[css-values-4][editorial] Pull IEEE stuff into a subsection.

Author: tabatkins

css-values-4/Overview.bs

@@ -17,7 +17,8 @@ Default Highlight: css
 Include Can I Use Panels: yes
 </pre>
 <pre class='link-defaults'>
-spec: css2; type: property; text: border-collapse
+spec: css2;
+	type: property; text: border-collapse
 spec: css-color-4; type: value; text: currentcolor
 spec: css-color-5; type: type; text: <color>
 spec: css-color-5; type:type; text: <absolute-color-function>
@@ -1157,7 +1158,7 @@ URL Processing Model</h4>
 			[=request/client=] is |environmentSettings|,
 			and whose [=request/referrer=] is |environmentSettings|'s [=API base URL=].
 
-		5. Apply any <dfn>URL request modifier steps</dfn> that apply to this request.
+		5. Apply any <dfn export>URL request modifier steps</dfn> that apply to this request.
 
 			Note: This specification does not define any URL request modification steps,
 			but other specs may do so.
@@ -3983,7 +3984,7 @@ Numeric Constants: ''e'', ''pi''</h3>
 Degenerate Numeric Constants: ''infinity'', <nobr>''-infinity''</nobr>, ''NaN''</h4>
 
 	When a [=calculation=] or a subtree of a [=calculation=]
-	becomes infinite or NaN,
+	becomes [=infinite=] or [=NaN=],
 	representing it with a numeric value is no longer possible.
 	To aid in serialization of these degenerate values,
 	the additional math constants
@@ -4197,90 +4198,6 @@ Type Checking</h3>
 	If it can't [=CSSNumericValue/match=] any of these,
 	the [=math function=] is invalid.
 
-	Division by zero is possible,
-	which introduces certain complications.
-	[=Math functions=] follow IEEE-754 semantics for these operations:
-
-	* Dividing a positive value by zero produces +∞.
-	* Dividing a negative value by zero produces −∞.
-	* Adding or subtracting ±∞ to anything produces the appropriate infinity,
-		unless a following rule would define it as producing NaN.
-	* Multiplying any value by ±∞ produces the appropriate infinity,
-		unless a following rule would define it as producing NaN.
-	* Dividing any value by ±∞ produces zero,
-		unless a following rule would define it as producing NaN.
-	* Dividing zero by zero,
-		dividing ±∞ by ±∞,
-		multiplying 0 by ±∞,
-		adding +∞ to −∞
-		(or the equivalent subtractions)
-		produces NaN.
-	* Any operation with at least one NaN argument produces NaN.
-
-	Additionally,
-	IEEE-754 introduces the concept of a "signed zero",
-	which is specifically positive or negative,
-	and which must be tracked within a calculation
-	and between nested calculations:
-
-	* Negative zero
-		(0⁻)
-		can be produced by a multiplication or division that produces zero
-		with exactly one negative argument
-		(such as ''-5 * 0'' or ''1 / (-infinity)''),
-		or by certain argument combinations in the other [=math functions=].
-
-		Note: Note that negative zeros don't escape a [=math function=];
-		as detailed below,
-		they're "censored" away into an "unsigned" zero.
-	* ''0⁻ + 0⁻''
-		or ''0⁻ - 0''
-		produces 0⁻.
-		All other additions or subtractions that would produce a zero
-		produce 0⁺.
-	* Multiplying or dividing 0⁻ with a positive number
-		(including 0⁺)
-		produces a negative result
-		(either 0⁻ or −∞),
-		while multiplying or dividing 0⁻ with a negative number
-		produces a positive result.
-
-		(In other words,
-		multiplying or dividing with 0⁻
-		follows standard sign rules.)
-	* When comparing 0⁺ and 0⁻,
-		0⁻ is less than 0⁺.
-		For example, ''min(0⁺, 0⁻)'' must produce 0⁻,
-		''max(0⁺, 0⁻)'' must produce 0⁺,
-		and ''clamp(0⁺, 0⁻, 1)'' must produce 0⁺.
-	* Unless otherwise specified,
-		any other operation that produces a zero
-		produces positive zero (0⁺).
-
-	If a <dfn export>top-level calculation</dfn>
-	(a [=math function=] not nested inside of another [=math function=])
-	would produce a value whose numeric part is NaN,
-	it instead act as though the numeric part is 0.
-	If a [=top-level calculation=]
-	would produce a value whose numeric part is 0⁻ or 0⁺,
-	it instead acts as though the numeric part is the standard "unsigned" zero.
-
-	<div class=example>
-		For example, ''calc(-5 * 0)'' produces an unsigned zero--
-		the calculation resolves to 0⁻,
-		but as it's a [=top-level calculation=],
-		it's then censored to an unsigned zero.
-
-		On the other hand, ''calc(1 / calc(-5 * 0))'' produces −∞,
-		same as ''calc(1 / (-5 * 0))''--
-		the inner calc resolves to 0⁻,
-		and as it's not a [=top-level calculation=],
-		it passes it up unchanged to the outer calc to produce −∞.
-		If it was censored into an unsigned zero,
-		it would instead produce +∞.
-	</div>
-
-
 	Note: Algebraic simplifications do not affect the validity of a [=math function=] or its resolved type.
 	For example, ''calc(5px - 5px + 10s)'' and ''calc(0 * 5px + 10s)'' are both invalid
 	due to the attempt to add a length and a time.
@@ -4323,6 +4240,130 @@ Type Checking</h3>
 	might become valid in Quirks Mode
 	(and have its result interpreted as a ''px'' length).
 
+<h4 id='calc-ieee'>
+Infinities, NaN, and Signed Zero</h4>
+
+	[=Math functions=] follow IEEE-754 semantics,
+	which means they recognize the concepts of
+	positive and negative zero,
+	positive and negative infinity,
+	and NaN (not a number).
+
+	However, these concepts are only retained within a [=calculation tree=];
+	if a <dfn export>top-level calculation</dfn>
+	(a [=math function=] not nested directly inside of another [=math function=])
+	would result in one of these special values,
+	they're instead "censored" into a standard representable value,
+	as defined below.
+
+	<dfn lt="signed zero|positive zero|negative zero" for=CSS export>Signed zeros</dfn>
+	(indicated here as 0⁺ or 0⁻)
+	can not be written directly in CSS;
+	''0'', ''+0'' and ''-0'' all produce the standard "unsigned" zero,
+	which is considered positive (0⁺)
+	for the purposes of these rules.
+
+	[=Signed zeroes=] are produced in the following ways:
+
+	* Negative zero
+		(0⁻)
+		can be produced by a multiplication or division that produces zero
+		with exactly one negative argument
+		(such as ''-5 * 0'' or ''1 / -infinity'').
+	* ''0⁻ + 0⁻''
+		or ''0⁻ - 0⁺''
+		produces 0⁻.
+		All other additions or subtractions that would produce a zero
+		produce 0⁺.
+	* Multiplying or dividing 0⁻ with a positive number
+		(including 0⁺)
+		produces a negative result
+		(either 0⁻ or −∞),
+		while multiplying or dividing 0⁻ with a negative number
+		produces a positive result.
+
+		(In other words,
+		multiplying or dividing with 0⁻
+		follows standard sign rules.)
+	* When comparing 0⁺ and 0⁻,
+		0⁻ is less than 0⁺.
+		For example, ''min(0⁺, 0⁻)'' must produce 0⁻,
+		''max(0⁺, 0⁻)'' must produce 0⁺,
+		and ''clamp(0⁺, 0⁻, 1)'' must produce 0⁺.
+	* Certain argument combinations in [=math functions=]
+		are defined to produce 0⁻
+		(for example, ''round(-1, infinity)'').
+		All other operations that produce a zero
+		produce positive zero (0⁺).
+
+	[=Signed zeroes=] do not escape a [=top-level calculation=];
+	they're censored into the "unsigned" zero.
+
+	<dfn lt="infinity|infinite|positive infinity|negative infinity" for=CSS export>Infinities</dfn>
+	(indicated here as +∞ or −∞)
+	can be written directly
+	using the [[#calc-error-constants|math constants]]
+	''infinity'' and ''-infinity'',
+	or produced as a result of some calculations:
+
+	* Dividing a value by zero produces either +∞ or −∞,
+		according to the standard sign rules.
+	* Adding or subtracting ±∞ to anything produces the appropriate infinity.
+	* Multiplying any value by ±∞ produces the appropriate infinity.
+	* Dividing any value by ±∞ produces zero.
+	* Certain argument combinations in [=math functions=]
+		are defined to produce [=infinities=]
+		(for example, ''pow(0, -1)'' produces +∞).
+
+	Note: The rules for producing [=NaN=], below,
+	supersede the above rules for producing [=infinities=].
+
+	[=Infinities=] do not escape a [=top-level calculation=];
+	they're clamped to the minimum or maximum value allowed in the context,
+	as defined in [[#calc-range]].
+
+	<dfn for=CSS export>NaN</dfn>
+	(short for "not a number")
+	is the result of certain operations
+	that don't have a well-defined value.
+	It can be written directly
+	using the [[#calc-error-constants|math constants]]
+	''NaN'',
+	or produced as a result of some calculations:
+
+	* Dividing zero by zero,
+		dividing ±∞ by ±∞,
+		multiplying 0 by ±∞,
+		adding +∞ to −∞,
+		or subtracting two infinities of the same sign
+		produces NaN.
+
+		These rules override any other result,
+		if there's a conflict.
+		For example, ''0 / 0'' is NaN, not +∞.
+	* Certain argument combinations in [=math functions=]
+		are defined to produce [=NaN=]
+		(for example, ''asin(2)'' produces NaN).
+	* Any operation with at least one NaN argument produces NaN.
+
+	[=NaN=] does not escape a [=top-level calculation=];
+	it's censored into a zero value
+
+	<div class=example>
+		For example, ''calc(-5 * 0)'' produces an unsigned zero--
+		the calculation resolves to 0⁻,
+		but as it's a [=top-level calculation=],
+		it's then censored to an unsigned zero.
+
+		On the other hand, ''calc(1 / calc(-5 * 0))'' produces −∞,
+		same as ''calc(1 / (-5 * 0))''--
+		the inner calc resolves to 0⁻,
+		and as it's not a [=top-level calculation=],
+		it passes it up unchanged to the outer calc to produce −∞.
+		If it was censored into an unsigned zero,
+		it would instead produce +∞.
+	</div>
+
 
 <h3 id='calc-internal'>
 Internal Representation</h3>