notebooks/research/benchmarking_di_approximations_grid_decimal.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import tanh\n",
    "import numpy as np\n",
    "import scipy.stats as st \n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd \n",
    "import plotly.express as px\n",
    "import plotly.io as pio\n",
    "from decimal import *\n",
    "from decimal import Decimal\n",
    "pio.renderers.default = \"png\"\n",
    "\n",
    "\n",
    "getcontext().prec = 60\n",
    "\n",
    "k_1 = Decimal(1523) / Decimal(2000)\n",
    "k_2 = Decimal(3) / Decimal(4)\n",
    "_c = Decimal(1.0)\n",
    "_d = Decimal(1.0)\n",
    "\n",
    "def a(S_r, b, c, d):\n",
    "    return S_r - b * Decimal(tanh(c * d))\n",
    "\n",
    "def b(S_r, F_bar):\n",
    "    return (S_r - max(S_r - F_bar, 0)) / F_bar\n",
    "\n",
    "def B(g, a, b, c, d):\n",
    "    return a + b * Decimal(tanh(-c * (g - d)))\n",
    "\n",
    "def B_equiv(g, S_r, b):\n",
    "\n",
    "    _a = a(S_r, b, _c, _d)\n",
    "    return B(g, _a, b, _c, _d)\n",
    "\n",
    "def B_approx(g, S_r, b):\n",
    "    return S_r - b * (k_1 - k_2 * (1 - g))\n",
    "\n",
    "def F(credit_supply, space_pledged, history_size, min_replication_factor):\n",
    "    return credit_supply / max((space_pledged/min_replication_factor - history_size), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"media/beta.png\" height=200>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# N_YEARS = 4\n",
    "# BLOCK_TIME_IN_SECONDS = 10\n",
    "# BLOCKS_PER_DAY = 24 * 60 * 60 / BLOCK_TIME_IN_SECONDS\n",
    "# BLOCKS_PER_YEAR = BLOCKS_PER_DAY * 365.25\n",
    "# BLOCKS_PER_N_YEARS = BLOCKS_PER_YEAR * N_YEARS\n",
    "# MAX_DISBURSAL_DURING_N_YEARS = 500_000_000 # 500 Million\n",
    "# MAX_AVG_BLOCK_REWARD_DURING_N_YEARS = MAX_DISBURSAL_DURING_N_YEARS / BLOCKS_PER_N_YEARS\n",
    "# MIN_DISBURSAL_DURING_N_YEARS = MAX_DISBURSAL_DURING_N_YEARS / 10\n",
    "# MIN_AVG_BLOCK_REWARD_DURING_N_YEARS = MIN_DISBURSAL_DURING_N_YEARS / BLOCKS_PER_N_YEARS\n",
    "\n",
    "KB = 2 ** (1 * 10)\n",
    "MB = 2 ** (2 * 10)\n",
    "GB = 2 ** (3 * 10)\n",
    "TB = 2 ** (4 * 10)\n",
    "PB = 2 ** (5 * 10)\n",
    "EB = 2 ** (6 * 10)\n",
    "ZB = 2 ** (7 * 10)\n",
    "world_datasphere_size = 15 * ZB\n",
    "max_credit_supply = 1_000_000_000\n",
    "max_block_size = Decimal(3.75 * MB)\n",
    "\n",
    "g = [Decimal(i) for i in np.linspace(0, 1, 21)]\n",
    "S_r = [Decimal(i) for i in np.linspace(0, 200, 200)]\n",
    "#_F = st.beta.rvs(a=1, b=1_000_000, size=300) * max_credit_supply\n",
    "#_F = np.log(np.linspace(1.01, 10, 1000)) \n",
    "\n",
    "\n",
    "_F = [Decimal(10 ** -i) for i in range(-6, 12)]\n",
    "\n",
    "\n",
    "data = []\n",
    "for g_i in g:\n",
    "    for S_r_i in S_r:\n",
    "        for _f in _F:\n",
    "            Fbar = _f * max_block_size\n",
    "            _b = b(S_r_i, Fbar)\n",
    "            reward_approx = B_approx(g_i, S_r_i, _b)\n",
    "            reward_true = B_equiv(g_i, S_r_i, _b)\n",
    "            reward_error = reward_true - reward_approx\n",
    "            data.append(dict(g=g_i, \n",
    "                             S_r=S_r_i,\n",
    "                             F=_f,\n",
    "                             Fbar=Fbar, \n",
    "                             b=_b, \n",
    "                             B_approx=reward_approx, \n",
    "                             B_true=reward_true, \n",
    "                             B_error=reward_true-reward_approx,\n",
    "                             B_rel_error=(reward_true-reward_approx)/reward_true if reward_true != 0.0 else None\n",
    "                             ))\n",
    "\n",
    "df = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.box(df, x='g', y='B_rel_error', labels={'g': 'Utilization Ratio', 'B_rel_error': 'Relative Error (positive = true is bigger)'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.box(df, x='S_r', y='B_rel_error', labels={'S_r': 'Reference Subsidy', 'B_rel_error': 'Relative Error (positive = true is bigger)'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.box(df, x='F', y='B_rel_error', log_x=True, labels={'F': 'Storage Fee per Byte', 'B_rel_error': 'Relative Error (positive = true is bigger)'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df.F, df.B_rel_error, 'x')\n",
    "plt.xscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-07"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "250_000_000 / (1 * PB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}