Merge pull request #2 from micahkendall/reduce_reduce

change div for sign invariant in numerator, add additional funcs, add…

lib/aiken/rats.ak

@@ -1,38 +1,69 @@
 // Rationals
 // Authors:
 // Micah Kendall
+// Ken Fritschy
 // <other authors go here>
 
+use aiken/math
+
+// Useful for using Rationals in datums/redeemers which cannot have opaque types
 pub type UncheckedRational {
   numerator: Int,
   denominator: Int,
 }
 
+// Opaque type used to ensure the sign of the Rational is managed strictly
+// in the numerator
 pub opaque type Rational {
   numerator: Int,
   denominator: Int,
 }
 
+// Converts an UncheckedRational to a Rational
 pub fn check_rational(num: UncheckedRational) -> Rational {
   let UncheckedRational { numerator, denominator } =
     num
   div_int(numerator, denominator)
 }
 
+// Multiplication
 pub fn mul(a: Rational, b: Rational) -> Rational {
   Rational {
     numerator: a.numerator * b.numerator,
     denominator: a.denominator * b.denominator,
   }
 }
 
+test mul_1() {
+  let a =
+    div_int(2, 3) |> mul(div_int(3, 4))
+  a == Rational { numerator: 6, denominator: 12 }
+}
+
+test mul_2() {
+  let a =
+    div_int(-2, 3) |> mul(div_int(-3, 4))
+  a == Rational { numerator: 6, denominator: 12 }
+}
+
+// Division
 pub fn div(a: Rational, b: Rational) -> Rational {
-  Rational {
-    numerator: a.numerator * b.denominator,
-    denominator: a.denominator * b.numerator,
-  }
+  recip(b) |> mul(a)
+}
+
+test div_1() {
+  let a =
+    div_int(2, 3) |> div(div_int(3, 4))
+  a == Rational { numerator: 8, denominator: 9 }
+}
+
+test div_2() {
+  let a =
+    div_int(2, 3) |> div(div_int(-3, 4))
+  a == Rational { numerator: -8, denominator: 9 }
 }
 
+// Create a new Rational
 pub fn div_int(numerator: Int, denominator: Int) -> Rational {
   if denominator < 0 {
     Rational { numerator: -numerator, denominator: -denominator }
@@ -41,48 +72,228 @@ pub fn div_int(numerator: Int, denominator: Int) -> Rational {
   }
 }
 
+test div_int_1() {
+  div_int(2, 3) == Rational { numerator: 2, denominator: 3 }
+}
+
+test div_int_2() {
+  div_int(-2, 3) == Rational { numerator: -2, denominator: 3 }
+}
+
+test div_int_3() {
+  div_int(2, -3) == Rational { numerator: -2, denominator: 3 }
+}
+
+test div_int_4() {
+  div_int(2, 4) == Rational { numerator: 2, denominator: 4 }
+}
+
+test div_int_5() {
+  div_int(-2, -3) == Rational { numerator: 2, denominator: 3 }
+}
+
+test div_int_6() {
+  div_int(-2, -4) == Rational { numerator: 2, denominator: 4 }
+}
+
+// Addition
 pub fn add(a: Rational, b: Rational) -> Rational {
   Rational {
     numerator: a.numerator * b.denominator + b.numerator * a.denominator,
     denominator: a.denominator * b.denominator,
   }
 }
 
+test add_1() {
+  let a =
+    div_int(2, 3) |> add(div_int(3, 4))
+  a == Rational { numerator: 17, denominator: 12 }
+}
+
+// Subtraction
 pub fn sub(a: Rational, b: Rational) -> Rational {
   Rational {
     numerator: a.numerator * b.denominator - b.numerator * a.denominator,
     denominator: a.denominator * b.denominator,
   }
 }
 
+test sub_1() {
+  let a =
+    div_int(2, 3) |> sub(div_int(3, 4))
+  a == Rational { numerator: -1, denominator: 12 }
+}
+
+// Greater than
 pub fn gt(a: Rational, b: Rational) -> Bool {
   a.numerator * b.denominator > b.numerator * a.denominator
 }
 
+test gt_1() {
+  div_int(2, 3) |> gt(div_int(1, 3))
+}
+
+test gt_2() {
+  let a =
+    div_int(2, 3) |> gt(div_int(2, 3))
+  a == False
+}
+
+// Less than
 pub fn lt(a: Rational, b: Rational) -> Bool {
   a.numerator * b.denominator < b.numerator * a.denominator
 }
 
+test lt_1() {
+  div_int(2, 3) |> lt(div_int(3, 4))
+}
+
+test lt_2() {
+  let a =
+    div_int(2, 3) |> lt(div_int(2, 3))
+  a == False
+}
+
+// Greater than or equal
 pub fn ge(a: Rational, b: Rational) -> Bool {
   a.numerator * b.denominator >= b.numerator * a.denominator
 }
 
+test ge_1() {
+  div_int(2, 3) |> ge(div_int(1, 3))
+}
+
+test ge_2() {
+  div_int(2, 3) |> ge(div_int(2, 3))
+}
+
+// Less than or equal
 pub fn le(a: Rational, b: Rational) -> Bool {
   a.numerator * b.denominator <= b.numerator * a.denominator
 }
 
+test le_1() {
+  div_int(2, 3) |> le(div_int(3, 4))
+}
+
+test le_2() {
+  div_int(2, 3) |> le(div_int(2, 3))
+}
+
+// Equal
 pub fn eq(a: Rational, b: Rational) -> Bool {
   a.numerator * b.denominator == b.numerator * a.denominator
 }
 
+test eq_1() {
+  div_int(2, 3) |> eq(div_int(2, 3))
+}
+
+// Not Equal
 pub fn neq(a: Rational, b: Rational) -> Bool {
   a.numerator * b.denominator != b.numerator * a.denominator
 }
 
+test neq_1() {
+  div_int(2, 3) |> neq(div_int(1, 3))
+}
+
+// Create a new Rational from an Int
 pub fn from_int(a: Int) -> Rational {
   Rational { numerator: a, denominator: 1 }
 }
 
+test from_int_1() {
+  from_int(3) == div_int(3, 1)
+}
+
+// Truncate a Rational to convert it to an Int
 pub fn truncate(a: Rational) -> Int {
   a.numerator / a.denominator
 }
+
+test truncate_1() {
+  let a =
+    div_int(8, 3) |> truncate
+  a == 2
+}
+
+// Change the sign of a Rational
+pub fn neg(a: Rational) -> Rational {
+  Rational { numerator: -a.numerator, denominator: a.denominator }
+}
+
+test neg_1() {
+  let a =
+    div_int(2, 3) |> neg
+  a == Rational { numerator: -2, denominator: 3 }
+}
+
+// Absolute value of a Rational
+pub fn abs(a: Rational) -> Rational {
+  Rational { numerator: math.abs(a.numerator), denominator: a.denominator }
+}
+
+test abs_1() {
+  let a =
+    div_int(-2, 3) |> abs
+  a == Rational { numerator: 2, denominator: 3 }
+}
+
+// Reciprocal of a Rational
+pub fn recip(a: Rational) -> Rational {
+  if a.numerator < 0 {
+    Rational { numerator: -a.denominator, denominator: -a.numerator }
+  } else if a.numerator > 0 {
+    Rational { numerator: a.denominator, denominator: a.numerator }
+  } else {
+    error @"Denominator cannot be 0"
+  }
+}
+
+test recip_1() {
+  let a =
+    div_int(2, 3) |> recip
+  a == Rational { numerator: 3, denominator: 2 }
+}
+
+test recip_2() {
+  let a =
+    div_int(-2, 3) |> recip
+  a == Rational { numerator: -3, denominator: 2 }
+}
+
+// Reduce a rational to its irreducible form
+pub fn reduce(a: Rational) -> Rational {
+  if a.denominator == 0 {
+    error @"Denominator cannot be 0"
+  } else {
+    let d =
+      gcd(a.numerator, a.denominator)
+    Rational { numerator: a.numerator / d, denominator: a.denominator / d }
+  }
+}
+
+test reduce_1() {
+  let a =
+    div_int(5040, 18018) |> reduce
+  a == Rational { numerator: 40, denominator: 143 }
+}
+
+test reduce_2() {
+  let a =
+    div_int(-20, 4) |> reduce
+  a == Rational { numerator: -5, denominator: 1 }
+}
+
+fn gcd(a: Int, b: Int) -> Int {
+  do_gcd(math.abs(a), math.abs(b))
+}
+
+fn do_gcd(a: Int, b: Int) -> Int {
+  if b == 0 {
+    a
+  } else {
+    do_gcd(b, a % b)
+  }
+}