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Date: Wed, 29 Aug 2007 16:17:28 +0100
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Subject: Re: [PHP-DEV] Testing math functions
From: zoe.slattery@googlemail.com (Zoe Slattery)

Richard Lynch wrote:
> On Thu, August 23, 2007 10:28 am, Zoe Slattery wrote:
>   
>> Hi - I've writing a few tests for the math extension and have a
>> question
>> about floating point precision.
>>
>> Here's a small example:
>>
>> --TEST--
>> Test return type and value for expected input sin()
>> --INI--
>> precision = 14
>> --FILE--
>> <?php
>>
>> $threesixty = pi() * 2.0;
>> echo "sin 360 = ";
>> var_dump(sin($threesixty));
>>
>> ?>
>> --EXPECT--
>> sin 360 = float(-2.4492127076448E-16)
>>
>> Is it right to test for an exact number in this way? I was slightly
>> suprised that I got the same number from Windows and Linux (maybe I
>> shouldn't be).
>>
>> If not, I could write the test above to check that sin 360 is zero
>> plus/minus some small number - but how small?
>>     
>
> Seems to me that if 'precision' setting is supposed to affect the
> output of your calculations, then you should, in theory, be able to
> rely on 14 decimal places, no?...
>   
Actually that isn't what "precision=14" does. Precision=14 will just 
print out the first 14 digits of the answer ignoring leading zeros.
So when I change the ini setting to precision=3, the result I get for 
sin(360) is -2.45E-16, this doesn't help if the processor rounding error 
is > 1.0 E-16 say.
> I realize that's an over-simplistic answer, perhaps, and I thought the
> precision only applied to BC_MATH and/or GMP calculations.
>   
I'm sorry - I don't know enough about BC_MATH or GMP to comment.
> I'd be surprised if it was ALWAYS right for every OS, and I strongly
> suspect it's going to fail on 64-bit hardware big-time.
>   
As Piere says - and I just verified by using a few different processors 
- the answer is processor dependent.
> I guess the first question I have is "What precisely are you testing?"
>
> The 'precision' setting?
>   
Nope :-)
> Or just that sin(2 * M_PI) is kinda sorta close to 0?
>   
Yes - the most simple test of sin() or cos() functions is that they 
should give the expected result for known values.
> If you just want "close to 0" then double the answer you are getting
> now, and call that "close enough" :-)
>   
Well - maybe. After trying a few different processors a reasonable thing 
to do seems to be to check that the answer of a floating point 
calculation is within  "plus or minus  1.0E-10"  of the expected result. 
This feels a bit arbitrary - but there doesn't seems to be a better 
solution (except maybe a lot of research into allowable rounding errors 
from each sort of processor technology and I don't think this particular 
case warrants that)
> If you think 'precision' is supposed to affect it and guarantee 14
> decimal places of precision, then 1.0E-14 to 1.0E14 should be your
> range, no?
>
>   
See above