floor_sum_polynomial_i64

Function floor_sum_polynomial_i64 

Source
pub fn floor_sum_polynomial_i64<T, const X: usize, const Y: usize>(
    l: i64,
    r: i64,
    a: i64,
    b: i64,
    m: u64,
) -> [[T; Y]; X]
where T: Clone + Zero + One + Add<Output = T> + Mul<Output = T>, AddMulOperation<T>: SemiRing<T = T, Additive: Invertible>,
Expand description

$$\sum_{i=l}^{r-1}i^X\left\lfloor\frac{a\times i+b}{m}\right\rfloor^Y$$

Examples found in repository?
crates/competitive/src/math/floor_sum.rs (line 315)
300pub fn floor_sum_polynomial_i64<T, const X: usize, const Y: usize>(
301    l: i64,
302    r: i64,
303    a: i64,
304    b: i64,
305    m: u64,
306) -> [[T; Y]; X]
307where
308    T: Clone + Zero + One + Add<Output = T> + Mul<Output = T>,
309    AddMulOperation<T>: SemiRing<T = T, Additive: Invertible>,
310{
311    assert!(l <= r);
312    assert!(m > 0);
313
314    if a < 0 {
315        let mut ans = floor_sum_polynomial_i64::<T, X, Y>(-r + 1, -l + 1, -a, b, m);
316        for ans in ans.iter_mut().skip(1).step_by(2) {
317            for ans in ans.iter_mut() {
318                *ans = AddMulOperation::<T>::neg(ans);
319            }
320        }
321        return ans;
322    }
323
324    let add_x = l;
325    let n = (r - l) as u64;
326    let b = a * add_x + b;
327
328    let add_y = b.div_euclid(m as i64);
329    let b = b.rem_euclid(m as i64);
330    assert!(a >= 0);
331    assert!(b >= 0);
332    let data = floor_monoid_product::<FloorSum<AddMulOperation<T>, X, Y>>(
333        FloorSum::<AddMulOperation<T>, X, Y>::to_x(),
334        FloorSum::<AddMulOperation<T>, X, Y>::to_y(),
335        n,
336        a as u64,
337        b as u64,
338        m,
339    );
340
341    let offset = FloorSum::<AddMulOperation<T>, X, Y>::offset(add_x, add_y);
342    FloorSum::<AddMulOperation<T>, X, Y>::operate(&offset, &data).dp
343}