diff --git a/src/Nat.mo b/src/Nat.mo index 8b0b9ded..6fd9fcf1 100644 --- a/src/Nat.mo +++ b/src/Nat.mo @@ -1,72 +1,308 @@ -/// Natural numbers +/// Natural numbers with infinite precision. /// /// Most operations on natural numbers (e.g. addition) are available as built-in operators (e.g. `1 + 1`). /// This module provides equivalent functions and `Text` conversion. +/// +/// Import from the base library to use this module. +/// ```motoko name=import +/// import Nat "mo:base/Nat"; +/// ``` import Int "Int"; import Order "Order"; import Prim "mo:⛔"; +import Char "Char"; module { /// Infinite precision natural numbers. public type Nat = Prim.Types.Nat; - /// Conversion. - public let toText : Nat -> Text = Int.toText; + /// Converts a natural number to its textual representation. Textual + /// representation _do not_ contain underscores to represent commas. + /// + /// Example: + /// ```motoko include=import + /// Nat.toText 1234 // => "1234" + /// ``` + public func toText(n : Nat) : Text = Int.toText n; + + /// Creates a natural number from its textual representation. Returns `null` + /// if the input is not a valid natural number. + /// + /// Note: The textual representation _must not_ contain underscores. + /// + /// Example: + /// ```motoko include=import + /// Nat.fromText "1234" // => ?1234 + /// ``` + public func fromText(text : Text) : ?Nat { + if (text == "") { + return null + }; + var n = 0; + for (c in text.chars()) { + if (Char.isDigit(c)) { + let charAsNat = Prim.nat32ToNat(Prim.charToNat32(c) -% Prim.charToNat32('0')); + n := n * 10 + charAsNat + } else { + return null + } + }; + ?n + }; /// Returns the minimum of `x` and `y`. + /// + /// Example: + /// ```motoko include=import + /// Nat.min(1, 2) // => 1 + /// ``` public func min(x : Nat, y : Nat) : Nat { if (x < y) { x } else { y } }; /// Returns the maximum of `x` and `y`. + /// + /// Example: + /// ```motoko include=import + /// Nat.max(1, 2) // => 2 + /// ``` public func max(x : Nat, y : Nat) : Nat { if (x < y) { y } else { x } }; - /// Returns `x == y`. + /// Equality function for Nat types. + /// This is equivalent to `x == y`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.equal(1, 1); // => true + /// 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(3); + /// let buffer2 = Buffer.Buffer(3); + /// Buffer.equal(buffer1, buffer2, Nat.equal) // => true + /// ``` public func equal(x : Nat, y : Nat) : Bool { x == y }; - /// Returns `x != y`. + /// Inequality function for Nat types. + /// This is equivalent to `x != y`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.notEqual(1, 2); // => true + /// 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 notEqual(x : Nat, y : Nat) : Bool { x != y }; - /// Returns `x < y`. + /// "Less than" function for Nat types. + /// This is equivalent to `x < y`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.less(1, 2); // => true + /// 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 : Nat, y : Nat) : Bool { x < y }; - /// Returns `x <= y`. + /// "Less than or equal" function for Nat types. + /// This is equivalent to `x <= y`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.lessOrEqual(1, 2); // => true + /// 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 lessOrEqual(x : Nat, y : Nat) : Bool { x <= y }; - /// Returns `x > y`. + /// "Greater than" function for Nat types. + /// This is equivalent to `x > y`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.greater(2, 1); // => true + /// 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 greater(x : Nat, y : Nat) : Bool { x > y }; - /// Returns `x >= y`. + /// "Greater than or equal" function for Nat types. + /// This is equivalent to `x >= y`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.greaterOrEqual(2, 1); // => true + /// 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 greaterOrEqual(x : Nat, y : Nat) : Bool { x >= y }; - /// Returns the order of `x` and `y`. + /// General purpose comparison function for `Nat`. Returns the `Order` ( + /// either `#less`, `#equal`, or `#greater`) of comparing `x` with `y`. + /// + /// Example: + /// ```motoko include=import + /// Nat.compare(2, 3) // => #less + /// ``` + /// + /// 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.sort([2, 3, 1], Nat.compare) // => [1, 2, 3] + /// ``` public func compare(x : Nat, y : Nat) : { #less; #equal; #greater } { if (x < y) { #less } else if (x == y) { #equal } else { #greater } }; - /// Returns the sum of `x` and `y`, `x + y`. + /// Returns the sum of `x` and `y`, `x + y`. This operator will never overflow + /// because `Nat` is infinite precision. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.add(1, 2); // => 3 + /// 1 + 2 // => 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: + /// ```motoko include=import + /// import Array "mo:base/Array"; + /// Array.foldLeft([2, 3, 1], 0, Nat.add) // => 6 + /// ``` public func add(x : Nat, y : Nat) : Nat { x + y }; /// Returns the difference of `x` and `y`, `x - y`. - /// Traps on underflow. + /// Traps on underflow below `0`. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.sub(2, 1); // => 1 + /// // Add a type annotation to avoid a warning about the subtraction + /// 2 - 1 : Nat // => 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: + /// ```motoko include=import + /// import Array "mo:base/Array"; + /// Array.foldLeft([2, 3, 1], 10, Nat.sub) // => 4 + /// ``` public func sub(x : Nat, y : Nat) : Nat { x - y }; - /// Returns the product of `x` and `y`, `x * y`. + /// Returns the product of `x` and `y`, `x * y`. This operator will never + /// overflow because `Nat` is infinite precision. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.mul(2, 3); // => 6 + /// 2 * 3 // => 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: + /// ```motoko include=import + /// import Array "mo:base/Array"; + /// Array.foldLeft([2, 3, 1], 1, Nat.mul) // => 6 + /// ``` public func mul(x : Nat, y : Nat) : Nat { x * y }; - /// Returns the division of `x` by `y`, `x / y`. + /// Returns the unsigned integer division of `x` by `y`, `x / y`. /// Traps when `y` is zero. + /// + /// The quotient is rounded down, which is equivalent to truncating the + /// decimal places of the quotient. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.div(6, 2); // => 3 + /// 6 / 2 // => 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 div(x : Nat, y : Nat) : Nat { x / y }; - /// Returns the remainder of `x` divided by `y`, `x % y`. + /// Returns the remainder of unsigned integer division of `x` by `y`, `x % y`. /// Traps when `y` is zero. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.rem(6, 4); // => 2 + /// 6 % 4 // => 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. public func rem(x : Nat, y : Nat) : Nat { x % y }; - /// Returns `x` to the power of `y`, `x ** y`. + /// Returns `x` to the power of `y`, `x ** y`. Traps when `y > 2^32`. This operator + /// will never overflow because `Nat` is infinite precision. + /// + /// Example: + /// ```motoko include=import + /// ignore Nat.pow(2, 3); // => 8 + /// 2 ** 3 // => 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 pow(x : Nat, y : Nat) : Nat { x ** y }; }