Testing math functions

Richard Lynch 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

Pierre 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?

It really depends on the architecture. Using a precision of 10 should
put you on the safe side, at least for the common architecture (intel,
amd and ppc).

Yes - you are right thanks. I'm currently testing that the answer is
within +/- 1.0E-10 of what I expect - that works on the processor
architectures that I have access to. I guess I'll find out what happens
on the others wheh I check the test cases in :-).

--Pierre