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Elm 0.19 renamed these two functions, so here they are with their new names.

modBy : Int -> Int -> Int

Perform modular arithmetic. A common trick is to use (n mod 2) to detect even and odd numbers:

```
modBy 2 0 --> 0
modBy 2 1 --> 1
modBy 2 2 --> 0
modBy 2 3 --> 1
```

Our `modBy`

function works in the typical mathematical way when you run into
negative numbers:

```
List.map (modBy 4)
[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ]
--> [ 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1 ]
```

Use `remainderBy`

for a different treatment of negative numbers,
or read Daan Leijen’s Division and Modulus for Computer Scientists for more
information.

remainderBy : Int -> Int -> Int

Get the remainder after division. Here are bunch of examples of dividing by four:

```
List.map (remainderBy 4)
[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ]
--> [ -1, 0, -3, -2, -1, 0, 1, 2, 3, 0, 1 ]
```

Use `modBy`

for a different treatment of negative numbers,
or read Daan Leijen’s Division and Modulus for Computer Scientists for more
information.

```
module Basics019 exposing (modBy, remainderBy)
{-| Elm 0.19 renamed these two functions, so here they are with their
new names.
@docs modBy, remainderBy
-}
{-| Perform [modular arithmetic](https://en.wikipedia.org/wiki/Modular_arithmetic).
A common trick is to use (n mod 2) to detect even and odd numbers:
modBy 2 0 --> 0
modBy 2 1 --> 1
modBy 2 2 --> 0
modBy 2 3 --> 1
Our `modBy` function works in the typical mathematical way when you run into
negative numbers:
List.map (modBy 4)
[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ]
--> [ 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1 ]
Use [`remainderBy`](#remainderBy) for a different treatment of negative numbers,
or read Daan Leijen’s [Division and Modulus for Computer Scientists][dm] for more
information.
[dm]: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
-}
modBy : Int -> Int -> Int
modBy =
flip (%)
{-| Get the remainder after division. Here are bunch of examples of dividing by four:
List.map (remainderBy 4)
[ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ]
--> [ -1, 0, -3, -2, -1, 0, 1, 2, 3, 0, 1 ]
Use [`modBy`](#modBy) for a different treatment of negative numbers,
or read Daan Leijen’s [Division and Modulus for Computer Scientists][dm] for more
information.
[dm]: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
-}
remainderBy : Int -> Int -> Int
remainderBy =
flip rem
```