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https://github.com/xddxdd/nix-math
Experimental mathematical library in pure Nix, using no external library.
https://github.com/xddxdd/nix-math
Last synced: 3 months ago
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Experimental mathematical library in pure Nix, using no external library.
- Host: GitHub
- URL: https://github.com/xddxdd/nix-math
- Owner: xddxdd
- License: mit
- Created: 2023-09-05T04:09:17.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-03-09T05:22:44.000Z (11 months ago)
- Last Synced: 2024-08-03T01:37:45.148Z (6 months ago)
- Language: Nix
- Homepage:
- Size: 28.3 KB
- Stars: 13
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# nix-math
Experimental mathematical library in pure Nix, using no external library.
## Why?
1. Because I can.
2. Because I want to approximate the network latency between my servers using their latitudes/longitudes. No, I don't want to run `traceroute` between my servers every now and then.
## Usage
```nix
{
inputs = {
nix-math.url = "github:xddxdd/nix-math";
};
outputs = inputs: let
math = inputs.nix-math.lib.math;
in{
value = math.sin (math.deg2rad 45);
};
}
```
## Provided functions
- `abs [x]`, `fabs [x]`: Absolute value of `x`
- `arange [min] [max] [step]`: Create a list of numbers from `min` (inclusive) to `max` (exclusive), adding `step` each time.
- `arange2 [min] [max] [step]`: Same as `arange`, but includes `max` as well.
- `div [a] [b]`: Divide `a` by `b` with no remainder.
- `mod [a] [b]`: Modulos of dividing `a` by `b`.
- `pow [a] [b]`: Returns `a` to the power of `b`. **Only supports integer for `b`!**
- `factorial [x]`: Returns factorial of `x`. `x` is an integer, `x >= 0`.
- `sin [x], cos [x], tan [x]`: Trigonometric function. Takes radian as input.
- `atan [x]`: Arctangent function.
- `deg2rad [x]`: Degrees to radian.
- `sqrt [x]`: Square root of `x`. `x >= 0`.
- `haversine [lat1] [lon1] [lat2] [lon2]`: Returns distance of two points on Earth for the given latitude/longitude.
## Implementation Details
- `sin` function is implemented with its Taylor series: for `x >= 0`, `sin(x) = x - x^3/3! + x^5/5!`. Calculation is repeated until the next value in series is less than epsilon (`1e-10`).
- `cos` is `sin (pi/2 - x)`.
- `tan` is `sin x / cos x`.
- For `sin`, `cos` and `tan`, result error is within 0.0001% as checked by unit test.
- `atan` is implemented with this estimation algorithm: . This is faster and more accurate than using `atan`'s Taylor series, because its Taylor series does not converge as fast as `sin`.
- For `atan`, result error is within 0.0001%.
- `sqrt` is implemented with Newtonian method. Calculation is repeated until the next value is less than epsilon (`1e-10`).
- For `sqrt`, result error is within `1e-10`.
- `haversine` is implemented based on .
## Unit test
Unit test is defined in `tests/test.py`. It invokes `tests/test.nix` which tests the mathematical functions with a range of inputs, and compares the output to the same function from Numpy.
To run the unit test:
```bash
nix run .
```
## License
MIT.