mirror of https://gitlab.com/rnger/amath
127 lines
3.8 KiB
C
127 lines
3.8 KiB
C
/*-
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* Copyright (c) 2014-2017 Carsten Sonne Larsen <cs@innolan.net>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* Project homepage:
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* https://amath.innolan.net
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*
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* The original source code can be obtained from:
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* http://www.netlib.org/fdlibm/s_cbrt.c
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*
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* =================================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* =================================================================
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*/
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/**
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* @file cbrt.c
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* @brief Cube root function
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*/
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#include "prim.h"
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static const unsigned
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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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static 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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/**
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* @brief Cube root function
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*/
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double cbrt(double x)
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{
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int32_t hx, lx, ht;
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double r, s, t = 0.0, w;
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uint32_t sign;
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GET_HIGH_WORD(hx, x);
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// sign = sign(x)
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sign = hx & 0x80000000;
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hx ^= sign;
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// cbrt(NaN,INF) is itself
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if (hx >= 0x7FF00000)
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{
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return x + x;
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}
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GET_LOW_WORD(lx, x);
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// cbrt(0) is itself
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if ((hx | lx) == 0)
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{
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return x;
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}
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// x <- |x|
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SET_HIGH_WORD(x, hx);
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// rough cbrt to 5 bits
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if (hx < 0x00100000) // subnormal number
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{
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SET_HIGH_WORD(t, 0x43500000); // set t= 2**54
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t *= x;
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GET_HIGH_WORD(ht, t);
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SET_HIGH_WORD(t, ht / 3 + B2);
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}
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else
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{
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SET_HIGH_WORD(t, hx / 3 + B1);
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}
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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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SET_LOW_WORD(t, 0);
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GET_HIGH_WORD(ht, t);
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SET_HIGH_WORD(t, ht + 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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GET_HIGH_WORD(ht, t);
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SET_HIGH_WORD(t, ht | sign);
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return (t);
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}
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