281 lines
3.3 KiB
C++
281 lines
3.3 KiB
C++
// Sine function of numerical and symbolic arguments
|
|
|
|
#include "stdafx.h"
|
|
#include "defs.h"
|
|
|
|
void
|
|
eval_sin(void)
|
|
{
|
|
push(cadr(p1));
|
|
eval();
|
|
sine();
|
|
}
|
|
|
|
void
|
|
sine(void)
|
|
{
|
|
save();
|
|
yysine();
|
|
restore();
|
|
}
|
|
|
|
void
|
|
yysine(void)
|
|
{
|
|
int n;
|
|
double d;
|
|
|
|
p1 = pop();
|
|
|
|
if (car(p1) == symbol(ARCSIN)) {
|
|
push(cadr(p1));
|
|
return;
|
|
}
|
|
|
|
if (isdouble(p1)) {
|
|
d = sin(p1->u.d);
|
|
if (fabs(d) < 1e-10)
|
|
d = 0.0;
|
|
push_double(d);
|
|
return;
|
|
}
|
|
|
|
// sin(arctan(x)) = x / sqrt(1 + x^2)
|
|
|
|
// see p. 173 of the CRC Handbook of Mathematical Sciences
|
|
|
|
if (car(p1) == symbol(ARCTAN)) {
|
|
push(cadr(p1));
|
|
push_integer(1);
|
|
push(cadr(p1));
|
|
push_integer(2);
|
|
power();
|
|
add();
|
|
push_rational(-1, 2);
|
|
power();
|
|
multiply();
|
|
return;
|
|
}
|
|
if (exp_flag) {
|
|
push(p1);
|
|
expsin();
|
|
return;
|
|
}
|
|
|
|
// sine function is antisymmetric, sin(-x) = -sin(x)
|
|
|
|
if (isnegative(p1)) {
|
|
push(p1);
|
|
negate();
|
|
sine();
|
|
negate();
|
|
return;
|
|
}
|
|
|
|
// multiply by 180/pi
|
|
|
|
push(p1);
|
|
push_integer(180);
|
|
multiply();
|
|
push_symbol(PI);
|
|
divide();
|
|
|
|
n = pop_integer();
|
|
|
|
if (n < 0) {
|
|
push(symbol(SIN));
|
|
push(p1);
|
|
list(2);
|
|
return;
|
|
}
|
|
|
|
switch (n % 360) {
|
|
case 0:
|
|
case 180:
|
|
push_integer(0);
|
|
break;
|
|
case 30:
|
|
case 150:
|
|
push_rational(1, 2);
|
|
break;
|
|
case 210:
|
|
case 330:
|
|
push_rational(-1, 2);
|
|
break;
|
|
case 45:
|
|
case 135:
|
|
push_rational(1, 2);
|
|
push_integer(2);
|
|
push_rational(1, 2);
|
|
power();
|
|
multiply();
|
|
break;
|
|
case 225:
|
|
case 315:
|
|
push_rational(-1, 2);
|
|
push_integer(2);
|
|
push_rational(1, 2);
|
|
power();
|
|
multiply();
|
|
break;
|
|
case 60:
|
|
case 120:
|
|
push_rational(1, 2);
|
|
push_integer(3);
|
|
push_rational(1, 2);
|
|
power();
|
|
multiply();
|
|
break;
|
|
case 240:
|
|
case 300:
|
|
push_rational(-1, 2);
|
|
push_integer(3);
|
|
push_rational(1, 2);
|
|
power();
|
|
multiply();
|
|
break;
|
|
case 90:
|
|
push_integer(1);
|
|
break;
|
|
case 270:
|
|
push_integer(-1);
|
|
break;
|
|
default:
|
|
push(symbol(SIN));
|
|
push(p1);
|
|
list(2);
|
|
break;
|
|
}
|
|
}
|
|
|
|
static char *s[] = {
|
|
|
|
"sin(x)",
|
|
"sin(x)",
|
|
|
|
"sin(-x)",
|
|
"-sin(x)",
|
|
|
|
"sin(b-a)",
|
|
"-sin(a-b)",
|
|
|
|
// check against the floating point math library
|
|
|
|
"f(a,x)=1+sin(float(a/360*2*pi))-float(x)+sin(a/360*2*pi)-x",
|
|
"",
|
|
|
|
"f(0,0)", // 0
|
|
"1",
|
|
|
|
"f(90,1)", // 90
|
|
"1",
|
|
|
|
"f(180,0)", // 180
|
|
"1",
|
|
|
|
"f(270,-1)", // 270
|
|
"1",
|
|
|
|
"f(360,0)", // 360
|
|
"1",
|
|
|
|
"f(-90,-1)", // -90
|
|
"1",
|
|
|
|
"f(-180,0)", // -180
|
|
"1",
|
|
|
|
"f(-270,1)", // -270
|
|
"1",
|
|
|
|
"f(-360,0)", // -360
|
|
"1",
|
|
|
|
"f(45,sqrt(2)/2)", // 45
|
|
"1",
|
|
|
|
"f(135,sqrt(2)/2)", // 135
|
|
"1",
|
|
|
|
"f(225,-sqrt(2)/2)", // 225
|
|
"1",
|
|
|
|
"f(315,-sqrt(2)/2)", // 315
|
|
"1",
|
|
|
|
"f(-45,-sqrt(2)/2)", // -45
|
|
"1",
|
|
|
|
"f(-135,-sqrt(2)/2)", // -135
|
|
"1",
|
|
|
|
"f(-225,sqrt(2)/2)", // -225
|
|
"1",
|
|
|
|
"f(-315,sqrt(2)/2)", // -315
|
|
"1",
|
|
|
|
"f(30,1/2)", // 30
|
|
"1",
|
|
|
|
"f(150,1/2)", // 150
|
|
"1",
|
|
|
|
"f(210,-1/2)", // 210
|
|
"1",
|
|
|
|
"f(330,-1/2)", // 330
|
|
"1",
|
|
|
|
"f(-30,-1/2)", // -30
|
|
"1",
|
|
|
|
"f(-150,-1/2)", // -150
|
|
"1",
|
|
|
|
"f(-210,1/2)", // -210
|
|
"1",
|
|
|
|
"f(-330,1/2)", // -330
|
|
"1",
|
|
|
|
"f(60,sqrt(3)/2)", // 60
|
|
"1",
|
|
|
|
"f(120,sqrt(3)/2)", // 120
|
|
"1",
|
|
|
|
"f(240,-sqrt(3)/2)", // 240
|
|
"1",
|
|
|
|
"f(300,-sqrt(3)/2)", // 300
|
|
"1",
|
|
|
|
"f(-60,-sqrt(3)/2)", // -60
|
|
"1",
|
|
|
|
"f(-120,-sqrt(3)/2)", // -120
|
|
"1",
|
|
|
|
"f(-240,sqrt(3)/2)", // -240
|
|
"1",
|
|
|
|
"f(-300,sqrt(3)/2)", // -300
|
|
"1",
|
|
|
|
"f=quote(f)",
|
|
"",
|
|
|
|
"sin(arcsin(x))",
|
|
"x",
|
|
|
|
"circexp(sin(x))",
|
|
"1/2*i*exp(-i*x)-1/2*i*exp(i*x)",
|
|
};
|
|
|
|
void
|
|
test_sin(void)
|
|
{
|
|
test(__FILE__, s, sizeof s / sizeof (char *));
|
|
}
|