381 lines
4.3 KiB
C++
381 lines
4.3 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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yycosine_phase();
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restore();
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}
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void
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yycosine_phase(void)
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{
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int n = 0;
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p1 = pop();
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if (car(p1) != symbol(ADD)) {
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push(p1);
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yycosine();
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return;
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}
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p2 = cdr(p1);
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while (iscons(p2)) {
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n = isnpi(car(p2));
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if (n)
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break;
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p2 = cdr(p2);
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}
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if (n == 0) {
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push(p1);
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yycosine();
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return;
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}
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push(p1);
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push(car(p2));
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subtract(); // remove phase
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switch (n) {
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case 1:
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yysine();
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negate();
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break;
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case 2:
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yycosine();
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negate();
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break;
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case 3:
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yysine();
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break;
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case 4:
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yycosine();
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break;
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}
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}
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void
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yycosine(void)
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{
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int n;
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double d;
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p1 = pop();
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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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}
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#if SELFTEST
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static char *s[] = {
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"cos(x)",
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"cos(x)",
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"cos(-x)",
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"cos(x)",
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"cos(b-a)",
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"cos(a-b)",
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// check against the floating point math library
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"f(a,x)=1+cos(float(a/360*2*pi))-float(x)+cos(a/360*2*pi)-x",
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"",
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"f(0,1)", // 0
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"1",
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"f(90,0)", // 90
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"1",
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"f(180,-1)", // 180
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"1",
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"f(270,0)", // 270
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"1",
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"f(360,1)", // 360
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"1",
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"f(-90,0)", // -90
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"1",
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"f(-180,-1)", // -180
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"1",
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"f(-270,0)", // -270
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"1",
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"f(-360,1)", // -360
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"1",
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"f(45,sqrt(2)/2)", // 45
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"1",
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"f(135,-sqrt(2)/2)", // 135
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"1",
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"f(225,-sqrt(2)/2)", // 225
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"1",
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"f(315,sqrt(2)/2)", // 315
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"1",
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"f(-45,sqrt(2)/2)", // -45
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"1",
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"f(-135,-sqrt(2)/2)", // -135
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"1",
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"f(-225,-sqrt(2)/2)", // -225
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"1",
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"f(-315,sqrt(2)/2)", // -315
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"1",
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"f(30,sqrt(3)/2)", // 30
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"1",
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"f(150,-sqrt(3)/2)", // 150
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"1",
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"f(210,-sqrt(3)/2)", // 210
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"1",
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"f(330,sqrt(3)/2)", // 330
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"1",
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"f(-30,sqrt(3)/2)", // -30
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"1",
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"f(-150,-sqrt(3)/2)", // -150
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"1",
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"f(-210,-sqrt(3)/2)", // -210
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"1",
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"f(-330,sqrt(3)/2)", // -330
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"1",
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"f(60,1/2)", // 60
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"1",
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"f(120,-1/2)", // 120
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"1",
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"f(240,-1/2)", // 240
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"1",
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"f(300,1/2)", // 300
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"1",
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"f(-60,1/2)", // -60
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"1",
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"f(-120,-1/2)", // -120
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"1",
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"f(-240,-1/2)", // -240
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"1",
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"f(-300,1/2)", // -300
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"1",
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"f=quote(f)",
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"",
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"cos(arccos(x))",
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"x",
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// bug fix for version 119
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"cos(1/12*pi)",
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"cos(1/12*pi)",
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"cos(arctan(4/3))",
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"3/5",
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"cos(-arctan(4/3))",
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"3/5",
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// phase
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"cos(x-8/2*pi)",
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"cos(x)",
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"cos(x-7/2*pi)",
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"-sin(x)",
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"cos(x-6/2*pi)",
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"-cos(x)",
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"cos(x-5/2*pi)",
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"sin(x)",
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"cos(x-4/2*pi)",
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"cos(x)",
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"cos(x-3/2*pi)",
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"-sin(x)",
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"cos(x-2/2*pi)",
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"-cos(x)",
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"cos(x-1/2*pi)",
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"sin(x)",
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"cos(x+0/2*pi)",
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"cos(x)",
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"cos(x+1/2*pi)",
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"-sin(x)",
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"cos(x+2/2*pi)",
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"-cos(x)",
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"cos(x+3/2*pi)",
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"sin(x)",
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"cos(x+4/2*pi)",
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"cos(x)",
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"cos(x+5/2*pi)",
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"-sin(x)",
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"cos(x+6/2*pi)",
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"-cos(x)",
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"cos(x+7/2*pi)",
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"sin(x)",
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"cos(x+8/2*pi)",
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"cos(x)",
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};
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void
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test_cos(void)
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{
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test(__FILE__, s, sizeof s / sizeof (char *));
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}
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#endif
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