Provides utility functions on 64-bit signed integers.
Note that most operations are available as built-in operators (e.g. 1 + 1
).
Import from the base library to use this module.
motoko name=import
import Int64 "mo:base/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 let 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 let 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 let 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 let 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 let 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 let 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 let 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
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:
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
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.
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
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.
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
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.
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
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.
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
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.
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
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.
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
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:
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
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:
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
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:
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
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.
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
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.
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
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.
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
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.
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
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.
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
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.
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
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.
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`.
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.
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)`
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.
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.
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.
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.
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.
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 let bitcountNonZero : (x : Int64) -> Int64
Returns the count of non-zero bits in x
.
Example:
motoko include=import
Int64.bitcountNonZero(0xffff) // => +16
public let bitcountLeadingZero : (x : Int64) -> Int64
Returns the count of leading zero bits in x
.
Example:
motoko include=import
Int64.bitcountLeadingZero(0x8000_0000) // => +32
public let bitcountTrailingZero : (x : Int64) -> Int64
Returns the count of trailing zero bits in x
.
Example:
motoko include=import
Int64.bitcountTrailingZero(0x0201_0000) // => +16
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
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.
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
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.
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
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.
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
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.