Check my math!

[Craig Bailey]

Someone please explain what alternate universe I fell into this
afternoon when PHP started telling me that 2 doesn't equal 2.

Not sure about you, but when I run this, it tells me 59001.31 doesn't
equal 59001.31. Change each side of the equation by a hundreth or two
and it checks. Change it a bit more, and it won't.

_What_ is going on here?!

<?php
$subtotal=59001 .31;
$principal=5860 5.33;
$interest=395.9 8;
$check=$princip al+$interest;
echo("<pre>");
echo("Check: " . $check . "\n");
echo("Subtotal: " . $subtotal . "\n");
if($check!=$sub total) {
echo("Check (" . $check . ") does not equal subtotal (" .
$subtotal . ")"); // Check doesn't equal subtotal
}
else {
echo("Check (" . $check . ") equals subtotal (" . $subtotal .
")"); // Check does equal subtotal
}
echo("</pre>");
?>

--
Craig Bailey, Communications Coordinator
Vermont Housing Finance Agency (VHFA)
164 St. Paul St., P.O. Box 408
Burlington, Vt. 05402-0408
Email: cb*****@vhfa.or g | Web: www.vhfa.org
Phone: [phone] | Fax: [phone]

[Chung Leong]

Floating operations always introduces small errors, that's why. Run this and
you'll see:

<?php
$subtotal=59001 .31;
$principal=5860 5.33;
$interest=395.9 8;
$check=$princip al+$interest;
$diff=$check - $subtotal;
echo("<pre>");
echo("Check: " . $check . "\n");
echo("Subtotal: " . $subtotal . "\n");
if($check!=$sub total) {
echo("Check (" . $check . ") does not equal subtotal (" .
$subtotal . ")."); // Check doesn't equal subtotal
printf("Their difference is %01.40f", $diff);
}
else {
echo("Check (" . $check . ") equals subtotal (" . $subtotal .
")"); // Check does equal subtotal
}
echo("</pre>");
?>

The decimal part of a float is represented internally as a fraction of some
denominator that is of the power of 2. Decimals that are not
1/(2^n)therefore cannot be represented precisely.

59001.31 is 59001 + 5325759447 / 2^34 or
59001.309999999 997671693563461 3037109375
58605.33 is 58605 + 22677427323 / 2^36 or
58605.330000000 001746229827404 022216796875
395.98 is 395 + 2155042790441 / 2^41 or
395.98000000000 001818989403545 85647583007813

When you add up the fractions, lo and behold, they don't add up exactly (the
error is 1/(2^37)).

You should do what Mike suggested. Whenever you divide something or multiple
something by a floating point number, pass the result through round().

Uzytkownik "Craig Bailey" <cb*****@vhfa.o rg> napisal w wiadomosci
news:cb******** *************** ****@sover.net. client.newsread .com...

Someone please explain what alternate universe I fell into this
afternoon when PHP started telling me that 2 doesn't equal 2.

Not sure about you, but when I run this, it tells me 59001.31 doesn't
equal 59001.31. Change each side of the equation by a hundreth or two
and it checks. Change it a bit more, and it won't.

_What_ is going on here?!

<?php
$subtotal=59001 .31;
$principal=5860 5.33;
$interest=395.9 8;
$check=$princip al+$interest;
echo("<pre>");
echo("Check: " . $check . "\n");
echo("Subtotal: " . $subtotal . "\n");
if($check!=$sub total) {
echo("Check (" . $check . ") does not equal subtotal (" .
$subtotal . ")"); // Check doesn't equal subtotal
}
else {
echo("Check (" . $check . ") equals subtotal (" . $subtotal .
")"); // Check does equal subtotal
}
echo("</pre>");
?>

--
Craig Bailey, Communications Coordinator
Vermont Housing Finance Agency (VHFA)
164 St. Paul St., P.O. Box 408
Burlington, Vt. 05402-0408
Email: cb*****@vhfa.or g | Web: www.vhfa.org
Phone: [phone] | Fax: [phone]

[Carl Melot]

"Chung Leong" <ch***********@ hotmail.com> wrote

You should do what Mike suggested. Whenever you divide something or multiple something by a floating point number, pass the result through round().

LOL somebody here capable of programming? Just ironic, reading too much
bulls*** here.

What should somebody use floats for, when always rounding that shit before
doing mathematics?

If you have to use floats and need to to compare them, round them before
comparing. But when using floats that have to be compared, your concept is
broken.

Carl

[Craig Bailey]

In article <2O************ *****@newssvr27 .news.prodigy.c om>,
"CountScubu la" <[e-mail] mail.com> wrote:

I did not get into it, but just for a quick reference, when you deal with
money in software/scripts, it is best to convert over to cents, thus 395.98
is 39598, deal with all numbers as whole numbers, and when you go to print
it then add the decimal, the decimal is a human thing, for parts of a
dollar.

Thanks for all the help. Though I admit that I'm a little floored that a
scripting language doesn't have a more elegant way to handle something
like ... er ... _numbers_.

And here I thought computers were _good_ with numbers ...

--
Craig Bailey, Communications Coordinator
Vermont Housing Finance Agency (VHFA)
164 St. Paul St., P.O. Box 408
Burlington, Vt. 05402-0408
Email: cb*****@vhfa.or g | Web: www.vhfa.org
Phone: [phone] | Fax: [phone]

[Andy Hassall]

On Tue, 13 Jan 2004 18:20:34 GMT, Craig Bailey <cb*****@vhfa.o rg> wrote:

In article <2O************ *****@newssvr27 .news.prodigy.c om>,
"CountScubu la" <[e-mail] mail.com> wrote:

I did not get into it, but just for a quick reference, when you deal with
money in software/scripts, it is best to convert over to cents, thus 395.98
is 39598, deal with all numbers as whole numbers, and when you go to print
it then add the decimal, the decimal is a human thing, for parts of a
dollar.

Thanks for all the help. Though I admit that I'm a little floored that a
scripting language doesn't have a more elegant way to handle something
like ... er ... _numbers_.

And here I thought computers were _good_ with numbers ...

They are. But there have to be compromises when storing floating point
numbers. For example, if you do 1.0/3.0, you get 0.33333 recurring. How do you
store an infinite number of decimal places in a (small) finite space?

There are floating point storage schemes that can represent recurring numbers
exactly, but they're relatively complicated. The IEEE format used by most
processors lets you store the number in a smallish space and have simpler
circuitry to process it, but the compromise is you lose accuracy after a
certain number of significant digits.

It's a hardware thing, not a language thing.

So, if you want exact maths on a computer, use integers, or find one of the
exact floating point maths libraries and put up with the performance penalties.

--
Andy Hassall <an**@andyh.co. uk> / Space: disk usage analysis tool
<http://www.andyh.co.uk > / <http://www.andyhsoftwa re.co.uk/space>

[Centurion]

CountScubula wrote:

I did not get into it, but just for a quick reference, when you deal with
money in software/scripts, it is best to convert over to cents, thus
395.98 is 39598, deal with all numbers as whole numbers, and when you go
to print it then add the decimal, the decimal is a human thing, for parts
of a dollar.

just my 2 cents or ($.02)

--
Mike Bradley "Craig Bailey" <cb*****@vhfa.o rg> wrote in message
news:cb******** *************** ****@sover.net. client.newsread .com...

Someone please explain what alternate universe I fell into this
afternoon when PHP started telling me that 2 doesn't equal 2.

Not sure about you, but when I run this, it tells me 59001.31 doesn't
equal 59001.31. Change each side of the equation by a hundreth or two
and it checks. Change it a bit more, and it won't.

_What_ is going on here?!

Heheh - I remember them telling us that in my 1st year of computer science
:) I so rarely deal with currency stuff I'd almost forgotten! Thanks for
the reminder.

James
--
Fortune cookie says:
America has been discovered before, but it has always been hushed up.
- Oscar Wilde

[Carl Melot]

"CountScubu la" <[e-mail] mail.com> schrieb im Newsbeitrag
news:2O******** *********@newss vr27.news.prodi gy.com...

I did not get into it, but just for a quick reference, when you deal with
money in software/scripts, it is best to convert over to cents, thus 395.98 is 39598, deal with all numbers as whole numbers, and when you go to print
it then add the decimal, the decimal is a human thing, for parts of a
dollar.

So when using signed 32 bit integer values (the only PHP knows) you have
2,000,000,000 Cent or better 20,000,000.00 $ to be the limit of economics.
PHP then starts converting values to FLOAT. So when handling huge values one
better doesn't compare without additional rounding.

Carl

[Craig Bailey]

In article <i4************ *************** *****@4ax.com>,
Andy Hassall <an**@andyh.co. uk> wrote:

But there have to be compromises when storing floating point
numbers. For example, if you do 1.0/3.0, you get 0.33333 recurring. How do
you
store an infinite number of decimal places in a (small) finite space?

But that's not what I'm doing. I'm doing addition. I'm taking 10.25 and
adding it to 11.4.

Why can't the computer recognize that as 21.65?

If $total=21.65 and I compare that to 10.25+11.4, the fact that the
computer might not be able to recognize a match perplexs me.

I set $total=21.65 and ask it to print $total. It prints 21.65.

I set $anotherTotal=1 0.25+11.4. I ask it to print $anotherTotal. It
prints 21.65.

_Then_ I ask it if $total equals $anotherTotal and is says "No."

Huh?

--
Floydian Slip(tm) - "Broadcasti ng from the dark side of the moon"
Random Precision Productions(tm)
67 Union St. #2D, Winooski, Vt. 05404-1948 USA
Sundays, 7-8 pm - Champ 101.3 FM, Colchester; 102.1 FM, Randolph, Vt.
cc*@floydiansli p.com - AIM: RandomPrec - www.floydianslip.com

[Chung Leong]

Mike's suggestion was to use fixed point math. Read the post, pal.

Uzytkownik "Carl Melot" <ca*****@linkwa ve.org> napisal w wiadomosci
news:bu******** *****@news.t-online.com...

What should somebody use floats for, when always rounding that shit before
doing mathematics?

If you have to use floats and need to to compare them, round them before
comparing. But when using floats that have to be compared, your concept is
broken.

Carl

[Andy Hassall]

On Wed, 14 Jan 2004 00:31:57 GMT, Craig Bailey <cc*@floydiansl ip.com> wrote:

In article <i4************ *************** *****@4ax.com>,
Andy Hassall <an**@andyh.co. uk> wrote:

But there have to be compromises when storing floating point
numbers. For example, if you do 1.0/3.0, you get 0.33333 recurring. How do
you
store an infinite number of decimal places in a (small) finite space?

But that's not what I'm doing. I'm doing addition. I'm taking 10.25 and
adding it to 11.4.

Why can't the computer recognize that as 21.65?

If $total=21.65 and I compare that to 10.25+11.4, the fact that the
computer might not be able to recognize a match perplexs me.

I set $total=21.65 and ask it to print $total. It prints 21.65.

I set $anotherTotal=1 0.25+11.4. I ask it to print $anotherTotal. It
prints 21.65.

_Then_ I ask it if $total equals $anotherTotal and is says "No."

For really gory details into Why, search for 'IEEE floating point
representation' . For example:

http://www.math.grin.edu/~stone/cour...EEE-reals.html

Since the system is based on binary powers, the inaccuracies don't come in
places that you might think if you're thinking in decimal. Various floating
point numbers that have an exact decimal representation end up as recurring
binary representation in the IEEE scheme, so get approximated. Taking the
numbers you pointed out:

<pre>
<?php
$x = 10.25;
$y = 11.4;

printf("x = %10.32f\n", $x);
printf("y = %10.32f\n", $y);
printf("x + y = %10.32f\n", $x+$y);
?>
</pre>

Outputs:

x = 10.250000000000 000000000000000 00000
y = 11.400000000000 000355271367880 05009
x + y = 21.649999999999 998578914528479 79963

I really can't remember the exact details of the IEEE representation any more,
I think like most people I just accept there are inaccuracies and so you
arrange code to expect them, and to minimise the number of repeated operations
(the more you do, the more inaccurate you get).

But from the above, you can see that 10.25 can be exactly represented, but
whilst it's got pretty close to 11.4, it's very slightly off. And again with
the sum of the two, it's slightly off.

With the IEEE representation, there is a (very small) value 'epsilon' which is
a limit of the inaccuracy between the number you want and the stored
representation of it. Check Google, and computer architecture books for the
boring but useful explanation of how it works.

--
Andy Hassall <an**@andyh.co. uk> / Space: disk usage analysis tool
<http://www.andyh.co.uk > / <http://www.andyhsoftwa re.co.uk/space>