[MLIR][Presburger] Fix reduce bug in Fraction class and add tests (#68298)

Modified `Fraction.reduce()` to work with negative fractions as well.
Added tests to verify the implementation of arithmetic and relational
operators on Fractions.

Author: Abhinav271828

mlir/include/mlir/Analysis/Presburger/Fraction.h

@@ -30,15 +30,17 @@ struct Fraction {
   Fraction() = default;
 
   /// Construct a Fraction from a numerator and denominator.
-  Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1)) : num(oNum), den(oDen) {
+  Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1))
+      : num(oNum), den(oDen) {
     if (den < 0) {
       num = -num;
       den = -den;
     }
   }
   /// Overloads for passing literals.
   Fraction(const MPInt &num, int64_t den = 1) : Fraction(num, MPInt(den)) {}
-  Fraction(int64_t num, const MPInt &den = MPInt(1)) : Fraction(MPInt(num), den) {}
+  Fraction(int64_t num, const MPInt &den = MPInt(1))
+      : Fraction(MPInt(num), den) {}
   Fraction(int64_t num, int64_t den) : Fraction(MPInt(num), MPInt(den)) {}
 
   // Return the value of the fraction as an integer. This should only be called
@@ -102,7 +104,7 @@ inline bool operator>=(const Fraction &x, const Fraction &y) {
 inline Fraction reduce(const Fraction &f) {
   if (f == Fraction(0))
     return Fraction(0, 1);
-  MPInt g = gcd(f.num, f.den);
+  MPInt g = gcd(abs(f.num), abs(f.den));
   return Fraction(f.num / g, f.den / g);
 }
 
@@ -122,22 +124,22 @@ inline Fraction operator-(const Fraction &x, const Fraction &y) {
   return reduce(Fraction(x.num * y.den - x.den * y.num, x.den * y.den));
 }
 
-inline Fraction& operator+=(Fraction &x, const Fraction &y) {
+inline Fraction &operator+=(Fraction &x, const Fraction &y) {
   x = x + y;
   return x;
 }
 
-inline Fraction& operator-=(Fraction &x, const Fraction &y) {
+inline Fraction &operator-=(Fraction &x, const Fraction &y) {
   x = x - y;
   return x;
 }
 
-inline Fraction& operator/=(Fraction &x, const Fraction &y) {
+inline Fraction &operator/=(Fraction &x, const Fraction &y) {
   x = x / y;
   return x;
 }
 
-inline Fraction& operator*=(Fraction &x, const Fraction &y) {
+inline Fraction &operator*=(Fraction &x, const Fraction &y) {
   x = x * y;
   return x;
 }

mlir/unittests/Analysis/Presburger/CMakeLists.txt

@@ -1,4 +1,5 @@
 add_mlir_unittest(MLIRPresburgerTests
+  FractionTest.cpp
   IntegerPolyhedronTest.cpp
   IntegerRelationTest.cpp
   LinearTransformTest.cpp

mlir/unittests/Analysis/Presburger/FractionTest.cpp

@@ -0,0 +1,51 @@
+#include "mlir/Analysis/Presburger/Fraction.h"
+#include "./Utils.h"
+#include <gmock/gmock.h>
+#include <gtest/gtest.h>
+
+using namespace mlir;
+using namespace presburger;
+
+TEST(FractionTest, getAsInteger) {
+  Fraction f(3, 1);
+  EXPECT_EQ(f.getAsInteger(), MPInt(3));
+}
+
+TEST(FractionTest, nearIntegers) {
+  Fraction f(52, 14);
+
+  EXPECT_EQ(floor(f), 3);
+  EXPECT_EQ(ceil(f), 4);
+}
+
+TEST(FractionTest, reduce) {
+  Fraction f(20, 35), g(-56, 63);
+  EXPECT_EQ(f, Fraction(4, 7));
+  EXPECT_EQ(g, Fraction(-8, 9));
+}
+
+TEST(FractionTest, arithmetic) {
+  Fraction f(3, 4), g(-2, 3);
+
+  EXPECT_EQ(f / g, Fraction(-9, 8));
+  EXPECT_EQ(f * g, Fraction(-1, 2));
+  EXPECT_EQ(f + g, Fraction(1, 12));
+  EXPECT_EQ(f - g, Fraction(17, 12));
+
+  f /= g;
+  EXPECT_EQ(f, Fraction(-9, 8));
+  f *= g;
+  EXPECT_EQ(f, Fraction(3, 4));
+  f += g;
+  EXPECT_EQ(f, Fraction(Fraction(1, 12)));
+  f -= g;
+  EXPECT_EQ(f, Fraction(3, 4));
+}
+
+TEST(FractionTest, relational) {
+  Fraction f(2, 5), g(3, 7);
+  EXPECT_TRUE(f < g);
+  EXPECT_FALSE(g < f);
+
+  EXPECT_EQ(f, Fraction(4, 10));
+}