fix: fixed floor_sum when a < 0 or b < 0.

Author: a1fredbao

src/alfred/math/flat-geometry.hpp

@@ -14,7 +14,7 @@ struct Double {
     static constexpr int sgn(long double x) {
         return (x > eps) - (x < -eps);
     }
-    constexpr long double val(void) const { return val; }
+    // constexpr long double val(void) const { return val; }
     constexpr operator long double(void) const { return val; }
     constexpr bool operator==(const Double &rhs) const { return sgn(val - rhs.val) == 0; }
     constexpr bool operator!=(const Double &rhs) const { return sgn(val - rhs.val) != 0; }

src/alfred/math/floor-sum.hpp

@@ -2,16 +2,30 @@
 #define AFMT_FLOOR_SUM
 
 // Calculate $\sum_{i = 0}^{n - 1} \lfloor \frac{ai + b}{m} \rfloor$ in $O(\min\{a, m, n\})$
-long long floor_sum(
-    long long a, long long b, long long m, long long n
+unsigned long long floor_sum_unsigned(
+    unsigned long long a, unsigned long long b,
+    unsigned long long m, unsigned long long n
 ) {
-    if (a == 0) return b / m * n;
     if (a >= m || b >= m) {
         return (a / m) * (n * (n - 1) / 2) + b / m * n +
-               floor_sum(a % m, b % m, m, n);
+               floor_sum_unsigned(a % m, b % m, m, n);
     }
-    long long mx = (a * (n - 1) + b) / m;
-    return (n - 1) * mx - floor_sum(m, m - b - 1, a, mx);
+    unsigned long long mx = (a * (n - 1) + b) / m;
+    return mx ? (n - 1) * mx - floor_sum_unsigned(m, m - b - 1, a, mx) : 0;
+}
+
+// Calculate $\sum_{i = 0}^{n - 1} \lfloor \frac{ai + b}{m} \rfloor$ in $O(\min\{a, m, n\})$
+long long floor_sum(long long a, long long b, long long m, long long n) {
+    unsigned long long ans = 0;
+    if (a < 0) {
+        unsigned long long a2 = (a % m + m) % m;
+        ans -= 1ull * n * (n - 1) / 2 * ((a2 - a) / m), a = a2;
+    }
+    if (b < 0) {
+        unsigned long long b2 = (b % m + m) % m;
+        ans -= 1ull * n * ((b2 - b) / m), b = b2;
+    }
+    return ans + floor_sum_unsigned(a, b, m, n);
 }
 
 #endif // !AFMT_FLOOR_SUM

src/alfred/math/utils.hpp

@@ -15,16 +15,6 @@ constexpr bool is_prime(T x) {
     return true;
 }
 
-template <class T>
-inline T gcd(T a, T b) {
-    return b == 0 ? a : gcd(b, a % b);
-}
-
-template <class T>
-inline T lcm(T a, T b) {
-    return a / gcd(a, b) * b;
-}
-
 template <class T>
 inline T isqrt(T x) {
     T res = std::sqrt(x);