1#[cfg(feature = "no-panic")]
2use no_panic::no_panic;
3
4/// Multiply unsigned 128 bit integers, return upper 128 bits of the result
5#[inline]
6#[cfg_attr(feature = "no-panic", no_panic)]
7fn u128_mulhi(x: u128, y: u128) -> u128 {
8 let x_lo = x as u64;
9 let x_hi = (x >> 64) as u64;
10 let y_lo = y as u64;
11 let y_hi = (y >> 64) as u64;
12
13 // handle possibility of overflow
14 let carry = (x_lo as u128 * y_lo as u128) >> 64;
15 let m = x_lo as u128 * y_hi as u128 + carry;
16 let high1 = m >> 64;
17
18 let m_lo = m as u64;
19 let high2 = (x_hi as u128 * y_lo as u128 + m_lo as u128) >> 64;
20
21 x_hi as u128 * y_hi as u128 + high1 + high2
22}
23
24/// Divide `n` by 1e19 and return quotient and remainder
25///
26/// Integer division algorithm is based on the following paper:
27///
28/// T. Granlund and P. Montgomery, “Division by Invariant Integers Using Multiplication”
29/// in Proc. of the SIGPLAN94 Conference on Programming Language Design and
30/// Implementation, 1994, pp. 61–72
31///
32#[inline]
33#[cfg_attr(feature = "no-panic", no_panic)]
34pub fn udivmod_1e19(n: u128) -> (u128, u64) {
35 let d = 10_000_000_000_000_000_000_u64; // 10^19
36
37 let quot = if n < 1 << 83 {
38 ((n >> 19) as u64 / (d >> 19)) as u128
39 } else {
40 u128_mulhi(n, 156927543384667019095894735580191660403) >> 62
41 };
42
43 let rem = (n - quot * d as u128) as u64;
44 debug_assert_eq!(quot, n / d as u128);
45 debug_assert_eq!(rem as u128, n % d as u128);
46
47 (quot, rem)
48}
49