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[css-values-4] Clean up trig function definitions #3761

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Merged
merged 2 commits into from
Mar 26, 2019
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[css-values-4] Clean up trig function definitions #3761

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c891d6c
Clean up trig function definitions
AmeliaBR Mar 26, 2019
004638a
Address Tab's comments on PR #3761
AmeliaBR Mar 26, 2019
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30 changes: 17 additions & 13 deletions css-values-4/Overview.bs
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Original file line number Diff line number Diff line change
Expand Up @@ -2472,13 +2472,13 @@ Trigonometric Functions: ''sin()'', ''cos()'', ''tan()'', ''asin()'', ''acos()''
''sin()'', ''cos()'', ''tan()'', ''asin()'', ''acos()'', ''atan()'', and ''atan2()''--
compute the various basic trigonometric relationships.

The <dfn lt="sin()">sin(A)</dfn>, <dfn lt="cos(A)">cos()</dfn>, and <dfn lt="tan()">tan(A)</dfn> functions
The <dfn lt="sin()">sin(A)</dfn>, <dfn lt="cos()">cos(A)</dfn>, and <dfn lt="tan()">tan(A)</dfn> functions
all contain a single [=calculation=]
which must resolve to either a <<number>>
or an <<angle>>,
and compute their corresponding function
by interpreting the result of their argument as radians.
(That is, ''sin(45deg)'', ''sin(.125)'', and ''sin(3.14159 / 4 * 1rad)''
(That is, ''sin(45deg)'', ''sin(.125turn)'', and ''sin(3.14159 / 4)''
all represent the same value,
approximately ''.707''.)
They all represent a <<number>>;
Expand All @@ -2499,21 +2499,23 @@ Trigonometric Functions: ''sin()'', ''cos()'', ''tan()'', ''asin()'', ''acos()''
and the angle returned by ''atan()'' to the range [''-90deg'', ''90deg''].

The <dfn lt="atan2()">atan2(A, B)</dfn> function
contains two comma-separated [=calculations=] A and B
that must resolve to <<number>>s,
and returns the <<angle>>
contains two comma-separated [=calculations=], A and B.
A and B can resolve to any <<number>>, <<dimension>>, or <<percentage>>,
but must have the <em>same</em> [=determine the type of a calculation|type=],
or else the function is invalid.
The function returns the <<angle>>
between the positive X-axis and the point (B,A).
The returned angle must be normalized to the interval (''-180deg'', ''180deg'']
(that is, greater than ''-180deg'', and less than or equal to ''180deg'').

Note: ''atan2(Y, X)'' is <em>generally</em> equivalent to ''atan(Y / X)'',
but it gives a better answer when the point in question is in the second (NW) or third (SW) quadrants of the plane.
''atan2(1, -1)'', corresponding to the point (-1, 1) in the NW of the plane,
but it gives a better answer when the point in question may include negative components.
''atan2(1, -1)'', corresponding to the point (-1, 1),
returns ''135deg'',
distinct from ''atan2(-1, 1)'', corresponding to the point (1, -1) in the SE of the plane,
distinct from ''atan2(-1, 1)'', corresponding to the point (1, -1),
which returns ''-45deg''.
However, as ''1 / -1'' and ''-1 / 1'' both resolve to ''-1'',
''atan()'' returns the same ''-45deg'' for both points.
In contrast, ''atan(1 / -1)'' and ''atan(-1 / 1)'' both return''-45deg'',
because the internal calculation resolves to ''-1'' for both.


<h4 id="trig-infinities">
Expand Down Expand Up @@ -2603,6 +2605,7 @@ Exponential Functions: ''pow()'', ''sqrt()'', ''hypot()''</h3>
and then the ''pow(X, 1/3)'' would cube-root the value back down to 30 and multiply the exponent by 1/3,
giving «[ "length" → 1 ]»,
which [=CSSNumericValue/matches=] <<length>>.

In the realm of pure mathematics, that's guaranteed to work out;
in the real-world of computers using binary floating-point arithmetic,
in some cases the powers might not exactly cancel out,
Expand Down Expand Up @@ -2652,7 +2655,8 @@ Exponential Functions: ''pow()'', ''sqrt()'', ''hypot()''</h3>
as the inputs and output all have the same type.
The result isn't unit-dependent, either,
due to the nature of the operation;
''hypot(3em, 4em)'' and ''hypot(48px, 64px)'' give the same result in both cases:
''hypot(3em, 4em)'' and ''hypot(48px, 64px)'' both result in the same length
when ''1em'' equals ''16px'':
''5em'' or ''80px''.
Thus it's fine to let author use dimensions directly in ''hypot()''.
</details>
Expand Down Expand Up @@ -2986,14 +2990,14 @@ Computed Value</h3>
so implementations can simplify the expressions
further than what is required here
when storing the values internally;
in particular, all [=math function=] expressions can be reduced
in particular, all [=calculation=] expressions can be reduced
to a sum of a <<number>>, a <<percentage>>, and some <<dimension>>s,
eliminating all multiplication or division,
and combining terms with identical units.

At this time, all units can be absolutized
to a single unit per type at computed-value time,
so at that point the [=math function=] can be reduced
so at that point the [=calculation=] can be reduced
to just a <<number>>, a <<percentage>>, and a single absolute <<dimension>> of the appropriate type,
per expression.
</div>
Expand Down