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

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.

## Modules

- Rounding

## Downloads

- RoundingFiasco-0.1.0.0.tar.gz [browse] (Cabal source package)
- Package description (revised from the package)

Note: This package has metadata revisions in the cabal description newer than included in the tarball. To unpack the package including the revisions, use 'cabal get'.

#### Maintainer's Corner

For package maintainers and hackage trustees

Candidates

- No Candidates

Versions [RSS] | 0.1.0.0 |
---|---|

Change log | CHANGELOG.md |

Dependencies | base (>=4.19.0.0 && <4.20 || >=4.20.0.0 && <4.21) [details] |

License | MIT |

Author | Paul Dennis |

Maintainer | paul.dennis2@gmx.de |

Revised | Revision 1 made by pauldennis at 2024-05-15T20:08:25Z |

Category | Numerical, Rounding, Interval, Mathematics |

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

Uploaded | by pauldennis at 2024-04-09T20:20:48Z |

Distributions | Stackage:0.1.0.0 |

Downloads | 55 total (3 in the last 30 days) |

Rating | (no votes yet) [estimated by Bayesian average] |

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Status | Docs not available [build log] All reported builds failed as of 2024-05-15 [all 4 reports] |