A.8.2 Arithmetic constraints

In modern Prolog systems, arithmetic constraints subsume and supersede low-level predicates over integers. The main advantage of arithmetic constraints is that they are true relations and can be used in all directions. For most programs, arithmetic constraints are the only predicates you will ever need from this library.

The most important arithmetic constraint is #=/2, which subsumes both (is)/2 and (=:=)/2 over integers. Use #=/2 to make your programs more general.

In total, the arithmetic constraints are:

Expr1 #= Expr2	Expr1 equals Expr2
Expr1 #\= Expr2	Expr1 is not equal to Expr2
Expr1 #>= Expr2	Expr1 is greater than or equal to Expr2
Expr1 #=< Expr2	Expr1 is less than or equal to Expr2
Expr1 #> Expr2	Expr1 is greater than Expr2
Expr1 #< Expr2	Expr1 is less than Expr2

Expr1 and Expr2 denote arithmetic expressions, which are:

integer	Given value
variable	Unknown integer
?(variable)	Unknown integer
-Expr	Unary minus
Expr + Expr	Addition
Expr * Expr	Multiplication
Expr - Expr	Subtraction
Expr ^ Expr	Exponentiation
min(Expr,Expr)	Minimum of two expressions
max(Expr,Expr)	Maximum of two expressions
Expr mod Expr	Modulo induced by floored division
Expr rem Expr	Modulo induced by truncated division
abs(Expr)	Absolute value
Expr // Expr	Truncated integer division
Expr div Expr	Floored integer division

where Expr again denotes an arithmetic expression.

The bitwise operations (\)/1, (/\)/2, (\/)/2, (>>)/2, (<<)/2, lsb/1, msb/1, popcount/1 and (xor)/2 are also supported.