/
cos.c
176 lines (157 loc) · 2.27 KB
/
cos.c
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// Cosine function of numerical and symbolic arguments
#include "stdafx.h"
#include "defs.h"
void
eval_cos(void)
{
push(cadr(p1));
eval();
cosine();
}
void
cosine(void)
{
save();
p1 = pop();
if (car(p1) == symbol(ADD))
cosine_of_angle_sum();
else
cosine_of_angle();
restore();
}
// Use angle sum formula for special angles.
#define A p3
#define B p4
void
cosine_of_angle_sum(void)
{
p2 = cdr(p1);
while (iscons(p2)) {
B = car(p2);
if (isnpi(B)) {
push(p1);
push(B);
subtract();
A = pop();
push(A);
cosine();
push(B);
cosine();
multiply();
push(A);
sine();
push(B);
sine();
multiply();
subtract();
return;
}
p2 = cdr(p2);
}
cosine_of_angle();
}
void
cosine_of_angle(void)
{
int n;
double d;
if (car(p1) == symbol(ARCCOS)) {
push(cadr(p1));
return;
}
if (isdouble(p1)) {
d = cos(p1->u.d);
if (fabs(d) < 1e-10)
d = 0.0;
push_double(d);
return;
}
// cosine function is symmetric, cos(-x) = cos(x)
if (isnegative(p1)) {
push(p1);
negate();
p1 = pop();
}
// cos(arctan(x)) = 1 / sqrt(1 + x^2)
// see p. 173 of the CRC Handbook of Mathematical Sciences
if (car(p1) == symbol(ARCTAN)) {
push_integer(1);
push(cadr(p1));
push_integer(2);
power();
add();
push_rational(-1, 2);
power();
return;
}
// multiply by 180/pi
push(p1);
push_integer(180);
multiply();
push_symbol(PI);
divide();
n = pop_integer();
if (n < 0) {
push(symbol(COS));
push(p1);
list(2);
return;
}
switch (n % 360) {
case 90:
case 270:
push_integer(0);
break;
case 60:
case 300:
push_rational(1, 2);
break;
case 120:
case 240:
push_rational(-1, 2);
break;
case 45:
case 315:
push_rational(1, 2);
push_integer(2);
push_rational(1, 2);
power();
multiply();
break;
case 135:
case 225:
push_rational(-1, 2);
push_integer(2);
push_rational(1, 2);
power();
multiply();
break;
case 30:
case 330:
push_rational(1, 2);
push_integer(3);
push_rational(1, 2);
power();
multiply();
break;
case 150:
case 210:
push_rational(-1, 2);
push_integer(3);
push_rational(1, 2);
power();
multiply();
break;
case 0:
push_integer(1);
break;
case 180:
push_integer(-1);
break;
default:
push(symbol(COS));
push(p1);
list(2);
break;
}
}