simd-to-numpy.ipynb

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    "# Hardware SIMD to Numpy cheat sheet\n",
    "\n",
    "## What it means:\n",
    "\n",
    "   * SSE (1999) executes 4/2 floats/doubles in one hardware instruction\n",
    "   * AVX (2008) and AVX2 (2011) executes 8/4 floats/doubles in one hardware instruction\n",
    "   * AVX-512 (2013) executes 16/8 floats/doubles in one hardware instruction\n",
    "   * NVidia GPUs execute 32 values in one hardware instruction (\"warps\")\n",
    "   * AMD GPUs execute 64 values in one hardware instruction (\"wavefront\")\n",
    "   * Numpy functions execute **an arbitrary number** (e.g. millions) of values in one **Python instruction**, and is implemented with the best hardware vectorization available.\n",
    "\n",
    "## Terminology:\n",
    "\n",
    "| hardware vectorization | Numpy vectorization |\n",
    "|-|-|\n",
    "| mask | [fancy indexing with boolean array](https://docs.scipy.org/doc/numpy-1.13.0/user/basics.indexing.html#boolean-or-mask-index-arrays) |\n",
    "| gather | [fancy indexing with integer array](https://docs.scipy.org/doc/numpy-1.13.0/user/basics.indexing.html#index-arrays) (get) |\n",
    "| scatter | [fancy indexing with integer array](https://docs.scipy.org/doc/numpy-1.13.0/user/basics.indexing.html#index-arrays) (set) |\n",
    "| stride | [strides](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.ndarray.strides.html) (or reshape-slice-reshape) |\n",
    "| structure packing | [structured array](https://docs.scipy.org/doc/numpy/user/basics.rec.html) or \"recarray\" |\n",
    "\n",
    "## Bottom lines:\n",
    "\n",
    "Numpy vectorization is the same *basic concept* as hardware vectorization, but at a higher level of abstraction: Single (Python) Instruction on Multiple Data, rather than a Single (hardware) Instruction on Multiple Data.\n",
    "\n",
    "Reorganizing code for Numpy speedups enables hardware vectorization: sequential access, simple loops with no loop-carried dependencies."
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