123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138 |
- /* 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();
- }
|