ceres-solver/include/ceres/internal/expression.h

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2019 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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//
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// Author: darius.rueckert@fau.de (Darius Rueckert)
//
//
// This file contains the basic expression type, which is used during code
// generation. Only assignment expressions of the following form are supported:
//
// result = [constant|binary_expr|functioncall]
//
// Examples:
// v_78 = v_28 / v_62;
// v_97 = exp(v_20);
// v_89 = 3.000000;
//
//
#ifndef CERES_PUBLIC_EXPRESSION_H_
#define CERES_PUBLIC_EXPRESSION_H_

#include <string>
#include <vector>

namespace ceres {
namespace internal {

using ExpressionId = int;
static constexpr ExpressionId kInvalidExpressionId = -1;

enum class ExpressionType {
  // v_0 = 3.1415;
  COMPILE_TIME_CONSTANT,

  // For example a local member of the cost-functor.
  // v_0 = _observed_point_x;
  RUNTIME_CONSTANT,

  // Input parameter
  // v_0 = parameters[1][5];
  PARAMETER,

  // Output Variable Assignemnt
  // residual[0] = v_51;
  OUTPUT_ASSIGNMENT,

  // Trivial Assignment
  // v_1 = v_0;
  ASSIGNMENT,

  // Binary Arithmetic Operations
  // v_2 = v_0 + v_1
  PLUS,
  MINUS,
  MULTIPLICATION,
  DIVISION,

  // Unary Arithmetic Operation
  // v_1 = -(v_0);
  // v_2 = +(v_1);
  UNARY_MINUS,
  UNARY_PLUS,

  // Binary Comparison. (<,>,&&,...)
  // This is the only expressions which returns a 'bool'.
  // const bool v_2 = v_0 < v_1
  BINARY_COMPARISON,

  // The !-operator on logical expression.
  LOGICAL_NEGATION,

  // General Function Call.
  // v_5 = f(v_0,v_1,...)
  FUNCTION_CALL,

  // The ternary ?-operator. Separated from the general function call for easier
  // access.
  // v_3 = ternary(v_0,v_1,v_2);
  TERNARY,

  // No Operation. A placeholder for an 'empty' expressions which will be
  // optimized out during code generation.
  NOP
};

// This class contains all data that is required to generate one line of code.
// Each line has the following form:
//
// lhs = rhs;
//
// The left hand side is the variable name given by its own id. The right hand
// side depends on the ExpressionType. For example, a COMPILE_TIME_CONSTANT
// expressions with id 4 generates the following line:
// v_4 = 3.1415;
//
// Objects of this class are created indirectly using the static CreateXX
// methods. During creation, the Expression objects are added to the
// ExpressionGraph (see expression_graph.h).
class Expression {
 public:
  // These functions create the corresponding expression, add them to an
  // internal vector and return a reference to them.
  static ExpressionId CreateCompileTimeConstant(double v);
  static ExpressionId CreateRuntimeConstant(const std::string& name);
  static ExpressionId CreateParameter(const std::string& name);
  static ExpressionId CreateOutputAssignment(ExpressionId v,
                                             const std::string& name);
  static ExpressionId CreateAssignment(ExpressionId v);
  static ExpressionId CreateBinaryArithmetic(ExpressionType type,
                                             ExpressionId l,
                                             ExpressionId r);
  static ExpressionId CreateUnaryArithmetic(ExpressionType type,
                                            ExpressionId v);
  static ExpressionId CreateBinaryCompare(const std::string& name,
                                          ExpressionId l,
                                          ExpressionId r);
  static ExpressionId CreateLogicalNegation(ExpressionId v);
  static ExpressionId CreateFunctionCall(
      const std::string& name, const std::vector<ExpressionId>& params);
  static ExpressionId CreateTernary(ExpressionId condition,
                                    ExpressionId if_true,
                                    ExpressionId if_false);

  // Returns true if the expression type is one of the basic math-operators:
  // +,-,*,/
  bool IsArithmetic() const;

  // If this expression is the compile time constant with the given value.
  // Used during optimization to collapse zero/one arithmetic operations.
  // b = a + 0;      ->    b = a;
  bool IsCompileTimeConstantAndEqualTo(double constant) const;

  // Checks if "other" is identical to "this" so that one of the epxressions can
  // be replaced by a trivial assignment. Used during common subexpression
  // elimination.
  bool IsReplaceableBy(const Expression& other) const;

  // Replace this expression by 'other'.
  // The current id will be not replaced. That means other experssions
  // referencing this one stay valid.
  void Replace(const Expression& other);

  // If this expression has 'other' as an argument.
  bool DirectlyDependsOn(ExpressionId other) const;

  // Converts this expression into a NOP
  void MakeNop();

 private:
  // Only ExpressionGraph is allowed to call the constructor, because it manages
  // the memory and ids.
  friend class ExpressionGraph;

  // Private constructor. Use the "CreateXX" functions instead.
  Expression(ExpressionType type, ExpressionId id);

  ExpressionType type_ = ExpressionType::NOP;
  const ExpressionId id_ = kInvalidExpressionId;

  // Expressions have different number of arguments. For example a binary "+"
  // has 2 parameters and a function call to "sin" has 1 parameter. Here, a
  // reference to these paratmers is stored. Note: The order matters!
  std::vector<ExpressionId> arguments_;

  // Depending on the type this name is one of the following:
  //  (type == FUNCTION_CALL) -> the function name
  //  (type == PARAMETER)     -> the parameter name
  //  (type == OUTPUT_ASSIGN) -> the output variable name
  //  (type == BINARY_COMPARE)-> the comparison symbol "<","&&",...
  //  else                    -> unused
  std::string name_;

  // Only valid if type == COMPILE_TIME_CONSTANT
  double value_ = 0;
};

}  // namespace internal
}  // namespace ceres
#endif