Inline the whole broadcast expression to avoid allocation

[YingboMa]

map has an inline limit of 16. To make sure that the whole broadcast tree gets inlined properly, I added the _inlined_map function. I am not sure if it is a good idea, but worth trying.

This PR solves the issue which I have mentioned in
#30973

julia> @allocated foo(tmp, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13,
                    k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25,
                    k26, k27, k28, k29, k30, k31, k32, k33, k34)
0

As LLVM vectorization cut-off is 10 arrays, it doesn't make sense to try to make map inline for more than 16 args. I have removed _inlined_map, but preserved other @inlines to ensure a 9-array broadcast has no allocation.

[YingboMa]

using Test
u, uprev, k1, k2, k3, k4, k5, k6, k7, k8 = (ones(1000) for i in 1:10)
function foo(u, uprev, k1, k2, k3, k4, k5, k6) # vectorized
    @. u = uprev + 0.1*(0.1*k1 + 0.2*k2 + 0.3*k3 + 0.4*k4 + 0.5*k5 + 0.6*k6)
    nothing
end
function goo(u, uprev, k1, k2, k3, k4, k5, k6, k7) # vectorized
    @. u = uprev + 0.1*(0.1*k1 + 0.2*k2 + 0.3*k3 + 0.4*k4 + 0.5*k5 + 0.6*k6 + 0.7*k7)
    nothing
end
function hoo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8) # not vectorized
    @. u = uprev + 0.1*(0.1*k1 + 0.2*k2 + 0.3*k3 + 0.4*k4 + 0.5*k5 + 0.6*k6 + 0.7*k7 + 0.8*k8)
    nothing
end
function ioo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8) # not vectorized
    @. u = uprev + k1 + k2 + k3 + k4 + k5 + k6 + k7 + k8
    nothing
end
@allocated foo(u, uprev, k1, k2, k3, k4, k5, k6)
@allocated goo(u, uprev, k1, k2, k3, k4, k5, k6, k7)
@allocated hoo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8)
@allocated ioo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8)
@test @allocated(foo(u, uprev, k1, k2, k3, k4, k5, k6)) == 0
@test @allocated(goo(u, uprev, k1, k2, k3, k4, k5, k6, k7)) == 0
@test @allocated(hoo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8)) == 0
@test @allocated(ioo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8)) == 0
@test occursin("vector.body", sprint(code_llvm, foo, NTuple{8, Vector{Float32}}))
@test occursin("vector.body", sprint(code_llvm, goo, NTuple{9, Vector{Float32}}))
@test occursin("vector.body", sprint(code_llvm, hoo, NTuple{10, Vector{Float32}}))
@test occursin("vector.body", sprint(code_llvm, ioo, NTuple{10, Vector{Float32}}))

julia> ioo(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8)
remark: simdloop.jl:71:0: loop not vectorized: cannot prove it is safe to reorder memory operations
remark: simdloop.jl:71:0: loop not vectorized
remark: simdloop.jl:71:0: loop not vectorized: cannot identify array bounds
remark: simdloop.jl:71:0: loop not vectorized
remark: simdloop.jl:71:0: loop not vectorized: cannot identify array bounds
remark: simdloop.jl:71:0: loop not vectorized
remark: simdloop.jl:71:0: loop not vectorized: cannot identify array bounds
remark: simdloop.jl:71:0: loop not vectorized
remark: simdloop.jl:71:0: loop not vectorized: cannot identify array bounds
remark: simdloop.jl:71:0: loop not vectorized

Looks like the new vectorization cut off is 10 arrays.
CC: @mbauman

[YingboMa]

https://github.com/JuliaLang/julia/pull/30986/files#diff-fdaf2dae46d7b04f9c9d9e3940188cb9R802 wouldn't pass because Julia enables bounds check during testing.

[mbauman]

Nice work — thanks!