Quick Reference: Variables and Expressions

Data types used in qbpp::Expr

• coeff_t: The integer data type used for coefficients in qbpp::Term objects. The default type is int32_t. To change this type, define the COEFF_TYPE macro at compile time, for example:

  -DCOEFF_TYPE=int16_t
  

• energy_t: The integer data type used to compute energy values of qbpp::Expr objects, as well as for integer constant terms in qbpp::Expr. The default type is int64_t. To change this type, define the ENERGY_TYPE macro at compile time, for example:

  -DENERGY_TYPE=int32_t
  

  The bit width of energy_t is guaranteed to be equal to or larger than that of coeff_t.

• vindex_t: Defined as uint32_t and used to store a unique integer ID for each qbpp::Var object. In most cases, it is not necessary to change this data type.

Available integer data types

• Standard integer types: int16_t, int32_t, int64_t

• Multiprecision integer types (implemented using the Boost.Multiprecision library): qbpp::int128_t, qbpp::cpp_int

• qbpp::cpp_int: An integer type with unlimited precision.

WARNING To maximize performance, QUBO++ does not check for arithmetic overflow. During development and testing, it is recommended to use wider bit widths for coeff_t and energy_t. If the required bit widths are unclear, use qbpp::cpp_int to ensure correctness, and switch to fixed-width integer types after validation.

Printing class objects

Most classes in QUBO++ can be printed using the << operator with std::ostream, which is useful for debugging. For example, an object obj in QUBO++ can be printed to std::cout as follows:

std::cout << obj << std::endl;

This invokes either obj.str() or str(obj), which returns a std::string containing a textual representation of obj. This design allows easy inspection of internal states without relying on a debugger.

Variable classes

• qbpp::Var: A class that holds a unique 32-bit integer ID. The variable name is stored in a global registry and can be retrieved via x.str().

NOTE A qbpp::Var object represents a variable symbolically. No specific data type is associated with it. It can be used to represent binary, spin, or other types of variables.

Variable creation functions

The following functions are provided to create variables:

• qbpp::var("name"): Creates a qbpp::Var object with the given name "name".

• qbpp::var("name", s1): Creates a one-dimensional array of qbpp::Var objects with the base name "name". Each element is represented as name[i]. The resulting type is qbpp::Array<1, qbpp::Var>.

• qbpp::var("name", s1, s2): Creates a two-dimensional array (matrix) of qbpp::Var objects with the base name "name". Each element is represented as name[i][j]. The resulting type is qbpp::Array<2, qbpp::Var>.

• qbpp::var("name", s1, s2, ...): Creates a higher-dimensional array of qbpp::Var objects with the base name "name". Each element is represented as name[i][j].... The resulting type is qbpp::Array<N, qbpp::Var> where N is the number of dimensions.

NOTE If "name" is omitted, numbered names such as "{0}", "{1}", … are automatically assigned in creation order.

qbpp::Var member functions

For a qbpp::Var instance x, the following member functions are available:

• std::string x.str(): Returns the name of x.

• vindex_t x.index(): Returns the unique integer ID of x.

Usually, there is no need to call these member functions explicitly in QUBO++ programs.

Integer variable class

• qbpp::VarInt: A class derived from qbpp::Expr that represents an integer variable with a specified range.

Integer variable creation functions

The following functions are provided to create integer variables:

• qbpp::var_int("name"): Returns an internally used helper object and does not create a qbpp::VarInt by itself. To define a qbpp::VarInt, the range must be specified using the <= operator, as shown below.

• l <= qbpp::var_int("name") <= u: Here, l and u must be integers. This expression creates a qbpp::VarInt object with the name "name", which internally contains a qbpp::Expr object representing all integers in the range [l, u]. Internally, this also creates qbpp::Var objects used in the underlying expression.

• l <= qbpp::var_int("name", s1) <= u: Creates a one-dimensional array (vector) of qbpp::VarInt objects with the base name "name" and the same range [l, u]. Each element is represented as name[i]. The resulting type is qbpp::Array<1, qbpp::VarInt>. Higher-dimensional arrays (e.g., qbpp::Array<2, qbpp::VarInt>) can be created in the same way as qbpp::Var objects.

Integer variable member functions

For a qbpp::VarInt instance x, the following member functions are available:

• std::string x.name(): Returns the name of x.

• std::string x.str(): Returns the string representation of the underlying expression.

• energy_t x.min_val(): Returns the minimum value l of x.

• energy_t x.max_val(): Returns the maximum value u of x.

• x.vars(): Returns the qbpp::Var object array used to represent the integer variable.

• x.coeffs(): Returns the integer coefficient array.

The following expression is equivalent to the expression stored in x:

x.min_val() + qbpp::sum(x.coeffs() * x.vars())