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