.. index:: single: number
.. _number/0:

.. rst-class:: right

**object**

``number``
==========

Number data type predicates.

| **Availability:** 
|    ``logtalk_load(types(loader))``

| **Author:** Paulo Moura
| **Version:** 1:15:0
| **Date:** 2026-02-11

| **Compilation flags:**
|    ``static, context_switching_calls``


| **Extends:**
|    ``public`` :ref:`atomic <atomic/0>`

| **Remarks:**
|    (none)

| **Inherited public predicates:**
|     :ref:`comparingp/0::(<)/2`  :ref:`comparingp/0::(=:=)/2`  :ref:`comparingp/0::(=<)/2`  :ref:`comparingp/0::(=\=)/2`  :ref:`comparingp/0::(>)/2`  :ref:`comparingp/0::(>=)/2`  :ref:`termp/0::check/1`  :ref:`termp/0::depth/2`  :ref:`termp/0::ground/1`  :ref:`termp/0::new/1`  :ref:`termp/0::numbervars/1`  :ref:`termp/0::numbervars/3`  :ref:`termp/0::occurs/2`  :ref:`termp/0::singletons/2`  :ref:`termp/0::subsumes/2`  :ref:`termp/0::subterm/2`  :ref:`termp/0::valid/1`  :ref:`termp/0::variables/2`  :ref:`termp/0::variant/2`  :ref:`termp/0::varnumbers/2`  :ref:`termp/0::varnumbers/3`  

.. contents::
   :local:
   :backlinks: top

Public predicates
-----------------

.. index:: approximately_equal/2
.. _number/0::approximately_equal/2:

``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``


------------

.. index:: approximately_equal/3
.. _number/0::approximately_equal/3:

``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.


------------

.. index:: essentially_equal/3
.. _number/0::essentially_equal/3:

``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.


------------

.. index:: tolerance_equal/4
.. _number/0::tolerance_equal/4:

``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``


------------

.. index:: =~= / 2
.. _number/0::=~= / 2:

``=~= / 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``



