Complex numbers

[Richard Harris]

I understand that C will suport complex values under iso99c. Does
anyone know of some examples that will show how to implement complex
functions?

 

[Simon Biber]

I understand that C will suport complex values under iso99c. Does
anyone know of some examples that will show how to implement complex
functions?

Here's an example of how to use the complex number support:

#include <stdio.h>
#include <complex.h>

int main(void)
{
double minx = -1.7, maxx = 0.7, sx = (maxx - minx) / 50;
double miny = -1.0, maxy = 1.0, sy = (maxy - miny) / 70;
int i, maxi = 64;
double bail = 4.0;
for(double x = minx; x < maxx; x += sx)
{
for(double y = miny; y < maxy; y += sy)
{
complex double c = x + I * y;
complex double z = c;
for(i = 0; i < maxi && cabs(z) < bail; i++)
{
z = z * z + c;
}
putchar(i == maxi ? ' '
: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[i % 36]);
}
putchar('\n');
}
return 0;
}

Here is the output:

22222222222223333333333344444455678 8765544444433333333333222222222222
22222222222333333333333444444555678 8765554444443333333333332222222222
22222222223333333333344444445556679 9766555444444433333333333222222222
22222222233333333333444444455566679 9766655544444443333333333322222222
2222222233333333333444444455566678A A876665554444444333333333332222222
2222222333333333334444445555667789C C987766555544444433333333333222222
222222333333333344444455555668HBACH HCABH86655555444444333333333322222
2222233333333334444455556666789BJOL LOJB987666655554444433333333332222
222233333333334444556667777789ADO ODA98777776665544443333333333222
223333333333344444568BBB9889BFDGIR RIGDFB9889BBB86544444333333333332
23333333333334444555689AGBBCE ECBBGA9865554444333333333333
333333333333444445556789EMY T T YME98765554444433333333333
333333333334444445556679C2 2C97665554444443333333333
333333333344444445556789BHN NHB98765554444444333333333
3333333334444444555668EEGLY YLGEE866555444444433333333
333333334444444455566789DQ0 0QD98766555444444443333333
333333334444444555566779TK1 1KT97766555544444443333333
3333333444444455556667789BI2 2IB987766655554444444333333
3333334444444555566667789ACP PCA987766665555444444433333
3333344444455555666777899ABCEI7 7IECBA998777666555554444443333
3333444444555566667889ABBFEHL 7 7 LHEFBBA988766665555444444333
333444444555666778AGCBL L L LBCGA87766655544444433
334444445567778889Q Q Q Q98887776554444443
34444445567AHJCBBBFK KFBBBCJHA7655444444
44444455567APEHHVI1 1IVHHEPA7655544444
44444555667ABZ ZBA7665554444
4444555666789CGO OGC987666555444
445555666789DEW WED98766655554
45555667778B B8777665555
55566888899B X X B9988886655
66679DDCHDCD DCDHCDD9766
7778ADP MN NM PDA877
A99BFH HFB99
BOEJ JEO
BNBCQHW U U WHQCBN
K9889BF S VGR RGV S FB9889
56667HBBAAABG GBAAABBH7666
55556667778AD DA8777666555
44455556677B B7766555544
444445556678ACF FCA87665554444
44444455566789BEM MEB9876655544444
3344444555667AL B M B LA766555444443
3334444455678AZ KJ A JK ZA876554444433
33333444456CESQFCD99ECI 9 NF98889FN 9 ICE99DCFQSEC6544443333
33333344445568B8777789E SABLHAD876666678DAHLBAS E9877778B8655444433333
333333334444555555566AAC87777666555555566677778CAA66555555544443333333
3333333333444444445555555555555555555555555555555555544444444333333333
3333333333333444444444444444444444444444444444444444444444333333333333
2233333333333333344444444444444444444444444444444444443333333333333332
2222233333333333333333333333334444444444433333333333333333333333332222

 

[Malcolm]

I understand that C will suport complex values under iso99c. Does
anyone know of some examples that will show how to implement complex
functions?

You have to understand the maths first.

Probably the most important thing for the maths library is the exponential
function, e^x. This can be expanded

e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! ...

Now simply plug an imaginary value into the series, and you understand what
it means to exponentiate by an imaginary power.

Once you understand the maths, you also have to understand the limits of
your floating point system, in order to produce results of known accuracy,
and the limits of the series expansions - some are acceptable to the
mathematician but in fact converge too slowly to be of practical use to the
computer programmer.

So to make a loose implementation is quite simple, but to code an industrial
strength complex maths library is more difficult.

 

[Dik T. Winter]

> Probably the most important thing for the maths library is the exponential
> function, e^x. This can be expanded
>
> e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! ...
>
> Now simply plug an imaginary value into the series, and you understand what
> it means to exponentiate by an imaginary power.

Oh. I would simply go for:
exp(real_part(z)) * (cos(imag_part(z)) + i * sin(imag_part(z)))
or something like that. Industrial strength and all that stuff.