feat(libraries): add tick and sqrt-price conversion math
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dualfroz committed
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// SPDX-License-Identifier: MIT
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pragma solidity 0.8.36;
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/// @title Conversions between ticks and Q64.96 sqrt prices.
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library TickMath {
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int24 internal constant minTick = -887272;
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int24 internal constant maxTick = 887272;
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uint160 internal constant minSqrtRatio = 4295128739;
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uint160 internal constant maxSqrtRatio = 1461446703485210103287273052203988822378723970342;
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function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
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unchecked {
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uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
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require(absTick <= uint256(int256(maxTick)), "TickMath: TICK");
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uint256 ratio =
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absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
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if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
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if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
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if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
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if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
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if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
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if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
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if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
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if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
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if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
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if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
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if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
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if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
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if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
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if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
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if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
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if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
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if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;
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if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;
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if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;
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if (tick > 0) ratio = type(uint256).max / ratio;
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sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));
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}
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}
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function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {
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unchecked {
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require(sqrtPriceX96 >= minSqrtRatio && sqrtPriceX96 < maxSqrtRatio, "TickMath: RATIO");
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uint256 ratio = uint256(sqrtPriceX96) << 32;
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uint256 r = ratio;
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uint256 msb = 0;
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assembly {
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let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := shl(5, gt(r, 0xFFFFFFFF))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := shl(4, gt(r, 0xFFFF))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := shl(3, gt(r, 0xFF))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := shl(2, gt(r, 0xF))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := shl(1, gt(r, 0x3))
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msb := or(msb, f)
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r := shr(f, r)
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}
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assembly {
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let f := gt(r, 0x1)
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msb := or(msb, f)
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}
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if (msb >= 128) r = ratio >> (msb - 127);
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else r = ratio << (127 - msb);
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int256 log2X64 = (int256(msb) - 128) << 64;
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(63, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(62, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(61, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(60, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(59, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(58, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(57, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(56, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(55, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(54, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(53, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(52, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(51, f))
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r := shr(f, r)
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}
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assembly {
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r := shr(127, mul(r, r))
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let f := shr(128, r)
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log2X64 := or(log2X64, shl(50, f))
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}
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int256 logSqrt10001 = log2X64 * 255738958999603826347141;
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int24 tickLow = int24((logSqrt10001 - 3402992956809132418596140100660247210) >> 128);
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int24 tickHi = int24((logSqrt10001 + 291339464771989622907027621153398088495) >> 128);
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tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow;
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}
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}
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}
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