added rational numbers

tests/test_rational.nim

@@ -0,0 +1,96 @@
+import unittest
+from mmath/rational import newRational, `+`, `-`, `*`, `/`, `$`, simplify, gcd, pow, mcm, `==`, `cmp`, `<`, `>`, `<=`, `>=`, abs
+
+suite "Nim rational numbers":
+
+    test "gcd":
+        let a = 14
+        let b = 21
+        check 7 == gcd(a, b)
+
+    test "mcm":
+        let a = 14
+        let b = 21
+        check 42 == mcm(a, b)
+
+    test "pow":
+        check 625 == pow(5, 4)
+
+    test "==":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(5, 15)        
+        let r3 = newRational(35, 105)
+        check r1 == r2
+        check r1 == r3
+        check r2 == r3
+
+    test "+":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 + r2
+        check r3 == newRational(1)
+
+    test "-":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 - r2
+        check r3 == newRational(-1, 3)
+
+    test "*":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 * r2
+        check r3 == newRational(2, 9)
+
+    test "/":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 / r2
+        check r3 == newRational(1, 2)
+
+    test "simplify":
+        var r1 = newRational(65, 169)
+        check r1 == newRational(5, 13)
+        r1.simplify()
+        check r1.num == 5
+        check r1.den == 13
+
+    test "pow":
+        let r1 = newRational(65, 169)
+        let r2 = r1.pow(2)
+        check r2 == newRational(25, 169)
+
+    test "cmp":
+        let r1 = newRational(65, 169)
+        let r2 = newRational(5, 13)
+        let r3 = newRational(6, 13)
+        check r1 < r3
+        check r3 > r1
+        check r1 <= r3
+        check r1 <= r2
+        check r3 >= r1
+        check r2 >= r1
+        check r2 == r1
+
+    test "abs":
+        let r1 = newRational(-65, -169)
+        let r2 = newRational(65, -169)
+        check r1 == r1.abs()
+        check r1 == r2.abs()
+        check r1 != r2
+
+    test "i64":
+        let p1 = 32452867i64
+        let p2 = 49979687i64
+        let p3 = 15485867i64
+        let r1 = newRational(p3, p1 * p2)
+        let r2 = newRational(p2, p1 * p3)
+        var r3 = newRational(p2, p2 * p3)
+        check newRational(1i64, p3) == r3
+        r3.simplify()
+        check r3.num == 1i64
+        check r3.den == p3
+        expect(OverflowDefect):
+            discard r1 / r2
+        expect(OverflowDefect):
+            discard r1 + r2