add Impermanent loss calculator python code

analysis/uniV3Math.ipynb

@@ -0,0 +1,140 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Uniswap math functions\n",
+    "# https://youtu.be/_asFkMz4zhw?t=25 - Uniswap V3 - Liquidity | DeFi\n",
+    "\n",
+    "def get_liquidity_0(x, sp, sb):\n",
+    "    return x * sp * sb / (sb - sp)\n",
+    "\n",
+    "def get_liquidity_1(y, sp, sa):\n",
+    "    return y / (sp - sa)\n",
+    "\n",
+    "def get_liquidity(x, y, sp, sa, sb):\n",
+    "    if sp <= sa:\n",
+    "        liquidity = get_liquidity_0(x, sp, sb)\n",
+    "    elif sp < sb:\n",
+    "        liquidity0 = get_liquidity_0(x, sp, sb)\n",
+    "        liquidity1 = get_liquidity_1(y, sp, sa)\n",
+    "        liquidity = min(liquidity0, liquidity1)\n",
+    "    else:\n",
+    "        liquidity = get_liquidity_1(y, sp, sa)\n",
+    "    return liquidity\n",
+    "\n",
+    "\n",
+    "#\n",
+    "# Calculate x and y given liquidity and price range\n",
+    "#\n",
+    "def calculate_x(L, sp, sa, sb):\n",
+    "    sp = max(min(sp, sb), sa)     # if the price is outside the range, use the range endpoints instead\n",
+    "    return L * (sb - sp) / (sp * sb)\n",
+    "\n",
+    "def calculate_y(L, sp, sa, sb):\n",
+    "    sp = max(min(sp, sb), sa)     # if the price is outside the range, use the range endpoints instead\n",
+    "    return L * (sp - sa)\n",
+    "\n",
+    "def calculate_a1(L, sp, sb, x, y):\n",
+    "    # https://www.wolframalpha.com/input/?i=solve+L+%3D+y+%2F+%28sqrt%28P%29+-+a%29+for+a\n",
+    "    # sqrt(a) = sqrt(P) - y / L\n",
+    "    return (sp - y / L) ** 2\n",
+    "\n",
+    "def calculate_a2(sp, sb, x, y):\n",
+    "    # https://www.wolframalpha.com/input/?i=solve+++x+sqrt%28P%29+sqrt%28b%29+%2F+%28sqrt%28b%29++-+sqrt%28P%29%29+%3D+y+%2F+%28sqrt%28P%29+-+a%29%2C+for+a\n",
+    "    # sqrt(a) = (y/sqrt(b) + sqrt(P) x - y/sqrt(P))/x\n",
+    "    #    simplify:\n",
+    "    # sqrt(a) = y/(sqrt(b) x) + sqrt(P) - y/(sqrt(P) x)\n",
+    "    sa = y / (sb * x) + sp - y / (sp * x)\n",
+    "    return sa ** 2\n",
+    "\n",
+    "#\n",
+    "# Two different ways how to calculate p_b. calculate_b1() uses liquidity as an input, calculate_b2() does not.\n",
+    "#\n",
+    "def calculate_b1(L, sp, sa, x, y):\n",
+    "    # https://www.wolframalpha.com/input/?i=solve+L+%3D+x+sqrt%28P%29+sqrt%28b%29+%2F+%28sqrt%28b%29+-+sqrt%28P%29%29+for+b\n",
+    "    # sqrt(b) = (L sqrt(P)) / (L - sqrt(P) x)\n",
+    "    return ((L * sp) / (L - sp * x)) ** 2\n",
+    "\n",
+    "def calculate_b2(sp, sa, x, y):\n",
+    "    # find the square root of b:\n",
+    "    # https://www.wolframalpha.com/input/?i=solve+++x+sqrt%28P%29+b+%2F+%28b++-+sqrt%28P%29%29+%3D+y+%2F+%28sqrt%28P%29+-+sqrt%28a%29%29%2C+for+b\n",
+    "    # sqrt(b) = (sqrt(P) y)/(sqrt(a) sqrt(P) x - P x + y)\n",
+    "    P = sp ** 2\n",
+    "    return (sp * y / ((sa * sp - P) * x + y)) ** 2\n",
+    "\n",
+    "\n",
+    "\n",
+    "def calculate_P(x,y,sa,sb):\n",
+    "  p = sb*x\n",
+    "  q = y-x*sa*sb\n",
+    "  r = -sb*y\n",
+    "  return (math.pow(-1*q+(q**2 - 4*p*r),0.5)/(2*p) )\n",
+    "\n",
+    "def tick_price(t):\n",
+    "  return 1.0001**t\n",
+    "\n",
+    "def price_tick(p):\n",
+    "  return math.log(p,1.0001)\n",
+    "\n",
+    "def getYFromX(x,sa,sb,sp):\n",
+    "    return x * (sp - sa) * sp *sb /(sb - sp)\n",
+    "\n",
+    "# ? P is Y/X\n",
+    "def simulator_calc_L(x,pa,pb,p):\n",
+    "    sa = pa ** 0.5\n",
+    "    sb = pb ** 0.5\n",
+    "    sp = p ** 0.5\n",
+    "    if p >= pb:\n",
+    "        y=x\n",
+    "        x=0\n",
+    "        L = get_liquidity(x, y, sp, sa, sb)\n",
+    "    elif p <= pa:\n",
+    "        y = 0\n",
+    "    else:\n",
+    "        print(\"sim2\", sa, sb, sp, x)\n",
+    "        y = getYFromX(x, sa, sb, sp)\n",
+    "        L = get_liquidity(x, y, sp, sa, sb)\n",
+    "\n",
+    "    return L,y\n",
+    "\n",
+    "# ! Requires X token to be a stable token\n",
+    "def getXY(capitalDollar, token0Decimals, token1Decimals, Pxusd, Pyusd, sp, sa, sb):\n",
+    "    # captal = x * Pxusd / xdecimals + y * Pyusd / yDecimals  ----- eq1\n",
+    "    # replace y with x from getYFromX\n",
+    "\n",
+    "    factor1 = Pxusd / (10 ** token0Decimals)\n",
+    "    factor2 = Pyusd / (10 ** token1Decimals)\n",
+    "    factor3 = (sp - sa) * sp * sb / (sb - sp)\n",
+    "\n",
+    "    x = capitalDollar / (factor1 + factor3 * factor2)\n",
+    "    y = getYFromX(x, sa, sb, sp)\n",
+    "    return x, y"
+   ]
+  }
+ ],
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+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.11"
+  }
+ },
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+ "nbformat_minor": 2
+}