Expressions

Detailed Description

AmpGen Expressions are a set of classes for constructing functions from primatives such as the binary operators \((+,-,/,\times)\), and elementary functions such as trigonometric functions and sqrts. These are then compiled to conventional C++ at runtime, to allow fast and flexible evalulation of amplitudes. Expression trees can be built using overloaded operators, so

Expression x = a+b; 

will given an expression that can calculate the sum of expressions a and b. There are constructors for expressions from constants and corresponding overloads of operators, so for example

Expression x = a+5;

generates a tree that adds '5' to the the tree 'a'.
Assorted optimisations will generally be invoked on the AST if constants are included, such as reduction of products and sums of constants.

There is limited functionality for expressions to be evaluated in-situ to the default values associated with their parameters, which can useful for debugging purposes. The more typical usage is to use an expression to generate a CompiledExpression that compiles the expression and wraps the corresponding shared library with a functor.

For unary functions, it is recommend to use the functions contained in the fcn:: namespace that have the same names as those in std::math. For example,

Expression y = fcn::sin(x);

Use of the unary classes directly can cause unexpected behaviour if used in conjunction with the auto keyword, and does not include some optimisations as readily such as constant folding.

Classes
class	AmpGen::Array
	Expression for a fixed size array of values. More...
class	AmpGen::ASTResolver
	(Internal) class to aide in the resolution of the dependencies of expression trees. More...
class	AmpGen::IExpression
	Virtual base class for other expression tree components. More...
class	AmpGen::Expression
	Wrapper class for shared_ptrs to virtual expressions for use in conjunction with operators to build expression trees. More...
class	AmpGen::Constant
	Class to contain a constant (which can contain a complex value) More...
class	AmpGen::Parameter
	Free parameter for expression. More...
class	AmpGen::LambdaExpression
	Parameter that the value of which is given by some arbitrary C++ function. More...
class	AmpGen::Ternary
	Evaluates the ternary operator. More...
struct	AmpGen::SubTree
class	AmpGen::ExpressionPack
	A group of expressions packed into a single expression. More...
class	AmpGen::IBinaryExpression
	Base class for binary expressions, i.e. More...
class	AmpGen::Sum
	Binary expression that returns \(l+r\). More...
class	AmpGen::Sub
	Binary expression that returns \(l-r\). More...
class	AmpGen::Product
	Binary expression that returns \(l\times r\). More...
class	AmpGen::Divide
	Binary expression that returns \(l / r\). More...
class	AmpGen::Pow
	Binary expression that returns \( l^{r} \). More...
class	AmpGen::Fmod
	Binary expression that returns the fractional part of \( l \mathrm{mod} r \). More...
class	AmpGen::LessThan
	Binary expression that returns \(l < r\). More...
class	AmpGen::GreaterThan
	Binary expression that returns \(l > r\). More...
class	AmpGen::LessThanEqualTo
	Binary expression that returns \(l < r\). More...
class	AmpGen::GreaterThanEqualTo
	Binary expression that returns \(l > r\). More...
class	AmpGen::And
	Binary expression that returns \(l \wedge r\). More...
class	AmpGen::Or
	Binary expression that returns \(l \wedge r\). More...
class	AmpGen::IUnaryExpression
	Base class for unary expressions, i.e. More...
class	AmpGen::Log
	Unary expression that returns \(\log(x)\). More...
class	AmpGen::Exp
	Unary expression that returns \(e^x\). More...
class	AmpGen::Sqrt
	Unary expression that returns \(\sqrt{x}\). More...
class	AmpGen::Abs
	Unary expression that returns \(|z|\). More...
class	AmpGen::Norm
	Unary expression that returns \(|z|^2\). More...
class	AmpGen::Conj
	Unary expression that returns \(z^{*}\). More...
class	AmpGen::Real
	Unary expression that returns the real part of \(z\). More...
class	AmpGen::Imag
	Unary expression that returns the imaginary part of \(z\). More...
class	AmpGen::Sin
	Unary expression that returns \(\sin(z)\). More...
class	AmpGen::Cos
	Unary expression that returns \(\cos(z)\). More...
class	AmpGen::Tan
	Unary expression that returns \(\tan(z)\). More...
class	AmpGen::ASin
	Unary expression that returns \(\sin^{-1}(z)\). More...
class	AmpGen::ACos
	Unary expression that returns \(\cos^{-1}(z)\). More...
class	AmpGen::ATan
	Unary expression that returns \(\tan^{-1}(z)\). More...
class	AmpGen::ISqrt
	Unary expression that uses inverse sqrt (faster than dividing by sqrt) More...
class	AmpGen::LGamma
	Unary expression that returns \(\log\left|\Gamma(x)\right|\). More...

Macros
#define	ADD_DEBUG(X, Y)
	Make a (named) debugging expression and add to a set of DebugSymbols.
#define	DEFINE_CAST(X)
	Define a cast from an expression implementation to the shared_ptr wrapper.
#define	DECLARE_UNARY_OPERATOR(X)
	Macro to declare a unary operator, see IUnaryExpression.
#define	DECLARE_BINARY_OPERATOR(X)
	Macro to declare a binary operator, see IBinaryExpression.

Macro Definition Documentation

ADD_DEBUG

#define ADD_DEBUG	(		X,
			Y )

Value:

  if ( Y != 0 ) Y->push_back( DebugSymbol( std::string( #X ), X ) );    \

Definition at line 41 of file Expression.h.

DECLARE_BINARY_OPERATOR

#define DECLARE_BINARY_OPERATOR

(

X

)

Value:

  class X : public IBinaryExpression {                      \
    public:                                                 \
    X( const Expression& l, const Expression& r );          \
    X( const Expression& expr);                             \
    virtual std::string to_string(const ASTResolver* resolver=nullptr) const override ;        \
    operator Expression() const ;                           \
    virtual complex_t operator()() const override;          \
  }

Definition at line 80 of file Expression.h.

DECLARE_UNARY_OPERATOR

#define DECLARE_UNARY_OPERATOR

(

X

)

Value:

  class X : public IUnaryExpression {                       \
    public:                                                 \
    explicit X( const Expression& other );                  \
    virtual std::string to_string(const ASTResolver* resolver=nullptr) const override;         \
    virtual Expression d() const override;                  \
    operator Expression() const;                            \
    virtual complex_t operator()() const override;          \
  }

Definition at line 68 of file Expression.h.

DEFINE_CAST

#define DEFINE_CAST

(

X

)

Value:

  X::operator Expression() const                            \
{ return Expression( std::make_shared<X>( *this ) ); }

Definition at line 46 of file Expression.h.