object

number

Number data type predicates.

Author: Paulo Moura
Version: 1:12:0
Date: 2023-08-04
Compilation flags:
static, context_switching_calls
Extends:
public atomic
Remarks:
(none)
Inherited public predicates:
 (<)/2  (=:=)/2  (=<)/2  (=\=)/2  (>)/2  (>=)/2  check/1  depth/2  ground/1  new/1  numbervars/1  numbervars/3  occurs/2  singletons/2  subsumes/2  subterm/2  valid/1  variables/2  variant/2  varnumbers/2  varnumbers/3

Public predicates

approximately_equal/2

Compares two numbers for approximate equality given the epsilon arithmetic constant value using the de facto standard formula abs(Number1 - Number2) =< max(abs(Number1), abs(Number2)) * epsilon. No type-checking.

Compilation flags:
static
Template:
approximately_equal(Number1,Number2)
Mode and number of proofs:
approximately_equal(+number,+number) - zero_or_one

approximately_equal/3

Compares two numbers for approximate equality given a user-defined epsilon value using the de facto standard formula abs(Number1 - Number2) =< max(abs(Number1), abs(Number2)) * Epsilon. No type-checking.

Compilation flags:
static
Template:
approximately_equal(Number1,Number2,Epsilon)
Mode and number of proofs:
approximately_equal(+number,+number,+number) - zero_or_one
Remarks:

  • Epsilon range: Epsilon should be the epsilon arithmetic constant value or a small multiple of it. Only use a larger value if a greater error is expected.

  • Comparison with essential equality: For the same epsilon value, approximate equality is weaker requirement than essential equality.

essentially_equal/3

Compares two numbers for essential equality given an epsilon value using the de facto standard formula abs(Number1 - Number2) =< min(abs(Number1), abs(Number2)) * Epsilon. No type-checking.

Compilation flags:
static
Template:
essentially_equal(Number1,Number2,Epsilon)
Mode and number of proofs:
essentially_equal(+number,+number,+number) - zero_or_one
Remarks:

  • Comparison with approximate equality: For the same epsilon value, essential equality is a stronger requirement than approximate equality.

tolerance_equal/4

Compares two numbers for close equality given relative and absolute tolerances using the de facto standard formula abs(Number1 - Number2) =< max(RelativeTolerance * max(abs(Number1), abs(Number2)), AbsoluteTolerance). No type-checking.

Compilation flags:
static
Template:
tolerance_equal(Number1,Number2,RelativeTolerance,AbsoluteTolerance)
Mode and number of proofs:
tolerance_equal(+number,+number,+number,+number) - zero_or_one

=~= / 2

Compares two floats (or lists of floats) for approximate equality using 100*epsilon for the absolute error and, if that fails, 99.999% accuracy for the relative error. Note that these precision values may not be adequate for all cases. No type-checking.

Compilation flags:
static
Template:
=~=(Float1,Float2)
Mode and number of proofs:
=~=(+number,+number) - zero_or_one
=~=(+list(number),+list(number)) - zero_or_one

Protected predicates

(no local declarations; see entity ancestors if any)

Private predicates

(no local declarations; see entity ancestors if any)

Operators

op(700,xfx,=~=)

Scope:
public