Interval

This is an interval arithmetic library for OCaml. Here is a small example in the REPL:

# #require "interval_intel";;
~/.opam/4.06.1/lib/interval_base: added to search path
~/.opam/4.06.1/lib/interval_base/interval.cma: loaded
~/.opam/4.06.1/lib/interval_intel: added to search path
~/.opam/4.06.1/lib/interval_intel/interval_intel.cma: loaded
# open Interval_intel;;
# let v = I.v 1. 1.;;
val v : Interval.t = {Interval.low = 1.; high = 1.}
# I.sin v;;
- : Interval_intel.t =
{low = 0.841470984807896505; high = 0.841470984807896616}

Several OPAM packages are provided by this repository:

• interval_base: basic interval library that defines the datatype Interval.t and uses Intel assembly if possible or C99 instructions to perform arithmetic operations.
• interval_crlibm: relies on crlibm to implement the interval operations. CRlibm provides proved correctly-rounded operations, so this is the library of choice for computer assisted proofs.

• interval_intel: use Intel FPU instructions with directed rounding to implement interval operations. However, the Intel FPU operations may not always be correctly rounded for, say, trigonometric functions.

  interval_intel uses assembly code to compute all operations with proper rounding, and currently ONLY works on Intel processors. The package has been developed for Linux systems but works on MacOSX and Windows when compiled with GCC.

• interval is a meta-package installing all the packages above.

Note that ocamlopt does float constant propagation in round to the nearest mode which may invalidate interval computations. Use the compiler flag -no-float-const-prop to deactivate it.

Happy interval programming...