lib: add the toHex and toBase utility functions

`toHex` converts the given positive integer to a string of the hexadecimal
representation of that integer. For example:

```
toHex 0 => "0"

toHex 16 => "10"

toHex 250 => "FA"
```

`toBase base i` converts the positive integer `i` to a list of it
digits in the given `base`. For example:

```
toBase 10 123 => [ 1 2 3 ]

toBase 2 6 => [ 1 1 0 ]

toBase 16 250 => [ 15 10 ]
```

lib/default.nix

@@ -67,7 +67,7 @@ let
     inherit (trivial) id const pipe concat or and bitAnd bitOr bitXor
       bitNot boolToString mergeAttrs flip mapNullable inNixShell min max
       importJSON warn info showWarnings nixpkgsVersion version mod compare
-      splitByAndCompare functionArgs setFunctionArgs isFunction;
+      splitByAndCompare functionArgs setFunctionArgs isFunction toHex toBase;
     inherit (fixedPoints) fix fix' converge extends composeExtensions
       makeExtensible makeExtensibleWithCustomName;
     inherit (attrsets) attrByPath hasAttrByPath setAttrByPath

lib/tests/misc.nix

@@ -102,6 +102,16 @@ runTests {
     expected = 9;
   };
 
+  testToHex = {
+    expr = toHex 250;
+    expected = "FA";
+  };
+
+  testToBase = {
+    expr = toBase 2 6;
+    expected = [ 1 1 0 ];
+  };
+
 # STRINGS
 
   testConcatMapStrings = {

lib/trivial.nix

@@ -332,4 +332,55 @@ rec {
   */
   isFunction = f: builtins.isFunction f ||
     (f ? __functor && isFunction (f.__functor f));
+
+  /* Convert the given positive integer to a string of its hexadecimal
+     representation. For example:
+
+     toHex 0 => "0"
+
+     toHex 16 => "10"
+
+     toHex 250 => "FA"
+  */
+  toHex = i:
+    let
+      toHexDigit = d:
+        if d < 10
+        then toString d
+        else
+          {
+            "10" = "A";
+            "11" = "B";
+            "12" = "C";
+            "13" = "D";
+            "14" = "E";
+            "15" = "F";
+          }.${toString d};
+    in
+      lib.concatMapStrings toHexDigit (toBase 16 i);
+
+  /* `toBase base i` converts the positive integer i to a list of its
+     digits in the given base. For example:
+
+     toBase 10 123 => [ 1 2 3 ]
+
+     toBase 2 6 => [ 1 1 0 ]
+
+     toBase 16 250 => [ 15 10 ]
+  */
+  toBase = base: i:
+    let
+      go = i:
+        if i < base
+        then [i]
+        else
+          let
+            r = i - ((i / base) * base);
+            q = (i - r) / base;
+          in
+            [r] ++ go q;
+    in
+      assert (base >= 2);
+      assert (i >= 0);
+      lib.reverseList (go i);
 }