159 lines
2.0 KiB
C++
159 lines
2.0 KiB
C++
/* Magnitude of complex z
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z mag(z)
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- ------
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a a
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-a a
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(-1)^a 1
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exp(a + i b) exp(a)
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a b mag(a) mag(b)
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a + i b sqrt(a^2 + b^2)
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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. jean-francois.debroux reports that when z=(a+i*b)/(c+i*d) then
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mag(numerator(z)) / mag(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_mag(void)
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{
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push(cadr(p1));
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eval();
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mag();
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}
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void
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mag(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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yymag();
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push(p1);
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denominator();
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yymag();
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divide();
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restore();
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}
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void
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yymag(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(p1);
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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_integer(1);
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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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real();
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exponential();
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} else if (car(p1) == symbol(MULTIPLY)) {
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// product
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push_integer(1);
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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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mag();
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multiply();
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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
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push(p1);
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rect(); // convert polar terms, if any
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p1 = pop();
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push(p1);
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real();
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push_integer(2);
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power();
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push(p1);
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imag();
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push_integer(2);
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power();
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add();
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push_rational(1, 2);
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power();
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simplify_trig();
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} else
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// default (all real)
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push(p1);
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restore();
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}
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#if SELFTEST
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static char *s[] = {
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"mag(a+i*b)",
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"(a^2+b^2)^(1/2)",
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"mag(exp(a+i*b))",
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"exp(a)",
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"mag(1)",
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"1",
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"mag(-1)",
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"1",
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"mag(1+exp(i*pi/3))",
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"3^(1/2)",
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"mag((a+i*b)/(c+i*d))",
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"(a^2+b^2)^(1/2)/((c^2+d^2)^(1/2))",
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"mag(exp(i theta))",
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"1",
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"mag(exp(-i theta))",
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"1",
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"mag((-1)^theta)",
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"1",
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"mag((-1)^(-theta))",
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"1",
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"mag(3*(-1)^theta)",
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"3",
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"mag(3*(-1)^(-theta))",
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"3",
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"mag(-3*(-1)^theta)",
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"3",
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"mag(-3*(-1)^(-theta))",
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"3",
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};
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void
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test_mag(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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