Re: [CSSWG] Resolutions 2008-03-04 and 2008-03-11

On Mar 12, 2008, at 8:55 AM, Brad Kemper wrote:

> [...] This really is a mathematical formula, where "n" is the  
> progressively larger number representing the number of times  
> repeated so far, starting with zero and increasing by one with each  
> iteration (when using "+"). For each value of "n", solving the  
> formula tells you which child number to apply the style to. [...]
>
> I think the spec is not really that clear on the fact that this  
> really is a mathematical formula in which n = {0,1,2,3,4...}, where  
> solving the equation gives you the child number (assuming the child  
> elements are numbered starting with 1). It never really comes out  
> and says it that explicitly, even though it gives examples where  
> a=1 or b=0 or a is negative, etc. and the math continues to work.

One thing that seems very wrong with the spec is this part;

:nth-child(10n-1)  /* represents the 9th, 19th, 29th, etc, element */
:nth-child(10n+9)  /* Same */

In other words, if b is negative then b = (a + b)
(the negative b is added to a, thus reducing it by the absolute value  
of b; this now positive value is then substituted for the previously  
negative value in the equation) .
To my way of thinking, the two rules shown above should not be the  
same. Let me explain...

For all the other examples given for nth-child, the following all  
works out beautifully:

given (using existing (an+b) convention):
a = multiplier for "n". Absolute value of which is the "grouping  
size" of which only one element of the group receives the style of  
the rule
b = ordinal number of the child element within each "a" group that  
receives the style of the rule
n = set of integers starting with 0, inserted into the formula one  
integer at a time, stopping when there are no remaining elements.
c = total number of child elements
t = total number of child elements that receives the style of the rule
i = ignored solutions of equation after solving for the "n" values  
(where the equation equals a negative number or zero, since they  
repressent child element ordinal numbers that are not in the document  
tree)

then:
an-b = set of numbers representing ordinal identification of child  
elements
t = c / abs(a) - (number of "i" values)

So if you imagine a 12 row table, then the following is true given  
the selectors shown (and agrees with the spec):

tr:nth-child(2n+1) { color: red; }
number of rows colored red (t) = 12 / 2
red row numbers = 2 * { 0,1,2,3,4,5... } + 1
red row numbers =  { 0,2,4,6,8,10 } + 1
red row numbers =  { 1,3,5,7,9,11 }
t = 6 red rows

tr:nth-child(4n+1) { color: green; }
number of rows colored green (t) = 12 / 4
green row numbers = 4 * { 0,1,2,3,4,5... } + 1
green row numbers =  { 0,4,8 } + 1
green row numbers =  { 1,5,9 }
t = 3 green rows

tr:nth-child(-n+6) { color: blue; }
number of rows colored blue (t) = 12 / 1
blue row numbers = -1 * { 0,1,2,3,4,5... } + 6
blue row numbers =  { 0,-1,-2,-3,-4,-5 } + 6
blue row numbers =  { 6,5,4,3,2,1 }
t = 6 blue rows

However:
tr:nth-child(4n-1) { color: orange; }
number of rows colored orange (t) = 12 / 4
orange row numbers = 4 * { 0,1,2,3... } - 1
orange row numbers =  { 0,4,8,12 } - 1
orange row numbers =  { -1,3,7,11 }
orange row numbers =  { 3,7,11 } (nonsense values removed)
t = 3 orange rows

Not the same as:
tr:nth-child(4n+3) { color: orange; }
number of rows colored orange (t) = 12 / 4
orange row numbers = 4 * { 0,1,2,3... } +3
orange row numbers =  { 0,4,8,12 } +3
orange row numbers =  { 3,7,11,12 }
t = 4 orange rows

Thus:

Having a negative "b" value could add power to the spec by letting  
you style all but the last 1 or more child elements. This would also  
make the math more sensible, and lead to an easier time for  
JavaScript to be able to determine which rows received the style. I  
see no upside to having this single part of the spec deviate from  
mathematical perfection.