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