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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;
- }
- }
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