# [−][src]Crate nikisas

An implementation of common mathematical functions with focus on speed and
simplicity of implementation at the cost of precision, with support for
`no_std`

environments.

The implementations contain explanations of the algorithms and
Sollya programs for finding the
coefficients of polynomials reside in `sollya`

directory.

If you want a reasonable implementation of mathematical functions with small memory footprint and performance cost, you should use micromath crate.

# Usage

use nikisas::{ln, consts::E}; assert_eq!(ln(E), 1.0);

# What's included

Not much. This is (at least for now) for educational purposes. Here is the list:

- exponentiation -
`exp(x)`

,`pow(x, p)`

,`pow2(p)`

,`pow10(p)`

- logarithms -
`ln(x)`

,`log2(x)`

,`log10(x)`

- trigonometric functions -
`sin(x)`

,`cos(x)`

,`tan(x)`

,`cot(x)`

Note that implementation of trigonometric functions give poor results for some inputs (and therefore they fail our current tests).

# Errors

The implementations are thoroughly tested and the error is bound to be 0.1%
*or* 4 decimal places. The testing involves random sampling from valid
interval. The ground truth for error computation are the implementations of
the corresponding functions in the Rust's standard library.

The table of real errors is here:

function | maximum relative | root mean square (overall quality) |
---|---|---|

cos | N/A | N/A |

cot | N/A | N/A |

exp | 4.15e-6 | 1.39e-6 |

ln | 9.60e-8 | 4.05e-8 |

log2 | 1.29e-7 | 4.08e-8 |

log10 | 2.02e-7 | 6.24e-8 |

pow2 | 1.19e-7 | 3.53e-8 |

pow10 | 4.47e-6 | 1.49e-6 |

sin | N/A | N/A |

tan | N/A | N/A |

# Name

So this is the story. If we read "libm" (widely-used abbreviation for
mathematical library) as "lib em" and do not make the pause in the middle,
we get the word "libem". While employing little imagination, we could hear
"líbem" /'liːbɛm/, a colloquial form of czech word
"líbáme" /'liːbaːmɛ/, meaning
"we kiss". Now *wekiss* is not that cool name for a library, so it needs to
go through english-esperanto
translation
first and here we are: *nikisas*. Naming is hard, but at least you can
experience love while using this small piece of software.

# License

nikisas is licensed under MIT. Feel free to use it, contribute or spread the word.

## Modules

consts | A collection of mathematical constants. |

## Functions

cos | Computes the cosine of a number in radians. |

cot | Computes the cotangent of a number in radians. |

exp | Computes exponentiation function of a number. |

ln | Computes natural logarithm of a number. |

log2 | Computes binary logarithm of a number. |

log10 | Computes decimal logarithm of a number. |

pow | Computes a number raised to a power. |

pow2 | Computes 2 raised to a power. |

pow10 | Computes 10 raised to a power. |

sin | Computes the sine of a number in radians. |

tan | Computes tangent of a number. |