Comparing modulo arithmetic across languages

main.dart

// https://en.wikipedia.org/wiki/Modular_arithmetic#Examples
// https://dartpad.dev/?id=33cecccc7a5d998ac6c21a22838fc8fb

void main() {
  congruence(38, 14, mod: 12);
  congruence(2, -3, mod: 5);
  congruence(-8, 7, mod: 5);
  congruence(-3, -8, mod: 5);
}

void congruence(int x, y, {required int mod}) {
  String sym = (x % mod) == (y % mod) ? "≡" : "≢";
  print("$x $sym $y (euclidean mod $mod)");
}

/* Output:
38 ≡ 14 (euclidean mod 12)
2 ≡ -3 (euclidean mod 5)
-8 ≡ 7 (euclidean mod 5)
-3 ≡ -8 (euclidean mod 5)
*/

Main.elm

-- https://en.wikipedia.org/wiki/Modular_arithmetic#Examples
-- https://ellie-app.com/hd32NnLQSFqa1
-- Output:
-- 38 ≡ 14 (flooring mod 12)
-- 2 ≢ -3 (flooring mod 5)
-- -8 ≢ 7 (flooring mod 5)
-- -3 ≢ -8 (flooring mod 5)
--
-- 38 ≡ 14 (truncating mod 12)
-- 2 ≢ -3 (truncating mod 5)
-- -8 ≡ 7 (truncating mod 5)
-- -3 ≢ -8 (truncating mod 5)


module Main exposing (main)

import Html exposing (Html, pre, text)
import List
import String


equivalences =
    [ { x = 38, y = 14, mod = 12 }
    , { x = 2, y = -3, mod = 5 }
    , { x = -8, y = 7, mod = 5 }
    , { x = -3, y = -8, mod = 5 }
    ]


type alias Expr =
    { x : Int
    , y : Int
    , mod : Int
    }


main =
    view equivalences


view : List Expr -> Html msg
view exprs =
    let
        modCongruence =
            congruence modBy "flooring mod"

        remCongruence =
            congruence remainderBy "truncating mod"
    in
    pre [] <|
        List.map modCongruence exprs
            ++ [ text "\n" ]
            ++ List.map remCongruence exprs


congruence : (Int -> Int -> Int) -> String -> Expr -> Html msg
congruence fun label expr =
    let
        { x, y, mod } =
            expr

        sym =
            if fun x mod == fun y mod then
                "≡"

            else
                "≢"
    in
    text <| format label sym expr


format : String -> String -> Expr -> String
format label sym { x, y, mod } =
    let
        xStr =
            String.fromInt x

        yStr =
            String.fromInt y

        modStr =
            String.fromInt mod
    in
    xStr
        ++ " "
        ++ sym
        ++ " "
        ++ yStr
        ++ " ("
        ++ label
        ++ " "
        ++ modStr
        ++ ")\n"

main.go

// https://en.wikipedia.org/wiki/Modular_arithmetic#Examples
// https://go.dev/play/p/kPja5gaImqW

package main

import "fmt"

func main() {
	congruence(expr{38, 14, 12})
	congruence(expr{2, -3, 5})
	congruence(expr{-8, 7, 5})
	congruence(expr{-3, -8, 5})
}

type expr struct{ x, y, mod int }

func congruence(e expr) {
	sym := '≢'
	if e.x%e.mod == e.y%e.mod {
		sym = '≡'
	}

	fmt.Printf("%d %c %d (truncating mod %d)\n", e.x, sym, e.y, e.mod)
}

/* Output:
38 ≡ 14 (truncating mod 12)
2 ≢ -3 (truncating mod 5)
-8 ≢ 7 (truncating mod 5)
-3 ≡ -8 (truncating mod 5)
*/