121 lines
2.2 KiB
C
121 lines
2.2 KiB
C
/*
|
|
* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
|
|
* See the copyright notice in the ACK home directory, in the file "Copyright".
|
|
*
|
|
* Author: Ceriel J.H. Jacobs
|
|
*/
|
|
|
|
/* $Header$ */
|
|
|
|
#include <math.h>
|
|
|
|
static double
|
|
sinus(x, quadrant)
|
|
double x;
|
|
{
|
|
/* sin(0.5*pi*x) = x * P(x*x)/Q(x*x) for x in [0,1] */
|
|
/* Hart & Cheney # 3374 */
|
|
|
|
static double p[6] = {
|
|
0.4857791909822798473837058825e+10,
|
|
-0.1808816670894030772075877725e+10,
|
|
0.1724314784722489597789244188e+09,
|
|
-0.6351331748520454245913645971e+07,
|
|
0.1002087631419532326179108883e+06,
|
|
-0.5830988897678192576148973679e+03
|
|
};
|
|
|
|
static double q[6] = {
|
|
0.3092566379840468199410228418e+10,
|
|
0.1202384907680254190870913060e+09,
|
|
0.2321427631602460953669856368e+07,
|
|
0.2848331644063908832127222835e+05,
|
|
0.2287602116741682420054505174e+03,
|
|
0.1000000000000000000000000000e+01
|
|
};
|
|
|
|
double xsqr;
|
|
int t;
|
|
|
|
if (x < 0) {
|
|
quadrant += 2;
|
|
x = -x;
|
|
}
|
|
if (M_PI_2 - x == M_PI_2) {
|
|
switch(quadrant) {
|
|
case 0:
|
|
case 2:
|
|
return 0.0;
|
|
case 1:
|
|
return 1.0;
|
|
case 3:
|
|
return -1.0;
|
|
}
|
|
}
|
|
if (x >= M_2PI) {
|
|
if (x <= 0x7fffffff) {
|
|
/* Use extended precision to calculate reduced argument.
|
|
Split 2pi in 2 parts a1 and a2, of which the first only
|
|
uses some bits of the mantissa, so that n * a1 is
|
|
exactly representable, where n is the integer part of
|
|
x/pi.
|
|
Here we used 12 bits of the mantissa for a1.
|
|
Also split x in integer part x1 and fraction part x2.
|
|
We then compute x-n*2pi as ((x1 - n*a1) + x2) - n*a2.
|
|
*/
|
|
#define A1 6.2822265625
|
|
#define A2 0.00095874467958647692528676655900576
|
|
double n = (long) (x / M_2PI);
|
|
double x1 = (long) x;
|
|
double x2 = x - x1;
|
|
x = x1 - n * A1;
|
|
x += x2;
|
|
x -= n * A2;
|
|
#undef A1
|
|
#undef A2
|
|
}
|
|
else {
|
|
extern double _fif();
|
|
double dummy;
|
|
|
|
x = _fif(x/M_2PI, 1.0, &dummy) * M_2PI;
|
|
}
|
|
}
|
|
x /= M_PI_2;
|
|
t = x;
|
|
x -= t;
|
|
quadrant = (quadrant + (int)(t % 4)) % 4;
|
|
if (quadrant & 01) {
|
|
x = 1 - x;
|
|
}
|
|
if (quadrant > 1) {
|
|
x = -x;
|
|
}
|
|
xsqr = x * x;
|
|
x = x * POLYNOM5(xsqr, p) / POLYNOM5(xsqr, q);
|
|
return x;
|
|
}
|
|
|
|
double
|
|
_sin(x)
|
|
double x;
|
|
{
|
|
return sinus(x, 0);
|
|
}
|
|
|
|
double
|
|
_cos(x)
|
|
double x;
|
|
{
|
|
if (x < 0) x = -x;
|
|
return sinus(x, 1);
|
|
}
|
|
|
|
/* EXTENSION */
|
|
double
|
|
_tan(x)
|
|
double x;
|
|
{
|
|
return _sin(x)/_cos(x);
|
|
}
|