Tifa's CP Library

:heavy_check_mark: karatsuba (src/code/conv/karatsuba.hpp)

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#ifndef TIFALIBS_CONV_KARATSUBA
#define TIFALIBS_CONV_KARATSUBA

#include "../util/vec_op.hpp"
#include "conv_naive.hpp"

namespace tifa_libs::math {

template <class T>
constexpr vec<T> karatsuba(vec<T> const &a, vec<T> const &b) {
  if (a.empty() && b.empty()) return {};
  if (a.size() < b.size()) return karatsuba(b, a);
  if (a.size() < 32) return conv_naive(a, b);
  u32 d = (u32)a.size() / 2;
  vec<T> al(a.begin(), a.begin() + d), au(a.begin() + d, a.end());
  if (b.size() < d + 10) {
    auto cl = karatsuba(al, b), cu = karatsuba(au, b);
    vec<T> c(a.size() + b.size() - 1);
    for (u32 i = 0; i < cl.size(); ++i) c[i] = cl[i];
    for (u32 i = 0; i < cu.size(); ++i) c[i + d] += cu[i];
    return c;
  }
  vec<T> bl(b.begin(), b.begin() + d), bu(b.begin() + d, b.end());
  vec<T> alu{al}, blu{bl};
  alu += au;
  blu += bu;
  vec<T> cll = karatsuba(al, bl), cuu = karatsuba(au, bu), clu = karatsuba(alu, blu);
  (clu -= cll) -= cuu;
  vec<T> c(d);
  std::ranges::copy(clu, std::back_inserter(c));
  c.resize(a.size() + b.size() - 1);
  c += cll;
  for (u32 i = 0; i < cuu.size(); ++i) c[i + 2 * d] += cuu[i];
  c.resize(a.size() + b.size() - 1);
  return c;
}

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/conv/karatsuba.hpp"



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

#define OO_PTEQ_(op)                                             \
  template <class T>                                             \
  constexpr vec<T> &operator op##=(vec<T> &a, vec<T> const &b) { \
    if (a.size() < b.size()) a.resize(b.size());                 \
    for (usz i = 0; i < b.size(); ++i) a[i] op## = b[i];         \
    return a;                                                    \
  }                                                              \
  template <class T>                                             \
  constexpr vec<T> operator op(vec<T> a, vec<T> const &b) { return a op## = b; }

OO_PTEQ_(+)
OO_PTEQ_(-)
OO_PTEQ_(*)
OO_PTEQ_(/)
OO_PTEQ_(%)
OO_PTEQ_(&)
OO_PTEQ_(|)
OO_PTEQ_(^)
OO_PTEQ_(<<)
OO_PTEQ_(>>)

#undef OO_PTEQ_


#line 1 "src/code/conv/conv_naive.hpp"



#line 5 "src/code/conv/conv_naive.hpp"

namespace tifa_libs::math {

template <class U, class T = U>
requires(sizeof(U) <= sizeof(T))
constexpr vec<T> conv_naive(vec<U> const &l, vec<U> const &r, u32 ans_size = 0) {
  if (l.empty() || r.empty()) return {};
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  u32 n = (u32)l.size(), m = (u32)r.size();
  vec<T> ans(ans_size);
  if (n < m)
    for (u32 j = 0; j < m; ++j)
      for (u32 i = 0; i < n; ++i) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  else
    for (u32 i = 0; i < n; ++i)
      for (u32 j = 0; j < m; ++j) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/conv/karatsuba.hpp"

namespace tifa_libs::math {

template <class T>
constexpr vec<T> karatsuba(vec<T> const &a, vec<T> const &b) {
  if (a.empty() && b.empty()) return {};
  if (a.size() < b.size()) return karatsuba(b, a);
  if (a.size() < 32) return conv_naive(a, b);
  u32 d = (u32)a.size() / 2;
  vec<T> al(a.begin(), a.begin() + d), au(a.begin() + d, a.end());
  if (b.size() < d + 10) {
    auto cl = karatsuba(al, b), cu = karatsuba(au, b);
    vec<T> c(a.size() + b.size() - 1);
    for (u32 i = 0; i < cl.size(); ++i) c[i] = cl[i];
    for (u32 i = 0; i < cu.size(); ++i) c[i + d] += cu[i];
    return c;
  }
  vec<T> bl(b.begin(), b.begin() + d), bu(b.begin() + d, b.end());
  vec<T> alu{al}, blu{bl};
  alu += au;
  blu += bu;
  vec<T> cll = karatsuba(al, bl), cuu = karatsuba(au, bu), clu = karatsuba(alu, blu);
  (clu -= cll) -= cuu;
  vec<T> c(d);
  std::ranges::copy(clu, std::back_inserter(c));
  c.resize(a.size() + b.size() - 1);
  c += cll;
  for (u32 i = 0; i < cuu.size(); ++i) c[i + 2 * d] += cuu[i];
  c.resize(a.size() + b.size() - 1);
  return c;
}

}  // namespace tifa_libs::math


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