std.math unittests - accuracy of floating point results

[Kevin Brogan via digitalmars-d-ldc]

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.