Tifa's CP Library

:heavy_check_mark: jacobi_sym (src/code/nt/jacobi_sym.hpp)

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#ifndef TIFALIBS_MATH_JACOBI_SYM
#define TIFALIBS_MATH_JACOBI_SYM

#include "../util/util.hpp"

namespace tifa_libs::math {

constexpr int jacobi_sym(u64 a, u64 p) {
  assert(p & 1);
  if (!a) return 0;
  int s = 1, _ = 0;
  while (a > 1) {
    if (a == p || !a || p < 2) return 0;
    _ = std::countr_zero(a);
    if (((p - 1) & 7) && ((p + 1) & 7) && (_ & 1)) s = -s;
    if ((a >>= _) == 1) break;
    if ((((p - 1) & 7) * (a - 1)) & 7) s = -s;
    std::swap(a, p %= a);
  }
  return s;
}

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/nt/jacobi_sym.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/nt/jacobi_sym.hpp"

namespace tifa_libs::math {

constexpr int jacobi_sym(u64 a, u64 p) {
  assert(p & 1);
  if (!a) return 0;
  int s = 1, _ = 0;
  while (a > 1) {
    if (a == p || !a || p < 2) return 0;
    _ = std::countr_zero(a);
    if (((p - 1) & 7) && ((p + 1) & 7) && (_ & 1)) s = -s;
    if ((a >>= _) == 1) break;
    if ((((p - 1) & 7) * (a - 1)) & 7) s = -s;
    std::swap(a, p %= a);
  }
  return s;
}

}  // namespace tifa_libs::math


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