mirror of https://gitlab.com/rnger/amath
175 lines
6.0 KiB
C
175 lines
6.0 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_atan.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 atan.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 atanhi[] = {
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4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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};
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static const double atanlo[] = {
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2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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};
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static const double aT[] = {
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3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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};
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static const double
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one = 1.0,
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huge = 1.0e300;
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/**
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* @brief Inverse tangent function
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* @details
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* <pre>
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* Method
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* 1. Reduce x to positive by atan(x) = -atan(-x).
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* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
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* is further reduced to one of the following intervals and the
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* arctangent of t is evaluated by the corresponding formula:
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*
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* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
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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 atan(double x)
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{
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double w, s1, s2, z;
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int32_t ix, hx, id;
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GET_HIGH_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x44100000)
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{ /* if |x| >= 2^66 */
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uint32_t low;
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GET_LOW_WORD(low, x);
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if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (low != 0)))
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return NAN;
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if (hx > 0)
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return atanhi[3] + atanlo[3];
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else
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return -atanhi[3] - atanlo[3];
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}
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if (ix < 0x3fdc0000)
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{ /* |x| < 0.4375 */
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if (ix < 0x3e200000)
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{ /* |x| < 2^-29 */
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if (huge + x > one)
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return x; /* raise inexact */
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}
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id = -1;
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}
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else
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{
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x = fabs(x);
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if (ix < 0x3ff30000)
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{ /* |x| < 1.1875 */
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if (ix < 0x3fe60000)
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{ /* 7/16 <=|x|<11/16 */
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id = 0;
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x = (2.0 * x - one) / (2.0 + x);
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}
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else
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{ /* 11/16<=|x|< 19/16 */
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id = 1;
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x = (x - one) / (x + one);
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}
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}
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else
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{
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if (ix < 0x40038000)
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{ /* |x| < 2.4375 */
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id = 2;
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x = (x - 1.5) / (one + 1.5 * x);
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}
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else
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{ /* 2.4375 <= |x| < 2^66 */
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id = 3;
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x = -1.0 / x;
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}
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}
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}
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/* end of argument reduction */
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z = x * x;
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w = z * z;
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/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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s1 = z * (aT[0] + w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10])))));
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s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9]))));
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if (id < 0)
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{
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return x - x * (s1 + s2);
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}
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z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
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return (hx < 0) ? -z : z;
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}
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