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base/Int16

Provides utility functions on 16-bit signed integers.

Most operations are available as built-in operators (e.g. 1 + 1).

Function form for higher-order use

Several arithmetic and comparison functions (e.g. add, sub, bitor, bitand, pow) are defined in this module to enable their use as first-class function values, which is not possible with operators like +, -, ==, etc., in Motoko. This allows you to pass these operations to higher-order functions such as map, foldLeft, or sort.

Import from the base library to use this module.

import Int16 "mo:base/Int16";

Type Int16​

type Int16 = Prim.Types.Int16

16-bit signed integers.

Value minimumValue​

let minimumValue : Int16

Minimum 16-bit integer value, -2 ** 15.

Example:

Int16.minimumValue // => -32_768 : Int16

Value maximumValue​

let maximumValue : Int16

Maximum 16-bit integer value, +2 ** 15 - 1.

Example:

Int16.maximumValue // => +32_767 : Int16

Function toInt​

func toInt(_ : Int16) : Int

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

Example:

Int16.toInt(12_345) // => 12_345 : Int

Function fromInt​

func fromInt(_ : Int) : Int16

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

Traps on overflow/underflow.

Example:

Int16.fromInt(12_345) // => +12_345 : Int16

Function fromIntWrap​

func fromIntWrap(_ : Int) : Int16

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

Wraps on overflow/underflow.

Example:

Int16.fromIntWrap(-12_345) // => -12_345 : Int

Function fromInt8​

func fromInt8(_ : Int8) : Int16

Converts a 8-bit signed integer to a 16-bit signed integer.

Example:

Int16.fromInt8(-123) // => -123 : Int16

Function toInt8​

func toInt8(_ : Int16) : Int8

Converts a 16-bit signed integer to a 8-bit signed integer.

Traps on overflow/underflow.

Example:

Int16.toInt8(-123) // => -123 : Int8

Function fromInt32​

func fromInt32(_ : Int32) : Int16

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

Traps on overflow/underflow.

Example:

Int16.fromInt32(-12_345) // => -12_345 : Int16

Function toInt32​

func toInt32(_ : Int16) : Int32

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

Example:

Int16.toInt32(-12_345) // => -12_345 : Int32

Function fromNat16​

func fromNat16(_ : Nat16) : Int16

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

Wraps on overflow/underflow.

Example:

Int16.fromNat16(12_345) // => +12_345 : Int16

Function toNat16​

func toNat16(_ : Int16) : Nat16

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

Wraps on overflow/underflow.

Example:

Int16.toNat16(-1) // => 65_535 : Nat16 // underflow

Function toText​

func toText(x : Int16) : Text

Returns the Text representation of x. Textual representation do not contain underscores to represent commas.

Example:

Int16.toText(-12345) // => "-12345"

Function abs​

func abs(x : Int16) : Int16

Returns the absolute value of x.

Traps when x == -2 ** 15 (the minimum Int16 value).

Example:

Int16.abs(-12345) // => +12_345

Function min​

func min(x : Int16, y : Int16) : Int16

Returns the minimum of x and y.

Example:

Int16.min(+2, -3) // => -3

Function max​

func max(x : Int16, y : Int16) : Int16

Returns the maximum of x and y.

Example:

Int16.max(+2, -3) // => +2

Function equal​

func equal(x : Int16, y : Int16) : Bool

Equality function for Int16 types. This is equivalent to x == y.

Example:

Int16.equal(-1, -1); // => true

Example:

import Buffer "mo:base/Buffer";

let buffer1 = Buffer.Buffer<Int16>(1);
buffer1.add(-3);
let buffer2 = Buffer.Buffer<Int16>(1);
buffer2.add(-3);
Buffer.equal(buffer1, buffer2, Int16.equal) // => true

Function notEqual​

func notEqual(x : Int16, y : Int16) : Bool

Inequality function for Int16 types. This is equivalent to x != y.

Example:

Int16.notEqual(-1, -2); // => true

Function less​

func less(x : Int16, y : Int16) : Bool

"Less than" function for Int16 types. This is equivalent to x < y.

Example:

Int16.less(-2, 1); // => true

Function lessOrEqual​

func lessOrEqual(x : Int16, y : Int16) : Bool

"Less than or equal" function for Int16 types. This is equivalent to x <= y.

Example:

Int16.lessOrEqual(-2, -2); // => true

Function greater​

func greater(x : Int16, y : Int16) : Bool

"Greater than" function for Int16 types. This is equivalent to x > y.

Example:

Int16.greater(-2, 1); // => false

Function greaterOrEqual​

func greaterOrEqual(x : Int16, y : Int16) : Bool

"Greater than or equal" function for Int16 types. This is equivalent to x >= y.

Example:

Int16.greaterOrEqual(-2, -2); // => true

Function compare​

func compare(x : Int16, y : Int16) : {#less; #equal; #greater}

General-purpose comparison function for Int16. Returns the Order ( either #less, #equal, or #greater) of comparing x with y.

Example:

Int16.compare(-3, 2) // => #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([1, -2, -3] : [Int16], Int16.compare) // => [-3, -2, 1]

Function neg​

func neg(x : Int16) : Int16

Returns the negation of x, -x.

Traps on overflow, i.e. for neg(-2 ** 15).

Example:

Int16.neg(123) // => -123

Function add​

func add(x : Int16, y : Int16) : Int16

Returns the sum of x and y, x + y.

Traps on overflow/underflow.

Example:

Int16.add(100, 23) // => +123

Example:

import Array "mo:base/Array";
Array.foldLeft<Int16, Int16>([1, -2, -3], 0, Int16.add) // => -4

Function sub​

func sub(x : Int16, y : Int16) : Int16

Returns the difference of x and y, x - y.

Traps on overflow/underflow.

Example:

Int16.sub(123, 100) // => +23

Example:

import Array "mo:base/Array";
Array.foldLeft<Int16, Int16>([1, -2, -3], 0, Int16.sub) // => 4

Function mul​

func mul(x : Int16, y : Int16) : Int16

Returns the product of x and y, x * y.

Traps on overflow/underflow.

Example:

Int16.mul(12, 10) // => +120

Example:

import Array "mo:base/Array";
Array.foldLeft<Int16, Int16>([1, -2, -3], 1, Int16.mul) // => 6

Function div​

func div(x : Int16, y : Int16) : Int16

Returns the signed integer division of x by y, x / y. Rounds the quotient towards zero, which is the same as truncating the decimal places of the quotient.

Traps when y is zero.

Example:

Int16.div(123, 10) // => +12

Function rem​

func rem(x : Int16, y : Int16) : Int16

Returns the remainder of the signed integer division of x by y, x % y, which is defined as x - x / y * y.

Traps when y is zero.

Example:

Int16.rem(123, 10) // => +3

Function pow​

func pow(x : Int16, y : Int16) : Int16

Returns x to the power of y, x ** y.

Traps on overflow/underflow and when y < 0 or y >= 16.

Example:

Int16.pow(2, 10) // => +1_024

Function bitnot​

func bitnot(x : Int16) : Int16

Returns the bitwise negation of x, ^x.

Example:

Int16.bitnot(-256 /* 0xff00 */) // => +255 // 0xff

Function bitand​

func bitand(x : Int16, y : Int16) : Int16

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

Example:

Int16.bitand(0x0fff, 0x00f0) // => +240 // 0xf0

Function bitor​

func bitor(x : Int16, y : Int16) : Int16

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

Example:

Int16.bitor(0x0f0f, 0x00f0) // => +4_095 // 0x0fff

Function bitxor​

func bitxor(x : Int16, y : Int16) : Int16

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

Example:

Int16.bitxor(0x0fff, 0x00f0) // => +3_855 // 0x0f0f

Function bitshiftLeft​

func bitshiftLeft(x : Int16, y : Int16) : Int16

Returns the bitwise left shift of x by y, x << y. The right bits of the shift filled with zeros. Left-overflowing bits, including the sign bit, are discarded.

For y >= 16, the semantics is the same as for bitshiftLeft(x, y % 16). For y < 0, the semantics is the same as for bitshiftLeft(x, y + y % 16).

Example:

Int16.bitshiftLeft(1, 8) // => +256 // 0x100 equivalent to `2 ** 8`.

Function bitshiftRight​

func bitshiftRight(x : Int16, y : Int16) : Int16

Returns the signed bitwise right shift of x by y, x >> y. The sign bit is retained and the left side is filled with the sign bit. Right-underflowing bits are discarded, i.e. not rotated to the left side.

For y >= 16, the semantics is the same as for bitshiftRight(x, y % 16). For y < 0, the semantics is the same as for bitshiftRight (x, y + y % 16).

Example:

Int16.bitshiftRight(1024, 8) // => +4 // equivalent to `1024 / (2 ** 8)`

Function bitrotLeft​

func bitrotLeft(x : Int16, y : Int16) : Int16

Returns the bitwise left rotatation of x by y, x <<> y. Each left-overflowing bit is inserted again on the right side. The sign bit is rotated like other bits, i.e. the rotation interprets the number as unsigned.

Changes the direction of rotation for negative y. For y >= 16, the semantics is the same as for bitrotLeft(x, y % 16).

Example:

Int16.bitrotLeft(0x2001, 4) // => +18 // 0x12.

Function bitrotRight​

func bitrotRight(x : Int16, y : Int16) : Int16

Returns the bitwise right rotation of x by y, x <>> y. Each right-underflowing bit is inserted again on the right side. The sign bit is rotated like other bits, i.e. the rotation interprets the number as unsigned.

Changes the direction of rotation for negative y. For y >= 16, the semantics is the same as for bitrotRight(x, y % 16).

Example:

Int16.bitrotRight(0x2010, 8) // => +4_128 // 0x01020.

Function bittest​

func bittest(x : Int16, p : Nat) : Bool

Returns the value of bit p in x, x & 2**p == 2**p. If p >= 16, the semantics is the same as for bittest(x, p % 16). This is equivalent to checking if the p-th bit is set in x, using 0 indexing.

Example:

Int16.bittest(128, 7) // => true

Function bitset​

func bitset(x : Int16, p : Nat) : Int16

Returns the value of setting bit p in x to 1. If p >= 16, the semantics is the same as for bitset(x, p % 16).

Example:

Int16.bitset(0, 7) // => +128

Function bitclear​

func bitclear(x : Int16, p : Nat) : Int16

Returns the value of clearing bit p in x to 0. If p >= 16, the semantics is the same as for bitclear(x, p % 16).

Example:

Int16.bitclear(-1, 7) // => -129

Function bitflip​

func bitflip(x : Int16, p : Nat) : Int16

Returns the value of flipping bit p in x. If p >= 16, the semantics is the same as for bitclear(x, p % 16).

Example:

Int16.bitflip(255, 7) // => +127

Function bitcountNonZero​

func bitcountNonZero(x : Int16) : Int16

Returns the count of non-zero bits in x.

Example:

Int16.bitcountNonZero(0xff) // => +8

Function bitcountLeadingZero​

func bitcountLeadingZero(x : Int16) : Int16

Returns the count of leading zero bits in x.

Example:

Int16.bitcountLeadingZero(0x80) // => +8

Function bitcountTrailingZero​

func bitcountTrailingZero(x : Int16) : Int16

Returns the count of trailing zero bits in x.

Example:

Int16.bitcountTrailingZero(0x0100) // => +8

Function explode​

func explode(x : Int16) : (msb : Nat8, lsb : Nat8)

Returns the upper (i.e. most significant) and lower (least significant) byte of x.

Example:

Int16.explode 0x77ee // => (119, 238)

Function addWrap​

func addWrap(x : Int16, y : Int16) : Int16

Returns the sum of x and y, x +% y.

Wraps on overflow/underflow.

Example:

Int16.addWrap(2 ** 14, 2 ** 14) // => -32_768 // overflow

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 : Int16, y : Int16) : Int16

Returns the difference of x and y, x -% y.

Wraps on overflow/underflow.

Example:

Int16.subWrap(-2 ** 15, 1) // => +32_767 // underflow

Function mulWrap​

func mulWrap(x : Int16, y : Int16) : Int16

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

Wraps on overflow/underflow.

Example:

Int16.mulWrap(2 ** 8, 2 ** 8) // => 0 // overflow

Function powWrap​

func powWrap(x : Int16, y : Int16) : Int16

Returns x to the power of y, x **% y.

Wraps on overflow/underflow. Traps if y < 0 or y >= 16.

Example:


Int16.powWrap(2, 15) // => -32_768 // overflow