Hi all,
 I am working on making more of the std.math unittests pass (I'm new to the project, and it is a nice niche thing to tinker on, learning the codebase, workflow, etc.).
I've hit on a problem that I do not know how to handle: floating point comparison.

There are some tests that check whether exp(x) works well, including overflow checks for different x. See phobos/std/math.d line 2083. The checks are defined for 80-bit reals, and I am converting them to 64-bit reals (Win64). The problem is that the checks are bit-precise (i.e. assert(x == y)), but the calculation results are sometimes 1 ulp off. For example, the results of two tests:

std.math.E = 0x4005bf0a8b145769 = 2.7182818284590450
exp(1.0L)  = 0x4005bf0a8b145769 = 2.7182818284590450  [1]
Wolfram Alpha                   = 2.718281828459045235...

E*E*E     = 0x403415e5bf6fb105 = 20.085536923187664
exp(3.0L) = 0x403415e5bf6fb106 = 20.085536923187668
Wolfram Alpha                  = 20.08553692318766774...

I do not know how I can make the second test pass, without breaking the first one. I feel the tests are too strict and should allow an error of 1 ulp.
dmd 2.066.1 passes these unittests with values corresponding Wolfram Alpha.

(Incidentally, an inaccuracy of 1 ulp also haunts a std.csv unittest, but I do not yet know why exactly)

How should I go about fixing these unittests for us?

Thanks,
  Johan

[1] The correct result for exp(1.0L) I was able to obtain by enabling the LLVM intrinsic for exp, although there is a comment saying that that actually causes unittest failure. Without the LLVM intrinsic, exp(1.0L) is 1 ulp off.

On Sunday, 1 March 2015 at 23:08:54 UTC, Johan Engelen wrote:
> Hi all,
>  I am working on making more of the std.math unittests pass (I'm new to the project, and it is a nice niche thing to tinker on, learning the codebase, workflow, etc.).

Guess what I'm doing. :-)

> I've hit on a problem that I do not know how to handle: floating point comparison.
>
> There are some tests that check whether exp(x) works well, including overflow checks for different x. See phobos/std/math.d line 2083. The checks are defined for 80-bit reals, and I am converting them to 64-bit reals (Win64). The problem is that the checks are bit-precise (i.e. assert(x == y)), but the calculation results are sometimes 1 ulp off. For example, the results of two tests:
>
> std.math.E = 0x4005bf0a8b145769 = 2.7182818284590450
> exp(1.0L)  = 0x4005bf0a8b145769 = 2.7182818284590450  [1]
> Wolfram Alpha                   = 2.718281828459045235...
>
> E*E*E     = 0x403415e5bf6fb105 = 20.085536923187664
> exp(3.0L) = 0x403415e5bf6fb106 = 20.085536923187668
> Wolfram Alpha                  = 20.08553692318766774...
>
> I do not know how I can make the second test pass, without breaking the first one. I feel the tests are too strict and should allow an error of 1 ulp.

They are too strict. floating point math is not exact between different architectures, or even compilation flags. You can get a different result just because the compiler reordered two operations.

> dmd 2.066.1 passes these unittests with values corresponding Wolfram Alpha.
>
> (Incidentally, an inaccuracy of 1 ulp also haunts a std.csv unittest, but I do not yet know why exactly)
>
> How should I go about fixing these unittests for us?
>
> Thanks,
>   Johan
>
> [1] The correct result for exp(1.0L) I was able to obtain by enabling the LLVM intrinsic for exp, although there is a comment saying that that actually causes unittest failure. Without the LLVM intrinsic, exp(1.0L) is 1 ulp off.

Take a look at bool approxEqual in std.math. A lot of unit tests use it already, but some of them don't. Every floating point comparison should be using them, in my opinion.

"Johan Engelen" <j@j.nl> writes:

> Hi all,
>  I am working on making more of the std.math unittests pass (I'm new
> to the project, and it is a nice niche thing to tinker on, learning
> the codebase, workflow, etc.).
> I've hit on a problem that I do not know how to handle: floating point
> comparison.

Hi Johan.  I think you are running into similar problems I ran into with 64-bit reals on ARM.  Hopefully there is a common solution for all 64-bit real architectures.

>
> (Incidentally, an inaccuracy of 1 ulp also haunts a std.csv unittest, but I do not yet know why exactly)

I encountered this too.  I found that std.conv.parse!double with 64-bit real is often off by 1 ulp compared to strod().  For 80-bit reals, they match.  I think the fix for this problem is a change to std.conv.parse.

> How should I go about fixing these unittests for us?

You could look in https://github.com/smolt/phobos/blob/ios/std/math.d and see if any changes I made for iOS may help you.  I have all remaining problems marked with D versions that are prefixed with "WIP_", like WIP_FloatPrecIssue.

Here are the phobos files possibly of interest:
 std/csv.d
 std/internal/math/errorfunction.d
 std/internal/math/gammafunction.d
 std/math.d

Hope this helps,
Dan

Hi Kevin! Hi Johan!

On Monday, 2 March 2015 at 00:30:28 UTC, Kevin Brogan wrote:
> On Sunday, 1 March 2015 at 23:08:54 UTC, Johan Engelen wrote:
>> Hi all,
>> I am working on making more of the std.math unittests pass (I'm new to the project, and it is a nice niche thing to tinker on, learning the codebase, workflow, etc.).
>
> Guess what I'm doing. :-)
>
>> I've hit on a problem that I do not know how to handle: floating point comparison.
>>
>> There are some tests that check whether exp(x) works well, including overflow checks for different x. See phobos/std/math.d line 2083. The checks are defined for 80-bit reals, and I am converting them to 64-bit reals (Win64). The problem is that the checks are bit-precise (i.e. assert(x == y)), but the calculation results are sometimes 1 ulp off. For example, the results of two tests:
>>
>> std.math.E = 0x4005bf0a8b145769 = 2.7182818284590450
>> exp(1.0L)  = 0x4005bf0a8b145769 = 2.7182818284590450  [1]
>> Wolfram Alpha                   = 2.718281828459045235...
>>
>> E*E*E     = 0x403415e5bf6fb105 = 20.085536923187664
>> exp(3.0L) = 0x403415e5bf6fb106 = 20.085536923187668
>> Wolfram Alpha                  = 20.08553692318766774...
>>
>> I do not know how I can make the second test pass, without breaking the first one. I feel the tests are too strict and should allow an error of 1 ulp.
>
> They are too strict. floating point math is not exact between different architectures, or even compilation flags. You can get a different result just because the compiler reordered two operations.

I agree, too. Bitwise comparison is worse if you are working with floating points.

BTW: These fixes should go upstream. Please create Phobos PRs for them. I am happy to cherry-pick these changes as soon as they committed.

Regards,
Kai

Thanks for the link to your branch Dan.

A few 64-bit fixes for gammafunction.d :
https://github.com/D-Programming-Language/phobos/pull/3045

"Johan Engelen" <j@j.nl> writes:

> Thanks for the link to your branch Dan.
>
> A few 64-bit fixes for gammafunction.d : https://github.com/D-Programming-Language/phobos/pull/3045

Thanks back.  I'll have to try it out on ARM.