[css-values-4] Undefine the value of tan() at the asymptotes. #8527

Author: tabatkins

css-values-4/Overview.bs

@@ -3425,17 +3425,55 @@ Argument Ranges</h4>
 
 	In ''tan(A)'', if A is one of the asymptote values
 	(such as ''90deg'', ''270deg'', etc),
-	the result must be +∞ for ''90deg'' and all values a multiple of ''360deg'' from that
-	(such as ''-270deg'' or ''450deg''),
-	and −∞ for ''-90deg'' and all values a multiple of ''360deg'' from that
-	(such as ''-450deg'' or ''270deg'').
-
-	Note: This is only relevant for units that can exactly represent the asymptotic values,
-	such as ''deg'' or ''grad''.
-	''rad'' cannot,
-	and so whether the result is a very large negative or positive value
-	can depend on rounding and precise details of how numbers are internally stored.
-	It's recommended you don't depend on this behavior if using such units.
+	the result is <strong>explicitly undefined</strong>.
+	If an implementation is capable of exactly representing these inputs,
+	it <em>should</em> return
+	+∞ for the asymptotes at <code>90deg + N*360deg</code>,
+	and −∞ for the asymptotes at <code>-90deg + N*360deg</code>,
+	but implementations are not required to be able to exactly represent these inputs
+	(and if they can't, will return whatever the correct numeric answer is
+	for the closest approximation to the input
+	they are capable of representing).
+	Authors <em>must not</em> rely on ''tan()'' returning any particular value
+	for these inputs.
+
+	<details class=note>
+		<summary>Why are these undefined?</summary>
+
+		The tangent function is <em>discontinuous</em> at its asymptotes:
+		it approaches infinity from one side
+		<em>and</em> negative infinity from the other side,
+		and isn't defined at the exact values of the asymptote.
+
+		Further, whether or not the asymptotic values
+		are exactly representable in implementations
+		depends on how they internally store and manipulate angles;
+		when written in degrees the values are simple (''90deg'', etc),
+		but in radians the values are transcendental (''pi / 2'', etc)
+		and cannot be exactly represented.
+		So, even defining a specific behavior for these values is difficult;
+		if an implementation uses radians internally,
+		it would have to do some fuzzy matching
+		to return the defined value
+		when the input is <em>sufficiently close</em> to the asymptote.
+
+		The other major language for the Web, JavaScript,
+		exposes these functions as taking radians only,
+		so it can't hit the exact asymptotes either
+		(and this true for most other computer languages, too).
+		Authors writing code in JS, then,
+		can't rely on any specific behavior for these values either,
+		and it's unlikely that their needs in CSS are significantly different.
+
+		The suggested behavior for implementations that can exactly represent the asymptote values
+		preserves round-tripping with the ''atan()'' function:
+		''tan(atan(X))'' and ''atan(tan(X))''
+		will both return (approximately) X
+		for all possible X values,
+		given this definition.
+		It also means that within the supported output range of ''atan()'',
+		the function is continuous.
+	</details>
 
 	In ''asin(A)'' or ''acos(A)'',
 	if A is less than -1 or greater than 1,
@@ -3518,16 +3556,6 @@ Argument Ranges</h4>
 	as implemented by most programming languages,
 	in particular as implemented in JS.
 
-	Note: The behavior of ''tan(90deg)'',
-	while not constrained by JS behavior
-	(because the JS function's input is in radians,
-	and one cannot perfectly express a value of π/2 in JS numbers),
-	is defined so that roundtripping of values works;
-	''tan(atan(infinity))'' yields +∞,
-	''tan(atan(-infinity))'' yields −∞,
-	''atan(tan(90deg))'' yields ''90deg'',
-	and ''atan(tan(-90deg))'' yields ''-90deg''.
-
 
 <h3 id=exponent-funcs>
 Exponential  Functions: ''pow()'', ''sqrt()'', ''hypot()'', ''log()'', ''exp()''</h3>