Add rational-numbers exercise (#57)

* Add rational-numbers example and lib.cairo scaffold

* implement working example

* make denom u128 by default

* Refactor and turn lib.cairo back into scaffold

* refactor slightly + add concepts & difficulty to the practice in config

config.json

@@ -195,6 +195,18 @@
         ],
         "prerequisites": [],
         "difficulty": 5
+      },
+      {
+        "slug": "rational-numbers",
+        "name": "Rational Numbers",
+        "uuid": "9858a357-b935-437d-b4e0-c3aac20859cf",
+        "practices": [
+          "operator-overload",
+          "mutability",
+          "integers"
+        ],
+        "prerequisites": [],
+        "difficulty": 3
       }
     ],
     "foregone": [

exercises/practice/rational-numbers/.docs/instructions.md

@@ -0,0 +1,42 @@
+# Instructions
+
+A rational number is defined as the quotient of two integers `a` and `b`, called the numerator and denominator, respectively, where `b != 0`.
+
+~~~~exercism/note
+Note that mathematically, the denominator can't be zero.
+However in many implementations of rational numbers, you will find that the denominator is allowed to be zero with behaviour similar to positive or negative infinity in floating point numbers.
+In those cases, the denominator and numerator generally still can't both be zero at once.
+~~~~
+
+The absolute value `|r|` of the rational number `r = a/b` is equal to `|a|/|b|`.
+
+The sum of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ + r₂ = a₁/b₁ + a₂/b₂ = (a₁ * b₂ + a₂ * b₁) / (b₁ * b₂)`.
+
+The difference of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ - r₂ = a₁/b₁ - a₂/b₂ = (a₁ * b₂ - a₂ * b₁) / (b₁ * b₂)`.
+
+The product (multiplication) of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ * r₂ = (a₁ * a₂) / (b₁ * b₂)`.
+
+Dividing a rational number `r₁ = a₁/b₁` by another `r₂ = a₂/b₂` is `r₁ / r₂ = (a₁ * b₂) / (a₂ * b₁)` if `a₂` is not zero.
+
+Exponentiation of a rational number `r = a/b` to a non-negative integer power `n` is `r^n = (a^n)/(b^n)`.
+
+Exponentiation of a rational number `r = a/b` to a negative integer power `n` is `r^n = (b^m)/(a^m)`, where `m = |n|`.
+
+Exponentiation of a rational number `r = a/b` to a real (floating-point) number `x` is the quotient `(a^x)/(b^x)`, which is a real number.
+
+Exponentiation of a real number `x` to a rational number `r = a/b` is `x^(a/b) = root(x^a, b)`, where `root(p, q)` is the `q`th root of `p`.
+
+Implement the following operations:
+
+- addition, subtraction, multiplication and division of two rational numbers,
+- absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.
+
+Your implementation of rational numbers should always be reduced to lowest terms.
+For example, `4/4` should reduce to `1/1`, `30/60` should reduce to `1/2`, `12/8` should reduce to `3/2`, etc.
+To reduce a rational number `r = a/b`, divide `a` and `b` by the greatest common divisor (gcd) of `a` and `b`.
+So, for example, `gcd(12, 8) = 4`, so `r = 12/8` can be reduced to `(12/4)/(8/4) = 3/2`.
+The reduced form of a rational number should be in "standard form" (the denominator should always be a positive integer).
+If a denominator with a negative integer is present, multiply both numerator and denominator by `-1` to ensure standard form is reached.
+For example, `3/-4` should be reduced to `-3/4`
+
+Assume that the programming language you are using does not have an implementation of rational numbers.

exercises/practice/rational-numbers/.meta/config.json

@@ -0,0 +1,18 @@
+{
+  "authors": [],
+  "files": {
+    "solution": [
+      "src/lib.cairo",
+      "Scarb.toml"
+    ],
+    "test": [
+      "src/tests.cairo"
+    ],
+    "example": [
+      ".meta/example.cairo"
+    ]
+  },
+  "blurb": "Implement rational numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Rational_number"
+}

exercises/practice/rational-numbers/.meta/example.cairo

@@ -0,0 +1,149 @@
+use alexandria_math::gcd_of_n_numbers::gcd_two_numbers;
+use alexandria_math::fast_power::fast_power;
+use alexandria_math::fast_root::fast_nr_optimize;
+use core::fmt::{Debug, Formatter, Error};
+
+#[derive(Drop, Debug, Copy)]
+struct Rational {
+    numer: i128,
+    denom: u128,
+}
+
+#[generate_trait]
+impl RationalImpl of RationalTrait {
+    fn new(numer: i128, denom: i128) -> Rational {
+        assert!(denom != 0, "denominator cannot be 0");
+
+        let sign: i128 = if (numer < 0 && denom > 0) || (numer > 0 && denom < 0) {
+            -1
+        } else {
+            1
+        };
+
+        let numer = abs(numer);
+        let denom = abs(denom);
+        let gcd_num = gcd_two_numbers(numer, denom);
+
+        let numer = to_i128(numer / gcd_num) * sign;
+        let denom = denom / gcd_num;
+
+        Rational { numer, denom }
+    }
+}
+
+impl RationalPartialEq of PartialEq<Rational> {
+    fn eq(lhs: @Rational, rhs: @Rational) -> bool {
+        lhs.numer == rhs.numer && lhs.denom == rhs.denom
+    }
+
+    fn ne(lhs: @Rational, rhs: @Rational) -> bool {
+        !(lhs == rhs)
+    }
+}
+
+impl RationalNeg of Neg<Rational> {
+    fn neg(a: Rational) -> Rational {
+        RationalTrait::new(a.numer * -1, to_i128(a.denom))
+    }
+}
+
+impl RationalAdd of Add<Rational> {
+    fn add(lhs: Rational, rhs: Rational) -> Rational {
+        let numer = (lhs.numer * to_i128(rhs.denom)) + (to_i128(lhs.denom) * rhs.numer);
+        let denom = to_i128(lhs.denom * rhs.denom);
+        RationalTrait::new(numer, denom)
+    }
+}
+
+impl RationalSub of Sub<Rational> {
+    fn sub(lhs: Rational, rhs: Rational) -> Rational {
+        lhs + (-rhs)
+    }
+}
+
+impl RationalMul of Mul<Rational> {
+    fn mul(lhs: Rational, rhs: Rational) -> Rational {
+        RationalTrait::new(lhs.numer * rhs.numer, to_i128(lhs.denom * rhs.denom))
+    }
+}
+
+impl RationalDiv of Div<Rational> {
+    fn div(lhs: Rational, rhs: Rational) -> Rational {
+        RationalTrait::new(lhs.numer * to_i128(rhs.denom), to_i128(lhs.denom) * rhs.numer)
+    }
+}
+
+#[generate_trait]
+impl RationalAbs of RationalAbsTrait {
+    fn abs(self: @Rational) -> Rational {
+        RationalTrait::new(to_i128(abs(*self.numer)), to_i128(*self.denom))
+    }
+}
+
+#[generate_trait]
+impl RationalPow of RationalPowTrait {
+    fn pow(self: @Rational, power: i128) -> Rational {
+        if *self.numer == 0 {
+            return *self;
+        };
+
+        let power_abs = abs(power);
+
+        // determine the new number's sign
+        let sign: i128 = if *self.numer < 0 && power_abs % 2 == 1 {
+            -1
+        } else {
+            1
+        };
+
+        let numer = to_i128(fast_power(abs(*self.numer), power_abs)) * sign;
+        let denom = to_i128(fast_power(*self.denom, power_abs));
+
+        if power < 0 {
+            RationalTrait::new(denom, numer)
+        } else {
+            RationalTrait::new(numer, denom)
+        }
+    }
+
+    fn rpow(self: @u128, power: Rational) -> u128 {
+        // Cairo only supports integers, so a negative rational exponent
+        // will always return the result 0
+        if power.numer < 0 {
+            return 0;
+        };
+        fast_nr_optimize(fast_power(*self, to_u128(power.numer)), power.denom, 30)
+    }
+}
+
+// Enables printing i128 values in tests.
+// Note that this will soon be added to the core library.
+impl I128Debug of Debug<i128> {
+    fn fmt(self: @i128, ref f: Formatter) -> Result<(), Error> {
+        if *self < 0 {
+            f.buffer.append(@"-");
+        };
+        f.buffer.append(@format!("{}", abs(*self)));
+        Result::Ok(())
+    }
+}
+
+fn abs(n: i128) -> u128 {
+    let val = if n < 0 {
+        n * -1
+    } else {
+        n
+    };
+    to_u128(val)
+}
+
+fn to_i128(n: u128) -> i128 {
+    n.try_into().unwrap()
+}
+
+fn to_u128(n: i128) -> u128 {
+    n.try_into().unwrap()
+}
+
+#[cfg(test)]
+mod tests;

exercises/practice/rational-numbers/.meta/tests.toml

@@ -0,0 +1,139 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[0ba4d988-044c-4ed5-9215-4d0bb8d0ae9f]
+description = "Arithmetic -> Addition -> Add two positive rational numbers"
+
+[88ebc342-a2ac-4812-a656-7b664f718b6a]
+description = "Arithmetic -> Addition -> Add a positive rational number and a negative rational number"
+
+[92ed09c2-991e-4082-a602-13557080205c]
+description = "Arithmetic -> Addition -> Add two negative rational numbers"
+
+[6e58999e-3350-45fb-a104-aac7f4a9dd11]
+description = "Arithmetic -> Addition -> Add a rational number to its additive inverse"
+
+[47bba350-9db1-4ab9-b412-4a7e1f72a66e]
+description = "Arithmetic -> Subtraction -> Subtract two positive rational numbers"
+
+[93926e2a-3e82-4aee-98a7-fc33fb328e87]
+description = "Arithmetic -> Subtraction -> Subtract a positive rational number and a negative rational number"
+
+[a965ba45-9b26-442b-bdc7-7728e4b8d4cc]
+description = "Arithmetic -> Subtraction -> Subtract two negative rational numbers"
+
+[0df0e003-f68e-4209-8c6e-6a4e76af5058]
+description = "Arithmetic -> Subtraction -> Subtract a rational number from itself"
+
+[34fde77a-75f4-4204-8050-8d3a937958d3]
+description = "Arithmetic -> Multiplication -> Multiply two positive rational numbers"
+
+[6d015cf0-0ea3-41f1-93de-0b8e38e88bae]
+description = "Arithmetic -> Multiplication -> Multiply a negative rational number by a positive rational number"
+
+[d1bf1b55-954e-41b1-8c92-9fc6beeb76fa]
+description = "Arithmetic -> Multiplication -> Multiply two negative rational numbers"
+
+[a9b8f529-9ec7-4c79-a517-19365d779040]
+description = "Arithmetic -> Multiplication -> Multiply a rational number by its reciprocal"
+
+[d89d6429-22fa-4368-ab04-9e01a44d3b48]
+description = "Arithmetic -> Multiplication -> Multiply a rational number by 1"
+
+[0d95c8b9-1482-4ed7-bac9-b8694fa90145]
+description = "Arithmetic -> Multiplication -> Multiply a rational number by 0"
+
+[1de088f4-64be-4e6e-93fd-5997ae7c9798]
+description = "Arithmetic -> Division -> Divide two positive rational numbers"
+
+[7d7983db-652a-4e66-981a-e921fb38d9a9]
+description = "Arithmetic -> Division -> Divide a positive rational number by a negative rational number"
+
+[1b434d1b-5b38-4cee-aaf5-b9495c399e34]
+description = "Arithmetic -> Division -> Divide two negative rational numbers"
+
+[d81c2ebf-3612-45a6-b4e0-f0d47812bd59]
+description = "Arithmetic -> Division -> Divide a rational number by 1"
+
+[5fee0d8e-5955-4324-acbe-54cdca94ddaa]
+description = "Absolute value -> Absolute value of a positive rational number"
+
+[3cb570b6-c36a-4963-a380-c0834321bcaa]
+description = "Absolute value -> Absolute value of a positive rational number with negative numerator and denominator"
+
+[6a05f9a0-1f6b-470b-8ff7-41af81773f25]
+description = "Absolute value -> Absolute value of a negative rational number"
+
+[5d0f2336-3694-464f-8df9-f5852fda99dd]
+description = "Absolute value -> Absolute value of a negative rational number with negative denominator"
+
+[f8e1ed4b-9dca-47fb-a01e-5311457b3118]
+description = "Absolute value -> Absolute value of zero"
+
+[4a8c939f-f958-473b-9f88-6ad0f83bb4c4]
+description = "Absolute value -> Absolute value of a rational number is reduced to lowest terms"
+
+[ea2ad2af-3dab-41e7-bb9f-bd6819668a84]
+description = "Exponentiation of a rational number -> Raise a positive rational number to a positive integer power"
+
+[8168edd2-0af3-45b1-b03f-72c01332e10a]
+description = "Exponentiation of a rational number -> Raise a negative rational number to a positive integer power"
+
+[c291cfae-cfd8-44f5-aa6c-b175c148a492]
+description = "Exponentiation of a rational number -> Raise a positive rational number to a negative integer power"
+
+[45cb3288-4ae4-4465-9ae5-c129de4fac8e]
+description = "Exponentiation of a rational number -> Raise a negative rational number to an even negative integer power"
+
+[2d47f945-ffe1-4916-a399-c2e8c27d7f72]
+description = "Exponentiation of a rational number -> Raise a negative rational number to an odd negative integer power"
+
+[e2f25b1d-e4de-4102-abc3-c2bb7c4591e4]
+description = "Exponentiation of a rational number -> Raise zero to an integer power"
+
+[431cac50-ab8b-4d58-8e73-319d5404b762]
+description = "Exponentiation of a rational number -> Raise one to an integer power"
+
+[7d164739-d68a-4a9c-b99f-dd77ce5d55e6]
+description = "Exponentiation of a rational number -> Raise a positive rational number to the power of zero"
+
+[eb6bd5f5-f880-4bcd-8103-e736cb6e41d1]
+description = "Exponentiation of a rational number -> Raise a negative rational number to the power of zero"
+
+[30b467dd-c158-46f5-9ffb-c106de2fd6fa]
+description = "Exponentiation of a real number to a rational number -> Raise a real number to a positive rational number"
+
+[6e026bcc-be40-4b7b-ae22-eeaafc5a1789]
+description = "Exponentiation of a real number to a rational number -> Raise a real number to a negative rational number"
+
+[9f866da7-e893-407f-8cd2-ee85d496eec5]
+description = "Exponentiation of a real number to a rational number -> Raise a real number to a zero rational number"
+
+[0a63fbde-b59c-4c26-8237-1e0c73354d0a]
+description = "Reduction to lowest terms -> Reduce a positive rational number to lowest terms"
+
+[5ed6f248-ad8d-4d4e-a545-9146c6727f33]
+description = "Reduction to lowest terms -> Reduce places the minus sign on the numerator"
+
+[f87c2a4e-d29c-496e-a193-318c503e4402]
+description = "Reduction to lowest terms -> Reduce a negative rational number to lowest terms"
+
+[3b92ffc0-5b70-4a43-8885-8acee79cdaaf]
+description = "Reduction to lowest terms -> Reduce a rational number with a negative denominator to lowest terms"
+
+[c9dbd2e6-5ac0-4a41-84c1-48b645b4f663]
+description = "Reduction to lowest terms -> Reduce zero to lowest terms"
+
+[297b45ad-2054-4874-84d4-0358dc1b8887]
+description = "Reduction to lowest terms -> Reduce an integer to lowest terms"
+
+[a73a17fe-fe8c-4a1c-a63b-e7579e333d9e]
+description = "Reduction to lowest terms -> Reduce one to lowest terms"

exercises/practice/rational-numbers/Scarb.toml

@@ -0,0 +1,7 @@
+[package]
+name = "rational_numbers"
+version = "0.1.0"
+edition = "2023_11"
+
+[dependencies]
+alexandria_math = { git = "https://github.com/keep-starknet-strange/alexandria.git" }