mirror of https://gitlab.com/rnger/amath
183 lines
5.9 KiB
C
183 lines
5.9 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_atan2.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 atan2.c
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* @brief Inverse tangent function
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*/
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#include "prim.h"
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static const double
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tiny = 1.0e-300,
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zero = 0.0,
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pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
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pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
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pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
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pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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/**
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* @brief Inverse tangent function
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* @param y,x
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* @details
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* <pre>
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* Method
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* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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* 2. Reduce x to positive by (if x and y are unexceptional):
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* ARG (x+iy) = arctan(y/x) ... if x > 0,
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* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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*
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* Special cases
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* ATAN2((anything), NaN ) is NaN;
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* ATAN2(NAN , (anything) ) is NaN;
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* ATAN2(+-0, +(anything but NaN)) is +-0 ;
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* ATAN2(+-0, -(anything but NaN)) is +-pi ;
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* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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* ATAN2(+-INF,+INF ) is +-pi/4 ;
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* ATAN2(+-INF,-INF ) is +-3pi/4;
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* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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*
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* Constants
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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* </pre>
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*/
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double atan2(double y, double x)
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{
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double z;
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int32_t k, m, hx, hy, ix, iy;
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uint32_t lx, ly;
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EXTRACT_WORDS(hx, lx, x);
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ix = hx & 0x7fffffff;
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EXTRACT_WORDS(hy, ly, y);
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iy = hy & 0x7fffffff;
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if (((ix | ((lx | -lx) >> 31)) > 0x7ff00000) ||
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((iy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* x or y is NaN */
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return x + y;
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if (((hx - 0x3ff00000) | lx) == 0)
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return atan(y); /* x=1.0 */
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m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */
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/* when y = 0 */
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if ((iy | ly) == 0)
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{
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switch (m)
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{
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case 0:
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case 1:
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return y; /* atan(+-0,+anything)=+-0 */
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case 2:
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return pi + tiny; /* atan(+0,-anything) = pi */
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case 3:
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return -pi - tiny; /* atan(-0,-anything) =-pi */
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}
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}
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/* when x = 0 */
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if ((ix | lx) == 0)
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return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;
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/* when x is INF */
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if (ix == 0x7ff00000)
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{
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if (iy == 0x7ff00000)
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{
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switch (m)
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{
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case 0:
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return pi_o_4 + tiny; /* atan(+INF,+INF) */
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case 1:
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return -pi_o_4 - tiny; /* atan(-INF,+INF) */
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case 2:
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return 3.0 * pi_o_4 + tiny; /*atan(+INF,-INF)*/
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case 3:
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return -3.0 * pi_o_4 - tiny; /*atan(-INF,-INF)*/
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}
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}
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else
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{
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switch (m)
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{
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case 0:
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return zero; /* atan(+...,+INF) */
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case 1:
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return -zero; /* atan(-...,+INF) */
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case 2:
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return pi + tiny; /* atan(+...,-INF) */
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case 3:
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return -pi - tiny; /* atan(-...,-INF) */
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}
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}
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}
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/* when y is INF */
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if (iy == 0x7ff00000)
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return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;
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/* compute y/x */
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k = (iy - ix) >> 20;
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if (k > 60)
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z = pi_o_2 + 0.5 * pi_lo; /* |y/x| > 2**60 */
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else if (hx < 0 && k < -60)
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z = 0.0; /* |y|/x < -2**60 */
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else
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z = atan(fabs(y / x)); /* safe to do y/x */
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switch (m)
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{
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case 0:
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return z; /* atan(+,+) */
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case 1:
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{
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uint32_t zh;
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GET_HIGH_WORD(zh, z);
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SET_HIGH_WORD(z, zh ^ 0x80000000);
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}
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return z; /* atan(-,+) */
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case 2:
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return pi - (z - pi_lo); /* atan(+,-) */
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default: /* case 3 */
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return (z - pi_lo) - pi; /* atan(-,-) */
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}
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}
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