@gnosis.pm/conditional-tokens-market-makers
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Collection of Market Makers for Gnosis Conditional Tokens
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{"contractName":"Fixed192x64Math","abi":[{"constant":true,"inputs":[],"name":"LN2","outputs":[{"name":"","type":"uint256"}],"payable":false,"stateMutability":"view","type":"function"},{"constant":true,"inputs":[],"name":"LOG2_E","outputs":[{"name":"","type":"uint256"}],"payable":false,"stateMutability":"view","type":"function"},{"constant":true,"inputs":[],"name":"ONE","outputs":[{"name":"","type":"uint256"}],"payable":false,"stateMutability":"view","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"int256"}],"name":"exp","outputs":[{"name":"","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"int256"},{"name":"estimationMode","type":"Fixed192x64Math.EstimationMode"}],"name":"pow2","outputs":[{"name":"","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"int256"}],"name":"pow2Bounds","outputs":[{"name":"lower","type":"uint256"},{"name":"upper","type":"uint256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"uint256"}],"name":"ln","outputs":[{"name":"","type":"int256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"uint256"},{"name":"estimationMode","type":"Fixed192x64Math.EstimationMode"}],"name":"binaryLog","outputs":[{"name":"","type":"int256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"uint256"}],"name":"log2Bounds","outputs":[{"name":"lower","type":"int256"},{"name":"upper","type":"int256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"x","type":"uint256"}],"name":"floorLog2","outputs":[{"name":"lo","type":"int256"}],"payable":false,"stateMutability":"pure","type":"function"},{"constant":true,"inputs":[{"name":"nums","type":"int256[]"}],"name":"max","outputs":[{"name":"maxNum","type":"int256"}],"payable":false,"stateMutability":"pure","type":"function"}],"metadata":"{\"compiler\":{\"version\":\"0.5.10+commit.5a6ea5b1\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"constant\":true,\"inputs\":[],\"name\":\"LN2\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"},{\"name\":\"estimationMode\",\"type\":\"Fixed192x64Math.EstimationMode\"}],\"name\":\"binaryLog\",\"outputs\":[{\"name\":\"\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"}],\"name\":\"log2Bounds\",\"outputs\":[{\"name\":\"lower\",\"type\":\"int256\"},{\"name\":\"upper\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"int256\"},{\"name\":\"estimationMode\",\"type\":\"Fixed192x64Math.EstimationMode\"}],\"name\":\"pow2\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[],\"name\":\"LOG2_E\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"}],\"name\":\"ln\",\"outputs\":[{\"name\":\"\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"uint256\"}],\"name\":\"floorLog2\",\"outputs\":[{\"name\":\"lo\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"int256\"}],\"name\":\"pow2Bounds\",\"outputs\":[{\"name\":\"lower\",\"type\":\"uint256\"},{\"name\":\"upper\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[],\"name\":\"ONE\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"view\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"nums\",\"type\":\"int256[]\"}],\"name\":\"max\",\"outputs\":[{\"name\":\"maxNum\",\"type\":\"int256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"},{\"constant\":true,\"inputs\":[{\"name\":\"x\",\"type\":\"int256\"}],\"name\":\"exp\",\"outputs\":[{\"name\":\"\",\"type\":\"uint256\"}],\"payable\":false,\"stateMutability\":\"pure\",\"type\":\"function\"}],\"devdoc\":{\"author\":\"Alan Lu - <alan.lu@gnosis.pm>Stefan George - <stefan@gnosis.pm>\",\"methods\":{\"binaryLog(uint256,Fixed192x64Math.EstimationMode)\":{\"details\":\"Returns estimate of binaryLog(x) given x\",\"params\":{\"estimationMode\":\"whether to return a lower bound, upper bound, or a midpoint\",\"x\":\"logarithm argument in fixed point\"},\"return\":\"estimate of binaryLog(x) in fixed point\"},\"exp(int256)\":{\"details\":\"Returns natural exponential function value of given x\",\"params\":{\"x\":\"x\"},\"return\":\"e**x\"},\"floorLog2(uint256)\":{\"details\":\"Returns base 2 logarithm value of given x\",\"params\":{\"x\":\"x\"},\"return\":\"logarithmic value\"},\"ln(uint256)\":{\"details\":\"Returns natural logarithm value of given x\",\"params\":{\"x\":\"x\"},\"return\":\"ln(x)\"},\"log2Bounds(uint256)\":{\"details\":\"Returns bounds for value of binaryLog(x) given x\",\"params\":{\"x\":\"logarithm argument in fixed point\"},\"return\":\"{ \\\"lower\\\": \\\"lower bound of binaryLog(x) in fixed point\\\", \\\"upper\\\": \\\"upper bound of binaryLog(x) in fixed point\\\" }\"},\"max(int256[])\":{\"details\":\"Returns maximum of an array\",\"params\":{\"nums\":\"Numbers to look through\"},\"return\":\"Maximum number\"},\"pow2(int256,Fixed192x64Math.EstimationMode)\":{\"details\":\"Returns estimate of 2**x given x\",\"params\":{\"estimationMode\":\"whether to return a lower bound, upper bound, or a midpoint\",\"x\":\"exponent in fixed point\"},\"return\":\"estimate of 2**x in fixed point\"},\"pow2Bounds(int256)\":{\"details\":\"Returns bounds for value of 2**x given x\",\"params\":{\"x\":\"exponent in fixed point\"},\"return\":\"{ \\\"lower\\\": \\\"lower bound of 2**x in fixed point\\\", \\\"upper\\\": \\\"upper bound of 2**x in fixed point\\\" }\"}},\"title\":\"Fixed192x64Math library - Allows calculation of logarithmic and exponential 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solidity >=0.4.24 ^0.5.1;\n\n\n/// @title Fixed192x64Math library - Allows calculation of logarithmic and exponential functions\n/// @author Alan Lu - <alan.lu@gnosis.pm>\n/// @author Stefan George - <stefan@gnosis.pm>\nlibrary Fixed192x64Math {\n\n enum EstimationMode { LowerBound, UpperBound, Midpoint }\n\n /*\n * Constants\n */\n // This is equal to 1 in our calculations\n uint public constant ONE = 0x10000000000000000;\n uint public constant LN2 = 0xb17217f7d1cf79ac;\n uint public constant LOG2_E = 0x171547652b82fe177;\n\n /*\n * Public functions\n */\n /// @dev Returns natural exponential function value of given x\n /// @param x x\n /// @return e**x\n function exp(int x)\n public\n pure\n returns (uint)\n {\n // revert if x is > MAX_POWER, where\n // MAX_POWER = int(mp.floor(mp.log(mpf(2**256 - 1) / ONE) * ONE))\n require(x <= 2454971259878909886679);\n // return 0 if exp(x) is tiny, using\n // MIN_POWER = int(mp.floor(mp.log(mpf(1) / ONE) * ONE))\n if (x <= -818323753292969962227)\n return 0;\n\n // Transform so that e^x -> 2^x\n (uint lower, uint upper) = pow2Bounds(x * int(ONE) / int(LN2));\n return (upper - lower) / 2 + lower;\n }\n\n /// @dev Returns estimate of 2**x given x\n /// @param x exponent in fixed point\n /// @param estimationMode whether to return a lower bound, upper bound, or a midpoint\n /// @return estimate of 2**x in fixed point\n function pow2(int x, EstimationMode estimationMode)\n public\n pure\n returns (uint)\n {\n (uint lower, uint upper) = pow2Bounds(x);\n if(estimationMode == EstimationMode.LowerBound) {\n return lower;\n }\n if(estimationMode == EstimationMode.UpperBound) {\n return upper;\n }\n if(estimationMode == EstimationMode.Midpoint) {\n return (upper - lower) / 2 + lower;\n }\n revert();\n }\n\n /// @dev Returns bounds for value of 2**x given x\n /// @param x exponent in fixed point\n /// @return {\n /// \"lower\": \"lower bound of 2**x in fixed point\",\n /// \"upper\": \"upper bound of 2**x in fixed point\"\n /// }\n function pow2Bounds(int x)\n public\n pure\n returns (uint lower, uint upper)\n {\n // revert if x is > MAX_POWER, where\n // MAX_POWER = int(mp.floor(mp.log(mpf(2**256 - 1) / ONE, 2) * ONE))\n require(x <= 3541774862152233910271);\n // return 0 if exp(x) is tiny, using\n // MIN_POWER = int(mp.floor(mp.log(mpf(1) / ONE, 2) * ONE))\n if (x < -1180591620717411303424)\n return (0, 1);\n\n // 2^x = 2^(floor(x)) * 2^(x-floor(x))\n // ^^^^^^^^^^^^^^ is a bit shift of ceil(x)\n // so Taylor expand on z = x-floor(x), z in [0, 1)\n int shift;\n int z;\n if (x >= 0) {\n shift = x / int(ONE);\n z = x % int(ONE);\n }\n else {\n shift = (x+1) / int(ONE) - 1;\n z = x - (int(ONE) * shift);\n }\n assert(z >= 0);\n // 2^x = 1 + (ln 2) x + (ln 2)^2/2! x^2 + ...\n //\n // Can generate the z coefficients using mpmath and the following lines\n // >>> from mpmath import mp\n // >>> mp.dps = 100\n // >>> coeffs = [mp.log(2)**i / mp.factorial(i) for i in range(1, 21)]\n // >>> shifts = [64 - int(mp.log(c, 2)) for c in coeffs]\n // >>> print('\\n'.join(hex(int(c * (1 << s))) + ', ' + str(s) for c, s in zip(coeffs, shifts)))\n int result = int(ONE) << 64;\n int zpow = z;\n result += 0xb17217f7d1cf79ab * zpow;\n zpow = zpow * z / int(ONE);\n result += 0xf5fdeffc162c7543 * zpow >> (66 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xe35846b82505fc59 * zpow >> (68 - 64);\n zpow = zpow * z / int(ONE);\n result += 0x9d955b7dd273b94e * zpow >> (70 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xaec3ff3c53398883 * zpow >> (73 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xa184897c363c3b7a * zpow >> (76 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xffe5fe2c45863435 * zpow >> (80 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xb160111d2e411fec * zpow >> (83 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xda929e9caf3e1ed2 * zpow >> (87 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xf267a8ac5c764fb7 * zpow >> (91 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xf465639a8dd92607 * zpow >> (95 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xe1deb287e14c2f15 * zpow >> (99 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xc0b0c98b3687cb14 * zpow >> (103 - 64);\n zpow = zpow * z / int(ONE);\n result += 0x98a4b26ac3c54b9f * zpow >> (107 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xe1b7421d82010f33 * zpow >> (112 - 64);\n zpow = zpow * z / int(ONE);\n result += 0x9c744d73cfc59c91 * zpow >> (116 - 64);\n zpow = zpow * z / int(ONE);\n result += 0xcc2225a0e12d3eab * zpow >> (121 - 64);\n zpow = zpow * z / int(ONE);\n zpow = 0xfb8bb5eda1b4aeb9 * zpow >> (126 - 64);\n result += zpow;\n zpow = int(8 * ONE);\n\n shift -= 64;\n if (shift >= 0) {\n if (result >> (256-shift) == 0) {\n lower = uint(result) << shift;\n zpow <<= shift; // todo: is this safe?\n if (lower + uint(zpow) >= lower)\n upper = lower + uint(zpow);\n else\n upper = 2**256-1;\n return (lower, upper);\n }\n else\n return (2**256-1, 2**256-1);\n }\n zpow = (zpow >> (-shift)) + 1;\n lower = uint(result) >> (-shift);\n upper = lower + uint(zpow);\n return (lower, upper);\n }\n\n /// @dev Returns natural logarithm value of given x\n /// @param x x\n /// @return ln(x)\n function ln(uint x)\n public\n pure\n returns (int)\n {\n (int lower, int upper) = log2Bounds(x);\n return ((upper - lower) / 2 + lower) * int(ONE) / int(LOG2_E);\n }\n\n /// @dev Returns estimate of binaryLog(x) given x\n /// @param x logarithm argument in fixed point\n /// @param estimationMode whether to return a lower bound, upper bound, or a midpoint\n /// @return estimate of binaryLog(x) in fixed point\n function binaryLog(uint x, EstimationMode estimationMode)\n public\n pure\n returns (int)\n {\n (int lower, int upper) = log2Bounds(x);\n if(estimationMode == EstimationMode.LowerBound) {\n return lower;\n }\n if(estimationMode == EstimationMode.UpperBound) {\n return upper;\n }\n if(estimationMode == EstimationMode.Midpoint) {\n return (upper - lower) / 2 + lower;\n }\n revert();\n }\n\n /// @dev Returns bounds for value of binaryLog(x) given x\n /// @param x logarithm argument in fixed point\n /// @return {\n /// \"lower\": \"lower bound of binaryLog(x) in fixed point\",\n /// \"upper\": \"upper bound of binaryLog(x) in fixed point\"\n /// }\n function log2Bounds(uint x)\n public\n pure\n returns (int lower, int upper)\n {\n require(x > 0);\n // compute ⌊log₂x⌋\n lower = floorLog2(x);\n\n uint y;\n if (lower < 0)\n y = x << uint(-lower);\n else\n y = x >> uint(lower);\n\n lower *= int(ONE);\n\n // y = x * 2^(-⌊log₂x⌋)\n // so 1 <= y < 2\n // and log₂x = ⌊log₂x⌋ + log₂y\n for (int m = 1; m <= 64; m++) {\n if(y == ONE) {\n break;\n }\n y = y * y / ONE;\n if(y >= 2 * ONE) {\n lower += int(ONE >> m);\n y /= 2;\n }\n }\n\n return (lower, lower + 4);\n }\n\n /// @dev Returns base 2 logarithm value of given x\n /// @param x x\n /// @return logarithmic value\n function floorLog2(uint x)\n public\n pure\n returns (int lo)\n {\n lo = -64;\n int hi = 193;\n // I use a shift here instead of / 2 because it floors instead of rounding towards 0\n int mid = (hi + lo) >> 1;\n while((lo + 1) < hi) {\n if (mid < 0 && x << uint(-mid) < ONE || mid >= 0 && x >> uint(mid) < ONE)\n hi = mid;\n else\n lo = mid;\n mid = (hi + lo) >> 1;\n }\n }\n\n /// @dev Returns maximum of an array\n /// @param nums Numbers to look through\n /// @return Maximum number\n function max(int[] memory nums)\n public\n pure\n returns (int maxNum)\n {\n require(nums.length > 0);\n maxNum = -2**255;\n for (uint i = 0; i < nums.length; i++)\n if (nums[i] > maxNum)\n maxNum = nums[i];\n }\n}\n","compiler":{"name":"solc","version":"0.5.10+commit.5a6ea5b1.Emscripten.clang"},"networks":{"1":{"events":{},"links":{},"address":"0x75a6D6251511AF081f77F2B531C14808fB3805f3","transactionHash":"0x90ed58d6f44dda2d628c251cb64050eef0fc3fce7ca7896b1956b1e8c2dcc547"},"4":{"events":{},"links":{},"address":"0x81B086d91538fb1826F9D4e91662d4Fdd65Df413","transactionHash":"0xd65d0448076291d18f17d6cc563db55e0153fe171b9e92c0f005fabd3dc6606c"}},"schemaVersion":"3.0.16","updatedAt":"2020-03-16T19:03:53.179Z","devdoc":{"author":"Alan Lu - <alan.lu@gnosis.pm>Stefan George - <stefan@gnosis.pm>","methods":{"binaryLog(uint256,Fixed192x64Math.EstimationMode)":{"details":"Returns estimate of binaryLog(x) given x","params":{"estimationMode":"whether to return a lower bound, upper bound, or a midpoint","x":"logarithm argument in fixed point"},"return":"estimate of binaryLog(x) in fixed point"},"exp(int256)":{"details":"Returns natural exponential function value of given x","params":{"x":"x"},"return":"e**x"},"floorLog2(uint256)":{"details":"Returns base 2 logarithm value of given x","params":{"x":"x"},"return":"logarithmic value"},"ln(uint256)":{"details":"Returns natural logarithm value of given x","params":{"x":"x"},"return":"ln(x)"},"log2Bounds(uint256)":{"details":"Returns bounds for value of binaryLog(x) given x","params":{"x":"logarithm argument in fixed point"},"return":"{ \"lower\": \"lower bound of binaryLog(x) in fixed point\", \"upper\": \"upper bound of binaryLog(x) in fixed point\" }"},"max(int256[])":{"details":"Returns maximum of an array","params":{"nums":"Numbers to look through"},"return":"Maximum number"},"pow2(int256,Fixed192x64Math.EstimationMode)":{"details":"Returns estimate of 2**x given x","params":{"estimationMode":"whether to return a lower bound, upper bound, or a midpoint","x":"exponent in fixed point"},"return":"estimate of 2**x in fixed point"},"pow2Bounds(int256)":{"details":"Returns bounds for value of 2**x given x","params":{"x":"exponent in fixed point"},"return":"{ \"lower\": \"lower bound of 2**x in fixed point\", \"upper\": \"upper bound of 2**x in fixed point\" }"}},"title":"Fixed192x64Math library - Allows calculation of logarithmic and exponential functions"},"userdoc":{"methods":{}}}