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fix: relax the constraints of floor_sum #99

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fix: relax the constraints of floor_sum #99

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38624c9
fix: relax the constraints of floor_sum
nebocco Jun 9, 2022
4e6065b
fmt: cargo clippy
nebocco Jun 10, 2022
ac9ab7e
fmt: clippy
nebocco Jun 13, 2022
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35 changes: 35 additions & 0 deletions src/internal_math.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -235,6 +235,41 @@ pub(crate) fn primitive_root(m: i32) -> i32 {
// omitted
// template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

/// # Arguments
/// * `n` `n < 2^32`
/// * `m` `1 <= m < 2^32`
///
/// # Returns
/// `sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)`
/* const */
#[allow(clippy::many_single_char_names)]
pub(crate) fn floor_sum_unsigned(mut n: u64, mut m: u64, mut a: u64, mut b: u64) -> u64 {
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Let this function take Wrapping<u64> instead of u64 to avoid complication; it's an internal function anyway.

let mut ans = 0;
loop {
if a >= m {
if n > 0 {
ans += n * (n - 1) / 2 * (a / m);
}
a %= m;
}
if b >= m {
ans += n * (b / m);
b %= m;
}

let y_max = a * n + b;
if y_max < m {
break;
}
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = y_max / m;
b = y_max % m;
std::mem::swap(&mut m, &mut a);
}
ans
}

#[cfg(test)]
mod tests {
#![allow(clippy::unreadable_literal)]
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46 changes: 31 additions & 15 deletions src/math.rs
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Expand Up @@ -185,25 +185,22 @@ pub fn crt(r: &[i64], m: &[i64]) -> (i64, i64) {
///
/// assert_eq!(math::floor_sum(6, 5, 4, 3), 13);
/// ```
#[allow(clippy::many_single_char_names)]
pub fn floor_sum(n: i64, m: i64, mut a: i64, mut b: i64) -> i64 {
assert!(0 <= n && n < 1i64 << 32);
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Could you just replace it with something like matches!(n, 0..1 << 32)? This is slightly better than (0..1 << 32).contains(&n) because it does not involve taking a reference to n, which may avoid constant-factor performance degradation.

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Since the implementation of matches! macro seems to be insufficient, it causes error on parsing. Should I replace it with (0..1<<32).contains(&n) ?

% cargo build
   Compiling ac-library-rs v0.1.0 (/home/user/xxx/ac-library-rs)
error: no rules expected the token `<<`
   --> src/math.rs:190:33
    |
190 |     assert!(matches!(n, 0..1i64 << 32));
    |                                 ^^ no rules expected this token in macro call

error: no rules expected the token `<<`
   --> src/math.rs:191:33
    |
191 |     assert!(matches!(m, 1..1i64 << 32));
    |                                 ^^ no rules expected this token in macro call

error: aborting due to 2 previous errors

error: could not compile `ac-library-rs`.

To learn more, run the command again with --verbose.

assert!(1 <= m && m < 1i64 << 32);
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Same here

let mut ans = 0;
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@nebocco nebocco Jun 9, 2022 •
edited
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Since overflows occur in C++ without special handling, they use unsigned long long here to extend the range of values returned correctly; implementing this in Rust would require a lot of casting (as u64) and functions like u64::overflowing_sub. Since this is cumbersome, I've written the internal computation in i64, but this may have led to more cases of overflowing only in the middle of the computation. Which would be better?

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@TonalidadeHidrica TonalidadeHidrica Aug 21, 2022 •
edited by koba-e964
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Why not using wrapping_* variants?

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Let's wrap the variables with std::num::Wrapping<u64>. Note that if you shadow the variables, you need to check if a and b are negative beforehand.

if a >= m {
ans += (n - 1) * n * (a / m) / 2;
a %= m;
}
if b >= m {
ans += n * (b / m);
b %= m;
if a < 0 {
let a2 = internal_math::safe_mod(a, m);
ans -= n * (n - 1) / 2 * ((a2 - a) / m);
a = a2;
}

let y_max = (a * n + b) / m;
let x_max = y_max * m - b;
if y_max == 0 {
return ans;
if b < 0 {
let b2 = internal_math::safe_mod(b, m);
ans -= n * ((b2 - b) / m);
b = b2;
}
ans += (n - (x_max + a - 1) / a) * y_max;
ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
ans
ans + internal_math::floor_sum_unsigned(n as u64, m as u64, a as u64, b as u64) as i64
}

#[cfg(test)]
Expand Down Expand Up @@ -306,5 +303,24 @@ mod tests {
499_999_999_500_000_000
);
assert_eq!(floor_sum(332955, 5590132, 2231, 999423), 22014575);
for n in 0..20 {
for m in 1..20 {
for a in -20..20 {
for b in -20..20 {
assert_eq!(floor_sum(n, m, a, b), floor_sum_naive(n, m, a, b));
}
}
}
}
}

#[allow(clippy::many_single_char_names)]
fn floor_sum_naive(n: i64, m: i64, a: i64, b: i64) -> i64 {
let mut ans = 0;
for i in 0..n {
let z = a * i + b;
ans += (z - internal_math::safe_mod(z, m)) / m;
}
ans
}
}