memory-matrices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiments with Memory Access and Matrices\n",
    "\n",
    "In many problems, especially problems accessing lots of data and doing relatively simple computations on each datum, the performance bottleneck is memory rather than computational speed.  Because memory is arranged into a **memory hierarchy** of larger/slower and smaller/faster memories, it turns out that *changing the order* of memory access can have a huge impact on performance.\n",
    "\n",
    "In this notebook, we'll explore these performance issues with a few typical matrix algorithms, implemented in Julia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Julia Version 0.6.3\n",
      "Commit d55cadc350 (2018-05-28 20:20 UTC)\n",
      "Platform Info:\n",
      "  OS: macOS (x86_64-apple-darwin14.5.0)\n",
      "  CPU: Intel(R) Core(TM) i7-6820HQ CPU @ 2.70GHz\n",
      "  WORD_SIZE: 64\n",
      "  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)\n",
      "  LAPACK: libopenblas64_\n",
      "  LIBM: libopenlibm\n",
      "  LLVM: libLLVM-3.9.1 (ORCJIT, skylake)\n"
     ]
    }
   ],
   "source": [
    "using BenchmarkTools # a useful package of benchmarking utilities\n",
    "versioninfo() # a useful function to print out information about the machine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benchmarking Matrix Multiplication\n",
    "\n",
    "One of the most basic building blocks of numerical linear algebra is the computation of matrix multiplication: given an $m \\times n$ matrix $A$ and an $n \\times p$ matrix $B$, compute the $m \\times p$ matrix $C = AB$.   The entries of $C$ are given by the exact formula:\n",
    "$$\n",
    "C_{ik} = \\sum_{j=1}^n A_{ij} B_{jk}\n",
    "$$\n",
    "but there are many ways to implement this computation.   $\\approx 2mnp$ flops (floating-point additions and multiplications) are required, but they can re-ordered arbitrarily, leading to $\\sim (mnp)!$ possible orderings.\n",
    "\n",
    "It turns out that the ordering of the operations in the matrix multiplication has a *huge* impact on performance, along with low-level details of the inner loops.  Basically, three factors make the implementation of efficient matrix multiplication highly nontrivial:\n",
    "\n",
    "* [Caches](https://en.wikipedia.org/wiki/CPU_cache): the matrix accesses must be reordered to obtain [temporal locality](https://en.wikipedia.org/wiki/Locality_of_reference) and hence efficient memory (cache) usage.\n",
    "* [Registers](https://en.wikipedia.org/wiki/Processor_register): at the lowest level, the CPU registers form a kind of ideal cache.  The innermost loops of the matrix multiplication need to be unrolled in order to load many values into registers and perform as much work with them as possible (essentially a small submatrix multiplication).  It turns out that a [lot of tricks](http://cscads.rice.edu/workshops/july2007/autotune-slides-07/Frigo.pdf) are required to do this well.\n",
    "* [SIMD instructions](https://en.wikipedia.org/wiki/SIMD): modern CPUs include special instructions that can perform several arithmetic operations at once (e.g. 2, 4, or even 8 `Float64` operations), and to get the full benefit of these operations typically requires hand coding. \n",
    "\n",
    "As a consequence, there is a huge performance gap between the most obvious three-loop matrix-multiplication code and highly optimized code.  This gap has become the central factor in the design of dense linear-algebra libraries for several decades, especially the industry-standard free/open-source the [LAPACK](https://en.wikipedia.org/wiki/LAPACK) library: nearly all dense linear algebra is now organized around highly optimized [BLAS](https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms) libraries.\n",
    "\n",
    "Because Julia benefits from fast compilers, we can illustrate this performance gap fairly with simple Julia code.  (In contrast, similar implementation in Matlab or Python would be orders of magnitude slower, and would demonstrate mostly language rather than the algorithmic effects.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following is the simplest, most obvious, matrix-multiplication algorithm: just three nested loops, implementing a dot product for each output $C_{ik}$.\n",
    "\n",
    "The only concessions we have made to performance concerns here are (1) we implement an in-place `matmul!` variant that operates on a pre-existing `C` array, to avoid benchmarking the memory allocation/deallocation and (2) we use the `@inbounds` macro to turn off array bounds-checking in Julia for the inner loop.   Together, these make less than a factor of two difference in speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matmul (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute C = A * B, using naive matrix-multiplication algorithm,\n",
    "# with a pre-allocated output array C.  (\"!\" is a Julia convention\n",
    "# for functions that modify their arguments.)\n",
    "function matmul!(C, A, B)\n",
    "    m,n = size(A)\n",
    "    n,p = size(B)\n",
    "    size(C) == (m,p) || error(\"incorrect dimensions \", size(C), \" ≠ $m × $p\")\n",
    "    for i = 1:m\n",
    "        for k = 1:p\n",
    "            c = zero(eltype(C))\n",
    "            for j = 1:n\n",
    "                @inbounds c += A[i,j] * B[j,k]\n",
    "            end\n",
    "            @inbounds C[i,k] = c\n",
    "        end\n",
    "    end\n",
    "    return C\n",
    "end\n",
    "\n",
    "# a wrapper that allocates C of an appropriate type\n",
    "matmul(A, B) = matmul!(Array{promote_type(eltype(A), eltype(B))}(\n",
    "                             size(A,1), size(B,2)),\n",
    "                       A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.634357216034927e-16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# correctness check:\n",
    "A = rand(5,6)\n",
    "B = rand(6,7)\n",
    "norm(matmul(A,B) - A * B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Benchmarking naive `matmul`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we will benchmark our naive `matmul` implementation against the highly optimized [OpenBLAS library](http://www.openblas.net/) that Julia uses for its built-in matrix multiplication.   Like `matmul!`, we will call OpenBLAS with pre-allocated output via `A_mul_B!(C, A, B)` instead of the simpler `A * B`.  By default, OpenBLAS uses multiple CPU cores, which gives it an \"unfair\" parallel speedup, but we can disable this for benchmarking purposes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for benchmarking, use only single-threaded BLAS:\n",
    "BLAS.set_num_threads(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will benchmark $n \\times n$ matrix multiplications for various $n$ from 10 to 1000.  Julia's `@elapsed ...code...` macro is useful for benchmarking: it times the code and returns the time in seconds.   As we go, we will print the ratio of the naive time to the optimized time, to see the slowdown of our naive code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: slowdown of 0.003439432651965679\n",
      "finished n = 11: slowdown of 0.2545180722891566\n",
      "finished n = 12: slowdown of 0.873394495412844\n",
      "finished n = 13: slowdown of 0.9436201780415431\n",
      "finished n = 15: slowdown of 1.2254395036194417\n",
      "finished n = 16: slowdown of 1.7104773713577186\n",
      "finished n = 18: slowdown of 1.9799176107106071\n",
      "finished n = 20: slowdown of 2.508458192363461\n",
      "finished n = 22: slowdown of 2.62043795620438\n",
      "finished n = 24: slowdown of 0.5429614993114185\n",
      "finished n = 26: slowdown of 3.1448810478481692\n",
      "finished n = 29: slowdown of 3.594606164383561\n",
      "finished n = 32: slowdown of 5.246299977910316\n",
      "finished n = 35: slowdown of 3.394547759932375\n",
      "finished n = 39: slowdown of 5.196760362077179\n",
      "finished n = 43: slowdown of 3.9040229119488474\n",
      "finished n = 47: slowdown of 5.2670193034279045\n",
      "finished n = 52: slowdown of 7.325154234436344\n",
      "finished n = 57: slowdown of 7.124171499585749\n",
      "finished n = 63: slowdown of 7.51951927730279\n",
      "finished n = 69: slowdown of 7.154025331198136\n",
      "finished n = 76: slowdown of 10.848463210183173\n",
      "finished n = 84: slowdown of 12.168345969672787\n",
      "finished n = 92: slowdown of 9.894467228971601\n",
      "finished n = 102: slowdown of 10.929497196433495\n",
      "finished n = 112: slowdown of 13.0723730346671\n",
      "finished n = 123: slowdown of 12.980812000895588\n",
      "finished n = 136: slowdown of 15.590789142595378\n",
      "finished n = 150: slowdown of 16.17888519603147\n",
      "finished n = 165: slowdown of 17.58217862267965\n",
      "finished n = 182: slowdown of 18.747335209088245\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[33mWARNING: \u001b[39m\u001b[22m\u001b[33mround(::Type{T}, x::AbstractArray) where T is deprecated, use round.(T, x) instead.\u001b[39m\n",
      "Stacktrace:\n",
      " [1] \u001b[1mdepwarn\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::String, ::Symbol\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./deprecated.jl:70\u001b[22m\u001b[22m\n",
      " [2] \u001b[1mround\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Type{Int64}, ::Array{Float64,1}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./deprecated.jl:57\u001b[22m\u001b[22m\n",
      " [3] \u001b[1minclude_string\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::String, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./loading.jl:522\u001b[22m\u001b[22m\n",
      " [4] \u001b[1mexecute_request\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::ZMQ.Socket, ::IJulia.Msg\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/stevenj/.julia/v0.6/IJulia/src/execute_request.jl:193\u001b[22m\u001b[22m\n",
      " [5] \u001b[1m(::Compat.#inner#14{Array{Any,1},IJulia.#execute_request,Tuple{ZMQ.Socket,IJulia.Msg}})\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/stevenj/.julia/v0.6/Compat/src/Compat.jl:332\u001b[22m\u001b[22m\n",
      " [6] \u001b[1meventloop\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::ZMQ.Socket\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/stevenj/.julia/v0.6/IJulia/src/eventloop.jl:8\u001b[22m\u001b[22m\n",
      " [7] \u001b[1m(::IJulia.##13#16)\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./task.jl:335\u001b[22m\u001b[22m\n",
      "while loading In[5], in expression starting on line 1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 200: slowdown of 20.744656162817975\n",
      "finished n = 221: slowdown of 20.409211484147644\n",
      "finished n = 243: slowdown of 19.86331608581282\n",
      "finished n = 268: slowdown of 19.133545394614316\n",
      "finished n = 295: slowdown of 22.49223626607818\n",
      "finished n = 325: slowdown of 17.95879783625162\n",
      "finished n = 358: slowdown of 24.751094820215997\n",
      "finished n = 394: slowdown of 27.12657766258112\n",
      "finished n = 434: slowdown of 26.018988143044584\n",
      "finished n = 478: slowdown of 25.700658917753287\n",
      "finished n = 526: slowdown of 20.302710352017133\n",
      "finished n = 580: slowdown of 28.772426389152816\n",
      "finished n = 639: slowdown of 26.56611380542917\n",
      "finished n = 704: slowdown of 30.649836279537535\n",
      "finished n = 775: slowdown of 27.86497068494215\n",
      "finished n = 854: slowdown of 29.046256303689397\n",
      "finished n = 940: slowdown of 28.429680508365756\n",
      "finished n = 1036: slowdown of 25.603745960821687\n",
      "finished n = 1141: slowdown of 41.45394569890129\n",
      "finished n = 1257: slowdown of 34.7506882703886\n",
      "finished n = 1384: slowdown of 45.97549365476827\n",
      "finished n = 1525: slowdown of 48.71952280070161\n",
      "finished n = 1680: slowdown of 73.58641695193269\n",
      "finished n = 1850: slowdown of 114.76816140736328\n",
      "finished n = 2038: slowdown of 107.71858655541807\n",
      "finished n = 2245: slowdown of 102.92009033739124\n",
      "finished n = 2473: slowdown of 115.16402062685427\n",
      "finished n = 2724: slowdown of 128.69179358400956\n",
      "finished n = 3000: slowdown of 130.97465639341434\n"
     ]
    }
   ],
   "source": [
    "N = round.(Int, logspace(1, log10(3000), 60))  # 60 sizes from 10 to 3000\n",
    "# alternatively, use N = 10:1000 to see some interesting patterns due to cache associativity etc.\n",
    "t = Float64[]\n",
    "t0 = Float64[]\n",
    "for n in N\n",
    "    A = zeros(n,n)\n",
    "    B = zeros(n,n)\n",
    "    # preallocate output C so that allocation is not included in timing\n",
    "    C = zeros(n,n)\n",
    "    push!(t, @elapsed matmul!(C,A,B))\n",
    "    push!(t0, @elapsed A_mul_B!(C,A,B))\n",
    "    println(\"finished n = $n: slowdown of \", t[end]/t0[end])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot # a plotting library based on Python's Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will plot the results.  Since the number of flops is $2n^3$, we will plot $2n^3 / t$ for time $t$ in microseconds in order to plot the **gigaflops rate** (billions of flops per second).  If you naively think of a CPU as a box that performs floating-point instructions at a fixed rate, with all other instructions being negligible (a picture that *may* have been true circa 1985), this would be a flat horizontal line independent of $n$, but we will see that reality is quite different.\n",
    "\n",
    "The OpenBLAS library gets an \"unfair\" factor of 8 speedup on typical modern Intel processors thanks to hand-coded support for [AVX-512](https://en.wikipedia.org/wiki/Advanced_Vector_Extensions) SIMD instructions, which perform 8 double-precision floating-point operations simultaneously, so we will divide the BLAS performance by 8 for comparison purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x139e1dfd0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(N, 2N.^3 ./ t * 1e-9, \"rs-\")\n",
    "plot(N, 2N.^3 ./ t0 * 1e-9 / 8, \"b.-\")\n",
    "ylabel(L\"gigaflops $2n^3/t$\")\n",
    "xlabel(L\"matrix size $n$\")\n",
    "legend([\"naive matmul\", \"BLAS matmul / 8\"], loc=\"center right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Naive matmul in C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may be suspicious that the problem is simply that Julia is slow.   We can check this hypothesis by implementing the same algorithm in C, compiling it, and then calling it by Julia's built-in `ccall` instruction that makes it [easy to call C from Julia](http://docs.julialang.org/en/latest/manual/calling-c-and-fortran-code/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: redefining constant Clib\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "cmatmul (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# C implementation:\n",
    "Cmatmul = \"\"\"\n",
    "void Cmatmul(int m, int n, int p, double *C, double *A, double *B)\n",
    "{\n",
    "    int i, j, k;\n",
    "    for (i = 0; i < m; ++i)\n",
    "        for (j = 0; j < p; ++j) {\n",
    "            double c = 0.0;\n",
    "            for (k = 0; k < n; ++k)\n",
    "                c += A[i + m*k] * B[k + n*j];\n",
    "            C[i + m*j] = c;\n",
    "    }\n",
    "}\n",
    "\"\"\"\n",
    "# compile to a shared library by piping Cmatmul to gcc:\n",
    "# (only works if you have gcc installed)\n",
    "const Clib = tempname()\n",
    "open(`gcc -fPIC -O3 -xc -shared -o $(Clib * \".\" * Libdl.dlext) -`, \"w\") do f\n",
    "    print(f, Cmatmul)\n",
    "end\n",
    "\n",
    "# define a Julia cmatmul! function that simply calls the C code in the shared library we compiled\n",
    "function cmatmul!(C, A, B)\n",
    "    m,n = size(A)\n",
    "    n,p = size(B)\n",
    "    size(C) == (m,p) || error(\"incorrect dimensions \", size(C), \" ≠ $m × $p\")\n",
    "    ccall((\"Cmatmul\", Clib), Void, (Cint, Cint, Cint, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}),\n",
    "          m, n, p, C, A, B)\n",
    "    return C\n",
    "end\n",
    "cmatmul(A, B) = cmatmul!(Array{promote_type(eltype(A), eltype(B))}(\n",
    "                               size(A,1), size(B,2)),\n",
    "                         A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.803007031519277e-16"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# correctness check:\n",
    "A = rand(5,6)\n",
    "B = rand(6,7)\n",
    "norm(cmatmul(A,B) - A * B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's benchmark it and print out the \"speedup\" compared to pure Julia.  We see that it is **about the same speed**.  Julia's main claim to fame is that it is a dynamic language (like Python or Matlab) that stays within a factor of 2 (usually better) of C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: speedup of 1.108195211786372\n",
      "finished n = 11: speedup of 1.1926364234056541\n",
      "finished n = 12: speedup of 1.3158263305322129\n",
      "finished n = 13: speedup of 1.4289308176100628\n",
      "finished n = 15: speedup of 1.2974683544303798\n",
      "finished n = 16: speedup of 1.2631388184124683\n",
      "finished n = 18: speedup of 1.24629388816645\n",
      "finished n = 20: speedup of 1.184393063583815\n",
      "finished n = 22: speedup of 1.211845770414895\n",
      "finished n = 24: speedup of 1.179422143802382\n",
      "finished n = 26: speedup of 1.1528261793455163\n",
      "finished n = 29: speedup of 1.3317256162915327\n",
      "finished n = 32: speedup of 1.2341473684210527\n",
      "finished n = 35: speedup of 1.252817032932827\n",
      "finished n = 39: speedup of 1.280848918225156\n",
      "finished n = 43: speedup of 1.2828456879638317\n",
      "finished n = 47: speedup of 1.2779502295492486\n",
      "finished n = 52: speedup of 1.2538617613843002\n",
      "finished n = 57: speedup of 1.2922184588100187\n",
      "finished n = 63: speedup of 1.3378634944812127\n",
      "finished n = 69: speedup of 1.3836918255631754\n",
      "finished n = 76: speedup of 1.3386524873436378\n",
      "finished n = 84: speedup of 1.3184942877873016\n",
      "finished n = 92: speedup of 1.2824045760333846\n",
      "finished n = 102: speedup of 1.1891252880523457\n",
      "finished n = 112: speedup of 1.2026908095752704\n",
      "finished n = 123: speedup of 1.2032267022518843\n",
      "finished n = 136: speedup of 1.2063120336098843\n",
      "finished n = 150: speedup of 1.113183893952311\n",
      "finished n = 165: speedup of 0.9803828300232151\n",
      "finished n = 182: speedup of 0.9469263633941167\n",
      "finished n = 200: speedup of 0.9901730429296346\n",
      "finished n = 221: speedup of 0.894334509535846\n",
      "finished n = 243: speedup of 0.9427908792976597\n",
      "finished n = 268: speedup of 0.7753887482971524\n",
      "finished n = 295: speedup of 0.8098299659687535\n",
      "finished n = 325: speedup of 1.0431579976084586\n",
      "finished n = 358: speedup of 1.0124922253424962\n",
      "finished n = 394: speedup of 0.9213608207397664\n",
      "finished n = 434: speedup of 0.9293189249283453\n",
      "finished n = 478: speedup of 0.969904229601964\n",
      "finished n = 526: speedup of 0.929049849434872\n",
      "finished n = 580: speedup of 0.989403228449038\n",
      "finished n = 639: speedup of 0.9704020220981565\n",
      "finished n = 704: speedup of 0.9856967874489875\n",
      "finished n = 775: speedup of 1.1890452965257972\n",
      "finished n = 854: speedup of 1.1824314843502337\n",
      "finished n = 940: speedup of 1.2197478686093712\n"
     ]
    }
   ],
   "source": [
    "tc = Float64[]\n",
    "for n in N[N .<= 1000]\n",
    "    A = zeros(n,n)\n",
    "    B = zeros(n,n)\n",
    "    # preallocate output C so that allocation is not included in timing\n",
    "    C = zeros(n,n)\n",
    "    push!(tc, @elapsed cmatmul!(C,A,B))\n",
    "    println(\"finished n = $n: speedup of \", tc[end]/t[length(tc)])\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cache-oblivious matrix-multiplication"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a first step in the right direction, we'll implement a [cache-oblivious algorithm](https://en.wikipedia.org/wiki/Cache-oblivious_algorithm) for matrix multiplication: divide the matrices into four submatrices which are multiplied *recursively* until a sufficiently large base case is reached (large enough to amortize the recursion overhead).   This strategy erases the steep performance drop-off that occurs for large $n$ where the matrix goes out-of-cache, at the cost of ~25 lines of code rather than ~10 for the naive loops.\n",
    "\n",
    "(It still doesn't match the OpenBLAS performance because it fails to address the other two problems: unrolling and optimizing the base cases to optimize register utilization, and coding for SIMD instructions.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matmul_rec (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function add_matmul_rec!(m,n,p, i0,j0,k0, C,A,B)\n",
    "    if m+n+p <= 64   # base case: naive matmult for sufficiently large matrices\n",
    "        for i = 1:m\n",
    "            for k = 1:p\n",
    "                c = zero(eltype(C))\n",
    "                for j = 1:n\n",
    "                    @inbounds c += A[i0+i,j0+j] * B[j0+j,k0+k]\n",
    "                end\n",
    "                @inbounds C[i0+i,k0+k] += c\n",
    "            end\n",
    "        end\n",
    "    else\n",
    "        m2 = m ÷ 2; n2 = n ÷ 2; p2 = p ÷ 2\n",
    "        add_matmul_rec!(m2, n2, p2, i0, j0, k0, C, A, B)\n",
    "        \n",
    "        add_matmul_rec!(m-m2, n2, p2, i0+m2, j0, k0, C, A, B)\n",
    "        add_matmul_rec!(m2, n-n2, p2, i0, j0+n2, k0, C, A, B)\n",
    "        add_matmul_rec!(m2, n2, p-p2, i0, j0, k0+p2, C, A, B)\n",
    "        \n",
    "        add_matmul_rec!(m-m2, n-n2, p2, i0+m2, j0+n2, k0, C, A, B)\n",
    "        add_matmul_rec!(m2, n-n2, p-p2, i0, j0+n2, k0+p2, C, A, B)\n",
    "        add_matmul_rec!(m-m2, n2, p-p2, i0+m2, j0, k0+p2, C, A, B)\n",
    "        \n",
    "        add_matmul_rec!(m-m2, n-n2, p-p2, i0+m2, j0+n2, k0+p2, C, A, B)\n",
    "    end\n",
    "    return C\n",
    "end\n",
    "\n",
    "function matmul_rec!(C, A, B)\n",
    "    m,n = size(A)\n",
    "    n,p = size(B)\n",
    "    size(C) == (m,p) || error(\"incorrect dimensions \", size(C), \" ≠ $m × $p\")\n",
    "    fill!(C, 0)\n",
    "    return add_matmul_rec!(m,n,p, 0,0,0, C,A,B)\n",
    "end\n",
    "\n",
    "\n",
    "matmul_rec(A, B) = matmul_rec!(Array{promote_type(eltype(A), eltype(B))}(\n",
    "                                     size(A,1), size(B,2)),\n",
    "                               A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.02459954226118e-14"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# correctness check:\n",
    "A = rand(50,60)\n",
    "B = rand(60,70)\n",
    "norm(matmul_rec(A,B) - A * B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: slowdown of 0.004247034241515631\n",
      "finished n = 11: slowdown of 0.2916666666666667\n",
      "finished n = 12: slowdown of 1.1877675840978594\n",
      "finished n = 13: slowdown of 1.3780415430267063\n",
      "finished n = 15: slowdown of 1.7228541882109618\n",
      "finished n = 16: slowdown of 2.4463732176069435\n",
      "finished n = 18: slowdown of 2.7631307929969102\n",
      "finished n = 20: slowdown of 3.464475592073465\n",
      "finished n = 22: slowdown of 4.116019976949674\n",
      "finished n = 24: slowdown of 0.7785162565115861\n",
      "finished n = 26: slowdown of 4.373162256081262\n",
      "finished n = 29: slowdown of 4.785744863013698\n",
      "finished n = 32: slowdown of 6.425226419262205\n",
      "finished n = 35: slowdown of 3.9751690617075233\n",
      "finished n = 39: slowdown of 6.114816579323487\n",
      "finished n = 43: slowdown of 5.029305981084321\n",
      "finished n = 47: slowdown of 6.740811980490486\n",
      "finished n = 52: slowdown of 9.095975883342682\n",
      "finished n = 57: slowdown of 8.663421706710853\n",
      "finished n = 63: slowdown of 10.047144700758187\n",
      "finished n = 69: slowdown of 8.293463386227982\n",
      "finished n = 76: slowdown of 12.021608196212357\n",
      "finished n = 84: slowdown of 12.26975259377494\n",
      "finished n = 92: slowdown of 13.388857076530217\n",
      "finished n = 102: slowdown of 11.247150473389098\n",
      "finished n = 112: slowdown of 15.213226550669253\n",
      "finished n = 123: slowdown of 16.599843271885963\n",
      "finished n = 136: slowdown of 13.6900787787678\n",
      "finished n = 150: slowdown of 14.050381988513186\n",
      "finished n = 165: slowdown of 15.115296187140276\n",
      "finished n = 182: slowdown of 16.64155351190278\n",
      "finished n = 200: slowdown of 18.314074891077052\n",
      "finished n = 221: slowdown of 16.44658630030257\n",
      "finished n = 243: slowdown of 15.442286093969647\n",
      "finished n = 268: slowdown of 12.313240724043434\n",
      "finished n = 295: slowdown of 13.812655935266367\n",
      "finished n = 325: slowdown of 11.712873606714368\n",
      "finished n = 358: slowdown of 13.659886597026365\n",
      "finished n = 394: slowdown of 16.2042770759648\n",
      "finished n = 434: slowdown of 15.58330059240731\n",
      "finished n = 478: slowdown of 15.92241633628787\n",
      "finished n = 526: slowdown of 10.79735502923433\n",
      "finished n = 580: slowdown of 15.809205253055405\n",
      "finished n = 639: slowdown of 17.02777319254242\n",
      "finished n = 704: slowdown of 23.210988424379153\n",
      "finished n = 775: slowdown of 18.55598932185666\n",
      "finished n = 854: slowdown of 20.13601148380018\n",
      "finished n = 940: slowdown of 18.263319356282906\n",
      "finished n = 1036: slowdown of 14.171532855112906\n",
      "finished n = 1141: slowdown of 15.0526377983476\n",
      "finished n = 1257: slowdown of 15.304994137136635\n",
      "finished n = 1384: slowdown of 16.178849418892426\n",
      "finished n = 1525: slowdown of 15.050978587462133\n",
      "finished n = 1680: slowdown of 15.189220535090163\n",
      "finished n = 1850: slowdown of 16.36949944281203\n",
      "finished n = 2038: slowdown of 15.342610062722528\n",
      "finished n = 2245: slowdown of 16.53748083097306\n",
      "finished n = 2473: slowdown of 15.070185197905468\n",
      "finished n = 2724: slowdown of 19.232782848026844\n",
      "finished n = 3000: slowdown of 18.71581334351396\n"
     ]
    }
   ],
   "source": [
    "tco = Float64[]\n",
    "for n in N\n",
    "    A = zeros(n,n)\n",
    "    B = zeros(n,n)\n",
    "    # preallocate output C so that allocation is not included in timing\n",
    "    C = zeros(n,n)\n",
    "    push!(tco, @elapsed matmul_rec!(C,A,B))\n",
    "    println(\"finished n = $n: slowdown of \", tco[end]/t0[length(tco)])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x12c8d02e8>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(N, 2N.^3 ./ t * 1e-9, \"rs-\")\n",
    "plot(N, 2N.^3 ./ tco * 1e-9, \"ko-\")\n",
    "plot(N, 2N.^3 ./ t0 * 1e-9 / 8, \"b.-\")\n",
    "ylabel(L\"gigaflops $2n^3/t$\")\n",
    "xlabel(L\"matrix size $n$\")\n",
    "legend([\"naive matmul\", \"cache-oblivious\", \"BLAS matmul / 8\"], loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix addition\n",
    "\n",
    "Matrix addition is an interesting case because it has no data re-use, so there is no possible temporal locality, but depending on *what order* you use for the loops and *how matrices are stored* in memory, you may or may not get **spatial locality** that takes advantage of **cache lines**.\n",
    "\n",
    "Here let's implement matrix addition in two different ways.  As above, we'll use a pre-allocated output array so that our benchmark does not include the time for memory allocation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function matadd1!(C, A, B)\n",
    "    size(C) == size(A) == size(B) || throw(DimensionMismatchmatch())\n",
    "    m,n = size(A)\n",
    "    for i = 1:m\n",
    "        @simd for j = 1:n\n",
    "            @inbounds C[i,j] = A[i,j] + B[i,j]\n",
    "        end\n",
    "    end\n",
    "    return C\n",
    "end\n",
    "matadd1(A, B) = matadd1!(similar(A, promote_type(eltype(A), eltype(B))), A, B)\n",
    "\n",
    "function matadd2!(C, A, B)\n",
    "    size(C) == size(A) == size(B) || throw(DimensionMismatch())\n",
    "    m,n = size(A)\n",
    "    for j = 1:n\n",
    "        @simd for i = 1:m\n",
    "            @inbounds C[i,j] = A[i,j] + B[i,j]\n",
    "        end\n",
    "    end\n",
    "    return C\n",
    "end\n",
    "matadd2(A, B) = matadd2!(similar(A, promote_type(eltype(A), eltype(B))), A, B)\n",
    "\n",
    "A = rand(5,6)\n",
    "B = rand(5,6)\n",
    "A + B ≈ matadd1(A,B) ≈ matadd2(A,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: ratio t1/t2 of 0.12873563218390807\n",
      "finished n = 11: ratio t1/t2 of 0.7291066282420748\n",
      "finished n = 12: ratio t1/t2 of 0.7927631578947368\n",
      "finished n = 13: ratio t1/t2 of 0.7280701754385965\n",
      "finished n = 15: ratio t1/t2 of 0.82010582010582\n",
      "finished n = 16: ratio t1/t2 of 1.088815789473684\n",
      "finished n = 18: ratio t1/t2 of 0.9535452322738386\n",
      "finished n = 20: ratio t1/t2 of 1.2911764705882354\n",
      "finished n = 22: ratio t1/t2 of 0.9859719438877755\n",
      "finished n = 24: ratio t1/t2 of 1.2331838565022422\n",
      "finished n = 26: ratio t1/t2 of 1.1630036630036629\n",
      "finished n = 29: ratio t1/t2 of 1.29701230228471\n",
      "finished n = 32: ratio t1/t2 of 1.601317957166392\n",
      "finished n = 35: ratio t1/t2 of 1.1664766248574685\n",
      "finished n = 39: ratio t1/t2 of 1.5599999999999998\n",
      "finished n = 43: ratio t1/t2 of 2.246406570841889\n",
      "finished n = 47: ratio t1/t2 of 1.9421487603305783\n",
      "finished n = 52: ratio t1/t2 of 2.857379767827529\n",
      "finished n = 57: ratio t1/t2 of 2.660377358490566\n",
      "finished n = 63: ratio t1/t2 of 2.3063013698630135\n",
      "finished n = 69: ratio t1/t2 of 2.4278152069297403\n",
      "finished n = 76: ratio t1/t2 of 3.1430997876857747\n",
      "finished n = 84: ratio t1/t2 of 3.343392299687825\n",
      "finished n = 92: ratio t1/t2 of 3.2183241519280954\n",
      "finished n = 102: ratio t1/t2 of 3.286231884057971\n",
      "finished n = 112: ratio t1/t2 of 6.232216014897579\n",
      "finished n = 123: ratio t1/t2 of 3.4084070796460173\n",
      "finished n = 136: ratio t1/t2 of 2.504097900527675\n",
      "finished n = 150: ratio t1/t2 of 4.499827228749136\n",
      "finished n = 165: ratio t1/t2 of 4.922883064516129\n",
      "finished n = 182: ratio t1/t2 of 4.635826887878609\n",
      "finished n = 200: ratio t1/t2 of 4.051042486231314\n",
      "finished n = 221: ratio t1/t2 of 4.254618505534329\n",
      "finished n = 243: ratio t1/t2 of 3.9292869962473485\n",
      "finished n = 268: ratio t1/t2 of 4.033209453020774\n",
      "finished n = 295: ratio t1/t2 of 3.9236434108527134\n",
      "finished n = 325: ratio t1/t2 of 4.2774332913733355\n",
      "finished n = 358: ratio t1/t2 of 4.268018764500421\n",
      "finished n = 394: ratio t1/t2 of 4.215723016919239\n",
      "finished n = 434: ratio t1/t2 of 7.488951331296376\n",
      "finished n = 478: ratio t1/t2 of 4.678038425404657\n",
      "finished n = 526: ratio t1/t2 of 8.645783807228385\n",
      "finished n = 580: ratio t1/t2 of 12.523790190443323\n",
      "finished n = 639: ratio t1/t2 of 15.295931155097927\n",
      "finished n = 704: ratio t1/t2 of 15.407888809894658\n",
      "finished n = 775: ratio t1/t2 of 16.41821884920409\n",
      "finished n = 854: ratio t1/t2 of 15.360199111102776\n",
      "finished n = 940: ratio t1/t2 of 14.199748927234548\n",
      "finished n = 1036: ratio t1/t2 of 15.145200142221494\n",
      "finished n = 1141: ratio t1/t2 of 12.038810638767549\n",
      "finished n = 1257: ratio t1/t2 of 13.940558532243365\n",
      "finished n = 1384: ratio t1/t2 of 14.598619757485892\n",
      "finished n = 1525: ratio t1/t2 of 16.18552255214903\n",
      "finished n = 1680: ratio t1/t2 of 16.395168234614328\n",
      "finished n = 1850: ratio t1/t2 of 16.774064967911208\n",
      "finished n = 2038: ratio t1/t2 of 16.271256386694155\n",
      "finished n = 2245: ratio t1/t2 of 16.982404591030907\n",
      "finished n = 2473: ratio t1/t2 of 17.080904121812402\n",
      "finished n = 2724: ratio t1/t2 of 17.55659505793749\n",
      "finished n = 3000: ratio t1/t2 of 17.92689647105627\n"
     ]
    }
   ],
   "source": [
    "Na = round.(Int, logspace(1, log10(3000), 60))  # 60 sizes from 10 to 3000\n",
    "# alternatively, use N = 10:1000 to see some interesting patterns due to cache associativity etc.\n",
    "t1 = Float64[]\n",
    "t2 = Float64[]\n",
    "for n in Na\n",
    "    A = zeros(n,n)\n",
    "    B = zeros(n,n)\n",
    "    # preallocate output C so that allocation is not included in timing\n",
    "    C = zeros(n,n)\n",
    "    matadd1!(C,A,B) # add once just to make sure we are in cache if A and B are small\n",
    "    push!(t1, @elapsed matadd1!(C,A,B))\n",
    "    push!(t2, @elapsed matadd2!(C,A,B))\n",
    "    println(\"finished n = $n: ratio t1/t2 of \", t1[end]/t2[end])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x1248d0eb8>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Na, Na.^2 ./ t1 * 1e-9, \"rs-\")\n",
    "plot(Na, Na.^2 ./ t2 * 1e-9, \"bo-\")\n",
    "xlabel(L\"matrix size $n$\")\n",
    "ylabel(L\"gigaflops $n^2/t$\")\n",
    "legend([\"by row\", \"by column\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5,1,'ratio of matrix-addition algorithms')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Na, t1 ./ t2, \"rs-\")\n",
    "xlabel(L\"matrix size $n$\")\n",
    "ylabel(\"by row time / by column time\")\n",
    "title(\"ratio of matrix-addition algorithms\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that addition is about ***20 times slower*** if we add by rows rather than by columns.\n",
    "\n",
    "The reason for this is that **Julia stores matrices with consecutive columns**, which is known as **column-major storage** format."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.6.3",
   "language": "julia",
   "name": "julia-0.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}