Add more info on the nature of NAN

(cherry picked from commit 5e3c625e24b32fbc91a3cb17f74a16d45f9a5a66)

doc/classes/PackedFloat32Array.xml

@@ -53,6 +53,7 @@
 			<description>
 				Finds the index of an existing value (or the insertion index that maintains sorting order, if the value is not yet present in the array) using binary search. Optionally, a [param before] specifier can be passed. If [code]false[/code], the returned index comes after all existing entries of the value in the array.
 				[b]Note:[/b] Calling [method bsearch] on an unsorted array results in unexpected behavior.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="clear">
@@ -66,6 +67,7 @@
 			<param index="0" name="value" type="float" />
 			<description>
 				Returns the number of times an element is in the array.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="duplicate">
@@ -87,6 +89,7 @@
 			<param index="1" name="from" type="int" default="0" />
 			<description>
 				Searches the array for a value and returns its index or [code]-1[/code] if not found. Optionally, the initial search index can be passed.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="has" qualifiers="const">
@@ -94,6 +97,7 @@
 			<param index="0" name="value" type="float" />
 			<description>
 				Returns [code]true[/code] if the array contains [param value].
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="insert">
@@ -143,6 +147,7 @@
 			<param index="1" name="from" type="int" default="-1" />
 			<description>
 				Searches the array in reverse order. Optionally, a start search index can be passed. If negative, the start index is considered relative to the end of the array.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="set">
@@ -173,6 +178,7 @@
 			<return type="void" />
 			<description>
 				Sorts the elements of the array in ascending order.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="to_byte_array" qualifiers="const">

doc/classes/PackedFloat64Array.xml

@@ -53,6 +53,7 @@
 			<description>
 				Finds the index of an existing value (or the insertion index that maintains sorting order, if the value is not yet present in the array) using binary search. Optionally, a [param before] specifier can be passed. If [code]false[/code], the returned index comes after all existing entries of the value in the array.
 				[b]Note:[/b] Calling [method bsearch] on an unsorted array results in unexpected behavior.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="clear">
@@ -66,6 +67,7 @@
 			<param index="0" name="value" type="float" />
 			<description>
 				Returns the number of times an element is in the array.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="duplicate">
@@ -87,6 +89,7 @@
 			<param index="1" name="from" type="int" default="0" />
 			<description>
 				Searches the array for a value and returns its index or [code]-1[/code] if not found. Optionally, the initial search index can be passed.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="has" qualifiers="const">
@@ -94,6 +97,7 @@
 			<param index="0" name="value" type="float" />
 			<description>
 				Returns [code]true[/code] if the array contains [param value].
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="insert">
@@ -143,6 +147,7 @@
 			<param index="1" name="from" type="int" default="-1" />
 			<description>
 				Searches the array in reverse order. Optionally, a start search index can be passed. If negative, the start index is considered relative to the end of the array.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="set">
@@ -173,6 +178,7 @@
 			<return type="void" />
 			<description>
 				Sorts the elements of the array in ascending order.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="to_byte_array" qualifiers="const">

doc/classes/PackedVector2Array.xml

@@ -53,6 +53,7 @@
 			<description>
 				Finds the index of an existing value (or the insertion index that maintains sorting order, if the value is not yet present in the array) using binary search. Optionally, a [param before] specifier can be passed. If [code]false[/code], the returned index comes after all existing entries of the value in the array.
 				[b]Note:[/b] Calling [method bsearch] on an unsorted array results in unexpected behavior.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="clear">
@@ -66,6 +67,7 @@
 			<param index="0" name="value" type="Vector2" />
 			<description>
 				Returns the number of times an element is in the array.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="duplicate">
@@ -87,6 +89,7 @@
 			<param index="1" name="from" type="int" default="0" />
 			<description>
 				Searches the array for a value and returns its index or [code]-1[/code] if not found. Optionally, the initial search index can be passed.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="has" qualifiers="const">
@@ -94,6 +97,7 @@
 			<param index="0" name="value" type="Vector2" />
 			<description>
 				Returns [code]true[/code] if the array contains [param value].
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="insert">
@@ -143,6 +147,7 @@
 			<param index="1" name="from" type="int" default="-1" />
 			<description>
 				Searches the array in reverse order. Optionally, a start search index can be passed. If negative, the start index is considered relative to the end of the array.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="set">
@@ -173,6 +178,7 @@
 			<return type="void" />
 			<description>
 				Sorts the elements of the array in ascending order.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="to_byte_array" qualifiers="const">

doc/classes/PackedVector3Array.xml

@@ -52,6 +52,7 @@
 			<description>
 				Finds the index of an existing value (or the insertion index that maintains sorting order, if the value is not yet present in the array) using binary search. Optionally, a [param before] specifier can be passed. If [code]false[/code], the returned index comes after all existing entries of the value in the array.
 				[b]Note:[/b] Calling [method bsearch] on an unsorted array results in unexpected behavior.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="clear">
@@ -65,6 +66,7 @@
 			<param index="0" name="value" type="Vector3" />
 			<description>
 				Returns the number of times an element is in the array.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="duplicate">
@@ -86,6 +88,7 @@
 			<param index="1" name="from" type="int" default="0" />
 			<description>
 				Searches the array for a value and returns its index or [code]-1[/code] if not found. Optionally, the initial search index can be passed.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="has" qualifiers="const">
@@ -93,6 +96,7 @@
 			<param index="0" name="value" type="Vector3" />
 			<description>
 				Returns [code]true[/code] if the array contains [param value].
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="insert">
@@ -142,6 +146,7 @@
 			<param index="1" name="from" type="int" default="-1" />
 			<description>
 				Searches the array in reverse order. Optionally, a start search index can be passed. If negative, the start index is considered relative to the end of the array.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="set">
@@ -172,6 +177,7 @@
 			<return type="void" />
 			<description>
 				Sorts the elements of the array in ascending order.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this method may not be accurate if NaNs are included.
 			</description>
 		</method>
 		<method name="to_byte_array" qualifiers="const">

doc/classes/Vector2.xml

@@ -412,6 +412,7 @@
 			<description>
 				Returns [code]true[/code] if the vectors are not equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator *">
@@ -494,6 +495,7 @@
 			<param index="0" name="right" type="Vector2" />
 			<description>
 				Compares two [Vector2] vectors by first checking if the X value of the left vector is less than the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &lt;=">
@@ -501,6 +503,7 @@
 			<param index="0" name="right" type="Vector2" />
 			<description>
 				Compares two [Vector2] vectors by first checking if the X value of the left vector is less than or equal to the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator ==">
@@ -509,6 +512,7 @@
 			<description>
 				Returns [code]true[/code] if the vectors are exactly equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;">
@@ -516,6 +520,7 @@
 			<param index="0" name="right" type="Vector2" />
 			<description>
 				Compares two [Vector2] vectors by first checking if the X value of the left vector is greater than the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;=">
@@ -523,6 +528,7 @@
 			<param index="0" name="right" type="Vector2" />
 			<description>
 				Compares two [Vector2] vectors by first checking if the X value of the left vector is greater than or equal to the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator []">

doc/classes/Vector3.xml

@@ -417,6 +417,7 @@
 			<description>
 				Returns [code]true[/code] if the vectors are not equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator *">
@@ -513,6 +514,7 @@
 			<param index="0" name="right" type="Vector3" />
 			<description>
 				Compares two [Vector3] vectors by first checking if the X value of the left vector is less than the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &lt;=">
@@ -520,6 +522,7 @@
 			<param index="0" name="right" type="Vector3" />
 			<description>
 				Compares two [Vector3] vectors by first checking if the X value of the left vector is less than or equal to the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator ==">
@@ -528,6 +531,7 @@
 			<description>
 				Returns [code]true[/code] if the vectors are exactly equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;">
@@ -535,6 +539,7 @@
 			<param index="0" name="right" type="Vector3" />
 			<description>
 				Compares two [Vector3] vectors by first checking if the X value of the left vector is greater than the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;=">
@@ -542,6 +547,7 @@
 			<param index="0" name="right" type="Vector3" />
 			<description>
 				Compares two [Vector3] vectors by first checking if the X value of the left vector is greater than or equal to the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator []">

doc/classes/Vector4.xml

@@ -273,6 +273,7 @@
 			<description>
 				Returns [code]true[/code] if the vectors are not equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator *">
@@ -361,6 +362,7 @@
 			<param index="0" name="right" type="Vector4" />
 			<description>
 				Compares two [Vector4] vectors by first checking if the X value of the left vector is less than the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, Z values of the two vectors, and then with the W values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &lt;=">
@@ -368,6 +370,7 @@
 			<param index="0" name="right" type="Vector4" />
 			<description>
 				Compares two [Vector4] vectors by first checking if the X value of the left vector is less than or equal to the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, Z values of the two vectors, and then with the W values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator ==">
@@ -376,6 +379,7 @@
 			<description>
 				Returns [code]true[/code] if the vectors are exactly equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;">
@@ -383,6 +387,7 @@
 			<param index="0" name="right" type="Vector4" />
 			<description>
 				Compares two [Vector4] vectors by first checking if the X value of the left vector is greater than the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, Z values of the two vectors, and then with the W values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;=">
@@ -390,6 +395,7 @@
 			<param index="0" name="right" type="Vector4" />
 			<description>
 				Compares two [Vector4] vectors by first checking if the X value of the left vector is greater than or equal to the X value of the [param right] vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, Z values of the two vectors, and then with the W values. This operator is useful for sorting vectors.
+				[b]Note:[/b] Vectors with [constant @GDScript.NAN] elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator []">

doc/classes/float.xml

@@ -54,6 +54,7 @@
 			<param index="0" name="right" type="float" />
 			<description>
 				Returns [code]true[/code] if two floats are different from each other.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator !=">
@@ -215,6 +216,7 @@
 			<param index="0" name="right" type="float" />
 			<description>
 				Returns [code]true[/code] if the left float is less than the right one.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &lt;">
@@ -229,6 +231,7 @@
 			<param index="0" name="right" type="float" />
 			<description>
 				Returns [code]true[/code] if the left float is less than or equal to the right one.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &lt;=">
@@ -244,6 +247,7 @@
 			<description>
 				Returns [code]true[/code] if both floats are exactly equal.
 				[b]Note:[/b] Due to floating-point precision errors, consider using [method @GlobalScope.is_equal_approx] or [method @GlobalScope.is_zero_approx] instead, which are more reliable.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator ==">
@@ -258,6 +262,7 @@
 			<param index="0" name="right" type="float" />
 			<description>
 				Returns [code]true[/code] if the left float is greater than the right one.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;">
@@ -272,6 +277,7 @@
 			<param index="0" name="right" type="float" />
 			<description>
 				Returns [code]true[/code] if the left float is greater than or equal to the right one.
+				[b]Note:[/b] [constant @GDScript.NAN] doesn't behave the same as other numbers. Therefore, the results from this operator may not be accurate if NaNs are included.
 			</description>
 		</operator>
 		<operator name="operator &gt;=">

modules/gdscript/doc_classes/@GDScript.xml

@@ -274,7 +274,7 @@
 			[b]Warning:[/b] Numeric infinity is only a concept with floating-point numbers, and has no equivalent for integers. Dividing an integer number by [code]0[/code] will not result in [constant INF] and will result in a run-time error instead.
 		</constant>
 		<constant name="NAN" value="nan">
-			"Not a Number", an invalid floating-point value. [constant NAN] has special properties, including that it is not equal to itself ([code]NAN == NAN[/code] returns [code]false[/code]). It is output by some invalid operations, such as dividing floating-point [code]0.0[/code] by [code]0.0[/code].
+			"Not a Number", an invalid floating-point value. [constant NAN] has special properties, including that [code]!=[/code] always returns [code]true[/code], while other comparison operators always return [code]false[/code]. This is true even when comparing with itself ([code]NAN == NAN[/code] returns [code]false[/code] and [code]NAN != NAN[/code] returns [code]true[/code]). It is returned by some invalid operations, such as dividing floating-point [code]0.0[/code] by [code]0.0[/code].
 			[b]Warning:[/b] "Not a Number" is only a concept with floating-point numbers, and has no equivalent for integers. Dividing an integer [code]0[/code] by [code]0[/code] will not result in [constant NAN] and will result in a run-time error instead.
 		</constant>
 	</constants>