fix #149: improve barret algorithm

Author: yosupo06

atcoder/internal_math.hpp

@@ -26,7 +26,7 @@ struct barrett {
     unsigned int _m;
     unsigned long long im;
 
-    // @param m `1 <= m < 2^31`
+    // @param m `1 <= m`
     explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
 
     // @return m
@@ -55,9 +55,8 @@ struct barrett {
         unsigned long long x =
             (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
 #endif
-        unsigned int v = (unsigned int)(z - x * _m);
-        if (_m <= v) v += _m;
-        return v;
+        unsigned long long y = x * _m;
+        return (unsigned int)(z - y + (z < y ? _m : 0));
     }
 };
 

test/unittest/internal_math_test.cpp

@@ -56,7 +56,7 @@ TEST(InternalMathTest, Barrett) {
     ASSERT_EQ(0, bt.mul(0, 0));
 }
 
-TEST(InternalMathTest, BarrettBorder) {
+TEST(InternalMathTest, BarrettIntBorder) {
     const int mod_upper = std::numeric_limits<int>::max();
     for (unsigned int mod = mod_upper; mod >= mod_upper - 20; mod--) {
         internal::barrett bt(mod);
@@ -78,6 +78,28 @@ TEST(InternalMathTest, BarrettBorder) {
     }
 }
 
+TEST(InternalMathTest, BarrettUintBorder) {
+    const unsigned int mod_upper = std::numeric_limits<unsigned int>::max();
+    for (unsigned int mod = mod_upper; mod >= mod_upper - 20; mod--) {
+        internal::barrett bt(mod);
+        std::vector<unsigned int> v;
+        for (int i = 0; i < 10; i++) {
+            v.push_back(i);
+            v.push_back(mod - i);
+            v.push_back(mod / 2 + i);
+            v.push_back(mod / 2 - i);
+        }
+        for (auto a : v) {
+            ull a2 = a;
+            ASSERT_EQ(((a2 * a2) % mod * a2) % mod, bt.mul(a, bt.mul(a, a)));
+            for (auto b : v) {
+                ull b2 = b;
+                ASSERT_EQ((a2 * b2) % mod, bt.mul(a, b));
+            }
+        }
+    }
+}
+
 TEST(InternalMathTest, IsPrime) {
     ASSERT_FALSE(internal::is_prime<121>);
     ASSERT_FALSE(internal::is_prime<11 * 13>);