denius

const U = Union{Type{Val{true}}, Type{Val{false}}}

f1(p::U = Val{false}) = p isa Type{Val{true}}
f2(p::U = Val{false}) = p isa      Val{true}   # false
f3(p::U = Val{false}) = p <:  Type{Val{true}}  # false
f4(p::U = Val{false}) = p <:       Val{true}
f5(p::U = Val{false}) = p === Type{Val{true}}  # false
f6(p::U = Val{false}) = p ===      Val{true}
f7(p::U = Val{false}) = p ==  Type{Val{true}}  # false

denius

K=1
  0.403818 seconds (113.14 k allocations: 5.859 MiB)
  7.123 ns (0 allocations: 0 bytes)
  775.527 ns (21 allocations: 1.13 KiB)
K=2
  0.021828 seconds (19.79 k allocations: 1019.997 KiB)
  12.328 ns (0 allocations: 0 bytes)
  1.474 μs (21 allocations: 1.22 KiB)
K=3
  0.036278 seconds (38.94 k allocations: 1.880 MiB)

denius

using StaticArrays
using BenchmarkTools, Compat

a = m = 0
for K = 1:18
    a = rand(SMatrix{K,K,Float64,K*K})
    m = Matrix(a)
    print("K=$K\n")
    @time qr(a)
    @btime qr($a)

denius

"""
QR decomposition by givens rotations of matrix without pivoting.

```math
A = Q R
```

Thin (reduced) method will produce `Q` and `R` in truncated form,
in opposite case `thin=false` Q is full, but R is still reduced, see [`qr`](@ref).
"""

denius

# apply reflector from right
# derived from base/linalg/generic.jl
@inline function reflectorApplyRight!(x::AbstractVector, τ::Number, A::AbstractMatrix)
    m, n = size(A)
    if length(x) != n
        throw(DimensionMismatch("reflector has length $(length(x)), which must match the first dimension of matrix A, $n"))
    end
    @inbounds begin
        for i = 1:m
            # note: ommited x[1] == 1