Interval Arithmetic for Real Computation

Rival is a library for evaluating real expressions to high precision. Rival supports Racket 8.0+ and depends only on the standard math library, including math/bigfloat.

Using Rival

Rival is easiest to use from its REPL:

$ racket -l rival
> (eval (sin 1e100))
-0.3723761236612767
> (set precision 1000)
> (eval (sin 1e100))
-0.3723761236612766882620866955531642957...
> (set precision 100)
> (define (f x) (- (sin x) (- x (/ (pow x 3) 6))))
> (eval f 1e-100)
8.3333333333333333333333333333237e-503

The full documentation describes the Racket API and the underlying interval library.

Features

Rival provides a number of advanced features, which we believe makes Rival the state of the art real evaluation library:

• Support for all math.h functions, including arithmetic, trigonometric, power, remainder, rounding, and even gamma functions.
• Support for comparisons, conditionals, and boolean operations through boolean intervals
• Sound handling of domain errors through error intervals
• Fast and accurate mixed-precision assignments for evaluation
• Correct rounding
• Early exit using movability flags
• Well-tested soundness and robustness

Contributing

Please file issues and submit patches on Github. All code should be formatted using raco fmt; you can set this up to happen on commit with:

make hook

Additionally, all code must pass the automated tests, which you can run with:

raco test test.rkt

They also run in CI before merging. Finally, performance is a key metric for Rival; you can run the automated performance tests with:

racket -y time.rkt