Int64

Provides utility functions on 64-bit signed integers.

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

:::info 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.

motoko name=import
import Int64 "mo:base/Int64";

type Int64 = Prim.Types.Int64

64-bit signed integers.

public let minimumValue : Int64

Minimum 64-bit integer value, -2 ** 63.

Example:

motoko include=import
Int64.minimumValue // => -9_223_372_036_854_775_808

public let maximumValue : Int64

Maximum 64-bit integer value, +2 ** 63 - 1.

Example:

motoko include=import
Int64.maximumValue // => +9_223_372_036_854_775_807

public func toInt(_ : Int64) : Int

Converts a 64-bit signed integer to a signed integer with infinite precision.

Example:

motoko include=import
Int64.toInt(123_456) // => 123_456 : Int

public func fromInt(_ : Int) : Int64

Converts a signed integer with infinite precision to a 64-bit signed integer.

Traps on overflow/underflow.

Example:

motoko include=import
Int64.fromInt(123_456) // => +123_456 : Int64

public func fromInt32(_ : Int32) : Int64

Converts a 32-bit signed integer to a 64-bit signed integer.

Traps on overflow/underflow.

Example:

motoko include=import
Int64.fromInt32(-123_456) // => -123_456 : Int64

public func toInt32(_ : Int64) : Int32

Converts a 64-bit signed integer to a 32-bit signed integer.

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.toInt32(-123_456) // => -123_456 : Int32

public func fromIntWrap(_ : Int) : Int64

Converts a signed integer with infinite precision to a 64-bit signed integer.

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.fromIntWrap(-123_456) // => -123_456 : Int64

public func fromNat64(_ : Nat64) : Int64

Converts an unsigned 64-bit integer to a signed 64-bit integer.

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.fromNat64(123_456) // => +123_456 : Int64

public func toNat64(_ : Int64) : Nat64

Converts a signed 64-bit integer to an unsigned 64-bit integer.

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.toNat64(-1) // => 18_446_744_073_709_551_615 : Nat64 // underflow

public func toText(x : Int64) : Text

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

Example:

motoko include=import
Int64.toText(-123456) // => "-123456"

public func abs(x : Int64) : Int64

Returns the absolute value of x.

Traps when x == -2 ** 63 (the minimum Int64 value).

Example:

motoko include=import
Int64.abs(-123456) // => +123_456

public func min(x : Int64, y : Int64) : Int64

Returns the minimum of x and y.

Example:

motoko include=import
Int64.min(+2, -3) // => -3

public func max(x : Int64, y : Int64) : Int64

Returns the maximum of x and y.

Example:

motoko include=import
Int64.max(+2, -3) // => +2

public func equal(x : Int64, y : Int64) : Bool

Equality function for Int64 types. This is equivalent to x == y.

Example:

motoko include=import
Int64.equal(-1, -1); // => true

Example:

motoko include=import
import Buffer "mo:base/Buffer";

let buffer1 = Buffer.Buffer<Int64>(1);
buffer1.add(-3);
let buffer2 = Buffer.Buffer<Int64>(1);
buffer2.add(-3);
Buffer.equal(buffer1, buffer2, Int64.equal) // => true

public func notEqual(x : Int64, y : Int64) : Bool

Inequality function for Int64 types. This is equivalent to x != y.

Example:

motoko include=import
Int64.notEqual(-1, -2); // => true

public func less(x : Int64, y : Int64) : Bool

"Less than" function for Int64 types. This is equivalent to x < y.

Example:

motoko include=import
Int64.less(-2, 1); // => true

public func lessOrEqual(x : Int64, y : Int64) : Bool

"Less than or equal" function for Int64 types. This is equivalent to x <= y.

Example:

motoko include=import
Int64.lessOrEqual(-2, -2); // => true

public func greater(x : Int64, y : Int64) : Bool

"Greater than" function for Int64 types. This is equivalent to x > y.

Example:

motoko include=import
Int64.greater(-2, -3); // => true

public func greaterOrEqual(x : Int64, y : Int64) : Bool

"Greater than or equal" function for Int64 types. This is equivalent to x >= y.

Example:

motoko include=import
Int64.greaterOrEqual(-2, -2); // => true

public func compare(x : Int64, y : Int64) : {#less; #equal; #greater}

General-purpose comparison function for Int64. Returns the Order ( either #less, #equal, or #greater) of comparing x with y.

Example:

motoko include=import
Int64.compare(-3, 2) // => #less

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

Example:

motoko include=import
import Array "mo:base/Array";
Array.sort([1, -2, -3] : [Int64], Int64.compare) // => [-3, -2, 1]

public func neg(x : Int64) : Int64

Returns the negation of x, -x.

Traps on overflow, i.e. for neg(-2 ** 63).

Example:

motoko include=import
Int64.neg(123) // => -123

public func add(x : Int64, y : Int64) : Int64

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

Traps on overflow/underflow.

Example:

motoko include=import
Int64.add(1234, 123) // => +1_357

Example:

motoko include=import
import Array "mo:base/Array";
Array.foldLeft<Int64, Int64>([1, -2, -3], 0, Int64.add) // => -4

public func sub(x : Int64, y : Int64) : Int64

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

Traps on overflow/underflow.

Example:

motoko include=import
Int64.sub(123, 100) // => +23

Example:

motoko include=import
import Array "mo:base/Array";
Array.foldLeft<Int64, Int64>([1, -2, -3], 0, Int64.sub) // => 4

public func mul(x : Int64, y : Int64) : Int64

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

Traps on overflow/underflow.

Example:

motoko include=import
Int64.mul(123, 10) // => +1_230

Example:

motoko include=import
import Array "mo:base/Array";
Array.foldLeft<Int64, Int64>([1, -2, -3], 1, Int64.mul) // => 6

public func div(x : Int64, y : Int64) : Int64

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:

motoko include=import
Int64.div(123, 10) // => +12

public func rem(x : Int64, y : Int64) : Int64

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:

motoko include=import
Int64.rem(123, 10) // => +3

public func pow(x : Int64, y : Int64) : Int64

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

Traps on overflow/underflow and when y < 0 or y >= 64.

Example:

motoko include=import
Int64.pow(2, 10) // => +1_024

public func bitnot(x : Int64) : Int64

Returns the bitwise negation of x, ^x.

Example:

motoko include=import
Int64.bitnot(-256 /* 0xffff_ffff_ffff_ff00 */) // => +255 // 0xff

public func bitand(x : Int64, y : Int64) : Int64

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

Example:

motoko include=import
Int64.bitand(0xffff, 0x00f0) // => +240 // 0xf0

public func bitor(x : Int64, y : Int64) : Int64

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

Example:

motoko include=import
Int64.bitor(0xffff, 0x00f0) // => +65_535 // 0xffff

public func bitxor(x : Int64, y : Int64) : Int64

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

Example:

motoko include=import
Int64.bitxor(0xffff, 0x00f0) // => +65_295 // 0xff0f

public func bitshiftLeft(x : Int64, y : Int64) : Int64

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 >= 64, the semantics is the same as for bitshiftLeft(x, y % 64). For y < 0, the semantics is the same as for bitshiftLeft(x, y + y % 64).

Example:

motoko include=import
Int64.bitshiftLeft(1, 8) // => +256 // 0x100 equivalent to `2 ** 8`.

public func bitshiftRight(x : Int64, y : Int64) : Int64

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 >= 64, the semantics is the same as for bitshiftRight(x, y % 64). For y < 0, the semantics is the same as for bitshiftRight (x, y + y % 64).

Example:

motoko include=import
Int64.bitshiftRight(1024, 8) // => +4 // equivalent to `1024 / (2 ** 8)`

public func bitrotLeft(x : Int64, y : Int64) : Int64

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 >= 64, the semantics is the same as for bitrotLeft(x, y % 64).

Example:

motoko include=import

Int64.bitrotLeft(0x2000_0000_0000_0001, 4) // => +18 // 0x12.

public func bitrotRight(x : Int64, y : Int64) : Int64

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 >= 64, the semantics is the same as for bitrotRight(x, y % 64).

Example:

motoko include=import
Int64.bitrotRight(0x0002_0000_0000_0001, 48) // => +65538 // 0x1_0002.

public func bittest(x : Int64, p : Nat) : Bool

Returns the value of bit p in x, x & 2**p == 2**p. If p >= 64, the semantics is the same as for bittest(x, p % 64). This is equivalent to checking if the p-th bit is set in x, using 0 indexing.

Example:

motoko include=import
Int64.bittest(128, 7) // => true

public func bitset(x : Int64, p : Nat) : Int64

Returns the value of setting bit p in x to 1. If p >= 64, the semantics is the same as for bitset(x, p % 64).

Example:

motoko include=import
Int64.bitset(0, 7) // => +128

public func bitclear(x : Int64, p : Nat) : Int64

Returns the value of clearing bit p in x to 0. If p >= 64, the semantics is the same as for bitclear(x, p % 64).

Example:

motoko include=import
Int64.bitclear(-1, 7) // => -129

public func bitflip(x : Int64, p : Nat) : Int64

Returns the value of flipping bit p in x. If p >= 64, the semantics is the same as for bitclear(x, p % 64).

Example:

motoko include=import
Int64.bitflip(255, 7) // => +127

public func bitcountNonZero(x : Int64) : Int64

Returns the count of non-zero bits in x.

Example:

motoko include=import
Int64.bitcountNonZero(0xffff) // => +16

public func bitcountLeadingZero(x : Int64) : Int64

Returns the count of leading zero bits in x.

Example:

motoko include=import
Int64.bitcountLeadingZero(0x8000_0000) // => +32

public func bitcountTrailingZero(x : Int64) : Int64

Returns the count of trailing zero bits in x.

Example:

motoko include=import
Int64.bitcountTrailingZero(0x0201_0000) // => +16

public func explode(x : Int64) : (msb : Nat8, Nat8, Nat8, Nat8, Nat8, Nat8, Nat8, lsb : Nat8)

Returns the upper (i.e. most significant), lower (least significant) and in-between bytes of x.

Example:

motoko include=import
Int64.explode 0x33772266aa885511 // => (51, 119, 34, 102, 170, 136, 85, 17)

public func addWrap(x : Int64, y : Int64) : Int64

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

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.addWrap(2 ** 62, 2 ** 62) // => -9_223_372_036_854_775_808 // overflow

:::info 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. :::

public func subWrap(x : Int64, y : Int64) : Int64

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

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.subWrap(-2 ** 63, 1) // => +9_223_372_036_854_775_807 // underflow

public func mulWrap(x : Int64, y : Int64) : Int64

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

Wraps on overflow/underflow.

Example:

motoko include=import
Int64.mulWrap(2 ** 32, 2 ** 32) // => 0 // overflow

public func powWrap(x : Int64, y : Int64) : Int64

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

Wraps on overflow/underflow. Traps if y < 0 or y >= 64.

Example:

motoko include=import
Int64.powWrap(2, 63) // => -9_223_372_036_854_775_808 // overflow