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418 lines
7.8 KiB
C
418 lines
7.8 KiB
C
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/* atan.c
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*
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* Inverse circular tangent
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* (arctangent)
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, atan();
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*
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* y = atan( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns radian angle between -pi/2 and +pi/2 whose tangent
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* is x.
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*
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* Range reduction is from three intervals into the interval
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* from zero to 0.66. The approximant uses a rational
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* function of degree 4/5 of the form x + x**3 P(x)/Q(x).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC -10, 10 50000 2.4e-17 8.3e-18
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* IEEE -10, 10 10^6 1.8e-16 5.0e-17
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*
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*/
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/* atan2()
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*
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* Quadrant correct inverse circular tangent
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, z, atan2();
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*
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* z = atan2( y, x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns radian angle whose tangent is y/x.
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* Define compile time symbol ANSIC = 1 for ANSI standard,
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* range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
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* 0 to 2PI, args (x,y).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -10, 10 10^6 2.5e-16 6.9e-17
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* See atan.c.
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*
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*/
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/* atan.c */
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1995, 2000 by Stephen L. Moshier
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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 are met:
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1. Redistributions of source code must retain the above copyright notice,
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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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3. Neither the name of the <ORGANIZATION> nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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*/
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#include "mconf.h"
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/* arctan(x) = x + x^3 P(x^2)/Q(x^2)
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0 <= x <= 0.66
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Peak relative error = 2.6e-18 */
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#ifdef UNK
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static double P[5] = {
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-8.750608600031904122785E-1,
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-1.615753718733365076637E1,
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-7.500855792314704667340E1,
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-1.228866684490136173410E2,
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-6.485021904942025371773E1,
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};
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static double Q[5] = {
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/* 1.000000000000000000000E0, */
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2.485846490142306297962E1,
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1.650270098316988542046E2,
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4.328810604912902668951E2,
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4.853903996359136964868E2,
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1.945506571482613964425E2,
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};
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/* tan( 3*pi/8 ) */
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static double T3P8 = 2.41421356237309504880;
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#endif
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#ifdef DEC
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static short P[20] = {
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0140140,0001775,0007671,0026242,
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0141201,0041242,0155534,0001715,
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0141626,0002141,0132100,0011625,
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0141765,0142771,0064055,0150453,
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0141601,0131517,0164507,0062164,
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};
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static short Q[20] = {
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/* 0040200,0000000,0000000,0000000, */
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0041306,0157042,0154243,0000742,
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0042045,0003352,0016707,0150452,
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0042330,0070306,0113425,0170730,
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0042362,0130770,0116602,0047520,
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0042102,0106367,0156753,0013541,
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};
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/* tan( 3*pi/8 ) = 2.41421356237309504880 */
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static unsigned short T3P8A[] = {040432,0101171,0114774,0167462,};
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#define T3P8 *(double *)T3P8A
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#endif
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#ifdef IBMPC
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static short P[20] = {
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0x2594,0xa1f7,0x007f,0xbfec,
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0x807a,0x5b6b,0x2854,0xc030,
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0x0273,0x3688,0xc08c,0xc052,
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0xba25,0x2d05,0xb8bf,0xc05e,
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0xec8e,0xfd28,0x3669,0xc050,
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};
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static short Q[20] = {
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/* 0x0000,0x0000,0x0000,0x3ff0, */
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0x603c,0x5b14,0xdbc4,0x4038,
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0xfa25,0x43b8,0xa0dd,0x4064,
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0xbe3b,0xd2e2,0x0e18,0x407b,
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0x49ea,0x13b0,0x563f,0x407e,
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0x62ec,0xfbbd,0x519e,0x4068,
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};
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/* tan( 3*pi/8 ) = 2.41421356237309504880 */
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static unsigned short T3P8A[] = {0x9de6,0x333f,0x504f,0x4003};
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#define T3P8 *(double *)T3P8A
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#endif
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#ifdef MIEEE
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static short P[20] = {
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0xbfec,0x007f,0xa1f7,0x2594,
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0xc030,0x2854,0x5b6b,0x807a,
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0xc052,0xc08c,0x3688,0x0273,
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0xc05e,0xb8bf,0x2d05,0xba25,
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0xc050,0x3669,0xfd28,0xec8e,
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};
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static short Q[20] = {
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/* 0x3ff0,0x0000,0x0000,0x0000, */
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0x4038,0xdbc4,0x5b14,0x603c,
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0x4064,0xa0dd,0x43b8,0xfa25,
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0x407b,0x0e18,0xd2e2,0xbe3b,
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0x407e,0x563f,0x13b0,0x49ea,
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0x4068,0x519e,0xfbbd,0x62ec,
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};
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/* tan( 3*pi/8 ) = 2.41421356237309504880 */
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static unsigned short T3P8A[] = {
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0x4003,0x504f,0x333f,0x9de6
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};
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#define T3P8 *(double *)T3P8A
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#endif
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#ifdef ANSIPROT
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double atan ( double );
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extern double fabs ( double );
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extern int signbit ( double );
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extern int isnan ( double );
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#else
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double polevl(), p1evl(), atan(), fabs();
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int signbit(), isnan();
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#endif
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extern double PI, PIO2, PIO4, INFINITY, NEGZERO, MAXNUM;
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/* pi/2 = PIO2 + MOREBITS. */
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#ifdef DEC
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#define MOREBITS 5.721188726109831840122E-18
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#else
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#define MOREBITS 6.123233995736765886130E-17
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#endif
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double c_atan(x)
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double x;
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{
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double y, z;
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short sign, flag;
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#ifdef MINUSZERO
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if( x == 0.0 )
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return(x);
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#endif
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#ifdef INFINITIES
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if(x == INFINITY)
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return(PIO2);
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if(x == -INFINITY)
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return(-PIO2);
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#endif
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/* make argument positive and save the sign */
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sign = 1;
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if( x < 0.0 )
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{
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sign = -1;
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x = -x;
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}
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/* range reduction */
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flag = 0;
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if( x > T3P8 )
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{
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y = PIO2;
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flag = 1;
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x = -( 1.0/x );
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}
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else if( x <= 0.66 )
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{
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y = 0.0;
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}
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else
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{
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y = PIO4;
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flag = 2;
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x = (x-1.0)/(x+1.0);
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}
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z = x * x;
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z = z * polevl( z, P, 4 ) / p1evl( z, Q, 5 );
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z = x * z + x;
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if( flag == 2 )
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z += 0.5 * MOREBITS;
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else if( flag == 1 )
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z += MOREBITS;
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y = y + z;
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if( sign < 0 )
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y = -y;
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return(y);
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}
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/* atan2 */
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#ifdef ANSIC
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double c_atan2( y, x )
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#else
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double c_atan2( x, y )
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#endif
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double x, y;
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{
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double z, w;
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short code;
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code = 0;
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#ifdef NANS
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if( isnan(x) )
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return(x);
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if( isnan(y) )
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return(y);
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#endif
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#ifdef MINUSZERO
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if( y == 0.0 )
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{
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if( signbit(y) )
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{
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if( x > 0.0 )
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z = y;
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else if( x < 0.0 )
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z = -PI;
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else
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{
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if( signbit(x) )
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z = -PI;
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else
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z = y;
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}
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}
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else /* y is +0 */
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{
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if( x == 0.0 )
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{
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if( signbit(x) )
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z = PI;
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else
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z = 0.0;
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}
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else if( x > 0.0 )
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z = 0.0;
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else
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z = PI;
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}
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return z;
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}
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if( x == 0.0 )
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{
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if( y > 0.0 )
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z = PIO2;
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else
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z = -PIO2;
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return z;
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}
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#endif /* MINUSZERO */
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#ifdef INFINITIES
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if( x == INFINITY )
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{
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if( y == INFINITY )
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z = 0.25 * PI;
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else if( y == -INFINITY )
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z = -0.25 * PI;
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else if( y < 0.0 )
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z = NEGZERO;
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else
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z = 0.0;
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return z;
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}
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if( x == -INFINITY )
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{
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if( y == INFINITY )
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z = 0.75 * PI;
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else if( y <= -INFINITY )
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z = -0.75 * PI;
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else if( y >= 0.0 )
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z = PI;
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else
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z = -PI;
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return z;
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}
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if( y == INFINITY )
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return( PIO2 );
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if( y == -INFINITY )
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return( -PIO2 );
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#endif
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if( x < 0.0 )
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code = 2;
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if( y < 0.0 )
|
|||
|
|
code |= 1;
|
|||
|
|
|
|||
|
|
#ifdef INFINITIES
|
|||
|
|
if( x == 0.0 )
|
|||
|
|
#else
|
|||
|
|
if( fabs(x) <= (fabs(y) / MAXNUM) )
|
|||
|
|
#endif
|
|||
|
|
{
|
|||
|
|
if( code & 1 )
|
|||
|
|
{
|
|||
|
|
#if ANSIC
|
|||
|
|
return( -PIO2 );
|
|||
|
|
#else
|
|||
|
|
return( 3.0*PIO2 );
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
if( y == 0.0 )
|
|||
|
|
return( 0.0 );
|
|||
|
|
return( PIO2 );
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if( y == 0.0 )
|
|||
|
|
{
|
|||
|
|
if( code & 2 )
|
|||
|
|
return( PI );
|
|||
|
|
return( 0.0 );
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
switch( code )
|
|||
|
|
{
|
|||
|
|
#if ANSIC
|
|||
|
|
default:
|
|||
|
|
case 0:
|
|||
|
|
case 1: w = 0.0; break;
|
|||
|
|
case 2: w = PI; break;
|
|||
|
|
case 3: w = -PI; break;
|
|||
|
|
#else
|
|||
|
|
default:
|
|||
|
|
case 0: w = 0.0; break;
|
|||
|
|
case 1: w = 2.0 * PI; break;
|
|||
|
|
case 2:
|
|||
|
|
case 3: w = PI; break;
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
z = w + c_atan( y/x );
|
|||
|
|
#ifdef MINUSZERO
|
|||
|
|
if( z == 0.0 && y < 0 )
|
|||
|
|
z = NEGZERO;
|
|||
|
|
#endif
|
|||
|
|
return( z );
|
|||
|
|
}
|