e to the i pi

[Lane Straatman]

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <complex.h>
/*
double complex z1, z2, z3;
bool flag;
z1 = .4 + .7I;
z2 = cpow(z1, 2.0);
z3 = z1 * z1;
flag = false;
flag = true;
if (flag)
{
printf("%lf %lf\n", creal(z1), cimag(z1));
printf("%lf %lf\n", creal(z2), cimag(z2));
printf("%lf %lf\n", creal(z3), cimag(z3));
printf("%d\n", N);
}
*/

int main(int argc, char *argv[])
{
double complex z1, z2, z3, z4, z5;
z1=5 +7I;
z2=cpow(z1, 1I);
printf("%lf %lf\n", creal(z1), cimag(z1));
printf("%lf %lf\n", creal(z2), cimag(z2));
z5= 0 + I*(3.14159);

z3=2.54 + 0*I;
z4=cpow(z5,z3);
printf("%lf %lf\n", creal(z4), cimag(z4));

system("PAUSE") ;
return 0;
}
Why doesn't e^(i *pi) equal what most folks think it does? LS

[JimS]

On Sun, 04 Feb 2007 22:07:58 +0000, Richard Heathfield
<rj*@see.sig.in validwrote:

>Malcolm McLean said:

>>
"Keith Thompson" <ks***@mib.orgw rote in message

>>Let me guess, you were so certain you were right that you didn't
bother to try it.

Microsoft have taken away my compiler. I bought a brand new Windows Vista
machine, installed my copy of Visual Studio and - no executable.

You need Service Pack 7. Admittedly, Visual Studio won't work with that
either (possibly modulo emulators), but you get a perfectly capable C
compiler as part of the bundle. And of course it's completely free.

Vista supports Visual Studio 2005 only, as far as I can tell, and VS
needs a service pack to do that properly AND it has to be run as
Administrator.

Jim

[Lane Straatman]

"Keith Thompson" <ks***@mib.orgw rote in message
news:ln******** ****@nuthaus.mi b.org...

Richard Heathfield <rj*@see.sig.in validwrites:

>Eric Sosman said:

Malcolm McLean wrote:
"Lane Straatman" <in*****@invali d.netwrote in message
Why doesn't e^(i *pi) equal what most folks think it does? LS

Most folks would say that if you try to multiply a number by itself an
imaginary number of times, that is impossible.

That's plane wrong.

Either you have a couple of axes to grind, or you're misreading what
Malcolm wrote, which rings true.

Yes, what Malcolm wrote about "what most folks think" is at least
plausible (though I suspect that most people who would ask what
e^(i*pi) is in the first place are likely to know the answer). It
wasn't entirely clear to me that Malcolm understands the issue
himself.

I hope he takes from this a means to further his adducation.

On the other hand, perhaps Malcolm's subtlety just escaped me, in
which case I'm duly embarrassed to have missed it.

He's got me after complex roots, now, and I've thought about it enough to
want to write it from scratch.

The fact that I wrote the above *before* I got the "couple of axes"
joke makes this more likely. *Sigh*

Axis is correct, as one of them is Joshu's. LS

[Tim Prince]

Lane Straatman wrote:
Since we have a bunch of

rationals in C, we have a bunch of transcendentals as the arctan's of these
numbers. LS

In C, the atan() functions are a bunch of rationals. Ideally, in
certain ranges, with something resembling IEEE754 compliance, the
quality is measurable in ULPS difference between the actual result and
the mathematically correct one. It looks like you jumped from C to
something else in mid-sentence.

[Lane Straatman]

"Richard Heathfield" <rj*@see.sig.in validwrote in message
news:ta******** *************** *******@bt.com. ..

Malcolm McLean said:

>>
"Richard Heathfield" <rj*@see.sig.in validwrote in message

>>>Microsoft have taken away my compiler. I bought a brand new Windows
Vista
machine, installed my copy of Visual Studio and - no executable.

You need Service Pack 7. Admittedly, Visual Studio won't work with that
either (possibly modulo emulators), but you get a perfectly capable C
compiler as part of the bundle. And of course it's completely free.

Seriously?

Er, no. Sorry, Malcolm, I thought you knew - "Service Pack 7" is the
traditional
name for Linux when being recommended as a fix for a Windows-specific
problem.

>I need a Windows library to compile my games and BASICdraw,

You have just discovered that Microsoft aren't all that interested in
supporting
"legacy software" (e.g. their own two-year-old compiler, if your account
is
anything to go by). Have you considered porting your stuff to a more
stable
platform?

I don't want you to think that I would tea up on you for your lack of
proximity to the evil empire.* I have a linux disk, somewhere. I think it
had to do with a penguin; I can't quite remember the file. And that's what
happens every time with linux for people like me, who get knocked out every
couple of years: we forget that maze of files and switches and did I see
curses.h? LS
*it occurs to me that I made a spoonerism last night when I called you
"C-3pio."

[CBFalconer]

Lane Straatman wrote:

>

.... snip ...

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

int main(void)
{
double complex z3, z4, z5;
z5= 0 + I*(3.14159);
z3=2.71828 + 0*I;
z4=cpow(z3,z5);
printf("%lf %lf\n", creal(z4), cimag(z4));
return 0;
}
Thanks for replies. e is now set closer to what Dr. Kelly has
listed for it, and I've got the right order on cpow().

For kicks and giggles, I'd like to see how precise one can get
with this using these predefined types. arctan of 1.0 will
improve pi. Is there an easy way to adduce e in C to the full
width of a double? LS

How about "exp(1.0);" .

--
<http://www.cs.auckland .ac.nz/~pgut001/pubs/vista_cost.txt>

"A man who is right every time is not likely to do very much."
-- Francis Crick, co-discover of DNA
"There is nothing more amazing than stupidity in action."
-- Thomas Matthews

[Lane Straatman]

"Tim Prince" <tp*****@nospam computer.orgwro te in message
news:kY******** ********@newssv r23.news.prodig y.net...

Lane Straatman wrote:
Since we have a bunch of

>rationals in C, we have a bunch of transcendentals as the arctan's of
these numbers. LS

In C, the atan() functions are a bunch of rationals. Ideally, in certain
ranges, with something resembling IEEE754 compliance, the quality is
measurable in ULPS difference between the actual result and the
mathematically correct one. It looks like you jumped from C to something
else in mid-sentence.

You couldn't be more wrong. I had a conversation with C_Dreamer about this.
LS

[Richard Bos]

"Lane Straatman" <in*****@invali d.netwrote:

Devcpp doesn't even have tgmath.h .

Of course it doesn't. It's a C89 implementation, not a C99 one.

I copied it out of lcc

Bad idea, as you'd have known if you'd read the FAQ.

Is there something about tgmath.h that makes its inclusion here ill-advised?

<http://c-faq.com/cpp/missinghdr.html >

Richard

[Richard Bos]

"Malcolm McLean" <re*******@btin ternet.comwrote :

"Keith Thompson" <ks***@mib.orgw rote in message

Let me guess, you were so certain you were right that you didn't
bother to try it.

Microsoft have taken away my compiler. I bought a brand new Windows Vista
machine,

More fool you.

<http://www.theregister .co.uk/2006/11/22/vista_eula_worr ies/>
<http://www.securityfoc us.com/columnists/423>
<http://www.cs.auckland .ac.nz/~pgut001/pubs/vista_cost.html >

Richard

[Richard Heathfield]

Lane Straatman said:

>
"Tim Prince" <tp*****@nospam computer.orgwro te in message
news:kY******** ********@newssv r23.news.prodig y.net...

>Lane Straatman wrote:
Since we have a bunch of

>>rationals in C, we have a bunch of transcendentals as the arctan's
of
these numbers. LS

In C, the atan() functions are a bunch of rationals. Ideally, in
certain ranges, with something resembling IEEE754 compliance, the
quality is measurable in ULPS difference between the actual result
and the
mathematical ly correct one. It looks like you jumped from C to
something else in mid-sentence.

You couldn't be more wrong.

Tim is right - atan() returns a double, and doubles have a finite number
of bits, so they literally *cannot* store irrational numbers. The best
they can do is store the closest rational approximation one can find
within the bits available.

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at the above domain, - www.

[Hallvard B Furuseth]

Lane Straatman writes:

For kicks and giggles, I'd like to see how precise one can get with
this using these predefined types.

Use long double, then. And atanl, cexpl.

--
Hallvard