internal/ceres/codegen/expression_test.cc - ceres-solver - Git at Google


            
            // Ceres Solver - A fast non-linear least squares minimizer

            
            // Copyright 2019 Google Inc. All rights reserved.

            
            // http://code.google.com/p/ceres-solver/

            
            //

            
            // Redistribution and use in source and binary forms, with or without

            
            // modification, are permitted provided that the following conditions are met:

            
            //

            
            // * Redistributions of source code must retain the above copyright notice,

            
            //   this list of conditions and the following disclaimer.

            
            // * Redistributions in binary form must reproduce the above copyright notice,

            
            //   this list of conditions and the following disclaimer in the documentation

            
            //   and/or other materials provided with the distribution.

            
            // * Neither the name of Google Inc. nor the names of its contributors may be

            
            //   used to endorse or promote products derived from this software without

            
            //   specific prior written permission.

            
            //

            
            // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"

            
            // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

            
            // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

            
            // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE

            
            // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR

            
            // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF

            
            // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS

            
            // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN

            
            // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)

            
            // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE

            
            // POSSIBILITY OF SUCH DAMAGE.

            
            //

            
            // Author: darius.rueckert@fau.de (Darius Rueckert)

            
            //

            
            // This file tests the Expression class. For each member function one test is

            
            // included here.

            
            //

            
            #include "ceres/codegen/internal/expression.h"

            
            #include "gtest/gtest.h"


            namespace ceres {

            
            namespace internal {


            TEST(Expression, ConstructorAndAccessors) {

            
              Expression expr(ExpressionType::LOGICAL_NEGATION,

            
                              ExpressionReturnType::BOOLEAN,

            
                              12345,

            
                              {1, 5, 8, 10},

            
                              "TestConstructor",

            
                              57.25);

            
              EXPECT_EQ(expr.type(), ExpressionType::LOGICAL_NEGATION);

            
              EXPECT_EQ(expr.return_type(), ExpressionReturnType::BOOLEAN);

            
              EXPECT_EQ(expr.lhs_id(), 12345);

            
              EXPECT_EQ(expr.arguments(), std::vector<ExpressionId>({1, 5, 8, 10}));

            
              EXPECT_EQ(expr.name(), "TestConstructor");

            
              EXPECT_EQ(expr.value(), 57.25);

            
            }


            TEST(Expression, CreateFunctions) {

            
              // The default constructor creates a NOP!

            
              EXPECT_EQ(Expression(),

            
                        Expression(ExpressionType::NOP,

            
                                   ExpressionReturnType::VOID,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "",

            
                                   0));


              EXPECT_EQ(Expression::CreateCompileTimeConstant(72),

            
                        Expression(ExpressionType::COMPILE_TIME_CONSTANT,

            
                                   ExpressionReturnType::SCALAR,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "",

            
                                   72));


              EXPECT_EQ(Expression::CreateInputAssignment("arguments[0][0]"),

            
                        Expression(ExpressionType::INPUT_ASSIGNMENT,

            
                                   ExpressionReturnType::SCALAR,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "arguments[0][0]",

            
                                   0));


              EXPECT_EQ(Expression::CreateOutputAssignment(ExpressionId(5), "residuals[3]"),

            
                        Expression(ExpressionType::OUTPUT_ASSIGNMENT,

            
                                   ExpressionReturnType::SCALAR,

            
                                   kInvalidExpressionId,

            
                                   {5},

            
                                   "residuals[3]",

            
                                   0));


              EXPECT_EQ(Expression::CreateAssignment(ExpressionId(3), ExpressionId(5)),

            
                        Expression(ExpressionType::ASSIGNMENT,

            
                                   ExpressionReturnType::SCALAR,

            
                                   3,

            
                                   {5},

            
                                   "",

            
                                   0));


              EXPECT_EQ(

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5)),

            
                  Expression(ExpressionType::BINARY_ARITHMETIC,

            
                             ExpressionReturnType::SCALAR,

            
                             kInvalidExpressionId,

            
                             {3, 5},

            
                             "+",

            
                             0));


              EXPECT_EQ(Expression::CreateUnaryArithmetic("-", ExpressionId(5)),

            
                        Expression(ExpressionType::UNARY_ARITHMETIC,

            
                                   ExpressionReturnType::SCALAR,

            
                                   kInvalidExpressionId,

            
                                   {5},

            
                                   "-",

            
                                   0));


              EXPECT_EQ(

            
                  Expression::CreateBinaryCompare("<", ExpressionId(3), ExpressionId(5)),

            
                  Expression(ExpressionType::BINARY_COMPARISON,

            
                             ExpressionReturnType::BOOLEAN,

            
                             kInvalidExpressionId,

            
                             {3, 5},

            
                             "<",

            
                             0));


              EXPECT_EQ(Expression::CreateLogicalNegation(ExpressionId(5)),

            
                        Expression(ExpressionType::LOGICAL_NEGATION,

            
                                   ExpressionReturnType::BOOLEAN,

            
                                   kInvalidExpressionId,

            
                                   {5},

            
                                   "",

            
                                   0));


              EXPECT_EQ(Expression::CreateScalarFunctionCall(

            
                            "pow", {ExpressionId(3), ExpressionId(5)}),

            
                        Expression(ExpressionType::FUNCTION_CALL,

            
                                   ExpressionReturnType::SCALAR,

            
                                   kInvalidExpressionId,

            
                                   {3, 5},

            
                                   "pow",

            
                                   0));


              EXPECT_EQ(

            
                  Expression::CreateLogicalFunctionCall("isfinite", {ExpressionId(3)}),

            
                  Expression(ExpressionType::FUNCTION_CALL,

            
                             ExpressionReturnType::BOOLEAN,

            
                             kInvalidExpressionId,

            
                             {3},

            
                             "isfinite",

            
                             0));


              EXPECT_EQ(Expression::CreateIf(ExpressionId(5)),

            
                        Expression(ExpressionType::IF,

            
                                   ExpressionReturnType::VOID,

            
                                   kInvalidExpressionId,

            
                                   {5},

            
                                   "",

            
                                   0));


              EXPECT_EQ(Expression::CreateElse(),

            
                        Expression(ExpressionType::ELSE,

            
                                   ExpressionReturnType::VOID,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "",

            
                                   0));


              EXPECT_EQ(Expression::CreateEndIf(),

            
                        Expression(ExpressionType::ENDIF,

            
                                   ExpressionReturnType::VOID,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "",

            
                                   0));


              EXPECT_EQ(Expression::CreateComment("Test"),

            
                        Expression(ExpressionType::COMMENT,

            
                                   ExpressionReturnType::VOID,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "Test",

            
                                   0));

            
            }


            TEST(Expression, IsArithmeticExpression) {

            
              ASSERT_TRUE(

            
                  Expression::CreateCompileTimeConstant(5).IsArithmeticExpression());

            
              ASSERT_TRUE(Expression::CreateScalarFunctionCall("pow", {3, 5})

            
                              .IsArithmeticExpression());

            
              // Logical expression are also arithmetic!

            
              ASSERT_TRUE(

            
                  Expression::CreateBinaryCompare("<", 3, 5).IsArithmeticExpression());

            
              ASSERT_FALSE(Expression::CreateIf(5).IsArithmeticExpression());

            
              ASSERT_FALSE(Expression::CreateEndIf().IsArithmeticExpression());

            
              ASSERT_FALSE(Expression().IsArithmeticExpression());

            
            }


            TEST(Expression, IsControlExpression) {

            
              // In the current implementation this is the exact opposite of

            
              // IsArithmeticExpression.

            
              ASSERT_FALSE(Expression::CreateCompileTimeConstant(5).IsControlExpression());

            
              ASSERT_FALSE(Expression::CreateScalarFunctionCall("pow", {3, 5})

            
                               .IsControlExpression());

            
              ASSERT_FALSE(

            
                  Expression::CreateBinaryCompare("<", 3, 5).IsControlExpression());

            
              ASSERT_TRUE(Expression::CreateIf(5).IsControlExpression());

            
              ASSERT_TRUE(Expression::CreateEndIf().IsControlExpression());

            
              ASSERT_TRUE(Expression::CreateComment("Test").IsControlExpression());

            
              ASSERT_TRUE(Expression().IsControlExpression());

            
            }


            TEST(Expression, IsCompileTimeConstantAndEqualTo) {

            
              ASSERT_TRUE(

            
                  Expression::CreateCompileTimeConstant(5).IsCompileTimeConstantAndEqualTo(

            
                      5));

            
              ASSERT_FALSE(

            
                  Expression::CreateCompileTimeConstant(3).IsCompileTimeConstantAndEqualTo(

            
                      5));

            
              ASSERT_FALSE(Expression::CreateBinaryCompare("<", 3, 5)

            
                               .IsCompileTimeConstantAndEqualTo(5));

            
            }


            TEST(Expression, IsReplaceableBy) {

            
              // Create 2 identical expression

            
              auto expr1 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));


              auto expr2 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));


              // They are idendical and of course replaceable

            
              ASSERT_EQ(expr1, expr2);

            
              ASSERT_EQ(expr2, expr1);

            
              ASSERT_TRUE(expr1.IsReplaceableBy(expr2));

            
              ASSERT_TRUE(expr2.IsReplaceableBy(expr1));


              // Give them different left hand sides

            
              expr1.set_lhs_id(72);

            
              expr2.set_lhs_id(42);


              // v_72 = v_3 + v_5

            
              // v_42 = v_3 + v_5

            
              // -> They should be replaceable by each other


              ASSERT_NE(expr1, expr2);

            
              ASSERT_NE(expr2, expr1);


              ASSERT_TRUE(expr1.IsReplaceableBy(expr2));

            
              ASSERT_TRUE(expr2.IsReplaceableBy(expr1));


              // A slightly differnt expression with the argument flipped

            
              auto expr3 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(5), ExpressionId(3));


              ASSERT_NE(expr1, expr3);

            
              ASSERT_FALSE(expr1.IsReplaceableBy(expr3));

            
            }


            TEST(Expression, Replace) {

            
              auto expr1 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

            
              expr1.set_lhs_id(13);


              auto expr2 =

            
                  Expression::CreateAssignment(kInvalidExpressionId, ExpressionId(7));


              // We replace the arithmetic expr1 by an assignment from the variable 7. This

            
              // is the typical usecase in subexpression elimination.

            
              expr1.Replace(expr2);


              // expr1 should now be an assignment from 7 to 13

            
              EXPECT_EQ(expr1,

            
                        Expression(ExpressionType::ASSIGNMENT,

            
                                   ExpressionReturnType::SCALAR,

            
                                   13,

            
                                   {7},

            
                                   "",

            
                                   0));

            
            }


            TEST(Expression, DirectlyDependsOn) {

            
              auto expr1 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));


              ASSERT_TRUE(expr1.DirectlyDependsOn(ExpressionId(3)));

            
              ASSERT_TRUE(expr1.DirectlyDependsOn(ExpressionId(5)));

            
              ASSERT_FALSE(expr1.DirectlyDependsOn(ExpressionId(kInvalidExpressionId)));

            
              ASSERT_FALSE(expr1.DirectlyDependsOn(ExpressionId(42)));

            
            }

            
            TEST(Expression, MakeNop) {

            
              auto expr1 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));


              expr1.MakeNop();


              EXPECT_EQ(expr1,

            
                        Expression(ExpressionType::NOP,

            
                                   ExpressionReturnType::VOID,

            
                                   kInvalidExpressionId,

            
                                   {},

            
                                   "",

            
                                   0));

            
            }


            TEST(Expression, IsSemanticallyEquivalentTo) {

            
              // Create 2 identical expression

            
              auto expr1 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));


              auto expr2 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));


              ASSERT_TRUE(expr1.IsSemanticallyEquivalentTo(expr1));

            
              ASSERT_TRUE(expr1.IsSemanticallyEquivalentTo(expr2));


              auto expr3 =

            
                  Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(8));


              ASSERT_TRUE(expr1.IsSemanticallyEquivalentTo(expr3));


              auto expr4 =

            
                  Expression::CreateBinaryArithmetic("-", ExpressionId(3), ExpressionId(5));


              ASSERT_FALSE(expr1.IsSemanticallyEquivalentTo(expr4));

            
            }


            }  // namespace internal

            
            }  // namespace ceres
	// Ceres Solver - A fast non-linear least squares minimizer
	// Copyright 2019 Google Inc. All rights reserved.
	// http://code.google.com/p/ceres-solver/
	//
	// Redistribution and use in source and binary forms, with or without
	// modification, are permitted provided that the following conditions are met:
	//
	// * Redistributions of source code must retain the above copyright notice,
	// this list of conditions and the following disclaimer.
	// * Redistributions in binary form must reproduce the above copyright notice,
	// this list of conditions and the following disclaimer in the documentation
	// and/or other materials provided with the distribution.
	// * Neither the name of Google Inc. nor the names of its contributors may be
	// used to endorse or promote products derived from this software without
	// specific prior written permission.
	//
	// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
	// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
	// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
	// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
	// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
	// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
	// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
	// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
	// POSSIBILITY OF SUCH DAMAGE.
	//
	// Author: darius.rueckert@fau.de (Darius Rueckert)
	//
	// This file tests the Expression class. For each member function one test is
	// included here.
	//
	#include "ceres/codegen/internal/expression.h"
	#include "gtest/gtest.h"

	namespace ceres {
	namespace internal {

	TEST(Expression, ConstructorAndAccessors) {
	Expression expr(ExpressionType::LOGICAL_NEGATION,
	ExpressionReturnType::BOOLEAN,
	12345,
	{1, 5, 8, 10},
	"TestConstructor",
	57.25);
	EXPECT_EQ(expr.type(), ExpressionType::LOGICAL_NEGATION);
	EXPECT_EQ(expr.return_type(), ExpressionReturnType::BOOLEAN);
	EXPECT_EQ(expr.lhs_id(), 12345);
	EXPECT_EQ(expr.arguments(), std::vector<ExpressionId>({1, 5, 8, 10}));
	EXPECT_EQ(expr.name(), "TestConstructor");
	EXPECT_EQ(expr.value(), 57.25);
	}

	TEST(Expression, CreateFunctions) {
	// The default constructor creates a NOP!
	EXPECT_EQ(Expression(),
	Expression(ExpressionType::NOP,
	ExpressionReturnType::VOID,
	kInvalidExpressionId,
	{},
	"",
	0));

	EXPECT_EQ(Expression::CreateCompileTimeConstant(72),
	Expression(ExpressionType::COMPILE_TIME_CONSTANT,
	ExpressionReturnType::SCALAR,
	kInvalidExpressionId,
	{},
	"",
	72));

	EXPECT_EQ(Expression::CreateInputAssignment("arguments[0][0]"),
	Expression(ExpressionType::INPUT_ASSIGNMENT,
	ExpressionReturnType::SCALAR,
	kInvalidExpressionId,
	{},
	"arguments[0][0]",
	0));

	EXPECT_EQ(Expression::CreateOutputAssignment(ExpressionId(5), "residuals[3]"),
	Expression(ExpressionType::OUTPUT_ASSIGNMENT,
	ExpressionReturnType::SCALAR,
	kInvalidExpressionId,
	{5},
	"residuals[3]",
	0));

	EXPECT_EQ(Expression::CreateAssignment(ExpressionId(3), ExpressionId(5)),
	Expression(ExpressionType::ASSIGNMENT,
	ExpressionReturnType::SCALAR,
	3,
	{5},
	"",
	0));

	EXPECT_EQ(
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5)),
	Expression(ExpressionType::BINARY_ARITHMETIC,
	ExpressionReturnType::SCALAR,
	kInvalidExpressionId,
	{3, 5},
	"+",
	0));

	EXPECT_EQ(Expression::CreateUnaryArithmetic("-", ExpressionId(5)),
	Expression(ExpressionType::UNARY_ARITHMETIC,
	ExpressionReturnType::SCALAR,
	kInvalidExpressionId,
	{5},
	"-",
	0));

	EXPECT_EQ(
	Expression::CreateBinaryCompare("<", ExpressionId(3), ExpressionId(5)),
	Expression(ExpressionType::BINARY_COMPARISON,
	ExpressionReturnType::BOOLEAN,
	kInvalidExpressionId,
	{3, 5},
	"<",
	0));

	EXPECT_EQ(Expression::CreateLogicalNegation(ExpressionId(5)),
	Expression(ExpressionType::LOGICAL_NEGATION,
	ExpressionReturnType::BOOLEAN,
	kInvalidExpressionId,
	{5},
	"",
	0));

	EXPECT_EQ(Expression::CreateScalarFunctionCall(
	"pow", {ExpressionId(3), ExpressionId(5)}),
	Expression(ExpressionType::FUNCTION_CALL,
	ExpressionReturnType::SCALAR,
	kInvalidExpressionId,
	{3, 5},
	"pow",
	0));

	EXPECT_EQ(
	Expression::CreateLogicalFunctionCall("isfinite", {ExpressionId(3)}),
	Expression(ExpressionType::FUNCTION_CALL,
	ExpressionReturnType::BOOLEAN,
	kInvalidExpressionId,
	{3},
	"isfinite",
	0));

	EXPECT_EQ(Expression::CreateIf(ExpressionId(5)),
	Expression(ExpressionType::IF,
	ExpressionReturnType::VOID,
	kInvalidExpressionId,
	{5},
	"",
	0));

	EXPECT_EQ(Expression::CreateElse(),
	Expression(ExpressionType::ELSE,
	ExpressionReturnType::VOID,
	kInvalidExpressionId,
	{},
	"",
	0));

	EXPECT_EQ(Expression::CreateEndIf(),
	Expression(ExpressionType::ENDIF,
	ExpressionReturnType::VOID,
	kInvalidExpressionId,
	{},
	"",
	0));

	EXPECT_EQ(Expression::CreateComment("Test"),
	Expression(ExpressionType::COMMENT,
	ExpressionReturnType::VOID,
	kInvalidExpressionId,
	{},
	"Test",
	0));
	}

	TEST(Expression, IsArithmeticExpression) {
	ASSERT_TRUE(
	Expression::CreateCompileTimeConstant(5).IsArithmeticExpression());
	ASSERT_TRUE(Expression::CreateScalarFunctionCall("pow", {3, 5})
	.IsArithmeticExpression());
	// Logical expression are also arithmetic!
	ASSERT_TRUE(
	Expression::CreateBinaryCompare("<", 3, 5).IsArithmeticExpression());
	ASSERT_FALSE(Expression::CreateIf(5).IsArithmeticExpression());
	ASSERT_FALSE(Expression::CreateEndIf().IsArithmeticExpression());
	ASSERT_FALSE(Expression().IsArithmeticExpression());
	}

	TEST(Expression, IsControlExpression) {
	// In the current implementation this is the exact opposite of
	// IsArithmeticExpression.
	ASSERT_FALSE(Expression::CreateCompileTimeConstant(5).IsControlExpression());
	ASSERT_FALSE(Expression::CreateScalarFunctionCall("pow", {3, 5})
	.IsControlExpression());
	ASSERT_FALSE(
	Expression::CreateBinaryCompare("<", 3, 5).IsControlExpression());
	ASSERT_TRUE(Expression::CreateIf(5).IsControlExpression());
	ASSERT_TRUE(Expression::CreateEndIf().IsControlExpression());
	ASSERT_TRUE(Expression::CreateComment("Test").IsControlExpression());
	ASSERT_TRUE(Expression().IsControlExpression());
	}

	TEST(Expression, IsCompileTimeConstantAndEqualTo) {
	ASSERT_TRUE(
	Expression::CreateCompileTimeConstant(5).IsCompileTimeConstantAndEqualTo(
	5));
	ASSERT_FALSE(
	Expression::CreateCompileTimeConstant(3).IsCompileTimeConstantAndEqualTo(
	5));
	ASSERT_FALSE(Expression::CreateBinaryCompare("<", 3, 5)
	.IsCompileTimeConstantAndEqualTo(5));
	}

	TEST(Expression, IsReplaceableBy) {
	// Create 2 identical expression
	auto expr1 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

	auto expr2 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

	// They are idendical and of course replaceable
	ASSERT_EQ(expr1, expr2);
	ASSERT_EQ(expr2, expr1);
	ASSERT_TRUE(expr1.IsReplaceableBy(expr2));
	ASSERT_TRUE(expr2.IsReplaceableBy(expr1));

	// Give them different left hand sides
	expr1.set_lhs_id(72);
	expr2.set_lhs_id(42);

	// v_72 = v_3 + v_5
	// v_42 = v_3 + v_5
	// -> They should be replaceable by each other

	ASSERT_NE(expr1, expr2);
	ASSERT_NE(expr2, expr1);

	ASSERT_TRUE(expr1.IsReplaceableBy(expr2));
	ASSERT_TRUE(expr2.IsReplaceableBy(expr1));

	// A slightly differnt expression with the argument flipped
	auto expr3 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(5), ExpressionId(3));

	ASSERT_NE(expr1, expr3);
	ASSERT_FALSE(expr1.IsReplaceableBy(expr3));
	}

	TEST(Expression, Replace) {
	auto expr1 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));
	expr1.set_lhs_id(13);

	auto expr2 =
	Expression::CreateAssignment(kInvalidExpressionId, ExpressionId(7));

	// We replace the arithmetic expr1 by an assignment from the variable 7. This
	// is the typical usecase in subexpression elimination.
	expr1.Replace(expr2);

	// expr1 should now be an assignment from 7 to 13
	EXPECT_EQ(expr1,
	Expression(ExpressionType::ASSIGNMENT,
	ExpressionReturnType::SCALAR,
	13,
	{7},
	"",
	0));
	}

	TEST(Expression, DirectlyDependsOn) {
	auto expr1 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

	ASSERT_TRUE(expr1.DirectlyDependsOn(ExpressionId(3)));
	ASSERT_TRUE(expr1.DirectlyDependsOn(ExpressionId(5)));
	ASSERT_FALSE(expr1.DirectlyDependsOn(ExpressionId(kInvalidExpressionId)));
	ASSERT_FALSE(expr1.DirectlyDependsOn(ExpressionId(42)));
	}
	TEST(Expression, MakeNop) {
	auto expr1 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

	expr1.MakeNop();

	EXPECT_EQ(expr1,
	Expression(ExpressionType::NOP,
	ExpressionReturnType::VOID,
	kInvalidExpressionId,
	{},
	"",
	0));
	}

	TEST(Expression, IsSemanticallyEquivalentTo) {
	// Create 2 identical expression
	auto expr1 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

	auto expr2 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(5));

	ASSERT_TRUE(expr1.IsSemanticallyEquivalentTo(expr1));
	ASSERT_TRUE(expr1.IsSemanticallyEquivalentTo(expr2));

	auto expr3 =
	Expression::CreateBinaryArithmetic("+", ExpressionId(3), ExpressionId(8));

	ASSERT_TRUE(expr1.IsSemanticallyEquivalentTo(expr3));

	auto expr4 =
	Expression::CreateBinaryArithmetic("-", ExpressionId(3), ExpressionId(5));

	ASSERT_FALSE(expr1.IsSemanticallyEquivalentTo(expr4));
	}

	} // namespace internal
	} // namespace ceres