├── .editorconfig
├── .gitconfig
├── .gitignore
├── approximate_mpmath.ipynb
├── approximation_float.ipynb
├── evaluation.ipynb
├── foundry copy.toml
├── foundry.toml
├── simulation.ipynb
└── src
    ├── FixedPointMathLib.sol
    └── test
        ├── FixedPointMathLib.t.sol
        └── console.sol


/.editorconfig:
--------------------------------------------------------------------------------
 1 | # See <https://editorconfig.org/>
 2 | root = true
 3 | 
 4 | [*]
 5 | end_of_line = lf
 6 | charset = utf-8
 7 | trim_trailing_whitespace = true
 8 | insert_final_newline = true
 9 | indent_style = space
10 | indent_size = 4
11 | 
12 | [*.{yml,yaml}]
13 | indent_size = 2
14 | 


--------------------------------------------------------------------------------
/.gitconfig:
--------------------------------------------------------------------------------
1 | # git config --local include.path ../.gitconfig
2 | 
3 | [filter "jupyternotebook"]
4 |     clean = jupyter nbconvert --clear-output %f
5 |     required
6 | 


--------------------------------------------------------------------------------
/.gitignore:
--------------------------------------------------------------------------------
1 | cache
2 | out


--------------------------------------------------------------------------------
/evaluation.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "id": "35dfaedf-9233-4ac3-9861-d1b1f92f56ef",
  6 |    "metadata": {},
  7 |    "source": [
  8 |     "## Horner, Clenshaw, Knuth"
  9 |    ]
 10 |   },
 11 |   {
 12 |    "cell_type": "code",
 13 |    "execution_count": 4,
 14 |    "id": "955423fb-cdbd-45fd-818c-79dc3309cb47",
 15 |    "metadata": {},
 16 |    "outputs": [],
 17 |    "source": [
 18 |     "def poly_cond(start, stop, coefficients):\n",
 19 |     "    x = np.linspace(start, stop, 1000)\n",
 20 |     "    cond = evaluate(np.abs(coefficients), np.abs(x)) / np.abs(evaluate(coefficients, x))\n",
 21 |     "    plt.plot(x, cond)\n",
 22 |     "    return np.max(cond)"
 23 |    ]
 24 |   },
 25 |   {
 26 |    "cell_type": "code",
 27 |    "execution_count": 5,
 28 |    "id": "b74fd3cd-6af7-4123-b7c9-ee64828707df",
 29 |    "metadata": {},
 30 |    "outputs": [
 31 |     {
 32 |      "ename": "SyntaxError",
 33 |      "evalue": "invalid syntax (52742565.py, line 3)",
 34 |      "output_type": "error",
 35 |      "traceback": [
 36 |       "\u001b[0;36m  Input \u001b[0;32mIn [5]\u001b[0;36m\u001b[0m\n\u001b[0;31m    y = evaluate(coefficients, x)a\u001b[0m\n\u001b[0m                                 ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
 37 |      ]
 38 |     }
 39 |    ],
 40 |    "source": [
 41 |     "def shift_coefficients(coefficients, shift):\n",
 42 |     "    x = np.linspace(0, 1, coefficients.shape[0])\n",
 43 |     "    y = evaluate(coefficients, x)a\n",
 44 |     "    x -= shift\n",
 45 |     "    c = interpolate_poly(x, y)\n",
 46 |     "    return c"
 47 |    ]
 48 |   },
 49 |   {
 50 |    "cell_type": "code",
 51 |    "execution_count": 3,
 52 |    "id": "03f0898c-cc00-4344-a830-fed10b193801",
 53 |    "metadata": {},
 54 |    "outputs": [
 55 |     {
 56 |      "ename": "NameError",
 57 |      "evalue": "name 'np' is not defined",
 58 |      "output_type": "error",
 59 |      "traceback": [
 60 |       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
 61 |       "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
 62 |       "Input \u001b[0;32mIn [3]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39marray([ \u001b[38;5;241m1.\u001b[39m        , \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1.94817029\u001b[39m,  \u001b[38;5;241m1.86036663\u001b[39m])\n",
 63 |       "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
 64 |      ]
 65 |     }
 66 |    ],
 67 |    "source": [
 68 |     "c = np.array([ 1.        , -1.94817029,  1.86036663])"
 69 |    ]
 70 |   },
 71 |   {
 72 |    "cell_type": "code",
 73 |    "execution_count": null,
 74 |    "id": "67bf5fd3-201b-4dde-8b33-6b4a15f35463",
 75 |    "metadata": {},
 76 |    "outputs": [],
 77 |    "source": []
 78 |   }
 79 |  ],
 80 |  "metadata": {
 81 |   "kernelspec": {
 82 |    "display_name": "Python 3 (ipykernel)",
 83 |    "language": "python",
 84 |    "name": "python3"
 85 |   },
 86 |   "language_info": {
 87 |    "codemirror_mode": {
 88 |     "name": "ipython",
 89 |     "version": 3
 90 |    },
 91 |    "file_extension": ".py",
 92 |    "mimetype": "text/x-python",
 93 |    "name": "python",
 94 |    "nbconvert_exporter": "python",
 95 |    "pygments_lexer": "ipython3",
 96 |    "version": "3.9.10"
 97 |   }
 98 |  },
 99 |  "nbformat": 4,
100 |  "nbformat_minor": 5
101 | }
102 | 


--------------------------------------------------------------------------------
/foundry copy.toml:
--------------------------------------------------------------------------------
1 | [default]
2 | optimizer_runs = 1000000
3 | bytecode_hash = "none"
4 | 
5 | [intense]
6 | fuzz_runs = 10000
7 | 


--------------------------------------------------------------------------------
/foundry.toml:
--------------------------------------------------------------------------------
1 | [default]
2 | src = 'src'
3 | out = 'out'
4 | libs = ['lib']
5 | remappings = ['ds-test/=lib/ds-test/src/']
6 | 
7 | # See more config options https://github.com/gakonst/foundry/tree/master/config


--------------------------------------------------------------------------------
/simulation.ipynb:
--------------------------------------------------------------------------------
   1 | {
   2 |  "cells": [
   3 |   {
   4 |    "cell_type": "markdown",
   5 |    "metadata": {},
   6 |    "source": [
   7 |     "# Simulation"
   8 |    ]
   9 |   },
  10 |   {
  11 |    "cell_type": "markdown",
  12 |    "metadata": {
  13 |     "tags": []
  14 |    },
  15 |    "source": [
  16 |     "## Prelude"
  17 |    ]
  18 |   },
  19 |   {
  20 |    "cell_type": "code",
  21 |    "execution_count": 699,
  22 |    "metadata": {},
  23 |    "outputs": [
  24 |     {
  25 |      "name": "stdout",
  26 |      "output_type": "stream",
  27 |      "text": [
  28 |       "\u001b[33mDEPRECATION: Configuring installation scheme with distutils config files is deprecated and will no longer work in the near future. If you are using a Homebrew or Linuxbrew Python, please see discussion at https://github.com/Homebrew/homebrew-core/issues/76621\u001b[0m\u001b[33m\n",
  29 |       "\u001b[0mRequirement already satisfied: matplotlib in /opt/homebrew/lib/python3.9/site-packages (3.5.1)\n",
  30 |       "Requirement already satisfied: numpy in /opt/homebrew/lib/python3.9/site-packages (1.22.2)\n",
  31 |       "Requirement already satisfied: mpmath in /opt/homebrew/lib/python3.9/site-packages (1.2.1)\n",
  32 |       "Requirement already satisfied: watermark in /opt/homebrew/lib/python3.9/site-packages (2.3.0)\n",
  33 |       "Requirement already satisfied: packaging>=20.0 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (21.3)\n",
  34 |       "Requirement already satisfied: kiwisolver>=1.0.1 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (1.3.2)\n",
  35 |       "Requirement already satisfied: pyparsing>=2.2.1 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (3.0.7)\n",
  36 |       "Requirement already satisfied: pillow>=6.2.0 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (9.0.1)\n",
  37 |       "Requirement already satisfied: python-dateutil>=2.7 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (2.8.2)\n",
  38 |       "Requirement already satisfied: fonttools>=4.22.0 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (4.29.1)\n",
  39 |       "Requirement already satisfied: cycler>=0.10 in /opt/homebrew/lib/python3.9/site-packages (from matplotlib) (0.11.0)\n",
  40 |       "Requirement already satisfied: ipython in /opt/homebrew/lib/python3.9/site-packages (from watermark) (8.1.1)\n",
  41 |       "Requirement already satisfied: six>=1.5 in /opt/homebrew/lib/python3.9/site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n",
  42 |       "Requirement already satisfied: stack-data in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (0.2.0)\n",
  43 |       "Requirement already satisfied: prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0 in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (3.0.28)\n",
  44 |       "Requirement already satisfied: pexpect>4.3 in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (4.8.0)\n",
  45 |       "Requirement already satisfied: matplotlib-inline in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (0.1.3)\n",
  46 |       "Requirement already satisfied: traitlets>=5 in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (5.1.1)\n",
  47 |       "Requirement already satisfied: setuptools>=18.5 in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (60.9.3)\n",
  48 |       "Requirement already satisfied: pygments>=2.4.0 in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (2.11.2)\n",
  49 |       "Requirement already satisfied: backcall in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (0.2.0)\n",
  50 |       "Requirement already satisfied: pickleshare in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (0.7.5)\n",
  51 |       "Requirement already satisfied: decorator in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (5.1.1)\n",
  52 |       "Requirement already satisfied: jedi>=0.16 in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (0.18.1)\n",
  53 |       "Requirement already satisfied: appnope in /opt/homebrew/lib/python3.9/site-packages (from ipython->watermark) (0.1.2)\n",
  54 |       "Requirement already satisfied: parso<0.9.0,>=0.8.0 in /opt/homebrew/lib/python3.9/site-packages (from jedi>=0.16->ipython->watermark) (0.8.3)\n",
  55 |       "Requirement already satisfied: ptyprocess>=0.5 in /opt/homebrew/lib/python3.9/site-packages (from pexpect>4.3->ipython->watermark) (0.7.0)\n",
  56 |       "Requirement already satisfied: wcwidth in /opt/homebrew/lib/python3.9/site-packages (from prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0->ipython->watermark) (0.2.5)\n",
  57 |       "Requirement already satisfied: pure-eval in /opt/homebrew/lib/python3.9/site-packages (from stack-data->ipython->watermark) (0.2.2)\n",
  58 |       "Requirement already satisfied: asttokens in /opt/homebrew/lib/python3.9/site-packages (from stack-data->ipython->watermark) (2.0.5)\n",
  59 |       "Requirement already satisfied: executing in /opt/homebrew/lib/python3.9/site-packages (from stack-data->ipython->watermark) (0.8.3)\n",
  60 |       "\u001b[33mDEPRECATION: Configuring installation scheme with distutils config files is deprecated and will no longer work in the near future. If you are using a Homebrew or Linuxbrew Python, please see discussion at https://github.com/Homebrew/homebrew-core/issues/76621\u001b[0m\u001b[33m\n",
  61 |       "\u001b[0m"
  62 |      ]
  63 |     }
  64 |    ],
  65 |    "source": [
  66 |     "!pip install matplotlib numpy mpmath watermark"
  67 |    ]
  68 |   },
  69 |   {
  70 |    "cell_type": "code",
  71 |    "execution_count": 700,
  72 |    "metadata": {},
  73 |    "outputs": [],
  74 |    "source": [
  75 |     "%matplotlib inline\n",
  76 |     "\n",
  77 |     "import matplotlib\n",
  78 |     "import numpy as np\n",
  79 |     "from mpmath import mp\n",
  80 |     "import matplotlib.pyplot as plt\n",
  81 |     "import math\n",
  82 |     "import warnings\n",
  83 |     "from ipywidgets import interact, interactive, fixed, interact_manual"
  84 |    ]
  85 |   },
  86 |   {
  87 |    "cell_type": "code",
  88 |    "execution_count": 701,
  89 |    "metadata": {},
  90 |    "outputs": [],
  91 |    "source": [
  92 |     "plt.rcParams['figure.dpi'] = 90\n",
  93 |     "plt.rcParams['figure.figsize'] = [12.0, 8.0]\n",
  94 |     "plt.rcParams['text.usetex'] = False"
  95 |    ]
  96 |   },
  97 |   {
  98 |    "cell_type": "code",
  99 |    "execution_count": null,
 100 |    "metadata": {},
 101 |    "outputs": [],
 102 |    "source": []
 103 |   },
 104 |   {
 105 |    "cell_type": "code",
 106 |    "execution_count": 702,
 107 |    "metadata": {},
 108 |    "outputs": [
 109 |     {
 110 |      "name": "stdout",
 111 |      "output_type": "stream",
 112 |      "text": [
 113 |       "Python implementation: CPython\n",
 114 |       "Python version       : 3.9.10\n",
 115 |       "IPython version      : 8.1.0\n",
 116 |       "\n",
 117 |       "Compiler    : Clang 13.0.0 (clang-1300.0.29.3)\n",
 118 |       "OS          : Darwin\n",
 119 |       "Release     : 21.3.0\n",
 120 |       "Machine     : arm64\n",
 121 |       "Processor   : arm\n",
 122 |       "CPU cores   : 10\n",
 123 |       "Architecture: 64bit\n",
 124 |       "\n",
 125 |       "numpy     : 1.22.2\n",
 126 |       "matplotlib: 3.5.1\n",
 127 |       "\n"
 128 |      ]
 129 |     }
 130 |    ],
 131 |    "source": [
 132 |     "import watermark.watermark as watermark\n",
 133 |     "print(watermark(machine=True, iso8601=True, python=True, iversions=True, globals_=globals()))"
 134 |    ]
 135 |   },
 136 |   {
 137 |    "cell_type": "code",
 138 |    "execution_count": 703,
 139 |    "metadata": {},
 140 |    "outputs": [],
 141 |    "source": [
 142 |     "def intrange(bot, top, num = 100):\n",
 143 |     "    bot = int(bot)\n",
 144 |     "    top = int(top)\n",
 145 |     "    x = np.linspace(bot, top, num = num)\n",
 146 |     "    x = [max(min(int(x), top), bot) for x in x]\n",
 147 |     "    return x"
 148 |    ]
 149 |   },
 150 |   {
 151 |    "cell_type": "markdown",
 152 |    "metadata": {},
 153 |    "source": [
 154 |     "## EVM primitives"
 155 |    ]
 156 |   },
 157 |   {
 158 |    "cell_type": "code",
 159 |    "execution_count": 704,
 160 |    "metadata": {},
 161 |    "outputs": [],
 162 |    "source": [
 163 |     "BASE = 2**256\n",
 164 |     "SIGN = BASE // 2"
 165 |    ]
 166 |   },
 167 |   {
 168 |    "cell_type": "code",
 169 |    "execution_count": 705,
 170 |    "metadata": {},
 171 |    "outputs": [],
 172 |    "source": [
 173 |     "def _valid(a):\n",
 174 |     "    assert type(a) is int\n",
 175 |     "    assert a >= 0\n",
 176 |     "    assert a < BASE\n",
 177 |     "\n",
 178 |     "def _abs(a):\n",
 179 |     "    _valid(a)\n",
 180 |     "    if a > SIGN:\n",
 181 |     "        a = BASE - a\n",
 182 |     "    assert a >= 0 and a < SIGN\n",
 183 |     "    return a\n",
 184 |     "\n",
 185 |     "def bnot(a):\n",
 186 |     "    _valid(a)\n",
 187 |     "    return a ^ (BASE - 1)\n",
 188 |     "\n",
 189 |     "def bor(a, b):\n",
 190 |     "    _valid(a)\n",
 191 |     "    _valid(b)\n",
 192 |     "    return a | b\n",
 193 |     "\n",
 194 |     "def lt(a, b):\n",
 195 |     "    _valid(a)\n",
 196 |     "    _valid(b)\n",
 197 |     "    return 1 if a < b else 0\n",
 198 |     "\n",
 199 |     "def shl(a, b):\n",
 200 |     "    _valid(a)\n",
 201 |     "    _valid(b)\n",
 202 |     "    return (b << a) % BASE\n",
 203 |     "\n",
 204 |     "def shr(a, b):\n",
 205 |     "    _valid(a)\n",
 206 |     "    _valid(b)\n",
 207 |     "    return (b >> a) % BASE\n",
 208 |     "\n",
 209 |     "def sar(a, b):\n",
 210 |     "    _valid(a)\n",
 211 |     "    _valid(b)\n",
 212 |     "    if b >= SIGN:\n",
 213 |     "        b = BASE - b\n",
 214 |     "        b >>= a\n",
 215 |     "        b = BASE - max(b, 1)\n",
 216 |     "        return b\n",
 217 |     "    else:\n",
 218 |     "        return (b >> a) % BASE\n",
 219 |     "\n",
 220 |     "def add(a, b):\n",
 221 |     "    _valid(a)\n",
 222 |     "    _valid(b)\n",
 223 |     "    return (a + b) % BASE\n",
 224 |     "\n",
 225 |     "def sub(a, b):\n",
 226 |     "    _valid(a)\n",
 227 |     "    _valid(b)\n",
 228 |     "    return (a - b) % BASE\n",
 229 |     "\n",
 230 |     "def mul(a, b):\n",
 231 |     "    _valid(a)\n",
 232 |     "    _valid(b)\n",
 233 |     "    return (a * b) % BASE\n",
 234 |     "\n",
 235 |     "def div(a, b):\n",
 236 |     "    _valid(a)\n",
 237 |     "    _valid(b)\n",
 238 |     "    return a // b\n",
 239 |     "\n",
 240 |     "def sdiv(a, b):\n",
 241 |     "    _valid(a)\n",
 242 |     "    _valid(b)\n",
 243 |     "    r = _abs(a) // _abs(b)\n",
 244 |     "    assert r >= 0 and r < SIGN\n",
 245 |     "    if r > 0 and ((a >= SIGN) ^ (b >= SIGN)):\n",
 246 |     "        r = BASE - r\n",
 247 |     "    assert r >= 0 and r < BASE    \n",
 248 |     "    return r\n",
 249 |     "\n",
 250 |     "def mod(a, b):\n",
 251 |     "    _valid(a)\n",
 252 |     "    _valid(b)\n",
 253 |     "    return (a % b) % BASE\n",
 254 |     "\n",
 255 |     "def smod(a, b):\n",
 256 |     "    _valid(a)\n",
 257 |     "    _valid(b)\n",
 258 |     "    if b >= SIGN:\n",
 259 |     "        b = BASE - b\n",
 260 |     "    if a < SIGN:\n",
 261 |     "        return (a % b) % BASE\n",
 262 |     "    else:\n",
 263 |     "        a = BASE - a\n",
 264 |     "        return BASE - ((a % b) % BASE)\n",
 265 |     "\n",
 266 |     "def mulmod(a, b, c):\n",
 267 |     "    _valid(a)\n",
 268 |     "    _valid(b)\n",
 269 |     "    _valid(c)\n",
 270 |     "    return ((a * b) % c) % BASE"
 271 |    ]
 272 |   },
 273 |   {
 274 |    "cell_type": "code",
 275 |    "execution_count": null,
 276 |    "metadata": {},
 277 |    "outputs": [],
 278 |    "source": []
 279 |   },
 280 |   {
 281 |    "cell_type": "code",
 282 |    "execution_count": null,
 283 |    "metadata": {},
 284 |    "outputs": [],
 285 |    "source": []
 286 |   },
 287 |   {
 288 |    "cell_type": "markdown",
 289 |    "metadata": {},
 290 |    "source": [
 291 |     "## Ground truth"
 292 |    ]
 293 |   },
 294 |   {
 295 |    "cell_type": "code",
 296 |    "execution_count": 706,
 297 |    "metadata": {},
 298 |    "outputs": [],
 299 |    "source": [
 300 |     "PRECISION = 1024 # Bits\n",
 301 |     "mp.prec = PRECISION"
 302 |    ]
 303 |   },
 304 |   {
 305 |    "cell_type": "code",
 306 |    "execution_count": 707,
 307 |    "metadata": {},
 308 |    "outputs": [],
 309 |    "source": [
 310 |     "FIX_1 = 10**18\n",
 311 |     "MP_FIX_1 = mp.mpf(FIX_1)"
 312 |    ]
 313 |   },
 314 |   {
 315 |    "cell_type": "code",
 316 |    "execution_count": 708,
 317 |    "metadata": {},
 318 |    "outputs": [],
 319 |    "source": [
 320 |     "def fix_to_mp(x):\n",
 321 |     "    _valid(x)\n",
 322 |     "    if x < 2**255:\n",
 323 |     "        return mp.mpf(x) / MP_FIX_1\n",
 324 |     "    else:\n",
 325 |     "        x = 2**256 - x\n",
 326 |     "        return -mp.mpf(x) / MP_FIX_1"
 327 |    ]
 328 |   },
 329 |   {
 330 |    "cell_type": "code",
 331 |    "execution_count": 709,
 332 |    "metadata": {},
 333 |    "outputs": [],
 334 |    "source": [
 335 |     "def fix_to_f(x):\n",
 336 |     "    return float(fix_to_mp(x))"
 337 |    ]
 338 |   },
 339 |   {
 340 |    "cell_type": "code",
 341 |    "execution_count": 710,
 342 |    "metadata": {},
 343 |    "outputs": [],
 344 |    "source": [
 345 |     "def mp_to_fix(x):\n",
 346 |     "    # Closest approximation, clamping to MIN and MAX representable values, NaN maps to positive infinite\n",
 347 |     "    if mp.isnan(x):\n",
 348 |     "        return SIGN - 1\n",
 349 |     "    if x >= 0:\n",
 350 |     "        if x >= SIGN:\n",
 351 |     "            return SIGN - 1\n",
 352 |     "        x = int(mp.nint(x * MP_FIX_1))\n",
 353 |     "    else:\n",
 354 |     "        if -x > SIGN:\n",
 355 |     "            return SIGN\n",
 356 |     "        x = int(mp.nint(-x * MP_FIX_1))\n",
 357 |     "        if x > 0:\n",
 358 |     "            x = 2**256 - x\n",
 359 |     "    _valid(x)\n",
 360 |     "    return x"
 361 |    ]
 362 |   },
 363 |   {
 364 |    "cell_type": "code",
 365 |    "execution_count": 711,
 366 |    "metadata": {},
 367 |    "outputs": [],
 368 |    "source": [
 369 |     "def fmul(a, b):\n",
 370 |     "    return bf_to_fix(fix_to_mp(a) * fix_to_mp(b))"
 371 |    ]
 372 |   },
 373 |   {
 374 |    "cell_type": "code",
 375 |    "execution_count": 712,
 376 |    "metadata": {},
 377 |    "outputs": [],
 378 |    "source": [
 379 |     "def mp_log1(x):\n",
 380 |     "    return mp_to_fix(mp.log(fix_to_mp(x)))"
 381 |    ]
 382 |   },
 383 |   {
 384 |    "cell_type": "code",
 385 |    "execution_count": 713,
 386 |    "metadata": {},
 387 |    "outputs": [],
 388 |    "source": [
 389 |     "def mp_ln(x):\n",
 390 |     "    return mp_to_fix(mp.log(fix_to_mp(x)))"
 391 |    ]
 392 |   },
 393 |   {
 394 |    "cell_type": "code",
 395 |    "execution_count": 714,
 396 |    "metadata": {},
 397 |    "outputs": [],
 398 |    "source": [
 399 |     "def mp_exp(x):\n",
 400 |     "    return mp_to_fix(mp.exp(fix_to_mp(x)))"
 401 |    ]
 402 |   },
 403 |   {
 404 |    "cell_type": "code",
 405 |    "execution_count": 715,
 406 |    "metadata": {},
 407 |    "outputs": [],
 408 |    "source": [
 409 |     "assert fix_to_f(FIX_1) == 1.0"
 410 |    ]
 411 |   },
 412 |   {
 413 |    "cell_type": "markdown",
 414 |    "metadata": {},
 415 |    "source": [
 416 |     "## Cheby generator"
 417 |    ]
 418 |   },
 419 |   {
 420 |    "cell_type": "code",
 421 |    "execution_count": 716,
 422 |    "metadata": {},
 423 |    "outputs": [],
 424 |    "source": [
 425 |     "def chebyfun(f, domain, degree=11):\n",
 426 |     "    start, end = domain\n",
 427 |     "    start = mp.mpf(start)\n",
 428 |     "    end = mp.mpf(end)\n",
 429 |     "    mid = start + (end - start) / 2\n",
 430 |     "    \n",
 431 |     "    # To make the polynomial evaluate nicely, we center x around zero using an offset CENTER\n",
 432 |     "    # Alternatively we could use Clenshaw's algorithm\n",
 433 |     "    # TODO: Centering helps a lot, what about scaling?\n",
 434 |     "    coeffs = mp.chebyfit(lambda x: f(x + mid), [start - mid, end - mid], degree)\n",
 435 |     "    coeffs = [mp_to_fix(x) for x in coeffs]\n",
 436 |     "    mid = mp_to_fix(mid)\n",
 437 |     "    \n",
 438 |     "    # Solidity function\n",
 439 |     "    def func(x):\n",
 440 |     "        nonlocal mid, coeffs\n",
 441 |     "        x = sub(x, mid)\n",
 442 |     "        r = coeffs[0]\n",
 443 |     "        for coeff in coeffs[1:]:\n",
 444 |     "            # r = (r * x / 1e18) + coeff\n",
 445 |     "            r = mul(r, x)\n",
 446 |     "            r = sdiv(r, FIX_1)\n",
 447 |     "            r = add(r, coeff)\n",
 448 |     "        return r\n",
 449 |     "    \n",
 450 |     "    # Plot error\n",
 451 |     "    x = intrange(mp_to_fix(start), mp_to_fix(end), num = 10000)\n",
 452 |     "    xr = np.array([fix_to_f(x) for x in x])\n",
 453 |     "    y = np.array([mp_to_fix(f(fix_to_mp(x))) for x in x], dtype='object')\n",
 454 |     "    yr = np.array([fix_to_f(y) for y in y])\n",
 455 |     "    fy = np.array([func(x) for x in x], dtype='object')\n",
 456 |     "    fyr = np.array([fix_to_f(y) for y in fy])\n",
 457 |     "    plt.title('Error over domain')\n",
 458 |     "    plt.xlabel(\"$x$\")\n",
 459 |     "    plt.ylabel(\"$f(x) - r$\")\n",
 460 |     "    plt.plot(xr, (fyr - yr).astype(float))\n",
 461 |     "    plt.axhline(-0.5 / FIX_1, color='red')\n",
 462 |     "    plt.axhline(+0.5 / FIX_1, color='red')\n",
 463 |     "    error_fix = max(abs(fy - y))\n",
 464 |     "    error_bits = max(np.log2(abs(fy - y).astype(float)))\n",
 465 |     "    \n",
 466 |     "    # Print Solidity\n",
 467 |     "    print('// Chebyshev approximation on ({:.4g}, {:.4g}) deg {}.'.format(float(start), float(end), degree))\n",
 468 |     "    print('// Max observed error {:.2g}, last {:.2g} bits.'.format(fix_to_f(error_fix), error_bits))\n",
 469 |     "    if mid < SIGN:\n",
 470 |     "        print('x -= 0x{:x}; // {:.3g}'.format(mid, fix_to_f(mid)))\n",
 471 |     "    else:\n",
 472 |     "        print('x += 0x{:x}; // {:.3g}'.format(BASE - mid, fix_to_f(mid)))\n",
 473 |     "    if coeffs[0] < SIGN:\n",
 474 |     "        print('int256 r = 0x{:x}; // {:.3g}'.format(coeffs[0], fix_to_f(coeffs[0])))\n",
 475 |     "    else:\n",
 476 |     "        print('int256 r = -0x{:x}; // {:.3g}'.format(BASE - coeffs[0], fix_to_f(coeffs[0])))\n",
 477 |     "    for x in coeffs:\n",
 478 |     "        if x < SIGN:\n",
 479 |     "            print('r = ((r * x) / FIX_1) + 0x{:x}; // {:.3g}'.format(x, fix_to_f(x)))\n",
 480 |     "        else:\n",
 481 |     "            print('r = ((r * x) / FIX_1) - 0x{:x}; // {:.3g}'.format(BASE - x, fix_to_f(x)))\n",
 482 |     "\n",
 483 |     "    return func"
 484 |    ]
 485 |   },
 486 |   {
 487 |    "cell_type": "code",
 488 |    "execution_count": 717,
 489 |    "metadata": {},
 490 |    "outputs": [],
 491 |    "source": [
 492 |     "def fn_exp(x):\n",
 493 |     "    return mp.exp(x)"
 494 |    ]
 495 |   },
 496 |   {
 497 |    "cell_type": "code",
 498 |    "execution_count": 718,
 499 |    "metadata": {},
 500 |    "outputs": [],
 501 |    "source": [
 502 |     "domain = (0.0, 0.125)"
 503 |    ]
 504 |   },
 505 |   {
 506 |    "cell_type": "code",
 507 |    "execution_count": 719,
 508 |    "metadata": {},
 509 |    "outputs": [
 510 |     {
 511 |      "data": {
 512 |       "application/vnd.jupyter.widget-view+json": {
 513 |        "model_id": "915829888f96495eb8e3154383177fb8",
 514 |        "version_major": 2,
 515 |        "version_minor": 0
 516 |       },
 517 |       "text/plain": [
 518 |        "interactive(children=(IntSlider(value=8, description='d', max=24, min=-8), Output()), _dom_classes=('widget-in…"
 519 |       ]
 520 |      },
 521 |      "metadata": {},
 522 |      "output_type": "display_data"
 523 |     },
 524 |     {
 525 |      "data": {
 526 |       "text/plain": [
 527 |        "<function __main__.<lambda>(d)>"
 528 |       ]
 529 |      },
 530 |      "execution_count": 719,
 531 |      "metadata": {},
 532 |      "output_type": "execute_result"
 533 |     }
 534 |    ],
 535 |    "source": [
 536 |     "interact(lambda d:chebyfun(fn_exp, domain, degree=d), d=8)"
 537 |    ]
 538 |   },
 539 |   {
 540 |    "cell_type": "code",
 541 |    "execution_count": 720,
 542 |    "metadata": {},
 543 |    "outputs": [
 544 |     {
 545 |      "data": {
 546 |       "text/plain": [
 547 |        "mpf('1.0')"
 548 |       ]
 549 |      },
 550 |      "execution_count": 720,
 551 |      "metadata": {},
 552 |      "output_type": "execute_result"
 553 |     }
 554 |    ],
 555 |    "source": [
 556 |     "fix_to_mp(FIX_1)"
 557 |    ]
 558 |   },
 559 |   {
 560 |    "cell_type": "code",
 561 |    "execution_count": 721,
 562 |    "metadata": {},
 563 |    "outputs": [
 564 |     {
 565 |      "data": {
 566 |       "text/plain": [
 567 |        "115792089237316195423570985008687907853269984665640564039457084007913129639936"
 568 |       ]
 569 |      },
 570 |      "execution_count": 721,
 571 |      "metadata": {},
 572 |      "output_type": "execute_result"
 573 |     }
 574 |    ],
 575 |    "source": [
 576 |     "sdiv(115792089237316195423570985008687907853269484665640564039457584007913129639936, FIX_1)"
 577 |    ]
 578 |   },
 579 |   {
 580 |    "cell_type": "code",
 581 |    "execution_count": 722,
 582 |    "metadata": {},
 583 |    "outputs": [
 584 |     {
 585 |      "name": "stdout",
 586 |      "output_type": "stream",
 587 |      "text": [
 588 |       "// Chebyshev approximation on (0, 0.125) deg 11.\n",
 589 |       "// Max observed error 1e-18, last 0 bits.\n",
 590 |       "x -= 0xde0b6b3a764000; // 0.0625\n",
 591 |       "int256 r = 0x444e371820; // 2.93e-07\n",
 592 |       "r = ((r * x) / FIX_1) + 0x444e371820; // 2.93e-07\n",
 593 |       "r = ((r * x) / FIX_1) + 0x2ab10ff87b6; // 2.93e-06\n",
 594 |       "r = ((r * x) / FIX_1) + 0x1802ff4bd772; // 2.64e-05\n",
 595 |       "r = ((r * x) / FIX_1) + 0xc017fa590a66; // 0.000211\n",
 596 |       "r = ((r * x) / FIX_1) + 0x540a7d8e6d194; // 0.00148\n",
 597 |       "r = ((r * x) / FIX_1) + 0x1f83ef1568ed35; // 0.00887\n",
 598 |       "r = ((r * x) / FIX_1) + 0x9d93ab6b0c7caf; // 0.0444\n",
 599 |       "r = ((r * x) / FIX_1) + 0x2764eadac31f2ba; // 0.177\n",
 600 |       "r = ((r * x) / FIX_1) + 0x762ec090495d833; // 0.532\n",
 601 |       "r = ((r * x) / FIX_1) + 0xec5d812092bb066; // 1.06\n",
 602 |       "r = ((r * x) / FIX_1) + 0xec5d812092bb066; // 1.06\n"
 603 |      ]
 604 |     },
 605 |     {
 606 |      "name": "stderr",
 607 |      "output_type": "stream",
 608 |      "text": [
 609 |       "/var/folders/cb/n6k1dpbn7f1_n5m5dqv6rjvc0000gn/T/ipykernel_85508/2621324204.py:40: RuntimeWarning: divide by zero encountered in log2\n",
 610 |       "  error_bits = max(np.log2(abs(fy - y).astype(float)))\n"
 611 |      ]
 612 |     },
 613 |     {
 614 |      "data": {
 615 |       "image/png": 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qAIDTG30w3Kuqzkry2UnevM/j51RV27mttzqGsq6BW/Q+AspqbL5+7PuHGjsBAEzGpIJhzVpW/kKStyc573TPaa2d01qrndtaC1yzUXUlXbOeupL2NjPc8W49mHFtwnFVAwCc3hTOMUxyeyh8XpJPTPK41trJDZfEMVrXV8lF7yOgrMbm68e+f6ixEwDAZEwiGM5D4bmZNZ75F621azZcEgAAwNaYRDBM8twkn5fkC1trV226GAAAgG0y+nMMq+qhSb4js0NI311V181vz99waQAAAFth9DOGrbV3x5kqW2nRJSem2pW0sz4xC626KVySZHUH7Y9D7a+6kgLA9I1+xhB657s1AADHTTCcsDFNow51+YjDLkXH0DFbbXA2NbTbtE+N6VI2IyoFAFhAMAQAAOicYAgAANA5wRAAAKBzguGE9dyURPfP7WVoV9dG9AEZUSkAwAKCIaO0ri+2i97G99kV2YDd2O9z5JIjADAdguGE9dzsr6dOh73NuHQ0tMdGV1IAYFmCIaO0ri+2i97G99kV2YDd2O9zNNRlbACA4ycYAgAAdE4wBAAA6JxgCAAA0DnBkI1Z2BF0ol1JdWHcZcVN0VvTneNw0CYc6nOmKykATJ9gOGUj6uswVK+Ywy6np06HU/tyvfLYbGhwt2mXGtO6jKkWAGB/giEAAEDnBEMAAIDOCYYAAACdEwynbFqnng1KY5ItZnBXNqYtOKZaAID9CYaM0rq+TC5q7LKuzqjbytbrx35j7SMEANMhGAIAAHROMJyyjvvAd3W5it5mXXoa3GMypi04ploAgP0JhozSur5M1oJ3KgFlJbZeP/Ybax8hAJgOwRAAAKBzgiEAAEDnBEMAAIDOCYZszKKeKlO9XEV3jWIWWHVT2JSrO2h/HGobu1wFAEyfYDhhixqnrNtQlRx2nca07pxq1ZHZ1MhuVbOhEa3KNm1WANhmgiEAAEDnBEMAAIDOCYYTtuj8uG3X87pvOyM7gBFtROcZAsA0CIYAAACdEwwZpXXNMix6HxMdqzlKV1emab+xtgsAwHQIhhM2ps6cg3UePORyxrTunGrVfWFjXUk39L7HYkQroyspAEyDYNipoWdzBlucGYY7mNqsy9Tq3THRsgEABiEYMkrrmmVY9D4mOlazVdcFZKH9xtouAADTIRgCAAB0TjAEAADonGDIxiw6z3GqXUmdp/aPVj6P1cYcwOKNONTnTFdSAJg+wRAAAKBzguGEjamxw7ovV9FTZ5g2samzlS9XsaGx3aZdakzr4tIyADANgiEAAEDnBEMAAIDOCYYT1nVjh57Xfct1vV8PZEybcGqHQgNArwRDNmYbL4C+fWu0QTbmABZvxC38CAIARyQYsjErX85giBqO/OBgL9laK28LG3MA67lcxf7vbhABYCoEwwkb01/7h+o8eOiljGjdOdWq+8LGupJu0T41plXRlRQApkEw7NTQMwVDzQyYX7ijEUysLmWqs0RT284AAEMSDOnawrkMEx0rsfkwWwgA0yEYAgAAdE4wBAAA6JxgyMaM4ZSuwbuSjmGlRmLVTTHVcxXH5KD98bi3sDEEgOkQDCdsTGfvrLsr6ZjWnVOt3JV0oDqWft8t2qnGdI3QEZUCACwgGMLImXMBAOC4CYYAAACdEwwnrOeZpJ7XfdsZ29W1EZ3sOqJSAIAFBEM2ZhtPPXI+1XBcA291B+2PtjAAsEMwZGPGMJGwaDbjKB0VzY78o1W3hY6Wq1tXV9L93sfnAQCmQzAEAADonGA4YWM6DGyoQygPu5wxrTunWnVf2NjlKrZor3K5CgBgWYJhp4Y+wmuoQ8YcenZHY2okchgTK/d2Dl0FAHomGNK1RbMZ2zSDtAlmivqx31jbBwBgOgRDAACAzgmGAAAAnRMM2ZgxnIs2+OUqnKd2u5UvV2FTruygTTjU+asuVwEA0ycYTtiYzt9Ze1fSMa08p1i5K+mGxnabzikd05r4qALANAiGMHImXQAAOG6C4YT1fJjW1C7hwOEZ29WNaQsaTgCYBsEQAACgc4IhDGibzlPbNOemre6gTehcXQBgh2DIxoyjg+f+NRzlELhxrNM4rLotHIK4urV1Jd3nnQwhAEyHYDhhY/pj/1ClHHbGzUzHeK06MhvrSrpFu9SYVmWbtisAbDPBEAAAoHOCYaeG7vw41NIcinlHUzukcmLl3m5q2xkAYEiCIZ3b/zg3h8CtRiOefuw31vYAAJgOwRAAAKBzgiGbM4pD94btSjqOdRqHlbuSDlRHz4Y+ZHzf99GVFAAmTzAEAADonGA4YWM6h2vtl6sY6P0Y3sqXqxikiiO87xbtVGNalzH9ngIA9icYwtg5Hg8AgGMmGE5Yz5d26HfNt5+xXd2YLr3R8+8pAJgSwRCG5Ki5wdiUq6sxHVMKAIyaYMjGjGEeYdHMiq6kq1l11sqmXN3aupLu8zZjmrkEABYTDAEAADonGE7YqLr9DXTI2mEXM6I1Z49VD180tqsb0xGko/o9BQDsSzDs1OBHeA10zJhDz+5oas071nX4IgAAwxEMAQAAOicY0rVFh9yN6XC8KbL9+rHfWNsHAGA6BEMAAIDOCYZszBhORRv6chUjWKXRWPlyFWPYQSbuoC041CZ2uQoAmD7BcMJGdZjWuruSjmndOcXKXUmN7cpG1Ql0RKUAAPsTDAEAADonGE5Yz4dp9bTuPa1r0t/6HodRXeJkRKUAAPsTDGFAjpobzqqHpHLw/mgTAwA7BEMAAIDOCYZszBgOd1vYlfQoyztyJdtHV9LN23RXUp8IAJgOwRAAAKBzguGEjen8oKFKcbkKNjW227RPuVwFALAswbBTQx+lN9TiHD14RzbJetj3AICeCYYAAACdEwzp2qLDBx0Bt5ptOjSTxfYfazsBAEyFYMjGjOHQvcG7ko5hpUZi5a6kw5TRtYPGYKjOwLqSAsD0TSIYVtVTq+oNVXVTVZ2/6XoAAAC2yYlNF3BIlyV5dpLHJfmYDdcyGmM6SGvtXUkHej/GZ1MdNbfp0NcxrcuISgEAFphEMGytnZckVXV2BMPb9XyQVs/rvu2GOryxZ2M6onlEpQAAC0ziUNJlVNU5VdV2bpuuB1blvEUAAI7b1gXD1to5rbXauW26HvpSYzqGb+JsydUdtDtu6rBdAGB8ti4YAgAAsBzBkI0ZwwGSi85nO8ohnA77HI4tubq1Xa7iiO8PAIzHJJrPVNWJzGo9keSMqjorycnW2s2brWyzxnQQ2FBHUB720LYxrTunWnVf2FhX0i3aq8Z0RPOISgEAFphEMEzy9CTP3PXzjUleneSxG6kGAABgi0ziUNK9DWXmt8duuq4pG/qSAEMdMuZSBXc0tS0y1cMH7XsAQM8mEQwBAAA4PoIhXVt0XplLT8Dh7PdJ8RECgOkQDNmYMXTwHLwr6SrFcIoR7B6Td9A+PNwh4Me7fADg+AmGAAAAnRMMp2xEx2mt/XIVI1p3TrXy0GxoaLfpchVj4rMKANMgGE5Zx8dpjeEwVI6Jod0qPqsAMA2CIQzoOOZGev1ebaJpdQfN1tnGAMAOwRAAAKBzgiEbM4aZsEU1HKW8EazSaKx6COEY9o+pW1tX0n0WZAgBYDoEQwAAgM4JhlM2ohOEhuroeNhV0ulwvCbbldQudSx8VgFgGgRDAACAzgmGnRr6/K020NlEziu7o6G27bpMdQynWjcAwBAEQwAAgM4JhnRt0elPzoxajXPL+rHfWNsDAGA6BEO6NvjlKhyOeLtVL1fB6g4agaFGyOUqAGD6BMMJG9Nf49felXSQd+M4rDpRuKmx3aYJzjHN1o6nEgBgEcFwwnr+a3zP677tjO3qxjRbO55KAIBFBEMY0IgmauDA2Tq7KwCwQzCEsTPlAgDAMRMMAQAAOicYsjFjOA1qUQlHqW8M6zQWNsXmra0r6X73+0AAwGQIhgAAAJ0TDCdsTI0j1t10ZUzrzqlWvXSJy1WszuUqAIBlCYYAAACdEwwZhFOJjs/UNm2bXMUz9mEAoGeCIQAAQOcEQzZmqjNLi2zfGjFpB+yQZkkBgB2CIQAAQOcEQwYxoiaIbNiqXUk3xT4MAPRMMAQAAOicYAgDMunEqBywQ5olBQB2CIYwchqEAABw3ARDAACAzgmGpG1oSmoMM2GLa1i+wBGs0miMYXy7t67LVeyzHLsAAEyHYDhhYzo/aKhS6rArNaJ151Sr7peb2q+n2k31dMa0JmP6PQUA7E8wBAAA6JxgCAAA0DnBsFNDn/812KlKTky7gzaxM7WmOoRT284AAEMSDAEAADonGLKxGZ5tnJ8x48mYHLQ3miUFAHYIhgAAAJ0TDBnE2i9XwWhNdQi36XIVAADLEgxhQIItY3LQ3igMAwA7BEMAAIDOCYYwcvrZAABw3ARDNtaXcAwdPBd1ZTxKeWNYp7HQ8XLz1tWVdL/l+DgAwHQIhgAAAJ0TDCdsTI0jhuq5ctjFjGndOdWqI2NsVzemHkgjKgUAWEAwBAAA6JxgCAAA0DnBsFNDNwYZqsmEXhV3NLVtMrV6d2iWAwD0TDAEAADonGDIxi6xsI3zM9u4TkzXQZ9tl5MAAHYIhgxi3V1JGS9jCAAwPYIhAABA5wRDGJDZMsakDpjKH9P1DgGAzRIMAQAAOicYwshtqjkQAAD9EAzZWCfNUeSdBTUcpbwxrNJYjGJ8O7eurqT7LccuAADTIRgCAAB0TjCcsDE1jjioycXhlzPs81i/VfcFY7u6MW3DoX43AADHSzAEAADonGAIAADQOcGwU0M3Bhmqc6aGJXc0tW0y1S6qEy0bAGAQgiEb/EK8hd/Et3CVmC67IwBwWIIhAABA5wRDBrHurqSMly6UAADTIxjCkGQiRsTuCAAclmAIAADQOcEQAACgc4IhaRvqXTiGywMsKuFI9Y1gnRZZ56UkRr4purCuMdjvfaZ66RIA6JFgCAAA0DnBcMK2sbHEYddpG9d9W6w6Npqarq5G9AkZTyUAwCKCIQAAQOcEQwAAgM4JhgAAAJ0TDDs11l6BY61rk6bW2HFi5d5uatsZAGBIguGEDfU9dlNfiFd527F+h9/UpT8OawrhZwo1jt3OfnjQtlzH5SQMJwBMg2AIAADQOcFwwraxDfzUL1cxpssEbIrLVWzezn540LasNWxswwkA0yAYAgAAdE4wBAAA6JxgCAAA0DnBkI0ZQ/fJRV0Zj9Jh9Di6kg65zHVu8jGMb+/W1ZXUWAPA9AmGAAAAnVs6GFbVmVX1kqq603EUxOGNqXvjULUctkvimNadPVYcG51dVzeqz8eYagEA9rV0MGyt3Zbkc+O6xQAAAFvhqIeS/mKS/3PIQgAAANiME0d83ROSfGJVfWaSFyV5Q2vtuuHKAgAAYF2OOmP4zCQ/nuTBSX41ydVV9XdV9cLBKuNY7e5GOERHwaMs43TdNofqknj4GhY8dpR1Oobyh1zmWrZvu8P/TMJxdJTdtIPWaajdYb/30a0UAKbjSDOGrbXzk5y/83NV3S/Jp81vAAAATMhRDyU9RWvtiiSvmN/o0Lq7kg5l0buNqrPjlNQd/octt18nWZ8hAJgO1zGEAfkizJgcdOkP+ysAsEMwBAAA6NxKwbCqHjJUIQAAAGzGqjOG76yqjxykEgAAADZi1WDoDJUtsKk2/WNoZT+Jy1WMdFljezfuyOUqAIDDco4hAABA5wTDCVv3pR0WOaj74eGXs973Y3irjsyIduvJGtMm9FkFgGkQDAEAADq3ajBcyxkkVXWnqnpuVV1VVVdW1c9W1Yl1vDcAAMC2m0rzmacneXSST0ryyCSfn+Rpa3pvAACArVZthbZxVfXSJF/XWrtuuJJO+z7vTfLdrbWXzH9+UpKfbK099BCvbe1e9zrO8pZ2820tq2z3HbecbDl5cracu5xYLuO3JDffejJJcucTZ6yc8Jep5ab5+97pzDNyRp3+sYOWc/NtJ2/veLjsuu9+n6rkzmeecdrHTpxROXNvgQcs76j1LFrmquOzu7YhxnqZ91tlbI76+qM62ZJbbju59vc9Dgdtw53HzzijcqdD7uP7LT9JzjyjcmLXcnY/XpWVPqsAU3OyJSdbO+X3In1Zx/etZdU116S1trCslYLhOlTVfZJcmeTjW2sXz+/7+CQXJbl3a+2aPc8/J8kzd983tjUcWz0AAMBwRhcMk60Ihh+b5D1J7t9au2J+3/2TXJ7kY1trlxzw+tHNGN5ysg12fa/bTracccbROv+dnBdxxkBtIA9bS2uzq57t9763nTw5n6lbvJzbTrbMJvuOUn/LbSdz2hnBlpaT+zy2eHktZ54x3IzIQdtpmeXc1lrOqBpsrA8yG8Ojb4vD7gNDO9laKuPq+HtUi7bh0fbxXa+f75tV2Wc5p34eVvusAkzLh2+5LUly4szKiQG/FzAddzpzfD25DzNjOIUGLjuHqd4ryRW7/j9JPnSoJVx99bAVrehOmy4AAIBj8Qn/4feSJD/6VZ+Sr/vsh2y4Gpg7xB+9R/9njNbaVUkuSXL2rrvPTvLevYeRAgAAsLylZwyr6nOTPCGzcHafJFcluTDJy1prrx+yuF1+KckPVNXO8p+W5BeO6b0AAAC6cuhgWFVfmOQnMzuM84Ikr0hybZJ7ZnYZiV+pqmuSfG9r7U8GrvNZSe6b5K3zn38tyY8M/B4AAABdWmbG8PuTfFdr7TX7PaGqdq4vOGgwbK3dkuQp8xsAAAADOnQwbK19yc7/V9XDWmvvPM1zXpvk8QPVBgAAwBoctfnMa6rqU/beWVX3Xq0cAACYvrFdrgAOctRg+O+T/GFVPTpJquouVfX9Sd4xWGUAAACsxZGuY9haO6+qrkjyoqr65STfmOTSJE8asDYAAADWYJXrGH5kkhuS/H9Jzm+tfe4xdCMFAADgmB1pxrCq3pDkgUmemdk1DM+vqje21n55uNIAAABYhyMFwyTnJfmp1tqNSVJVj03y8qp6YGvtxwaqDQAAJqltugBY0pEOJW2t/chOKJz//I4kj07yNUMVBgAAwHqsco7hKVpr70/ymKGWBwAAU+VyFUzNoYNhVf1mVX3SAU/72Kp64Yo1AQAAsEbLnGP420leWlUfTPInSd6W5Nok90zyT5N8YZL7Jnna0EUCAABwfJYJhs9I8ogkX5bkCUm+Pcl9klyVWWfSH07y+621kwPXCAAAwDFaJhg+IElaay+rql9vrd3rmGoCAABgjZYJhhckeVlVvSTJGVV1Vmvtw8dUFwAAAGuyTDD8xiRPSfJ1Se6e5ENVdVGSN+26Xdhau3LwKgEAYEJKW1Im5tBdSVtrN7XW/ktr7YuTXJnkwUm+J8nfJvmcJC9IcvmxVAkAAMCxWWbGcLcHzJvMvHx+S5JUlfMOAQAAJuZIF7jfr/Noa+2a1coBAABg3Y4UDAEAANgegiEAAEDnBEMAAIDOCYYAAACdEwwBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAAAGVqlNlwBLEQwBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBAAA6JxgCAAA0DnBEAAAhlabLgCWIxgCAAB0TjAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBAAA6JxgCAAA0DnBEAAAoHOCIQAADKw2XQAsSTAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBAAA6JxgCAAA0DnBEAAAoHOCIQAADKyqNl0CLEUwBAAA6JxgCAAA0DnBEAAAoHOCIQAAQOcEQwAAgM4JhgAAAJ0TDAEAADonGAIAAHROMAQAAOicYAgAANA5wRAAAKBzgiEAAEDnBEMAABhYbboAWJJgCAAA0DnBEAAAoHOCIQAAQOcEQwAAgM4JhgAAAJ0TDAEAYGClLSkTIxgCAMDAWtt0BbAcwRAAAKBzgiEAAEDnBEMAAIDOCYYAAACdEwwBAAA6JxgCAMDAXK6CqREMAQAAOicYAgAAdE4wBAAA6JxgCAAA0DnBEAAAoHOCIQAADExXUqZGMAQAgIG1tukKYDmCIQAAQOcEQwAAgM4JhgAAAJ0TDAEAADo36mBYVQ+qqt+tqsuqqlXV2ZuuCQAADqIrKVMz6mCY5GSSlyd54obrAAAA2FonNl3AIq219yd5XpKUP7sAAAAci7HPGC6tqs6ZH3baqsoVZAAAAA6wsWBYVS/bHeBOc/u4oyy3tXZOa612bgOXDQAAsHU2eSjp1ye584LHr1xXIQAAAD3bWDBsrV27qfcGAIDjVHHgGtMy6uYzSVJVZ+368c7zn29urZ3cVE0AAADbZArNZ26c35Lkz+f//79vrhwAAFisRQ9EpmX0M4YayAAAAByvKcwYAgAAcIwEQwAAgM4JhgAAAJ0TDAEAYGAuV8HUCIYAAACdEwwBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAAAGVpqSMjGCIQAAQOcEQwAAGFhrm64AliMYAgAAdE4wBAAA6JxgCAAA0DnBEAAABqYrKVMjGAIAAHROMAQAAOicYAgAANA5wRAAAKBzgiEAAEDnBEMAAIDOCYYAAACdEwwBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBAAA6JxgCAAAA6uqTZcASxEMAQAAOicYAgAAdE4wBACAgbXWNl0CLEUwBAAA6JxgCAAA0DnBEAAAoHOCIQAADMzlKpgawRAAAKBzgiEAAEDnBEMAAIDOCYYAAACdEwwBAAA6JxgCAMDA9CRlagRDAACAzgmGAAAAnRMMAQBgYG3TBcCSBEMAAIDOCYYAAACdEwwBAGBgupIyNYIhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBAAA6JxgCAAAAyvXq2BiBEMAAIDOCYYAAACdEwwBAGBgrW26AliOYAgAANA5wRAAAKBzgiEAAAxMV1KmRjAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAwsIq2pEyLYAgAANA5wRAAAKBzgiEAAEDnBEMAABhYS9t0CbAUwRAAAKBzgiEAAEDnBEMAABiYy1UwNYIhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBACAgZWmpEyMYAgAANA5wRAAAKBzgiEAAEDnBEMAABhYa5uuAJYjGAIAAHROMAQAgIHpSsrUCIYAAACdEwwBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAAAGpikpUyMYAgAAdE4wBAAA6JxgCAAA0LlRB8Oq+rKqek1VXVVVl1fVS6rqYzZdFwAAwDYZdTBMcq8kP57kY5M8LMm1SV680YoAAOAAbdMFwJJObLqARVprv7H756p6TpI3VdWJ1tqtm6kKAABgu4x9xnCvxyR566JQWFXnVFXbua2xNgAASOJyFUzPxoJhVb1sd4A7ze3j9jz/05I8K8l3L1pua+2c1lrt3I5xFQAAALbCJg8l/fokd17w+JU7/1NVn5LkD5I8tbX2iuMuDAAAoCcbC4attWsP87x5KPzjJP+htfZrx1sVAABAf0Z9jmFVPTKzUPj01tovbboeAACAbTTqYJjke5PcP8lPVdV1u24P2XRhAAAA22Lsl6v45iTfvOk6AABgGaUFIhMz9hlDAAAAjplgCAAA0DnBEAAAoHOCIQAAQOcEQwAAgM4JhgAAAJ0TDAEAADonGAIAAHROMAQAAOicYAgAANA5wRAAAKBzgiEAAEDnBEMAABhcbboAWIpgCAAA0DnBEAAAoHOCIQAAQOcEQwAAgM4JhgAAMLCPvvdZmy4BllKttU3XcKyqqm37OgIAMA7vuuL6vOWya/Nln/qgTZcCt6uqtNYWtsoVDAEAALbYYYKhQ0kBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBAAA6JxgCAAA0DnBEAAAoHOCIQAAQOcEQwAAgM4JhgAAAJ0TDAEAADonGAIAAHROMAQAAOicYAgAANA5wRAAAKBzgiEAAEDnTmy6gHWoqk2XAAAAMFrVWtt0DV2qqtZak1i3nHHug3Hefsa4D8a5D8a5D8Z5eQ4lBQAA6JxgCAAA0DnBcHN+aNMFsBbGuQ/GefsZ4z4Y5z4Y5z4Y5yU5xxAAAKBzZgwBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAACgc4LhQKrqTlX13Kq6qqqurKqfraoTR3nuMstivYYa56q6S1W9oKreWVUfqqq3VdW3rHdt2M+Qn+ddz7trVV1cVVcf+wpwoKHHuKqeUFUXVtX1VXVZVX3betaERQb+t/nBVXV+VX2wqq6oqhdX1f3XtzbsZ8lxfmpVvaGqbqqq80/z+D2r6jeq6tqqen9V/eCxrwCHMtQ4V9UDqurXq+qS+Ti/qaqesJaVGDnBcDhPT/LoJJ+U5JFJPj/J04743GWWxXoNNc4nkrwvyeOS3DPJNyX5z1X1xcdVOEsZ8vO844eTvHvwSjmqwca4qr40yfOSfFdmn+dHJnnV8ZTNkob8LJ87/+9DkzwsyVlJfmb4kjmCZcb5siTPTvKCfR7/2SQfmeQh8+U8uar+zaDVclRDjfM9krwpyeckuXeSZyR5YVV90sD1Tk9rzW2AW5L3JvlXu35+UpJ3H+W5yyzLbbrjfJrnn5fkhze9jm7Dj3OSz0jy10m+OMnVm14/t8F/Z/9lkn+76XVyO/ZxfnOSr9/18zck+ZtNr6Pb0b43JTknyfl77rtbkpuSfOau+74vyas3vY5uw43zPs97Y5Jv2fQ6bvpmxnAAVXWfJB+T5MJdd1+Y5CFVda9lnrvMslivIcf5NMs+K8lnZ/bFgw0aepznh7m8IMlTktx8TGWzhIF/Z989s+D/4Kq6qKr+oap+q6oedHxrwGEcw+/s/5LkSfNxv3eSr0vy0mMonSUM/L3pE5Pc+TTL+tQjF8ggjvP7cVU9IMk/i+9gguFA7jH/79W77tv5/49Y8rnLLIv1GnKcb1dVleQXkrw9s1lDNmvocf6+JG9qrb1mkOoYwpBjfJ8kleSJSb4oySMym3H4tQHqZDVDf5Zfn+QBSa5KcmVmY/+jK1fJqob83nSPJNe31m7dsyzfvzbvWL4fV9Wdk/xmkhe31t5w1OVsC8FwGNfN/7v7LxY7//+hJZ+7zLJYryHHOcntofB5mf2V8omttZPDlMoKBhvnqnpEkm/LLBwyHsfxO/tnWmvvbq1dl+SZSb5gPpvI5gz5WT4jySsyC4f3mN9en+SPBquWoxrye9N1Se62p6HJvY6wHIY3+PfjeSh8SZIbkjz56KVtD8FwAK21q5JckuTsXXefneS9rbVrlnnuMstivYYc5+T2UHhukkcl+WLjOw4Dj/Ojk3xUkouq6ookv5PknvOOho86plXgAAP/zr46yXv2easapGCOZODP8kdm1nTmZ1prN7TWbsisScmjqup+x7QKHMLA35v+LsktSf63Pcv666NXyBCG/n48D4W/ldmhw1/dWnOqRwTDIf1Skh+oqgdW1QMz65L0C0d87jLLYr2GHOfnJvm8JF80/4XHeAw1zi/O7NDCs+e3b83sL5tnZ9YRjc0Z8rP880m+c345g7tm1uHulfPZQzZrkHFurV2R5OIkT6mqs+bnhT8lySXzx9isQ49zVZ2Yj9+JJGfMx/POSTIP/C9K8qz5uaQfn+Q791sWazfIOFfVnTL79/numR2tddN6yp+ATXe/2ZZbkjtlNvtz1fz2s0lOzB97fpLnH+a5h3ncbfrjnNlfnluSD2d2eMTO7fnrXie34xvn0yz3sdGVdBS3gX9nn5nkPye5Yn77rSQP3PQ6ug0+zp+U5A+TfHD++J8k+bRNr6Pb0uN8zvzf3923V+16/J5JXpjZH/EuT/KMTa+f27DjnOQx859v3PMd7GmbXsdN32q+gQAAAOiUQ0kBAAA6JxgCAAB0TjAEAADonGAIAADQOcEQAACgc4IhAABA5wRDAACAzgmGAAAAnRMMAQAAOicYAgAAdE4wBIBjUFU/UFV/tevnr6qqS6vq4ZusCwBOp1prm64BALZOVd0tycVJnprkiiQvTvKlrbULN1kXAJyOYAgAx6Sqnpzk+5PcPcn/0Vp79YZLAoDTcigpAByfNyZ5eJJfFgoBGDMzhgBwDObnEr46yflJnpjk41trN26yJgDYjxlDABhYVX1Ukj9M8szW2lOTXJLk32+2KgDYnxlDABhQVd0zs5nCl7TW/uP8vn+R5CVJHt5au3KT9QHA6QiGAAAAnXMoKQAAQOcEQwAAgM4JhgAAAJ0TDAEAADonGAIAAHROMAQAAOicYAgAANA5wRAAAKBzgiEAAEDnBEMAAIDO/f+SOM6pxvI+TAAAAABJRU5ErkJggg==\n",
 616 |       "text/plain": [
 617 |        "<Figure size 1080x720 with 1 Axes>"
 618 |       ]
 619 |      },
 620 |      "metadata": {
 621 |       "needs_background": "light"
 622 |      },
 623 |      "output_type": "display_data"
 624 |     }
 625 |    ],
 626 |    "source": [
 627 |     "my_log1 = chebyfun(fn_exp, domain, degree=11)"
 628 |    ]
 629 |   },
 630 |   {
 631 |    "cell_type": "code",
 632 |    "execution_count": 723,
 633 |    "metadata": {},
 634 |    "outputs": [
 635 |     {
 636 |      "name": "stdout",
 637 |      "output_type": "stream",
 638 |      "text": [
 639 |       "// Chebyshev approximation on (0, 0.125) deg 17.\n",
 640 |       "// Max observed error 1e-18, last 0 bits.\n",
 641 |       "x -= 0xde0b6b3a764000; // 0.0625\n",
 642 |       "int256 r = 0xc6c0; // 5.09e-14\n",
 643 |       "r = ((r * x) / FIX_1) + 0xc6c0; // 5.09e-14\n",
 644 |       "r = ((r * x) / FIX_1) + 0xc6c06; // 8.14e-13\n",
 645 |       "r = ((r * x) / FIX_1) + 0xba5171; // 1.22e-11\n",
 646 |       "r = ((r * x) / FIX_1) + 0xa30742f; // 1.71e-10\n",
 647 |       "r = ((r * x) / FIX_1) + 0x8475e66d; // 2.22e-09\n",
 648 |       "r = ((r * x) / FIX_1) + 0x63586cd21; // 2.67e-08\n",
 649 |       "r = ((r * x) / FIX_1) + 0x444ccad066; // 2.93e-07\n",
 650 |       "r = ((r * x) / FIX_1) + 0x2aaffec23f8; // 2.93e-06\n",
 651 |       "r = ((r * x) / FIX_1) + 0x1802ff4d43bb; // 2.64e-05\n",
 652 |       "r = ((r * x) / FIX_1) + 0xc017fa6a1dda; // 0.000211\n",
 653 |       "r = ((r * x) / FIX_1) + 0x540a7d8e6d0f5; // 0.00148\n",
 654 |       "r = ((r * x) / FIX_1) + 0x1f83ef1568e5bd; // 0.00887\n",
 655 |       "r = ((r * x) / FIX_1) + 0x9d93ab6b0c7caf; // 0.0444\n",
 656 |       "r = ((r * x) / FIX_1) + 0x2764eadac31f2bc; // 0.177\n",
 657 |       "r = ((r * x) / FIX_1) + 0x762ec090495d833; // 0.532\n",
 658 |       "r = ((r * x) / FIX_1) + 0xec5d812092bb066; // 1.06\n",
 659 |       "r = ((r * x) / FIX_1) + 0xec5d812092bb066; // 1.06\n"
 660 |      ]
 661 |     },
 662 |     {
 663 |      "name": "stderr",
 664 |      "output_type": "stream",
 665 |      "text": [
 666 |       "/var/folders/cb/n6k1dpbn7f1_n5m5dqv6rjvc0000gn/T/ipykernel_85508/2621324204.py:40: RuntimeWarning: divide by zero encountered in log2\n",
 667 |       "  error_bits = max(np.log2(abs(fy - y).astype(float)))\n"
 668 |      ]
 669 |     },
 670 |     {
 671 |      "data": {
 672 |       "image/png": 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\n",
 673 |       "text/plain": [
 674 |        "<Figure size 1080x720 with 1 Axes>"
 675 |       ]
 676 |      },
 677 |      "metadata": {
 678 |       "needs_background": "light"
 679 |      },
 680 |      "output_type": "display_data"
 681 |     }
 682 |    ],
 683 |    "source": [
 684 |     "my_exp = chebyfun(mp.exp, (0.0, 0.125), degree=17)"
 685 |    ]
 686 |   },
 687 |   {
 688 |    "cell_type": "code",
 689 |    "execution_count": null,
 690 |    "metadata": {},
 691 |    "outputs": [],
 692 |    "source": []
 693 |   },
 694 |   {
 695 |    "cell_type": "code",
 696 |    "execution_count": 724,
 697 |    "metadata": {},
 698 |    "outputs": [],
 699 |    "source": [
 700 |     "def chebyshev_nodes(domain, n):\n",
 701 |     "    start, end = domain\n",
 702 |     "    start = mp.mpf(start)\n",
 703 |     "    end = mp.mpf(end)\n",
 704 |     "    mid = (start + end) / 2\n",
 705 |     "    amp = (end - start) / 2\n",
 706 |     "    xs = []\n",
 707 |     "    for i in range(n):\n",
 708 |     "        f = mp.mpf(2 * i + 1) / mp.mpf(2 * n)\n",
 709 |     "        xs += [mid - amp * mp.cos(mp.pi * f)]\n",
 710 |     "    return xs"
 711 |    ]
 712 |   },
 713 |   {
 714 |    "cell_type": "code",
 715 |    "execution_count": 725,
 716 |    "metadata": {},
 717 |    "outputs": [],
 718 |    "source": [
 719 |     "def least_squares(A, b):\n",
 720 |     "    U, S, V = mp.svd_r(A)\n",
 721 |     "    for i in range(len(S)):\n",
 722 |     "        if S[i] != 0:\n",
 723 |     "            S[i] = mp.one / S[i]\n",
 724 |     "    return V.T * mp.diag(S) * U.T * b"
 725 |    ]
 726 |   },
 727 |   {
 728 |    "cell_type": "code",
 729 |    "execution_count": 726,
 730 |    "metadata": {},
 731 |    "outputs": [],
 732 |    "source": [
 733 |     "def vandermonde(x, n):\n",
 734 |     "    A = mp.matrix(len(x), n)\n",
 735 |     "    for i, x in enumerate(x):\n",
 736 |     "        r = mp.one\n",
 737 |     "        for j in range(n):\n",
 738 |     "            A[i, j] = r\n",
 739 |     "            r *= x\n",
 740 |     "    return A"
 741 |    ]
 742 |   },
 743 |   {
 744 |    "cell_type": "code",
 745 |    "execution_count": 727,
 746 |    "metadata": {},
 747 |    "outputs": [
 748 |     {
 749 |      "data": {
 750 |       "text/plain": [
 751 |        "['0xec5d812092bb066',\n",
 752 |        " '0xec5d812092bb066',\n",
 753 |        " '0x762ec090495d833',\n",
 754 |        " '0x2764eadac31f2bc',\n",
 755 |        " '0x9d93ab6b0c7caf',\n",
 756 |        " '0x1f83ef1568e5bd',\n",
 757 |        " '0x540a7d8e6d0f5',\n",
 758 |        " '0xc017fa6a1dda',\n",
 759 |        " '0x1802ff4d43bb',\n",
 760 |        " '0x2aaffec23f8',\n",
 761 |        " '0x444ccad066',\n",
 762 |        " '0x63586cd21',\n",
 763 |        " '0x8475e66d',\n",
 764 |        " '0xa30742f',\n",
 765 |        " '0xba5171',\n",
 766 |        " '0xc6c06',\n",
 767 |        " '0xc6c0']"
 768 |       ]
 769 |      },
 770 |      "execution_count": 727,
 771 |      "metadata": {},
 772 |      "output_type": "execute_result"
 773 |     }
 774 |    ],
 775 |    "source": [
 776 |     "f = lambda x: mp.exp(x + 0.0625)\n",
 777 |     "d = (0.0 - 0.0625, 0.125 - 0.0625)\n",
 778 |     "x = chebyshev_nodes(d, 17)\n",
 779 |     "y = mp.matrix([f(x) for x in x])\n",
 780 |     "c = least_squares(vandermonde(x, 17), y)\n",
 781 |     "[hex(mp_to_fix(c)) for c in c]"
 782 |    ]
 783 |   },
 784 |   {
 785 |    "cell_type": "code",
 786 |    "execution_count": 728,
 787 |    "metadata": {},
 788 |    "outputs": [],
 789 |    "source": [
 790 |     "def extrema(domain, f, c, derivative=None):\n",
 791 |     "    # If no derivative of f is provided, produce one numerically\n",
 792 |     "    if derivative is None:\n",
 793 |     "        derivative = lambda x: mp.diff(f, x)\n",
 794 |     "    \n",
 795 |     "    # Create a derivative of the polynomial\n",
 796 |     "    c = reversed([c for i, c in enumerate(c[0:-1:-1])])\n",
 797 |     "    \n",
 798 |     "    # Find extrema in the domain\n",
 799 |     "    f = lambda x: polyval(c, x) - derivative(x)\n",
 800 |     "    "
 801 |    ]
 802 |   },
 803 |   {
 804 |    "cell_type": "code",
 805 |    "execution_count": 729,
 806 |    "metadata": {},
 807 |    "outputs": [],
 808 |    "source": [
 809 |     "def remez(x, n):\n",
 810 |     "    A = mp.matrix(len(x), n + 1)\n",
 811 |     "    for i, x in enumerate(x):\n",
 812 |     "        r = mp.one\n",
 813 |     "        for j in range(n):\n",
 814 |     "            A[i, j] = r\n",
 815 |     "            r *= x\n",
 816 |     "        A[i, n] = mp.one if i % 2 == 0 else -mp.one\n",
 817 |     "    return A"
 818 |    ]
 819 |   },
 820 |   {
 821 |    "cell_type": "code",
 822 |    "execution_count": 730,
 823 |    "metadata": {},
 824 |    "outputs": [
 825 |     {
 826 |      "name": "stdout",
 827 |      "output_type": "stream",
 828 |      "text": [
 829 |       "[                                        1.064494458917859429563390594642889673102196875845794886517105937190162527623104184288352002087062444916185097998146973676999146529590008869969558781261740862644423323725219259737153328509480186422719447146723913658882839342929673106434827099147177303050246944554417728929839725312684720785776136017026261039]\n",
 830 |       "[                                        1.064494458917859429563390594642889673058638708206661182621077187627694944548695685861988047180905087922655644777457560275773875519471511126695473462269441402302811719248095048074577457344620877539438423036294088876980319546748464921955284949935366206750043877210754826871189247789411550281646876626372126051]\n",
 831 |       "[                                       0.5322472294589297147816952973214447861877371852109614158614529618145239852511230477816272801728021393842138151567391157349025865086517863474588381859957546764036157429393020264486787014960261009671326603765063351888450741892558684401618698421040369310270487880334208761277878188066047815642755478104255637959]\n",
 832 |       "[                                       0.1774157431529765715938984324404821293451363008884221562673741528286033602790247606113395713244427903294379088956445096432690941495974669098187620466597710916335819272159171663748525220097881359932119099643833700023678038839018264954224561343300176033191462110905524568998980126312729010890864859423679277937]\n",
 833 |       "[                                      0.04435393578824414289847460811040169638558935999550219019600012577428252419029176129720657217111801958622629401914239016398579085708572519781968259212681188470632535726210828531782092334376872371855751965449720232486071850525929150245689523233112996021276596682506205964409221394257109250694943261398639586048]\n",
 834 |       "[                                     0.008870787157648828579694921620170574211778441766741225886392207673862217363527027027994327029843252747852255426782551505820971911161826253563799887087396849608956870923828882195037716440322517466525915144871094371936815356809525534161493974231078616321057454477915025448362730426348494087005016215369773610703]\n",
 835 |       "[                                     0.001478464526274804763282486341020008507843939390120061333548149389461093885524685736214496380096604811601977988234493475053708228978206173139891688916536696166237742610156804419798534217825896102783033298942173529242375558195441439643276516510394534575900561294398819742451043395797392214552645987363728813045]\n",
 836 |       "[                                    0.0002112092180392578233260725449827385242474029286366626446912591078878299455949309852059837681589736374173695146854557474852717772167112343118603472054323138888774269998561426741390692716833238535411926250158546181315122476111039946097861300779102896863406390529719733563423955867295843427742447214566066582942]\n",
 837 |       "[                                   0.00002640115225490722791637665270187381182223604592382667902888782965398002543642847201361788676449415392011491971055695950685089442978671412984589901237076371763921452476100471425904939188551916263744192982664613017569236824655144534977705676332511542232073928968878965707704996552535222085790509995142891228852]\n",
 838 |       "[                                  0.000002933461361656358654761413396555577759312275864282002112377339452850687643494615219533458725343036122619926254085912656819913932269749989232553712669837832568712228608471573132602128698762537241006259927782469949018533614077108138788010969322957562286534829109240961534064587744942498486417159570005307555519]\n",
 839 |       "[                                 0.0000002933461361656355187716101747547717051128770154261382896708750346835614928252142630546329535399550317661517908692416726191722924144275612791077871113295198244835843958003762679764043598113685212360648321041107664679937591519597167455799341725361916141019068145953593893197208893345795490823766583533874396553]\n",
 840 |       "[                                0.00000002666783056051358344435688355989109368905536499996616184171899096032037950805539384121847888299859255616004166046670942933554052978853498693997002846099119113811019187735235463391833593167832785787286529231426485773827825728105263085342318774631992402951418918800325983597321820739642926568376413590843380949]\n",
 841 |       "[                               0.000000002222319213483695566085043037615234360784726907232005495962150954283183042996818085662455512097014610571674745459463862964105445046119852599246858722416293470032911727373837150397032762185845275879002143622683663271371167652053464643611693602239230879377625753136811526898146595857841396408034711217463790307]\n",
 842 |       "[                              0.0000000001709476314585007848091367921242652192428219746577821311755912158880750126689089922542150719515826024828600493658254776690945397129872037528872055512419768420995947037871067204355927749876907271226395738407031090330709878232102960023408322072090373798131522425701453176651237511876447851299945561694842554428]\n",
 843 |       "[                             0.00000000001221052776319518549224144419398202219187214992634455672704926532638613638477163597384450511585967466381659297825311609960429337378131006722266763401889846828818995132844690298280858317289886087476687149474365319749255042546885773018490872277671925243615826435050738966319537882400060412697919258397829979339]\n",
 844 |       "[                           0.0000000000008140860281500512199639816991120330555884641522815948709273907803742559617303110490875172598620926764296349823804507832069197589768303095703751469392497830979132055120769091137956018190277241529773327260565140391869782551939712231476054242012793792879373709441442248825659197346342913872405712167652681914737]\n",
 845 |       "[                          0.00000000000005201409733527632613040307414885359809460083486869950745818992943664225980169588296119916754734262759233841579432272079176846455241866796218359986827207878227646485655673266473922933636030540845684146737967903231891274344161593831710522606046519740488174150648930764868817295177397154051253706227958096491148]\n",
 846 |       "[-0.000000000000000000000000000000000000001471432196441584997798426554598590794938177954058566580185820540672115016885791603144789875692927614644983060318552472207906744523033825022712613377345581026661215079249119965924364521284736843761059250523113637593653057215717725913902335878477973941937519287961456950450090807542296157914869959680613856647]\n"
 847 |      ]
 848 |     },
 849 |     {
 850 |      "data": {
 851 |       "text/plain": [
 852 |        "['0xec5d812092bb066',\n",
 853 |        " '0xec5d812092bb066',\n",
 854 |        " '0x762ec090495d833',\n",
 855 |        " '0x2764eadac31f2bc',\n",
 856 |        " '0x9d93ab6b0c7caf',\n",
 857 |        " '0x1f83ef1568e5bd',\n",
 858 |        " '0x540a7d8e6d0f5',\n",
 859 |        " '0xc017fa6a1dda',\n",
 860 |        " '0x1802ff4d43bb',\n",
 861 |        " '0x2aaffec23f8',\n",
 862 |        " '0x444ccad066',\n",
 863 |        " '0x63586cd21',\n",
 864 |        " '0x8475e66d',\n",
 865 |        " '0xa30742f',\n",
 866 |        " '0xba5160',\n",
 867 |        " '0xc6c06',\n",
 868 |        " '0xcb2e',\n",
 869 |        " '0x0']"
 870 |       ]
 871 |      },
 872 |      "execution_count": 730,
 873 |      "metadata": {},
 874 |      "output_type": "execute_result"
 875 |     }
 876 |    ],
 877 |    "source": [
 878 |     "c = least_squares(remez(x, 17), y)\n",
 879 |     "print(c)\n",
 880 |     "[hex(mp_to_fix(c)) for c in c]"
 881 |    ]
 882 |   },
 883 |   {
 884 |    "cell_type": "code",
 885 |    "execution_count": null,
 886 |    "metadata": {},
 887 |    "outputs": [],
 888 |    "source": []
 889 |   },
 890 |   {
 891 |    "cell_type": "code",
 892 |    "execution_count": null,
 893 |    "metadata": {},
 894 |    "outputs": [],
 895 |    "source": []
 896 |   },
 897 |   {
 898 |    "cell_type": "code",
 899 |    "execution_count": null,
 900 |    "metadata": {},
 901 |    "outputs": [],
 902 |    "source": []
 903 |   },
 904 |   {
 905 |    "cell_type": "markdown",
 906 |    "metadata": {},
 907 |    "source": [
 908 |     "## LibFixMath\n",
 909 |     "\n",
 910 |     "**TODO.** LibFixedMath uses signed int, not unsigned"
 911 |    ]
 912 |   },
 913 |   {
 914 |    "cell_type": "code",
 915 |    "execution_count": null,
 916 |    "metadata": {},
 917 |    "outputs": [],
 918 |    "source": [
 919 |     "FIXED_1 = 0x0000000000000000000000000000000080000000000000000000000000000000\n",
 920 |     "MANTISA_MASK = 0x7fffffffffffffffffffffffffffffff\n",
 921 |     "LN_MIN_VAL = 0x0000000000000000000000000000000000000000000000000000000733048c5a\n",
 922 |     "LN_MAX_VAL = FIXED_1\n",
 923 |     "EXP_MIN_VAL = BASE - 0x0000000000000000000000000000001ff0000000000000000000000000000000"
 924 |    ]
 925 |   },
 926 |   {
 927 |    "cell_type": "code",
 928 |    "execution_count": null,
 929 |    "metadata": {},
 930 |    "outputs": [],
 931 |    "source": [
 932 |     "def lib_toInteger(x):\n",
 933 |     "    return div(x, FIXED_1)"
 934 |    ]
 935 |   },
 936 |   {
 937 |    "cell_type": "code",
 938 |    "execution_count": null,
 939 |    "metadata": {},
 940 |    "outputs": [],
 941 |    "source": [
 942 |     "def lib_toMantissa(x):\n",
 943 |     "    if x > 0:\n",
 944 |     "        return x & MANTISSA_MASK"
 945 |    ]
 946 |   },
 947 |   {
 948 |    "cell_type": "code",
 949 |    "execution_count": null,
 950 |    "metadata": {},
 951 |    "outputs": [],
 952 |    "source": [
 953 |     "def lib_mul(a, b):\n",
 954 |     "    aI = lib_toInteger(a)\n",
 955 |     "    aM = lib_toMantissa(a)\n",
 956 |     "    aI = lib_toInteger(b)\n",
 957 |     "    aM = lib_toMantissa(b)\n",
 958 |     "    \n",
 959 |     "    integerPart = mul(FIXED_1, mul(aI, bI))"
 960 |    ]
 961 |   },
 962 |   {
 963 |    "cell_type": "code",
 964 |    "execution_count": null,
 965 |    "metadata": {},
 966 |    "outputs": [],
 967 |    "source": [
 968 |     "def lib_log1(x):\n",
 969 |     "    # Valid over range ~0.87 - 1.0\n",
 970 |     "    r = 0\n",
 971 |     "    y = sub(x, FIXED_1)\n",
 972 |     "    z = y\n",
 973 |     "    w = sdiv(mul(y, y), FIXED_1)\n",
 974 |     "    r = add(r, sdiv(mul(z, sub(0x100000000000000000000000000000000, y)), 0x100000000000000000000000000000000))\n",
 975 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 976 |     "    r = add(r, sdiv(mul(z, sub(0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa, y)), 0x200000000000000000000000000000000))\n",
 977 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 978 |     "    r = add(r, sdiv(mul(z, sub(0x099999999999999999999999999999999, y)), 0x300000000000000000000000000000000))\n",
 979 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 980 |     "    r = add(r, sdiv(mul(z, sub(0x092492492492492492492492492492492, y)), 0x400000000000000000000000000000000))\n",
 981 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 982 |     "    r = add(r, sdiv(mul(z, sub(0x08e38e38e38e38e38e38e38e38e38e38e, y)), 0x500000000000000000000000000000000))\n",
 983 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 984 |     "    r = add(r, sdiv(mul(z, sub(0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b, y)), 0x600000000000000000000000000000000))\n",
 985 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 986 |     "    r = add(r, sdiv(mul(z, sub(0x089d89d89d89d89d89d89d89d89d89d89, y)), 0x700000000000000000000000000000000))\n",
 987 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
 988 |     "    r = add(r, sdiv(mul(z, sub(0x088888888888888888888888888888888, y)), 0x800000000000000000000000000000000))\n",
 989 |     "    return r"
 990 |    ]
 991 |   },
 992 |   {
 993 |    "cell_type": "code",
 994 |    "execution_count": null,
 995 |    "metadata": {},
 996 |    "outputs": [],
 997 |    "source": []
 998 |   },
 999 |   {
1000 |    "cell_type": "code",
1001 |    "execution_count": null,
1002 |    "metadata": {},
1003 |    "outputs": [],
1004 |    "source": []
1005 |   },
1006 |   {
1007 |    "cell_type": "code",
1008 |    "execution_count": null,
1009 |    "metadata": {},
1010 |    "outputs": [],
1011 |    "source": [
1012 |     "t = []\n",
1013 |     "def lib_ln(x, reductions='old', log='old'):\n",
1014 |     "    global t\n",
1015 |     "    _valid(x)\n",
1016 |     "    if x > LN_MAX_VAL:\n",
1017 |     "        raise \"ln: value too large\"\n",
1018 |     "    if x == 0 or x >= SIGN:\n",
1019 |     "        raise \"ln: value too small\"\n",
1020 |     "    if x == FIXED_1:\n",
1021 |     "        return 0\n",
1022 |     "    if x <= LN_MIN_VAL:\n",
1023 |     "        return EXP_MIN_VAL\n",
1024 |     "    \n",
1025 |     "    r = 0\n",
1026 |     "    y = 0\n",
1027 |     "    z = 0\n",
1028 |     "    w = 0\n",
1029 |     "    \n",
1030 |     "    old_values = [\n",
1031 |     "        0x00000000000000000000000000000000000000000001c8464f76164760000000,\n",
1032 |     "        0x00000000000000000000000000000000000000f1aaddd7742e90000000000000,\n",
1033 |     "        0x00000000000000000000000000000000000afe10820813d78000000000000000,\n",
1034 |     "        0x0000000000000000000000000000000002582ab704279ec00000000000000000,\n",
1035 |     "        0x000000000000000000000000000000001152aaa3bf81cc000000000000000000,\n",
1036 |     "        0x000000000000000000000000000000002f16ac6c59de70000000000000000000,\n",
1037 |     "        0x000000000000000000000000000000004da2cbf1be5828000000000000000000,\n",
1038 |     "        0x0000000000000000000000000000000063afbe7ab2082c000000000000000000,\n",
1039 |     "        0x0000000000000000000000000000000070f5a893b608861e1f58934f97aea57d,\n",
1040 |     "    ]\n",
1041 |     "    new_values = [\n",
1042 |     "        0x1c8464f76164681e299a0,\n",
1043 |     "        0xf1aaddd7742e56d32fb9f99744,\n",
1044 |     "        0xafe10820813d65dfe6a33c07f738f,\n",
1045 |     "        0x2582ab704279e8efd15e0265855c47b,\n",
1046 |     "        0x1152aaa3bf81cb9fdb76eae12d029572,\n",
1047 |     "        0x2f16ac6c59de6f8d5d6f63c1482a7c87,\n",
1048 |     "        0x4da2cbf1be5827f9eb3ad1aa9866ebb4,\n",
1049 |     "        0x63afbe7ab2082ba1a0ae5e4eb1b479dd,\n",
1050 |     "        0x70f5a893b608861e1f58934f97aea57d,\n",
1051 |     "    ]\n",
1052 |     "    reduction_values = old_values if reductions == 'old' else new_values\n",
1053 |     "    for i, v in enumerate(reduction_values):\n",
1054 |     "        if x <= v:\n",
1055 |     "            r = sub(r, 0x0000000000000000000000000000001000000000000000000000000000000000 >> i)\n",
1056 |     "            x = sdiv(mul(x, FIXED_1), v)\n",
1057 |     "    \n",
1058 |     "    t += [x]\n",
1059 |     "    if log == 'new':\n",
1060 |     "        return add(r, my_log1(x))\n",
1061 |     "    \n",
1062 |     "    y = sub(x, FIXED_1)\n",
1063 |     "    z = y\n",
1064 |     "    w = sdiv(mul(y, y), FIXED_1)\n",
1065 |     "    r = add(r, sdiv(mul(z, sub(0x100000000000000000000000000000000, y)), 0x100000000000000000000000000000000))\n",
1066 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1067 |     "    r = add(r, sdiv(mul(z, sub(0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa, y)), 0x200000000000000000000000000000000))\n",
1068 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1069 |     "    r = add(r, sdiv(mul(z, sub(0x099999999999999999999999999999999, y)), 0x300000000000000000000000000000000))\n",
1070 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1071 |     "    r = add(r, sdiv(mul(z, sub(0x092492492492492492492492492492492, y)), 0x400000000000000000000000000000000))\n",
1072 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1073 |     "    r = add(r, sdiv(mul(z, sub(0x08e38e38e38e38e38e38e38e38e38e38e, y)), 0x500000000000000000000000000000000))\n",
1074 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1075 |     "    r = add(r, sdiv(mul(z, sub(0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b, y)), 0x600000000000000000000000000000000))\n",
1076 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1077 |     "    r = add(r, sdiv(mul(z, sub(0x089d89d89d89d89d89d89d89d89d89d89, y)), 0x700000000000000000000000000000000))\n",
1078 |     "    z = sdiv(mul(z, w), FIXED_1)\n",
1079 |     "    r = add(r, sdiv(mul(z, sub(0x088888888888888888888888888888888, y)), 0x800000000000000000000000000000000))\n",
1080 |     "    \n",
1081 |     "    return r"
1082 |    ]
1083 |   },
1084 |   {
1085 |    "cell_type": "code",
1086 |    "execution_count": null,
1087 |    "metadata": {},
1088 |    "outputs": [],
1089 |    "source": [
1090 |     "for i in range(-3,6):\n",
1091 |     "    print(2**i)\n",
1092 |     "    print(hex( mp_to_fix( mp.exp(-mp.mpf(2) ** (i)) )))"
1093 |    ]
1094 |   },
1095 |   {
1096 |    "cell_type": "code",
1097 |    "execution_count": null,
1098 |    "metadata": {},
1099 |    "outputs": [],
1100 |    "source": [
1101 |     "def my_mul(a, b):\n",
1102 |     "    mm = mulmod(a, b, bnot(0))\n",
1103 |     "    r0 = mul(a, b)\n",
1104 |     "    r1 = sub(sub(mm, r0), lt(mm, r0))\n",
1105 |     "    r1 = add(r1, mul(sar(256, a), b))\n",
1106 |     "    r1 = add(r1, mul(sar(256, b), a))\n",
1107 |     "    r = bor(shl(129, r1), shr(127, r0))\n",
1108 |     "    return r"
1109 |    ]
1110 |   },
1111 |   {
1112 |    "cell_type": "code",
1113 |    "execution_count": null,
1114 |    "metadata": {},
1115 |    "outputs": [],
1116 |    "source": [
1117 |     "a = 2617556668622594272776707985386330127\n",
1118 |     "b = BASE - 130444458470968929913751441309200329514"
1119 |    ]
1120 |   },
1121 |   {
1122 |    "cell_type": "code",
1123 |    "execution_count": null,
1124 |    "metadata": {},
1125 |    "outputs": [],
1126 |    "source": [
1127 |     "fix_to_f(a)"
1128 |    ]
1129 |   },
1130 |   {
1131 |    "cell_type": "code",
1132 |    "execution_count": null,
1133 |    "metadata": {},
1134 |    "outputs": [],
1135 |    "source": [
1136 |     "fix_to_f(b)"
1137 |    ]
1138 |   },
1139 |   {
1140 |    "cell_type": "code",
1141 |    "execution_count": null,
1142 |    "metadata": {},
1143 |    "outputs": [],
1144 |    "source": [
1145 |     "d = my_mul(a, b)\n",
1146 |     "d"
1147 |    ]
1148 |   },
1149 |   {
1150 |    "cell_type": "code",
1151 |    "execution_count": null,
1152 |    "metadata": {},
1153 |    "outputs": [],
1154 |    "source": [
1155 |     "fix_to_f(d)"
1156 |    ]
1157 |   },
1158 |   {
1159 |    "cell_type": "code",
1160 |    "execution_count": null,
1161 |    "metadata": {},
1162 |    "outputs": [],
1163 |    "source": [
1164 |     "0.01538461538461533 * -0.7666836201434823"
1165 |    ]
1166 |   },
1167 |   {
1168 |    "cell_type": "code",
1169 |    "execution_count": null,
1170 |    "metadata": {},
1171 |    "outputs": [],
1172 |    "source": [
1173 |     "hex(sar(256, mp_to_fix(-2)))"
1174 |    ]
1175 |   },
1176 |   {
1177 |    "cell_type": "code",
1178 |    "execution_count": null,
1179 |    "metadata": {},
1180 |    "outputs": [],
1181 |    "source": []
1182 |   },
1183 |   {
1184 |    "cell_type": "code",
1185 |    "execution_count": null,
1186 |    "metadata": {},
1187 |    "outputs": [],
1188 |    "source": []
1189 |   },
1190 |   {
1191 |    "cell_type": "code",
1192 |    "execution_count": null,
1193 |    "metadata": {},
1194 |    "outputs": [],
1195 |    "source": []
1196 |   },
1197 |   {
1198 |    "cell_type": "markdown",
1199 |    "metadata": {},
1200 |    "source": [
1201 |     "# Evaluate"
1202 |    ]
1203 |   },
1204 |   {
1205 |    "cell_type": "code",
1206 |    "execution_count": null,
1207 |    "metadata": {},
1208 |    "outputs": [],
1209 |    "source": [
1210 |     "x = intrange(mp_to_fix(0.875), mp_to_fix(1.0), num = 10000)\n",
1211 |     "xr = [fix_to_f(x) for x in x]"
1212 |    ]
1213 |   },
1214 |   {
1215 |    "cell_type": "code",
1216 |    "execution_count": null,
1217 |    "metadata": {},
1218 |    "outputs": [],
1219 |    "source": [
1220 |     "def fix_exp(x):\n",
1221 |     "    return x.pow(1/(1-x))"
1222 |    ]
1223 |   },
1224 |   {
1225 |    "cell_type": "code",
1226 |    "execution_count": null,
1227 |    "metadata": {},
1228 |    "outputs": [],
1229 |    "source": [
1230 |     "y = np.array([fix_exp(x) for x in x])\n",
1231 |     "yr = np.array([fix_to_f(y) for y in y])"
1232 |    ]
1233 |   },
1234 |   {
1235 |    "cell_type": "markdown",
1236 |    "metadata": {},
1237 |    "source": [
1238 |     "### Log(1 + z)"
1239 |    ]
1240 |   },
1241 |   {
1242 |    "cell_type": "code",
1243 |    "execution_count": null,
1244 |    "metadata": {},
1245 |    "outputs": [],
1246 |    "source": [
1247 |     "x = intrange(mp_to_fix(0.875), mp_to_fix(1.0), num = 10000)\n",
1248 |     "xr = [fix_to_f(x) for x in x]"
1249 |    ]
1250 |   },
1251 |   {
1252 |    "cell_type": "code",
1253 |    "execution_count": null,
1254 |    "metadata": {},
1255 |    "outputs": [],
1256 |    "source": [
1257 |     "y = np.array([mp_log1(x) for x in x])\n",
1258 |     "yr = np.array([fix_to_f(y) for y in y])"
1259 |    ]
1260 |   },
1261 |   {
1262 |    "cell_type": "code",
1263 |    "execution_count": null,
1264 |    "metadata": {},
1265 |    "outputs": [],
1266 |    "source": [
1267 |     "ly = np.array([lib_log1(x) for x in x])\n",
1268 |     "lyr = np.array([fix_to_f(y) for y in ly])"
1269 |    ]
1270 |   },
1271 |   {
1272 |    "cell_type": "code",
1273 |    "execution_count": null,
1274 |    "metadata": {},
1275 |    "outputs": [],
1276 |    "source": [
1277 |     "my = np.array([my_log1(x) for x in x])\n",
1278 |     "myr = np.array([fix_to_f(y) for y in my])"
1279 |    ]
1280 |   },
1281 |   {
1282 |    "cell_type": "code",
1283 |    "execution_count": null,
1284 |    "metadata": {},
1285 |    "outputs": [],
1286 |    "source": [
1287 |     "plt.plot(xr, yr)\n",
1288 |     "plt.plot(xr, lyr)\n",
1289 |     "plt.plot(xr, myr)"
1290 |    ]
1291 |   },
1292 |   {
1293 |    "cell_type": "code",
1294 |    "execution_count": null,
1295 |    "metadata": {},
1296 |    "outputs": [],
1297 |    "source": [
1298 |     "plt.plot(xr, np.log2(abs(ly - y).astype(float)))\n",
1299 |     "plt.plot(xr, np.log2(abs(my - y).astype(float)))"
1300 |    ]
1301 |   },
1302 |   {
1303 |    "cell_type": "markdown",
1304 |    "metadata": {},
1305 |    "source": [
1306 |     "### Exp(x)"
1307 |    ]
1308 |   },
1309 |   {
1310 |    "cell_type": "code",
1311 |    "execution_count": null,
1312 |    "metadata": {},
1313 |    "outputs": [],
1314 |    "source": [
1315 |     "x = intrange(mp_to_fix(0.0), mp_to_fix(0.125), num = 10000)\n",
1316 |     "xr = [fix_to_f(x) for x in x]"
1317 |    ]
1318 |   },
1319 |   {
1320 |    "cell_type": "code",
1321 |    "execution_count": null,
1322 |    "metadata": {},
1323 |    "outputs": [],
1324 |    "source": [
1325 |     "y = np.array([mp_exp(x) for x in x])\n",
1326 |     "yr = np.array([fix_to_f(y) for y in y])"
1327 |    ]
1328 |   },
1329 |   {
1330 |    "cell_type": "code",
1331 |    "execution_count": null,
1332 |    "metadata": {},
1333 |    "outputs": [],
1334 |    "source": [
1335 |     "my = np.array([my_exp(x) for x in x])\n",
1336 |     "myr = np.array([fix_to_f(y) for y in my])"
1337 |    ]
1338 |   },
1339 |   {
1340 |    "cell_type": "code",
1341 |    "execution_count": null,
1342 |    "metadata": {},
1343 |    "outputs": [],
1344 |    "source": [
1345 |     "plt.plot(xr, yr)\n",
1346 |     "plt.plot(xr, myr)"
1347 |    ]
1348 |   },
1349 |   {
1350 |    "cell_type": "code",
1351 |    "execution_count": null,
1352 |    "metadata": {},
1353 |    "outputs": [],
1354 |    "source": [
1355 |     "plt.plot(xr, np.log2(abs(my - y).astype(float)))"
1356 |    ]
1357 |   },
1358 |   {
1359 |    "cell_type": "markdown",
1360 |    "metadata": {},
1361 |    "source": [
1362 |     "### Ln(x)"
1363 |    ]
1364 |   },
1365 |   {
1366 |    "cell_type": "code",
1367 |    "execution_count": null,
1368 |    "metadata": {},
1369 |    "outputs": [],
1370 |    "source": [
1371 |     "t = []"
1372 |    ]
1373 |   },
1374 |   {
1375 |    "cell_type": "code",
1376 |    "execution_count": null,
1377 |    "metadata": {},
1378 |    "outputs": [],
1379 |    "source": [
1380 |     "x = intrange(LN_MIN_VAL, LN_MAX_VAL, num = 10000)\n",
1381 |     "xr = [fix_to_f(x) for x in x]"
1382 |    ]
1383 |   },
1384 |   {
1385 |    "cell_type": "code",
1386 |    "execution_count": null,
1387 |    "metadata": {},
1388 |    "outputs": [],
1389 |    "source": [
1390 |     "y = np.array([mp_ln(x) for x in x])\n",
1391 |     "yr = np.array([fix_to_f(y) for y in y])"
1392 |    ]
1393 |   },
1394 |   {
1395 |    "cell_type": "code",
1396 |    "execution_count": null,
1397 |    "metadata": {},
1398 |    "outputs": [],
1399 |    "source": [
1400 |     "ly = np.array([lib_ln(x) for x in x])\n",
1401 |     "lyr = np.array([fix_to_f(y) for y in ly])"
1402 |    ]
1403 |   },
1404 |   {
1405 |    "cell_type": "code",
1406 |    "execution_count": null,
1407 |    "metadata": {},
1408 |    "outputs": [],
1409 |    "source": [
1410 |     "lz = np.array([lib_ln(x, reductions='new', log='new') for x in x])\n",
1411 |     "lzr = np.array([fix_to_f(z) for z in lz])"
1412 |    ]
1413 |   },
1414 |   {
1415 |    "cell_type": "code",
1416 |    "execution_count": null,
1417 |    "metadata": {},
1418 |    "outputs": [],
1419 |    "source": [
1420 |     "plt.plot(xr, yr)\n",
1421 |     "plt.plot(xr, lyr)\n",
1422 |     "plt.plot(xr, lzr)"
1423 |    ]
1424 |   },
1425 |   {
1426 |    "cell_type": "code",
1427 |    "execution_count": null,
1428 |    "metadata": {},
1429 |    "outputs": [],
1430 |    "source": [
1431 |     "plt.plot(xr, np.log2(abs(ly - y).astype(float)))\n",
1432 |     "plt.plot(xr, np.log2(abs(lz - y).astype(float)))"
1433 |    ]
1434 |   },
1435 |   {
1436 |    "cell_type": "code",
1437 |    "execution_count": null,
1438 |    "metadata": {},
1439 |    "outputs": [],
1440 |    "source": [
1441 |     "(fix_to_f(min(t)), fix_to_f(max(t)))"
1442 |    ]
1443 |   },
1444 |   {
1445 |    "cell_type": "code",
1446 |    "execution_count": null,
1447 |    "metadata": {},
1448 |    "outputs": [],
1449 |    "source": [
1450 |     "plt.plot([fix_to_f(t) for t in t])"
1451 |    ]
1452 |   },
1453 |   {
1454 |    "cell_type": "code",
1455 |    "execution_count": null,
1456 |    "metadata": {},
1457 |    "outputs": [],
1458 |    "source": []
1459 |   },
1460 |   {
1461 |    "cell_type": "code",
1462 |    "execution_count": null,
1463 |    "metadata": {},
1464 |    "outputs": [],
1465 |    "source": []
1466 |   },
1467 |   {
1468 |    "cell_type": "code",
1469 |    "execution_count": null,
1470 |    "metadata": {},
1471 |    "outputs": [],
1472 |    "source": []
1473 |   },
1474 |   {
1475 |    "cell_type": "code",
1476 |    "execution_count": null,
1477 |    "metadata": {},
1478 |    "outputs": [],
1479 |    "source": []
1480 |   },
1481 |   {
1482 |    "cell_type": "code",
1483 |    "execution_count": null,
1484 |    "metadata": {},
1485 |    "outputs": [],
1486 |    "source": []
1487 |   },
1488 |   {
1489 |    "cell_type": "code",
1490 |    "execution_count": null,
1491 |    "metadata": {},
1492 |    "outputs": [],
1493 |    "source": []
1494 |   },
1495 |   {
1496 |    "cell_type": "code",
1497 |    "execution_count": null,
1498 |    "metadata": {},
1499 |    "outputs": [],
1500 |    "source": []
1501 |   },
1502 |   {
1503 |    "cell_type": "code",
1504 |    "execution_count": null,
1505 |    "metadata": {},
1506 |    "outputs": [],
1507 |    "source": []
1508 |   },
1509 |   {
1510 |    "cell_type": "code",
1511 |    "execution_count": null,
1512 |    "metadata": {},
1513 |    "outputs": [],
1514 |    "source": []
1515 |   }
1516 |  ],
1517 |  "metadata": {
1518 |   "kernelspec": {
1519 |    "display_name": "Python 3 (ipykernel)",
1520 |    "language": "python",
1521 |    "name": "python3"
1522 |   },
1523 |   "language_info": {
1524 |    "codemirror_mode": {
1525 |     "name": "ipython",
1526 |     "version": 3
1527 |    },
1528 |    "file_extension": ".py",
1529 |    "mimetype": "text/x-python",
1530 |    "name": "python",
1531 |    "nbconvert_exporter": "python",
1532 |    "pygments_lexer": "ipython3",
1533 |    "version": "3.9.10"
1534 |   }
1535 |  },
1536 |  "nbformat": 4,
1537 |  "nbformat_minor": 4
1538 | }
1539 | 


--------------------------------------------------------------------------------
/src/FixedPointMathLib.sol:
--------------------------------------------------------------------------------
  1 | // SPDX-License-Identifier: UNLICENSED
  2 | pragma solidity ^0.8.10;
  3 | 
  4 | import "./test/console.sol";
  5 | 
  6 | library FixedPointMathLib {
  7 | 
  8 |     error Overflow();
  9 |     error LnNegativeUndefined();
 10 | 
 11 |     // Integer log2 (alternative implementation)
 12 |     // @returns floor(log2(x)) if x is nonzero, otherwise 0.
 13 |     // Consumes 317 gas. This could have been an 3 gas EVM opcode though.
 14 |     function ilog2_alt(uint256 x) internal returns (uint256 r) {
 15 |         unchecked {
 16 |             // Repeat first zero all the way to the right
 17 |             x |= x >> 1;
 18 |             x |= x >> 2;
 19 |             x |= x >> 4;
 20 |             x |= x >> 8;
 21 |             x |= x >> 16;
 22 |             x |= x >> 32;
 23 |             x |= x >> 64;
 24 |             x |= x >> 128;
 25 | 
 26 |             // Count 32 bit chunks
 27 |             r = x & 0x100000001000000010000000100000001000000010000000100000001;
 28 |             r *= 0x20000000200000002000000020000000200000002000000020;
 29 |             r >>= 224;
 30 | 
 31 |             // Extract highest bit
 32 |             x ^= x >> 1;
 33 | 
 34 |             // Copy to lowest 32 bit chunk
 35 |             x |= x >> 32;
 36 |             x |= x >> 64;
 37 |             x |= x >> 128;
 38 |             // No need to clear the other chunks
 39 | 
 40 |             // Map to 0-31 using the B(2, 5) de Bruijn sequence 0x077CB531.
 41 |             // See <https://en.wikipedia.org/wiki/De_Bruijn_sequence#Finding_least-_or_most-significant_set_bit_in_a_word>
 42 |             x = ((x * 0x077CB531) >> 27) & 0x1f;
 43 | 
 44 |             // Use a bytes32 32 entry lookup table
 45 |             assembly {
 46 |                 // Need assembly here because solidity introduces an uncessary bounds
 47 |                 // check.
 48 |                 r := add(r, byte(x, 0x11c021d0e18031e16140f191104081f1b0d17151310071a0c12060b050a09))
 49 |             }
 50 |         }
 51 |     }
 52 | 
 53 |     // Integer log2
 54 |     // @returns floor(log2(x)) if x is nonzero, otherwise 0. This is the same
 55 |     //          as the location of the highest set bit.
 56 |     // Consumes 232 gas. This could have been an 3 gas EVM opcode though.
 57 |     function ilog2(uint256 x) internal returns (uint256 r) {
 58 |         assembly {
 59 |             r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
 60 |             r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
 61 |             r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
 62 |             r := or(r, shl(4, lt(0xffff, shr(r, x))))
 63 |             r := or(r, shl(3, lt(0xff, shr(r, x))))
 64 |             r := or(r, shl(2, lt(0xf, shr(r, x))))
 65 |             r := or(r, shl(1, lt(0x3, shr(r, x))))
 66 |             r := or(r, lt(0x1, shr(r, x)))
 67 |         }
 68 |     }
 69 | 
 70 |     function ln_pub(int256 x) public returns (int256 r) {
 71 |         return ln(x);
 72 |     }
 73 | 
 74 |     // Computes ln(x) in 1e18 fixed point.
 75 |     // Reverts if x is negative or zero.
 76 |     // Consumes 670 gas.
 77 |     function ln(int256 x) internal returns (int256 r) { unchecked {
 78 |         if (x < 1) {
 79 |             if (x < 0) revert LnNegativeUndefined();
 80 |             revert Overflow();
 81 |         }
 82 | 
 83 |         // We want to convert x from 10**18 fixed point to 2**96 fixed point.
 84 |         // We do this by multiplying by 2**96 / 10**18.
 85 |         // But since ln(x * C) = ln(x) + ln(C), we can simply do nothing here
 86 |         // and add ln(2**96 / 10**18) at the end.
 87 | 
 88 |         // Reduce range of x to (1, 2) * 2**96
 89 |         // ln(2^k * x) = k * ln(2) + ln(x)
 90 |         // Note: inlining ilog2 saves 8 gas.
 91 |         int256 k = int256(ilog2(uint256(x))) - 96;
 92 |         x <<= uint256(159 - k);
 93 |         x = int256(uint256(x) >> 159);
 94 | 
 95 |         // Evaluate using a (8, 8)-term rational approximation
 96 |         // p is made monic, we will multiply by a scale factor later
 97 |         int256 p = x      +     3273285459638523848632254066296;
 98 |         p = (p * x >> 96) +    24828157081833163892658089445524;
 99 |         p = (p * x >> 96) +    43456485725739037958740375743393;
100 |         p = (p * x >> 96) -    11111509109440967052023855526967;
101 |         p = (p * x >> 96) -    45023709667254063763336534515857;
102 |         p = (p * x >> 96) -    14706773417378608786704636184526;
103 |         p = p * x         -     (795164235651350426258249787498 << 96);
104 |         //emit log_named_int("p", p);
105 |         // We leave p in 2**192 basis so we don't need to scale it back up for the division.
106 |         // q is monic by convention
107 |         int256 q = x      +     5573035233440673466300451813936;
108 |         q = (q * x >> 96) +    71694874799317883764090561454958;
109 |         q = (q * x >> 96) +   283447036172924575727196451306956;
110 |         q = (q * x >> 96) +   401686690394027663651624208769553;
111 |         q = (q * x >> 96) +   204048457590392012362485061816622;
112 |         q = (q * x >> 96) +    31853899698501571402653359427138;
113 |         q = (q * x >> 96) +      909429971244387300277376558375;
114 |         assembly {
115 |             // Div in assembly because solidity adds a zero check despite the `unchecked`.
116 |             // The q polynomial is known not to have zeros in the domain. (All roots are complex)
117 |             // No scaling required because p is already 2**96 too large.
118 |             r := sdiv(p, q)
119 |         }
120 |         // r is in the range (0, 0.125) * 2**96
121 | 
122 |         // Finalization, we need to
123 |         // * multiply by the scale factor s = 5.549…
124 |         // * add ln(2**96 / 10**18)
125 |         // * add k * ln(2)
126 |         // * multiply by 10**18 / 2**96 = 5**18 >> 78
127 |         // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
128 |         r *= 1677202110996718588342820967067443963516166;
129 |         // add ln(2) * k * 5e18 * 2**192
130 |         r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
131 |         // add ln(2**96 / 10**18) * 5e18 * 2**192
132 |         r += 600920179829731861736702779321621459595472258049074101567377883020018308;
133 |         // base conversion: mul 2**18 / 2**192
134 |         r >>= 174;
135 |     }}
136 | 
137 |     // Computes e^x in 1e18 fixed point.
138 |     function exp(int256 x) internal pure returns (int256 r) { unchecked {
139 |         // Input x is in fixed point format, with scale factor 1/1e18.
140 | 
141 |         // When the result is < 0.5 we return zero. This happens when
142 |         // x <= floor(log(0.5e18) * 1e18) ~ -42e18
143 |         if (x <= -42139678854452767551) {
144 |             return 0;
145 |         }
146 | 
147 |         // When the result is > (2**255 - 1) / 1e18 we can not represent it
148 |         // as an int256. This happens when x >= floor(log((2**255 -1) / 1e18) * 1e18) ~ 135.
149 |         if (x >= 135305999368893231589) revert Overflow();
150 | 
151 |         // x is now in the range (-42, 136) * 1e18. Convert to (-42, 136) * 2**96
152 |         // for more intermediate precision and a binary basis. This base conversion
153 |         // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
154 |         x = (x << 78) / 5**18;
155 | 
156 |         // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers of two
157 |         // such that exp(x) = exp(x') * 2**k, where k is an integer.
158 |         // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
159 |         int256 k = ((x << 96) / 54916777467707473351141471128 + 2**95) >> 96;
160 |         x = x - k * 54916777467707473351141471128;
161 |         // k is in the range [-61, 195].
162 | 
163 |         // Evaluate using a (6, 7)-term rational approximation
164 |         // p is made monic, we will multiply by a scale factor later
165 |         int256 p = x      +     2772001395605857295435445496992;
166 |         p = (p * x >> 96) +    44335888930127919016834873520032;
167 |         p = (p * x >> 96) +   398888492587501845352592340339721;
168 |         p = (p * x >> 96) +  1993839819670624470859228494792842;
169 |         p = p * x         + (4385272521454847904632057985693276 << 96);
170 |         // We leave p in 2**192 basis so we don't need to scale it back up for the division.
171 |         // Evaluate using using Knuth's scheme from p. 491.
172 |         int256 z = x      +     750530180792738023273180420736;
173 |         z = (z * x >> 96) +   32788456221302202726307501949080;
174 |         int256 w = x      -    2218138959503481824038194425854;
175 |         w = (w * z >> 96) +  892943633302991980437332862907700;
176 |         int256 q = z + w  -   78174809823045304726920794422040;
177 |         q = (q * w >> 96) + 4203224763890128580604056984195872;
178 |         assembly {
179 |             // Div in assembly because solidity adds a zero check despite the `unchecked`.
180 |             // The q polynomial is known not to have zeros in the domain. (All roots are complex)
181 |             // No scaling required because p is already 2**96 too large.
182 |             r := sdiv(p, q)
183 |         }
184 |         // r should be in the range (0.09, 0.25) * 2**96.
185 | 
186 |         // We now need to multiply r by 
187 |         //  * the scale factor s = ~6.031367120...,
188 |         //  * the 2**k factor from the range reduction, and
189 |         //  * the 1e18 / 2**96 factor for base converison.
190 |         // We do all of this at once, with an intermediate result in 2**213 basis
191 |         // so the final right shift is always by a positive amount.
192 |         r = int((uint(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k));
193 |     }}
194 | }
195 | 


--------------------------------------------------------------------------------
/src/test/FixedPointMathLib.t.sol:
--------------------------------------------------------------------------------
  1 | // SPDX-License-Identifier: UNLICENSED
  2 | pragma solidity 0.8.10;
  3 | 
  4 | import "ds-test/test.sol";
  5 | import "../FixedPointMathLib.sol";
  6 | import "./console.sol";
  7 | 
  8 | contract FixedPointMathLibTest is DSTest {
  9 |     function setUp() public {}
 10 | 
 11 |     function testIlog1() public {
 12 |         FixedPointMathLib.ilog2(2 ** 196 - 1);
 13 |     }
 14 | 
 15 |     function testIlog2() public {
 16 |         FixedPointMathLib.ilog2(1e18);
 17 |         FixedPointMathLib.ilog2(1e20);
 18 |     }
 19 | 
 20 |     function testIlog() public {
 21 |         assertEq(FixedPointMathLib.ilog2(0), 0);
 22 |         for(uint256 i = 1; i < 255; i++) {
 23 |             assertEq(FixedPointMathLib.ilog2((1 << i) - 1), i - 1);
 24 |             assertEq(FixedPointMathLib.ilog2((1 << i)), i);
 25 |             assertEq(FixedPointMathLib.ilog2((1 << i) + 1), i);
 26 |         }
 27 |     }
 28 | 
 29 |     function testIlogGas() public {
 30 |         uint256 count = 0;
 31 |         uint256 sum = 0;
 32 |         uint256 sum_sq = 0;
 33 |         for(uint256 i = 1; i < 255; i++) {
 34 |             uint256 k = (1 << i) - 1;
 35 |             uint g0 = gasleft();
 36 |             FixedPointMathLib.ilog2(k);
 37 |             uint g1 = gasleft();
 38 |             sum += g0 - g1;
 39 |             sum_sq += (g0 - g1) * (g0 - g1);
 40 |             ++count;
 41 |             ++k;
 42 |             g0 = gasleft();
 43 |             FixedPointMathLib.ilog2(k);
 44 |             g1 = gasleft();
 45 |             sum += g0 - g1;
 46 |             sum_sq += (g0 - g1) * (g0 - g1);
 47 |             ++count;
 48 |             ++k;
 49 |             g0 = gasleft();
 50 |             FixedPointMathLib.ilog2(k);
 51 |             g1 = gasleft();
 52 |             sum += g0 - g1;
 53 |             sum_sq += (g0 - g1) * (g0 - g1);
 54 |             ++count;
 55 |         }
 56 |         console.Log("gas", sum / count);
 57 |         console.Log("gas_var", (sum_sq - sum * sum / count)/ (count - 1));
 58 |     }
 59 | 
 60 |     function testLn1() public {
 61 |         assertEq(FixedPointMathLib.ln(1e18), 0);
 62 |     }
 63 | 
 64 |     function testLn() public {
 65 |         assertEq(FixedPointMathLib.ln(1e18), 0);
 66 | 
 67 |         // Actual: 999999999999999999.8674576…
 68 |         assertEq(FixedPointMathLib.ln(2718281828459045235), 999999999999999999);
 69 | 
 70 |         // Actual: 2461607324344817917.963296…
 71 |         assertEq(FixedPointMathLib.ln(11723640096265400935), 2461607324344817918);
 72 |     }
 73 | 
 74 |     function testLnSmall() public {
 75 |         // Actual: -41446531673892822312.3238461…
 76 |         assertEq(FixedPointMathLib.ln(1), -41446531673892822313);
 77 | 
 78 |         // Actual: -37708862055609454006.40601608…
 79 |         assertEq(FixedPointMathLib.ln(42), -37708862055609454007);
 80 | 
 81 |         // Actual: -32236191301916639576.251880365581…
 82 |         assertEq(FixedPointMathLib.ln(1e4), -32236191301916639577);
 83 | 
 84 |         // Actual: -20723265836946411156.161923092…
 85 |         assertEq(FixedPointMathLib.ln(1e9), -20723265836946411157);
 86 |     }
 87 | 
 88 |     function testLnBig() public {
 89 |         // Actual: 135305999368893231589.070344787…
 90 |         assertEq(FixedPointMathLib.ln(2**255 - 1), 135305999368893231589);
 91 | 
 92 |         // Actual: 76388489021297880288.605614463571…
 93 |         assertEq(FixedPointMathLib.ln(2**170), 76388489021297880288);
 94 | 
 95 |         // Actual: 47276307437780177293.081865…
 96 |         assertEq(FixedPointMathLib.ln(2**128), 47276307437780177293);
 97 |     }
 98 | 
 99 |     function testLnGas() public {
100 |         uint256 count = 0;
101 |         uint256 sum = 0;
102 |         uint256 sum_sq = 0;
103 |         for(uint256 i = 1; i < 255; i++) {
104 |             int256 k = int256(1 << i) - 1;
105 |             uint g0 = gasleft();
106 |             FixedPointMathLib.ln(k);
107 |             uint g1 = gasleft();
108 |             sum += g0 - g1;
109 |             sum_sq += (g0 - g1) * (g0 - g1);
110 |             ++count;
111 |             ++k;
112 |             g0 = gasleft();
113 |             FixedPointMathLib.ln(k);
114 |             g1 = gasleft();
115 |             sum += g0 - g1;
116 |             sum_sq += (g0 - g1) * (g0 - g1);
117 |             ++count;
118 |             ++k;
119 |             g0 = gasleft();
120 |             FixedPointMathLib.ln(k);
121 |             g1 = gasleft();
122 |             sum += g0 - g1;
123 |             sum_sq += (g0 - g1) * (g0 - g1);
124 |             ++count;
125 |         }
126 |         console.Log("gas", sum / count);
127 |         console.Log("gas_var", (sum_sq - sum * sum / count)/ (count - 1));
128 |     }
129 | 
130 |     function testExp1() public {
131 |         assertEq(FixedPointMathLib.exp(-1e18), 367879441171442321);
132 |     }
133 |     
134 |     function testSmallest() public {
135 |         FixedPointMathLib.exp(-42139678854452767550);
136 |     }
137 | 
138 |     function testLargest() public {
139 |         FixedPointMathLib.exp(135305999368893231588);
140 |     }
141 | 
142 |     function testSome() public {
143 |         console.logInt(FixedPointMathLib.exp(5e18));
144 |     }
145 | 
146 |     function testExpGas() public {
147 |         uint g0 = gasleft();
148 |         FixedPointMathLib.exp(133e18);
149 |         uint g1 = gasleft();
150 |         FixedPointMathLib.exp(-23e18);
151 |         uint g2 = gasleft();
152 |         FixedPointMathLib.exp(5e18);
153 |         uint g3 = gasleft();
154 |         console.logUint(g0 - g1);
155 |         console.logUint(g1 - g2);
156 |         console.logUint(g2 - g3);
157 |     }
158 | 
159 |     function testExp3() public {
160 |         FixedPointMathLib.exp(133e18);
161 |         FixedPointMathLib.exp(10e18);
162 |         FixedPointMathLib.exp(-23e18);
163 |     }
164 | }
165 | 


--------------------------------------------------------------------------------
/src/test/console.sol:
--------------------------------------------------------------------------------
   1 | // SPDX-License-Identifier: MIT
   2 | pragma solidity >=0.4.22 <0.9.0;
   3 | 
   4 | library console {
   5 |     address constant CONSOLE_ADDRESS = address(0x000000000000000000636F6e736F6c652e6c6f67);
   6 | 
   7 |     // Copied from https://github.com/dapphub/ds-test/blob/master/src/test.sol
   8 |     event log_named_int          (string key, int val);
   9 |     event log_named_uint         (string key, uint val);
  10 | 
  11 | 
  12 |     function Log(string memory name, int p0) internal {
  13 |         emit log_named_int(name, p0);
  14 |     }
  15 | 
  16 |     function Log(string memory name, uint p0) internal {
  17 |         emit log_named_uint(name, p0);
  18 |     }
  19 | 
  20 |     function _sendLogPayload(bytes memory payload) private view {
  21 |         uint256 payloadLength = payload.length;
  22 |         address consoleAddress = CONSOLE_ADDRESS;
  23 |         assembly {
  24 |             let payloadStart := add(payload, 32)
  25 |             let r := staticcall(gas(), consoleAddress, payloadStart, payloadLength, 0, 0)
  26 |         }
  27 |     }
  28 | 
  29 |     function log() internal view {
  30 |         _sendLogPayload(abi.encodeWithSignature("log()"));
  31 |     }
  32 | 
  33 |     function logInt(int p0) internal view {
  34 |         _sendLogPayload(abi.encodeWithSignature("log(int)", p0));
  35 |     }
  36 | 
  37 |     function logUint(uint p0) internal view {
  38 |         _sendLogPayload(abi.encodeWithSignature("log(uint)", p0));
  39 |     }
  40 | 
  41 |     function logString(string memory p0) internal view {
  42 |         _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
  43 |     }
  44 | 
  45 |     function logBool(bool p0) internal view {
  46 |         _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
  47 |     }
  48 | 
  49 |     function logAddress(address p0) internal view {
  50 |         _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
  51 |     }
  52 | 
  53 |     function logBytes(bytes memory p0) internal view {
  54 |         _sendLogPayload(abi.encodeWithSignature("log(bytes)", p0));
  55 |     }
  56 | 
  57 |     function logBytes1(bytes1 p0) internal view {
  58 |         _sendLogPayload(abi.encodeWithSignature("log(bytes1)", p0));
  59 |     }
  60 | 
  61 |     function logBytes2(bytes2 p0) internal view {
  62 |         _sendLogPayload(abi.encodeWithSignature("log(bytes2)", p0));
  63 |     }
  64 | 
  65 |     function logBytes3(bytes3 p0) internal view {
  66 |         _sendLogPayload(abi.encodeWithSignature("log(bytes3)", p0));
  67 |     }
  68 | 
  69 |     function logBytes4(bytes4 p0) internal view {
  70 |         _sendLogPayload(abi.encodeWithSignature("log(bytes4)", p0));
  71 |     }
  72 | 
  73 |     function logBytes5(bytes5 p0) internal view {
  74 |         _sendLogPayload(abi.encodeWithSignature("log(bytes5)", p0));
  75 |     }
  76 | 
  77 |     function logBytes6(bytes6 p0) internal view {
  78 |         _sendLogPayload(abi.encodeWithSignature("log(bytes6)", p0));
  79 |     }
  80 | 
  81 |     function logBytes7(bytes7 p0) internal view {
  82 |         _sendLogPayload(abi.encodeWithSignature("log(bytes7)", p0));
  83 |     }
  84 | 
  85 |     function logBytes8(bytes8 p0) internal view {
  86 |         _sendLogPayload(abi.encodeWithSignature("log(bytes8)", p0));
  87 |     }
  88 | 
  89 |     function logBytes9(bytes9 p0) internal view {
  90 |         _sendLogPayload(abi.encodeWithSignature("log(bytes9)", p0));
  91 |     }
  92 | 
  93 |     function logBytes10(bytes10 p0) internal view {
  94 |         _sendLogPayload(abi.encodeWithSignature("log(bytes10)", p0));
  95 |     }
  96 | 
  97 |     function logBytes11(bytes11 p0) internal view {
  98 |         _sendLogPayload(abi.encodeWithSignature("log(bytes11)", p0));
  99 |     }
 100 | 
 101 |     function logBytes12(bytes12 p0) internal view {
 102 |         _sendLogPayload(abi.encodeWithSignature("log(bytes12)", p0));
 103 |     }
 104 | 
 105 |     function logBytes13(bytes13 p0) internal view {
 106 |         _sendLogPayload(abi.encodeWithSignature("log(bytes13)", p0));
 107 |     }
 108 | 
 109 |     function logBytes14(bytes14 p0) internal view {
 110 |         _sendLogPayload(abi.encodeWithSignature("log(bytes14)", p0));
 111 |     }
 112 | 
 113 |     function logBytes15(bytes15 p0) internal view {
 114 |         _sendLogPayload(abi.encodeWithSignature("log(bytes15)", p0));
 115 |     }
 116 | 
 117 |     function logBytes16(bytes16 p0) internal view {
 118 |         _sendLogPayload(abi.encodeWithSignature("log(bytes16)", p0));
 119 |     }
 120 | 
 121 |     function logBytes17(bytes17 p0) internal view {
 122 |         _sendLogPayload(abi.encodeWithSignature("log(bytes17)", p0));
 123 |     }
 124 | 
 125 |     function logBytes18(bytes18 p0) internal view {
 126 |         _sendLogPayload(abi.encodeWithSignature("log(bytes18)", p0));
 127 |     }
 128 | 
 129 |     function logBytes19(bytes19 p0) internal view {
 130 |         _sendLogPayload(abi.encodeWithSignature("log(bytes19)", p0));
 131 |     }
 132 | 
 133 |     function logBytes20(bytes20 p0) internal view {
 134 |         _sendLogPayload(abi.encodeWithSignature("log(bytes20)", p0));
 135 |     }
 136 | 
 137 |     function logBytes21(bytes21 p0) internal view {
 138 |         _sendLogPayload(abi.encodeWithSignature("log(bytes21)", p0));
 139 |     }
 140 | 
 141 |     function logBytes22(bytes22 p0) internal view {
 142 |         _sendLogPayload(abi.encodeWithSignature("log(bytes22)", p0));
 143 |     }
 144 | 
 145 |     function logBytes23(bytes23 p0) internal view {
 146 |         _sendLogPayload(abi.encodeWithSignature("log(bytes23)", p0));
 147 |     }
 148 | 
 149 |     function logBytes24(bytes24 p0) internal view {
 150 |         _sendLogPayload(abi.encodeWithSignature("log(bytes24)", p0));
 151 |     }
 152 | 
 153 |     function logBytes25(bytes25 p0) internal view {
 154 |         _sendLogPayload(abi.encodeWithSignature("log(bytes25)", p0));
 155 |     }
 156 | 
 157 |     function logBytes26(bytes26 p0) internal view {
 158 |         _sendLogPayload(abi.encodeWithSignature("log(bytes26)", p0));
 159 |     }
 160 | 
 161 |     function logBytes27(bytes27 p0) internal view {
 162 |         _sendLogPayload(abi.encodeWithSignature("log(bytes27)", p0));
 163 |     }
 164 | 
 165 |     function logBytes28(bytes28 p0) internal view {
 166 |         _sendLogPayload(abi.encodeWithSignature("log(bytes28)", p0));
 167 |     }
 168 | 
 169 |     function logBytes29(bytes29 p0) internal view {
 170 |         _sendLogPayload(abi.encodeWithSignature("log(bytes29)", p0));
 171 |     }
 172 | 
 173 |     function logBytes30(bytes30 p0) internal view {
 174 |         _sendLogPayload(abi.encodeWithSignature("log(bytes30)", p0));
 175 |     }
 176 | 
 177 |     function logBytes31(bytes31 p0) internal view {
 178 |         _sendLogPayload(abi.encodeWithSignature("log(bytes31)", p0));
 179 |     }
 180 | 
 181 |     function logBytes32(bytes32 p0) internal view {
 182 |         _sendLogPayload(abi.encodeWithSignature("log(bytes32)", p0));
 183 |     }
 184 | 
 185 |     function log(uint p0) internal view {
 186 |         _sendLogPayload(abi.encodeWithSignature("log(uint)", p0));
 187 |     }
 188 | 
 189 |     function log(string memory p0) internal view {
 190 |         _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
 191 |     }
 192 | 
 193 |     function log(bool p0) internal view {
 194 |         _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
 195 |     }
 196 | 
 197 |     function log(address p0) internal view {
 198 |         _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
 199 |     }
 200 | 
 201 |     function log(uint p0, uint p1) internal view {
 202 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint)", p0, p1));
 203 |     }
 204 | 
 205 |     function log(uint p0, string memory p1) internal view {
 206 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string)", p0, p1));
 207 |     }
 208 | 
 209 |     function log(uint p0, bool p1) internal view {
 210 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool)", p0, p1));
 211 |     }
 212 | 
 213 |     function log(uint p0, address p1) internal view {
 214 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address)", p0, p1));
 215 |     }
 216 | 
 217 |     function log(string memory p0, uint p1) internal view {
 218 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint)", p0, p1));
 219 |     }
 220 | 
 221 |     function log(string memory p0, string memory p1) internal view {
 222 |         _sendLogPayload(abi.encodeWithSignature("log(string,string)", p0, p1));
 223 |     }
 224 | 
 225 |     function log(string memory p0, bool p1) internal view {
 226 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool)", p0, p1));
 227 |     }
 228 | 
 229 |     function log(string memory p0, address p1) internal view {
 230 |         _sendLogPayload(abi.encodeWithSignature("log(string,address)", p0, p1));
 231 |     }
 232 | 
 233 |     function log(bool p0, uint p1) internal view {
 234 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint)", p0, p1));
 235 |     }
 236 | 
 237 |     function log(bool p0, string memory p1) internal view {
 238 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string)", p0, p1));
 239 |     }
 240 | 
 241 |     function log(bool p0, bool p1) internal view {
 242 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool)", p0, p1));
 243 |     }
 244 | 
 245 |     function log(bool p0, address p1) internal view {
 246 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address)", p0, p1));
 247 |     }
 248 | 
 249 |     function log(address p0, uint p1) internal view {
 250 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint)", p0, p1));
 251 |     }
 252 | 
 253 |     function log(address p0, string memory p1) internal view {
 254 |         _sendLogPayload(abi.encodeWithSignature("log(address,string)", p0, p1));
 255 |     }
 256 | 
 257 |     function log(address p0, bool p1) internal view {
 258 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool)", p0, p1));
 259 |     }
 260 | 
 261 |     function log(address p0, address p1) internal view {
 262 |         _sendLogPayload(abi.encodeWithSignature("log(address,address)", p0, p1));
 263 |     }
 264 | 
 265 |     function log(uint p0, uint p1, uint p2) internal view {
 266 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint)", p0, p1, p2));
 267 |     }
 268 | 
 269 |     function log(uint p0, uint p1, string memory p2) internal view {
 270 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string)", p0, p1, p2));
 271 |     }
 272 | 
 273 |     function log(uint p0, uint p1, bool p2) internal view {
 274 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool)", p0, p1, p2));
 275 |     }
 276 | 
 277 |     function log(uint p0, uint p1, address p2) internal view {
 278 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address)", p0, p1, p2));
 279 |     }
 280 | 
 281 |     function log(uint p0, string memory p1, uint p2) internal view {
 282 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint)", p0, p1, p2));
 283 |     }
 284 | 
 285 |     function log(uint p0, string memory p1, string memory p2) internal view {
 286 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,string)", p0, p1, p2));
 287 |     }
 288 | 
 289 |     function log(uint p0, string memory p1, bool p2) internal view {
 290 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool)", p0, p1, p2));
 291 |     }
 292 | 
 293 |     function log(uint p0, string memory p1, address p2) internal view {
 294 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,address)", p0, p1, p2));
 295 |     }
 296 | 
 297 |     function log(uint p0, bool p1, uint p2) internal view {
 298 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint)", p0, p1, p2));
 299 |     }
 300 | 
 301 |     function log(uint p0, bool p1, string memory p2) internal view {
 302 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string)", p0, p1, p2));
 303 |     }
 304 | 
 305 |     function log(uint p0, bool p1, bool p2) internal view {
 306 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool)", p0, p1, p2));
 307 |     }
 308 | 
 309 |     function log(uint p0, bool p1, address p2) internal view {
 310 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address)", p0, p1, p2));
 311 |     }
 312 | 
 313 |     function log(uint p0, address p1, uint p2) internal view {
 314 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint)", p0, p1, p2));
 315 |     }
 316 | 
 317 |     function log(uint p0, address p1, string memory p2) internal view {
 318 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,string)", p0, p1, p2));
 319 |     }
 320 | 
 321 |     function log(uint p0, address p1, bool p2) internal view {
 322 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool)", p0, p1, p2));
 323 |     }
 324 | 
 325 |     function log(uint p0, address p1, address p2) internal view {
 326 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,address)", p0, p1, p2));
 327 |     }
 328 | 
 329 |     function log(string memory p0, uint p1, uint p2) internal view {
 330 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint)", p0, p1, p2));
 331 |     }
 332 | 
 333 |     function log(string memory p0, uint p1, string memory p2) internal view {
 334 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,string)", p0, p1, p2));
 335 |     }
 336 | 
 337 |     function log(string memory p0, uint p1, bool p2) internal view {
 338 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool)", p0, p1, p2));
 339 |     }
 340 | 
 341 |     function log(string memory p0, uint p1, address p2) internal view {
 342 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,address)", p0, p1, p2));
 343 |     }
 344 | 
 345 |     function log(string memory p0, string memory p1, uint p2) internal view {
 346 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,uint)", p0, p1, p2));
 347 |     }
 348 | 
 349 |     function log(string memory p0, string memory p1, string memory p2) internal view {
 350 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,string)", p0, p1, p2));
 351 |     }
 352 | 
 353 |     function log(string memory p0, string memory p1, bool p2) internal view {
 354 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,bool)", p0, p1, p2));
 355 |     }
 356 | 
 357 |     function log(string memory p0, string memory p1, address p2) internal view {
 358 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,address)", p0, p1, p2));
 359 |     }
 360 | 
 361 |     function log(string memory p0, bool p1, uint p2) internal view {
 362 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint)", p0, p1, p2));
 363 |     }
 364 | 
 365 |     function log(string memory p0, bool p1, string memory p2) internal view {
 366 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,string)", p0, p1, p2));
 367 |     }
 368 | 
 369 |     function log(string memory p0, bool p1, bool p2) internal view {
 370 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool)", p0, p1, p2));
 371 |     }
 372 | 
 373 |     function log(string memory p0, bool p1, address p2) internal view {
 374 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,address)", p0, p1, p2));
 375 |     }
 376 | 
 377 |     function log(string memory p0, address p1, uint p2) internal view {
 378 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,uint)", p0, p1, p2));
 379 |     }
 380 | 
 381 |     function log(string memory p0, address p1, string memory p2) internal view {
 382 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,string)", p0, p1, p2));
 383 |     }
 384 | 
 385 |     function log(string memory p0, address p1, bool p2) internal view {
 386 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,bool)", p0, p1, p2));
 387 |     }
 388 | 
 389 |     function log(string memory p0, address p1, address p2) internal view {
 390 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,address)", p0, p1, p2));
 391 |     }
 392 | 
 393 |     function log(bool p0, uint p1, uint p2) internal view {
 394 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint)", p0, p1, p2));
 395 |     }
 396 | 
 397 |     function log(bool p0, uint p1, string memory p2) internal view {
 398 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string)", p0, p1, p2));
 399 |     }
 400 | 
 401 |     function log(bool p0, uint p1, bool p2) internal view {
 402 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool)", p0, p1, p2));
 403 |     }
 404 | 
 405 |     function log(bool p0, uint p1, address p2) internal view {
 406 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address)", p0, p1, p2));
 407 |     }
 408 | 
 409 |     function log(bool p0, string memory p1, uint p2) internal view {
 410 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint)", p0, p1, p2));
 411 |     }
 412 | 
 413 |     function log(bool p0, string memory p1, string memory p2) internal view {
 414 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,string)", p0, p1, p2));
 415 |     }
 416 | 
 417 |     function log(bool p0, string memory p1, bool p2) internal view {
 418 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool)", p0, p1, p2));
 419 |     }
 420 | 
 421 |     function log(bool p0, string memory p1, address p2) internal view {
 422 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,address)", p0, p1, p2));
 423 |     }
 424 | 
 425 |     function log(bool p0, bool p1, uint p2) internal view {
 426 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint)", p0, p1, p2));
 427 |     }
 428 | 
 429 |     function log(bool p0, bool p1, string memory p2) internal view {
 430 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string)", p0, p1, p2));
 431 |     }
 432 | 
 433 |     function log(bool p0, bool p1, bool p2) internal view {
 434 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool)", p0, p1, p2));
 435 |     }
 436 | 
 437 |     function log(bool p0, bool p1, address p2) internal view {
 438 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address)", p0, p1, p2));
 439 |     }
 440 | 
 441 |     function log(bool p0, address p1, uint p2) internal view {
 442 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint)", p0, p1, p2));
 443 |     }
 444 | 
 445 |     function log(bool p0, address p1, string memory p2) internal view {
 446 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,string)", p0, p1, p2));
 447 |     }
 448 | 
 449 |     function log(bool p0, address p1, bool p2) internal view {
 450 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool)", p0, p1, p2));
 451 |     }
 452 | 
 453 |     function log(bool p0, address p1, address p2) internal view {
 454 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,address)", p0, p1, p2));
 455 |     }
 456 | 
 457 |     function log(address p0, uint p1, uint p2) internal view {
 458 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint)", p0, p1, p2));
 459 |     }
 460 | 
 461 |     function log(address p0, uint p1, string memory p2) internal view {
 462 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,string)", p0, p1, p2));
 463 |     }
 464 | 
 465 |     function log(address p0, uint p1, bool p2) internal view {
 466 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool)", p0, p1, p2));
 467 |     }
 468 | 
 469 |     function log(address p0, uint p1, address p2) internal view {
 470 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,address)", p0, p1, p2));
 471 |     }
 472 | 
 473 |     function log(address p0, string memory p1, uint p2) internal view {
 474 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,uint)", p0, p1, p2));
 475 |     }
 476 | 
 477 |     function log(address p0, string memory p1, string memory p2) internal view {
 478 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,string)", p0, p1, p2));
 479 |     }
 480 | 
 481 |     function log(address p0, string memory p1, bool p2) internal view {
 482 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,bool)", p0, p1, p2));
 483 |     }
 484 | 
 485 |     function log(address p0, string memory p1, address p2) internal view {
 486 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,address)", p0, p1, p2));
 487 |     }
 488 | 
 489 |     function log(address p0, bool p1, uint p2) internal view {
 490 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint)", p0, p1, p2));
 491 |     }
 492 | 
 493 |     function log(address p0, bool p1, string memory p2) internal view {
 494 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,string)", p0, p1, p2));
 495 |     }
 496 | 
 497 |     function log(address p0, bool p1, bool p2) internal view {
 498 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool)", p0, p1, p2));
 499 |     }
 500 | 
 501 |     function log(address p0, bool p1, address p2) internal view {
 502 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,address)", p0, p1, p2));
 503 |     }
 504 | 
 505 |     function log(address p0, address p1, uint p2) internal view {
 506 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,uint)", p0, p1, p2));
 507 |     }
 508 | 
 509 |     function log(address p0, address p1, string memory p2) internal view {
 510 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,string)", p0, p1, p2));
 511 |     }
 512 | 
 513 |     function log(address p0, address p1, bool p2) internal view {
 514 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,bool)", p0, p1, p2));
 515 |     }
 516 | 
 517 |     function log(address p0, address p1, address p2) internal view {
 518 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,address)", p0, p1, p2));
 519 |     }
 520 | 
 521 |     function log(uint p0, uint p1, uint p2, uint p3) internal view {
 522 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,uint)", p0, p1, p2, p3));
 523 |     }
 524 | 
 525 |     function log(uint p0, uint p1, uint p2, string memory p3) internal view {
 526 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,string)", p0, p1, p2, p3));
 527 |     }
 528 | 
 529 |     function log(uint p0, uint p1, uint p2, bool p3) internal view {
 530 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,bool)", p0, p1, p2, p3));
 531 |     }
 532 | 
 533 |     function log(uint p0, uint p1, uint p2, address p3) internal view {
 534 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,address)", p0, p1, p2, p3));
 535 |     }
 536 | 
 537 |     function log(uint p0, uint p1, string memory p2, uint p3) internal view {
 538 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,uint)", p0, p1, p2, p3));
 539 |     }
 540 | 
 541 |     function log(uint p0, uint p1, string memory p2, string memory p3) internal view {
 542 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,string)", p0, p1, p2, p3));
 543 |     }
 544 | 
 545 |     function log(uint p0, uint p1, string memory p2, bool p3) internal view {
 546 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,bool)", p0, p1, p2, p3));
 547 |     }
 548 | 
 549 |     function log(uint p0, uint p1, string memory p2, address p3) internal view {
 550 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,address)", p0, p1, p2, p3));
 551 |     }
 552 | 
 553 |     function log(uint p0, uint p1, bool p2, uint p3) internal view {
 554 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,uint)", p0, p1, p2, p3));
 555 |     }
 556 | 
 557 |     function log(uint p0, uint p1, bool p2, string memory p3) internal view {
 558 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,string)", p0, p1, p2, p3));
 559 |     }
 560 | 
 561 |     function log(uint p0, uint p1, bool p2, bool p3) internal view {
 562 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,bool)", p0, p1, p2, p3));
 563 |     }
 564 | 
 565 |     function log(uint p0, uint p1, bool p2, address p3) internal view {
 566 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,address)", p0, p1, p2, p3));
 567 |     }
 568 | 
 569 |     function log(uint p0, uint p1, address p2, uint p3) internal view {
 570 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,uint)", p0, p1, p2, p3));
 571 |     }
 572 | 
 573 |     function log(uint p0, uint p1, address p2, string memory p3) internal view {
 574 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,string)", p0, p1, p2, p3));
 575 |     }
 576 | 
 577 |     function log(uint p0, uint p1, address p2, bool p3) internal view {
 578 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,bool)", p0, p1, p2, p3));
 579 |     }
 580 | 
 581 |     function log(uint p0, uint p1, address p2, address p3) internal view {
 582 |         _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,address)", p0, p1, p2, p3));
 583 |     }
 584 | 
 585 |     function log(uint p0, string memory p1, uint p2, uint p3) internal view {
 586 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,uint)", p0, p1, p2, p3));
 587 |     }
 588 | 
 589 |     function log(uint p0, string memory p1, uint p2, string memory p3) internal view {
 590 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,string)", p0, p1, p2, p3));
 591 |     }
 592 | 
 593 |     function log(uint p0, string memory p1, uint p2, bool p3) internal view {
 594 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,bool)", p0, p1, p2, p3));
 595 |     }
 596 | 
 597 |     function log(uint p0, string memory p1, uint p2, address p3) internal view {
 598 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,address)", p0, p1, p2, p3));
 599 |     }
 600 | 
 601 |     function log(uint p0, string memory p1, string memory p2, uint p3) internal view {
 602 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,uint)", p0, p1, p2, p3));
 603 |     }
 604 | 
 605 |     function log(uint p0, string memory p1, string memory p2, string memory p3) internal view {
 606 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,string)", p0, p1, p2, p3));
 607 |     }
 608 | 
 609 |     function log(uint p0, string memory p1, string memory p2, bool p3) internal view {
 610 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,bool)", p0, p1, p2, p3));
 611 |     }
 612 | 
 613 |     function log(uint p0, string memory p1, string memory p2, address p3) internal view {
 614 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,address)", p0, p1, p2, p3));
 615 |     }
 616 | 
 617 |     function log(uint p0, string memory p1, bool p2, uint p3) internal view {
 618 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,uint)", p0, p1, p2, p3));
 619 |     }
 620 | 
 621 |     function log(uint p0, string memory p1, bool p2, string memory p3) internal view {
 622 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,string)", p0, p1, p2, p3));
 623 |     }
 624 | 
 625 |     function log(uint p0, string memory p1, bool p2, bool p3) internal view {
 626 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,bool)", p0, p1, p2, p3));
 627 |     }
 628 | 
 629 |     function log(uint p0, string memory p1, bool p2, address p3) internal view {
 630 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,address)", p0, p1, p2, p3));
 631 |     }
 632 | 
 633 |     function log(uint p0, string memory p1, address p2, uint p3) internal view {
 634 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,uint)", p0, p1, p2, p3));
 635 |     }
 636 | 
 637 |     function log(uint p0, string memory p1, address p2, string memory p3) internal view {
 638 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,string)", p0, p1, p2, p3));
 639 |     }
 640 | 
 641 |     function log(uint p0, string memory p1, address p2, bool p3) internal view {
 642 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,bool)", p0, p1, p2, p3));
 643 |     }
 644 | 
 645 |     function log(uint p0, string memory p1, address p2, address p3) internal view {
 646 |         _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,address)", p0, p1, p2, p3));
 647 |     }
 648 | 
 649 |     function log(uint p0, bool p1, uint p2, uint p3) internal view {
 650 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,uint)", p0, p1, p2, p3));
 651 |     }
 652 | 
 653 |     function log(uint p0, bool p1, uint p2, string memory p3) internal view {
 654 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,string)", p0, p1, p2, p3));
 655 |     }
 656 | 
 657 |     function log(uint p0, bool p1, uint p2, bool p3) internal view {
 658 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,bool)", p0, p1, p2, p3));
 659 |     }
 660 | 
 661 |     function log(uint p0, bool p1, uint p2, address p3) internal view {
 662 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,address)", p0, p1, p2, p3));
 663 |     }
 664 | 
 665 |     function log(uint p0, bool p1, string memory p2, uint p3) internal view {
 666 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,uint)", p0, p1, p2, p3));
 667 |     }
 668 | 
 669 |     function log(uint p0, bool p1, string memory p2, string memory p3) internal view {
 670 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,string)", p0, p1, p2, p3));
 671 |     }
 672 | 
 673 |     function log(uint p0, bool p1, string memory p2, bool p3) internal view {
 674 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,bool)", p0, p1, p2, p3));
 675 |     }
 676 | 
 677 |     function log(uint p0, bool p1, string memory p2, address p3) internal view {
 678 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,address)", p0, p1, p2, p3));
 679 |     }
 680 | 
 681 |     function log(uint p0, bool p1, bool p2, uint p3) internal view {
 682 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,uint)", p0, p1, p2, p3));
 683 |     }
 684 | 
 685 |     function log(uint p0, bool p1, bool p2, string memory p3) internal view {
 686 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,string)", p0, p1, p2, p3));
 687 |     }
 688 | 
 689 |     function log(uint p0, bool p1, bool p2, bool p3) internal view {
 690 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,bool)", p0, p1, p2, p3));
 691 |     }
 692 | 
 693 |     function log(uint p0, bool p1, bool p2, address p3) internal view {
 694 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,address)", p0, p1, p2, p3));
 695 |     }
 696 | 
 697 |     function log(uint p0, bool p1, address p2, uint p3) internal view {
 698 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,uint)", p0, p1, p2, p3));
 699 |     }
 700 | 
 701 |     function log(uint p0, bool p1, address p2, string memory p3) internal view {
 702 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,string)", p0, p1, p2, p3));
 703 |     }
 704 | 
 705 |     function log(uint p0, bool p1, address p2, bool p3) internal view {
 706 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,bool)", p0, p1, p2, p3));
 707 |     }
 708 | 
 709 |     function log(uint p0, bool p1, address p2, address p3) internal view {
 710 |         _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,address)", p0, p1, p2, p3));
 711 |     }
 712 | 
 713 |     function log(uint p0, address p1, uint p2, uint p3) internal view {
 714 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,uint)", p0, p1, p2, p3));
 715 |     }
 716 | 
 717 |     function log(uint p0, address p1, uint p2, string memory p3) internal view {
 718 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,string)", p0, p1, p2, p3));
 719 |     }
 720 | 
 721 |     function log(uint p0, address p1, uint p2, bool p3) internal view {
 722 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,bool)", p0, p1, p2, p3));
 723 |     }
 724 | 
 725 |     function log(uint p0, address p1, uint p2, address p3) internal view {
 726 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,address)", p0, p1, p2, p3));
 727 |     }
 728 | 
 729 |     function log(uint p0, address p1, string memory p2, uint p3) internal view {
 730 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,uint)", p0, p1, p2, p3));
 731 |     }
 732 | 
 733 |     function log(uint p0, address p1, string memory p2, string memory p3) internal view {
 734 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,string)", p0, p1, p2, p3));
 735 |     }
 736 | 
 737 |     function log(uint p0, address p1, string memory p2, bool p3) internal view {
 738 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,bool)", p0, p1, p2, p3));
 739 |     }
 740 | 
 741 |     function log(uint p0, address p1, string memory p2, address p3) internal view {
 742 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,address)", p0, p1, p2, p3));
 743 |     }
 744 | 
 745 |     function log(uint p0, address p1, bool p2, uint p3) internal view {
 746 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,uint)", p0, p1, p2, p3));
 747 |     }
 748 | 
 749 |     function log(uint p0, address p1, bool p2, string memory p3) internal view {
 750 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,string)", p0, p1, p2, p3));
 751 |     }
 752 | 
 753 |     function log(uint p0, address p1, bool p2, bool p3) internal view {
 754 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,bool)", p0, p1, p2, p3));
 755 |     }
 756 | 
 757 |     function log(uint p0, address p1, bool p2, address p3) internal view {
 758 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,address)", p0, p1, p2, p3));
 759 |     }
 760 | 
 761 |     function log(uint p0, address p1, address p2, uint p3) internal view {
 762 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,uint)", p0, p1, p2, p3));
 763 |     }
 764 | 
 765 |     function log(uint p0, address p1, address p2, string memory p3) internal view {
 766 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,string)", p0, p1, p2, p3));
 767 |     }
 768 | 
 769 |     function log(uint p0, address p1, address p2, bool p3) internal view {
 770 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,bool)", p0, p1, p2, p3));
 771 |     }
 772 | 
 773 |     function log(uint p0, address p1, address p2, address p3) internal view {
 774 |         _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,address)", p0, p1, p2, p3));
 775 |     }
 776 | 
 777 |     function log(string memory p0, uint p1, uint p2, uint p3) internal view {
 778 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,uint)", p0, p1, p2, p3));
 779 |     }
 780 | 
 781 |     function log(string memory p0, uint p1, uint p2, string memory p3) internal view {
 782 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,string)", p0, p1, p2, p3));
 783 |     }
 784 | 
 785 |     function log(string memory p0, uint p1, uint p2, bool p3) internal view {
 786 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,bool)", p0, p1, p2, p3));
 787 |     }
 788 | 
 789 |     function log(string memory p0, uint p1, uint p2, address p3) internal view {
 790 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,address)", p0, p1, p2, p3));
 791 |     }
 792 | 
 793 |     function log(string memory p0, uint p1, string memory p2, uint p3) internal view {
 794 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,uint)", p0, p1, p2, p3));
 795 |     }
 796 | 
 797 |     function log(string memory p0, uint p1, string memory p2, string memory p3) internal view {
 798 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,string)", p0, p1, p2, p3));
 799 |     }
 800 | 
 801 |     function log(string memory p0, uint p1, string memory p2, bool p3) internal view {
 802 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,bool)", p0, p1, p2, p3));
 803 |     }
 804 | 
 805 |     function log(string memory p0, uint p1, string memory p2, address p3) internal view {
 806 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,address)", p0, p1, p2, p3));
 807 |     }
 808 | 
 809 |     function log(string memory p0, uint p1, bool p2, uint p3) internal view {
 810 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,uint)", p0, p1, p2, p3));
 811 |     }
 812 | 
 813 |     function log(string memory p0, uint p1, bool p2, string memory p3) internal view {
 814 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,string)", p0, p1, p2, p3));
 815 |     }
 816 | 
 817 |     function log(string memory p0, uint p1, bool p2, bool p3) internal view {
 818 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,bool)", p0, p1, p2, p3));
 819 |     }
 820 | 
 821 |     function log(string memory p0, uint p1, bool p2, address p3) internal view {
 822 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,address)", p0, p1, p2, p3));
 823 |     }
 824 | 
 825 |     function log(string memory p0, uint p1, address p2, uint p3) internal view {
 826 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,uint)", p0, p1, p2, p3));
 827 |     }
 828 | 
 829 |     function log(string memory p0, uint p1, address p2, string memory p3) internal view {
 830 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,string)", p0, p1, p2, p3));
 831 |     }
 832 | 
 833 |     function log(string memory p0, uint p1, address p2, bool p3) internal view {
 834 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,bool)", p0, p1, p2, p3));
 835 |     }
 836 | 
 837 |     function log(string memory p0, uint p1, address p2, address p3) internal view {
 838 |         _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,address)", p0, p1, p2, p3));
 839 |     }
 840 | 
 841 |     function log(string memory p0, string memory p1, uint p2, uint p3) internal view {
 842 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,uint)", p0, p1, p2, p3));
 843 |     }
 844 | 
 845 |     function log(string memory p0, string memory p1, uint p2, string memory p3) internal view {
 846 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,string)", p0, p1, p2, p3));
 847 |     }
 848 | 
 849 |     function log(string memory p0, string memory p1, uint p2, bool p3) internal view {
 850 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,bool)", p0, p1, p2, p3));
 851 |     }
 852 | 
 853 |     function log(string memory p0, string memory p1, uint p2, address p3) internal view {
 854 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,address)", p0, p1, p2, p3));
 855 |     }
 856 | 
 857 |     function log(string memory p0, string memory p1, string memory p2, uint p3) internal view {
 858 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,string,uint)", p0, p1, p2, p3));
 859 |     }
 860 | 
 861 |     function log(string memory p0, string memory p1, string memory p2, string memory p3) internal view {
 862 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,string,string)", p0, p1, p2, p3));
 863 |     }
 864 | 
 865 |     function log(string memory p0, string memory p1, string memory p2, bool p3) internal view {
 866 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,string,bool)", p0, p1, p2, p3));
 867 |     }
 868 | 
 869 |     function log(string memory p0, string memory p1, string memory p2, address p3) internal view {
 870 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,string,address)", p0, p1, p2, p3));
 871 |     }
 872 | 
 873 |     function log(string memory p0, string memory p1, bool p2, uint p3) internal view {
 874 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,uint)", p0, p1, p2, p3));
 875 |     }
 876 | 
 877 |     function log(string memory p0, string memory p1, bool p2, string memory p3) internal view {
 878 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,string)", p0, p1, p2, p3));
 879 |     }
 880 | 
 881 |     function log(string memory p0, string memory p1, bool p2, bool p3) internal view {
 882 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,bool)", p0, p1, p2, p3));
 883 |     }
 884 | 
 885 |     function log(string memory p0, string memory p1, bool p2, address p3) internal view {
 886 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,address)", p0, p1, p2, p3));
 887 |     }
 888 | 
 889 |     function log(string memory p0, string memory p1, address p2, uint p3) internal view {
 890 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,address,uint)", p0, p1, p2, p3));
 891 |     }
 892 | 
 893 |     function log(string memory p0, string memory p1, address p2, string memory p3) internal view {
 894 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,address,string)", p0, p1, p2, p3));
 895 |     }
 896 | 
 897 |     function log(string memory p0, string memory p1, address p2, bool p3) internal view {
 898 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,address,bool)", p0, p1, p2, p3));
 899 |     }
 900 | 
 901 |     function log(string memory p0, string memory p1, address p2, address p3) internal view {
 902 |         _sendLogPayload(abi.encodeWithSignature("log(string,string,address,address)", p0, p1, p2, p3));
 903 |     }
 904 | 
 905 |     function log(string memory p0, bool p1, uint p2, uint p3) internal view {
 906 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,uint)", p0, p1, p2, p3));
 907 |     }
 908 | 
 909 |     function log(string memory p0, bool p1, uint p2, string memory p3) internal view {
 910 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,string)", p0, p1, p2, p3));
 911 |     }
 912 | 
 913 |     function log(string memory p0, bool p1, uint p2, bool p3) internal view {
 914 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,bool)", p0, p1, p2, p3));
 915 |     }
 916 | 
 917 |     function log(string memory p0, bool p1, uint p2, address p3) internal view {
 918 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,address)", p0, p1, p2, p3));
 919 |     }
 920 | 
 921 |     function log(string memory p0, bool p1, string memory p2, uint p3) internal view {
 922 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,uint)", p0, p1, p2, p3));
 923 |     }
 924 | 
 925 |     function log(string memory p0, bool p1, string memory p2, string memory p3) internal view {
 926 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,string)", p0, p1, p2, p3));
 927 |     }
 928 | 
 929 |     function log(string memory p0, bool p1, string memory p2, bool p3) internal view {
 930 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,bool)", p0, p1, p2, p3));
 931 |     }
 932 | 
 933 |     function log(string memory p0, bool p1, string memory p2, address p3) internal view {
 934 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,address)", p0, p1, p2, p3));
 935 |     }
 936 | 
 937 |     function log(string memory p0, bool p1, bool p2, uint p3) internal view {
 938 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,uint)", p0, p1, p2, p3));
 939 |     }
 940 | 
 941 |     function log(string memory p0, bool p1, bool p2, string memory p3) internal view {
 942 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,string)", p0, p1, p2, p3));
 943 |     }
 944 | 
 945 |     function log(string memory p0, bool p1, bool p2, bool p3) internal view {
 946 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,bool)", p0, p1, p2, p3));
 947 |     }
 948 | 
 949 |     function log(string memory p0, bool p1, bool p2, address p3) internal view {
 950 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,address)", p0, p1, p2, p3));
 951 |     }
 952 | 
 953 |     function log(string memory p0, bool p1, address p2, uint p3) internal view {
 954 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,uint)", p0, p1, p2, p3));
 955 |     }
 956 | 
 957 |     function log(string memory p0, bool p1, address p2, string memory p3) internal view {
 958 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,string)", p0, p1, p2, p3));
 959 |     }
 960 | 
 961 |     function log(string memory p0, bool p1, address p2, bool p3) internal view {
 962 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,bool)", p0, p1, p2, p3));
 963 |     }
 964 | 
 965 |     function log(string memory p0, bool p1, address p2, address p3) internal view {
 966 |         _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,address)", p0, p1, p2, p3));
 967 |     }
 968 | 
 969 |     function log(string memory p0, address p1, uint p2, uint p3) internal view {
 970 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,uint)", p0, p1, p2, p3));
 971 |     }
 972 | 
 973 |     function log(string memory p0, address p1, uint p2, string memory p3) internal view {
 974 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,string)", p0, p1, p2, p3));
 975 |     }
 976 | 
 977 |     function log(string memory p0, address p1, uint p2, bool p3) internal view {
 978 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,bool)", p0, p1, p2, p3));
 979 |     }
 980 | 
 981 |     function log(string memory p0, address p1, uint p2, address p3) internal view {
 982 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,address)", p0, p1, p2, p3));
 983 |     }
 984 | 
 985 |     function log(string memory p0, address p1, string memory p2, uint p3) internal view {
 986 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,string,uint)", p0, p1, p2, p3));
 987 |     }
 988 | 
 989 |     function log(string memory p0, address p1, string memory p2, string memory p3) internal view {
 990 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,string,string)", p0, p1, p2, p3));
 991 |     }
 992 | 
 993 |     function log(string memory p0, address p1, string memory p2, bool p3) internal view {
 994 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,string,bool)", p0, p1, p2, p3));
 995 |     }
 996 | 
 997 |     function log(string memory p0, address p1, string memory p2, address p3) internal view {
 998 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,string,address)", p0, p1, p2, p3));
 999 |     }
1000 | 
1001 |     function log(string memory p0, address p1, bool p2, uint p3) internal view {
1002 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,uint)", p0, p1, p2, p3));
1003 |     }
1004 | 
1005 |     function log(string memory p0, address p1, bool p2, string memory p3) internal view {
1006 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,string)", p0, p1, p2, p3));
1007 |     }
1008 | 
1009 |     function log(string memory p0, address p1, bool p2, bool p3) internal view {
1010 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,bool)", p0, p1, p2, p3));
1011 |     }
1012 | 
1013 |     function log(string memory p0, address p1, bool p2, address p3) internal view {
1014 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,address)", p0, p1, p2, p3));
1015 |     }
1016 | 
1017 |     function log(string memory p0, address p1, address p2, uint p3) internal view {
1018 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,address,uint)", p0, p1, p2, p3));
1019 |     }
1020 | 
1021 |     function log(string memory p0, address p1, address p2, string memory p3) internal view {
1022 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,address,string)", p0, p1, p2, p3));
1023 |     }
1024 | 
1025 |     function log(string memory p0, address p1, address p2, bool p3) internal view {
1026 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,address,bool)", p0, p1, p2, p3));
1027 |     }
1028 | 
1029 |     function log(string memory p0, address p1, address p2, address p3) internal view {
1030 |         _sendLogPayload(abi.encodeWithSignature("log(string,address,address,address)", p0, p1, p2, p3));
1031 |     }
1032 | 
1033 |     function log(bool p0, uint p1, uint p2, uint p3) internal view {
1034 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,uint)", p0, p1, p2, p3));
1035 |     }
1036 | 
1037 |     function log(bool p0, uint p1, uint p2, string memory p3) internal view {
1038 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,string)", p0, p1, p2, p3));
1039 |     }
1040 | 
1041 |     function log(bool p0, uint p1, uint p2, bool p3) internal view {
1042 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,bool)", p0, p1, p2, p3));
1043 |     }
1044 | 
1045 |     function log(bool p0, uint p1, uint p2, address p3) internal view {
1046 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,address)", p0, p1, p2, p3));
1047 |     }
1048 | 
1049 |     function log(bool p0, uint p1, string memory p2, uint p3) internal view {
1050 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,uint)", p0, p1, p2, p3));
1051 |     }
1052 | 
1053 |     function log(bool p0, uint p1, string memory p2, string memory p3) internal view {
1054 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,string)", p0, p1, p2, p3));
1055 |     }
1056 | 
1057 |     function log(bool p0, uint p1, string memory p2, bool p3) internal view {
1058 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,bool)", p0, p1, p2, p3));
1059 |     }
1060 | 
1061 |     function log(bool p0, uint p1, string memory p2, address p3) internal view {
1062 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,address)", p0, p1, p2, p3));
1063 |     }
1064 | 
1065 |     function log(bool p0, uint p1, bool p2, uint p3) internal view {
1066 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,uint)", p0, p1, p2, p3));
1067 |     }
1068 | 
1069 |     function log(bool p0, uint p1, bool p2, string memory p3) internal view {
1070 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,string)", p0, p1, p2, p3));
1071 |     }
1072 | 
1073 |     function log(bool p0, uint p1, bool p2, bool p3) internal view {
1074 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,bool)", p0, p1, p2, p3));
1075 |     }
1076 | 
1077 |     function log(bool p0, uint p1, bool p2, address p3) internal view {
1078 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,address)", p0, p1, p2, p3));
1079 |     }
1080 | 
1081 |     function log(bool p0, uint p1, address p2, uint p3) internal view {
1082 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,uint)", p0, p1, p2, p3));
1083 |     }
1084 | 
1085 |     function log(bool p0, uint p1, address p2, string memory p3) internal view {
1086 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,string)", p0, p1, p2, p3));
1087 |     }
1088 | 
1089 |     function log(bool p0, uint p1, address p2, bool p3) internal view {
1090 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,bool)", p0, p1, p2, p3));
1091 |     }
1092 | 
1093 |     function log(bool p0, uint p1, address p2, address p3) internal view {
1094 |         _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,address)", p0, p1, p2, p3));
1095 |     }
1096 | 
1097 |     function log(bool p0, string memory p1, uint p2, uint p3) internal view {
1098 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,uint)", p0, p1, p2, p3));
1099 |     }
1100 | 
1101 |     function log(bool p0, string memory p1, uint p2, string memory p3) internal view {
1102 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,string)", p0, p1, p2, p3));
1103 |     }
1104 | 
1105 |     function log(bool p0, string memory p1, uint p2, bool p3) internal view {
1106 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,bool)", p0, p1, p2, p3));
1107 |     }
1108 | 
1109 |     function log(bool p0, string memory p1, uint p2, address p3) internal view {
1110 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,address)", p0, p1, p2, p3));
1111 |     }
1112 | 
1113 |     function log(bool p0, string memory p1, string memory p2, uint p3) internal view {
1114 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,uint)", p0, p1, p2, p3));
1115 |     }
1116 | 
1117 |     function log(bool p0, string memory p1, string memory p2, string memory p3) internal view {
1118 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,string)", p0, p1, p2, p3));
1119 |     }
1120 | 
1121 |     function log(bool p0, string memory p1, string memory p2, bool p3) internal view {
1122 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,bool)", p0, p1, p2, p3));
1123 |     }
1124 | 
1125 |     function log(bool p0, string memory p1, string memory p2, address p3) internal view {
1126 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,address)", p0, p1, p2, p3));
1127 |     }
1128 | 
1129 |     function log(bool p0, string memory p1, bool p2, uint p3) internal view {
1130 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,uint)", p0, p1, p2, p3));
1131 |     }
1132 | 
1133 |     function log(bool p0, string memory p1, bool p2, string memory p3) internal view {
1134 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,string)", p0, p1, p2, p3));
1135 |     }
1136 | 
1137 |     function log(bool p0, string memory p1, bool p2, bool p3) internal view {
1138 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,bool)", p0, p1, p2, p3));
1139 |     }
1140 | 
1141 |     function log(bool p0, string memory p1, bool p2, address p3) internal view {
1142 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,address)", p0, p1, p2, p3));
1143 |     }
1144 | 
1145 |     function log(bool p0, string memory p1, address p2, uint p3) internal view {
1146 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,uint)", p0, p1, p2, p3));
1147 |     }
1148 | 
1149 |     function log(bool p0, string memory p1, address p2, string memory p3) internal view {
1150 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,string)", p0, p1, p2, p3));
1151 |     }
1152 | 
1153 |     function log(bool p0, string memory p1, address p2, bool p3) internal view {
1154 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,bool)", p0, p1, p2, p3));
1155 |     }
1156 | 
1157 |     function log(bool p0, string memory p1, address p2, address p3) internal view {
1158 |         _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,address)", p0, p1, p2, p3));
1159 |     }
1160 | 
1161 |     function log(bool p0, bool p1, uint p2, uint p3) internal view {
1162 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,uint)", p0, p1, p2, p3));
1163 |     }
1164 | 
1165 |     function log(bool p0, bool p1, uint p2, string memory p3) internal view {
1166 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,string)", p0, p1, p2, p3));
1167 |     }
1168 | 
1169 |     function log(bool p0, bool p1, uint p2, bool p3) internal view {
1170 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,bool)", p0, p1, p2, p3));
1171 |     }
1172 | 
1173 |     function log(bool p0, bool p1, uint p2, address p3) internal view {
1174 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,address)", p0, p1, p2, p3));
1175 |     }
1176 | 
1177 |     function log(bool p0, bool p1, string memory p2, uint p3) internal view {
1178 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,uint)", p0, p1, p2, p3));
1179 |     }
1180 | 
1181 |     function log(bool p0, bool p1, string memory p2, string memory p3) internal view {
1182 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,string)", p0, p1, p2, p3));
1183 |     }
1184 | 
1185 |     function log(bool p0, bool p1, string memory p2, bool p3) internal view {
1186 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,bool)", p0, p1, p2, p3));
1187 |     }
1188 | 
1189 |     function log(bool p0, bool p1, string memory p2, address p3) internal view {
1190 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,address)", p0, p1, p2, p3));
1191 |     }
1192 | 
1193 |     function log(bool p0, bool p1, bool p2, uint p3) internal view {
1194 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,uint)", p0, p1, p2, p3));
1195 |     }
1196 | 
1197 |     function log(bool p0, bool p1, bool p2, string memory p3) internal view {
1198 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,string)", p0, p1, p2, p3));
1199 |     }
1200 | 
1201 |     function log(bool p0, bool p1, bool p2, bool p3) internal view {
1202 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,bool)", p0, p1, p2, p3));
1203 |     }
1204 | 
1205 |     function log(bool p0, bool p1, bool p2, address p3) internal view {
1206 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,address)", p0, p1, p2, p3));
1207 |     }
1208 | 
1209 |     function log(bool p0, bool p1, address p2, uint p3) internal view {
1210 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,uint)", p0, p1, p2, p3));
1211 |     }
1212 | 
1213 |     function log(bool p0, bool p1, address p2, string memory p3) internal view {
1214 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,string)", p0, p1, p2, p3));
1215 |     }
1216 | 
1217 |     function log(bool p0, bool p1, address p2, bool p3) internal view {
1218 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,bool)", p0, p1, p2, p3));
1219 |     }
1220 | 
1221 |     function log(bool p0, bool p1, address p2, address p3) internal view {
1222 |         _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,address)", p0, p1, p2, p3));
1223 |     }
1224 | 
1225 |     function log(bool p0, address p1, uint p2, uint p3) internal view {
1226 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,uint)", p0, p1, p2, p3));
1227 |     }
1228 | 
1229 |     function log(bool p0, address p1, uint p2, string memory p3) internal view {
1230 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,string)", p0, p1, p2, p3));
1231 |     }
1232 | 
1233 |     function log(bool p0, address p1, uint p2, bool p3) internal view {
1234 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,bool)", p0, p1, p2, p3));
1235 |     }
1236 | 
1237 |     function log(bool p0, address p1, uint p2, address p3) internal view {
1238 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,address)", p0, p1, p2, p3));
1239 |     }
1240 | 
1241 |     function log(bool p0, address p1, string memory p2, uint p3) internal view {
1242 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,uint)", p0, p1, p2, p3));
1243 |     }
1244 | 
1245 |     function log(bool p0, address p1, string memory p2, string memory p3) internal view {
1246 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,string)", p0, p1, p2, p3));
1247 |     }
1248 | 
1249 |     function log(bool p0, address p1, string memory p2, bool p3) internal view {
1250 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,bool)", p0, p1, p2, p3));
1251 |     }
1252 | 
1253 |     function log(bool p0, address p1, string memory p2, address p3) internal view {
1254 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,address)", p0, p1, p2, p3));
1255 |     }
1256 | 
1257 |     function log(bool p0, address p1, bool p2, uint p3) internal view {
1258 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,uint)", p0, p1, p2, p3));
1259 |     }
1260 | 
1261 |     function log(bool p0, address p1, bool p2, string memory p3) internal view {
1262 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,string)", p0, p1, p2, p3));
1263 |     }
1264 | 
1265 |     function log(bool p0, address p1, bool p2, bool p3) internal view {
1266 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,bool)", p0, p1, p2, p3));
1267 |     }
1268 | 
1269 |     function log(bool p0, address p1, bool p2, address p3) internal view {
1270 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,address)", p0, p1, p2, p3));
1271 |     }
1272 | 
1273 |     function log(bool p0, address p1, address p2, uint p3) internal view {
1274 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,uint)", p0, p1, p2, p3));
1275 |     }
1276 | 
1277 |     function log(bool p0, address p1, address p2, string memory p3) internal view {
1278 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,string)", p0, p1, p2, p3));
1279 |     }
1280 | 
1281 |     function log(bool p0, address p1, address p2, bool p3) internal view {
1282 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,bool)", p0, p1, p2, p3));
1283 |     }
1284 | 
1285 |     function log(bool p0, address p1, address p2, address p3) internal view {
1286 |         _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,address)", p0, p1, p2, p3));
1287 |     }
1288 | 
1289 |     function log(address p0, uint p1, uint p2, uint p3) internal view {
1290 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,uint)", p0, p1, p2, p3));
1291 |     }
1292 | 
1293 |     function log(address p0, uint p1, uint p2, string memory p3) internal view {
1294 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,string)", p0, p1, p2, p3));
1295 |     }
1296 | 
1297 |     function log(address p0, uint p1, uint p2, bool p3) internal view {
1298 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,bool)", p0, p1, p2, p3));
1299 |     }
1300 | 
1301 |     function log(address p0, uint p1, uint p2, address p3) internal view {
1302 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,address)", p0, p1, p2, p3));
1303 |     }
1304 | 
1305 |     function log(address p0, uint p1, string memory p2, uint p3) internal view {
1306 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,uint)", p0, p1, p2, p3));
1307 |     }
1308 | 
1309 |     function log(address p0, uint p1, string memory p2, string memory p3) internal view {
1310 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,string)", p0, p1, p2, p3));
1311 |     }
1312 | 
1313 |     function log(address p0, uint p1, string memory p2, bool p3) internal view {
1314 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,bool)", p0, p1, p2, p3));
1315 |     }
1316 | 
1317 |     function log(address p0, uint p1, string memory p2, address p3) internal view {
1318 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,address)", p0, p1, p2, p3));
1319 |     }
1320 | 
1321 |     function log(address p0, uint p1, bool p2, uint p3) internal view {
1322 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,uint)", p0, p1, p2, p3));
1323 |     }
1324 | 
1325 |     function log(address p0, uint p1, bool p2, string memory p3) internal view {
1326 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,string)", p0, p1, p2, p3));
1327 |     }
1328 | 
1329 |     function log(address p0, uint p1, bool p2, bool p3) internal view {
1330 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,bool)", p0, p1, p2, p3));
1331 |     }
1332 | 
1333 |     function log(address p0, uint p1, bool p2, address p3) internal view {
1334 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,address)", p0, p1, p2, p3));
1335 |     }
1336 | 
1337 |     function log(address p0, uint p1, address p2, uint p3) internal view {
1338 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,uint)", p0, p1, p2, p3));
1339 |     }
1340 | 
1341 |     function log(address p0, uint p1, address p2, string memory p3) internal view {
1342 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,string)", p0, p1, p2, p3));
1343 |     }
1344 | 
1345 |     function log(address p0, uint p1, address p2, bool p3) internal view {
1346 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,bool)", p0, p1, p2, p3));
1347 |     }
1348 | 
1349 |     function log(address p0, uint p1, address p2, address p3) internal view {
1350 |         _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,address)", p0, p1, p2, p3));
1351 |     }
1352 | 
1353 |     function log(address p0, string memory p1, uint p2, uint p3) internal view {
1354 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,uint)", p0, p1, p2, p3));
1355 |     }
1356 | 
1357 |     function log(address p0, string memory p1, uint p2, string memory p3) internal view {
1358 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,string)", p0, p1, p2, p3));
1359 |     }
1360 | 
1361 |     function log(address p0, string memory p1, uint p2, bool p3) internal view {
1362 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,bool)", p0, p1, p2, p3));
1363 |     }
1364 | 
1365 |     function log(address p0, string memory p1, uint p2, address p3) internal view {
1366 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,address)", p0, p1, p2, p3));
1367 |     }
1368 | 
1369 |     function log(address p0, string memory p1, string memory p2, uint p3) internal view {
1370 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,string,uint)", p0, p1, p2, p3));
1371 |     }
1372 | 
1373 |     function log(address p0, string memory p1, string memory p2, string memory p3) internal view {
1374 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,string,string)", p0, p1, p2, p3));
1375 |     }
1376 | 
1377 |     function log(address p0, string memory p1, string memory p2, bool p3) internal view {
1378 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,string,bool)", p0, p1, p2, p3));
1379 |     }
1380 | 
1381 |     function log(address p0, string memory p1, string memory p2, address p3) internal view {
1382 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,string,address)", p0, p1, p2, p3));
1383 |     }
1384 | 
1385 |     function log(address p0, string memory p1, bool p2, uint p3) internal view {
1386 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,uint)", p0, p1, p2, p3));
1387 |     }
1388 | 
1389 |     function log(address p0, string memory p1, bool p2, string memory p3) internal view {
1390 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,string)", p0, p1, p2, p3));
1391 |     }
1392 | 
1393 |     function log(address p0, string memory p1, bool p2, bool p3) internal view {
1394 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,bool)", p0, p1, p2, p3));
1395 |     }
1396 | 
1397 |     function log(address p0, string memory p1, bool p2, address p3) internal view {
1398 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,address)", p0, p1, p2, p3));
1399 |     }
1400 | 
1401 |     function log(address p0, string memory p1, address p2, uint p3) internal view {
1402 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,address,uint)", p0, p1, p2, p3));
1403 |     }
1404 | 
1405 |     function log(address p0, string memory p1, address p2, string memory p3) internal view {
1406 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,address,string)", p0, p1, p2, p3));
1407 |     }
1408 | 
1409 |     function log(address p0, string memory p1, address p2, bool p3) internal view {
1410 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,address,bool)", p0, p1, p2, p3));
1411 |     }
1412 | 
1413 |     function log(address p0, string memory p1, address p2, address p3) internal view {
1414 |         _sendLogPayload(abi.encodeWithSignature("log(address,string,address,address)", p0, p1, p2, p3));
1415 |     }
1416 | 
1417 |     function log(address p0, bool p1, uint p2, uint p3) internal view {
1418 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,uint)", p0, p1, p2, p3));
1419 |     }
1420 | 
1421 |     function log(address p0, bool p1, uint p2, string memory p3) internal view {
1422 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,string)", p0, p1, p2, p3));
1423 |     }
1424 | 
1425 |     function log(address p0, bool p1, uint p2, bool p3) internal view {
1426 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,bool)", p0, p1, p2, p3));
1427 |     }
1428 | 
1429 |     function log(address p0, bool p1, uint p2, address p3) internal view {
1430 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,address)", p0, p1, p2, p3));
1431 |     }
1432 | 
1433 |     function log(address p0, bool p1, string memory p2, uint p3) internal view {
1434 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,uint)", p0, p1, p2, p3));
1435 |     }
1436 | 
1437 |     function log(address p0, bool p1, string memory p2, string memory p3) internal view {
1438 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,string)", p0, p1, p2, p3));
1439 |     }
1440 | 
1441 |     function log(address p0, bool p1, string memory p2, bool p3) internal view {
1442 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,bool)", p0, p1, p2, p3));
1443 |     }
1444 | 
1445 |     function log(address p0, bool p1, string memory p2, address p3) internal view {
1446 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,address)", p0, p1, p2, p3));
1447 |     }
1448 | 
1449 |     function log(address p0, bool p1, bool p2, uint p3) internal view {
1450 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,uint)", p0, p1, p2, p3));
1451 |     }
1452 | 
1453 |     function log(address p0, bool p1, bool p2, string memory p3) internal view {
1454 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,string)", p0, p1, p2, p3));
1455 |     }
1456 | 
1457 |     function log(address p0, bool p1, bool p2, bool p3) internal view {
1458 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,bool)", p0, p1, p2, p3));
1459 |     }
1460 | 
1461 |     function log(address p0, bool p1, bool p2, address p3) internal view {
1462 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,address)", p0, p1, p2, p3));
1463 |     }
1464 | 
1465 |     function log(address p0, bool p1, address p2, uint p3) internal view {
1466 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,uint)", p0, p1, p2, p3));
1467 |     }
1468 | 
1469 |     function log(address p0, bool p1, address p2, string memory p3) internal view {
1470 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,string)", p0, p1, p2, p3));
1471 |     }
1472 | 
1473 |     function log(address p0, bool p1, address p2, bool p3) internal view {
1474 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,bool)", p0, p1, p2, p3));
1475 |     }
1476 | 
1477 |     function log(address p0, bool p1, address p2, address p3) internal view {
1478 |         _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,address)", p0, p1, p2, p3));
1479 |     }
1480 | 
1481 |     function log(address p0, address p1, uint p2, uint p3) internal view {
1482 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,uint)", p0, p1, p2, p3));
1483 |     }
1484 | 
1485 |     function log(address p0, address p1, uint p2, string memory p3) internal view {
1486 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,string)", p0, p1, p2, p3));
1487 |     }
1488 | 
1489 |     function log(address p0, address p1, uint p2, bool p3) internal view {
1490 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,bool)", p0, p1, p2, p3));
1491 |     }
1492 | 
1493 |     function log(address p0, address p1, uint p2, address p3) internal view {
1494 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,address)", p0, p1, p2, p3));
1495 |     }
1496 | 
1497 |     function log(address p0, address p1, string memory p2, uint p3) internal view {
1498 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,string,uint)", p0, p1, p2, p3));
1499 |     }
1500 | 
1501 |     function log(address p0, address p1, string memory p2, string memory p3) internal view {
1502 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,string,string)", p0, p1, p2, p3));
1503 |     }
1504 | 
1505 |     function log(address p0, address p1, string memory p2, bool p3) internal view {
1506 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,string,bool)", p0, p1, p2, p3));
1507 |     }
1508 | 
1509 |     function log(address p0, address p1, string memory p2, address p3) internal view {
1510 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,string,address)", p0, p1, p2, p3));
1511 |     }
1512 | 
1513 |     function log(address p0, address p1, bool p2, uint p3) internal view {
1514 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,uint)", p0, p1, p2, p3));
1515 |     }
1516 | 
1517 |     function log(address p0, address p1, bool p2, string memory p3) internal view {
1518 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,string)", p0, p1, p2, p3));
1519 |     }
1520 | 
1521 |     function log(address p0, address p1, bool p2, bool p3) internal view {
1522 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,bool)", p0, p1, p2, p3));
1523 |     }
1524 | 
1525 |     function log(address p0, address p1, bool p2, address p3) internal view {
1526 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,address)", p0, p1, p2, p3));
1527 |     }
1528 | 
1529 |     function log(address p0, address p1, address p2, uint p3) internal view {
1530 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,address,uint)", p0, p1, p2, p3));
1531 |     }
1532 | 
1533 |     function log(address p0, address p1, address p2, string memory p3) internal view {
1534 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,address,string)", p0, p1, p2, p3));
1535 |     }
1536 | 
1537 |     function log(address p0, address p1, address p2, bool p3) internal view {
1538 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,address,bool)", p0, p1, p2, p3));
1539 |     }
1540 | 
1541 |     function log(address p0, address p1, address p2, address p3) internal view {
1542 |         _sendLogPayload(abi.encodeWithSignature("log(address,address,address,address)", p0, p1, p2, p3));
1543 |     }
1544 | 
1545 | }
1546 | 


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