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

[Glenn Hutchings]

On 4 Feb, 18:49, rich...@cogsci. ed.ac.uk (Richard Tobin) wrote:

For fun, try 23.140693 ^ i.

For even more fun, try computing i ^ i. Betcha didn't see that
coming!

Glenn

[CBFalconer]

Keith Thompson wrote:

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

.... snip ...

>

>I've never seen a stdbool.h that differed at all.

That differed from what?

>From any other stdbool.h, I assume. This is probably connected

with the fact that stdbool.h is completely described in N869,
leaving nothing to the imagination. <Append something about female
garments here.>

--
<http://www.cs.auckland .ac.nz/~pgut001/pubs/vista_cost.txt>
<http://www.securityfoc us.com/columnists/423>

"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]

"Glenn Hutchings" <zo*****@google mail.comwrote in message
news:11******** *************@a 75g2000cwd.goog legroups.com...

On 4 Feb, 18:49, rich...@cogsci. ed.ac.uk (Richard Tobin) wrote:

>For fun, try 23.140693 ^ i.

For even more fun, try computing i ^ i. Betcha didn't see that
coming!

We know that it exists as a complex that C can calculate from first
principles. LS

[Lane Straatman]

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

Lane Straatman said:

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

<snip>

>>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.

The point is that if you have arctan of a rational then the *next*
digit in its expansion is not something that algebraic methods can get
a hold of. Where Dr. Kelly

Actually, Ian is a very very very clever man, a fine fellow, an
excellent host, a talented musician, a superb programmer, and a quite
astounding linguist, but it has to be said, when all's said and done,
that he's not a doctor. I know the book says he is - at least three
times - but the book is wrong. That's probably my fault, because I
think I just kind of assumed he had a doctorate when I was setting up
the team, and it turns out he hasn't. If ever there were a failure of
the British education system, it is this: that it does not regard Ian
as a doctor. Having said that, I'm now going to stop making a fuss
about it. Instead, I would like to award Ian an honorary doctorate from
the University of Common Sense.

ABD is a common affliction in the US (All But Disseration). If you make it
sound really serious,

>

>at the end of chp 24 of _Unleashed_ expands e to a page and
a half then has 99860 , do you have a bet what the next number would
be? If you expand one third for a page and a half, I could get that
digit.

Ian's expansion of e, however, was not done via calls to atan(), which
is what Tim Prince was talking about. atan() returns a double, and a
double cannot store an irrational number precisely. A circle can, but a
double can't.

You can re-topologize and get a line from whatever circle you created* **, a
line in which, you claim, "almost all" numbers are absent. If you think
almost all numbers are absent in C's ability to work with, say, the segment
[-1.01, -.99], you're a different kind of cat than I.

Do you honestly believe that 42 * arctan(1.0) is in Q?
--
LS
*with the same set-theoretic properties
**give or take a point with Riemannian steriographic projection

[Lane Straatman]

"CBFalconer " <cb********@yah oo.comwrote in message
news:45******** *******@yahoo.c om...

Keith Thompson wrote:

>"Lane Straatman" <in*****@invali d.netwrites:

... snip ...

>>

>>I've never seen a stdbool.h that differed at all.

I meant to differ from itself. Another example of this is iso646.h .

>>
That differed from what?

>>From any other stdbool.h, I assume. This is probably connected

with the fact that stdbool.h is completely described in N869,
leaving nothing to the imagination. <Append something about female
garments here.>

Carla left her purse.
The heel on Jenn's boot was 4 inches.
Misty was outlaw. LS

[Keith Thompson]

CBFalconer <cb********@yah oo.comwrites:

Keith Thompson wrote:

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

... snip ...

I've never seen a stdbool.h that differed at all.

That differed from what?

From any other stdbool.h, I assume. This is probably connected

with the fact that stdbool.h is completely described in N869,
leaving nothing to the imagination. <Append something about female
garments here.>

The standard completely describes the visible declarations, but not
the whole file. For example, the version provided on one Linux system
I use has a large comment block, include guards using the symbol
"_STDBOOL_H ", and a test for __cplusplus (supporting <stdbool.hin
C++ is a gcc extension).

But it's true that copying <stdbool.hfro m one implementation to
another is less likely to cause problems than most other predefined
headers.

--
Keith Thompson (The_Other_Keit h) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

[Keith Thompson]

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

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

[...]

Ian's expansion of e, however, was not done via calls to atan(), which
is what Tim Prince was talking about. atan() returns a double, and a
double cannot store an irrational number precisely. A circle can, but a
double can't.

You can re-topologize and get a line from whatever circle you created* **, a
line in which, you claim, "almost all" numbers are absent. If you think
almost all numbers are absent in C's ability to work with, say, the segment
[-1.01, -.99], you're a different kind of cat than I.

Different in that he knows what he's talking about.

A double is typically 64 bits. That means it can represent at most
2**64 distinct values. Some small subset of those values will be in
the range [-1.01, -.99], a range that includes infinitely many real
numbers. Yes, almost all numbers are absent in C's ability to work
with, say, the segment [-1.01, -.99].

Do you honestly believe that 42 * arctan(1.0) is in Q?

Q is the set of rational numbers, yes? (Please don't assume everone
here is familiar with that particular mathematical notation.)

If by "42 * arctan(1.0)" you mean the result of the mathematical
formula over real numbers, then no, the result is not rational; in
fact, it's trancendental (10.5 * pi).

If instead you're referring to the result of the C expression
"42 * atan(1.0)" (the function declared in <math.his "atan", not
"arctan"), then yes, that result is rational. It is a value of type
double, which is a floating-point type whose representation is a
finite number of bits. It can *only* represent rational numbers. In
fact, it can only represent a tiny subset of the rational numbers.
(In a typical implementation, all representable numbers are integer
multiples of a power of 2.)

C floating-point types cannot represent irrational numbers. They are
not mathematical real numbers; they are only a discrete approximation,
good enough for many purposes.

You might want to look up Goldberg's "What Every Computer Scientist
Should Know About Floating-Point Arithmetic".

--
Keith Thompson (The_Other_Keit h) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

[Richard Heathfield]

Malcolm McLean said:

<snip>

[MS] do offer a free compiler. It looks pretty horrid, but at least it
compiled "Hello World" - not without five minutes tweaking to get rid
of a file called stdafx.h it insisted on adding.

Anyway I have registered and agreed not to distribute any programs
compiled with it as open source, etc, etc, etc. I've no real choice.

Yes, you do. Your original problem - software you purchased failing to
run on your new machine - was caused by Microsoft. Your fix, supplied
by Microsoft, is unsatisfactoril y restrictive. You have no reasonable
assurance that Microsoft isn't going to cause you even more problems in
the future. It seems to me that the obvious thing to do is knock
Microsoft out of the loop, even if that means spending some time
porting your stuff to a more sensible platform.

A computer isn't a computer without a programming environment - it's
just a glorified typewriter.

A compiler whose licence agreement requires you not to allow your users
access to source code is not a compiler - it's a prison.

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

[Richard Heathfield]

Lane Straatman said:

>
If you
think almost all numbers are absent in C's ability to work with, say,
the segment
[-1.01, -.99], you're a different kind of cat than I.

Miaow. C programs are capable of representing almost none of the numbers
in the that range.

Do you honestly believe that 42 * arctan(1.0) is in Q?

If you mean 42 * atan(1.0), then yes, I do.

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

[santosh]

Malcolm McLean wrote:

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

<snip>

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?

They do offer a free compiler. It looks pretty horrid, but at least it
compiled "Hello World" - not without five minutes tweaking to get rid of a
file called stdafx.h it insisted on adding.

Anyway I have registered and agreed not to distribute any programs compiled
with it as open source, etc, etc, etc. I've no real choice. A computer isn't
a computer without a programming environment - it's just a glorified
typewriter.

Why don't you purchase a copy of Visual Studio (TM)? Then you can
distribute your applications with source.