lectures/lecture4/memory-matrices.ipynb

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    "# 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."
   ]
  },
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   "execution_count": 1,
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     "text": [
      "Julia Version 0.5.0\n",
      "Commit 3c9d753 (2016-09-19 18:14 UTC)\n",
      "Platform Info:\n",
      "  System: Darwin (x86_64-apple-darwin13.4.0)\n",
      "  CPU: Intel(R) Core(TM) i7-4870HQ CPU @ 2.50GHz\n",
      "  WORD_SIZE: 64\n",
      "  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)\n",
      "  LAPACK: libopenblas64_\n",
      "  LIBM: libopenlibm\n",
      "  LLVM: libLLVM-3.7.1 (ORCJIT, haswell)\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.)"
   ]
  },
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   "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": {
    "collapsed": false
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   "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": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.780116419453638e-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": {
    "collapsed": false
   },
   "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": {
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: slowdown of 0.002335922060811982\n",
      "finished n = 11: slowdown of 0.33070744516527645\n",
      "finished n = 12: slowdown of 1.2193080357142856\n",
      "finished n = 13: slowdown of 1.0458572173006773\n",
      "finished n = 15: slowdown of 1.4153732446415372\n",
      "finished n = 16: slowdown of 2.430735930735931\n",
      "finished n = 18: slowdown of 2.7261731978713115\n",
      "finished n = 20: slowdown of 3.1798964624676445\n",
      "finished n = 22: slowdown of 2.873990306946688\n",
      "finished n = 24: slowdown of 0.6522436815863374\n",
      "finished n = 26: slowdown of 1.6655930058667894\n",
      "finished n = 29: slowdown of 3.301819546051397\n",
      "finished n = 32: slowdown of 5.761379310344828\n",
      "finished n = 35: slowdown of 2.6761102005775386\n",
      "finished n = 39: slowdown of 3.3022725601235567\n",
      "finished n = 43: slowdown of 3.699258220898312\n",
      "finished n = 47: slowdown of 4.809542181069959\n",
      "finished n = 52: slowdown of 6.6241255758403\n",
      "finished n = 57: slowdown of 3.180450617563227\n",
      "finished n = 63: slowdown of 5.603082851637764\n",
      "finished n = 69: slowdown of 5.888858428711762\n",
      "finished n = 76: slowdown of 9.67729517114403\n",
      "finished n = 84: slowdown of 7.989632500289827\n",
      "finished n = 92: slowdown of 8.910855215483735\n",
      "finished n = 102: slowdown of 6.146395970380334\n",
      "finished n = 112: slowdown of 11.646014116001508\n",
      "finished n = 123: slowdown of 10.492688507540302\n",
      "finished n = 136: slowdown of 12.485194866222209\n",
      "finished n = 150: slowdown of 12.341359459267668\n",
      "finished n = 165: slowdown of 12.51781817470129\n",
      "finished n = 182: slowdown of 12.60854819467777\n",
      "finished n = 200: slowdown of 14.938942973393264\n",
      "finished n = 221: slowdown of 14.624375478102888\n",
      "finished n = 243: slowdown of 13.966451067256445\n",
      "finished n = 268: slowdown of 16.351358413771806\n",
      "finished n = 295: slowdown of 14.670104109555476\n",
      "finished n = 325: slowdown of 16.622091025367098\n",
      "finished n = 358: slowdown of 16.330973786690574\n",
      "finished n = 394: slowdown of 17.58797188709191\n",
      "finished n = 434: slowdown of 15.868238060549045\n",
      "finished n = 478: slowdown of 17.7160886685992\n",
      "finished n = 526: slowdown of 16.118796914811398\n",
      "finished n = 580: slowdown of 18.351318324219033\n",
      "finished n = 639: slowdown of 18.202082181840154\n",
      "finished n = 704: slowdown of 41.862809512442944\n",
      "finished n = 775: slowdown of 17.476939519101936\n",
      "finished n = 854: slowdown of 20.45003932992871\n",
      "finished n = 940: slowdown of 22.449601770030466\n",
      "finished n = 1036: slowdown of 47.76409516534963\n",
      "finished n = 1141: slowdown of 115.93164154118749\n",
      "finished n = 1257: slowdown of 143.46138853312144\n",
      "finished n = 1384: slowdown of 147.92205320672943\n",
      "finished n = 1525: slowdown of 155.74150801294206\n",
      "finished n = 1680: slowdown of 158.0423444571076\n",
      "finished n = 1850: slowdown of 162.25299701225484\n",
      "finished n = 2038: slowdown of 163.49126161407656\n",
      "finished n = 2245: slowdown of 173.5451624668125\n",
      "finished n = 2473: slowdown of 187.68157229315298\n",
      "finished n = 2724: slowdown of 203.47218650587592\n",
      "finished n = 3000: slowdown of 218.74359784041732\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": {
    "collapsed": false
   },
   "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": 8,
   "metadata": {
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   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3257497d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x32b812bd0>"
      ]
     },
     "execution_count": 8,
     "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": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cmatmul (generic function with 1 method)"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.932264640530591e-16"
      ]
     },
     "execution_count": 10,
     "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": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: speedup of 1.2878787878787878\n",
      "finished n = 11: speedup of 0.6132648295189164\n",
      "finished n = 12: speedup of 0.9482837528604119\n",
      "finished n = 13: speedup of 0.7817638266068759\n",
      "finished n = 15: speedup of 0.6060052219321149\n",
      "finished n = 16: speedup of 0.7284060552092609\n",
      "finished n = 18: speedup of 0.6269742679680568\n",
      "finished n = 20: speedup of 0.6335639668973002\n",
      "finished n = 22: speedup of 0.8658797077009556\n",
      "finished n = 24: speedup of 0.6770934012828399\n",
      "finished n = 26: speedup of 0.6769804544512743\n",
      "finished n = 29: speedup of 0.828883081468015\n",
      "finished n = 32: speedup of 0.9529737679127194\n",
      "finished n = 35: speedup of 0.9166496544081191\n",
      "finished n = 39: speedup of 0.7973987216320348\n",
      "finished n = 43: speedup of 0.757937949001342\n",
      "finished n = 47: speedup of 0.8361052434557075\n",
      "finished n = 52: speedup of 0.7299608489594065\n",
      "finished n = 57: speedup of 0.8085707173085813\n",
      "finished n = 63: speedup of 0.8534132759462217\n",
      "finished n = 69: speedup of 0.8384741613745428\n",
      "finished n = 76: speedup of 0.8324051172953745\n",
      "finished n = 84: speedup of 0.8634701568336436\n",
      "finished n = 92: speedup of 0.8448911396148302\n",
      "finished n = 102: speedup of 0.8412410027867853\n",
      "finished n = 112: speedup of 0.9328333796887445\n",
      "finished n = 123: speedup of 0.9326653926365287\n",
      "finished n = 136: speedup of 0.9523580338567764\n",
      "finished n = 150: speedup of 0.9628254698520933\n",
      "finished n = 165: speedup of 0.9283279154153339\n",
      "finished n = 182: speedup of 1.0341915330635492\n",
      "finished n = 200: speedup of 1.0165576087570307\n",
      "finished n = 221: speedup of 1.0223817896318756\n",
      "finished n = 243: speedup of 1.105102439505193\n",
      "finished n = 268: speedup of 1.0477491375152304\n",
      "finished n = 295: speedup of 0.9189273641249359\n",
      "finished n = 325: speedup of 0.8628178269813745\n",
      "finished n = 358: speedup of 1.0369569657470359\n",
      "finished n = 394: speedup of 0.9195350836527012\n",
      "finished n = 434: speedup of 1.0314244148837193\n",
      "finished n = 478: speedup of 0.928633861949043\n",
      "finished n = 526: speedup of 0.9888490640242205\n",
      "finished n = 580: speedup of 0.9777302042587722\n",
      "finished n = 639: speedup of 1.0338761727456214\n",
      "finished n = 704: speedup of 0.9658738238550412\n",
      "finished n = 775: speedup of 1.0784209504119282\n",
      "finished n = 854: speedup of 0.9841823718812687\n",
      "finished n = 940: speedup of 0.9187317167531202\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": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matmul_rec (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.379819757715681e-14"
      ]
     },
     "execution_count": 13,
     "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": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: slowdown of 0.001863537080054086\n",
      "finished n = 11: slowdown of 0.35418597466790236\n",
      "finished n = 12: slowdown of 1.4720982142857144\n",
      "finished n = 13: slowdown of 0.9062011464304325\n",
      "finished n = 15: slowdown of 0.8181818181818181\n",
      "finished n = 16: slowdown of 1.5405844155844157\n",
      "finished n = 18: slowdown of 1.7232704402515724\n",
      "finished n = 20: slowdown of 2.091458153580673\n",
      "finished n = 22: slowdown of 2.3809369951534736\n",
      "finished n = 24: slowdown of 0.6528740902057425\n",
      "finished n = 26: slowdown of 1.467387553203727\n",
      "finished n = 29: slowdown of 2.99230913524667\n",
      "finished n = 32: slowdown of 4.980492610837438\n",
      "finished n = 35: slowdown of 2.3542495902598923\n",
      "finished n = 39: slowdown of 2.951459880856071\n",
      "finished n = 43: slowdown of 3.635885754336779\n",
      "finished n = 47: slowdown of 4.524241255144033\n",
      "finished n = 52: slowdown of 5.267815503611443\n",
      "finished n = 57: slowdown of 2.9036782337239284\n",
      "finished n = 63: slowdown of 5.515911492323948\n",
      "finished n = 69: slowdown of 4.393256116784319\n",
      "finished n = 76: slowdown of 8.452924930956566\n",
      "finished n = 84: slowdown of 6.780361371954754\n",
      "finished n = 92: slowdown of 7.613578571522681\n",
      "finished n = 102: slowdown of 5.546205418129086\n",
      "finished n = 112: slowdown of 10.300613779205124\n",
      "finished n = 123: slowdown of 9.383172126885075\n",
      "finished n = 136: slowdown of 15.425016887426944\n",
      "finished n = 150: slowdown of 12.799447381493046\n",
      "finished n = 165: slowdown of 14.084016974971375\n",
      "finished n = 182: slowdown of 12.450570934677282\n",
      "finished n = 200: slowdown of 14.935477067933451\n",
      "finished n = 221: slowdown of 10.19227206444827\n",
      "finished n = 243: slowdown of 10.672423856968853\n",
      "finished n = 268: slowdown of 14.253211929969039\n",
      "finished n = 295: slowdown of 11.712886735297092\n",
      "finished n = 325: slowdown of 11.465633852464585\n",
      "finished n = 358: slowdown of 12.310613354190965\n",
      "finished n = 394: slowdown of 14.602652887377506\n",
      "finished n = 434: slowdown of 11.548132931448455\n",
      "finished n = 478: slowdown of 13.805379167920124\n",
      "finished n = 526: slowdown of 10.843162076650172\n",
      "finished n = 580: slowdown of 13.056188841460859\n",
      "finished n = 639: slowdown of 13.506987115876836\n",
      "finished n = 704: slowdown of 17.04702974768928\n",
      "finished n = 775: slowdown of 14.58141440169659\n",
      "finished n = 854: slowdown of 15.836454410024539\n",
      "finished n = 940: slowdown of 14.607325956584733\n",
      "finished n = 1036: slowdown of 14.213737197184367\n",
      "finished n = 1141: slowdown of 15.638244450704352\n",
      "finished n = 1257: slowdown of 14.239787472675578\n",
      "finished n = 1384: slowdown of 14.742565482364883\n",
      "finished n = 1525: slowdown of 16.341324890533237\n",
      "finished n = 1680: slowdown of 15.444487300665212\n",
      "finished n = 1850: slowdown of 14.90408917012598\n",
      "finished n = 2038: slowdown of 14.363571900323663\n",
      "finished n = 2245: slowdown of 15.478218922279632\n",
      "finished n = 2473: slowdown of 14.992286233416111\n",
      "finished n = 2724: slowdown of 18.24230116643573\n",
      "finished n = 3000: slowdown of 14.822236011949936\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": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31faf5ed0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x32558fc90>"
      ]
     },
     "execution_count": 19,
     "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": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Method definition matadd1!(Any, Any, Any) in module Main at In[23]:2 overwritten at In[24]:2.\n",
      "WARNING: Method definition matadd1(Any, Any) in module Main at In[23]:11 overwritten at In[24]:11.\n",
      "WARNING: Method definition matadd2!(Any, Any, Any) in module Main at In[23]:14 overwritten at In[24]:14.\n",
      "WARNING: Method definition matadd2(Any, Any) in module Main at In[23]:23 overwritten at In[24]:23.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 24,
     "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": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished n = 10: ratio t1/t2 of 0.15634365634365635\n",
      "finished n = 11: ratio t1/t2 of 0.3225419664268585\n",
      "finished n = 12: ratio t1/t2 of 0.4653061224489796\n",
      "finished n = 13: ratio t1/t2 of 7.17250126839168\n",
      "finished n = 15: ratio t1/t2 of 0.7116788321167884\n",
      "finished n = 16: ratio t1/t2 of 0.9323529411764706\n",
      "finished n = 18: ratio t1/t2 of 0.9845679012345678\n",
      "finished n = 20: ratio t1/t2 of 1.1845238095238095\n",
      "finished n = 22: ratio t1/t2 of 1.1076923076923075\n",
      "finished n = 24: ratio t1/t2 of 1.5365168539325842\n",
      "finished n = 26: ratio t1/t2 of 1.1340425531914895\n",
      "finished n = 29: ratio t1/t2 of 0.9741267787839586\n",
      "finished n = 32: ratio t1/t2 of 1.471304347826087\n",
      "finished n = 35: ratio t1/t2 of 1.6293103448275863\n",
      "finished n = 39: ratio t1/t2 of 2.1358760429082237\n",
      "finished n = 43: ratio t1/t2 of 1.5953096812988574\n",
      "finished n = 47: ratio t1/t2 of 1.3201811125485121\n",
      "finished n = 52: ratio t1/t2 of 2.525530243519246\n",
      "finished n = 57: ratio t1/t2 of 2.8564964447317394\n",
      "finished n = 63: ratio t1/t2 of 1.883874518436984\n",
      "finished n = 69: ratio t1/t2 of 2.010446343779677\n",
      "finished n = 76: ratio t1/t2 of 3.1184046530951393\n",
      "finished n = 84: ratio t1/t2 of 2.0815915386552506\n",
      "finished n = 92: ratio t1/t2 of 1.608768406961178\n",
      "finished n = 102: ratio t1/t2 of 3.511298421807748\n",
      "finished n = 112: ratio t1/t2 of 4.8946138437569555\n",
      "finished n = 123: ratio t1/t2 of 3.071875630930749\n",
      "finished n = 136: ratio t1/t2 of 2.214634146341463\n",
      "finished n = 150: ratio t1/t2 of 3.5581541628545286\n",
      "finished n = 165: ratio t1/t2 of 3.51385112503448\n",
      "finished n = 182: ratio t1/t2 of 4.453341711926028\n",
      "finished n = 200: ratio t1/t2 of 3.2995200469473724\n",
      "finished n = 221: ratio t1/t2 of 3.956627155172414\n",
      "finished n = 243: ratio t1/t2 of 5.139483520217465\n",
      "finished n = 268: ratio t1/t2 of 5.316008540188488\n",
      "finished n = 295: ratio t1/t2 of 5.040863981319323\n",
      "finished n = 325: ratio t1/t2 of 4.9714586473360605\n",
      "finished n = 358: ratio t1/t2 of 5.022322909873111\n",
      "finished n = 394: ratio t1/t2 of 4.915084228750447\n",
      "finished n = 434: ratio t1/t2 of 12.617099004085636\n",
      "finished n = 478: ratio t1/t2 of 21.23453118185783\n",
      "finished n = 526: ratio t1/t2 of 23.888944394253425\n",
      "finished n = 580: ratio t1/t2 of 16.289901505312063\n",
      "finished n = 639: ratio t1/t2 of 14.174946269950837\n",
      "finished n = 704: ratio t1/t2 of 12.478124824466626\n",
      "finished n = 775: ratio t1/t2 of 13.387479677085604\n",
      "finished n = 854: ratio t1/t2 of 14.674006299735304\n",
      "finished n = 940: ratio t1/t2 of 13.647782963019816\n",
      "finished n = 1036: ratio t1/t2 of 13.919763637073578\n",
      "finished n = 1141: ratio t1/t2 of 15.584105007641822\n",
      "finished n = 1257: ratio t1/t2 of 15.924452891481216\n",
      "finished n = 1384: ratio t1/t2 of 17.522825944358946\n",
      "finished n = 1525: ratio t1/t2 of 17.421498370904725\n",
      "finished n = 1680: ratio t1/t2 of 17.765693908977443\n",
      "finished n = 1850: ratio t1/t2 of 19.7557655022265\n",
      "finished n = 2038: ratio t1/t2 of 20.03357099410763\n",
      "finished n = 2245: ratio t1/t2 of 22.431939084079012\n",
      "finished n = 2473: ratio t1/t2 of 21.903825264210962\n",
      "finished n = 2724: ratio t1/t2 of 22.737932980780645\n",
      "finished n = 3000: ratio t1/t2 of 23.246140852389207\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": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x325624810>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x3256a2350>"
      ]
     },
     "execution_count": 26,
     "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": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x32d364a90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x32b76a950>"
      ]
     },
     "execution_count": 29,
     "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other examples: vectorized vs. devectorized operations\n",
    "\n",
    "Another example of the importance of spatial locality can be seen in vectorized operations.\n",
    "\n",
    "Consider the following function, which computes $f(x) = 2x^2 - 3x + 4$ *element-wise* for an array of $x$ values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Method definition f_vec(Any) in module Main at In[30]:1 overwritten at In[31]:1.\n",
      "WARNING: Method definition f_devec(Any) in module Main at In[30]:2 overwritten at In[31]:2.\n"
     ]
    }
   ],
   "source": [
    "f_vec(x) = 2 * x.^2 - 3 * x + 4\n",
    "f_devec(X) = map(f_vec, X)\n",
    "\n",
    "X = rand(10^6);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  samples:          317\n",
       "  evals/sample:     1\n",
       "  time tolerance:   5.00%\n",
       "  memory tolerance: 1.00%\n",
       "  memory estimate:  38.15 mb\n",
       "  allocs estimate:  11\n",
       "  minimum time:     14.23 ms (19.39% GC)\n",
       "  median time:      16.05 ms (23.22% GC)\n",
       "  mean time:        15.79 ms (22.26% GC)\n",
       "  maximum time:     19.90 ms (22.29% GC)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark f_vec($X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  samples:          1749\n",
       "  evals/sample:     1\n",
       "  time tolerance:   5.00%\n",
       "  memory tolerance: 1.00%\n",
       "  memory estimate:  7.63 mb\n",
       "  allocs estimate:  4\n",
       "  minimum time:     2.01 ms (0.00% GC)\n",
       "  median time:      2.13 ms (0.00% GC)\n",
       "  mean time:        2.86 ms (25.38% GC)\n",
       "  maximum time:     6.46 ms (47.31% GC)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark f_devec($X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `f_devec` function is about **7 times faster** than the vectorized version, and allocates about **1/5 the memory**.   That is because `f_vec` is effectively equivalent to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f_vec_really (generic function with 1 method)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function f_vec_really(x)\n",
    "    tmp1 = x.^2\n",
    "    tmp2 = 2 * tmp1\n",
    "    tmp3 = 3 * x\n",
    "    tmp4 = tmp2 - tmp3\n",
    "    tmp5 = tmp4 + 4\n",
    "    return tmp5\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is, each \"vectorized\" operation, like `x.^2`, while it is *individually fast*, does a *separate loop* over its data and *allocates a temporary array for the result*.  This is slow for three reasons:\n",
    "\n",
    "* It has poor temporal locality.\n",
    "* It is expensive to allocate all those temporary arrays.\n",
    "* The overhead of looping (incrementing/testing a counter, fetching elements `x[i]`, etcetera), is incurred multiple times rather than once.\n",
    "\n",
    "In Julia 0.6, there is a new syntax `2 .* x.^2 .- 3 .* x .+ 4` in which the compiler is guaranteed to \"fuse\" the operations into a single loop, allocating no temporary arrays.  In Julia 0.5, we can't do that, but it is sufficient to use `map(f, X)`, which does a single loop over `X`, calling `f(x)` for each element `x`, returning a new array."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.0",
   "language": "julia",
   "name": "julia-0.5"
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   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
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