123 lines
2.6 KiB
C
123 lines
2.6 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 <math.h>
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#include "localmath.h"
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double
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tan(double x)
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{
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/* First reduce range to [0, pi/4].
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Then use approximation tan(x*pi/4) = x * P(x*x)/Q(x*x).
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Hart & Cheney # 4288
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Use: tan(x) = 1/tan(pi/2 - x)
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tan(-x) = -tan(x)
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tan(x+k*pi) = tan(x)
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*/
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static double p[5] = {
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-0.5712939549476836914932149599e+10,
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0.4946855977542506692946040594e+09,
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-0.9429037070546336747758930844e+07,
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0.5282725819868891894772108334e+05,
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-0.6983913274721550913090621370e+02
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};
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static double q[6] = {
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-0.7273940551075393257142652672e+10,
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0.2125497341858248436051062591e+10,
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-0.8000791217568674135274814656e+08,
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0.8232855955751828560307269007e+06,
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-0.2396576810261093558391373322e+04,
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0.1000000000000000000000000000e+01
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};
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int negative = x < 0;
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double tmp, tmp1, tmp2;
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double xsq;
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int invert = 0;
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int ip;
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if (negative) x = -x;
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/* first reduce to [0, pi) */
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if (x >= M_PI) {
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if (x <= 0x7fffffff) {
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/* Use extended precision to calculate reduced argument.
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Split pi in 2 parts a1 and a2, of which the first only
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uses some bits of the mantissa, so that n * a1 is
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exactly representable, where n is the integer part of
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x/pi.
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Here we used 12 bits of the mantissa for a1.
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Also split x in integer part x1 and fraction part x2.
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We then compute x-n*pi as ((x1 - n*a1) + x2) - n*a2.
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*/
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#define A1 3.14111328125
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#define A2 0.00047937233979323846264338327950288
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double n = (long) (x / M_PI);
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double x1 = (long) x;
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double x2 = x - x1;
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x = x1 - n * A1;
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x += x2;
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x -= n * A2;
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#undef A1
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#undef A2
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}
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else {
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x = modf(x/M_PI, &tmp) * M_PI;
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}
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}
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/* because the approximation uses x*pi/4, we reverse this */
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x /= M_PI_4;
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ip = (int) x;
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x -= ip;
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switch(ip) {
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case 0:
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/* [0,pi/4] */
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break;
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case 1:
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/* [pi/4, pi/2]
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tan(x+pi/4) = 1/tan(pi/2 - (x+pi/4)) = 1/tan(pi/4 - x)
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*/
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invert = 1;
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x = 1.0 - x;
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break;
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case 2:
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/* [pi/2, 3pi/4]
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tan(x+pi/2) = tan((x+pi/2)-pi) = -tan(pi/2 - x) =
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-1/tan(x)
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*/
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negative = ! negative;
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invert = 1;
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break;
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case 3:
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/* [3pi/4, pi)
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tan(x+3pi/4) = tan(x-pi/4) = - tan(pi/4-x)
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*/
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x = 1.0 - x;
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negative = ! negative;
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break;
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}
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xsq = x * x;
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tmp1 = x*POLYNOM4(xsq, p);
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tmp2 = POLYNOM5(xsq, q);
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tmp = tmp1 / tmp2;
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if (invert) {
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if (tmp == 0.0) {
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errno = ERANGE;
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tmp = HUGE_VAL;
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}
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else tmp = tmp2 / tmp1;
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}
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return negative ? -tmp : tmp;
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}
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