{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8431e4b9-cba8-4d63-ada0-5fefc48ebc26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "half (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "half(x::Int)::Int = x/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ead86e3-3ecf-464f-a39b-45c6835a0fec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "half(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bb8c36a3-af33-41dc-ba18-0d434da96d57",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "InexactError: Int64(1.5)",
     "output_type": "error",
     "traceback": [
      "InexactError: Int64(1.5)",
      "",
      "Stacktrace:",
      " [1] Int64",
      "   @ .\\float.jl:812 [inlined]",
      " [2] convert",
      "   @ .\\number.jl:7 [inlined]",
      " [3] half(x::Int64)",
      "   @ Main .\\In[1]:1",
      " [4] top-level scope",
      "   @ In[3]:1",
      " [5] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [6] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "half(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d2186a6f-e109-4667-8962-6218a4787643",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CodeInfo(\n",
       "\u001b[90m1 ─\u001b[39m %1 = Main.Int\n",
       "\u001b[90m│  \u001b[39m %2 = x / 2\n",
       "\u001b[90m│  \u001b[39m %3 = Base.convert(%1, %2)\n",
       "\u001b[90m│  \u001b[39m %4 = Core.typeassert(%3, %1)\n",
       "\u001b[90m└──\u001b[39m      return %4\n",
       ")"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@code_lowered half(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d4c31280-570f-40d7-9570-a5180302c5b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function f(n::Integer)::Vector{Real}\n",
    "    randn(n)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2419a220-7089-4aaf-92c1-66d298b992c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.352352 seconds (2 allocations: 762.939 MiB, 1.84% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-14842.156808955893"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time sum(randn(10^8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3d290022-08d4-40f5-a9d6-7d9e799ebcb8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  9.420157 seconds (200.00 M allocations: 4.470 GiB, 58.79% gc time, 0.03% compilation time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4626.280496458812"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time sum(f(10^8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1505636d-3066-4d12-b75a-5e16049ad90f",
   "metadata": {},
   "outputs": [],
   "source": [
    "abstract type AbstractFoo{T} end\n",
    "\n",
    "struct Foo{T} <: AbstractFoo{T} a::T end\n",
    "double(x::Foo) = Foo(2x.a)\n",
    "\n",
    "struct Bar{T} <: AbstractFoo{T} a::T end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0ca151bf-2108-4d8f-adf2-5dfc7055f0b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Foo{Float64}(2.46)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "double(Foo(1.23))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "756319b4-0e1a-4736-b3c0-7ec5b51a2254",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching double(::Bar{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  double(\u001b[91m::Foo\u001b[39m) at In[8]:4",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching double(::Bar{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  double(\u001b[91m::Foo\u001b[39m) at In[8]:4",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[10]:1",
      " [2] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "double(Bar(1.23))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c45f6fa6-5757-4f08-87c0-127c9b4baf13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "double (generic function with 2 methods)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "double(x::AbstractFoo) = throw(MethodError(double, (x,)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2606fa41-1c56-486c-9524-cad69b5b95ca",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching double(::Bar{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  double(::AbstractFoo) at In[11]:1\n\u001b[0m  double(\u001b[91m::Foo\u001b[39m) at In[8]:4",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching double(::Bar{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  double(::AbstractFoo) at In[11]:1\n\u001b[0m  double(\u001b[91m::Foo\u001b[39m) at In[8]:4",
      "",
      "Stacktrace:",
      " [1] double(x::Bar{Float64})",
      "   @ Main .\\In[11]:1",
      " [2] top-level scope",
      "   @ In[12]:1",
      " [3] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [4] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "double(Bar(1.23))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0602f90e-be25-495c-bb78-f760d7f233a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "multiply (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multiply(x::Foo, y::Number) = Foo(x.a * y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "89b60f4a-2b17-49dd-bbb4-8c1c4440d396",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Foo{Float64}(30.0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multiply(Foo(3), 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d09742d6-8ec9-4799-97db-e71468039033",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching multiply(::Bar{Int64}, ::Float64)\n\u001b[0mClosest candidates are:\n\u001b[0m  multiply(\u001b[91m::Foo\u001b[39m, ::Number) at In[13]:1",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching multiply(::Bar{Int64}, ::Float64)\n\u001b[0mClosest candidates are:\n\u001b[0m  multiply(\u001b[91m::Foo\u001b[39m, ::Number) at In[13]:1",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[15]:1",
      " [2] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "multiply(Bar(3), 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ace4dbd6-1dc3-4195-a399-73de62cc3158",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "multiply (generic function with 2 methods)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multiply(x::AbstractFoo, y) = error(\"`myltiply` has not been implemented for $(typeof(x))\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "98c79eec-bc23-45d1-942d-6c8e1eb77801",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "`myltiply` has not been implemented for Bar{Int64}",
     "output_type": "error",
     "traceback": [
      "`myltiply` has not been implemented for Bar{Int64}",
      "",
      "Stacktrace:",
      " [1] error(s::String)",
      "   @ Base .\\error.jl:33",
      " [2] multiply(x::Bar{Int64}, y::Float64)",
      "   @ Main .\\In[16]:1",
      " [3] top-level scope",
      "   @ In[17]:1",
      " [4] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [5] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "multiply(Bar(3), 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6b4e50dd-7d93-4ae6-b8b9-9c1134c5a1b1",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "`myltiply` has not been implemented for Foo{Int64}",
     "output_type": "error",
     "traceback": [
      "`myltiply` has not been implemented for Foo{Int64}",
      "",
      "Stacktrace:",
      " [1] error(s::String)",
      "   @ Base .\\error.jl:33",
      " [2] multiply(x::Foo{Int64}, y::Vector{Float64})",
      "   @ Main .\\In[16]:1",
      " [3] top-level scope",
      "   @ In[18]:1",
      " [4] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [5] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "multiply(Foo(3), [10.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "85c73214-69b5-48fe-9739-e1df13857e6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "multiply (generic function with 2 methods)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multiply(x::AbstractFoo, y) = throw(MethodError(multiply, (x, y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "89a5e8af-47e3-4661-b5db-762d27746e0b",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching multiply(::Foo{Int64}, ::Vector{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  multiply(::AbstractFoo, ::Any) at In[19]:1\n\u001b[0m  multiply(::Foo, \u001b[91m::Number\u001b[39m) at In[13]:1",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching multiply(::Foo{Int64}, ::Vector{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  multiply(::AbstractFoo, ::Any) at In[19]:1\n\u001b[0m  multiply(::Foo, \u001b[91m::Number\u001b[39m) at In[13]:1",
      "",
      "Stacktrace:",
      " [1] multiply(x::Foo{Int64}, y::Vector{Float64})",
      "   @ Main .\\In[19]:1",
      " [2] top-level scope",
      "   @ In[20]:1",
      " [3] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [4] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "multiply(Foo(3), [10.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "656360cb-0bac-43d6-b9b0-687924635c0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "double! (generic function with 1 method)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function double!(a::Array)\n",
    "    @. a = 2a\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4c172625-c1a1-4129-a276-b9f847a86475",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "double!(v) = [2, 4, 6, 8]\n",
      "v = [2, 4, 6, 8]\n"
     ]
    }
   ],
   "source": [
    "v = [1, 2, 3, 4]\n",
    "@show double!(v)\n",
    "@show v;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "09ad41bf-679a-4af3-910e-a3cd13c92ec6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element view(::Vector{Int64}, 2:3) with eltype Int64:\n",
       " 4\n",
       " 6"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = view(v, 2:3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "282d110e-6342-4933-8ad6-52e97b43a48a",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching double!(::SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true})\n\u001b[0mClosest candidates are:\n\u001b[0m  double!(\u001b[91m::Array\u001b[39m) at In[21]:1",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching double!(::SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true})\n\u001b[0mClosest candidates are:\n\u001b[0m  double!(\u001b[91m::Array\u001b[39m) at In[21]:1",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[24]:1",
      " [2] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "double!(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "32e6d977-7fff-4988-ae4d-5383cc6acb7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "double! (generic function with 2 methods)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function double!(v)\n",
    "    @. v = 2v\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "979f8aaf-40a6-4660-844a-d82b788867b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "double!(w) = [8, 12]\n",
      "w = [8, 12]\n",
      "v = [2, 8, 12, 8]\n"
     ]
    }
   ],
   "source": [
    "@show double!(w)\n",
    "@show w\n",
    "@show v;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b74e19e7-9a48-4739-b436-84ce6718f28d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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