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Thu May 30 18:55:25 EDT 2013

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On Thu, 30 May 2013 12:07:40 +0300, Jussi Piitulainen wrote:

> I suppose this depends on the complexity of the process and the amount
> of data that produced the numbers of interest. Many individual
> floating point operations are required to be within an ulp or two of
> the mathematically correct result, I think, and the rounding error
> when parsing a written representation of a number should be similar.

Elementary operations (+, -, *, /, %, sqrt) are supposed to be within
+/- 0.5 ULP (for round-to-nearest), i.e. the actual result should be the
closest representable value to the exact result.

Transcendental functions should ideally be within +/- 1 ULP, i.e. the
actual result should be one of the two closest representable values to the
exact result. Determining the closest value isn't always feasible due to
the "table-maker's dilemma", i.e. the fact that regardless of the number
of digits used for intermediate results, the upper and lower bounds
can remain on opposite sides of the dividing line.

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