asdasdasd1

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using BenchmarkTools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original code:\n",
    "```C\n",
    "double mat[N][N], s[N][N], val;\n",
    "int i, j, v[N];\n",
    "//\n",
    "// ... v[] and s[][] may be assumed to contain valid data\n",
    "//\n",
    "for(i=0; i<N ; ++i) {\n",
    "  for(j=0; j<N; ++j) {\n",
    "    val = (double)(v[i] % 256);\n",
    "    mat[j][i] = s[j][i]*(sin(val)*sin(val)-cos(val)*cos(val));\n",
    "  }\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "work (generic function with 2 methods)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function work(mat, s, v, N)\n",
    "    val = 0.0\n",
    "    @inbounds for i in 1:N\n",
    "        for j in 1:N\n",
    "            val = mod(v[i],256);\n",
    "            mat[i,j] = s[i,j]*(sin(val)*sin(val)-cos(val)*cos(val));\n",
    "        end\n",
    "    end;\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Test\n",
    "x = rand()\n",
    "@test 1-2*cos(x)*cos(x) ≈ sin(x)*sin(x)-cos(x)*cos(x)\n",
    "@test -cos(2*x) ≈ sin(x)*sin(x)-cos(x)*cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "opt1 (generic function with 2 methods)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pulling out + analytical opt\n",
    "function opt1(mat, s, v, N)\n",
    "    val = 0.0\n",
    "    @inbounds for i in 1:N\n",
    "        val = mod(v[i],256);\n",
    "        val = -cos(2*val)\n",
    "        for j in 1:N\n",
    "            mat[i,j] = s[i,j]*val;\n",
    "        end\n",
    "    end;\n",
    "    mat\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "opt12 (generic function with 2 methods)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pulling out + analytical opt + allocate values\n",
    "function opt12(mat, s, v, N)\n",
    "    val = Vector{Float64}(undef, length(v))\n",
    "    @inbounds for i in eachindex(val)\n",
    "        val[i] = -cos(2*mod(v[i],256));\n",
    "    end\n",
    "    \n",
    "    @inbounds for i in 1:N\n",
    "        for j in 1:N\n",
    "            mat[i,j] = s[i,j]*val[i];\n",
    "        end\n",
    "    end;\n",
    "    mat\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "opt2 (generic function with 2 methods)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reordering loops\n",
    "function opt2(mat, s, v, N)\n",
    "    val = 0.0\n",
    "    @inbounds for j in 1:N\n",
    "        for i in 1:N\n",
    "            val = mod(v[i],256);\n",
    "            val = -cos(2*val)\n",
    "            mat[i,j] = s[i,j]*val;\n",
    "        end\n",
    "    end;\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "opt22 (generic function with 1 method)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reordering loops + allocate values\n",
    "function opt22(mat, s, v, N)\n",
    "    val = Vector{Float64}(undef, length(v))\n",
    "    @inbounds for i in eachindex(val)\n",
    "        val[i] = -cos(2*mod(v[i],256));\n",
    "    end\n",
    "    \n",
    "    @inbounds for j in 1:N\n",
    "        for i in 1:N\n",
    "            mat[i,j] = s[i,j]*val[i];\n",
    "        end\n",
    "    end;\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Hwloc\n",
    "Hwloc.num_physical_cores()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "opt22_threaded (generic function with 1 method)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function opt22_threaded(mat, s, v, N)\n",
    "    val = Vector{Float64}(undef, length(v))\n",
    "    @inbounds for i in eachindex(val)\n",
    "        val[i] = -cos(2*mod(v[i],256));\n",
    "    end\n",
    "    \n",
    "    @inbounds Threads.@threads for j in 1:N\n",
    "        for i in 1:N\n",
    "            mat[i,j] = s[i,j]*val[i];\n",
    "        end\n",
    "    end;\n",
    "    mat\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 4000\n",
    "mat = zeros(N,N)\n",
    "s = rand(N,N)\n",
    "v = rand(Int, N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt22_threaded(mat, s, v, N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance: 9.096081484617212 MIt/s\n"
     ]
    }
   ],
   "source": [
    "runtime = @belapsed work($mat, $s, $v, $N);\n",
    "perf = N*N*1e-6/runtime # MIt/s\n",
    "println(\"Performance: $perf MIt/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance: 19.456335886711514 MIt/s\n"
     ]
    }
   ],
   "source": [
    "runtime = @belapsed opt1($mat, $s, $v, $N);\n",
    "perf = N*N*1e-6/runtime # MIt/s\n",
    "println(\"Performance: $perf MIt/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance: 19.358628902845535 MIt/s\n"
     ]
    }
   ],
   "source": [
    "runtime = @belapsed opt12($mat, $s, $v, $N);\n",
    "perf = N*N*1e-6/runtime # MIt/s\n",
    "println(\"Performance: $perf MIt/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance: 65.3802668739134 MIt/s\n"
     ]
    }
   ],
   "source": [
    "runtime = @belapsed opt2($mat, $s, $v, $N);\n",
    "perf = N*N*1e-6/runtime # MIt/s\n",
    "println(\"Performance: $perf MIt/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance: 658.4475132762567 MIt/s\n"
     ]
    }
   ],
   "source": [
    "runtime = @belapsed opt22($mat, $s, $v, $N);\n",
    "perf = N*N*1e-6/runtime # MIt/s\n",
    "println(\"Performance: $perf MIt/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73.11111111111111"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "658/9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "86"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emmy = 86"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "emmy_opt = 600"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "emmy_opt_threaded = 1.8 * 1e9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple `N`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "\n",
    "runtime = @belapsed work($mat, $s, $v);\n",
    "perf = N*N*1e-6/runtime # MIt/s\n",
    "println(\"Performance: $perf MIt/s\")"
   ]
  }
 ],
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