105 lines
2.4 KiB
C
105 lines
2.4 KiB
C
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/*
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* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
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* See the copyright notice in the ACK home directory, in the file "Copyright".
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*
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* Author: Ceriel J.H. Jacobs
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*/
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/* $Header$ */
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#include <errno.h>
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#include <float.h>
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#include <math.h>
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#include "localmath.h"
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double
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atan(double x)
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{
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/* The interval [0, infinity) is treated as follows:
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Define partition points Xi
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X0 = 0
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X1 = tan(pi/16)
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X2 = tan(3pi/16)
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X3 = tan(5pi/16)
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X4 = tan(7pi/16)
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X5 = infinity
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and evaluation nodes xi
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x2 = tan(2pi/16)
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x3 = tan(4pi/16)
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x4 = tan(6pi/16)
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x5 = infinity
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An argument x in [Xn-1, Xn] is now reduced to an argument
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t in [-X1, X1] by the following formulas:
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t = 1/xn - (1/(xn*xn) + 1)/((1/xn) + x)
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arctan(x) = arctan(xi) + arctan(t)
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For the interval [0, p/16] an approximation is used:
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arctan(x) = x * P(x*x)/Q(x*x)
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*/
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static struct precomputed {
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double X; /* partition point */
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double arctan; /* arctan of evaluation node */
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double one_o_x; /* 1 / xn */
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double one_o_xsq_p_1; /* 1 / (xn*xn) + 1 */
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} prec[5] = {
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{ 0.19891236737965800691159762264467622,
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0.0,
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0.0, /* these don't matter */
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0.0 } ,
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{ 0.66817863791929891999775768652308076, /* tan(3pi/16) */
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M_PI_8,
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2.41421356237309504880168872420969808,
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6.82842712474619009760337744841939616 },
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{ 1.49660576266548901760113513494247691, /* tan(5pi/16) */
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M_PI_4,
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1.0,
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2.0 },
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{ 5.02733949212584810451497507106407238, /* tan(7pi/16) */
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M_3PI_8,
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0.41421356237309504880168872420969808,
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1.17157287525380998659662255158060384 },
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{ DBL_MAX,
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M_PI_2,
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0.0,
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1.0 }};
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/* Hart & Cheney # 5037 */
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static double p[5] = {
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0.7698297257888171026986294745e+03,
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0.1557282793158363491416585283e+04,
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0.1033384651675161628243434662e+04,
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0.2485841954911840502660889866e+03,
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0.1566564964979791769948970100e+02
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};
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static double q[6] = {
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0.7698297257888171026986294911e+03,
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0.1813892701754635858982709369e+04,
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0.1484049607102276827437401170e+04,
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0.4904645326203706217748848797e+03,
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0.5593479839280348664778328000e+02,
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0.1000000000000000000000000000e+01
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};
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int negative = x < 0.0;
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register struct precomputed *pr = prec;
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if (negative) {
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x = -x;
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}
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while (x > pr->X) pr++;
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if (pr != prec) {
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x = pr->arctan +
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atan(pr->one_o_x - pr->one_o_xsq_p_1/(pr->one_o_x + x));
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}
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else {
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double xsq = x*x;
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x = x * POLYNOM4(xsq, p)/POLYNOM5(xsq, q);
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}
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return negative ? -x : x;
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}
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