{ "contractName": "TickMath", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.7.6+commit.7338295f\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"stateVariables\":{\"MAX_SQRT_RATIO\":{\"details\":\"The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)\"},\"MAX_TICK\":{\"details\":\"The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128\"},\"MIN_SQRT_RATIO\":{\"details\":\"The minimum value that can be returned from #getSqrtRatioAtTick. 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Supports\n/// prices between 2**-128 and 2**128\nlibrary TickMath {\n /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128\n int24 internal constant MIN_TICK = -887272;\n /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128\n int24 internal constant MAX_TICK = -MIN_TICK;\n\n /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)\n uint160 internal constant MIN_SQRT_RATIO = 4295128739;\n /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)\n uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;\n\n /// @notice Calculates sqrt(1.0001^tick) * 2^96\n /// @dev Throws if |tick| > max tick\n /// @param tick The input tick for the above formula\n /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)\n /// at the given tick\n function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {\n uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));\n require(absTick <= uint256(MAX_TICK), 'T');\n\n uint256 ratio = absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;\n if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;\n if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;\n if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;\n if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;\n if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;\n if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;\n if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;\n if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;\n if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;\n if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;\n if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;\n if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;\n if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;\n if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;\n if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;\n if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;\n if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;\n if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;\n if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;\n\n if (tick > 0) ratio = type(uint256).max / ratio;\n\n // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.\n // we then downcast because we know the result always fits within 160 bits due to our tick input constraint\n // we round up in the division so getTickAtSqrtRatio of the output price is always consistent\n sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));\n }\n\n /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio\n /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may\n /// ever return.\n /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96\n /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio\n function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {\n // second inequality must be < because the price can never reach the price at the max tick\n require(sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO, 'R');\n uint256 ratio = uint256(sqrtPriceX96) << 32;\n\n uint256 r = ratio;\n uint256 msb = 0;\n\n assembly {\n let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := shl(5, gt(r, 0xFFFFFFFF))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := shl(4, gt(r, 0xFFFF))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := shl(3, gt(r, 0xFF))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := shl(2, gt(r, 0xF))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := shl(1, gt(r, 0x3))\n msb := or(msb, f)\n r := shr(f, r)\n }\n assembly {\n let f := gt(r, 0x1)\n msb := or(msb, f)\n }\n\n if (msb >= 128) r = ratio >> (msb - 127);\n else r = ratio << (127 - msb);\n\n int256 log_2 = (int256(msb) - 128) << 64;\n\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(63, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(62, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(61, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(60, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(59, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(58, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(57, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(56, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(55, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(54, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(53, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(52, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(51, f))\n r := shr(f, r)\n }\n assembly {\n r := shr(127, mul(r, r))\n let f := shr(128, r)\n log_2 := or(log_2, shl(50, f))\n }\n\n int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number\n\n int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);\n int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);\n\n tick = tickLow == tickHi ? 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false, "isPure": true, "lValueRequested": false, "memberName": "max", "nodeType": "MemberAccess", "src": "3521:17:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "/", "rightExpression": { "id": 7001, "name": "ratio", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 6697, "src": "3541:5:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "3521:25:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "3513:33:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 7004, "nodeType": "ExpressionStatement", "src": "3513:33:30" } }, { "expression": { "id": 7027, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 7006, "name": "sqrtPriceX96", "nodeType": "Identifier", "overloadedDeclarations": [], 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7024, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "3895:32:30", "typeDescriptions": { "typeIdentifier": "t_uint8", "typeString": "uint8" } }, "src": "3879:48:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 7008, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "3871:7:30", "typeDescriptions": { "typeIdentifier": "t_type$_t_uint160_$", "typeString": "type(uint160)" }, "typeName": { "id": 7007, "name": "uint160", "nodeType": "ElementaryTypeName", "src": "3871:7:30", "typeDescriptions": {} } }, "id": 7026, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "3871:57:30", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint160", "typeString": "uint160" } }, "src": "3856:72:30", "typeDescriptions": { "typeIdentifier": "t_uint160", "typeString": "uint160" } }, "id": 7028, "nodeType": "ExpressionStatement", "src": "3856:72:30" } ] }, "documentation": { "id": 6657, "nodeType": "StructuredDocumentation", "src": "1053:297:30", "text": "@notice Calculates sqrt(1.0001^tick) * 2^96\n @dev Throws if |tick| > max tick\n @param tick The input tick for the above formula\n @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)\n at the given tick" }, "id": 7030, "implemented": true, "kind": "function", "modifiers": [], "name": "getSqrtRatioAtTick", "nodeType": "FunctionDefinition", "parameters": { "id": 6660, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 6659, "mutability": "mutable", "name": "tick", "nodeType": "VariableDeclaration", "scope": 7030, 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"1355:2580:30", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 7168, "nodeType": "Block", "src": "4439:4196:30", "statements": [ { "expression": { "arguments": [ { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 7045, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint160", "typeString": "uint160" }, "id": 7041, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 7039, "name": "sqrtPriceX96", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 7033, "src": "4556:12:30", "typeDescriptions": { "typeIdentifier": "t_uint160", "typeString": "uint160" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "id": 7040, "name": "MIN_SQRT_RATIO", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 6652, "src": "4572:14:30", "typeDescriptions": { "typeIdentifier": "t_uint160", "typeString": "uint160" } }, "src": "4556:30:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "&&", "rightExpression": { "commonType": { "typeIdentifier": "t_uint160", "typeString": "uint160" }, "id": 7044, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 7042, "name": "sqrtPriceX96", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 7033, "src": "4590:12:30", "typeDescriptions": { "typeIdentifier": "t_uint160", "typeString": "uint160" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "id": 7043, "name": "MAX_SQRT_RATIO", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 6656, "src": "4605:14:30", "typeDescriptions": { "typeIdentifier": "t_uint160", "typeString": "uint160" } }, "src": "4590:29:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "4556:63:30", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, { "hexValue": "52", "id": 7046, "isConstant": false, "isLValue": false, "isPure": true, "kind": "string", "lValueRequested": false, "nodeType": "Literal", "src": "4621:3:30", "typeDescriptions": { "typeIdentifier": "t_stringliteral_ef22bddd350b943170a67d35191c27e310709a28c38b5762a152ff640108f5b2", "typeString": "literal_string \"R\"" }, "value": "R" } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_bool", "typeString": "bool" }, { "typeIdentifier": "t_stringliteral_ef22bddd350b943170a67d35191c27e310709a28c38b5762a152ff640108f5b2", "typeString": "literal_string \"R\"" } ], "id": 7038, "name": "require", "nodeType": "Identifier", "overloadedDeclarations": [ 4294967278, 4294967278 ], "referencedDeclaration": 4294967278, "src": "4548:7:30", "typeDescriptions": { "typeIdentifier": "t_function_require_pure$_t_bool_$_t_string_memory_ptr_$returns$__$", "typeString": "function (bool,string memory) pure" } }, "id": 7047, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "4548:77:30", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 7048, "nodeType": "ExpressionStatement", "src": "4548:77:30" }, { "assignments": [ 7050 ], "declarations": [ { "constant": false, "id": 7050, "mutability": "mutable", "name": "ratio", "nodeType": "VariableDeclaration", "scope": 7168, "src": "4635:13:30", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 7049, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "4635:7:30", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": 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