Proposal: expose flags set by floating-point exceptions

[jiahao]

There is currently no Base function that allows users to check for the flags set by floating-point operations.1 This does not allow the user to compute in a fully IEEE-compatible manner and could decrease code legibility should the user be forced to test implicitly for a raised flag by inspecting the consequences of the computation.

This continues a discussion started in #2085, and extends the concept of overflow checking proposed for integers in #855.

• Detect the five flags raised by floating-point exceptions
  • Invalid
  • Division by zero
  • Overflow
  • Underflow
  • Inexact
• Allow the floating-point rounding mode to be set:
  • round to nearest, ties round to the nearest even digit in the required position
  • round to nearest, ties round away from zero
  • round up toward Inf
  • round down toward -Inf
  • round toward 0
• [ ] Honor the difference between quiet and signaling NaNs
• Expose similar flag-handling behavior from MPFR

cc: @andrioni @JeffBezanson

[andrioni]

I'd really like the flags to be extendable, if possible, as MPFR also uses a range one (for impossible conversions, i.e. a NaN to int), and flags seem to be a good alternative to return the rounding of the last operation.

I'm not sure though what's the best way to implement them, my first idea for MPFR was using a ENV-like dict and/or constants, as the precision is currently stored.

[andrioni]

Also, I may be wrong (and I do hope so), but I think LLVM just ignores the floating point flags, so we would have to detect and trap them manually in intrinsics.cpp.

[bkalpert]

This capability would seem to go well with the capability to set the floating-point rounding mode (to nearest, upward, downward, toward zero), which is very helpful for checking the stability of a numerical code (and is a key component of the IEEE 754 standard). A bonus is that it would distinguish Julia, for it is unavailable in most other high-level environments.

[jiahao]

@bkalpert yeah, that would be nice. I've added that as a todo item

[andrioni]

Some[1] [2] references on changing the rounding mode on LLVM.

[StefanKarpinski]

We will definitely do this – it's absolutely necessary for getting the Kahan stamp of approval (or even getting close).

[ViralBShah]

For setting the floating point environment, how feasible is it to ccall the various fenv functions? eg. fegetround, fesetround, etc.?

[andrioni]

I think they wouldn't work on Windows and/or Visual C++, as fenv.h is POSIX/C99.

[andrioni]

Also,

julia> ccall(:fegetround, Cint, ())
0

julia> ccall(:fesetround, Cint, (Cint, ), 1)
1

julia> ccall(:fegetround, Cint, ())
0

[andrioni]

Ah, binary enum:

julia> ccall((:fesetround, :libm), Cint, (Cint,), 1024)
0

julia> ccall((:fegetround, :libm), Cint, ())
1024

Seems good!

[bkalpert]

Looks like excellent progress!

[quinnj]

Bump. @jiahao, is the TODO list at the top still up to date? Anyone feel like tackling this?

[andrioni]

It is nearly finished in #6170, IIRC, just needs some final touches and a merge.