI(t)/3+B2);
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}
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else
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t = __HI(t, hx/3+B1);
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/* new cbrt to 23 bits, may be implemented in single precision */
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r=t*t/x;
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s=C+r*t;
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t*=G+F/(s+E+D/s);
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/* chopped to 20 bits and make it larger than cbrt(x) */
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t = __LO(t, 0); t = __HI(t, __HI(t) + 0x00000001);
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/* one step newton iteration to 53 bits with error less than 0.667 ulps */
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s=t*t; /* t*t is exact */
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r=x/s;
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w=t+t;
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r=(r-t)/(w+r); /* r-s is exact */
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t=t+t*r;
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/* retore the sign bit */
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t = __HI(t, __HI(t) | sign);
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return(t);
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}
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}
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