#[cfg(feature = "no-panic")]

use no_panic::no_panic;

/// Multiply unsigned 128 bit integers, return upper 128 bits of the result

#[inline]

#[cfg_attr(feature = "no-panic", no_panic)]

fn u128_mulhi(x: u128, y: u128) -> u128 {

    let x_lo = x as u64;

    let x_hi = (x >> 64) as u64;

    let y_lo = y as u64;

    let y_hi = (y >> 64) as u64;

    // handle possibility of overflow

    let carry = (x_lo as u128 * y_lo as u128) >> 64;

    let m = x_lo as u128 * y_hi as u128 + carry;

    let high1 = m >> 64;

    let m_lo = m as u64;

    let high2 = (x_hi as u128 * y_lo as u128 + m_lo as u128) >> 64;

    x_hi as u128 * y_hi as u128 + high1 + high2

}

/// Divide `n` by 1e19 and return quotient and remainder

///

/// Integer division algorithm is based on the following paper:

///

///   T. Granlund and P. Montgomery, “Division by Invariant Integers Using Multiplication”

///   in Proc. of the SIGPLAN94 Conference on Programming Language Design and

///   Implementation, 1994, pp. 61–72

///

#[inline]

#[cfg_attr(feature = "no-panic", no_panic)]

pub fn udivmod_1e19(n: u128) -> (u128, u64) {

    let d = 10_000_000_000_000_000_000_u64; // 10^19

    let quot = if n < 1 << 83 {

        ((n >> 19) as u64 / (d >> 19)) as u128

    } else {

        u128_mulhi(n, 156927543384667019095894735580191660403) >> 62

    };

    let rem = (n - quot * d as u128) as u64;

    debug_assert_eq!(quot, n / d as u128);

    debug_assert_eq!(rem as u128, n % d as u128);

    (quot, rem)

}