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

.. rst-class:: right

**object**

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

Number data type predicates.

| **Author:** Paulo Moura
| **Version:** 1.6
| **Date:** 2019/3/7

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


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

| **Remarks:**
|    (none)

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

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

.. raw:: html

   <div id="approximately_equal/3"> </div>

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

``approximately_equal/3``
^^^^^^^^^^^^^^^^^^^^^^^^^

Compares two numbers for approximate equality given an 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``


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

.. raw:: html

   <div id="essentially_equal/3"> </div>

.. 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``


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

.. raw:: html

   <div id="tolerance_equal/4"> </div>

.. 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``


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

.. raw:: html

   <div id="=~= / 2"> </div>

.. 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
--------------------

(see entity ancestors)

Private predicates
------------------

(see entity ancestors)

Operators
---------

``op(700,xfx,=~=)``
^^^^^^^^^^^^^^^^^^^

| **Scope:**
|    ``public``



