hash.cpp

//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include <__hash_table>
#include <algorithm>
#include <stdexcept>

_LIBCPP_CLANG_DIAGNOSTIC_IGNORED("-Wtautological-constant-out-of-range-compare")

_LIBCPP_BEGIN_NAMESPACE_STD

namespace {

// handle all next_prime(i) for i in [1, 210), special case 0
const unsigned small_primes[] = {
    0,   2,   3,   5,   7,   11,  13,  17,  19,  23,  29,  31,  37,  41,  43,  47,
    53,  59,  61,  67,  71,  73,  79,  83,  89,  97,  101, 103, 107, 109, 113, 127,
    131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211};

// potential primes = 210*k + indices[i], k >= 1
//   these numbers are not divisible by 2, 3, 5 or 7
//   (or any integer 2 <= j <= 10 for that matter).
const unsigned indices[] = {
    1,   11,  13,  17,  19,  23,  29,  31,  37,  41,  43,  47,  53,  59,  61,  67,
    71,  73,  79,  83,  89,  97,  101, 103, 107, 109, 113, 121, 127, 131, 137, 139,
    143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209};

} // namespace

// Returns:  If n == 0, returns 0.  Else returns the lowest prime number that
// is greater than or equal to n.
//
// The algorithm creates a list of small primes, plus an open-ended list of
// potential primes.  All prime numbers are potential prime numbers.  However
// some potential prime numbers are not prime.  In an ideal world, all potential
// prime numbers would be prime.  Candidate prime numbers are chosen as the next
// highest potential prime.  Then this number is tested for prime by dividing it
// by all potential prime numbers less than the sqrt of the candidate.
//
// This implementation defines potential primes as those numbers not divisible
// by 2, 3, 5, and 7.  Other (common) implementations define potential primes
// as those not divisible by 2.  A few other implementations define potential
// primes as those not divisible by 2 or 3.  By raising the number of small
// primes which the potential prime is not divisible by, the set of potential
// primes more closely approximates the set of prime numbers.  And thus there
// are fewer potential primes to search, and fewer potential primes to divide
// against.

inline void __check_for_overflow(size_t N) {
  if constexpr (sizeof(size_t) == 4) {
    if (N > 0xFFFFFFFB)
      std::__throw_overflow_error("__next_prime overflow");
  } else {
    if (N > 0xFFFFFFFFFFFFFFC5ull)
      std::__throw_overflow_error("__next_prime overflow");
  }
}

size_t __next_prime(size_t n) {
  const size_t L = 210;
  const size_t N = sizeof(small_primes) / sizeof(small_primes[0]);
  // If n is small enough, search in small_primes
  if (n <= small_primes[N - 1])
    return *std::lower_bound(small_primes, small_primes + N, n);
  // Else n > largest small_primes
  // Check for overflow
  __check_for_overflow(n);
  // Start searching list of potential primes: L * k0 + indices[in]
  const size_t M = sizeof(indices) / sizeof(indices[0]);
  // Select first potential prime >= n
  //   Known a-priori n >= L
  size_t k0 = n / L;
  size_t in = static_cast<size_t>(std::lower_bound(indices, indices + M, n - k0 * L) - indices);
  n         = L * k0 + indices[in];
  while (true) {
    // Divide n by all primes or potential primes (i) until:
    //    1.  The division is even, so try next potential prime.
    //    2.  The i > sqrt(n), in which case n is prime.
    // It is known a-priori that n is not divisible by 2, 3, 5 or 7,
    //    so don't test those (j == 5 ->  divide by 11 first).  And the
    //    potential primes start with 211, so don't test against the last
    //    small prime.
    for (size_t j = 5; j < N - 1; ++j) {
      const std::size_t p = small_primes[j];
      const std::size_t q = n / p;
      if (q < p)
        return n;
      if (n == q * p)
        goto next;
    }
    // n wasn't divisible by small primes, try potential primes
    {
      size_t i = 211;
      while (true) {
        std::size_t q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 10;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 8;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 8;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 6;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 4;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 2;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        i += 10;
        q = n / i;
        if (q < i)
          return n;
        if (n == q * i)
          break;

        // This will loop i to the next "plane" of potential primes
        i += 2;
      }
    }
  next:
    // n is not prime.  Increment n to next potential prime.
    if (++in == M) {
      ++k0;
      in = 0;
    }
    n = L * k0 + indices[in];
  }
}

_LIBCPP_END_NAMESPACE_STD