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

[mark_bluemel]

On 12 Jul, 11:14, Adam <a...@sendnospa m.comwrote:

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,

The usual issues with floating point accuracy, I'd think.

and what I can do about it?

See if your target implementation has an alternative sin()
implementation (sinl(), which takes and returns long double, may be
available for example) and a suitable definition of PI.

[mark_bluemel]

On 12 Jul, 11:26, mark_blue...@po box.com wrote:

On 12 Jul, 11:14, Adam <a...@sendnospa m.comwrote:

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,

The usual issues with floating point accuracy, I'd think.

and what I can do about it?

See if your target implementation has an alternative sin()
implementation (sinl(), which takes and returns long double, may be
available for example) and a suitable definition of PI.

I must give up replying to myself...

sinl() is part of the standard and should be available. Finding a good
definition of PI may be more difficult, but a GNU libc header gives:-

# define M_PIl 3.1415926535897 932384626433832 795029L /*
pi */

[santosh]

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?

Firstly M_PI is not defined in Standard C, though most implementations
define it as an extension. You can also compute it's value at runtime
or define it yourself.

Secondly make sure you include stdio.h and math.h for printf and sin.
And try using the %f format specifier.

[Adam]

santosh 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?

Firstly M_PI is not defined in Standard C, though most implementations
define it as an extension. You can also compute it's value at runtime
or define it yourself.

Secondly make sure you include stdio.h and math.h for printf and sin.
And try using the %f format specifier.

Using %f works, but isn't a suitable solution, as my code is actually
printf("%g", sin(x)), where x could be pi, or something else, and %f
messes up the formatting for the other possibilities for x.

[santosh]

Adam wrote:

santosh 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?

Firstly M_PI is not defined in Standard C, though most implementations
define it as an extension. You can also compute it's value at runtime
or define it yourself.

Secondly make sure you include stdio.h and math.h for printf and sin.
And try using the %f format specifier.

Using %f works, but isn't a suitable solution, as my code is actually
printf("%g", sin(x)), where x could be pi, or something else, and %f
messes up the formatting for the other possibilities for x.

One possibility is to compare x with M_PI and if they're near enough,
print zero.
Something like:

if(abs(M_PI - x) <= delta) puts("0000e0");

[Jens Thoms Toerring]

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). Computers can't deal with
irrational numbers very well (i.e. at all) since in a
computer you can only store a finite number of digits.
Thus what you use for pi is never the true value of pi
but an approximation. So you can't expect more that an
approximation of the value of sin of pi when you use an
approximation of pi to start with.

Whenever you use floating point numbers you must consider
that the computer only stores a limited number of (binary)
digits. In many cases the number of digits that can be
stored is less than the true number of digits of the
floating point number - rather obvious for irrational
numbers like pi, but even a simple looking number like 0.1
becomes a number with infinitely many digits when expressed
in binary (like 1/3 has an infinite number of digits when
written in decimal). Thus in many (if not most) cases you
do calculations with approximations only. And that's not
the end of it. E.g. function like sin are computed using
(clever) approximate algorithms (which tend to be a limi-
ted number of summands of an infinite sum). So you do ap-
proximate calculations of functions on approximate values.
And the result is, of course, that you end up with more or
less good approximate results. And when you think of it,
1e-16 is a rather good approximation for a 0 when you con-
sider the range [-1:1] of the sin function.

Thus if you do floating point calculations you have to be
aware of the approximate nature of such computations. And
you have to be aware that small errors due to the approxi-
mations can sum up considerably - if you aren't careful
you can end up with completely bogus results.

Regards, Jens
--
\ Jens Thoms Toerring ___ [e-mail]
\______________ ____________ http://toerring.de

[santosh]

santosh wrote:

Adam wrote:

santosh 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?
>
Firstly M_PI is not defined in Standard C, though most implementations
define it as an extension. You can also compute it's value at runtime
or define it yourself.
>
Secondly make sure you include stdio.h and math.h for printf and sin.
And try using the %f format specifier.
>

Using %f works, but isn't a suitable solution, as my code is actually
printf("%g", sin(x)), where x could be pi, or something else, and %f
messes up the formatting for the other possibilities for x.

One possibility is to compare x with M_PI and if they're near enough,
print zero.
Something like:

if(abs(M_PI - x) <= delta) puts("0000e0");

Sorry about that. Use fabs instead of abs:

if(fabs(M_PI - x) <= delta) printf("%g\n", 0.0);

[Eric Sosman]

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?

Ponder these questions:

1: Is M_PI exactly equal to pi, or is it equal to pi+x
for some small x?

2: What is the value of sin(pi+x)?

--
Eric Sosman
es*****@ieee-dot-org.invalid

[Richard Heathfield]

Adam said:

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?

Presumably M_PI represents a value close to pi. It cannot represent pi
exactly, because pi is irrational. Given the nature of a sine wave, you
can expect sin(reasonable_ approximation_t o_pi) to be a reasonable
approximation to 0, and indeed that is what you are getting.

If you want to round the value, decide at which decimal place or
significant figure you wish to round it, and whether you wish to round
it up, down, or nearest. Then write code to do the rounding for you.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999