From 39a3a1a6f8c0a5bd387dcddf07ea686a3f2e493d Mon Sep 17 00:00:00 2001
From: Benedikt Peetz <benedikt.peetz@b-peetz.de>
Date: Mon, 2 Nov 2026 15:19:44 +0100
Subject: treewide: Add new math and options subcategories and restructure

---
 math.nix | 95 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 95 insertions(+)
 create mode 100644 math.nix

(limited to 'math.nix')

diff --git a/math.nix b/math.nix
new file mode 100644
index 0000000..9860449
--- /dev/null
+++ b/math.nix
@@ -0,0 +1,95 @@
+{lib}: rec {
+  /*
+  source: https://github.com/NixOS/nix/issues/10387#issuecomment-2494597690
+
+  Raises the `base` to the power of `power`.
+
+  Considering the small input size and the lack of a built-in power function [2],
+  this naive power implementation should satisfy reasonable performance
+  requirements.
+
+  Due to the lack of a modulo and bitwise AND operator, it is questionable whether
+  the recursive exponentiation by squaring [1] implementation would even be
+  faster.
+
+  [1]: https://en.wikipedia.org/wiki/Exponentiation_by_squaring
+  [2]: https://github.com/NixOS/nix/issues/10387
+
+  # Type
+
+  pow :: Number -> Number -> Number
+
+  # Arguments
+
+  base
+  : The base number to be raised.
+
+  power
+  : The exponent to raise `base` to.
+
+  # Examples
+
+  pow 2 5
+  => 32
+  */
+  pow = base: power:
+    if power == 0
+    then 1
+    else if power > 0
+    then (base * (pow base (power - 1)))
+    else builtins.throw "Negative powers are not supported";
+
+  /*
+  Converts `number` from a binary number to a decimal one.
+
+  The input is indented to be a number composed only of `1`s and `0` (e.g., 10010.)
+
+  # Type
+
+  binaryToDecimal :: Int -> Int
+
+  # Arguments
+
+  number
+  : The sequence of `1`s and `0`s defining a binary number, in little endian.
+
+  # Examples
+
+  binaryToDecimal 1001
+  => 9
+  */
+  binaryToDecimal = number: let
+    binaryList =
+      builtins.map lib.strings.toInt (lib.lists.reverseList (lib.strings.stringToCharacters (builtins.toString number)));
+  in
+    builtins.foldl' (acc: num: acc + num) 0
+    (lib.lists.imap0 (index: elem: elem * (pow 2 index)) binaryList);
+
+  /*
+  Converts `string` to a (probably) unique numerical id.
+
+  This is achieved by hashing the string and returning the first six hex-digits
+  converted to a base 10 number.
+
+  # Type
+
+  idFromString :: String -> Int
+
+  # Arguments
+
+  string
+  : The string to use as seed for the id generation.
+
+  # Examples
+
+  idFromString "3d-printer"
+  => 10365713
+  */
+  idFromString = string: let
+    inputSeed =
+      builtins.concatStringsSep ""
+      (lib.lists.take 6
+        (lib.strings.stringToCharacters (builtins.hashString "sha256" string)));
+  in
+    lib.trivial.fromHexString inputSeed;
+}
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