Mod2Pi Test failure in 0.31 and master branch when compiled with Intel tool chain and MKL

[starrynight]

Environment: Ubuntu 14.04 icc 15.0 ifort 15.0 mkl 11.2
source /opt/intel/composerxe/bin/compilervars.sh intel64
source /opt/intel/mkl/bin/mklvars.sh intel64 ilp64
export LD=/opt/intel/composerxe/bin/xild
export AR=/opt/intel/composerxe/bin/xiar
export MKL_INTERFACE_LAYER=ILP64
export MKLROOT = /opt/intel/composerxe/mkl

Make.user:
USE_INTEL_MKL = 1
USE_INTEL_MKL_FFT = 1
USE_INTEL_LIBM = 1
USEICC = 1
USEIFC = 1

Built succesful. However, when running make test, it stopped at mod2pi unit test

ERROR: assertion failed: |totalErrNew - 0.0| <= 1.7763568394002505e-11
totalErrNew = 12.56641004881809
0.0 = 0.0
difference = 12.56641004881809 > 1.7763568394002505e-11
in error at error.jl:22
in test_approx_eq at test.jl:109
in testModPi at mod2pi.jl:182
in runtests at /home/mickey/Sources_ML/julia/test/testdefs.jl:5
in anonymous at multi.jl:855
in run_work_thunk at multi.jl:621
in anonymous at task.jl:855
while loading mod2pi.jl, in expression starting on line 184
ERROR: assertion failed: |totalErrNew - 0.0| <= 1.7763568394002505e-11
totalErrNew = 12.56641004881809
0.0 = 0.0
difference = 12.56641004881809 > 1.7763568394002505e-11
in anonymous at task.jl:1367
while loading mod2pi.jl, in expression starting on line 184
while loading /home/mickey/Sources_ML/julia/test/runtests.jl, in expression starting on line 35

[ViralBShah]

Does this happen on master too? I have icc 14 where I had tried everything before. Trying the 0.3 release branch now.

[starrynight]

Yes, it happens on master too. I've tried on 0.32 as well but 0.32 has some other errors. So far, 0.31 and master are the branches giving minimum errors.

[jiahao]

The problem lies in Base.Math.ieee754_rem_pio2, which is a wrapper around libopenspecfun:__ieee754_rem_pio2.

ᐅ ~/julia-release/julia -e 'println(Base.Math.ieee754_rem_pio2(17.0))'
(11,[-0.2787595947438628,-7.421924678439073e-18])
ᐅ  ~/julia-intel/julia -e 'println(Base.Math.ieee754_rem_pio2(17.0))' 
(10,[-2.782002278622783e-16,0.0])

[ViralBShah]

It would be nice to have a julia implementation. We have other problems with rem_pio2 as well in openlibm, where it produces the wrong result on i486.

[simonbyrne]

I agree on having a Julia implementation: it would also avoid the overhead of allocating a 2-element array on each call.

[tkelman]

It's not in openlibm any more, but presumably moving it to openspecfun didn't fix it on i486. Replacing it with a Julia implementation would be a good way of making openspecfun smaller (along with #8536). Openspecfun probably doesn't need to exist forever as an independent library, especially since we're not far at all from really only needing Faddeeva from it.

[simonbyrne]

If anyone really wants to debug this, it seems like these are the lines causing the problem:
https://github.com/JuliaLang/openspecfun/blob/381db9bc865e51de67be9dcaa1610a6f90029c72/rem_pio2/e_rem_pio2.c#L132-L138

My usual guess for things like this are unexpected use of x87 80bit floats: one option would be to try playing around with compiler options, and see if that fixes it.

I've made a start on translating it to Julia here:
https://github.com/simonbyrne/libm.jl/blob/master/src/rempio2.jl

It still requires an implementation of the Payne-Hanek reduction for large numbers (I might not have much time to look at this for a week or two), but it at least solves the above issue.

[ViralBShah]

Glenn Chisholm mentioned that this can be fixed with

CFLAGS = -mieee-fp -std=c99 -Wall -O3

[ViralBShah]

I don't think icc 14 has -mieee-fp. We already use -fp-model precise, but this is not passed to openlibm and openspecfun. It is worth trying that to fix this issue.

[gchisholm]

Decided to run it quickly but yes:

CFLAGS = -fp-model precise -std=c99 -Wall -O3

[julia]$ ./julia test/runtests.jl mod2pi
* mod2pi
SUCCESS

[julia]$ icc -v
icc version 15.0.1 (gcc version 4.8.2 compatibility)