cabal-version:      3.0

name:               RoundingFiasco

version:            0.1.0.0
x-revision: 1

synopsis:
    rounding variants floor, ceil and truncate for floating point operations +-*/√…

description:
    There is an exact definition for `+-*/√` over the real numbers in mathematics.
    However for performant, flexible and ergonomic numerical computations one ought
    to restrict oneself only having a finite subset of rational numbers. The most
    common data type for such use cases is the single and double floating point
    format.

    Combining two real floating point numbers by an operator yield a mathematical
    and exactly defined result. This exact result might not be representable as a
    floating point number. One has to round. The most common way of rounding is
    rounding to the nearest representable float. This rounding variant helps to
    minimize the accumulation of rounding errors over several floating point
    operations.

    Other rounding variants floor, ceil and truncate are useful for computing
    error bounds of chained floating point instructions. floor chooses the lesser
    neighbor of the representable results. ceil chooses the greater float. truncate
    chooses the float that is closest to zero.

    This library implements the floating point instructions in pure hasekell. They
    do not use `c++` with `fegetround` for example. That way they can be used in
    the WebAssembly backend of ghc since WebAssembly does neither support rounding
    variants nor `fegetround`.

    This module is supposed to expose the fastest possible clean interface of
    rounding variants. Should there ever be some compiler intrinsics for rounding
    variants then these shall be used in a future version.

    Internally the module heavily utilizes the `Rational` data type. First the
    operations result is calculated twice. One time exact with the help of
    `Rational`. Then there is also a round-to-nearest-even-on-tie result
    calculated. After that both numbers are compared to investigate if the
    round-to-nearest-even-on-tie result was rounded in the correct direction by
    chance. Should that not be the case the other neighbor is determined and
    returned.

    Every combination of number type (`Float`, `Double`) and operator
    (`+`,`-`,`*`,`/`,`√`,`id`) is exported separately. The exported functions are
    supposed to be useful for interval arithmetic.

homepage:
    https://gitlab.com/pauldennis/rounding-fiasco-hackage-package/-/tree/master/rounding-fiasco-hackage-package/processing/RoundingFiasco

license:            MIT

license-file:       LICENSE

author:             Paul Dennis

maintainer:         paul.dennis2@gmx.de

category:           Numerical,Rounding,Interval,Mathematics
build-type:         Simple

extra-doc-files:    CHANGELOG.md

common warnings
    ghc-options: -Wall

library
    import:           warnings

    exposed-modules:  Rounding

    build-depends:    base ^>=4.19.0.0 || ^>=4.20.0.0

    hs-source-dirs:   source

    default-language: GHC2021

test-suite RoundingFiasco-test
    import:           warnings

    default-language: GHC2021

    type:             exitcode-stdio-1.0

    hs-source-dirs:   test

    main-is:          Main.hs

    build-depends:
        base ^>=4.19.0.0 || ^>=4.20.0.0,
        RoundingFiasco