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/*
* complex.c
*
* This file provides the standard complex arithmetic functions:
*
* Complex complex_minus (Complex z0, Complex z1),
* complex_plus (Complex z0, Complex z1),
* complex_mult (Complex z0, Complex z1),
* complex_div (Complex z0, Complex z1),
* complex_sqrt (Complex z),
* complex_conjugate (Complex z),
* complex_negate (Complex z),
* complex_real_mult (double r, Complex z),
* complex_exp (Complex z),
* complex_log (Complex z, double approx_arg);
* double complex_modulus (Complex z);
* double complex_modulus_squared (Complex z);
* Boolean complex_nonzero (Complex z);
* Boolean complex_infinite (Complex z);
*/
#include "kernel.h"
Complex Zero = { 0.0, 0.0};
Complex One = { 1.0, 0.0};
Complex Two = { 2.0, 0.0};
Complex Four = { 4.0, 0.0};
Complex MinusOne = {-1.0, 0.0};
Complex I = { 0.0, 1.0};
Complex TwoPiI = { 0.0, TWO_PI};
Complex Infinity = {1e34, 0.0};
Complex complex_plus(
Complex z0,
Complex z1)
{
Complex sum;
sum.real = z0.real + z1.real;
sum.imag = z0.imag + z1.imag;
return sum;
}
Complex complex_minus(
Complex z0,
Complex z1)
{
Complex diff;
diff.real = z0.real - z1.real;
diff.imag = z0.imag - z1.imag;
return diff;
}
Complex complex_div(
Complex z0,
Complex z1)
{
double mod_sq;
Complex quotient;
mod_sq = z1.real * z1.real + z1.imag * z1.imag;
if (mod_sq == 0.0)
{
if (z0.real != 0.0 || z0.imag != 0.0)
return Infinity;
else
uFatalError("complex_div", "complex");
}
quotient.real = (z0.real * z1.real + z0.imag * z1.imag)/mod_sq;
quotient.imag = (z0.imag * z1.real - z0.real * z1.imag)/mod_sq;
return quotient;
}
Complex complex_mult(
Complex z0,
Complex z1)
{
Complex product;
product.real = z0.real * z1.real - z0.imag * z1.imag;
product.imag = z0.real * z1.imag + z0.imag * z1.real;
return product;
}
Complex complex_sqrt(
Complex z)
{
double mod,
arg;
Complex root;
mod = sqrt(complex_modulus(z)); /* no need for safe_sqrt() */
if (mod == 0.0)
return Zero;
arg = 0.5 * atan2(z.imag, z.real);
root.real = mod * cos(arg);
root.imag = mod * sin(arg);
return root;
}
Complex complex_conjugate(
Complex z)
{
z.imag = - z.imag;
return z;
}
Complex complex_negate(
Complex z)
{
z.real = - z.real;
z.imag = - z.imag;
return z;
}
Complex complex_real_mult(
double r,
Complex z)
{
Complex multiple;
multiple.real = r * z.real;
multiple.imag = r * z.imag;
return multiple;
}
Complex complex_exp(
Complex z)
{
double modulus;
Complex result;
modulus = exp(z.real);
result.real = modulus * cos(z.imag);
result.imag = modulus * sin(z.imag);
return result;
}
Complex complex_log(
Complex z,
double approx_arg)
{
Complex result;
if (z.real == 0.0 && z.imag == 0.0)
{
uAcknowledge("log(0 + 0i) encountered");
result.real = - DBL_MAX;
result.imag = approx_arg;
return result;
}
result.real = 0.5 * log(z.real * z.real + z.imag * z.imag);
result.imag = atan2(z.imag, z.real);
while (result.imag - approx_arg > PI)
result.imag -= TWO_PI;
while (approx_arg - result.imag > PI)
result.imag += TWO_PI;
return result;
}
double complex_modulus(
Complex z)
{
return sqrt(z.real * z.real + z.imag * z.imag); /* no need for safe_sqrt() */
}
double complex_modulus_squared(
Complex z)
{
return (z.real * z.real + z.imag * z.imag);
}
Boolean complex_nonzero(
Complex z)
{
return (z.real || z.imag);
}
Boolean complex_infinite(
Complex z)
{
return (z.real == Infinity.real && z.imag == Infinity.imag);
}
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