mlir/unittests/Analysis/Presburger/PWMAFunctionTest.cpp - rust-lang/llvm-project - Git at Google

 //===- PWMAFunctionTest.cpp - Tests for PWMAFunction ----------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 //
 // This file contains tests for PWMAFunction.
 //
 //===----------------------------------------------------------------------===//

 #include "Parser.h"

 #include "mlir/Analysis/Presburger/PWMAFunction.h"
 #include "mlir/Analysis/Presburger/PresburgerRelation.h"
 #include "mlir/IR/MLIRContext.h"

 #include <gmock/gmock.h>
 #include <gtest/gtest.h>

 using namespace mlir;
 using namespace presburger;

 using testing::ElementsAre;

 TEST(PWAFunctionTest, isEqual) {
   // The output expressions are different but it doesn't matter because they are
   // equal in this domain.
   PWMAFunction idAtZeros =
       parsePWMAF({{"(x, y) : (y == 0)", "(x, y) -> (x, y)"},
                   {"(x, y) : (y - 1 >= 0, x == 0)", "(x, y) -> (x, y)"},
                   {"(x, y) : (-y - 1 >= 0, x == 0)", "(x, y) -> (x, y)"}});
   PWMAFunction idAtZeros2 =
       parsePWMAF({{"(x, y) : (y == 0)", "(x, y) -> (x, 20*y)"},
                   {"(x, y) : (y - 1 >= 0, x == 0)", "(x, y) -> (30*x, y)"},
                   {"(x, y) : (-y - 1 > =0, x == 0)", "(x, y) -> (30*x, y)"}});
   EXPECT_TRUE(idAtZeros.isEqual(idAtZeros2));

   PWMAFunction notIdAtZeros = parsePWMAF({
       {"(x, y) : (y == 0)", "(x, y) -> (x, y)"},
       {"(x, y) : (y - 1 >= 0, x == 0)", "(x, y) -> (x, 2*y)"},
       {"(x, y) : (-y - 1 >= 0, x == 0)", "(x, y) -> (x, 2*y)"},
   });
   EXPECT_FALSE(idAtZeros.isEqual(notIdAtZeros));

   // These match at their intersection but one has a bigger domain.
   PWMAFunction idNoNegNegQuadrant =
       parsePWMAF({{"(x, y) : (x >= 0)", "(x, y) -> (x, y)"},
                   {"(x, y) : (-x - 1 >= 0, y >= 0)", "(x, y) -> (x, y)"}});
   PWMAFunction idOnlyPosX = parsePWMAF({
       {"(x, y) : (x >= 0)", "(x, y) -> (x, y)"},
   });
   EXPECT_FALSE(idNoNegNegQuadrant.isEqual(idOnlyPosX));

   // Different representations of the same domain.
   PWMAFunction sumPlusOne = parsePWMAF({
       {"(x, y) : (x >= 0)", "(x, y) -> (x + y + 1)"},
       {"(x, y) : (-x - 1 >= 0, -y - 1 >= 0)", "(x, y) -> (x + y + 1)"},
       {"(x, y) : (-x - 1 >= 0, y >= 0)", "(x, y) -> (x + y + 1)"},
   });
   PWMAFunction sumPlusOne2 = parsePWMAF({
       {"(x, y) : ()", "(x, y) -> (x + y + 1)"},
   });
   EXPECT_TRUE(sumPlusOne.isEqual(sumPlusOne2));

   // Functions with zero input dimensions.
   PWMAFunction noInputs1 = parsePWMAF({
       {"() : ()", "() -> (1)"},
   });
   PWMAFunction noInputs2 = parsePWMAF({
       {"() : ()", "() -> (2)"},
   });
   EXPECT_TRUE(noInputs1.isEqual(noInputs1));
   EXPECT_FALSE(noInputs1.isEqual(noInputs2));

   // Mismatched dimensionalities.
   EXPECT_FALSE(noInputs1.isEqual(sumPlusOne));
   EXPECT_FALSE(idOnlyPosX.isEqual(sumPlusOne));

   // Divisions.
   // Domain is only multiples of 6; x = 6k for some k.
   // x + 4(x/2) + 4(x/3) == 26k.
   PWMAFunction mul2AndMul3 = parsePWMAF({
       {"(x) : (x - 2*(x floordiv 2) == 0, x - 3*(x floordiv 3) == 0)",
        "(x) -> (x + 4 * (x floordiv 2) + 4 * (x floordiv 3))"},
   });
   PWMAFunction mul6 = parsePWMAF({
       {"(x) : (x - 6*(x floordiv 6) == 0)", "(x) -> (26 * (x floordiv 6))"},
   });
   EXPECT_TRUE(mul2AndMul3.isEqual(mul6));

   PWMAFunction mul6diff = parsePWMAF({
       {"(x) : (x - 5*(x floordiv 5) == 0)", "(x) -> (52 * (x floordiv 6))"},
   });
   EXPECT_FALSE(mul2AndMul3.isEqual(mul6diff));

   PWMAFunction mul5 = parsePWMAF({
       {"(x) : (x - 5*(x floordiv 5) == 0)", "(x) -> (26 * (x floordiv 5))"},
   });
   EXPECT_FALSE(mul2AndMul3.isEqual(mul5));
 }

 TEST(PWMAFunction, valueAt) {
   PWMAFunction nonNegPWMAF = parsePWMAF(
       {{"(x, y) : (x >= 0)", "(x, y) -> (x + 2*y + 3, 3*x + 4*y + 5)"},
        {"(x, y) : (y >= 0, -x - 1 >= 0)",
         "(x, y) -> (-x + 2*y + 3, -3*x + 4*y + 5)"}});
   EXPECT_THAT(*nonNegPWMAF.valueAt({2, 3}), ElementsAre(11, 23));
   EXPECT_THAT(*nonNegPWMAF.valueAt({-2, 3}), ElementsAre(11, 23));
   EXPECT_THAT(*nonNegPWMAF.valueAt({2, -3}), ElementsAre(-1, -1));
   EXPECT_FALSE(nonNegPWMAF.valueAt({-2, -3}).has_value());

   PWMAFunction divPWMAF = parsePWMAF(
       {{"(x, y) : (x >= 0, x - 2*(x floordiv 2) == 0)",
         "(x, y) -> (2*y + (x floordiv 2) + 3, 4*y + 3*(x floordiv 2) + 5)"},
        {"(x, y) : (y >= 0, -x - 1 >= 0)",
         "(x, y) -> (-x + 2*y + 3, -3*x + 4*y + 5)"}});
   EXPECT_THAT(*divPWMAF.valueAt({4, 3}), ElementsAre(11, 23));
   EXPECT_THAT(*divPWMAF.valueAt({4, -3}), ElementsAre(-1, -1));
   EXPECT_FALSE(divPWMAF.valueAt({3, 3}).has_value());
   EXPECT_FALSE(divPWMAF.valueAt({3, -3}).has_value());

   EXPECT_THAT(*divPWMAF.valueAt({-2, 3}), ElementsAre(11, 23));
   EXPECT_FALSE(divPWMAF.valueAt({-2, -3}).has_value());
 }

 TEST(PWMAFunction, removeIdRangeRegressionTest) {
   PWMAFunction pwmafA = parsePWMAF({
       {"(x, y) : (x == 0, y == 0, x - 2*(x floordiv 2) == 0, y - 2*(y floordiv "
        "2) == 0)",
        "(x, y) -> (0, 0)"},
   });
   PWMAFunction pwmafB = parsePWMAF({
       {"(x, y) : (x - 11*y == 0, 11*x - y == 0, x - 2*(x floordiv 2) == 0, "
        "y - 2*(y floordiv 2) == 0)",
        "(x, y) -> (0, 0)"},
   });
   EXPECT_TRUE(pwmafA.isEqual(pwmafB));
 }

 TEST(PWMAFunction, eliminateRedundantLocalIdRegressionTest) {
   PWMAFunction pwmafA = parsePWMAF({
       {"(x, y) : (x - 2*(x floordiv 2) == 0, x - 2*y == 0)", "(x, y) -> (y)"},
   });
   PWMAFunction pwmafB = parsePWMAF({
       {"(x, y) : (x - 2*(x floordiv 2) == 0, x - 2*y == 0)",
        "(x, y) -> (x - y)"},
   });
   EXPECT_TRUE(pwmafA.isEqual(pwmafB));
 }

 TEST(PWMAFunction, unionLexMaxSimple) {
   // func2 is better than func1, but func2's domain is empty.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : ()", "(x) -> (1)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : (1 == 0)", "(x) -> (2)"},
     });

     EXPECT_TRUE(func1.unionLexMax(func2).isEqual(func1));
     EXPECT_TRUE(func2.unionLexMax(func1).isEqual(func1));
   }

   // func2 is better than func1 on a subset of func1.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : ()", "(x) -> (1)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (2)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x) : (-1 - x >= 0)", "(x) -> (1)"},
         {"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (2)"},
         {"(x) : (x - 11 >= 0)", "(x) -> (1)"},
     });

     EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
   }

   // func1 and func2 are defined over the whole domain with different outputs.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : ()", "(x) -> (x)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : ()", "(x) -> (-x)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x) : (x >= 0)", "(x) -> (x)"},
         {"(x) : (-1 - x >= 0)", "(x) -> (-x)"},
     });

     EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
   }

   // func1 and func2 have disjoint domains.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (1)"},
         {"(x) : (x - 71 >= 0, 80 - x >= 0)", "(x) -> (1)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : (x - 20 >= 0, 41 - x >= 0)", "(x) -> (2)"},
         {"(x) : (x - 101 >= 0, 120 - x >= 0)", "(x) -> (2)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (1)"},
         {"(x) : (x - 71 >= 0, 80 - x >= 0)", "(x) -> (1)"},
         {"(x) : (x - 20 >= 0, 41 - x >= 0)", "(x) -> (2)"},
         {"(x) : (x - 101 >= 0, 120 - x >= 0)", "(x) -> (2)"},
     });

     EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
   }
 }

 TEST(PWMAFunction, unionLexMinSimple) {
   // func2 is better than func1, but func2's domain is empty.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : ()", "(x) -> (-1)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : (1 == 0)", "(x) -> (-2)"},
     });

     EXPECT_TRUE(func1.unionLexMin(func2).isEqual(func1));
     EXPECT_TRUE(func2.unionLexMin(func1).isEqual(func1));
   }

   // func2 is better than func1 on a subset of func1.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : ()", "(x) -> (-1)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (-2)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x) : (-1 - x >= 0)", "(x) -> (-1)"},
         {"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (-2)"},
         {"(x) : (x - 11 >= 0)", "(x) -> (-1)"},
     });

     EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
   }

   // func1 and func2 are defined over the whole domain with different outputs.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : ()", "(x) -> (-x)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : ()", "(x) -> (x)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x) : (x >= 0)", "(x) -> (-x)"},
         {"(x) : (-1 - x >= 0)", "(x) -> (x)"},
     });

     EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
   }
 }

 TEST(PWMAFunction, unionLexMaxComplex) {
   // Union of function containing 4 different pieces of output.
   //
   // x >= 21               --> func1 (func2 not defined)
   // x <= 0                --> func2 (func1 not defined)
   // 10 <= x <= 20, y >  0 --> func1 (x + y  > x - y for y >  0)
   // 10 <= x <= 20, y <= 0 --> func2 (x + y <= x - y for y <= 0)
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x, y) : (x >= 10)", "(x, y) -> (x + y)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x, y) : (x <= 20)", "(x, y) -> (x - y)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x, y) : (x >= 10, x <= 20, y >= 1)", "(x, y) -> (x + y)"},
         {"(x, y) : (x >= 21)", "(x, y) -> (x + y)"},
         {"(x, y) : (x <= 9)", "(x, y) -> (x - y)"},
         {"(x, y) : (x >= 10, x <= 20, y <= 0)", "(x, y) -> (x - y)"},
     });

     EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
   }

   // Functions with more than one output, with contribution from both functions.
   //
   // If y >= 1, func1 is better because in the first output,
   // x + y (func1) > x (func2), when y >= 1
   //
   // If y == 0, the first output is same for both functions, so we look at the
   // second output. -2x + 4 (func1) > 2x - 2 (func2) when 0 <= x <= 1, so we
   // take func1 for this domain and func2 for the remaining.
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x, y) : (x >= 0, y >= 0)", "(x, y) -> (x + y, -2*x + 4)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x, y) : (x >= 0, y >= 0)", "(x, y) -> (x, 2*x - 2)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x, y) : (x >= 0, y >= 1)", "(x, y) -> (x + y, -2*x + 4)"},
         {"(x, y) : (x >= 0, x <= 1, y == 0)", "(x, y) -> (x + y, -2*x + 4)"},
         {"(x, y) : (x >= 2, y == 0)", "(x, y) -> (x, 2*x - 2)"},
     });

     EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
   }

   // Function with three boolean variables `a, b, c` used to control which
   // output will be taken lexicographically.
   //
   // a == 1                 --> Take func2
   // a == 0, b == 1         --> Take func1
   // a == 0, b == 0, c == 1 --> Take func2
   {
     PWMAFunction func1 = parsePWMAF({
         {"(a, b, c) : (a >= 0, 1 - a >= 0, b >= 0, 1 - b >= 0, c "
          ">= 0, 1 - c >= 0)",
          "(a, b, c) -> (0, b, 0)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(a, b, c) : (a >= 0, 1 - a >= 0, b >= 0, 1 - b >= 0, c >= 0, 1 - "
          "c >= 0)",
          "(a, b, c) -> (a, 0, c)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(a, b, c) : (a - 1 == 0, b >= 0, 1 - b >= 0, c >= 0, 1 - c >= 0)",
          "(a, b, c) -> (a, 0, c)"},
         {"(a, b, c) : (a == 0, b - 1 == 0, c >= 0, 1 - c >= 0)",
          "(a, b, c) -> (0, b, 0)"},
         {"(a, b, c) : (a == 0, b == 0, c >= 0, 1 - c >= 0)",
          "(a, b, c) -> (a, 0, c)"},
     });

     EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
     EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
   }
 }

 TEST(PWMAFunction, unionLexMinComplex) {
   // Regression test checking if lexicographic tiebreak produces disjoint
   // domains.
   //
   // If x == 1, func1 is better since in the first output,
   // -x (func1) is < 0 (func2) when x == 1.
   //
   // If x == 0, func1 and func2 both have the same first output. So we take a
   // look at the second output. func2 is better since in the second output,
   // y - 1 (func2) is < y (func1).
   PWMAFunction func1 = parsePWMAF({
       {"(x, y) : (x >= 0, x <= 1, y >= 0, y <= 1)", "(x, y) -> (-x, y)"},
   });

   PWMAFunction func2 = parsePWMAF({
       {"(x, y) : (x >= 0, x <= 1, y >= 0, y <= 1)", "(x, y) -> (0, y - 1)"},
   });

   PWMAFunction result = parsePWMAF({
       {"(x, y) : (x == 1, y >= 0, y <= 1)", "(x, y) -> (-x, y)"},
       {"(x, y) : (x == 0, y >= 0, y <= 1)", "(x, y) -> (0, y - 1)"},
   });

   EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
   EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
 }

 TEST(PWMAFunction, unionLexMinWithDivs) {
   {
     PWMAFunction func1 = parsePWMAF({
         {"(x, y) : (x mod 5 == 0)", "(x, y) -> (x, 1)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x, y) : (x mod 7 == 0)", "(x, y) -> (x + y, 2)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x, y) : (x mod 5 == 0, x mod 7 >= 1)", "(x, y) -> (x, 1)"},
         {"(x, y) : (x mod 7 == 0, x mod 5 >= 1)", "(x, y) -> (x + y, 2)"},
         {"(x, y) : (x mod 5 == 0, x mod 7 == 0, y >= 0)", "(x, y) -> (x, 1)"},
         {"(x, y) : (x mod 7 == 0, x mod 5 == 0, y <= -1)",
          "(x, y) -> (x + y, 2)"},
     });

     EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
   }

   {
     PWMAFunction func1 = parsePWMAF({
         {"(x) : (x >= 0, x <= 1000)", "(x) -> (x floordiv 16)"},
     });

     PWMAFunction func2 = parsePWMAF({
         {"(x) : (x >= 0, x <= 1000)", "(x) -> ((x + 10) floordiv 17)"},
     });

     PWMAFunction result = parsePWMAF({
         {"(x) : (x >= 0, x <= 1000, x floordiv 16 <= (x + 10) floordiv 17)",
          "(x) -> (x floordiv 16)"},
         {"(x) : (x >= 0, x <= 1000, x floordiv 16 >= (x + 10) floordiv 17 + 1)",
          "(x) -> ((x + 10) floordiv 17)"},
     });

     EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
   }
 }
	//===- PWMAFunctionTest.cpp - Tests for PWMAFunction ----------------------===//
	//
	// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
	// See https://llvm.org/LICENSE.txt for license information.
	// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
	//
	//===----------------------------------------------------------------------===//
	//
	// This file contains tests for PWMAFunction.
	//
	//===----------------------------------------------------------------------===//

	#include "Parser.h"

	#include "mlir/Analysis/Presburger/PWMAFunction.h"
	#include "mlir/Analysis/Presburger/PresburgerRelation.h"
	#include "mlir/IR/MLIRContext.h"

	#include <gmock/gmock.h>
	#include <gtest/gtest.h>

	using namespace mlir;
	using namespace presburger;

	using testing::ElementsAre;

	TEST(PWAFunctionTest, isEqual) {
	// The output expressions are different but it doesn't matter because they are
	// equal in this domain.
	PWMAFunction idAtZeros =
	parsePWMAF({{"(x, y) : (y == 0)", "(x, y) -> (x, y)"},
	{"(x, y) : (y - 1 >= 0, x == 0)", "(x, y) -> (x, y)"},
	{"(x, y) : (-y - 1 >= 0, x == 0)", "(x, y) -> (x, y)"}});
	PWMAFunction idAtZeros2 =
	parsePWMAF({{"(x, y) : (y == 0)", "(x, y) -> (x, 20*y)"},
	{"(x, y) : (y - 1 >= 0, x == 0)", "(x, y) -> (30*x, y)"},
	{"(x, y) : (-y - 1 > =0, x == 0)", "(x, y) -> (30*x, y)"}});
	EXPECT_TRUE(idAtZeros.isEqual(idAtZeros2));

	PWMAFunction notIdAtZeros = parsePWMAF({
	{"(x, y) : (y == 0)", "(x, y) -> (x, y)"},
	{"(x, y) : (y - 1 >= 0, x == 0)", "(x, y) -> (x, 2*y)"},
	{"(x, y) : (-y - 1 >= 0, x == 0)", "(x, y) -> (x, 2*y)"},
	});
	EXPECT_FALSE(idAtZeros.isEqual(notIdAtZeros));

	// These match at their intersection but one has a bigger domain.
	PWMAFunction idNoNegNegQuadrant =
	parsePWMAF({{"(x, y) : (x >= 0)", "(x, y) -> (x, y)"},
	{"(x, y) : (-x - 1 >= 0, y >= 0)", "(x, y) -> (x, y)"}});
	PWMAFunction idOnlyPosX = parsePWMAF({
	{"(x, y) : (x >= 0)", "(x, y) -> (x, y)"},
	});
	EXPECT_FALSE(idNoNegNegQuadrant.isEqual(idOnlyPosX));

	// Different representations of the same domain.
	PWMAFunction sumPlusOne = parsePWMAF({
	{"(x, y) : (x >= 0)", "(x, y) -> (x + y + 1)"},
	{"(x, y) : (-x - 1 >= 0, -y - 1 >= 0)", "(x, y) -> (x + y + 1)"},
	{"(x, y) : (-x - 1 >= 0, y >= 0)", "(x, y) -> (x + y + 1)"},
	});
	PWMAFunction sumPlusOne2 = parsePWMAF({
	{"(x, y) : ()", "(x, y) -> (x + y + 1)"},
	});
	EXPECT_TRUE(sumPlusOne.isEqual(sumPlusOne2));

	// Functions with zero input dimensions.
	PWMAFunction noInputs1 = parsePWMAF({
	{"() : ()", "() -> (1)"},
	});
	PWMAFunction noInputs2 = parsePWMAF({
	{"() : ()", "() -> (2)"},
	});
	EXPECT_TRUE(noInputs1.isEqual(noInputs1));
	EXPECT_FALSE(noInputs1.isEqual(noInputs2));

	// Mismatched dimensionalities.
	EXPECT_FALSE(noInputs1.isEqual(sumPlusOne));
	EXPECT_FALSE(idOnlyPosX.isEqual(sumPlusOne));

	// Divisions.
	// Domain is only multiples of 6; x = 6k for some k.
	// x + 4(x/2) + 4(x/3) == 26k.
	PWMAFunction mul2AndMul3 = parsePWMAF({
	{"(x) : (x - 2(x floordiv 2) == 0, x - 3(x floordiv 3) == 0)",
	"(x) -> (x + 4 * (x floordiv 2) + 4 * (x floordiv 3))"},
	});
	PWMAFunction mul6 = parsePWMAF({
	{"(x) : (x - 6(x floordiv 6) == 0)", "(x) -> (26 (x floordiv 6))"},
	});
	EXPECT_TRUE(mul2AndMul3.isEqual(mul6));

	PWMAFunction mul6diff = parsePWMAF({
	{"(x) : (x - 5(x floordiv 5) == 0)", "(x) -> (52 (x floordiv 6))"},
	});
	EXPECT_FALSE(mul2AndMul3.isEqual(mul6diff));

	PWMAFunction mul5 = parsePWMAF({
	{"(x) : (x - 5(x floordiv 5) == 0)", "(x) -> (26 (x floordiv 5))"},
	});
	EXPECT_FALSE(mul2AndMul3.isEqual(mul5));
	}

	TEST(PWMAFunction, valueAt) {
	PWMAFunction nonNegPWMAF = parsePWMAF(
	{{"(x, y) : (x >= 0)", "(x, y) -> (x + 2y + 3, 3x + 4*y + 5)"},
	{"(x, y) : (y >= 0, -x - 1 >= 0)",
	"(x, y) -> (-x + 2y + 3, -3x + 4*y + 5)"}});
	EXPECT_THAT(*nonNegPWMAF.valueAt({2, 3}), ElementsAre(11, 23));
	EXPECT_THAT(*nonNegPWMAF.valueAt({-2, 3}), ElementsAre(11, 23));
	EXPECT_THAT(*nonNegPWMAF.valueAt({2, -3}), ElementsAre(-1, -1));
	EXPECT_FALSE(nonNegPWMAF.valueAt({-2, -3}).has_value());

	PWMAFunction divPWMAF = parsePWMAF(
	{{"(x, y) : (x >= 0, x - 2*(x floordiv 2) == 0)",
	"(x, y) -> (2y + (x floordiv 2) + 3, 4y + 3*(x floordiv 2) + 5)"},
	{"(x, y) : (y >= 0, -x - 1 >= 0)",
	"(x, y) -> (-x + 2y + 3, -3x + 4*y + 5)"}});
	EXPECT_THAT(*divPWMAF.valueAt({4, 3}), ElementsAre(11, 23));
	EXPECT_THAT(*divPWMAF.valueAt({4, -3}), ElementsAre(-1, -1));
	EXPECT_FALSE(divPWMAF.valueAt({3, 3}).has_value());
	EXPECT_FALSE(divPWMAF.valueAt({3, -3}).has_value());

	EXPECT_THAT(*divPWMAF.valueAt({-2, 3}), ElementsAre(11, 23));
	EXPECT_FALSE(divPWMAF.valueAt({-2, -3}).has_value());
	}

	TEST(PWMAFunction, removeIdRangeRegressionTest) {
	PWMAFunction pwmafA = parsePWMAF({
	{"(x, y) : (x == 0, y == 0, x - 2(x floordiv 2) == 0, y - 2(y floordiv "
	"2) == 0)",
	"(x, y) -> (0, 0)"},
	});
	PWMAFunction pwmafB = parsePWMAF({
	{"(x, y) : (x - 11y == 0, 11x - y == 0, x - 2*(x floordiv 2) == 0, "
	"y - 2*(y floordiv 2) == 0)",
	"(x, y) -> (0, 0)"},
	});
	EXPECT_TRUE(pwmafA.isEqual(pwmafB));
	}

	TEST(PWMAFunction, eliminateRedundantLocalIdRegressionTest) {
	PWMAFunction pwmafA = parsePWMAF({
	{"(x, y) : (x - 2(x floordiv 2) == 0, x - 2y == 0)", "(x, y) -> (y)"},
	});
	PWMAFunction pwmafB = parsePWMAF({
	{"(x, y) : (x - 2(x floordiv 2) == 0, x - 2y == 0)",
	"(x, y) -> (x - y)"},
	});
	EXPECT_TRUE(pwmafA.isEqual(pwmafB));
	}

	TEST(PWMAFunction, unionLexMaxSimple) {
	// func2 is better than func1, but func2's domain is empty.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : ()", "(x) -> (1)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : (1 == 0)", "(x) -> (2)"},
	});

	EXPECT_TRUE(func1.unionLexMax(func2).isEqual(func1));
	EXPECT_TRUE(func2.unionLexMax(func1).isEqual(func1));
	}

	// func2 is better than func1 on a subset of func1.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : ()", "(x) -> (1)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (2)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x) : (-1 - x >= 0)", "(x) -> (1)"},
	{"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (2)"},
	{"(x) : (x - 11 >= 0)", "(x) -> (1)"},
	});

	EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
	}

	// func1 and func2 are defined over the whole domain with different outputs.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : ()", "(x) -> (x)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : ()", "(x) -> (-x)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x) : (x >= 0)", "(x) -> (x)"},
	{"(x) : (-1 - x >= 0)", "(x) -> (-x)"},
	});

	EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
	}

	// func1 and func2 have disjoint domains.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (1)"},
	{"(x) : (x - 71 >= 0, 80 - x >= 0)", "(x) -> (1)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : (x - 20 >= 0, 41 - x >= 0)", "(x) -> (2)"},
	{"(x) : (x - 101 >= 0, 120 - x >= 0)", "(x) -> (2)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (1)"},
	{"(x) : (x - 71 >= 0, 80 - x >= 0)", "(x) -> (1)"},
	{"(x) : (x - 20 >= 0, 41 - x >= 0)", "(x) -> (2)"},
	{"(x) : (x - 101 >= 0, 120 - x >= 0)", "(x) -> (2)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
	}
	}

	TEST(PWMAFunction, unionLexMinSimple) {
	// func2 is better than func1, but func2's domain is empty.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : ()", "(x) -> (-1)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : (1 == 0)", "(x) -> (-2)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(func1));
	EXPECT_TRUE(func2.unionLexMin(func1).isEqual(func1));
	}

	// func2 is better than func1 on a subset of func1.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : ()", "(x) -> (-1)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (-2)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x) : (-1 - x >= 0)", "(x) -> (-1)"},
	{"(x) : (x >= 0, 10 - x >= 0)", "(x) -> (-2)"},
	{"(x) : (x - 11 >= 0)", "(x) -> (-1)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
	}

	// func1 and func2 are defined over the whole domain with different outputs.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : ()", "(x) -> (-x)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : ()", "(x) -> (x)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x) : (x >= 0)", "(x) -> (-x)"},
	{"(x) : (-1 - x >= 0)", "(x) -> (x)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
	}
	}

	TEST(PWMAFunction, unionLexMaxComplex) {
	// Union of function containing 4 different pieces of output.
	//
	// x >= 21 --> func1 (func2 not defined)
	// x <= 0 --> func2 (func1 not defined)
	// 10 <= x <= 20, y > 0 --> func1 (x + y > x - y for y > 0)
	// 10 <= x <= 20, y <= 0 --> func2 (x + y <= x - y for y <= 0)
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x, y) : (x >= 10)", "(x, y) -> (x + y)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x, y) : (x <= 20)", "(x, y) -> (x - y)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x, y) : (x >= 10, x <= 20, y >= 1)", "(x, y) -> (x + y)"},
	{"(x, y) : (x >= 21)", "(x, y) -> (x + y)"},
	{"(x, y) : (x <= 9)", "(x, y) -> (x - y)"},
	{"(x, y) : (x >= 10, x <= 20, y <= 0)", "(x, y) -> (x - y)"},
	});

	EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
	}

	// Functions with more than one output, with contribution from both functions.
	//
	// If y >= 1, func1 is better because in the first output,
	// x + y (func1) > x (func2), when y >= 1
	//
	// If y == 0, the first output is same for both functions, so we look at the
	// second output. -2x + 4 (func1) > 2x - 2 (func2) when 0 <= x <= 1, so we
	// take func1 for this domain and func2 for the remaining.
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x, y) : (x >= 0, y >= 0)", "(x, y) -> (x + y, -2*x + 4)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x, y) : (x >= 0, y >= 0)", "(x, y) -> (x, 2*x - 2)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x, y) : (x >= 0, y >= 1)", "(x, y) -> (x + y, -2*x + 4)"},
	{"(x, y) : (x >= 0, x <= 1, y == 0)", "(x, y) -> (x + y, -2*x + 4)"},
	{"(x, y) : (x >= 2, y == 0)", "(x, y) -> (x, 2*x - 2)"},
	});

	EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
	}

	// Function with three boolean variables `a, b, c` used to control which
	// output will be taken lexicographically.
	//
	// a == 1 --> Take func2
	// a == 0, b == 1 --> Take func1
	// a == 0, b == 0, c == 1 --> Take func2
	{
	PWMAFunction func1 = parsePWMAF({
	{"(a, b, c) : (a >= 0, 1 - a >= 0, b >= 0, 1 - b >= 0, c "
	">= 0, 1 - c >= 0)",
	"(a, b, c) -> (0, b, 0)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(a, b, c) : (a >= 0, 1 - a >= 0, b >= 0, 1 - b >= 0, c >= 0, 1 - "
	"c >= 0)",
	"(a, b, c) -> (a, 0, c)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(a, b, c) : (a - 1 == 0, b >= 0, 1 - b >= 0, c >= 0, 1 - c >= 0)",
	"(a, b, c) -> (a, 0, c)"},
	{"(a, b, c) : (a == 0, b - 1 == 0, c >= 0, 1 - c >= 0)",
	"(a, b, c) -> (0, b, 0)"},
	{"(a, b, c) : (a == 0, b == 0, c >= 0, 1 - c >= 0)",
	"(a, b, c) -> (a, 0, c)"},
	});

	EXPECT_TRUE(func1.unionLexMax(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMax(func1).isEqual(result));
	}
	}

	TEST(PWMAFunction, unionLexMinComplex) {
	// Regression test checking if lexicographic tiebreak produces disjoint
	// domains.
	//
	// If x == 1, func1 is better since in the first output,
	// -x (func1) is < 0 (func2) when x == 1.
	//
	// If x == 0, func1 and func2 both have the same first output. So we take a
	// look at the second output. func2 is better since in the second output,
	// y - 1 (func2) is < y (func1).
	PWMAFunction func1 = parsePWMAF({
	{"(x, y) : (x >= 0, x <= 1, y >= 0, y <= 1)", "(x, y) -> (-x, y)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x, y) : (x >= 0, x <= 1, y >= 0, y <= 1)", "(x, y) -> (0, y - 1)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x, y) : (x == 1, y >= 0, y <= 1)", "(x, y) -> (-x, y)"},
	{"(x, y) : (x == 0, y >= 0, y <= 1)", "(x, y) -> (0, y - 1)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
	EXPECT_TRUE(func2.unionLexMin(func1).isEqual(result));
	}

	TEST(PWMAFunction, unionLexMinWithDivs) {
	{
	PWMAFunction func1 = parsePWMAF({
	{"(x, y) : (x mod 5 == 0)", "(x, y) -> (x, 1)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x, y) : (x mod 7 == 0)", "(x, y) -> (x + y, 2)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x, y) : (x mod 5 == 0, x mod 7 >= 1)", "(x, y) -> (x, 1)"},
	{"(x, y) : (x mod 7 == 0, x mod 5 >= 1)", "(x, y) -> (x + y, 2)"},
	{"(x, y) : (x mod 5 == 0, x mod 7 == 0, y >= 0)", "(x, y) -> (x, 1)"},
	{"(x, y) : (x mod 7 == 0, x mod 5 == 0, y <= -1)",
	"(x, y) -> (x + y, 2)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
	}

	{
	PWMAFunction func1 = parsePWMAF({
	{"(x) : (x >= 0, x <= 1000)", "(x) -> (x floordiv 16)"},
	});

	PWMAFunction func2 = parsePWMAF({
	{"(x) : (x >= 0, x <= 1000)", "(x) -> ((x + 10) floordiv 17)"},
	});

	PWMAFunction result = parsePWMAF({
	{"(x) : (x >= 0, x <= 1000, x floordiv 16 <= (x + 10) floordiv 17)",
	"(x) -> (x floordiv 16)"},
	{"(x) : (x >= 0, x <= 1000, x floordiv 16 >= (x + 10) floordiv 17 + 1)",
	"(x) -> ((x + 10) floordiv 17)"},
	});

	EXPECT_TRUE(func1.unionLexMin(func2).isEqual(result));
	}
	}