244 lines
2.8 KiB
C++
244 lines
2.8 KiB
C++
// Tangent 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_tan(void)
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{
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push(cadr(p1));
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eval();
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tangent();
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}
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void
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tangent(void)
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{
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save();
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yytangent();
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restore();
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}
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void
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yytangent(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(ARCTAN)) {
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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 = tan(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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// tan function is antisymmetric, tan(-x) = -tan(x)
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if (isnegative(p1)) {
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push(p1);
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negate();
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tangent();
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negate();
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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(TAN));
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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 210:
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push_rational(1, 3);
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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 330:
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push_rational(-1, 3);
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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 45:
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case 225:
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push_integer(1);
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break;
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case 135:
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case 315:
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push_integer(-1);
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break;
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case 60:
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case 240:
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push_integer(3);
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push_rational(1, 2);
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power();
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break;
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case 120:
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case 300:
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push_integer(3);
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push_rational(1, 2);
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power();
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negate();
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break;
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default:
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push(symbol(TAN));
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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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"tan(x)",
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"tan(x)",
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"tan(-x)",
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"-tan(x)",
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"tan(b-a)",
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"-tan(a-b)",
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// check against the floating point math library
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"f(a,x)=1+tan(float(a/360*2*pi))-float(x)+tan(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(180,0)", // 180
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"1",
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"f(360,0)", // 360
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"1",
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"f(-180,0)", // -180
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"1",
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"f(-360,0)", // -360
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"1",
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"f(45,1)", // 45
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"1",
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"f(135,-1)", // 135
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"1",
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"f(225,1)", // 225
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"1",
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"f(315,-1)", // 315
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"1",
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"f(-45,-1)", // -45
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"1",
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"f(-135,1)", // -135
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"1",
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"f(-225,-1)", // -225
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"1",
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"f(-315,1)", // -315
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"1",
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"f(30,sqrt(3)/3)", // 30
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"1",
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"f(150,-sqrt(3)/3)", // 150
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"1",
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"f(210,sqrt(3)/3)", // 210
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"1",
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"f(330,-sqrt(3)/3)", // 330
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"1",
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"f(-30,-sqrt(3)/3)", // -30
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"1",
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"f(-150,sqrt(3)/3)", // -150
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"1",
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"f(-210,-sqrt(3)/3)", // -210
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"1",
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"f(-330,sqrt(3)/3)", // -330
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"1",
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"f(60,sqrt(3))", // 60
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"1",
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"f(120,-sqrt(3))", // 120
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"1",
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"f(240,sqrt(3))", // 240
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"1",
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"f(300,-sqrt(3))", // 300
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"1",
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"f(-60,-sqrt(3))", // -60
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"1",
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"f(-120,sqrt(3))", // -120
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"1",
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"f(-240,-sqrt(3))", // -240
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"1",
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"f(-300,sqrt(3))", // -300
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"1",
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"f=quote(f)",
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"",
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"tan(arctan(x))",
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"x",
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// check the default case
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"tan(1/12*pi)",
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"tan(1/12*pi)",
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};
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void
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test_tan(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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