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exp contract function test max values different
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packages/protocol/contracts/thirdparty/LibFixedPointMath.sol
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| // SPDX-License-Identifier: UNLICENSED | ||
| // Taken from: | ||
| // https://github.com/recmo/experiment-solexp/blob/main/src/FixedPointMathLib.sol | ||
| // SPDX-License-Identifier: MIT | ||
| pragma solidity ^0.8.20; | ||
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| library LibFixedPointMath { | ||
| uint128 public constant MAX_EXP_INPUT = 135_305_999_368_893_231_588; | ||
| uint256 public constant SCALING_FACTOR_1E18 = 1e18; // For fixed point | ||
| // representation factor | ||
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| error Overflow(); | ||
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| // Computes e^x in 1e18 fixed point. | ||
| function exp(int256 x) internal pure returns (int256 r) { | ||
| unchecked { | ||
| // Input x is in fixed point format, with scale factor 1/1e18. | ||
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| // When the result is < 0.5 we return zero. This happens when | ||
| // x <= floor(log(0.5e18) * 1e18) ~ -42e18 | ||
| if (x <= -42_139_678_854_452_767_551) { | ||
| return 0; | ||
| } | ||
| import { SD59x18, sd } from "https://github.com/PaulRBerg/prb-math/blob/main/src/SD59x18.sol"; | ||
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| // When the result is > (2**255 - 1) / 1e18 we can not represent it | ||
| // as an int256. This happens when x >= floor(log((2**255 -1) / | ||
| // 1e18) * 1e18) ~ 135. | ||
| if (x >= 135_305_999_368_893_231_589) revert Overflow(); | ||
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| // x is now in the range (-42, 136) * 1e18. Convert to (-42, 136) * | ||
| // 2**96 | ||
| // for more intermediate precision and a binary basis. This base | ||
| // conversion | ||
| // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78. | ||
| x = (x << 78) / 5 ** 18; | ||
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| // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out | ||
| // powers of two | ||
| // such that exp(x) = exp(x') * 2**k, where k is an integer. | ||
| // Solving this gives k = round(x / log(2)) and x' = x - k * log(2). | ||
| int256 k = ( | ||
| (x << 96) / 54_916_777_467_707_473_351_141_471_128 + 2 ** 95 | ||
| ) >> 96; | ||
| x = x - k * 54_916_777_467_707_473_351_141_471_128; | ||
| // k is in the range [-61, 195]. | ||
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| // Evaluate using a (6, 7)-term rational approximation | ||
| // p is made monic, we will multiply by a scale factor later | ||
| int256 p = x + 2_772_001_395_605_857_295_435_445_496_992; | ||
| p = ((p * x) >> 96) + 44_335_888_930_127_919_016_834_873_520_032; | ||
| p = ((p * x) >> 96) + 398_888_492_587_501_845_352_592_340_339_721; | ||
| p = ((p * x) >> 96) + 1_993_839_819_670_624_470_859_228_494_792_842; | ||
| p = p * x + (4_385_272_521_454_847_904_632_057_985_693_276 << 96); | ||
| // We leave p in 2**192 basis so we don't need to scale it back up | ||
| // for the division. | ||
| // Evaluate using using Knuth's scheme from p. 491. | ||
| int256 z = x + 750_530_180_792_738_023_273_180_420_736; | ||
| z = ((z * x) >> 96) + 32_788_456_221_302_202_726_307_501_949_080; | ||
| int256 w = x - 2_218_138_959_503_481_824_038_194_425_854; | ||
| w = ((w * z) >> 96) + 892_943_633_302_991_980_437_332_862_907_700; | ||
| int256 q = z + w - 78_174_809_823_045_304_726_920_794_422_040; | ||
| q = ((q * w) >> 96) + 4_203_224_763_890_128_580_604_056_984_195_872; | ||
| assembly { | ||
| // Div in assembly because solidity adds a zero check despite | ||
| // the `unchecked`. | ||
| // The q polynomial is known not to have zeros in the domain. | ||
| // (All roots are complex) | ||
| // No scaling required because p is already 2**96 too large. | ||
| r := sdiv(p, q) | ||
| } | ||
| // r should be in the range (0.09, 0.25) * 2**96. | ||
| library LibFixedPointMath { | ||
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| // We now need to multiply r by | ||
| // * the scale factor s = ~6.031367120..., | ||
| // * the 2**k factor from the range reduction, and | ||
| // * the 1e18 / 2**96 factor for base converison. | ||
| // We do all of this at once, with an intermediate result in 2**213 | ||
| // basis | ||
| // so the final right shift is always by a positive amount. | ||
| r = int256( | ||
| ( | ||
| uint256(r) | ||
| * | ||
| 3_822_833_074_963_236_453_042_738_258_902_158_003_155_416_615_667 | ||
| ) >> uint256(195 - k) | ||
| ); | ||
| } | ||
| } | ||
| } | ||
| /// @notice Calculates the natural exponent of x using the following formula: | ||
| /// | ||
| /// $$ | ||
| /// e^x = 2^{x * log_2{e}} | ||
| /// $$ | ||
| /// | ||
| /// @dev Notes: | ||
| /// - Refer to the notes in {exp2}. | ||
| /// | ||
| /// Requirements: | ||
| /// - Refer to the requirements in {exp2}. | ||
| /// - x must be less than 133_084258667509499441. | ||
| /// | ||
| /// @param x The exponent as an SD59x18 number. | ||
| /// @return result The result as an SD59x18 number. | ||
| /// @custom:smtchecker abstract-function-nondet | ||
| function exp(SD59x18 x) internal pure returns (SD59x18 result) { | ||
| result = x.exp(); | ||
| } | ||
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| } |