library LogPowMath {

    int24 internal constant MIN_POINT = -887272;

    int24 internal constant MAX_POINT = -MIN_POINT;


    uint160 internal constant MIN_SQRT_PRICE = 4295128739;

    uint160 internal constant MAX_SQRT_PRICE = 1461446703485210103287273052203988822378723970342;

    /// @notice sqrt(1.0001^point) in form oy 96-bit fix point num
    function getSqrtPrice(int24 point) internal pure returns (uint160 sqrtPrice_96) {
        uint256 absIdx = point < 0 ? uint256(-int256(point)) : uint256(int256(point));
        require(absIdx <= uint256(int256(MAX_POINT)), 'T');

        uint256 value = absIdx & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
        if (absIdx & 0x2 != 0) value = (value * 0xfff97272373d413259a46990580e213a) >> 128;
        if (absIdx & 0x4 != 0) value = (value * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
        if (absIdx & 0x8 != 0) value = (value * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
        if (absIdx & 0x10 != 0) value = (value * 0xffcb9843d60f6159c9db58835c926644) >> 128;
        if (absIdx & 0x20 != 0) value = (value * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
        if (absIdx & 0x40 != 0) value = (value * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
        if (absIdx & 0x80 != 0) value = (value * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
        if (absIdx & 0x100 != 0) value = (value * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
        if (absIdx & 0x200 != 0) value = (value * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
        if (absIdx & 0x400 != 0) value = (value * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
        if (absIdx & 0x800 != 0) value = (value * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
        if (absIdx & 0x1000 != 0) value = (value * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
        if (absIdx & 0x2000 != 0) value = (value * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
        if (absIdx & 0x4000 != 0) value = (value * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
        if (absIdx & 0x8000 != 0) value = (value * 0x31be135f97d08fd981231505542fcfa6) >> 128;
        if (absIdx & 0x10000 != 0) value = (value * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
        if (absIdx & 0x20000 != 0) value = (value * 0x5d6af8dedb81196699c329225ee604) >> 128;
        if (absIdx & 0x40000 != 0) value = (value * 0x2216e584f5fa1ea926041bedfe98) >> 128;
        if (absIdx & 0x80000 != 0) value = (value * 0x48a170391f7dc42444e8fa2) >> 128;

        if (point > 0) value = type(uint256).max / value;

        sqrtPrice_96 = uint160((value >> 32) + (value % (1 << 32) == 0 ? 0 : 1));
    }

    // floor(log1.0001(sqrtPrice_96))
    function getLogSqrtPriceFloor(uint160 sqrtPrice_96) internal pure returns (int24 logValue) {
        // second inequality must be < because the price can nevex reach the price at the max tick
        require(sqrtPrice_96 >= MIN_SQRT_PRICE && sqrtPrice_96 < MAX_SQRT_PRICE, 'R');
        uint256 sqrtPrice_128 = uint256(sqrtPrice_96) << 32;

        uint256 x = sqrtPrice_128;
        uint256 m = 0;

        assembly {
            let y := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(5, gt(x, 0xFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(4, gt(x, 0xFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(3, gt(x, 0xFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(2, gt(x, 0xF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(1, gt(x, 0x3))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := gt(x, 0x1)
            m := or(m, y)
        }

        if (m >= 128) x = sqrtPrice_128 >> (m - 127);
        else x = sqrtPrice_128 << (127 - m);

        int256 l2 = (int256(m) - 128) << 64;

        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(63, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(62, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(61, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(60, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(59, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(58, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(57, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(56, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(55, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(54, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(53, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(52, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(51, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(50, y))
        }

        int256 ls10001 = l2 * 255738958999603826347141;

        int24 logFloor = int24((ls10001 - 3402992956809132418596140100660247210) >> 128);
        int24 logUpper = int24((ls10001 + 291339464771989622907027621153398088495) >> 128);

        logValue = logFloor == logUpper ? logFloor : getSqrtPrice(logUpper) <= sqrtPrice_96 ? logUpper : logFloor;
    }

    function getLogSqrtPriceFU(uint160 sqrtPrice_96) internal pure returns (int24 logFloor, int24 logUpper) {
        // second inequality must be < because the price can nevex reach the price at the max tick
        require(sqrtPrice_96 >= MIN_SQRT_PRICE && sqrtPrice_96 < MAX_SQRT_PRICE, 'R');
        uint256 sqrtPrice_128 = uint256(sqrtPrice_96) << 32;

        uint256 x = sqrtPrice_128;
        uint256 m = 0;

        assembly {
            let y := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(5, gt(x, 0xFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(4, gt(x, 0xFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(3, gt(x, 0xFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(2, gt(x, 0xF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(1, gt(x, 0x3))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := gt(x, 0x1)
            m := or(m, y)
        }

        if (m >= 128) x = sqrtPrice_128 >> (m - 127);
        else x = sqrtPrice_128 << (127 - m);

        int256 l2 = (int256(m) - 128) << 64;

        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(63, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(62, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(61, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(60, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(59, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(58, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(57, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(56, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(55, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(54, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(53, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(52, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(51, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(50, y))
        }

        int256 ls10001 = l2 * 255738958999603826347141;

        logFloor = int24((ls10001 - 3402992956809132418596140100660247210) >> 128);
        logUpper = int24((ls10001 + 291339464771989622907027621153398088495) >> 128);
    }
}
function getLogSqrtPriceFloor(uint160 sqrtPrice_96) internal pure returns (int24 logValue) {
        // second inequality must be < because the price can nevex reach the price at the max tick
        require(sqrtPrice_96 >= MIN_SQRT_PRICE && sqrtPrice_96 < MAX_SQRT_PRICE, 'R');
        uint256 sqrtPrice_128 = uint256(sqrtPrice_96) << 32;

        uint256 x = sqrtPrice_128;
        uint256 m = 0;

        assembly {
            let y := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(5, gt(x, 0xFFFFFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(4, gt(x, 0xFFFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(3, gt(x, 0xFF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(2, gt(x, 0xF))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := shl(1, gt(x, 0x3))
            m := or(m, y)
            x := shr(y, x)
        }
        assembly {
            let y := gt(x, 0x1)
            m := or(m, y)
        }

        if (m >= 128) x = sqrtPrice_128 >> (m - 127);
        else x = sqrtPrice_128 << (127 - m);

        int256 l2 = (int256(m) - 128) << 64;

        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(63, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(62, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(61, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(60, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(59, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(58, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(57, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(56, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(55, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(54, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(53, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(52, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(51, y))
            x := shr(y, x)
        }
        assembly {
            x := shr(127, mul(x, x))
            let y := shr(128, x)
            l2 := or(l2, shl(50, y))
        }

        int256 ls10001 = l2 * 255738958999603826347141;

        int24 logFloor = int24((ls10001 - 3402992956809132418596140100660247210) >> 128);
        int24 logUpper = int24((ls10001 + 291339464771989622907027621153398088495) >> 128);

        logValue = logFloor == logUpper ? logFloor : getSqrtPrice(logUpper) <= sqrtPrice_96 ? logUpper : logFloor;
    }
// floor(log1.0001(sqrtPrice_96))