Definition of BlockUnitRange

[putianyi889]

A single firsts field should work, where the last index of the range is firsts[end]-1. The advantages are:

• The codes will become cleaner and the performance can be better. There are currently many conditional statements on the first block. The proposed definition eliminates them.
• The type stability can be improved. Now blocklengths(::BlockUnitRange{<:AbstractUnitRange}) is clearly a Fill and blocklengths(::BlockUnitRange{<:AbstractRange}) is a Vcat(::Int,::Fill). reference:

  BlockArrays.jl/src/blockaxis.jl

  Lines 449 to 468 in 2c86412

  	function blockfirsts(a::BlockedUnitRange{Base.OneTo{Int}})
  	first(a) == 1 || error("Offset axes not supported")
  	Base.OneTo{Int}(length(blocklasts(a)))
  	end
  	function blocklengths(a::BlockedUnitRange{Base.OneTo{Int}})
  	first(a) == 1 || error("Offset axes not supported")
  	Ones{Int}(length(blocklasts(a)))
  	end
  	function blockfirsts(a::BlockedUnitRange{<:AbstractRange})
  	st = step(blocklasts(a))
  	first(a) == 1 || error("Offset axes not supported")
  	@assert first(blocklasts(a))-first(a)+1 == st
  	range(1; step=st, length=length(blocklasts(a)))
  	end
  	function blocklengths(a::BlockedUnitRange{<:AbstractRange})
  	st = step(blocklasts(a))
  	first(a) == 1 || error("Offset axes not supported")
  	@assert first(blocklasts(a))-first(a)+1 == st
  	Fill(st,length(blocklasts(a)))
  	end

[jishnub]

See #348, which generalizes a BlockedUnitRange to allow a first value that's not 1, and adds a BlockedOneTo type that enforces the first value to be 1.

julia> b = blockedrange(Ones(Int,3))
3-blocked 3-element BlockedOneTo{Base.OneTo{Int64}}:
 1
 ─
 2
 ─
 3

julia> blocklasts(b)
Base.OneTo(3)

julia> blockfirsts(b)
Base.OneTo(3)

julia> blocklengths(b)
3-element Ones{Int64}

julia> b = blockedrange(Fill(2,3))
3-blocked 6-element BlockedOneTo{StepRangeLen{Int64, Int64, Int64, Int64}}:
 1
 2
 ─
 3
 4
 ─
 5
 6

julia> blocklengths(b)
3-element Fill{Int64}, with entries equal to 2

julia> blockfirsts(b)
1:2:5

julia> blocklasts(b)
2:2:6

[putianyi889]

This proposal is not about the first entry of the range. It's rather about the first block being separately processed.

[jishnub]

Could you create a PR with this change to BlockedUnitRange to the release-1.0 branch? It would be good to test out the implications.