sin (M_PI)

[Adam]

Hi,
I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

Thanks,
Adam

[Tim Prince]

Adam wrote:

Hi,
I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

As the other responders have pointed out, this is to be expected. If you
had opened up your search engine, you surely would have found some close
references.
As you haven't said anything about your goals for modifying this
behavior, the suggestion about sinl(M_PIl) is as good as any, keeping in
mind that default Windows behavior is for long double to be simply an
alias for double.

Think about the steps you are taking here.
M_PI (not defined in std C) is likely a truncated decimal approximation
to the irrational value of pi.
The argument to sin() is at best the nearest binary value to the decimal
value. It could be as much as DBL_EPSILON larger or smaller than the
ideal value. A little application of high school math should help you
figure out how much difference this makes to the ideal value of sin().

If you are writing the code for a compiler to use in constant
propagation, say for a target processor like x87 which has some built-in
extra precision constants, you could take the position that you should
pick the closest of those built-in constants, when it satisfies the
demands of the C standard for closeness to the value in question. This
would enable the compiler to evaluate sin(M_PI) as 0. at compile time,
but then you would have a discrepancy against the behavior of values
generated at run time. Unless you want to write a sin() function which
searches for a match to certain multiples of the built-in pi before
evaluation. Where do you draw the line? pi/4,..., INT_MAX/4*PI ?

I understand there has been academic work on the precision attainable by
math functions including sin(). When people are building careers on this
subject, can you seriously ask "does anyone have any idea?"

[osmium]

"Jens Thoms Toerring" wrote:

Adam <ad**@sendnospa m.comwrote:

>I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

Pi is an irrational number, i.e. you can't write it down
exactly without giving an infinite number of digits (what-
ever number system you use)

One nitpick. I think pi is transcendental rather than irrational.

http://en.wikipedia.org/wiki/Lindema...strass_theorem

[jacob navia]

Tim Prince wrote:

Adam wrote:

>Hi,
I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

As the other responders have pointed out, this is to be expected. If you
had opened up your search engine, you surely would have found some close
references.
As you haven't said anything about your goals for modifying this
behavior, the suggestion about sinl(M_PIl) is as good as any, keeping in
mind that default Windows behavior is for long double to be simply an
alias for double.

This is wrong. The lcc-win32 compiler features full precision (80 bits
floating point) for long double. The long double equals double
feature is just a feature of one compiler system under windows:
Microsoft MSVC. Other compilers under windows offer more precision.

jacob

[Richard Bos]

"osmium" <r1********@com cast.netwrote:

"Jens Thoms Toerring" wrote:

Adam <ad**@sendnospa m.comwrote:

I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

Pi is an irrational number, i.e. you can't write it down
exactly without giving an infinite number of digits (what-
ever number system you use)

One nitpick. I think pi is transcendental rather than irrational.

http://en.wikipedia.org/wiki/Lindema...strass_theorem

Transcendental, and _therefore_ irrational. The transcendental numbers
are a strict subset of the rational ones.

Richard

[osmium]

"Richard Bos" writes:

"osmium" <r1********@com cast.netwrote:

>"Jens Thoms Toerring" wrote:

Adam <ad**@sendnospa m.comwrote:
I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

Pi is an irrational number, i.e. you can't write it down
exactly without giving an infinite number of digits (what-
ever number system you use)

One nitpick. I think pi is transcendental rather than irrational.

http://en.wikipedia.org/wiki/Lindema...strass_theorem

Transcendental, and _therefore_ irrational. The transcendental numbers
are a strict subset of the rational ones.

I already said it was a nitpick. But the subject of the thread *is*
precision, so one should use the most precise word. "Apple" is more precise
than "fruit".

[Chris Dollin]

osmium wrote:

"Jens Thoms Toerring" wrote:

>Adam <ad**@sendnospa m.comwrote:

>>I am using the following code:
printf("%g" , sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

Pi is an irrational number, i.e. you can't write it down
exactly without giving an infinite number of digits (what-
ever number system you use)

One nitpick. I think pi is transcendental rather than irrational.

(fx:counter-nitpick)

All the transcendentals are irrational. "Pi isn't just irrational;
it's transcendental" is better than "... rather than ...".

It's certainly a subject one can get one's teeth into.

--
RIP Donald Michie 11 November 1923 - 7 July 2007

Hewlett-Packard Limited registered no:
registered office: Cain Road, Bracknell, Berks RG12 1HN 690597 England

[Chris Dollin]

osmium wrote:

I already said it was a nitpick. But the subject of the thread *is*
precision, so one should use the most precise word.

That doesn't follow. (Covariance and contravariance come to mind.
Possibly only metaphorically. )

--
RIP Donald Michie 11 November 1923 - 7 July 2007

Hewlett-Packard Limited Cain Road, Bracknell, registered no:
registered office: Berks RG12 1HN 690597 England

[Chris Dollin]

Richard Bos wrote:

Transcendental, and _therefore_ irrational. The transcendental numbers
are a strict subset of the rational ones.

s/rat/irrat/?

--
RIP Donald Michie 11 November 1923 - 7 July 2007

Hewlett-Packard Limited registered no:
registered office: Cain Road, Bracknell, Berks RG12 1HN 690597 England

[Dale Henderson]

>>>>"JT" == Jens Thoms Toerring <[e-mail] writes:

JTPi is an irrational number, i.e. you can't write it down
JTexactly without giving an infinite number of digits (what-
JTever number system you use).

This isn't so. You can use base pi where pi becomes 10 of course 4 is
a problem. :)

See http://mathworld.wolfram.com/Base.html and
http://www.dwheeler.com/essays/bases.html

[Keith Thompson]

rl*@hoekstra-uitgeverij.nl (Richard Bos) writes:

"osmium" <r1********@com cast.netwrote:

>"Jens Thoms Toerring" wrote:

Adam <ad**@sendnospa m.comwrote:
I am using the following code:
printf("%g", sin(M_PI))
and getting 1.22461e-16 instead of zero.
Does anyone have any idea why, and what I can do about it?

Pi is an irrational number, i.e. you can't write it down
exactly without giving an infinite number of digits (what-
ever number system you use)

One nitpick. I think pi is transcendental rather than irrational.

http://en.wikipedia.org/wiki/Lindema...strass_theorem

Transcendental, and _therefore_ irrational. The transcendental numbers
are a strict subset of the rational ones.

(s/rational/irrational/)

And the relevant point here is that pi cannot be represented exactly
as a floating-point number. That's merely because it's not an integer
multiple of a power of 2.0. The same issue can arise even for
rational numbers. For example, mathematically, sqrt(1.0/9.0) =
1.0/3.0, but neither 1.0/9.0 nor 1.0/3.0 can be represented exactly in
most floating-point systems.

(Quibble: C doesn't require binary floating-point. A trinary
floating-point system could represent 1.0/3.0 and 1.0/9.0 exactly --
but not 0.5. Conceivably a base-pi system could represent pi exactly,
but not 1.0.)

--
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."
-- Antony Jay and Jonathan Lynn, "Yes Minister"