e to the i pi

[Richard Bos]

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.

*Wow*. That's... amazing. Just amazing. The _wisdom_ that flows out of
Redmond, the attention to _security_, the great sense of _solid
build_... it's to be found nowhere else.

Richard

 

[Dik T. Winter]

> In article <[email protected]>,

>
> If I understand your post correctly, this should be
> z3=2.718281828459045 + 0*I;
>
>
> 'Tmight come closer if e were what most people think it is.

It might also come closer if the arguments to cpow were in the
proper order.

 

[Fred Kleinschmidt]

If this is meant to be e, it's wrong. e is 2.718281828+


If this is meant to be approximately e ^ (i*pi), it should be
cpow(z3,z5).


What is the point of this?

For fun, try 23.140693 ^ i.

-- Richard

Aren't M_PI and M_E defined in math.h?

 

[Richard Heathfield]

Fred Kleinschmidt said:

Aren't M_PI and M_E defined in math.h?

No.

 

[CBFalconer]

.... snip ...

Aren't M_PI and M_E defined in math.h?

No.

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

 

[Richard Tobin]

Aren't M_PI and M_E defined in math.h?

Yes, but unfortunately not on systems conforming only to the C
standard.

-- Richard

 

[osmium]

Aren't M_PI and M_E defined in math.h?

Thankfully, no. Only in grotesque extensions to the language made by
certain vendors.

Definitions of constants have no proper place in a programming language, it
just leads to two sets of constants, a private set, for M_AVOGADRO and the
like, and the set that came with the compiler, M_PI. and friends.

 

[jacob navia]

:




Thankfully, no. Only in grotesque extensions to the language made by
certain vendors.

Definitions of constants have no proper place in a programming language, it
just leads to two sets of constants, a private set, for M_AVOGADRO and the
like, and the set that came with the compiler, M_PI. and friends.

lcc-win32 defines M_PI if not in conforming mode, as gcc does, for
instance.
They are not standard C but are POSIX. I do not see the point
in defining PI again and again...

 

[Richard Tobin]

Definitions of constants have no proper place in a programming language, it
just leads to two sets of constants, a private set, for M_AVOGADRO and the
like, and the set that came with the compiler, M_PI. and friends.

Definitions of functions have no proper place in a programming
language, it just leads to two sets of functions, a private set, for
print_bank_balance and the like, and the set that came with the
compiler, strlen and friends.

-- Richard

 

[Fred Kleinschmidt]

Thankfully, no. Only in grotesque extensions to the language made by
certain vendors.

Definitions of constants have no proper place in a programming language,
it just leads to two sets of constants, a private set, for M_AVOGADRO and
the like, and the set that came with the compiler, M_PI. and friends.

And thus we should get rid of defined constants like INT_MAX, INT_MIN, etc.,
since they have no place in a programming language.

 

[user923005]

Eric Sosman said:



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

Actually, it's hilarious (if you consider the deliberate misspelling).
IMO-YMMV.

This is referring to the famous equation e^(i*pi) - 1 = 0
which is certainly true in the complex plane.

 

[Keith Thompson]

lcc-win32 defines M_PI if not in conforming mode, as gcc does, for
instance.
They are not standard C but are POSIX. I do not see the point
in defining PI again and again...

No, gcc doesn't define M_PI. <math.h> is part of the C library, not
part of the compiler. gcc uses whatever <math.h> file is provided by
the system (that's glibc on some, but by no means all, systems).
(Minor detail: the "fixincludes" program creates a modified version of
<math.h> when gcc is installed, but that doesn't affect M_PI.)

If we're going to discuss specific implementations, we need to know
what we're talking about. gcc is a compiler, not a full
implementation.

The point is that any program that depends on M_PI is non-portable.
A conforming C implementation *may not* define M_PI in <math.h>.

 

[Keith Thompson]

Actually, it's hilarious (if you consider the deliberate misspelling).
IMO-YMMV.

You missed something. Hint: What is the singular of "axes"? (There
are two correct answers.)

This is referring to the famous equation e^(i*pi) - 1 = 0
which is certainly true in the complex plane.

Or perhaps to the even more famous equation e^(i*pi) + 1 = 0
(which I used to have on a t-shirt).

 

[user923005]

You missed something. Hint: What is the singular of "axes"? (There
are two correct answers.)

Is there anything more ironic than ironically missing the irony?

Or perhaps to the even more famous equation e^(i*pi) + 1 = 0
(which I used to have on a t-shirt).

Do I have to turn in my "math major" badge now?
:-(

 

[Lane Straatman]

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

#include <stdio.h>
#include <stdlib.h>
#include <complex.h>
#include <math.h>
int main(void)
{
double complex z1, z3, z4, z5;
double mod, phi, a, b, c, d;
z1 = .4 + .7I;
a = creal(z1);
b = cimag(z1);
mod = sqrt(pow(a, 2) + pow(b, 2));
phi = atan(b/a);
c = ( (sqrt(mod)) * cos( .5 * phi ) );
d = ( (sqrt(mod)) * sin( .5 * phi ) );
z4 = c + d*I;
z5 = cpow(z1, .5);
z3 = cpow(z4, 2.0);
printf("The square root of %lf %lfi\n", creal(z1), cimag(z1));
printf("is : %lf %lfi\n", creal(z4), cimag(z4));
printf("using cpow to get the root: %lf %lfi\n", creal(z5), cimag(z5));
printf("using cpow to check the square: %lf %lfi\n", creal(z3),
cimag(z3));
system("PAUSE");
return 0;
}
Am I going to get in trouble with atan as I've got it? LS

 

[Lane Straatman]

Lane Straatman said:


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 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. LS

 

[Lane Straatman]

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

"It" refers to what? ^^

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

It's certainly not jacob's fault that I sniped his header and got errors by
the hundred.

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

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

 

[Keith Thompson]

"It" refers to what? ^^

Um, devcpp? What else would it refer to?

It's certainly not jacob's fault that I sniped his header and got errors by
the hundred.

Nobody said it was jacob's fault.

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

That differed from what?

 

[Richard Heathfield]

Lane Straatman said:

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.

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.

 

[Malcolm McLean]

Malcolm McLean said:


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.


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.