199 lines
2.6 KiB
C++
199 lines
2.6 KiB
C++
/* Argument (angle) of complex z
|
|
|
|
z arg(z)
|
|
- ------
|
|
|
|
a 0
|
|
|
|
-a -pi See note 3 below
|
|
|
|
(-1)^a a pi
|
|
|
|
exp(a + i b) b
|
|
|
|
a b arg(a) + arg(b)
|
|
|
|
a + i b arctan(b/a)
|
|
|
|
Result by quadrant
|
|
|
|
z arg(z)
|
|
- ------
|
|
|
|
1 + i 1/4 pi
|
|
|
|
1 - i -1/4 pi
|
|
|
|
-1 + i 3/4 pi
|
|
|
|
-1 - i -3/4 pi
|
|
|
|
Notes
|
|
|
|
1. Handles mixed polar and rectangular forms, e.g. 1 + exp(i pi/3)
|
|
|
|
2. Symbols in z are assumed to be positive and real.
|
|
|
|
3. Negative direction adds -pi to angle.
|
|
|
|
Example: z = (-1)^(1/3), mag(z) = 1/3 pi, mag(-z) = -2/3 pi
|
|
|
|
4. jean-francois.debroux reports that when z=(a+i*b)/(c+i*d) then
|
|
|
|
arg(numerator(z)) - arg(denominator(z))
|
|
|
|
must be used to get the correct answer. Now the operation is
|
|
automatic.
|
|
*/
|
|
|
|
#include "stdafx.h"
|
|
#include "defs.h"
|
|
|
|
void
|
|
eval_arg(void)
|
|
{
|
|
push(cadr(p1));
|
|
eval();
|
|
arg();
|
|
}
|
|
|
|
void
|
|
arg(void)
|
|
{
|
|
save();
|
|
p1 = pop();
|
|
push(p1);
|
|
numerator();
|
|
yyarg();
|
|
push(p1);
|
|
denominator();
|
|
yyarg();
|
|
subtract();
|
|
restore();
|
|
}
|
|
|
|
#define RE p2
|
|
#define IM p3
|
|
|
|
void
|
|
yyarg(void)
|
|
{
|
|
save();
|
|
p1 = pop();
|
|
if (isnegativenumber(p1)) {
|
|
push(symbol(PI));
|
|
negate();
|
|
} else if (car(p1) == symbol(POWER) && equaln(cadr(p1), -1)) {
|
|
// -1 to a power
|
|
push(symbol(PI));
|
|
push(caddr(p1));
|
|
multiply();
|
|
} else if (car(p1) == symbol(POWER) && cadr(p1) == symbol(E)) {
|
|
// exponential
|
|
push(caddr(p1));
|
|
imag();
|
|
} else if (car(p1) == symbol(MULTIPLY)) {
|
|
// product of factors
|
|
push_integer(0);
|
|
p1 = cdr(p1);
|
|
while (iscons(p1)) {
|
|
push(car(p1));
|
|
arg();
|
|
add();
|
|
p1 = cdr(p1);
|
|
}
|
|
} else if (car(p1) == symbol(ADD)) {
|
|
// sum of terms
|
|
push(p1);
|
|
rect();
|
|
p1 = pop();
|
|
push(p1);
|
|
real();
|
|
RE = pop();
|
|
push(p1);
|
|
imag();
|
|
IM = pop();
|
|
if (iszero(RE)) {
|
|
push(symbol(PI));
|
|
if (isnegative(IM))
|
|
negate();
|
|
} else {
|
|
push(IM);
|
|
push(RE);
|
|
divide();
|
|
arctan();
|
|
if (isnegative(RE)) {
|
|
push_symbol(PI);
|
|
if (isnegative(IM))
|
|
subtract(); // quadrant 1 -> 3
|
|
else
|
|
add(); // quadrant 4 -> 2
|
|
}
|
|
}
|
|
} else
|
|
// pure real
|
|
push_integer(0);
|
|
restore();
|
|
}
|
|
|
|
#if SELFTEST
|
|
|
|
static char *s[] = {
|
|
|
|
"arg(1+i)",
|
|
"1/4*pi",
|
|
|
|
"arg(1-i)",
|
|
"-1/4*pi",
|
|
|
|
"arg(-1+i)",
|
|
"3/4*pi",
|
|
|
|
"arg(-1-i)",
|
|
"-3/4*pi",
|
|
|
|
"arg((-1)^(1/3))",
|
|
"1/3*pi",
|
|
|
|
"arg(1+exp(i*pi/3))",
|
|
"1/6*pi",
|
|
|
|
"arg((-1)^(1/6)*exp(i*pi/6))",
|
|
"1/3*pi",
|
|
|
|
"arg(a)",
|
|
"0",
|
|
|
|
"arg(a*exp(b+i*pi/5))",
|
|
"1/5*pi",
|
|
|
|
"arg(-1)",
|
|
"-pi",
|
|
|
|
"arg(a)",
|
|
"0",
|
|
|
|
"arg(-a)",
|
|
"-pi",
|
|
|
|
"arg(-(-1)^(1/3))",
|
|
"-2/3*pi",
|
|
|
|
"arg(-exp(i*pi/3))",
|
|
"-2/3*pi",
|
|
|
|
"arg(-i)",
|
|
"-1/2*pi",
|
|
|
|
"arg((a+b*i)/(c+d*i))",
|
|
"arctan(b/a)-arctan(d/c)",
|
|
};
|
|
|
|
void
|
|
test_arg(void)
|
|
{
|
|
test(__FILE__, s, sizeof s / sizeof (char *));
|
|
}
|
|
|
|
#endif
|