Forcing divisions to be a machine-precision floating point divisions instead of multiplication by inverse

Question

I want to imitate machine-precision, de facto IEEE division on Mathematica. On my quick trials I find this surprisingly hard to accomplish, since Mma rewrites a / b as a (b^-1) and these are not identical on finite-precision math.

For an explicit example, consider the following:

49. / 49. // FullForm

0.9999999999999999`

EDIT: As @J.M. points out, this works:

Divide[49., 49.] // FullForm

1.`

... but if I do the following, for instance, the finite-precision multiplication by inverse is seen again:

Divide[x, 49.] // FullForm

Times[0.02040816326530612`, x]

... which is bad.

How would I implement a "use native (IEEE) division semantics on machine-precision arguments of this division, even later down the evaluation chain" operation instead of Mma being too clever for its' own sake?

EDIT: In this specific case I'm not interested in other IEEE semantics, for instance strict order of operations (a + b + c is not the same as c + b + a!). I just want divisions to stay as divisions, which may be a bit of a half-way goal, but sounds more feasible to implement that the whole shebang.

Answer 1

You can define your own divide function:

divide[a_Real, b_Real] := Divide[a, b]
MakeBoxes[divide[a_, b_], StandardForm] := MakeBoxes[Divide[a, b], StandardForm]

Then:

divide[49., 49.]

1.

And:

r = divide[x, 49.]
r /. x->49.

x/49.

1.

Some more work is needed to define how divide works with other arithmetical operations.