std.math unittests - accuracy of floating point results

[Johan Engelen via digitalmars-d-ldc]

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.