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<!doctype html> <html lang="en"> <head> <title>Code coverage report for contracts/libraries/TickMath.sol</title> <meta charset="utf-8" /> <link rel="stylesheet" href="../../prettify.css" /> <link rel="stylesheet" href="../../base.css" /> <meta name="viewport" content="width=device-width, initial-scale=1"> <style type='text/css'> .coverage-summary .sorter { background-image: url(../../sort-arrow-sprite.png); } </style> </head> <body> <div class='wrapper'> <div class='pad1'> <h1> <a href="../../index.html">all files</a> / <a href="index.html">contracts/libraries/</a> TickMath.sol </h1> <div class='clearfix'> <div class='fl pad1y space-right2'> <span class="strong">0% </span> <span class="quiet">Statements</span> <span class='fraction'>0/56</span> </div> <div class='fl pad1y space-right2'> <span class="strong">0% </span> <span class="quiet">Branches</span> <span class='fraction'>0/46</span> </div> <div class='fl pad1y space-right2'> <span class="strong">0% </span> <span 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<span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-no">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-no">&nbsp;</span> <span class="cline-any cline-no">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-no">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span> <span class="cline-any cline-neutral">&nbsp;</span></td><td class="text"><pre class="prettyprint lang-js">// SPDX-License-Identifier: GPL-2.0-or-later pragma solidity &gt;=0.5.0; &nbsp; // solhint-disable &nbsp; /// @title Math library for computing sqrt prices from ticks and vice versa /// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports /// prices between 2**-128 and 2**128 library TickMath { /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128 int24 internal constant MIN_TICK = -887272; /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128 int24 internal constant MAX_TICK = -MIN_TICK; &nbsp; /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK) uint160 internal constant MIN_SQRT_RATIO = 4295128739; /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK) uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342; &nbsp; /// @notice Calculates sqrt(1.0001^tick) * 2^96 /// @dev Throws if |tick| &gt; max tick /// @param tick The input tick for the above formula /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0) /// at the given tick <span class="fstat-no" title="function not covered" > function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {</span> <span class="cstat-no" title="statement not covered" > uint256 absTick = tick &lt; 0 ? uint256(-int256(tick)) : uint256(int256(tick));</span> <span class="cstat-no" title="statement not covered" > require(absTick &lt;= uint256(int256(MAX_TICK)), 'T')</span>; &nbsp; <span class="cstat-no" title="statement not covered" > uint256 ratio = absTick &amp; 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x2 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xfff97272373d413259a46990580e213a) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x4 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x8 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x10 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x20 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x40 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x80 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x100 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x200 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x400 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x800 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x1000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x2000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x4000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x8000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x10000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x20000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x40000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) &gt;&gt; 128</span>;</span> <span class="cstat-no" title="statement not covered" > if (absTick &amp; 0x80000 != 0) <span class="cstat-no" title="statement not covered" >ratio = (ratio * 0x48a170391f7dc42444e8fa2) &gt;&gt; 128</span>;</span> &nbsp; <span class="cstat-no" title="statement not covered" > if (tick &gt; 0) <span class="cstat-no" title="statement not covered" >ratio = type(uint256).max / ratio</span>;</span> &nbsp; // Divides by 1&lt;&lt;32 rounding up to go from a Q128.128 to a Q128.96. // we then downcast because we know the result always fits within 160 bits due to our tick input constraint // we round up in the division so getTickAtSqrtRatio of the output price is always consistent <span class="cstat-no" title="statement not covered" > sqrtPriceX96 = uint160((ratio &gt;&gt; 32) + (ratio % (1 &lt;&lt; 32) == 0 ? 0 : 1))</span>; } &nbsp; /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) &lt;= ratio /// @dev Throws in case sqrtPriceX96 &lt; MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may ever return. /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96 /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio <span class="fstat-no" title="function not covered" > function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {</span> // Second inequality must be &lt; because the price can never reach the price at the max tick <span class="cstat-no" title="statement not covered" > require(sqrtPriceX96 &gt;= MIN_SQRT_RATIO &amp;&amp; sqrtPriceX96 &lt; MAX_SQRT_RATIO, 'R')</span>; <span class="cstat-no" title="statement not covered" > uint256 ratio = uint256(sqrtPriceX96) &lt;&lt; 32;</span> &nbsp; <span class="cstat-no" title="statement not covered" > uint256 r = ratio;</span> <span class="cstat-no" title="statement not covered" > uint256 msb = 0;</span> &nbsp; assembly { let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) msb := or(msb, f) r := shr(f, r) } assembly { let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF)) msb := or(msb, f) r := shr(f, r) } assembly { let f := shl(5, gt(r, 0xFFFFFFFF)) msb := or(msb, f) r := shr(f, r) } assembly { let f := shl(4, gt(r, 0xFFFF)) msb := or(msb, f) r := shr(f, r) } assembly { let f := shl(3, gt(r, 0xFF)) msb := or(msb, f) r := shr(f, r) } assembly { let f := shl(2, gt(r, 0xF)) msb := or(msb, f) r := shr(f, r) } assembly { let f := shl(1, gt(r, 0x3)) msb := or(msb, f) r := shr(f, r) } assembly { let f := gt(r, 0x1) msb := or(msb, f) } &nbsp; <span class="cstat-no" title="statement not covered" > if (msb &gt;= 128) <span class="cstat-no" title="statement not covered" >r = ratio &gt;&gt; (msb - 127)</span>;</span> else <span class="cstat-no" title="statement not covered" >r = ratio &lt;&lt; (127 - msb)</span>; &nbsp; <span class="cstat-no" title="statement not covered" > int256 log_2 = (int256(msb) - 128) &lt;&lt; 64;</span> &nbsp; assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(63, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(62, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(61, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(60, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(59, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(58, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(57, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(56, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(55, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(54, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(53, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(52, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(51, f)) r := shr(f, r) } assembly { r := shr(127, mul(r, r)) let f := shr(128, r) log_2 := or(log_2, shl(50, f)) } &nbsp; <span class="cstat-no" title="statement not covered" > int256 log_sqrt10001 = log_2 * 255738958999603826347141;</span> // 128.128 number &nbsp; <span class="cstat-no" title="statement not covered" > int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) &gt;&gt; 128);</span> <span class="cstat-no" title="statement not covered" > int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) &gt;&gt; 128);</span> &nbsp; <span class="cstat-no" title="statement not covered" > tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) &lt;= sqrtPriceX96 ? tickHi : tickLow</span>; } } &nbsp;</pre></td></tr> </table></pre> <div class='push'></div><!-- for sticky footer --> </div><!-- /wrapper --> <div class='footer quiet pad2 space-top1 center small'> Code coverage generated by <a href="http://istanbul-js.org/" target="_blank">istanbul</a> at Fri May 20 2022 12:16:04 GMT+0200 (Central European Summer Time) </div> </div> <script src="../../prettify.js"></script> <script> window.onload = function () { if (typeof prettyPrint === 'function') { prettyPrint(); 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