# Nat16

Provides utility functions on 16-bit unsigned integers.

Note that most operations are available as built-in operators (e.g. `1 + 1`).

Import from the base library to use this module.

``import Nat16 "mo:base/Nat16";``

## Type `Nat16`​

``type Nat16 = Prim.Types.Nat16``

16-bit natural numbers.

## Value `maximumValue`​

``let maximumValue : Nat16``

Maximum 16-bit natural number. `2 ** 16 - 1`.

Example:

``Nat16.maximumValue; // => 65536 : Nat16``

## Value `toNat`​

``let toNat : Nat16 -> Nat``

Converts a 16-bit unsigned integer to an unsigned integer with infinite precision.

Example:

``Nat16.toNat(123); // => 123 : Nat``

## Value `fromNat`​

``let fromNat : Nat -> Nat16``

Converts an unsigned integer with infinite precision to a 16-bit unsigned integer.

Traps on overflow.

Example:

``Nat16.fromNat(123); // => 123 : Nat16``

## Function `fromNat8`​

``func fromNat8(x : Nat8) : Nat16``

Converts an 8-bit unsigned integer to a 16-bit unsigned integer.

Example:

``Nat16.fromNat8(123); // => 123 : Nat16``

## Function `toNat8`​

``func toNat8(x : Nat16) : Nat8``

Converts a 16-bit unsigned integer to an 8-bit unsigned integer.

Traps on overflow.

Example:

``Nat16.toNat8(123); // => 123 : Nat8``

## Function `fromNat32`​

``func fromNat32(x : Nat32) : Nat16``

Converts a 32-bit unsigned integer to a 16-bit unsigned integer.

Traps on overflow.

Example:

``Nat16.fromNat32(123); // => 123 : Nat16``

## Function `toNat32`​

``func toNat32(x : Nat16) : Nat32``

Converts a 16-bit unsigned integer to a 32-bit unsigned integer.

Example:

``Nat16.toNat32(123); // => 123 : Nat32``

## Value `fromIntWrap`​

``let fromIntWrap : Int -> Nat16``

Converts a signed integer with infinite precision to a 16-bit unsigned integer.

Wraps on overflow/underflow.

Example:

``Nat16.fromIntWrap(123 : Int); // => 123 : Nat16``

## Function `toText`​

``func toText(x : Nat16) : Text``

Converts `x` to its textual representation. Textual representation do not contain underscores to represent commas.

Example:

``Nat16.toText(1234); // => "1234" : Text``

## Function `min`​

``func min(x : Nat16, y : Nat16) : Nat16``

Returns the minimum of `x` and `y`.

Example:

``Nat16.min(123, 200); // => 123 : Nat16``

## Function `max`​

``func max(x : Nat16, y : Nat16) : Nat16``

Returns the maximum of `x` and `y`.

Example:

``Nat16.max(123, 200); // => 200 : Nat16``

## Function `equal`​

``func equal(x : Nat16, y : Nat16) : Bool``

Equality function for Nat16 types. This is equivalent to `x == y`.

Example:

``ignore Nat16.equal(1, 1); // => true(1 : Nat16) == (1 : Nat16) // => true``

Note: The reason why this function is defined in this library (in addition to the existing `==` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `==` as a function value at the moment.

Example:

``import Buffer "mo:base/Buffer";let buffer1 = Buffer.Buffer<Nat16>(3);let buffer2 = Buffer.Buffer<Nat16>(3);Buffer.equal(buffer1, buffer2, Nat16.equal) // => true``

## Function `notEqual`​

``func notEqual(x : Nat16, y : Nat16) : Bool``

Inequality function for Nat16 types. This is equivalent to `x != y`.

Example:

``ignore Nat16.notEqual(1, 2); // => true(1 : Nat16) != (2 : Nat16) // => true``

Note: The reason why this function is defined in this library (in addition to the existing `!=` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `!=` as a function value at the moment.

## Function `less`​

``func less(x : Nat16, y : Nat16) : Bool``

"Less than" function for Nat16 types. This is equivalent to `x < y`.

Example:

``ignore Nat16.less(1, 2); // => true(1 : Nat16) < (2 : Nat16) // => true``

Note: The reason why this function is defined in this library (in addition to the existing `<` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<` as a function value at the moment.

## Function `lessOrEqual`​

``func lessOrEqual(x : Nat16, y : Nat16) : Bool``

"Less than or equal" function for Nat16 types. This is equivalent to `x <= y`.

Example:

``ignore Nat16.lessOrEqual(1, 2); // => true(1 : Nat16) <= (2 : Nat16) // => true``

Note: The reason why this function is defined in this library (in addition to the existing `<=` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<=` as a function value at the moment.

## Function `greater`​

``func greater(x : Nat16, y : Nat16) : Bool``

"Greater than" function for Nat16 types. This is equivalent to `x > y`.

Example:

``ignore Nat16.greater(2, 1); // => true(2 : Nat16) > (1 : Nat16) // => true``

Note: The reason why this function is defined in this library (in addition to the existing `>` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `>` as a function value at the moment.

## Function `greaterOrEqual`​

``func greaterOrEqual(x : Nat16, y : Nat16) : Bool``

"Greater than or equal" function for Nat16 types. This is equivalent to `x >= y`.

Example:

``ignore Nat16.greaterOrEqual(2, 1); // => true(2 : Nat16) >= (1 : Nat16) // => true``

Note: The reason why this function is defined in this library (in addition to the existing `>=` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `>=` as a function value at the moment.

## Function `compare`​

``func compare(x : Nat16, y : Nat16) : {#less; #equal; #greater}``

General purpose comparison function for `Nat16`. Returns the `Order` ( either `#less`, `#equal`, or `#greater`) of comparing `x` with `y`.

Example:

``Nat16.compare(2, 3) // => #less``

This function can be used as value for a high order function, such as a sort function.

Example:

``import Array "mo:base/Array";Array.sort([2, 3, 1] : [Nat16], Nat16.compare) // => [1, 2, 3]``

## Function `add`​

``func add(x : Nat16, y : Nat16) : Nat16``

Returns the sum of `x` and `y`, `x + y`. Traps on overflow.

Example:

``ignore Nat16.add(1, 2); // => 3(1 : Nat16) + (2 : Nat16) // => 3``

Note: The reason why this function is defined in this library (in addition to the existing `+` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `+` as a function value at the moment.

Example:

``import Array "mo:base/Array";Array.foldLeft<Nat16, Nat16>([2, 3, 1], 0, Nat16.add) // => 6``

## Function `sub`​

``func sub(x : Nat16, y : Nat16) : Nat16``

Returns the difference of `x` and `y`, `x - y`. Traps on underflow.

Example:

``ignore Nat16.sub(2, 1); // => 1(2 : Nat16) - (1 : Nat16) // => 1``

Note: The reason why this function is defined in this library (in addition to the existing `-` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `-` as a function value at the moment.

Example:

``import Array "mo:base/Array";Array.foldLeft<Nat16, Nat16>([2, 3, 1], 20, Nat16.sub) // => 14``

## Function `mul`​

``func mul(x : Nat16, y : Nat16) : Nat16``

Returns the product of `x` and `y`, `x * y`. Traps on overflow.

Example:

``ignore Nat16.mul(2, 3); // => 6(2 : Nat16) * (3 : Nat16) // => 6``

Note: The reason why this function is defined in this library (in addition to the existing `*` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `*` as a function value at the moment.

Example:

``import Array "mo:base/Array";Array.foldLeft<Nat16, Nat16>([2, 3, 1], 1, Nat16.mul) // => 6``

## Function `div`​

``func div(x : Nat16, y : Nat16) : Nat16``

Returns the quotient of `x` divided by `y`, `x / y`. Traps when `y` is zero.

Example:

``ignore Nat16.div(6, 2); // => 3(6 : Nat16) / (2 : Nat16) // => 3``

Note: The reason why this function is defined in this library (in addition to the existing `/` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `/` as a function value at the moment.

## Function `rem`​

``func rem(x : Nat16, y : Nat16) : Nat16``

Returns the remainder of `x` divided by `y`, `x % y`. Traps when `y` is zero.

Example:

``ignore Nat16.rem(6, 4); // => 2(6 : Nat16) % (4 : Nat16) // => 2``

Note: The reason why this function is defined in this library (in addition to the existing `%` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `%` as a function value at the moment.

## Function `pow`​

``func pow(x : Nat16, y : Nat16) : Nat16``

Returns the power of `x` to `y`, `x ** y`. Traps on overflow.

Example:

``ignore Nat16.pow(2, 3); // => 8(2 : Nat16) ** (3 : Nat16) // => 8``

Note: The reason why this function is defined in this library (in addition to the existing `**` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `**` as a function value at the moment.

## Function `bitnot`​

``func bitnot(x : Nat16) : Nat16``

Returns the bitwise negation of `x`, `^x`.

Example:

``ignore Nat16.bitnot(0); // => 65535^(0 : Nat16) // => 65535``

Note: The reason why this function is defined in this library (in addition to the existing `^` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `^` as a function value at the moment.

## Function `bitand`​

``func bitand(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise and of `x` and `y`, `x & y`.

Example:

``ignore Nat16.bitand(0, 1); // => 0(0 : Nat16) & (1 : Nat16) // => 0``

Note: The reason why this function is defined in this library (in addition to the existing `&` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `&` as a function value at the moment.

## Function `bitor`​

``func bitor(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise or of `x` and `y`, `x | y`.

Example:

``ignore Nat16.bitor(0, 1); // => 1(0 : Nat16) | (1 : Nat16) // => 1``

## Function `bitxor`​

``func bitxor(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise exclusive or of `x` and `y`, `x ^ y`.

Example:

``ignore Nat16.bitxor(0, 1); // => 1(0 : Nat16) ^ (1 : Nat16) // => 1``

## Function `bitshiftLeft`​

``func bitshiftLeft(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise shift left of `x` by `y`, `x << y`.

Example:

``ignore Nat16.bitshiftLeft(1, 3); // => 8(1 : Nat16) << (3 : Nat16) // => 8``

Note: The reason why this function is defined in this library (in addition to the existing `<<` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<<` as a function value at the moment.

## Function `bitshiftRight`​

``func bitshiftRight(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise shift right of `x` by `y`, `x >> y`.

Example:

``ignore Nat16.bitshiftRight(8, 3); // => 1(8 : Nat16) >> (3 : Nat16) // => 1``

Note: The reason why this function is defined in this library (in addition to the existing `>>` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `>>` as a function value at the moment.

## Function `bitrotLeft`​

``func bitrotLeft(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise rotate left of `x` by `y`, `x <<> y`.

Example:

``ignore Nat16.bitrotLeft(2, 1); // => 4(2 : Nat16) <<> (1 : Nat16) // => 4``

Note: The reason why this function is defined in this library (in addition to the existing `<<>` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<<>` as a function value at the moment.

## Function `bitrotRight`​

``func bitrotRight(x : Nat16, y : Nat16) : Nat16``

Returns the bitwise rotate right of `x` by `y`, `x <>> y`.

Example:

``ignore Nat16.bitrotRight(1, 1); // => 32768(1 : Nat16) <>> (1 : Nat16) // => 32768``

Note: The reason why this function is defined in this library (in addition to the existing `<>>` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `<>>` as a function value at the moment.

## Function `bittest`​

``func bittest(x : Nat16, p : Nat) : Bool``

Returns the value of bit `p mod 16` in `x`, `(x & 2^(p mod 16)) == 2^(p mod 16)`. This is equivalent to checking if the `p`-th bit is set in `x`, using 0 indexing.

Example:

``Nat16.bittest(5, 2); // => true``

## Function `bitset`​

``func bitset(x : Nat16, p : Nat) : Nat16``

Returns the value of setting bit `p mod 16` in `x` to `1`.

Example:

``Nat16.bitset(0, 2); // => 4``

## Function `bitclear`​

``func bitclear(x : Nat16, p : Nat) : Nat16``

Returns the value of clearing bit `p mod 16` in `x` to `0`.

Example:

``Nat16.bitclear(5, 2); // => 1``

## Function `bitflip`​

``func bitflip(x : Nat16, p : Nat) : Nat16``

Returns the value of flipping bit `p mod 16` in `x`.

Example:

``Nat16.bitflip(5, 2); // => 1``

## Value `bitcountNonZero`​

``let bitcountNonZero : (x : Nat16) -> Nat16``

Returns the count of non-zero bits in `x`.

Example:

``Nat16.bitcountNonZero(5); // => 2``

## Value `bitcountLeadingZero`​

``let bitcountLeadingZero : (x : Nat16) -> Nat16``

Returns the count of leading zero bits in `x`.

Example:

``Nat16.bitcountLeadingZero(5); // => 13``

## Value `bitcountTrailingZero`​

``let bitcountTrailingZero : (x : Nat16) -> Nat16``

Returns the count of trailing zero bits in `x`.

Example:

``Nat16.bitcountTrailingZero(5); // => 0``

## Function `addWrap`​

``func addWrap(x : Nat16, y : Nat16) : Nat16``

Returns the sum of `x` and `y`, `x +% y`. Wraps on overflow.

Example:

``ignore Nat16.addWrap(65532, 5); // => 1(65532 : Nat16) +% (5 : Nat16) // => 1``

Note: The reason why this function is defined in this library (in addition to the existing `+%` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `+%` as a function value at the moment.

## Function `subWrap`​

``func subWrap(x : Nat16, y : Nat16) : Nat16``

Returns the difference of `x` and `y`, `x -% y`. Wraps on underflow.

Example:

``ignore Nat16.subWrap(1, 2); // => 65535(1 : Nat16) -% (2 : Nat16) // => 65535``

Note: The reason why this function is defined in this library (in addition to the existing `-%` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `-%` as a function value at the moment.

## Function `mulWrap`​

``func mulWrap(x : Nat16, y : Nat16) : Nat16``

Returns the product of `x` and `y`, `x *% y`. Wraps on overflow.

Example:

``ignore Nat16.mulWrap(655, 101); // => 619(655 : Nat16) *% (101 : Nat16) // => 619``

Note: The reason why this function is defined in this library (in addition to the existing `*%` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `*%` as a function value at the moment.

## Function `powWrap`​

``func powWrap(x : Nat16, y : Nat16) : Nat16``

Returns `x` to the power of `y`, `x **% y`. Wraps on overflow.

Example:

``ignore Nat16.powWrap(2, 16); // => 0(2 : Nat16) **% (16 : Nat16) // => 0``

Note: The reason why this function is defined in this library (in addition to the existing `**%` operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use `**%` as a function value at the moment.