mirror of https://gitlab.com/rnger/amath
210 lines
5.3 KiB
C
210 lines
5.3 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/e_hypot.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 hypot.c
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*/
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#include "prim.h"
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/**
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* @brief hypot
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* @details
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* <pre>
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* Method
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* If (assume round-to-nearest) z=x*x+y*y
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* has error less than sqrt(2)/2 ulp, than
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* sqrt(z) has error less than 1 ulp (exercise).
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*
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* So, compute sqrt(x*x+y*y) with some care as
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* follows to get the error below 1 ulp:
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*
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* Assume x>y>0;
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* (if possible, set rounding to round-to-nearest)
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* 1. if x > 2y use
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* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
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* 2. if x <= 2y use
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* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
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* y1= y with lower 32 bits chopped, y2 = y-y1.
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*
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* NOTE: scaling may be necessary if some argument is too
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* large or too tiny
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*
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* Special cases:
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* hypot(x,y) is INF if x or y is +INF or -INF; else
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* hypot(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypot(x,y) returns sqrt(x^2+y^2) with error less
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* than 1 ulps (units in the last place)
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* </pre>
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*/
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double hypot(double x, double y)
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{
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double a = x, b = y, t1, t2, y1, y2, w;
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uint32_t j, k, ha, hb, hx, hy;
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GET_HIGH_WORD(hx, x);
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GET_HIGH_WORD(hy, y);
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ha = hx & 0x7FFFFFFF; // high word of x
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hb = hy & 0x7FFFFFFF; // high word of y
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if (hb > ha)
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{
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a = y;
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b = x;
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j = ha;
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ha = hb;
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hb = j;
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}
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else
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{
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a = x;
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b = y;
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}
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SET_HIGH_WORD(a, ha); // a <- |a|
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SET_HIGH_WORD(b, hb); // b <- |b|
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// x/y > 2**60
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if ((ha - hb) > 0x3C00000)
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{
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return a + b;
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}
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k = 0;
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// a>2**500
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if (ha > 0x5F300000)
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{
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// Inf or NaN
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if (ha >= 0x7FF00000)
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{
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uint32_t la, lb;
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w = a + b; // for sNaN
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GET_LOW_WORD(la, a);
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GET_LOW_WORD(lb, b);
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if (((ha & 0xFFFFF) | la) == 0)
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{
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w = a;
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}
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if (((hb ^ 0x7FF00000) | lb) == 0)
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{
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w = b;
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}
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return w;
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}
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// scale a and b by 2**-600
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ha -= 0x25800000;
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hb -= 0x25800000;
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k += 600;
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SET_HIGH_WORD(a, ha);
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SET_HIGH_WORD(b, hb);
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}
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// b < 2**-500
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if (hb < 0x20B00000)
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{
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// subnormal b or 0
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if (hb <= 0x000FFFFF)
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{
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uint32_t lb;
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GET_LOW_WORD(lb, b);
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if ((hb | lb) == 0)
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{
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return a;
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}
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t1 = 0;
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SET_HIGH_WORD(t1, 0x7FD00000); /* t1=2^1022 */
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b *= t1;
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a *= t1;
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k -= 1022;
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}
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else
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{ /* scale a and b by 2^600 */
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ha += 0x25800000; /* a *= 2^600 */
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hb += 0x25800000; /* b *= 2^600 */
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k -= 600;
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SET_HIGH_WORD(a, ha);
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SET_HIGH_WORD(b, hb);
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}
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}
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// medium size a and b
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w = a - b;
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if (w > b)
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{
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t1 = 0;
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SET_HIGH_WORD(t1, ha);
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t2 = a - t1;
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w = sqrt(t1 * t1 - (b * (-b) - t2 * (a + t1)));
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}
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else
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{
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a = a + a;
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y1 = 0;
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SET_HIGH_WORD(y1, hb);
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y2 = b - y1;
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t1 = 0;
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SET_HIGH_WORD(t1, ha + 0x00100000);
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t2 = a - t1;
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w = sqrt(t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
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}
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if (k != 0)
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{
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uint32_t ht1;
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t1 = 1.0;
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GET_HIGH_WORD(ht1, t1);
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SET_HIGH_WORD(t1, ht1 + (k << 20));
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return t1 * w;
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}
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return w;
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}
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