doc/Curve.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "#import matplotlib\n",
    "#matplotlib.use('tkAgg')\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "import math\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.optimize\n",
    "import scipy.misc\n",
    "import scipy.special"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "EUR_DECIMALS = 10**18\n",
    "NMK_DECIMALS = 10**18\n",
    "CAP = 15 * 10**8\n",
    "S = -6.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def issued(cummulative_euros):\n",
    "    return np.floor((- np.expm1(S * cummulative_euros / EUR_DECIMALS / CAP) ) * NMK_DECIMALS * CAP)\n",
    "\n",
    "def frac(cummulative_euros):\n",
    "    return issued(cummulative_euros) / issued(CAP)\n",
    "\n",
    "def issuance(cummulative_euros):\n",
    "    return - S * NMK_DECIMALS / EUR_DECIMALS * np.exp(S * cummulative_euros / EUR_DECIMALS / CAP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ud2G2Bslk/Dxwh7vvAnD3rRHM6EC/cLg/H3w6YUq5+4u0/rTD84H7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\n/x/O/wyAchRcewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dabb52518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = np.arange(0.0, 1.0 * CAP, 1.0 * CAP / 1000 )\n",
    "n = issued(e * EUR_DECIMALS) / NMK_DECIMALS\n",
    "plt.plot(e, n)\n",
    "\n",
    "plt.xlabel('€ invested')\n",
    "plt.ylabel('NMK issued')\n",
    "plt.title('Neumark issuance curve')\n",
    "plt.grid(True)\n",
    "plt.savefig(\"Issued.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OOaY/D8/foHHyRaRTS0vBd/eZ3swJ287isolD2Vtdp5uci0inpiP8JIwf0p0j+5Vy15y1\nDSekRUQ6HRX8JJgZl00cwqKNu1mwXidvRaRzUsFP0oXHDaRLfpy75qyNOoqISLuo4CeptDCPC8YN\n4O9vvMOu/TVRxxERabMWC76ZfdbMrm5m/lVmdkXqYmWmyyYOZX9NHQ9qfB0R6YRaO8L/MvAHADP7\nrZkVhfP/BHw1lcEy0diB3Rg/pDt/fGkN9Ro2WUQ6mdYKfiHQUNkmADPDxw4UpChTRvv85MNYu20f\nzy7dHHUUEZE2aa3gPwQ8ZGYTw3ULwsd/DZflnI8e1Y/+3Qr5w4uro44iItImLRZ8d78B+BtwM3BU\nON0MPOzu30t9vMyTF49x+aShzF6xjWXv7ok6johI0lq9Ssfd73D3KcD9wP3uPsXd70h5sgz2qQ8N\noTAvxh9m6yhfRDqP1q7SmWtmt5jZmcDn3P3TacqV0XoU5/Ox4wbx0PwNbN+rm6OISOfQ2hH+CQR9\n9VOA58zsMTO71sxGpTxZhvvcScOoqq3nnlc0iqaIdA6t9eHXhgOffdvdJwJXAXuAH5rZa2b267Sk\nzECjyko5eWRv7nxxDZU1dVHHERFpVWtdOsc2fu7u74R9+p8guE/tXakMl+m+cOpwtuyp4qH5G6KO\nIiLSqlYvyzSz8qYzzez7wNXuPjslqTqJE4f34uiB3bh91irq9EUsEclwrRX8S4D7zWwSgAVuA04h\n6NfPaWbGF6cMZ/XWvTy56N2o44iItKi1Pvx5wIXAX8IrdR4A+gBnuvvuNOTLeB89qh+H9S7mtudW\naqx8EclorfXh9wTWA58F/gLUAP8KlITLcl48Zkw75XAWrN/Fiyu3RR1HROSgWuvSmQfMBf5McHXO\nROCVRvMF+NhxA+lTWsBtz62MOoqIyEElWlro7oelK0hnVpgX56rJh/Gfjy/l9bd3Mm5w96gjiYh8\nQGtdOuNbmtIVsjO4/ISh9OiSxy+efivqKCIizWrxCJ+g22YRsCV8bo2WOfDhVITqjIoLEkw7ZTg3\nP7GU+et2cNyQHlFHEhF5n9b68K8DdgH7CW6Ecp67Tw2nFou9mRWa2Stm9oaZLTKzH3RQ5ox1xaSG\no/zlUUcREfmA1i7L/Lm7Twa+AgwGnjGz+8xsXBL7rgI+7O7HAuOAM83shENOnMEajvKfe2sLr63b\nEXUcEZH3Seom5u6+mmBc/H8CxwOtDp7mgYrwaV44Zf2F6ldMGkrP4nwd5YtIxrGWvixkZocDlwIX\nAG8D04FH3b0yqZ2bxQku4RwB3Oru32pmnWnANICysrLy6dOnt/V3AKCiooKSkpJ2bdvRHltVzX1v\n1XD9xEJG9ogDmZXvYJTx0GV6PlDGjpBJ+aZOnTrP3ScktbK7H3QC6oHXgR8Q9Od/rfHU0rZN9tMd\nmAGMbWm98vJyb68ZM2a0e9uOVlFZ4+U3/dMvue1Fr6+vd/fMyncwynjoMj2fuzJ2hEzKB8z1JGtx\na106NxKMh18PlAClTaZk31R2EtwA/cxkt+nMigsSfPW0kbyyejszl21pfQMRkTRo7YtX32/vjs2s\nD1Dj7jvNrAg4neB+uDnh0g8N4fcvrObmJ5Zyyqg+UccREWm54JtZSzcqd3e/qYXl/YE/hv34MeA+\nd3+0HRk7pfxEjK+fcQTX3DOfh+dvoFfUgUQk57XWpbO3mQmCO1994ARsY+6+wN2Pc/dj3H2su994\nyGk7mXOO7s/RA7vxP0+9RXVd1l+gJCIZrrXr8H/WMAG3A0XA5wiu1jk8Dfk6tVjM+PZZR7Jh536e\nXVcbdRwRyXGtXodvZj3N7IfAAoIuoPHu/i1335zydFngpBG9OWVUHx5ZWc32vdVRxxGRHNba4Gk/\nBV4lGBr5aHf/vrvrK6Rt9N1zRlNZB//z1LKoo4hIDktmLJ0BwHeBjWa2O5z2mJnueJWkUWWlfHhw\ngrvnrGPJO3rZRCQarfXhx9y9yN1L3b1ro6nU3bumK2Q2uHBEPl2L8rjx74t1K0QRiURSY+nIoSvJ\nN677yCheWrVNNzwXkUio4KfRp44fwhFlpfzwH0uorKmLOo6I5BgV/DRKxGPccP4Y1u/Yz6+eXRF1\nHBHJMSr4aXbi8N58/LiB/GbWSpZv2hN1HBHJISr4Ebj+nNEUFyS4/qGF1NfrBK6IpIcKfgR6lRTw\nnbOO5JU123lg3vqo44hIjlDBj8gl5YM5flhPfvz4ErZVVEUdR0RygAp+RGIx40cfG8veqlp++I8l\nUccRkRyggh+hkWWlfPHU4Tw0fwNPLd4UdRwRyXIq+BH7yodHMrp/V77z1zfZocHVRCSFVPAjlp+I\n8bNLjmXX/mq+98iiqOOISBZTwc8AYwZ05asfHsnf39jIY2++E3UcEclSKvgZ4gtThnP0wG589+GF\nbNVVOyKSAir4GSIvHuNnnziWiqpavvnAAo2oKSIdTgU/g4wqK+X6s0fz7NLN/GH2mqjjiEiWUcHP\nMFdMGsrpo8v4z8eXsnDDrqjjiEgWSVnBN7PBZjbDzJaY2SIzuzZVbWUTM+OnFx9Dz+J8vnrPfPZW\n6ebnItIxUnmEXwtc5+6jgROAL5vZmBS2lzV6FOfz80+OY/W2vdygSzVFpIOkrOC7+zvu/lr4eA+w\nBBiYqvayzaThvbhm6ggemLeee19dF3UcEckClo6rQcxsGDALGOvuu5ssmwZMAygrKyufPn16u9qo\nqKigpKTk0IKmUHvy1bvzs7mVLNtRz39MLOTwbvEUpQtk+msImZ8x0/OBMnaETMo3derUee4+IamV\n3T2lE1ACzAM+3tq65eXl3l4zZsxo97bp0N582yqq/MSfPOOTfvy0b91T2bGhmsj019A98zNmej53\nZewImZQPmOtJ1uOUXqVjZnnAg8Bd7v7XVLaVrXoW53PbZ8rZureaa+6ZT21dfdSRRKSTSuVVOgb8\nHlji7v+TqnZywdGDuvGjC8fy4spt3PzE0qjjiEgnlcoj/JOAy4EPm9nr4XR2CtvLapdMGMwVk4by\n2+dXM/0VncQVkbZLpGrH7v4CYKnafy763rljWL11L999eCGDe3bhpBG9o44kIp2IvmnbiSTiMW69\nbDyH9ynmi3+Zx4rNFVFHEpFORAW/k+lamMfvP/sh8hMxPn/nq7ofrogkTQW/Exrcswu/vWICm3ZX\n8rk7X6VCwy+ISBJU8Dup44b04NZPj2fRxt1M+9Ncqmrroo4kIhlOBb8TO31MGf910TG8uHIb197z\nOnX1GkNfRA5OBb+Tu6h8EP/v3DE8sehdrn/oTd04RUQOKmWXZUr6XDX5MHbsreZXM1aQF49x4wVH\nEXzvTUTkPSr4WeK6M0ZRXVfP7bNWAajoi8gHqOBnCTPjO2cdCcDts1ZhBj84X0VfRN6jgp9FmhZ9\ngO+fdxSxmIq+iKjgZ52mRb+ispabLz6GvLjOz4vkOhX8LNRQ9EsLEvzsqbfYub+GWz89nqL81N5A\nRUQymw77spSZcc1pI/nhhWOZsWwzV9wxh137a6KOJSIRUsHPcp85YSi//NRxvP72Tj75m5fYsHN/\n1JFEJCIq+Dng3GMG8Icrj2fDjv1ceOtsXn97Z9SRRCQCKvg5YvLI3jz4pRMpSMT45G9e4h8L3ok6\nkoikmQp+DhlVVsrfvnwSYwd248t3v8Yvn1lOvcbfEckZKvg5pldJAXddPZELxw3gZ0+9xbQ/z9PJ\nXJEcoYKfgwrz4vz8k+P43rljmLlsM+f/6gUWb9wddSwRSTEV/BxlZnx+8mFMn3YClTV1fOzXs3lh\ng470RbKZCn6OmzCsJ49eczLHDenO796s5t/vfZ3dlSr8ItlIBV/oU1rAX66ayIUj8njkjY2c9Yvn\neXXN9qhjiUgHS1nBN7M7zGyzmS1MVRvScRLxGBeOyOe+f51EPGZ88jcv8d9PLqOmrj7qaCLSQVJ5\nhH8ncGYK9y8pUD60B49dezIXjR/Er2as4PxfzebN9buijiUiHSBlBd/dZwHqF+iESgoS/PSSY/nN\n5eVsq6jigltf4CePLWF/tW6ULtKZWSrvgWpmw4BH3X1sC+tMA6YBlJWVlU+fPr1dbVVUVFBSUtKu\nbdMh0/NB8xn31jj3LavmufW19O1iXHlUAWN6RTfqZqa/jpmeD5SxI2RSvqlTp85z9wlJrezuKZuA\nYcDCZNcvLy/39poxY0a7t02HTM/n3nLG2Su2+Cn/9awP/daj/sW/zPX1O/alL1gjmf46Zno+d2Xs\nCJmUD5jrSdZYXaUjSTlxeG+e/LdTuO4jo3h26WZO+9lMbnl6OZU16uYR6SxU8CVphXlxrjltJM9c\nN4XTRpfx86ff4vT/eY6/vb5BY/KIdAKpvCzzHuAl4AgzW29mV6WqLUmvgd2LuPXT47n7XyZSWpjH\ntdNf59xfvsDMZZsbuvJEJAOl8iqdT7l7f3fPc/dB7v77VLUl0ThxeG/+cc1kbrl0HBVVtVz5h1e5\n9PaXmbd2R9TRRKQZ6tKRQxKLGReMG8jTXzuVGy84ipVb9nLR/73IZb97mRdXbtURv0gGUcGXDpGf\niHHFpGHM+uYUvnvOaJZvquDTv53DRf/3Is8u3aTCL5IBVPClQ3XJT3D1yYcz65tTuenCsWzaXcXn\n75zLWbc8z72vrtNVPSIRUsGXlCjMi3P5CUOZ+Y0p/PTiYwD41oNvMuknz/DTJ5fy7q7KiBOK5J5E\n1AEku+XFY1wyYTAXlw/i5VXb+cPs1fzfzJX85rlVfHRsPy790GBOGt6bWMyijiqS9VTwJS3MjEnD\nezFpeC/e3r6PP720hvvnrecfC95hYPciLpkwiEsmDGZg96Koo4pkLRV8SbvBPbtw/TljuO6MI3hq\n8Sbum/s2tzyznFueWc7kEb352HED+ciYMkoL86KOKpJVVPAlMoV5cc47dgDnHTuA9Tv28cC89dw/\ndz1fu+8N8hMxph7Rh/OOHcBpR5ZRlB/dgG0i2UIFXzLCoB5d+LfTR3HtaSN5bd1O/v7GRv7x5js8\nuWgTXfLjnDa6jI+MKSNeo8s7RdpLBV8yiplRPrQH5UN78P/OHcMrq7fz9wUbeWLhu/z9jY3EDe5a\n8zKnjS7j9NF9GdqrOOrIIp2GCr5krHjsvRO9N10wlvnrdnDHk3NZvqeKmx5dzE2PLmZk3xJOHtmH\nySN7cfxhvSgp0J+0yMHof4d0CvGYMWFYTyqOyGfKlFNZu20vTy/ZzIylm7lrzlrumL2aRMwYN7g7\nJ47ozeQRvRk3uDv5CX3VRKSBCr50SkN7FXPV5MO4avJhVNbU8draHbywYiuzV2zlV88u53+fWU5B\nIsaxg7pTPqwH5UOCbqIexflRRxeJjAq+dHqFeXFOHNGbE0f0BmDXvhpeWrWNV9dsZ+7aHfx21ir+\nLxyvf3ifYiYM7ckxg7tx9MBuHNGvlIKErgCS3KCCL1mnW5c8zhzbjzPH9gNgf3UdC9bvZO7aHcxb\nu4MnFr3LvXPfBiARM0aVlXL0wG6MHRS8CRzZr5TCPL0JSPZRwZesV5QfZ+LhvZh4eC8guI/z+h37\neXPDLt7csIuFG3bxz8XvvQmYwZCeXRjZt5RRZSWMKitlZFkJw/uU6I1AOjUVfMk5Zsbgnl0Y3LML\nZx/dHwjeBDbuquTN9btY+u5ulm+q4K1Ne5i5bDO1YXdQzIJzB8P7FDO0VzHDenVhWO9ihvUqZkD3\nIuIaD0gynAq+CMGbwMDuRQzsXnSgKwiguraeNdv2suzdPSzftIe3NlWweuteXlixlcqa+gPr5cWN\nwT26UGKVzNy9iIHdixjQvYgB3QsZ2L2I3iUFGiBOIqeCL9KC/ESMUWWljCorfd/8+npn854q1mzb\ny9pte1mzbR9rt+1l4Zr93D/3bfZWv3/c/7y40a9bIQO6FR14MyjrWkCf0kL6lBbQt7SAPqUF6jKS\nlFLBF2mHWCwo4P26FXJCeG4AYObMmZx66qnsrqxl4879B6YNOyt5Z1fweM7q7by7u5K6+g8OE1Fa\nkKBPWPwbpt4lBfTokk+PLnl075JPj+I8enbJp3uXfH3PQNpEBV+kg5kZ3Yry6FaUx+j+XZtdp7au\nnu37qtm8u4otFVVs2fPBadHG3WzZU0VFVe1B2yrOjx94EwjeFPLpWpSgtDCPkoIEXQvfe1waPt6y\nr56d+6qv+/uhAAAK70lEQVQpKUiQiOsNI5ektOCb2ZnALUAc+J27/2cq2xPpLBLxGH1LC+lbWtjq\nupU1dezYV82OvTXs3FfNjn01bN9Xzc69weNgXvB43fZ97KmsZU9lDTV1LQw0N+spAIry4pQWJigu\nSFCUF6dLfpyi/OBnl/xE8PjA/ARFebH35ofrFuXFKUjEyU/EKEjEKMiLURCPU5AXIz8e07mLDJKy\ngm9mceBW4CPAeuBVM3vE3Renqk2RbFSYF6d/tyL6d0v+5jDuTlVt/YHiH/yspaKqhldfX8iAYSOo\naLRsb3Ut+6vr2Fddx+7KWjbtrmRfdR2VNcG8fdXtvxdxXtwoSMQpSMTee1No8gaRHw+WJeIx8mLG\n1i1VPLl9AYlYjETcyIvHSMTswPJEPEZe3N6bF7f3rRuP2fvmJWIxYhZ0xcXNiMeMWPgzHuPA45jZ\ngXViMd5bt8l29e64O2ad680slUf4xwMr3H0VgJlNBy4AVPBFUszMKMyLU5gXp09pwfuWFW5dxpTJ\nh7Vpf+5OZU09+6pr2Vddx/4DbwS1VNXUU1VbT1VtHVW19VTXvvf8wOOaeqrr6g6sW91o/aqaenbv\nr6Wqto7aOqe23qnYV8ey3Zupraunts6pqa8/sCxjPPkYZoRvDo3fEDjwxmAWPI+FP80Ma/Q8Fj7v\nVVzAfV+YlPLI5p6aF9DMLgbOdPerw+eXAxPd/StN1psGTAMoKysrnz59ervaq6iooKSk5NBCp1Cm\n5wNl7AiZng86d0Z3p84JpvqGn+/Nq200r77RPAfqPZj3von3HnvDcsCbrudQz3vbV1VVk8jLb7Ku\nv2+/NNqXN1oPgn25v7esMGF8fmzBB37fZEydOnWeu09IamUPP5p09ARcQtBv3/D8cuCXLW1TXl7u\n7TVjxox2b5sOmZ7PXRk7Qqbnc1fGjpBJ+YC5nmRdTuUp+vXA4EbPBwEbU9ieiIi0IJUF/1VgpJkd\nZmb5wKXAIylsT0REWpCyk7buXmtmXwGeJLgs8w53X5Sq9kREpGUpvQ7f3R8DHktlGyIikhx9zU5E\nJEeo4IuI5AgVfBGRHKGCLyKSI1L2Tdv2MLMtwNp2bt4b2NqBcTpapucDZewImZ4PlLEjZFK+oe7e\nJ5kVM6rgHwozm+vJfr04ApmeD5SxI2R6PlDGjpDp+Q5GXToiIjlCBV9EJEdkU8G/PeoArcj0fKCM\nHSHT84EydoRMz9esrOnDFxGRlmXTEb6IiLRABV9EJEd0uoJvZmea2TIzW2Fm325meYGZ3Rsun2Nm\nwzIs39fMbLGZLTCzZ8xsaDrzJZOx0XoXm5mbWVovP0smn5l9InwdF5nZ3enMl0xGMxtiZjPMbH74\nb312mvPdYWabzWzhQZabmf1vmH+BmY1PZ74kM14WZltgZi+a2bGZlK/Reh8ys7rwLn+ZLdk7pWTC\nRDDM8krgcCAfeAMY02SdLwG3hY8vBe7NsHxTgS7h4y+mM1+yGcP1SoFZwMvAhEzKB4wE5gM9wud9\nM+01JDip98Xw8RhgTZozngKMBxYeZPnZwOOAAScAc9KZL8mMJzb6Nz4r3Rlby9fob+FZglGBL073\na9jWqbMd4R+4Mbq7VwMNN0Zv7ALgj+HjB4DTLH23lm81n7vPcPd94dOXCe4Elk7JvIYANwH/BVSm\nMxzJ5fsX4FZ33wHg7pszMKMDXcPH3Ujz3d7cfRawvYVVLgD+5IGXge5m1j896QKtZXT3Fxv+jYng\n/0oSryHANcCDQLr/BtulsxX8gcDbjZ6vD+c1u4671wK7gF5pSZdcvsauIjjKSqdWM5rZccBgd380\nncFCybyGo4BRZjbbzF42szPTli6QTMbvA58xs/UER3/XpCda0tr6txq1KP6vtMjMBgIfA26LOkuy\nUnoDlBRo7ki96XWlyayTKkm3bWafASYAp6Y0UTNNNzPvQEYziwE/B65MV6AmknkNEwTdOlMIjvqe\nN7Ox7r4zxdkaJJPxU8Cd7v4zM5sE/DnMWJ/6eEmJ8v9Jm5jZVIKCPznqLE38AviWu9elrxPh0HS2\ngp/MjdEb1llvZgmCj9OtfSzrKEnduN3MTgeuB05196o0ZWvQWsZSYCwwM/wj7gc8Ymbnu/vcDMjX\nsM7L7l4DrDazZQRvAK+mIV9D+61lvAo4E8DdXzKzQoIBtzLlo39Sf6tRM7NjgN8BZ7n7tqjzNDEB\nmB7+P+kNnG1mte7+cLSxWhD1SYQ2nkRJAKuAw3jvZNlRTdb5Mu8/aXtfhuU7juCE38hMfQ2brD+T\n9J60TeY1PBP4Y/i4N0HXRK8My/g4cGX4eDRBMbU0/1sP4+AnRM/h/SdtX4no77GljEOAFcCJUWRr\nLV+T9e6kE5y07VRH+H6QG6Ob2Y3AXHd/BPg9wcfnFQRH9pdmWL6fAiXA/eGRwTp3Pz/DMkYmyXxP\nAmeY2WKgDviGp/HoL8mM1wG/NbN/J+gqudLDypAOZnYPQZdX7/A8wg1AXpj/NoLzCmcTFNR9wOfS\nla0NGb9HcP7t1+H/lVpP4wiVSeTrdDS0gohIjuhsV+mIiEg7qeCLiOQIFXwRkRyhgi8ikiNU8EVE\nIpLsAG3hukPDARcXmNlMM2vzUBMq+NLphSM//sDM3jSzuWb2gUsMzewLZnZFGrJ0N7MvtWO775vZ\n11ORSTLanYRf0EvCfxOMf3QMcCPwk7Y2poIv2eBzBKMajgcmEV4r3Zi73+buf0pDlu4EI7aKtMqb\nGaDNzIab2RNmNs/MnjezI8NFY4BnwsczaH7Qwxap4Es2+CzwY3evCacP3G+08RF0+HH4ZjN7xcze\nMrOTw/lzzOyoRtvMNLNyMysOP3q/Go5vf0G4/KhwH6+HH7NHAv8JDA/n/TRc7xvhtgvM7AeN9n99\n2P4LwBGpfIGkU7kduMbdy4GvA78O578BXBQ+/hhQamZtGhiyU33TVqSp8NuQk4HfmFk9MM/dr0pi\n04S7H2/BjUluAE4nGOb4E8AN4VDBA9x9npn9GHjW3T9vZt2BV8zsaeALwC3ufpeZ5RN86/bbwFh3\nHxfmO4NgnJ/jCYYxeMTMTgH2EnwLfBzB/8PXgHkd8qJIp2VmJQT3AWj4Jj5AQfjz68CvzOxKgntV\nbABq27J/FXzJJrXAV5Nc96/hz3kE46UA3Ac8RfAG8Ang/nD+GcD5jfrYCwnGeXkJuD48efZXd1/e\nzKiJZ4TT/PB5CcEbQCnwkIf3RjCzSIe0kIwRA3Y2HDA05u4bgY/DgTeGi9x9V1t3LtJpufungNnA\nv7r7BHffm+SmDaOU1hEe+Lj7BmBbOELjJwmO+CE4Mr/I3ceF0xB3X+LudwPnA/uBx8zsw820Y8BP\nGm07wt1/3xC/rb+vZDd3300wAuwlcOCChGPDx73D4csBvgPc0db9q+BLNvgj8B9mlhdOVx/CvqYD\n3wS6ufub4bwngWssPHy34AYxmNnhwCp3/1/gb8AxwB6Co3cabfv58IgMMxtoZn0JPpJ/zMyKzKwU\nOO8QMksnFXZJvgQcYWbrzewq4DLgKjN7A1jEeydnpwDLzOwtoAz4UVvbU5eOZIM7CLpl5gPVwP8e\nwr4eAG4huMVjg5sIbnaxICz6a4BzCT4FfMbMaoB3CU4cb7fgTlwLgcfd/RtmNhp4KXy/qAA+4+6v\nmdm9BCfiNpO+sfwlg4SfUJvzgUs13f0Bgr/PdtNomSIiOUJdOiIiOUIFX0QkR6jgi4jkCBV8EZEc\noYIvIpIjVPBFRHKECr6ISI74/9/wXcEzPy1MAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dabadefd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = np.arange(0.0, 1.0 * CAP, 1.0 * CAP / 10**3)\n",
    "n = issuance(e * EUR_DECIMALS) \n",
    "plt.plot(e, n)\n",
    "\n",
    "plt.xlabel('€ invested')\n",
    "plt.ylabel('NMK/€')\n",
    "plt.title('Neumark \"price\" curve')\n",
    "plt.grid(True)\n",
    "plt.savefig(\"Issuance.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5304606143628922e-09"
      ]
     },
     "execution_count": 389,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issuance(5 * 10**9 * EUR_DECIMALS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ref_exp(k, n, d, e):\n",
    "    '''Computes k · (1 - n / d)^e '''\n",
    "    return k * (1 - n / d) ** e\n",
    "\n",
    "def binomial_exp(k, n, d, e):\n",
    "    '''Computes k · (1 - n / d)^e '''\n",
    "    # https://ethereum.stackexchange.com/questions/10425/is-there-any-efficient-way-to-compute-the-exponentiation-of-a-fraction-and-an-in/10432\n",
    "    s = 0\n",
    "    N = 1\n",
    "    B = 1 # Binomial coefficient\n",
    "    for i in range(22):\n",
    "        \n",
    "        s += k * (N / B) * (-1)**i * ((n ** i) / (d ** i))\n",
    "        \n",
    "        # Update binomial fraction\n",
    "        N = N * (e - i)\n",
    "        B = B * (i + 1)\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def nChoose(n):\n",
    "    k = 0\n",
    "    N = 1\n",
    "    yield 1\n",
    "    while k < n:\n",
    "        N *= (n - k)\n",
    "        k += 1\n",
    "        N = N // k\n",
    "        yield N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1]"
      ]
     },
     "execution_count": 325,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x for x in nChoose(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 553,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A = 1 - np.exp(S * EUR_DECIMALS / CAP)\n",
    "D = 2**54\n",
    "N = int(np.round(A * D))\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 / (15 * 10^9 * 10^18)  ]) * 2^64  ]\n",
    "D = 2**64\n",
    "N = 0\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 / (15 * 10^9 * 10^18)  ]) * 2^96  ]\n",
    "#D = 2**96\n",
    "#N = 343\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 / (15 * 10^9 * 10^18)  ]) * 2^128  ]\n",
    "# F = 1\n",
    "# D = 2**128\n",
    "# N = 1474556923324\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 * 2^9 / (15 * 10^9 * 10^18)  ]) * 2^128  ]\n",
    "# F = 2**9\n",
    "# D = 2**128\n",
    "# N = 754973144741922\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 * 2^18 / (15 * 10^9 * 10^18)  ]) * 2^128  ]\n",
    "F = 2**18\n",
    "D = 2**128\n",
    "N = 386546250107864134\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 * 2^32 / (15 * 10^9 * 10^18)  ]) * 2^128  ]\n",
    "#F = 2**32\n",
    "#D = 2**128\n",
    "#N = 6333173761767245919948\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 * 2^64 / (15 * 10^9 * 10^18)  ]) * 2^128  ]\n",
    "# F = 2**64\n",
    "# D = 2**128\n",
    "# N = 27200773099516585549495154777920\n",
    "\n",
    "# Mathematica: round[ (1 - exp[ -65 * 2^0 / (15 * 10^9 * 10^18)  ]) * 2^256  ]\n",
    "# F = 2**0\n",
    "# D = 2**256\n",
    "# N = 501765720028370180168807600617155207302701209852026\n",
    "\n",
    "# Mathematica: Rationalize[ (1 - exp[ -65 * 2^18 / (15 * 10^9 * 10^18)  ]), 2^-140 ]\n",
    "F = 2**18\n",
    "D = 880314753605769230770\n",
    "N = 1\n",
    "\n",
    "# Mathematica: Round[1 / (1 - exp[ -65 * 2^0 / (15 * 10^9 * 10^18)  ])]\n",
    "F = 2**0\n",
    "D = 230769230769230769230769231\n",
    "N = 1\n",
    "\n",
    "check = True\n",
    "debug = True\n",
    "def opt_exp_old(k, n, d, e):\n",
    "    '''Computes k - k · (1 - 1 / d)^e '''\n",
    "    global debug, check\n",
    "    i = 0\n",
    "    N = k\n",
    "    s = 0\n",
    "    e += F // 2\n",
    "    e = e // F\n",
    "    while N > 0:\n",
    "        N *= e - i\n",
    "        if check:\n",
    "            assert(N < 2**256)\n",
    "        i += 1\n",
    "        N = N // i\n",
    "        N *= n\n",
    "        if check:\n",
    "            assert(N < 2**256)\n",
    "        N = N // d\n",
    "        s += N\n",
    "        if debug:\n",
    "            print(N)\n",
    "        if N == 0:\n",
    "            break\n",
    "        N *= e - i\n",
    "        if check:\n",
    "            assert(N < 2**256)\n",
    "        i += 1\n",
    "        N = N // i\n",
    "        N *= n\n",
    "        if check:\n",
    "            assert(N < 2**256)\n",
    "        N = N // d\n",
    "        s -= N\n",
    "        if debug:\n",
    "            print(N)\n",
    "    return s\n",
    "\n",
    "def opt_exp(k, d, e):\n",
    "    '''Computes k - k · (1 - 1 / d)^e '''\n",
    "    global debug, check\n",
    "    i = 0\n",
    "    N = k\n",
    "    s = 0\n",
    "    D = d\n",
    "    while N > 0:\n",
    "        N *= e\n",
    "        if check:\n",
    "            assert(N < 2**256)\n",
    "            assert(D < 2**256)\n",
    "            assert(e >= 0)\n",
    "        N = N // D\n",
    "        if debug:\n",
    "            print(N)\n",
    "        if N == 0:\n",
    "            break\n",
    "        s += N\n",
    "        # e -= 1\n",
    "        D += d\n",
    "        \n",
    "        N *= e\n",
    "        if check:\n",
    "            assert(D < 2**256)\n",
    "            assert(N < 2**256)\n",
    "            assert(e >= 0)\n",
    "        N = N // D\n",
    "        if debug:\n",
    "            print(N)\n",
    "        if N == 0:\n",
    "            break\n",
    "        s -= N\n",
    "        # e -= 1\n",
    "        D += d\n",
    "    return s\n",
    "\n",
    "L = 83\n",
    "def implementation(x):\n",
    "    x = int(x)\n",
    "    if x >= L * 10**8 * EUR_DECIMALS:\n",
    "        return CAP * NMK_DECIMALS\n",
    "    my = opt_exp(CAP * NMK_DECIMALS, D, x)\n",
    "    return my"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 554,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n",
      "0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6e-18"
      ]
     },
     "execution_count": 554,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implementation(1) / NMK_DECIMALS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 555,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8300000000000000000000000000"
      ]
     },
     "execution_count": 555,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L * 10**8 * EUR_DECIMALS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 556,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1500000000.0"
      ]
     },
     "execution_count": 556,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implementation(L * 10**8 * EUR_DECIMALS) / NMK_DECIMALS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 557,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1499999999.9999995"
      ]
     },
     "execution_count": 557,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issued(L * 10**8 * EUR_DECIMALS) / NMK_DECIMALS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 558,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SOFLSlTmuz8xK+ES6Fcst4UfElyNit4gYB5wI3BERp+S1PjNrX53e7bRVuB++mVmXyPuk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\nIN6aVIsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0d6d90afd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "debug = False\n",
    "e = np.arange(0.0, 10.0 * 10**9, 10**6)\n",
    "i = np.array([implementation(x * EUR_DECIMALS) for x in e]) / NMK_DECIMALS\n",
    "a = issued(e * EUR_DECIMALS) / NMK_DECIMALS\n",
    "n = np.abs(i - a)\n",
    "plt.plot(e, n)\n",
    "\n",
    "plt.xlabel('€ invested')\n",
    "plt.ylabel('Absolute error (NMK)')\n",
    "plt.title('Neumark curve approximation')\n",
    "plt.grid(True)\n",
    "plt.savefig(\"Issuance.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 559,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3y0TEx3paZ3rV0ZdKjNNsQKnmFVBWvyrxv6bUp6ReCrwIfDT9rAH+lFVQZgNV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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0d6d7d6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "debug = False\n",
    "e = np.arange(0.0, 1.0, 0.0001)\n",
    "i = np.array([implementation(x * EUR_DECIMALS) for x in e]) / NMK_DECIMALS\n",
    "a = issued(e * EUR_DECIMALS) / NMK_DECIMALS\n",
    "n = np.abs(i - a)\n",
    "plt.plot(e, n)\n",
    "\n",
    "plt.xlabel('€ invested')\n",
    "plt.ylabel('Absolute error (NMK)')\n",
    "plt.title('Neumark curve approximation')\n",
    "plt.grid(True)\n",
    "plt.savefig(\"Issuance.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 532,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implementation(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "previous = 0\n",
    "for x in range(10**4):\n",
    "    new = implementation(x)\n",
    "    assert(new >= previous)\n",
    "    previous = new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.06666666665297862"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implementation(10**8)/implementation(CAP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "876676907"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implementation(135000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "877500006.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.floor(issued(135000001))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "664341210"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "664341210 # Wolfram alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "343"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "78062393"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "78062393"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-6.5"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.333333333333333e-09"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S/CAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1500000000"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 6, 13, 19, 26, 32, 39, 45, 52, 58]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[int(x) for x in \n",
    "issued(np.array(range(10)))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implementation(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 0],\n",
       " [1, 6],\n",
       " [2, 13],\n",
       " [3, 19],\n",
       " [4, 26],\n",
       " [5, 32],\n",
       " [6, 39],\n",
       " [7, 45],\n",
       " [8, 52],\n",
       " [9, 58]]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[[x, int(issued(x))] for x in range(0, 10**1, 10**0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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