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//! Adds the divisor back to the dividend after a quotient overestimate (Knuth Algorithm D correction step).
use super::KnuthD;
impl KnuthD {
/// Adds `vn[0..n]` to `u[0..n+1]` (Knuth Algorithm D add-back correction).
///
/// Called when the quotient digit was overestimated by 1 and the
/// multiply-subtract produced a negative result. Restores `u` by
/// adding the divisor back. This path is extremely rare in practice
/// (probability ~2/b where b = 2^64).
#[inline]
pub(crate) fn add_back(&self, u: &mut [u64]) {
let mut carry: u64 = 0;
// Range loop is faster than zip+take iterators here (measured ~17% regression).
#[allow(clippy::needless_range_loop)]
for i in 0..self.n {
let sum = (u[i] as u128) + (self.vn[i] as u128) + (carry as u128);
u[i] = sum as u64;
carry = (sum >> 64) as u64;
}
u[self.n] = u[self.n].wrapping_add(carry);
}
}
#[cfg(test)]
mod ai_tests {
use super::*;
/// Adding back after zeroing gives the divisor itself.
#[test]
fn add_back_to_zero() {
let kd = KnuthD::new(&[3, 1u64 << 63, 0, 0], 2);
let mut u = [0u64, 0, 0];
kd.add_back(&mut u);
assert_eq!(u[0], kd.vn[0]);
assert_eq!(u[1], kd.vn[1]);
}
/// Adding back with carry propagation.
#[test]
fn add_back_with_carry() {
let kd = KnuthD::new(&[u64::MAX, 1u64 << 63, 0, 0], 2);
let mut u = [1u64, 0, 0];
kd.add_back(&mut u);
// u[0] = 1 + MAX = 0 (carry 1)
// u[1] = 0 + (1<<63) + 1 = (1<<63) + 1
assert_eq!(u[0], 0);
assert_eq!(u[1], (1u64 << 63) + 1);
}
}