Use 0-size tidyverse recycling rules consistently

[DavisVaughan]

Closes #299

These changes to vec_size2() and shape_broadcast() enforce correct tidyverse recycling rules when comparing length-0 dimensions (those laid out in tidyverse/design#13 (comment)).

Specifically, the common length of 0 and 2 is now an error.

x  <- array(1, c(1, 2))
to <- array(1, c(1, 0))
vctrs:::shape_common(x, to)
#> Incompatible lengths: 2, 0.

The common length of 0 and 1 is 0, as it was before.

x  <- array(1, c(1, 1))
to <- array(1, c(1, 0))
vctrs:::shape_common(x, to)
#> [1] 0

When broadcasting to a shape, the dimensions you are broadcasting to must be exactly the same, unless the dimension you are broadcasting from is 1, in which case that can be broadcast to anything. All but the last of these examples produce the same result as before this PR, but I present them as a group to make the argument (the last one previously allowed you to broadcast from 2 down to 0)

# 1 can be broadcast _to_ anything
x  <- array(1, c(1, 1))
to <- array(1, c(1, 0))
vctrs:::shape_broadcast(x, to)
#>     
#> [1,]

to <- array(1, c(1, 2))
vctrs:::shape_broadcast(x, to)
#>      [,1] [,2]
#> [1,]    1    1

# everything else must be broadcast
# to the _exact_ same dimensions to be allowed

# 0 cannot be broadcast to 1
x  <- array(1, c(1, 0))
to <- array(1, c(1, 1))
vctrs:::shape_broadcast(x, to)
#> Can't cast <double[,0]> to <double[,1]>
#> Non-recyclable dimensions

# 2 cannot be broadcast to 0
x  <- array(1, c(1, 2))
to <- array(1, c(1, 0))
vctrs:::shape_broadcast(x, to)
#> Can't cast <double[,2]> to <double[,0]>
#> Non-recyclable dimensions

I think the only thing you might have a question about is the fact that this means you can't broadcast from 2 down to 0. You can currently do this with vec_recycle().

vctrs::vec_recycle(1:2, 0)
#> integer(0)

It also occurred to me while thinking about this that there are really two types of recycling rules. One set for determining a common length. And one set for determining if you can actually recycle from length X to length Y. The result of the first set of rules is guaranteed to be an allowed length in the second set of rules. The current impl of vec_recycle() implies that the second set of rules might be more flexible though, allowing that you can recycle from 2 down to 0, where the first set of rules would have never generated 0 as the common length of 2 and something else.

[DavisVaughan]

Hmm I also think this should be an error, which would imply that you can't vec_recycle_common() those inputs either. (this would match the tibble example tidyverse/tibble#435 (comment))

vctrs::vec_size_common(1:2, numeric())
#> [1] 0

[lionel-]

I think we should first reach a conclusion in the principles issues, before making any changes to vctrs.

This PR also needs to make broadcasting and recycling rules consistent by changing the common size code in size.c.

[DavisVaughan]

• The table in man/figures/size-recycling.png needs to be updated. Should the 0 row / col be removed entirely since it is now not a special case?

• vec_recycle()'s documentation suggests that that table should have been included in the docs. Should it be?

[DavisVaughan]

• If you have a better idea than shape_size2() I'm open to it. What I'm trying to do is find the common size of, say, x and y's 2nd dimension. Maybe axis2()?

Changed to axis2()

• For the recycling image above, should the first row and first column be removed since 0 is not a special case?

Removed them

• vec_recycle()'s documentation suggests that that table should have been included in the docs. Should it be?

Added the table png to the docs page

[DavisVaughan]

@lionel- good to go for a final review when you have time! (I don't know why the travis build isn't completing, it passed)

[lionel-]

Looks good!

[hadley]

Thanks @DavisVaughan!