h3 id="sec:logic-int-arith">4.27.1 Special
purpose integer arithmetic

The predicates in this section provide more logical operations between integers. They are not covered by the ISO standard, although they areāpart of the community' and found as either library or built-in in many other Prolog systems.

**between**(`+Low, +High, ?Value`)`Low`and`High`are integers,. If`High`>=`Low``Value`is an integer,. When`Low`=<`Value`=<`High``Value`is a variable it is successively bound to all integers between`Low`and`High`. If`High`is`inf`

or`infinite`

^{114We prefer infinite, but some other Prolog systems already use inf for infinity; we accept both for the time being.}between/3 is true iff, a feature that is particularly interesting for generating integers from a certain value.`Value`>=`Low`**succ**(`?Int1, ?Int2`)- True if
and`Int2`=`Int1`+ 1. At least one of the arguments must be instantiated to a natural number. This predicate raises the domain error`Int1`>= 0`not_less_than_zero`

if called with a negative integer. E.g.`succ(X, 0)`

fails silently and`succ(X, -1)`

raises a domain error.^{115The behaviour to deal with natural numbers only was defined by Richard O'Keefe to support the common count-down-to-zero in a natural way. Up to 5.1.8, succ/2 also accepted negative integers.} **plus**(`?Int1, ?Int2, ?Int3`)- True if
. At least two of the three arguments must be instantiated to integers.`Int3`=`Int1`+`Int2` **divmod**(`+Dividend, +Divisor, -Quotient, -Remainder`)- This predicate is a shorthand for computing both the
`Quotient`and`Remainder`of two integers in a single operation. This allows for exploiting the fact that the low level implementation for computing the quotient also produces the remainder. Timing confirms that this predicate is almost twice as fast as performing the steps independently. Semantically, divmod/4 is defined as below.divmod(Dividend, Divisor, Quotient, Remainder) :- Quotient is Dividend div Divisor, Remainder is Dividend mod Divisor.

Note that this predicate is only available if SWI-Prolog is compiled with unbounded integer support. This is the case for all packaged versions.

**nth_integer_root_and_remainder**(`+N, +I, -Root, -Remainder`)- True when
`Root ** N + Remainder = I`.`N`and`I`must be integers.^{116This predicate was suggested by Markus Triska. The final name and argument order is by Richard O'Keefe. The decision to include the remainder is by Jan Wielemaker. Including the remainder makes this predicate about twice as slow if Root is not exact.}`N`must be one or more. If`I`is negative and`N`is*odd*,`Root`and`Remainder`are negative, i.e., the following holds for:`I`< 0% I < 0, % N mod 2 =\= 0, nth_integer_root_and_remainder( N, I, Root, Remainder), IPos is -I, nth_integer_root_and_remainder( N, IPos, RootPos, RemainderPos), Root =:= -RootPos, Remainder =:= -RemainderPos.

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