RE: [PHP] Math Weirdness

On 14 July 2008 20:47, tedd advised:

> Round-off errors normally don't enter into things unless your doing
> multiplication and division operations. At that point, what you get
> back from the operation is an approximation and not the actual
> number.

Bull! Nearly all computer floating point numbers are approximations
because of being held in binary rather than decimal. Any number with a
(decimal) fractional part that doesn't end with the digit 5 is
necessarily an approximation, and that's only half the story. So as soon
as you involve numbers like 0.1 or 0.2, you've already got minor
inaccuracies which will propagate through any kind of arithmetic -- it's
just worse with multiplication or division because these tend to result
in inaccuracy in more significant digits!

Bottom line: a floating point value should *always* be treated with an
appropriate degree of suspicion.

Cheers!

Mike

--
Mike Ford, Electronic Information Developer,
C507, Leeds Metropolitan University, Civic Quarter Campus,
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Email: m.ford@leedsmet.ac.uk
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2008/7/15 tedd <tedd.sperling@gmail.com>:
>
> I said:
>
> "Round-off errors normally don't enter into things unless your doing
> multiplication and division operations."
>
> And that is not "Bull" -- it's true. You can add and subtract all the
> floating point numbers (the one's we are talking about here) you want
> without any rounding errors whatsoever.

$ php -r 'echo 0.7 - 0.2 == 0.5 ? "true\n" : "false\n";'
false

The operation you do isn't important. You just can't represent certain
numbers exactly in binary, just as you can't represent 1/3 exactly in
decimal. They have to be rounded internally.

-robin

Robin Vickery schreef:
> 2008/7/15 tedd <tedd.sperling@gmail.com>:
>> I said:
>>
>> "Round-off errors normally don't enter into things unless your doing
>> multiplication and division operations."
>>
>> And that is not "Bull" -- it's true. You can add and subtract all the
>> floating point numbers (the one's we are talking about here) you want
>> without any rounding errors whatsoever.
>
> $ php -r 'echo 0.7 - 0.2 == 0.5 ? "true\n" : "false\n";'
> false
>
> The operation you do isn't important. You just can't represent certain
> numbers exactly in binary, just as you can't represent 1/3 exactly in
> decimal. They have to be rounded internally.

which makes php casting so much fun:

$ php -r 'echo (string)(0.7 - 0.2) == 0.5 ? "true\n" : "false\n";'
true



>
> -robin
>