{ "contractName": "ABDKMath64x64", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.7.6+commit.7338295f\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"notice\":\"Smart contract library of mathematical functions operating with signed 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is basically a simple fraction whose numerator is signed 128-bit integer and denominator is 2^64. As long as denominator is always the same, there is no need to store it, thus in Solidity signed 64.64-bit fixed point numbers are represented by int128 type holding only the numerator.\",\"version\":1}},\"settings\":{\"compilationTarget\":{\"abdk-libraries-solidity/ABDKMath64x64.sol\":\"ABDKMath64x64\"},\"evmVersion\":\"istanbul\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":1000000},\"remappings\":[]},\"sources\":{\"abdk-libraries-solidity/ABDKMath64x64.sol\":{\"keccak256\":\"0x67609bc0923563d05d3a8a7c681056f9702a92120777cb0bcbb40d0afbb4a015\",\"license\":\"BSD-4-Clause\",\"urls\":[\"bzz-raw://55e817969394d4e0201a8cd3763ad6776bc9fddc986febe9b4acf120e8b7ad0d\",\"dweb:/ipfs/QmNMve5ZjUfA8DJYic4sYTrDEAN6VyxcC7jWUTX25Wmnnp\"]}},\"version\":1}", "bytecode": "0x60566023600b82828239805160001a607314601657fe5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea2646970667358221220d1cb4c0f3fad64eb5bfc79d08e599e994f24796a57e649e9779d00f3b0bf01da64736f6c63430007060033", "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea2646970667358221220d1cb4c0f3fad64eb5bfc79d08e599e994f24796a57e649e9779d00f3b0bf01da64736f6c63430007060033", "immutableReferences": {}, "generatedSources": [], "deployedGeneratedSources": [], "sourceMap": "686:24031:38:-:0;;;;;;;;;;;;;;;;;;;;;;;;;", "deployedSourceMap": "686:24031:38:-:0;;;;;;;;", "source": "// SPDX-License-Identifier: BSD-4-Clause\n/*\n * ABDK Math 64.64 Smart Contract Library. Copyright © 2019 by ABDK Consulting.\n * Author: Mikhail Vladimirov \n */\npragma solidity ^0.5.0 || ^0.6.0 || ^0.7.0;\n\n/**\n * Smart contract library of mathematical functions operating with signed\n * 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is\n * basically a simple fraction whose numerator is signed 128-bit integer and\n * denominator is 2^64. As long as denominator is always the same, there is no\n * need to store it, thus in Solidity signed 64.64-bit fixed point numbers are\n * represented by int128 type holding only the numerator.\n */\nlibrary ABDKMath64x64 {\n /*\n * Minimum value signed 64.64-bit fixed point number may have. \n */\n int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;\n\n /*\n * Maximum value signed 64.64-bit fixed point number may have. \n */\n int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;\n\n /**\n * Convert signed 256-bit integer number into signed 64.64-bit fixed point\n * number. Revert on overflow.\n *\n * @param x signed 256-bit integer number\n * @return signed 64.64-bit fixed point number\n */\n function fromInt (int256 x) internal pure returns (int128) {\n require (x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);\n return int128 (x << 64);\n }\n\n /**\n * Convert signed 64.64 fixed point number into signed 64-bit integer number\n * rounding down.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64-bit integer number\n */\n function toInt (int128 x) internal pure returns (int64) {\n return int64 (x >> 64);\n }\n\n /**\n * Convert unsigned 256-bit integer number into signed 64.64-bit fixed point\n * number. Revert on overflow.\n *\n * @param x unsigned 256-bit integer number\n * @return signed 64.64-bit fixed point number\n */\n function fromUInt (uint256 x) internal pure returns (int128) {\n require (x <= 0x7FFFFFFFFFFFFFFF);\n return int128 (x << 64);\n }\n\n /**\n * Convert signed 64.64 fixed point number into unsigned 64-bit integer\n * number rounding down. Revert on underflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @return unsigned 64-bit integer number\n */\n function toUInt (int128 x) internal pure returns (uint64) {\n require (x >= 0);\n return uint64 (x >> 64);\n }\n\n /**\n * Convert signed 128.128 fixed point number into signed 64.64-bit fixed point\n * number rounding down. Revert on overflow.\n *\n * @param x signed 128.128-bin fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function from128x128 (int256 x) internal pure returns (int128) {\n int256 result = x >> 64;\n require (result >= MIN_64x64 && result <= MAX_64x64);\n return int128 (result);\n }\n\n /**\n * Convert signed 64.64 fixed point number into signed 128.128 fixed point\n * number.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 128.128 fixed point number\n */\n function to128x128 (int128 x) internal pure returns (int256) {\n return int256 (x) << 64;\n }\n\n /**\n * Calculate x + y. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function add (int128 x, int128 y) internal pure returns (int128) {\n int256 result = int256(x) + y;\n require (result >= MIN_64x64 && result <= MAX_64x64);\n return int128 (result);\n }\n\n /**\n * Calculate x - y. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function sub (int128 x, int128 y) internal pure returns (int128) {\n int256 result = int256(x) - y;\n require (result >= MIN_64x64 && result <= MAX_64x64);\n return int128 (result);\n }\n\n /**\n * Calculate x * y rounding down. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function mul (int128 x, int128 y) internal pure returns (int128) {\n int256 result = int256(x) * y >> 64;\n require (result >= MIN_64x64 && result <= MAX_64x64);\n return int128 (result);\n }\n\n /**\n * Calculate x * y rounding towards zero, where x is signed 64.64 fixed point\n * number and y is signed 256-bit integer number. Revert on overflow.\n *\n * @param x signed 64.64 fixed point number\n * @param y signed 256-bit integer number\n * @return signed 256-bit integer number\n */\n function muli (int128 x, int256 y) internal pure returns (int256) {\n if (x == MIN_64x64) {\n require (y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&\n y <= 0x1000000000000000000000000000000000000000000000000);\n return -y << 63;\n } else {\n bool negativeResult = false;\n if (x < 0) {\n x = -x;\n negativeResult = true;\n }\n if (y < 0) {\n y = -y; // We rely on overflow behavior here\n negativeResult = !negativeResult;\n }\n uint256 absoluteResult = mulu (x, uint256 (y));\n if (negativeResult) {\n require (absoluteResult <=\n 0x8000000000000000000000000000000000000000000000000000000000000000);\n return -int256 (absoluteResult); // We rely on overflow behavior here\n } else {\n require (absoluteResult <=\n 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n return int256 (absoluteResult);\n }\n }\n }\n\n /**\n * Calculate x * y rounding down, where x is signed 64.64 fixed point number\n * and y is unsigned 256-bit integer number. Revert on overflow.\n *\n * @param x signed 64.64 fixed point number\n * @param y unsigned 256-bit integer number\n * @return unsigned 256-bit integer number\n */\n function mulu (int128 x, uint256 y) internal pure returns (uint256) {\n if (y == 0) return 0;\n\n require (x >= 0);\n\n uint256 lo = (uint256 (x) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;\n uint256 hi = uint256 (x) * (y >> 128);\n\n require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n hi <<= 64;\n\n require (hi <=\n 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo);\n return hi + lo;\n }\n\n /**\n * Calculate x / y rounding towards zero. Revert on overflow or when y is\n * zero.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function div (int128 x, int128 y) internal pure returns (int128) {\n require (y != 0);\n int256 result = (int256 (x) << 64) / y;\n require (result >= MIN_64x64 && result <= MAX_64x64);\n return int128 (result);\n }\n\n /**\n * Calculate x / y rounding towards zero, where x and y are signed 256-bit\n * integer numbers. Revert on overflow or when y is zero.\n *\n * @param x signed 256-bit integer number\n * @param y signed 256-bit integer number\n * @return signed 64.64-bit fixed point number\n */\n function divi (int256 x, int256 y) internal pure returns (int128) {\n require (y != 0);\n\n bool negativeResult = false;\n if (x < 0) {\n x = -x; // We rely on overflow behavior here\n negativeResult = true;\n }\n if (y < 0) {\n y = -y; // We rely on overflow behavior here\n negativeResult = !negativeResult;\n }\n uint128 absoluteResult = divuu (uint256 (x), uint256 (y));\n if (negativeResult) {\n require (absoluteResult <= 0x80000000000000000000000000000000);\n return -int128 (absoluteResult); // We rely on overflow behavior here\n } else {\n require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n return int128 (absoluteResult); // We rely on overflow behavior here\n }\n }\n\n /**\n * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit\n * integer numbers. Revert on overflow or when y is zero.\n *\n * @param x unsigned 256-bit integer number\n * @param y unsigned 256-bit integer number\n * @return signed 64.64-bit fixed point number\n */\n function divu (uint256 x, uint256 y) internal pure returns (int128) {\n require (y != 0);\n uint128 result = divuu (x, y);\n require (result <= uint128 (MAX_64x64));\n return int128 (result);\n }\n\n /**\n * Calculate -x. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function neg (int128 x) internal pure returns (int128) {\n require (x != MIN_64x64);\n return -x;\n }\n\n /**\n * Calculate |x|. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function abs (int128 x) internal pure returns (int128) {\n require (x != MIN_64x64);\n return x < 0 ? -x : x;\n }\n\n /**\n * Calculate 1 / x rounding towards zero. Revert on overflow or when x is\n * zero.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function inv (int128 x) internal pure returns (int128) {\n require (x != 0);\n int256 result = int256 (0x100000000000000000000000000000000) / x;\n require (result >= MIN_64x64 && result <= MAX_64x64);\n return int128 (result);\n }\n\n /**\n * Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function avg (int128 x, int128 y) internal pure returns (int128) {\n return int128 ((int256 (x) + int256 (y)) >> 1);\n }\n\n /**\n * Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.\n * Revert on overflow or in case x * y is negative.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function gavg (int128 x, int128 y) internal pure returns (int128) {\n int256 m = int256 (x) * int256 (y);\n require (m >= 0);\n require (m <\n 0x4000000000000000000000000000000000000000000000000000000000000000);\n return int128 (sqrtu (uint256 (m)));\n }\n\n /**\n * Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number\n * and y is unsigned 256-bit integer number. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @param y uint256 value\n * @return signed 64.64-bit fixed point number\n */\n function pow (int128 x, uint256 y) internal pure returns (int128) {\n uint256 absoluteResult;\n bool negativeResult = false;\n if (x >= 0) {\n absoluteResult = powu (uint256 (x) << 63, y);\n } else {\n // We rely on overflow behavior here\n absoluteResult = powu (uint256 (uint128 (-x)) << 63, y);\n negativeResult = y & 1 > 0;\n }\n\n absoluteResult >>= 63;\n\n if (negativeResult) {\n require (absoluteResult <= 0x80000000000000000000000000000000);\n return -int128 (absoluteResult); // We rely on overflow behavior here\n } else {\n require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n return int128 (absoluteResult); // We rely on overflow behavior here\n }\n }\n\n /**\n * Calculate sqrt (x) rounding down. Revert if x < 0.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function sqrt (int128 x) internal pure returns (int128) {\n require (x >= 0);\n return int128 (sqrtu (uint256 (x) << 64));\n }\n\n /**\n * Calculate binary logarithm of x. Revert if x <= 0.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function log_2 (int128 x) internal pure returns (int128) {\n require (x > 0);\n\n int256 msb = 0;\n int256 xc = x;\n if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }\n if (xc >= 0x100000000) { xc >>= 32; msb += 32; }\n if (xc >= 0x10000) { xc >>= 16; msb += 16; }\n if (xc >= 0x100) { xc >>= 8; msb += 8; }\n if (xc >= 0x10) { xc >>= 4; msb += 4; }\n if (xc >= 0x4) { xc >>= 2; msb += 2; }\n if (xc >= 0x2) msb += 1; // No need to shift xc anymore\n\n int256 result = msb - 64 << 64;\n uint256 ux = uint256 (x) << uint256 (127 - msb);\n for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {\n ux *= ux;\n uint256 b = ux >> 255;\n ux >>= 127 + b;\n result += bit * int256 (b);\n }\n\n return int128 (result);\n }\n\n /**\n * Calculate natural logarithm of x. Revert if x <= 0.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function ln (int128 x) internal pure returns (int128) {\n require (x > 0);\n\n return int128 (\n uint256 (log_2 (x)) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128);\n }\n\n /**\n * Calculate binary exponent of x. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function exp_2 (int128 x) internal pure returns (int128) {\n require (x < 0x400000000000000000); // Overflow\n\n if (x < -0x400000000000000000) return 0; // Underflow\n\n uint256 result = 0x80000000000000000000000000000000;\n\n if (x & 0x8000000000000000 > 0)\n result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;\n if (x & 0x4000000000000000 > 0)\n result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;\n if (x & 0x2000000000000000 > 0)\n result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;\n if (x & 0x1000000000000000 > 0)\n result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128;\n if (x & 0x800000000000000 > 0)\n result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;\n if (x & 0x400000000000000 > 0)\n result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;\n if (x & 0x200000000000000 > 0)\n result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;\n if (x & 0x100000000000000 > 0)\n result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;\n if (x & 0x80000000000000 > 0)\n result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;\n if (x & 0x40000000000000 > 0)\n result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;\n if (x & 0x20000000000000 > 0)\n result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;\n if (x & 0x10000000000000 > 0)\n result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;\n if (x & 0x8000000000000 > 0)\n result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;\n if (x & 0x4000000000000 > 0)\n result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;\n if (x & 0x2000000000000 > 0)\n result = result * 0x1000162E525EE054754457D5995292026 >> 128;\n if (x & 0x1000000000000 > 0)\n result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128;\n if (x & 0x800000000000 > 0)\n result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;\n if (x & 0x400000000000 > 0)\n result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;\n if (x & 0x200000000000 > 0)\n result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128;\n if (x & 0x100000000000 > 0)\n result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128;\n if (x & 0x80000000000 > 0)\n result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;\n if (x & 0x40000000000 > 0)\n result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;\n if (x & 0x20000000000 > 0)\n result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128;\n if (x & 0x10000000000 > 0)\n result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;\n if (x & 0x8000000000 > 0)\n result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;\n if (x & 0x4000000000 > 0)\n result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128;\n if (x & 0x2000000000 > 0)\n result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;\n if (x & 0x1000000000 > 0)\n result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;\n if (x & 0x800000000 > 0)\n result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;\n if (x & 0x400000000 > 0)\n result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;\n if (x & 0x200000000 > 0)\n result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;\n if (x & 0x100000000 > 0)\n result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128;\n if (x & 0x80000000 > 0)\n result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;\n if (x & 0x40000000 > 0)\n result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;\n if (x & 0x20000000 > 0)\n result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128;\n if (x & 0x10000000 > 0)\n result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;\n if (x & 0x8000000 > 0)\n result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;\n if (x & 0x4000000 > 0)\n result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;\n if (x & 0x2000000 > 0)\n result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128;\n if (x & 0x1000000 > 0)\n result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128;\n if (x & 0x800000 > 0)\n result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;\n if (x & 0x400000 > 0)\n result = result * 0x100000000002C5C85FDF477B662B26945 >> 128;\n if (x & 0x200000 > 0)\n result = result * 0x10000000000162E42FEFA3AE53369388C >> 128;\n if (x & 0x100000 > 0)\n result = result * 0x100000000000B17217F7D1D351A389D40 >> 128;\n if (x & 0x80000 > 0)\n result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;\n if (x & 0x40000 > 0)\n result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;\n if (x & 0x20000 > 0)\n result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128;\n if (x & 0x10000 > 0)\n result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;\n if (x & 0x8000 > 0)\n result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;\n if (x & 0x4000 > 0)\n result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128;\n if (x & 0x2000 > 0)\n result = result * 0x1000000000000162E42FEFA39F02B772C >> 128;\n if (x & 0x1000 > 0)\n result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128;\n if (x & 0x800 > 0)\n result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;\n if (x & 0x400 > 0)\n result = result * 0x100000000000002C5C85FDF473DEA871F >> 128;\n if (x & 0x200 > 0)\n result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128;\n if (x & 0x100 > 0)\n result = result * 0x100000000000000B17217F7D1CF79E949 >> 128;\n if (x & 0x80 > 0)\n result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128;\n if (x & 0x40 > 0)\n result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128;\n if (x & 0x20 > 0)\n result = result * 0x100000000000000162E42FEFA39EF366F >> 128;\n if (x & 0x10 > 0)\n result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128;\n if (x & 0x8 > 0)\n result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128;\n if (x & 0x4 > 0)\n result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128;\n if (x & 0x2 > 0)\n result = result * 0x1000000000000000162E42FEFA39EF358 >> 128;\n if (x & 0x1 > 0)\n result = result * 0x10000000000000000B17217F7D1CF79AB >> 128;\n\n result >>= uint256 (63 - (x >> 64));\n require (result <= uint256 (MAX_64x64));\n\n return int128 (result);\n }\n\n /**\n * Calculate natural exponent of x. Revert on overflow.\n *\n * @param x signed 64.64-bit fixed point number\n * @return signed 64.64-bit fixed point number\n */\n function exp (int128 x) internal pure returns (int128) {\n require (x < 0x400000000000000000); // Overflow\n\n if (x < -0x400000000000000000) return 0; // Underflow\n\n return exp_2 (\n int128 (int256 (x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128));\n }\n\n /**\n * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit\n * integer numbers. Revert on overflow or when y is zero.\n *\n * @param x unsigned 256-bit integer number\n * @param y unsigned 256-bit integer number\n * @return unsigned 64.64-bit fixed point number\n */\n function divuu (uint256 x, uint256 y) private pure returns (uint128) {\n require (y != 0);\n\n uint256 result;\n\n if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)\n result = (x << 64) / y;\n else {\n uint256 msb = 192;\n uint256 xc = x >> 192;\n if (xc >= 0x100000000) { xc >>= 32; msb += 32; }\n if (xc >= 0x10000) { xc >>= 16; msb += 16; }\n if (xc >= 0x100) { xc >>= 8; msb += 8; }\n if (xc >= 0x10) { xc >>= 4; msb += 4; }\n if (xc >= 0x4) { xc >>= 2; msb += 2; }\n if (xc >= 0x2) msb += 1; // No need to shift xc anymore\n\n result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);\n require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n\n uint256 hi = result * (y >> 128);\n uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n\n uint256 xh = x >> 192;\n uint256 xl = x << 64;\n\n if (xl < lo) xh -= 1;\n xl -= lo; // We rely on overflow behavior here\n lo = hi << 128;\n if (xl < lo) xh -= 1;\n xl -= lo; // We rely on overflow behavior here\n\n assert (xh == hi >> 128);\n\n result += xl / y;\n }\n\n require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);\n return uint128 (result);\n }\n\n /**\n * Calculate x^y assuming 0^0 is 1, where x is unsigned 129.127 fixed point\n * number and y is unsigned 256-bit integer number. Revert on overflow.\n *\n * @param x unsigned 129.127-bit fixed point number\n * @param y uint256 value\n * @return unsigned 129.127-bit fixed point number\n */\n function powu (uint256 x, uint256 y) private pure returns (uint256) {\n if (y == 0) return 0x80000000000000000000000000000000;\n else if (x == 0) return 0;\n else {\n int256 msb = 0;\n uint256 xc = x;\n if (xc >= 0x100000000000000000000000000000000) { xc >>= 128; msb += 128; }\n if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }\n if (xc >= 0x100000000) { xc >>= 32; msb += 32; }\n if (xc >= 0x10000) { xc >>= 16; msb += 16; }\n if (xc >= 0x100) { xc >>= 8; msb += 8; }\n if (xc >= 0x10) { xc >>= 4; msb += 4; }\n if (xc >= 0x4) { xc >>= 2; msb += 2; }\n if (xc >= 0x2) msb += 1; // No need to shift xc anymore\n\n int256 xe = msb - 127;\n if (xe > 0) x >>= uint256 (xe);\n else x <<= uint256 (-xe);\n\n uint256 result = 0x80000000000000000000000000000000;\n int256 re = 0;\n\n while (y > 0) {\n if (y & 1 > 0) {\n result = result * x;\n y -= 1;\n re += xe;\n if (result >=\n 0x8000000000000000000000000000000000000000000000000000000000000000) {\n result >>= 128;\n re += 1;\n } else result >>= 127;\n if (re < -127) return 0; // Underflow\n require (re < 128); // Overflow\n } else {\n x = x * x;\n y >>= 1;\n xe <<= 1;\n if (x >=\n 0x8000000000000000000000000000000000000000000000000000000000000000) {\n x >>= 128;\n xe += 1;\n } else x >>= 127;\n if (xe < -127) return 0; // Underflow\n require (xe < 128); // Overflow\n }\n }\n\n if (re > 0) result <<= uint256 (re);\n else if (re < 0) result >>= uint256 (-re);\n\n return result;\n }\n }\n\n /**\n * Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer\n * number.\n *\n * @param x unsigned 256-bit integer number\n * @return unsigned 128-bit integer number\n */\n function sqrtu (uint256 x) private pure returns (uint128) {\n if (x == 0) return 0;\n else {\n uint256 xx = x;\n uint256 r = 1;\n if (xx >= 0x100000000000000000000000000000000) { xx >>= 128; r <<= 64; }\n if (xx >= 0x10000000000000000) { xx >>= 64; r <<= 32; }\n if (xx >= 0x100000000) { xx >>= 32; r <<= 16; }\n if (xx >= 0x10000) { xx >>= 16; r <<= 8; }\n if (xx >= 0x100) { xx >>= 8; r <<= 4; }\n if (xx >= 0x10) { xx >>= 4; r <<= 2; }\n if (xx >= 0x8) { r <<= 1; }\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1;\n r = (r + x / r) >> 1; // Seven iterations should be enough\n uint256 r1 = x / r;\n return uint128 (r < r1 ? r : r1);\n }\n }\n}\n", "sourcePath": "abdk-libraries-solidity/ABDKMath64x64.sol", "ast": { "absolutePath": "abdk-libraries-solidity/ABDKMath64x64.sol", "exportedSymbols": { "ABDKMath64x64": [ 10621 ] }, "id": 10622, "license": "BSD-4-Clause", "nodeType": "SourceUnit", "nodes": [ { "id": 7845, "literals": [ "solidity", "^", "0.5", ".0", "||", "^", "0.6", ".0", "||", "^", "0.7", ".0" ], "nodeType": "PragmaDirective", "src": "191:43:38" }, { "abstract": false, "baseContracts": [], "contractDependencies": [], "contractKind": "library", "documentation": { "id": 7846, "nodeType": "StructuredDocumentation", "src": "236:449:38", "text": " Smart contract library of mathematical functions operating with signed\n 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is\n basically a simple fraction whose numerator is signed 128-bit integer and\n denominator is 2^64. As long as denominator is always the same, there is no\n need to store it, thus in Solidity signed 64.64-bit fixed point numbers are\n represented by int128 type holding only the numerator." }, "fullyImplemented": true, "id": 10621, "linearizedBaseContracts": [ 10621 ], "name": "ABDKMath64x64", "nodeType": "ContractDefinition", "nodes": [ { "constant": true, "id": 7850, "mutability": "constant", "name": "MIN_64x64", "nodeType": "VariableDeclaration", "scope": 10621, "src": "789:71:38", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" }, "typeName": { "id": 7847, "name": "int128", "nodeType": "ElementaryTypeName", "src": "789:6:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "value": { "id": 7849, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "UnaryOperation", "operator": "-", "prefix": true, "src": "825:35:38", "subExpression": { "hexValue": "30783830303030303030303030303030303030303030303030303030303030303030", "id": 7848, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "826:34:38", "typeDescriptions": { "typeIdentifier": "t_rational_170141183460469231731687303715884105728_by_1", "typeString": "int_const 1701...(31 digits omitted)...5728" }, "value": "0x80000000000000000000000000000000" }, "typeDescriptions": { "typeIdentifier": "t_rational_minus_170141183460469231731687303715884105728_by_1", "typeString": "int_const -170...(32 digits omitted)...5728" } }, "visibility": "private" }, { "constant": true, "id": 7853, "mutability": "constant", "name": "MAX_64x64", "nodeType": "VariableDeclaration", "scope": 10621, "src": "942:70:38", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" }, "typeName": { "id": 7851, "name": "int128", "nodeType": "ElementaryTypeName", "src": "942:6:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "value": { "hexValue": "30783746464646464646464646464646464646464646464646464646464646464646", "id": 7852, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "978:34:38", "typeDescriptions": { "typeIdentifier": "t_rational_170141183460469231731687303715884105727_by_1", "typeString": "int_const 1701...(31 digits omitted)...5727" }, "value": "0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" }, "visibility": "private" }, { "body": { "id": 7879, "nodeType": "Block", "src": "1297:101:38", "statements": [ { "expression": { "arguments": [ { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 7869, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_int256", "typeString": "int256" }, "id": 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Revert on overflow.\n @param x signed 256-bit integer number\n @return signed 64.64-bit fixed point number" }, "id": 7880, "implemented": true, "kind": "function", "modifiers": [], "name": "fromInt", "nodeType": "FunctionDefinition", "parameters": { "id": 7857, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 7856, "mutability": "mutable", "name": "x", "nodeType": "VariableDeclaration", "scope": 7880, "src": "1256:8:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 7855, "name": "int256", "nodeType": "ElementaryTypeName", "src": "1256:6:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "src": "1255:10:38" }, "returnParameters": { "id": 7860, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 7859, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", 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64.64-bit fixed point number\n @return signed 64.64-bit fixed point number" }, "id": 8547, "implemented": true, "kind": "function", "modifiers": [], "name": "avg", "nodeType": "FunctionDefinition", "parameters": { "id": 8526, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 8523, "mutability": "mutable", "name": "x", "nodeType": "VariableDeclaration", "scope": 8547, "src": "9689:8:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" }, "typeName": { "id": 8522, "name": "int128", "nodeType": "ElementaryTypeName", "src": "9689:6:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "visibility": "internal" }, { "constant": false, "id": 8525, "mutability": "mutable", "name": "y", "nodeType": "VariableDeclaration", "scope": 8547, "src": "9699:8:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int128", 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false, "lValueRequested": false, "leftExpression": { "id": 8745, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 8729, "src": "12063:2:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030", "id": 8746, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12069:11:38", "typeDescriptions": { "typeIdentifier": "t_rational_4294967296_by_1", "typeString": "int_const 4294967296" }, "value": "0x100000000" }, "src": "12063:17:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 8757, "nodeType": "IfStatement", "src": "12059:48:38", "trueBody": { "id": 8756, "nodeType": "Block", "src": "12082:25:38", "statements": [ { "expression": { "id": 8750, "isConstant": false, "isLValue": false, "isPure": false, 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"typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 8762, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "12140:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "12133:9:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 8764, "nodeType": "ExpressionStatement", "src": "12133:9:38" }, { "expression": { "id": 8767, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 8765, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 8725, "src": "12144:3:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": 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Revert if x <= 0.\n @param x signed 64.64-bit fixed point number\n @return signed 64.64-bit fixed point number" }, "id": 8913, "implemented": true, "kind": "function", "modifiers": [], "name": "ln", "nodeType": "FunctionDefinition", "parameters": { "id": 8888, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 8887, "mutability": "mutable", "name": "x", "nodeType": "VariableDeclaration", "scope": 8913, "src": "12834:8:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" }, "typeName": { "id": 8886, "name": "int128", "nodeType": "ElementaryTypeName", "src": "12834:6:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "visibility": "internal" } ], "src": "12833:10:38" }, "returnParameters": { "id": 8891, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 8890, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", 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9748, "nodeType": "ExpressionStatement", "src": "18981:60:38" } }, { "condition": { "commonType": { "typeIdentifier": "t_int128", "typeString": "int128" }, "id": 9754, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_int128", "typeString": "int128" }, "id": 9752, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 9750, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 8916, "src": "19051:1:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "nodeType": "BinaryOperation", "operator": "&", "rightExpression": { "hexValue": "30783230", "id": 9751, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "19055:4:38", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": 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"typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463872536484078253192815_by_1", "typeString": "int_const 3402...(31 digits omitted)...2815" }, "value": "0x100000000000000162E42FEFA39EF366F" }, "src": "19080:44:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "313238", "id": 9759, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "19128:3:38", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "19080:51:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "19071:60:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 9762, "nodeType": "ExpressionStatement", "src": "19071:60:38" } }, { "condition": { "commonType": { 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"isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_int128", "typeString": "int128" }, "id": 9780, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 9778, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 8916, "src": "19231:1:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "nodeType": "BinaryOperation", "operator": "&", "rightExpression": { "hexValue": "307838", "id": 9779, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "19235:3:38", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "0x8" }, "src": "19231:7:38", "typeDescriptions": { "typeIdentifier": "t_int128", "typeString": "int128" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { 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"src": "21301:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 10067, "initialValue": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10066, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10064, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9900, "src": "21314:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "hexValue": "3634", "id": 10065, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "21319:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "21314:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "21301:20:38" }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10070, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10068, "name": "xl", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10063, "src": "21334:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 10069, "name": "lo", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10048, "src": "21339:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21334:7:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10075, "nodeType": "IfStatement", "src": "21330:20:38", "trueBody": { "expression": { "id": 10073, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10071, "name": "xh", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10057, "src": "21343:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "-=", "rightHandSide": { "hexValue": "31", "id": 10072, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "21349:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "21343:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10074, "nodeType": "ExpressionStatement", "src": "21343:7:38" } }, { "expression": { "id": 10078, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10076, "name": "xl", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10063, "src": "21358:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "-=", "rightHandSide": { "id": 10077, "name": "lo", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10048, "src": "21364:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21358:8:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10079, "nodeType": "ExpressionStatement", "src": "21358:8:38" }, { "expression": { "id": 10084, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10080, "name": "lo", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10048, "src": "21411:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10083, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10081, "name": "hi", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10039, "src": "21416:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "hexValue": "313238", "id": 10082, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "21422:3:38", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "21416:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21411:14:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10085, "nodeType": "ExpressionStatement", "src": "21411:14:38" }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10088, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10086, "name": "xl", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10063, "src": "21437:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 10087, "name": "lo", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10048, "src": "21442:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21437:7:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10093, "nodeType": 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}, "value": "128" }, "src": "21529:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21523:15:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_bool", "typeString": "bool" } ], "id": 10098, "name": "assert", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4294967293, "src": "21515:6:38", "typeDescriptions": { "typeIdentifier": "t_function_assert_pure$_t_bool_$returns$__$", "typeString": "function (bool) pure" } }, "id": 10104, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "21515:24:38", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 10105, "nodeType": "ExpressionStatement", "src": "21515:24:38" }, { "expression": { "id": 10110, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10106, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9914, "src": "21548:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10109, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10107, "name": "xl", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10063, "src": "21558:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 10108, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9902, "src": "21563:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21558:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "21548:16:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10111, "nodeType": "ExpressionStatement", "src": "21548:16:38" } ] }, "id": 10113, "nodeType": "IfStatement", "src": "20566:1005:38", "trueBody": { "expression": { "id": 9926, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 9919, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9914, "src": "20633:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 9925, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 9922, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 9920, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9900, "src": "20643:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<<", "rightExpression": { "hexValue": "3634", "id": 9921, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "20648:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "20643:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 9923, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "20642:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 9924, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9902, "src": "20654:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "20642:13:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "20633:22:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 9927, "nodeType": "ExpressionStatement", "src": "20633:22:38" } }, { "expression": { "arguments": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10117, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10115, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9914, "src": "21586:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "<=", "rightExpression": { "hexValue": "30784646464646464646464646464646464646464646464646464646464646464646", "id": 10116, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "21596:34:38", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211455_by_1", "typeString": "int_const 3402...(31 digits omitted)...1455" }, "value": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" }, "src": "21586:44:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_bool", "typeString": "bool" } ], "id": 10114, "name": "require", "nodeType": "Identifier", "overloadedDeclarations": [ 4294967278, 4294967278 ], "referencedDeclaration": 4294967278, "src": "21577:7:38", "typeDescriptions": { "typeIdentifier": "t_function_require_pure$_t_bool_$returns$__$", "typeString": "function (bool) pure" } }, "id": 10118, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "21577:54:38", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 10119, "nodeType": "ExpressionStatement", "src": "21577:54:38" }, { "expression": { "arguments": [ { "id": 10122, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 9914, "src": "21653:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 10121, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "21644:7:38", "typeDescriptions": { "typeIdentifier": "t_type$_t_uint128_$", "typeString": "type(uint128)" }, "typeName": { "id": 10120, "name": "uint128", "nodeType": "ElementaryTypeName", "src": "21644:7:38", "typeDescriptions": {} } }, "id": 10123, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "21644:16:38", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint128", "typeString": "uint128" } }, "functionReturnParameters": 9906, "id": 10124, "nodeType": "Return", "src": "21637:23:38" } ] }, "documentation": { "id": 9898, "nodeType": "StructuredDocumentation", "src": "20147:297:38", "text": " Calculate x / y rounding towards zero, where x and y are unsigned 256-bit\n integer numbers. Revert on overflow or when y is zero.\n @param x unsigned 256-bit integer number\n @param y unsigned 256-bit integer number\n @return unsigned 64.64-bit fixed point number" }, "id": 10126, "implemented": true, "kind": "function", "modifiers": [], "name": "divuu", "nodeType": "FunctionDefinition", "parameters": { "id": 9903, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 9900, "mutability": "mutable", "name": "x", "nodeType": "VariableDeclaration", "scope": 10126, "src": "20463:9:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 9899, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "20463:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 9902, "mutability": "mutable", "name": "y", "nodeType": "VariableDeclaration", "scope": 10126, "src": "20474:9:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 9901, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "20474:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "20462:22:38" }, "returnParameters": { "id": 9906, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 9905, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", "scope": 10126, "src": "20507:7:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint128", "typeString": "uint128" }, "typeName": { "id": 9904, "name": "uint128", "nodeType": "ElementaryTypeName", "src": "20507:7:38", "typeDescriptions": { "typeIdentifier": "t_uint128", "typeString": "uint128" } }, "visibility": "internal" } ], "src": "20506:9:38" }, "scope": 10621, "src": "20447:1218:38", "stateMutability": "pure", "virtual": false, "visibility": "private" }, { "body": { "id": 10415, "nodeType": "Block", "src": "22042:1656:38", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10138, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10136, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10131, "src": "22052:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 10137, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22057:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "22052:6:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseBody": { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10143, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10141, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10129, "src": "22116:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 10142, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22121:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "22116:6:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseBody": { "id": 10412, "nodeType": "Block", "src": "22143:1551:38", "statements": [ { "assignments": [ 10147 ], "declarations": [ { "constant": false, "id": 10147, "mutability": "mutable", "name": "msb", "nodeType": "VariableDeclaration", "scope": 10412, "src": "22151:10:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" }, "typeName": { "id": 10146, "name": "int256", "nodeType": "ElementaryTypeName", "src": "22151:6:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "visibility": "internal" } ], "id": 10149, "initialValue": { "hexValue": "30", "id": 10148, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22164:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "nodeType": "VariableDeclarationStatement", "src": "22151:14:38" }, { "assignments": [ 10151 ], "declarations": [ { "constant": false, 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10154, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22199:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030303030303030303030303030303030303030303030303030", "id": 10155, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22205:35:38", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" }, "value": "0x100000000000000000000000000000000" }, "src": "22199:41:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10166, "nodeType": "IfStatement", "src": "22195:74:38", "trueBody": { "id": 10165, "nodeType": "Block", "src": "22242:27:38", "statements": [ { "expression": 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{ "id": 10170, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22309:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 10171, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22316:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "22309:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10173, "nodeType": "ExpressionStatement", "src": "22309:9:38" }, { "expression": { "id": 10176, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10174, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10147, "src": 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"typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030", "id": 10181, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22349:11:38", "typeDescriptions": { "typeIdentifier": "t_rational_4294967296_by_1", "typeString": "int_const 4294967296" }, "value": "0x100000000" }, "src": "22343:17:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10192, "nodeType": "IfStatement", "src": "22339:48:38", "trueBody": { "id": 10191, "nodeType": "Block", "src": "22362:25:38", "statements": [ { "expression": { "id": 10185, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10183, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22364:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 10184, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22371:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "22364:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10186, "nodeType": "ExpressionStatement", "src": "22364:9:38" }, { "expression": { "id": 10189, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10187, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10147, "src": "22375:3:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { 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10194, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22404:7:38", "typeDescriptions": { "typeIdentifier": "t_rational_65536_by_1", "typeString": "int_const 65536" }, "value": "0x10000" }, "src": "22398:13:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10205, "nodeType": "IfStatement", "src": "22394:44:38", "trueBody": { "id": 10204, "nodeType": "Block", "src": "22413:25:38", "statements": [ { "expression": { "id": 10198, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10196, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22415:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 10197, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22422:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "22415:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10199, "nodeType": "ExpressionStatement", "src": "22415:9:38" }, { "expression": { "id": 10202, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10200, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10147, "src": "22426:3:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "3136", "id": 10201, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22433:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "22426:9:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 10203, "nodeType": "ExpressionStatement", "src": "22426:9:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10208, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10206, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22449:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030", "id": 10207, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22455:5:38", "typeDescriptions": { 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"typeString": "int_const 8" }, "value": "8" }, "src": "22464:8:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10212, "nodeType": "ExpressionStatement", "src": "22464:8:38" }, { "expression": { "id": 10215, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10213, "name": "msb", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10147, "src": "22474:3:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "Assignment", "operator": "+=", "rightHandSide": { "hexValue": "38", "id": 10214, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22481:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "22474:8:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "id": 10216, "nodeType": "ExpressionStatement", "src": "22474:8:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10221, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10219, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22496:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "30783130", "id": 10220, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22502:4:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "0x10" }, "src": "22496:10:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 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"isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10232, "name": "xc", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10151, "src": "22542:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "307834", "id": 10233, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22548:3:38", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "0x4" }, "src": "22542:9:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10244, "nodeType": "IfStatement", "src": "22538:38:38", "trueBody": { "id": 10243, "nodeType": "Block", "src": "22553:23:38", "statements": [ { "expression": { "id": 10237, "isConstant": false, "isLValue": false, 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"names": [], "nodeType": "FunctionCall", "src": "23184:18:38", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 10337, "nodeType": "ExpressionStatement", "src": "23184:18:38" } ] } } ] }, "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10288, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10286, "name": "y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10131, "src": "22835:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 10287, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22839:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "22835:5:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10386, "nodeType": "WhileStatement", "src": "22828:745:38" }, { "condition": { "commonType": { "typeIdentifier": "t_int256", "typeString": "int256" }, "id": 10389, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10387, "name": "re", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10283, "src": "23585:2:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 10388, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23590:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "23585:6:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseBody": { "condition": { "commonType": { "typeIdentifier": "t_int256", "typeString": "int256" }, "id": 10399, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10397, "name": "re", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10283, "src": "23633:2:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "hexValue": "30", "id": 10398, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23638:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "23633:6:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10408, "nodeType": "IfStatement", "src": "23629:36:38", "trueBody": { "expression": { "id": 10406, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10400, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10279, "src": "23641:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "arguments": [ { "id": 10404, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "UnaryOperation", "operator": "-", "prefix": true, "src": "23661:3:38", "subExpression": { "id": 10403, "name": "re", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10283, "src": "23662:2:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_int256", "typeString": "int256" } ], "id": 10402, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "23652:7:38", "typeDescriptions": { "typeIdentifier": "t_type$_t_uint256_$", "typeString": "type(uint256)" }, "typeName": { "id": 10401, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "23652:7:38", "typeDescriptions": {} } }, "id": 10405, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "23652:13:38", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "23641:24:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10407, "nodeType": "ExpressionStatement", "src": "23641:24:38" } }, "id": 10409, "nodeType": "IfStatement", "src": "23581:84:38", "trueBody": { "expression": { "id": 10395, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10390, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10279, "src": "23593:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "arguments": [ { "id": 10393, "name": "re", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10283, "src": "23613:2:38", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_int256", "typeString": "int256" } ], "id": 10392, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "23604:7:38", "typeDescriptions": { "typeIdentifier": "t_type$_t_uint256_$", "typeString": "type(uint256)" }, "typeName": { "id": 10391, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "23604:7:38", "typeDescriptions": {} } }, "id": 10394, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "23604:12:38", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "23593:23:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10396, "nodeType": "ExpressionStatement", "src": "23593:23:38" } }, { "expression": { "id": 10410, "name": "result", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10279, "src": "23681:6:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 10135, "id": 10411, "nodeType": "Return", "src": "23674:13:38" } ] }, "id": 10413, "nodeType": "IfStatement", "src": "22112:1582:38", "trueBody": { "expression": { "hexValue": "30", "id": 10144, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22131:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "functionReturnParameters": 10135, "id": 10145, "nodeType": "Return", "src": "22124:8:38" } }, "id": 10414, "nodeType": "IfStatement", "src": "22048:1646:38", "trueBody": { "expression": { "hexValue": "30783830303030303030303030303030303030303030303030303030303030303030", "id": 10139, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "22067:34:38", "typeDescriptions": { "typeIdentifier": "t_rational_170141183460469231731687303715884105728_by_1", "typeString": "int_const 1701...(31 digits omitted)...5728" }, "value": "0x80000000000000000000000000000000" }, "functionReturnParameters": 10135, "id": 10140, "nodeType": "Return", "src": "22060:41:38" } } ] }, "documentation": { "id": 10127, "nodeType": "StructuredDocumentation", "src": "21669:302:38", "text": " Calculate x^y assuming 0^0 is 1, where x is unsigned 129.127 fixed point\n number and y is unsigned 256-bit integer number. Revert on overflow.\n @param x unsigned 129.127-bit fixed point number\n @param y uint256 value\n @return unsigned 129.127-bit fixed point number" }, "id": 10416, "implemented": true, "kind": "function", "modifiers": [], "name": "powu", "nodeType": "FunctionDefinition", "parameters": { "id": 10132, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 10129, "mutability": "mutable", "name": "x", "nodeType": "VariableDeclaration", "scope": 10416, "src": "21989:9:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 10128, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "21989:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 10131, "mutability": "mutable", "name": "y", "nodeType": "VariableDeclaration", "scope": 10416, "src": "22000:9:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 10130, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "22000:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "21988:22:38" }, "returnParameters": { "id": 10135, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 10134, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", "scope": 10416, "src": "22033:7:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 10133, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "22033:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "22032:9:38" }, "scope": 10621, "src": "21974:1724:38", "stateMutability": "pure", "virtual": false, "visibility": "private" }, { "body": { "id": 10619, "nodeType": "Block", "src": "23956:759:38", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10426, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10424, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10419, "src": "23966:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 10425, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "23971:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "23966:6:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "falseBody": { "id": 10617, "nodeType": "Block", "src": "23993:718:38", "statements": [ { "assignments": [ 10430 ], "declarations": [ { "constant": false, "id": 10430, "mutability": "mutable", "name": "xx", "nodeType": "VariableDeclaration", "scope": 10617, "src": "24001:10:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 10429, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "24001:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 10432, "initialValue": { "id": 10431, "name": "x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10419, "src": "24014:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "VariableDeclarationStatement", "src": "24001:14:38" }, { "assignments": [ 10434 ], "declarations": [ { "constant": false, "id": 10434, "mutability": "mutable", "name": "r", "nodeType": "VariableDeclaration", "scope": 10617, "src": "24023:9:38", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 10433, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "24023:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 10436, "initialValue": { "hexValue": "31", "id": 10435, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24035:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "nodeType": "VariableDeclarationStatement", "src": "24023:13:38" }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10439, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10437, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24048:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030303030303030303030303030303030303030303030303030", "id": 10438, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24054:35:38", "typeDescriptions": { "typeIdentifier": "t_rational_340282366920938463463374607431768211456_by_1", "typeString": "int_const 3402...(31 digits omitted)...1456" }, "value": "0x100000000000000000000000000000000" }, "src": "24048:41:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10449, "nodeType": "IfStatement", "src": "24044:72:38", "trueBody": { "id": 10448, "nodeType": "Block", "src": "24091:25:38", "statements": [ { "expression": { "id": 10442, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10440, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24093:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "313238", "id": 10441, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24100:3:38", "typeDescriptions": { "typeIdentifier": "t_rational_128_by_1", "typeString": "int_const 128" }, "value": "128" }, "src": "24093:10:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10443, "nodeType": "ExpressionStatement", "src": "24093:10:38" }, { "expression": { "id": 10446, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10444, "name": "r", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10434, "src": "24105:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3634", "id": 10445, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24111:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "24105:8:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10447, "nodeType": "ExpressionStatement", "src": "24105:8:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10452, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10450, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24127:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "30783130303030303030303030303030303030", "id": 10451, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24133:19:38", "typeDescriptions": { "typeIdentifier": "t_rational_18446744073709551616_by_1", "typeString": "int_const 18446744073709551616" }, "value": "0x10000000000000000" }, "src": "24127:25:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10462, "nodeType": "IfStatement", "src": "24123:55:38", "trueBody": { "id": 10461, "nodeType": "Block", "src": "24154:24:38", "statements": [ { "expression": { "id": 10455, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10453, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24156:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3634", "id": 10454, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24163:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_64_by_1", "typeString": "int_const 64" }, "value": "64" }, "src": "24156:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10456, "nodeType": "ExpressionStatement", "src": "24156:9:38" }, { "expression": { "id": 10459, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10457, "name": "r", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10434, "src": "24167:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3332", "id": 10458, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24173:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "24167:8:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10460, "nodeType": "ExpressionStatement", "src": "24167:8:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10465, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10463, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24189:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030303030303030", "id": 10464, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24195:11:38", "typeDescriptions": { "typeIdentifier": "t_rational_4294967296_by_1", "typeString": "int_const 4294967296" }, "value": "0x100000000" }, "src": "24189:17:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10475, "nodeType": "IfStatement", "src": "24185:47:38", "trueBody": { "id": 10474, "nodeType": "Block", "src": "24208:24:38", "statements": [ { "expression": { "id": 10468, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10466, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24210:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3332", "id": 10467, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24217:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_32_by_1", "typeString": "int_const 32" }, "value": "32" }, "src": "24210:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10469, "nodeType": "ExpressionStatement", "src": "24210:9:38" }, { "expression": { "id": 10472, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10470, "name": "r", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10434, "src": "24221:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "3136", "id": 10471, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24227:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "24221:8:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10473, "nodeType": "ExpressionStatement", "src": "24221:8:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10478, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10476, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24243:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "30783130303030", "id": 10477, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24249:7:38", "typeDescriptions": { "typeIdentifier": "t_rational_65536_by_1", "typeString": "int_const 65536" }, "value": "0x10000" }, "src": "24243:13:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10488, "nodeType": "IfStatement", "src": "24239:42:38", "trueBody": { "id": 10487, "nodeType": "Block", "src": "24258:23:38", "statements": [ { "expression": { "id": 10481, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10479, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24260:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "3136", "id": 10480, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24267:2:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "16" }, "src": "24260:9:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10482, "nodeType": "ExpressionStatement", "src": "24260:9:38" }, { "expression": { "id": 10485, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10483, "name": "r", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10434, "src": "24271:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "38", "id": 10484, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24277:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "24271:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10486, "nodeType": "ExpressionStatement", "src": "24271:7:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10491, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10489, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24292:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "3078313030", "id": 10490, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24298:5:38", "typeDescriptions": { "typeIdentifier": "t_rational_256_by_1", "typeString": "int_const 256" }, "value": "0x100" }, "src": "24292:11:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10501, "nodeType": "IfStatement", "src": "24288:39:38", "trueBody": { "id": 10500, "nodeType": "Block", "src": "24305:22:38", "statements": [ { "expression": { "id": 10494, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10492, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24307:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "38", "id": 10493, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24314:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_8_by_1", "typeString": "int_const 8" }, "value": "8" }, "src": "24307:8:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10495, "nodeType": "ExpressionStatement", "src": "24307:8:38" }, { "expression": { "id": 10498, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10496, "name": "r", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10434, "src": "24317:1:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "<<=", "rightHandSide": { "hexValue": "34", "id": 10497, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24323:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "24317:7:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 10499, "nodeType": "ExpressionStatement", "src": "24317:7:38" } ] } }, { "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 10504, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 10502, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24338:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "hexValue": "30783130", "id": 10503, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24344:4:38", "typeDescriptions": { "typeIdentifier": "t_rational_16_by_1", "typeString": "int_const 16" }, "value": "0x10" }, "src": "24338:10:38", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 10514, "nodeType": "IfStatement", "src": "24334:38:38", "trueBody": { "id": 10513, "nodeType": "Block", "src": "24350:22:38", "statements": [ { "expression": { "id": 10507, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 10505, "name": "xx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 10430, "src": "24352:2:38", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": ">>=", "rightHandSide": { "hexValue": "34", "id": 10506, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "24359:1:38", "typeDescriptions": { "typeIdentifier": "t_rational_4_by_1", "typeString": "int_const 4" }, "value": "4" }, "src": "24352:8:38", 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