//===- 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 #include 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)); } }