AReal direct

Overview

template <class Scalar, std::size_t N=1>
struct ARealDirect : public RealDirect<AReal<Scalar, N>, ARealDirect<Scalar, N>>

The class ARealDirect has the same interface as AReal, but does not use expression templates for the operations: each operation returns an ARealDirect straight away. It is a drop-in replacement for AReal (see below), for existing code bases which may have issues with expression templates; it also makes debugging easier.

Compatibility with AReal

ARealDirect is designed as a drop-in replacement for AReal in generic code, for example large numerical libraries that are templated on (or typedef) their floating point type. For first-order and higher-order direct mode types (such as ARealDirect<FRealDirect<double>>), XAD provides the same functionality as for AReal:

• Arithmetic and comparisons with the same type, with any built-in arithmetic type (including integer literals, e.g. x < 0 or 2 * x), with XAD expressions, and with types that implicitly convert to ARealDirect (for example a type with a conversion operator, like QuantLib's Null<Real>). As for AReal, higher-order types do not mix in arithmetic with their inner active type. Compound assignments and ++ / -- return a reference to ARealDirect.
• Conversions: implicit conversion from built-in arithmetic types, no implicit conversion to double or int (as for AReal), explicit conversion to bool and (with XAD_ALLOW_INT_CONVERSION, the default) explicit conversion to integer types via static_cast. ARealDirect is not constructible from unrelated types, so that std::is_constructible and std::is_convertible give the same answers as for AReal.
• Mathematical functions: all functions listed in Mathematical Operations, in the xad namespace and (after including XAD/StdCompatibility.hpp) in the std namespace, with the same mixed-argument overloads as AReal. All of them propagate derivatives.
• std compatibility (XAD/StdCompatibility.hpp): std::numeric_limits (all members, returning the underlying passive type as for AReal), std::hash, std::to_string, and the type traits std::is_floating_point, std::is_arithmetic, std::is_signed, std::is_fundamental, std::is_scalar and std::is_compound (including the C++17 _v variable templates).
• Complex numbers (XAD/Complex.hpp): std::complex<ARealDirect<T>> with the same operators and functions as std::complex<AReal<T>>.
• Stream operators << and >>.
• Mode interface: adjd<T> and the higher-order mode classes use ARealDirect as the active type, and the Tape registration functions (registerInput, registerOutput, registerInputs, registerOutputs) accept ARealDirect variables and std::complex<ARealDirect<T>> directly. Jacobian and Hessian helpers are available for ARealDirect<T> and ARealDirect<FRealDirect<T>>.