[Octave-bug-tracker] [bug #45587] rem(-0, 1) returns 0 instead of -0

[Charles Karney]

Follow-up Comment #9, bug #45587 (project octave):

A key point about the C/C++ function fmod (and the related remainder
function) is that it is exact (even with floating-point numbers).  In
lots of applications this is important.

It is unfortunate the Octave (and MATLAB) resort to cosmetic "fixes" to
ensure that

  rem(0.94, 0.01)

returns 0.

Let's see how to do the rem operation exactly

  a=0.94;
  b=0.01;

a and b are now the closest floating point numbers to 0.94 and 0.01.
Now compute

  ((((a-64*b)-16*b)-8*b)-4*b)-b

Each of the multiplication and subtraction operations here is exact and
this yields

  0.00999999999999993

and this is less that b

  ans < b  -> 1


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