nexttoward(+X, +Y, -Result)

X

A number

Y

A number

Result

Output: number

Description

    Result is nexttoward(X, Y)

Result is the next representable number following X in the direction of Y. If Y is greater than X, the result is the smallest representable number greater than X. If Y is smaller than X, the result is the greatest representable number smaller than X. Otherwise the result is identical to X or Y.

If X and Y are floats, the next representable value depends on the floating point representation.

If X and Y are integers, the next representable value is the next integer.

If X and Y are breals, the result is the smallest interval enclosing all possible results of doing the operation on elements of the input intervals.

If X and Y are rationals, the operation is undefined.

If X and Y are of different types, the types are first made equal (via conversions integer -> rational -> float -> breal), then the result is computed as above.

In coroutining mode, if X or Y is uninstantiated, the predicate delays.

Modes and Determinism

• nexttoward(+, +, -) is det

Exceptions

(4) instantiation fault

X or Y is not instantiated (non-coroutining mode only).

(5) type error

Operation not defined on rational numbers

(24) number expected

Number is not of a numeric type.

Examples

Success:
      Result is nexttoward(1.0, 2.0).	% gives Result = 1.0000000000000002
      Result is nexttoward(1.0, 0.0).	% gives Result = 0.99999999999999989
      Result is nexttoward(1.0, 1.0).	% gives Result = 1.0

      Result is nexttoward(0.0, 1.0).	% gives Result = 4.94065645841247e-324
      Result is nexttoward(1.0Inf, 0.0)	% gives Result = 1.7976931348623157e+308

      Result is nexttoward(5, 9).	% gives Result = 6
      Result is nexttoward(5, 0).	% gives Result = 4
      Result is nexttoward(5, 5).	% gives Result = 5

Error:
      Result is nexttoward(3_4, 2_1).	% type error

See Also