Trig value errors

[jzakiya]

On Dec 23, 12:35 pm, jzakiya [email protected] wrote:

or what libraries they decided to use. I don’t
know (or care) about any of those under-the-hood
things.

What I do KNOW is that the people who designed and
implemented this calculator CARED that it produced
the mathematically exact results for those angles.

This makes me happy.

Perhaps you should look under the hood to see what its doing.

for angles on an axis too. So when I use this calculator,

This makes me happy.

PURE speculation, but this sounds like its just rounding off the
results for a pretty display for the end user. (Again, look at the
source)

So I am asking you to see that these errors be fixed.

The language should work to please the user.
The language should be intuitive to the user.
The language should not cause unnecessary surprises.

So please, fix these errors.

This will make me happy.

Thanks

This has already been explained. The ratio of a circle’s circumference
to its diameter cannot be fully actualized in finite bytes (and
certainly not in floats). Calculations using Math::PI, therefor,
unless given a special representation, and the language/library has
been built from the ground up to handle calculations with that special
representation (and similarly with all other sorts of irrational
numbers) will never yield a 100% result. If you need more precision
than floating point arithmatic provides, use a specialized language.
If you want your values that, for you, are sufficiently close to zero
to be zero, then its easy enough to round them. However, that decision
CANNOT be made for everybody using the language, as different
people have different expectations of precision, and as has been
mentioned before libraries will break.

[jzakiya]

Respectifully…

On Wed, Dec 23, 2009 at 9:42 AM, jzakiya [email protected] wrote:

The language should be intuitive to the user.
The language should not cause unnecessary surprises.

So please, fix these errors.

This will make me happy.

What would make pretty much everyone on this list happy is if you took
1/10
the amount of time you’ve spent calling the Ruby community idiots
actually
investigating why your tool of choice works better than you are getting
from
the C STANDARD (note that nasty 8 letter word again) library. I took a 1
minute look at the Qalculate website and discovered that it uses the CLN
library for its math functions. Apparently that library has a higher
degree
of precision that the C STANDARD library used by Ruby.

Shockingly choices are made that have nothing to do with people caring
or
not. Clearly since a number of folks have decided to attempt to assist
you
in even with your ignorant rant against the community we must care about
even the ignorant amongst us.

You may feel absolutely free to build an extension to access the
library.

Also, taking another 2 minutes to investigate just a bit further I came
across a post from matz himself discussing this exact library (along
with
GMP - another alternative).
OSDIR The problem is that
LEGALLY they cannot link a pure GPL library into ruby because of
licensing
issues. Again, sometimes decisions are made that affect 1% of the user
base
that are unfortunate but unless you step up and help (and bitching isn’t
helping) - you are never going to get what you want. BTW, there appears
to
be at least some form of an extension to access GMP which may be of
assistance to you -
taw's blog: Resurrection of libgmp-ruby

Please step up yourself and assist the community in gaining access to
more
precise mathematical functionality rather than making unfounded and
exceptionally ignorant accusations. No one years ago got a big chuckle
out
of placing barriers to someone’s future attempt to use sin and cos -
we’re
just plugging along doing the best we can.

John

[jzakiya]

On 23.12.2009 18:42, jzakiya wrote:
[…]

This makes me happy.
[…]
This makes me happy.
[…]
This makes me happy.
[…]

This makes me unhappy.
[…]
So please, fix these errors.

This will make me happy.
[…]

Bluntly speaking, your happiness is your probem, and not relevant to me,
Matz, or indeed anyone.

If you don’t like the result Ruby provides, do something constructive.
Bitching and yapping about minute details, the reasoning for which have
been put before you more often than to be expected (i.e. more than
once), will earn you increasing animosity, if not hostility.

If you don’t like how Ruby does math, feel free to investigate
alternatives to Ruby, or write a math library that does its calculations
to the level of accuracy that makes you happy.

Nobody forces you to use Ruby (unless it is your employer, in which case
I’d suggest investigating alternative employment, nice as Ruby is).

You could use JRuby and a Java library with “better” maths; you could
use IronRuby and a .NET library with “better” maths.

Nobody forces you to use Ruby as is, either. It’s open source. Change
Ruby’s behavior, if you like.

[jzakiya]

On Dec 23, 12:35 pm, jzakiya [email protected] wrote:

or what libraries they decided to use. I don’t
tada! Calculator. Again, I don’t know the people who

The language should work to please the user.
The language should be intuitive to the user.
The language should not cause unnecessary surprises.

So please, fix these errors.

This will make me happy.

Thanks

Also, as an example:

static VALUE
math_cos(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(cos(RFLOAT_VALUE(x)));
}

If you have a beef with anyone, its with the implementers of the C
standard library, but…

[jzakiya]

On Dec 23, 12:14 pm, Phillip G. [email protected] wrote:

And while maths, unlike other support sciences does have decent, and
interesting research all of its own, if it weren’t for sciences that
need maths, nobody would need it.

Now that we’re thoroughly off topic

This is like saying if people didn’t need to eat, there’d be no need
for food. Just because a statement is true does not mean it is
relevant.

There isn’t a single field of research that yields practical
application who’s core isn’t founded in some sort of math. I’m not a
mathematician (or even a math major) but my understanding has always
been that maths have been discovered, not necessarily invented.

[jzakiya]

On 2009-12-24, pharrington [email protected] wrote:

Let him break his Ruby install if he wants. Best to learn through
experience.

Yeah, but he seems to want to know why we aren’t all rushing to fix a
couple of special cases.

(Hint to the OP: You’re fixing “180”, but not “179.99999” or
“180.0000001”.)

-s

[jzakiya]

On Thu, Dec 24, 2009 at 10:48 AM, Colin B.
[email protected] wrote:

As a general comment: “MINASWAN”, or to be precise “MINASWA mostly N”
“And your Mom, too.” Ruby-talk best practices
http://blog.rubybestpractices.com/posts/jamesbritt/and_your_Mom_too.html

Nice post, but I think I found a typo where a ‘not’ is missing:

And being wrong on one thing does make make a person wrong on
everything.

–
Paul S.
http://www.nomadicfun.co.uk

[email protected]

[jzakiya]

On 2009-12-24, jzakiya [email protected] wrote:

Try this (with correct syntax if wrong).
Do similar for sin.

static VALUE
math_cos(VALUE obj, VALUE x)
{
Need_Float(x);
cos_value = DBL2NUM(cos(RFLOAT_VALUE(x)));
if (abs(cos_value) < 1e-10) cos_value 0.0;
return cos_value;
}

That’d be exceptionally stupid.

Here’s the problem: There exists at least one value for which the
correct
value of cos(x) is about 9e-11, which can be correctly represented
(within
a much, much, smaller margin of error) in a floating point value, and
which
you would then “fix” by changing it from not-zero to exactly-zero.

Which is to say, this would introduce a comparatively HUGE error, much
larger
than the alleged error you’re complaining about.

If you want approximate values, round them.

-s

[jzakiya]

If you have a beef with anyone, its with the implementers of the C
if (abs(cos_value) < 1e-10) cos_value 0.0;
return cos_value;
}

please Excuse the typo:

if (abs(cos_value) < 1e-10) cos_value = 0.0;

[jzakiya]

On 23.12.2009 18:45, pharrington wrote:

Now that we’re thoroughly off topic

My pleasure.

There isn’t a single field of research that yields practical
application who’s core isn’t founded in some sort of math. I’m not a
mathematician (or even a math major) but my understanding has always
been that maths have been discovered, not necessarily invented.

I have to disagree. While physics, or chemistry, uses math to yield
results of some form (statistics, for example, to evaluate an
experiment), you could replace math with something, if you so desired.

Essentially, what happens in physics happens whether there is math or
not.

Of course, since math is very, very useful, it rose to the level of
prominence it has achieved in all the siences. It is, however, not the
driving factor behind these discoveries.

But be that as it may, math is a science, and leads to mathematical
discoveries. However, these discoveries are true in the framework “we”
(i.e. the body of human work in the sciences, including maths) arrived
at.

In any case, math has its beauty (even if a lot of it will forever be
closed to me, since I lack the knowledge and the will to investigate it
deeper than I have to), and thus can be valued in and of itself.

And thusly, I’ll keep my mouth shut about the topic now, but if further
discussion is desired, I’m more than happy to continue it off-list.

[jzakiya]

On Dec 23, 1:05 pm, pharrington [email protected] wrote:

When I put in sin(180) it outputs ‘0’

to make sure the answers came out correctly (exact)

to assure other people get the same (exact) results I do.

}

If you have a beef with anyone, its with the implementers of the C
standard library, but…

Try this (with correct syntax if wrong).
Do similar for sin.

static VALUE
math_cos(VALUE obj, VALUE x)
{
Need_Float(x);
cos_value = DBL2NUM(cos(RFLOAT_VALUE(x)));
if (abs(cos_value) < 1e-10) cos_value 0.0;
return cos_value;
}

[jzakiya]

On 2009-12-24, jzakiya [email protected] wrote:

seebs wrote:

Here’s the problem: There exists at least one value for which the correct
value of cos(x) is about 9e-11, which can be correctly represented (within)

And what (extremely small) angle(s) would that be?

Are you really this stupid?

if (abs(cos_value) < 1e-14) cos_value = 0.0;

This provides the correct answers for the errors I illustrated.

Again:

If you can measure, in a float, the amount of the error, then there
exists
a value for which that number is closer than 0, and you’re introducing
an error larger than you’re correcting.

This makes me happy.

Have you considered masturbating in public? It would also make you
happy,
and be easier for other people to ignore.

Again:

If you want rounded values, round them yourself. You’ve just
demonstrated
that you know how to round (albeit poorly). Great. When you want
rounded
values, you go ahead and round them, then.

-s

[jzakiya]

On Dec 23, 8:04 pm, Seebs [email protected] wrote:

This provides the correct answers for the errors I illustrated.
and be easier for other people to ignore.

Again:

If you want rounded values, round them yourself. You’ve just demonstrated
that you know how to round (albeit poorly). Great. When you want rounded
values, you go ahead and round them, then.

-s

Copyright 2009, all wrongs reversed. Peter S. / [email protected]://www.seebs.net/log/<-- lawsuits, religion, and funny pictureshttp://en.wikipedia.org/wiki/Fair_Game_(Scientology) ← get educated!

Let him break his Ruby install if he wants. Best to learn through
experience.

[jzakiya]

The answers given by sin() and cos() are already the most accurate which
could be provided given the constraints of floating-point
representation.

Why would you want to make them less accurate? Surely it would be a bug
if the values returned were less accurate than the representation
allows?

Floating-point can represent smaller increments the closer you get to
zero. So values of 0 +/- dX can be represented much more accurately than
1 +/- dX.

[jzakiya]

On Dec 23, 7:45 pm, Seebs [email protected] wrote:

return cos_value;

than the alleged error you’re complaining about.

If you want approximate values, round them.

-s

Copyright 2009, all wrongs reversed. PeterSeebach/ [email protected]://www.seebs.net/log/<-- lawsuits, religion, and funny pictureshttp://en.wikipedia.org/wiki/Fair_Game_(Scientology) ← get educated!

Here’s the problem: There exists at least one value for which the correct
value of cos(x) is about 9e-11, which can be correctly represented (within)

And what (extremely small) angle(s) would that be?
Provide examples please:

If so then do:

if (abs(cos_value) < 1e-14) cos_value = 0.0;

This provides the correct answers for the errors I illustrated.

This makes me happy.

[jzakiya]

On 2009-12-26, Brian C. [email protected] wrote:

Why would you want to make them less accurate? Surely it would be a bug
if the values returned were less accurate than the representation
allows?

Because our hero is obsessed with the unrounded results of
intrinsically-rounded cases, and hasn’t thought about the question
of whether, say, sin(45) or sin(60) is returning “exactly” the
right value. Special-casing zeroes implies a deep failure to
understand trig.

-s

[jzakiya]

On Sat, Dec 26, 2009 at 4:56 AM, Brian C. [email protected]
wrote:

Floating-point can represent smaller increments the closer you get to
zero. So values of 0 +/- dX can be represented much more accurately than
1 +/- dX.

Strictly speaking they can be represented much more precisely.

Precision and accuracy are different things.

Accuracy and precision

–
Rick DeNatale

Blog: http://talklikeaduck.denhaven2.com/
Twitter: http://twitter.com/RickDeNatale
WWR: http://www.workingwithrails.com/person/9021-rick-denatale
LinkedIn: Rick DeNatale - Developer - IBM | LinkedIn

[jzakiya]

On 26.12.2009 15:43, Rick DeNatale wrote:

On Sat, Dec 26, 2009 at 4:56 AM, Brian C. [email protected] wrote:

Floating-point can represent smaller increments the closer you get to
zero. So values of 0 +/- dX can be represented much more accurately than
1 +/- dX.

Strictly speaking they can be represented much more precisely.

Are you sure you meant “precisely” and not “accurately”? Given the
Wikipedia article you quote it seems that is what you rather wanted to
say.

Precision and accuracy are different things.

Accuracy and precision - Wikipedia

In light of the article the term “precision” (aka “repeatability”) is
pretty meaningless in this case (you could also say “uninteresting”)
because due to the deterministic nature of the implementation of
trigonometric functions the result is always identical for the same
input. It is the accuracy that the whole thread revolves around. IEEE
standards mandate a certain accuracy and people who need better accuracy
need to use specialized tools - either math libraries with higher
accuracy (or even selectable accuracy) or tools that do symbolic math.

Also, as elsewhere in this thread has been explained, the “correction”
approach suggested (if the abs is lower than a particular epsilon,
return 0 instead of the value) is a pretty bad one - much worse than
general rounding of values because it introduces distorted accuracy.
Rounding is better because it generally cuts off digits; which is ironic
because it reduces overall accuracy of the function…

Kind regards

robert

A program that nicely demonstrates the nonlinearity of the error
introduced by the suggested “fix”:

module Math
def sin2(x, epsilon = 1e-10)
y = sin(x)
y.abs < epsilon ? 0.0 : y
end
end

include Math

find interesting start value

div = 1.2
x = 1.0
x /= div while sin(x) == sin2(x)

x *= div ** 10

do the test

100.times do |i|
y1 = sin(x)
y2 = sin2(x)
printf “%6d %20e %20e %20e error: %20e\n”, i, x, y1, y2,
((y2-y1)/x).abs
x /= div
end

[jzakiya]

As a general comment: “MINASWAN”, or to be precise “MINASWA mostly N”
“And your Mom, too.” Ruby-talk best practices
http://blog.rubybestpractices.com/posts/jamesbritt/and_your_Mom_too.html

And now thoroughly OT:
On Wed, Dec 23, 2009 at 10:15 PM, Phillip G. [email protected]
wrote:

On 23.12.2009 18:45, pharrington wrote:

Now that we’re thoroughly off topic

Not necessarily a bad thing!

My pleasure.

I have to disagree. While physics, or chemistry, uses math to yield results
of some form (statistics, for example, to evaluate an experiment), you could
replace math with something, if you so desired.
Essentially, what happens in physics happens whether there is math or not.

A mathematician (I think Ian Stewart) has observed that the physicists
would have derived the parts of group theory that they needed if
it hadn’t been previously derived by the mathematicians.

And thusly, I’ll keep my mouth shut about the topic now, but if further
discussion is desired, I’m more than happy to continue it off-list.

Same here: I think my email address is visible?
I even have an (ancient) mathematical joke to illustrate the points,
which I hesitate to inflict on ruby-talk in general.

Colin B.

[jzakiya]

On Sat, Dec 26, 2009 at 12:45 PM, Robert K.
[email protected] wrote:

Are you sure you meant “precisely” and not “accurately”? Given the
Wikipedia article you quote it seems that is what you rather wanted to
say.
No I meant what I said, although I might have picked a better source to
quote.

Precision refers to the smallest increment between floating point
numbers, the smaller the exponent the smaller the value of the least
sign, so one might be able to represent both

0.000000001
and
0.000000002

but, say

10000000.000000001 would have to be represented as

10000000.00
because you only have so many digits

Now one might compute a value of Pi

as

3.14
which would be more accurate, although less precise than a
miscalculated value like
4.3259890880890

One of the mistaken notions of novice programmers is to expect that
large amounts of precision in floating point arithmethic are always
good. However, in doing calculations with physical measurements of
various precisions, one can’t get any better precision than what you
start with. One can be fooled that the low order digits of
calculations represent precision that really isn’t there, and if one
isn’t careful about things like the order of floating point operations
when dealing with either very close or very distant values, accuracy
can easily be lost.

http://docs.sun.com/source/806-3568/ncg_goldberg.html

–
Rick DeNatale

Blog: http://talklikeaduck.denhaven2.com/
Twitter: http://twitter.com/RickDeNatale
WWR: http://www.workingwithrails.com/person/9021-rick-denatale
LinkedIn: Rick DeNatale - Developer - IBM | LinkedIn