Add pow10, log10i and digits10 functions

These are used by a couple of solutions now.

lib/aoc.ml

@@ -66,3 +66,18 @@ module Grid = struct
       (String.sub grid.grid (idx + 1) (length grid - idx - 1));
     { grid with grid = Buffer.contents builder }
 end
+
+let log10i i =
+  let rec impl acc = function 0 -> acc | x -> impl (acc + 1) (x / 10) in
+  assert (i > 0);
+  impl ~-1 i
+
+let digits10 = function
+  | 0 -> 1
+  | n when n > 0 -> 1 + log10i n
+  | n (* when n < 0 *) -> 1 + log10i (-n)
+
+let pow10 n =
+  let rec impl acc = function 0 -> acc | x -> impl (acc * 10) (x - 1) in
+  assert (n >= 0);
+  impl 1 n

lib/aoc.mli

@@ -9,6 +9,17 @@ val strings_of_file : string -> string list
 (** [strings_from_file fname] returns a list of strings from the file [fname].
     Each string represents a line from the file. *)
 
+val log10i : int -> int
+(** [log10i n] returns the floor of [(log10 (float_of_int n))]. [n] must be
+    positive. *)
+
+val digits10 : int -> int
+(** [digits10 n] returns the number of base-10 digits in [n]. *)
+
+val pow10 : int -> int
+(** [pow10 n] returns [int_of_float (10. ** float_of_int n)]. [n] must be
+    non-negative. *)
+
 val main : (string -> 'a) -> (('b -> string) * ('a -> 'b)) list -> unit
 (** [main prep parts] executes an advent of code problem. [prep fname] should be
     a function that returns the input from [fname]. Each elemet of [parts] is a