haampie

"""
This is the implementation currently in SparseArrays
"""
function simple_mul!(y, A, x)
    @inbounds for i = Base.OneTo(A.n)
        xi = x[i]

        for j = A.colptr[i] : A.colptr[i + 1] - 1
            y[A.rowval[j]] += A.nzval[j] * xi
        end

haampie

#include <cstdint>
#include <cmath>

// g++ -Wall -O3 -std=c++14 -march=native -fPIC -shared -o givenlib.so micro.cc

extern "C" {
void fused_horizontal(double * __restrict__ A, int64_t cols, double c1, double s1, double c2, double s2, double c3, double s3, double c4, double s4)
{
    for (int64_t col = 0; col < cols; ++col, A += 4)
    {

haampie

using BenchmarkTools
using LinearAlgebra
using LinearAlgebra: givensAlgorithm

"""
I want to apply 4 'fused' Givens rotations to 4 columns of matrix Q. Here Q
is a n x 4 matrix. In the benchmarks I compare the number of GFLOP/s when the
rotations are applied to Q directly (vertical) versus when Q is first 
transposed (horizontal).

haampie

using LinearAlgebra
using LinearAlgebra: givensAlgorithm
using Test
using BenchmarkTools

import LinearAlgebra: rmul!

abstract type SmallRotation end

struct Rotation2{Tc,Ts} <: SmallRotation

haampie

using LinearAlgebra
using LinearAlgebra: givensAlgorithm
using Test
using BenchmarkTools

import LinearAlgebra: rmul!

abstract type SmallRotation end

struct Rotation2{Tc,Ts} <: SmallRotation

haampie

Chasing two double-shift-bulges one step forward using two 
reflections G1 and G2 of size 3 (they are each composed of 
two Givens rotations).

x x x x x x x x                         x x x x x x x x
x x x x x x x x ┐                       x x x x x x x x
x x x x x x x x │ double shift G2       . x x x x x x x
x x x x x x x x ┘                       . x x x x x x x
. . . x x x x x ┐                       . x x x x x x x
. . . x x x x x │ double shift G1       . . . . x x x x

haampie

using Base: tail

abstract type Ord end

# Composable ordering objects

struct Op{F} <: Ord
    isless::F
end

haampie

using StaticArrays

import Base: \
import LinearAlgebra: lu
using Base: OneTo

struct CompletelyPivotedLU{T,N,TA<:SMatrix{N,N,T},TP}
    A::TA
    p::TP
    q::TP

haampie

module TupleBench

using BenchmarkTools

const t32 = ntuple(identity, Val(32))
const t256 = ntuple(identity, Val(256))
const t1024 = ntuple(identity, Val(1024))
const v32 = collect(1:32)
const v256 = collect(1:256)
const v1024 = collect(1:1024)

haampie