377 lines
4.4 KiB
C++
377 lines
4.4 KiB
C++
// Sine 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_sin(void)
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{
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push(cadr(p1));
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eval();
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sine();
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}
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void
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sine(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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sine_of_angle_sum();
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else
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sine_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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sine_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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sine();
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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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cosine();
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push(B);
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sine();
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multiply();
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add();
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return;
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}
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p2 = cdr(p2);
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}
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sine_of_angle();
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}
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void
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sine_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(ARCSIN)) {
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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 = sin(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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// sine function is antisymmetric, sin(-x) = -sin(x)
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if (isnegative(p1)) {
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push(p1);
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negate();
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sine();
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negate();
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return;
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}
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// sin(arctan(x)) = x / 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(cadr(p1));
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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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multiply();
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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(SIN));
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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 0:
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case 180:
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push_integer(0);
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break;
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case 30:
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case 150:
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push_rational(1, 2);
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break;
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case 210:
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case 330:
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push_rational(-1, 2);
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break;
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case 45:
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case 135:
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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 225:
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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 60:
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case 120:
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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 240:
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case 300:
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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 90:
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push_integer(1);
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break;
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case 270:
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push_integer(-1);
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break;
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default:
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push(symbol(SIN));
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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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"sin(x)",
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"sin(x)",
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"sin(-x)",
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"-sin(x)",
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"sin(b-a)",
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"-sin(a-b)",
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// check against the floating point math library
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"f(a,x)=1+sin(float(a/360*2*pi))-float(x)+sin(a/360*2*pi)-x",
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"",
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"f(0,0)", // 0
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"1",
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"f(90,1)", // 90
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"1",
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"f(180,0)", // 180
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"1",
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"f(270,-1)", // 270
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"1",
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"f(360,0)", // 360
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"1",
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"f(-90,-1)", // -90
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"1",
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"f(-180,0)", // -180
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"1",
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"f(-270,1)", // -270
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"1",
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"f(-360,0)", // -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(30,1/2)", // 30
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"1",
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"f(150,1/2)", // 150
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"1",
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"f(210,-1/2)", // 210
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"1",
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"f(330,-1/2)", // 330
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"1",
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"f(-30,-1/2)", // -30
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"1",
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"f(-150,-1/2)", // -150
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"1",
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"f(-210,1/2)", // -210
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"1",
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"f(-330,1/2)", // -330
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"1",
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"f(60,sqrt(3)/2)", // 60
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"1",
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"f(120,sqrt(3)/2)", // 120
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"1",
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"f(240,-sqrt(3)/2)", // 240
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"1",
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"f(300,-sqrt(3)/2)", // 300
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"1",
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"f(-60,-sqrt(3)/2)", // -60
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"1",
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"f(-120,-sqrt(3)/2)", // -120
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"1",
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"f(-240,sqrt(3)/2)", // -240
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"1",
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"f(-300,sqrt(3)/2)", // -300
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"1",
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"f=quote(f)",
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"",
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"sin(arcsin(x))",
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"x",
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// check the default case
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"sin(1/12*pi)",
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"sin(1/12*pi)",
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"sin(arctan(4/3))",
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"4/5",
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"sin(-arctan(4/3))",
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"-4/5",
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// phase
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"sin(x-8/2*pi)",
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"sin(x)",
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"sin(x-7/2*pi)",
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"cos(x)",
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"sin(x-6/2*pi)",
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"-sin(x)",
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"sin(x-5/2*pi)",
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"-cos(x)",
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"sin(x-4/2*pi)",
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"sin(x)",
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"sin(x-3/2*pi)",
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"cos(x)",
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"sin(x-2/2*pi)",
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"-sin(x)",
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"sin(x-1/2*pi)",
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"-cos(x)",
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"sin(x+0/2*pi)",
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"sin(x)",
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"sin(x+1/2*pi)",
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"cos(x)",
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"sin(x+2/2*pi)",
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"-sin(x)",
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"sin(x+3/2*pi)",
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"-cos(x)",
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"sin(x+4/2*pi)",
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"sin(x)",
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"sin(x+5/2*pi)",
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"cos(x)",
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"sin(x+6/2*pi)",
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"-sin(x)",
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"sin(x+7/2*pi)",
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"-cos(x)",
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"sin(x+8/2*pi)",
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"sin(x)",
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};
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void
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test_sin(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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