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