[std-interval] Current draft of the proposal for std::interval

[Guillaume Melquiond]

Dear subscribers,

First, a bit of history. We (Hervé Brönnimann, Guillaume Melquiond, and
Sylvain Pion) have written a C++ library for interval arithmetic that is
part of the Boost project. This work gave us a better understanding on
how to provide interval arithmetic in C++. So we submitted a proposal
for adding this arithmetic to the C++ Standard Library. We had decided
that the template classes would be simple, and in particular that they
would not be policy-based, contrarily to the Boost library.

This proposal was presented during the Fall'05 meeting of the C++
standardization committee. It was rather well received, but developers
of implementations of the STL were concerned whether there was or not a
sufficient user demand for interval arithmetic.

Anyway, we have decided to submit a revised version of the proposal to
the Spring'06 meeting. Since the first release of our proposal, a lot of
comments have been sent to us and we have tried to take them into
account. This is a draft of our revised proposal. Please note that
interval comparisons have been temporarily left aside from this draft
because we have yet to converge on a syntax.

Among these comments, a major concern was the kind of interval
arithmetic. The current proposal implements an arithmetic that is usable
for doing forward evaluation on the set of real numbers. Some would like
the computations to be on the set of extended real numbers: it would for
example allow <0,inf> * <1,inf> = <-inf,inf>. Some would like the
computations to have backward propagation properties: <0,0> / <0,0> =
<-inf,inf>. Some would like both forward and backward semantics in order
to do global optimization. And so on.

As long as intervals have finite bounds and do not contain zero, all
these semantics are equivalent. But in presence of infinities and zeroes
(that is as soon as there is an underflow or an overflow on the
floating-point bounds), these various arithmetics produce incompatible
results. And they all have their own use cases. As a consequence, this
is the main point left unsolved.

We are interested in your comments on this draft.

Best regards,

Hervé, Guillaume, and Sylvain

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