day 58 - integer exponentation.ipynb

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   "source": [
    "import numpy as np"
   ]
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   "source": [
    "## algorithm"
   ]
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   "source": [
    "def _power(x, y, identity=None, op=None):\n",
    "    p = identity\n",
    "\n",
    "    while y:\n",
    "        p = op(p, x) if y & 1 else p\n",
    "        x = op(x, x)\n",
    "        y >>= 1\n",
    "\n",
    "    return p"
   ]
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   "cell_type": "code",
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   "source": [
    "def power(x, y):\n",
    "    return _power(x, y, identity=type(x)(1), op=type(x).__mul__)"
   ]
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   "source": [
    "def mod_power(x, y, n):\n",
    "    return _power(x, y, \n",
    "                  identity=1,\n",
    "                  op=lambda a, b: (a * b) % n)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "def matrix_power(x, y):\n",
    "    return _power(x, y, \n",
    "                  identity=np.eye(x.shape[0], dtype=x.dtype),\n",
    "                  op=np.ndarray.__matmul__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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    "collapsed": false
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   "outputs": [
    {
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      "text/plain": [
       "(1267650600228229401496703205376, 1267650600228229401496703205376)"
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "power(2, 100), 2 ** 100"
   ]
  },
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   "execution_count": 7,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.2676506002282294e+30, 1.2676506002282294e+30)"
      ]
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power(2., 100), 2. ** 100"
   ]
  },
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   "execution_count": 8,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(562, 562)"
      ]
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     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "mod_power(2, 100, 1001), (2 ** 100) % 1001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1, 1000],\n",
       "       [   0,    1]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_power(np.array([[1, 1], [0, 1]]), 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.67041885e+111,   3.44456780e+111,   4.21871675e+111],\n",
       "       [  8.19736832e+111,   1.05737686e+112,   1.29501688e+112],\n",
       "       [  1.37243178e+112,   1.77029694e+112,   2.16816209e+112]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_power(np.arange(9, dtype=float).reshape(3, 3), 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": []
  }
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