1//===----------------------------------------------------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8
9#include <__hash_table>
10#include <algorithm>
11#include <stdexcept>
12
13_LIBCPP_CLANG_DIAGNOSTIC_IGNORED("-Wtautological-constant-out-of-range-compare")
14
15_LIBCPP_BEGIN_NAMESPACE_STD
16
17namespace {
18
19// handle all next_prime(i) for i in [1, 210), special case 0
20const unsigned small_primes[] = {
21 0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
22 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
23 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211};
24
25// potential primes = 210*k + indices[i], k >= 1
26// these numbers are not divisible by 2, 3, 5 or 7
27// (or any integer 2 <= j <= 10 for that matter).
28const unsigned indices[] = {
29 1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
30 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139,
31 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209};
32
33// These are the amount we increment by when checking for potential
34// primes in the loop in __next_prime.
35const uint8_t increments[] = {
36 0, 10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2,
37 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10,
38};
39
40} // namespace
41
42// Returns: If n == 0, returns 0. Else returns the lowest prime number that
43// is greater than or equal to n.
44//
45// The algorithm creates a list of small primes, plus an open-ended list of
46// potential primes. All prime numbers are potential prime numbers. However
47// some potential prime numbers are not prime. In an ideal world, all potential
48// prime numbers would be prime. Candidate prime numbers are chosen as the next
49// highest potential prime. Then this number is tested for prime by dividing it
50// by all potential prime numbers less than the sqrt of the candidate.
51//
52// This implementation defines potential primes as those numbers not divisible
53// by 2, 3, 5, and 7. Other (common) implementations define potential primes
54// as those not divisible by 2. A few other implementations define potential
55// primes as those not divisible by 2 or 3. By raising the number of small
56// primes which the potential prime is not divisible by, the set of potential
57// primes more closely approximates the set of prime numbers. And thus there
58// are fewer potential primes to search, and fewer potential primes to divide
59// against.
60
61inline void __check_for_overflow(size_t N) {
62 if constexpr (sizeof(size_t) == 4) {
63 if (N > 0xFFFFFFFB)
64 std::__throw_overflow_error(msg: "__next_prime overflow");
65 } else {
66 if (N > 0xFFFFFFFFFFFFFFC5ull)
67 std::__throw_overflow_error(msg: "__next_prime overflow");
68 }
69}
70
71size_t __next_prime(size_t n) {
72 const size_t L = 210;
73 const size_t N = sizeof(small_primes) / sizeof(small_primes[0]);
74 // If n is small enough, search in small_primes
75 if (n <= small_primes[N - 1])
76 return *std::lower_bound(first: small_primes, last: small_primes + N, value: n);
77 // Else n > largest small_primes
78 // Check for overflow
79 __check_for_overflow(N: n);
80 // Start searching list of potential primes: L * k0 + indices[in]
81 const size_t M = sizeof(indices) / sizeof(indices[0]);
82 // Select first potential prime >= n
83 // Known a-priori n >= L
84 size_t k0 = n / L;
85 size_t in = static_cast<size_t>(std::lower_bound(first: indices, last: indices + M, value: n - k0 * L) - indices);
86 n = L * k0 + indices[in];
87 while (true) {
88 // Divide n by all primes or potential primes (i) until:
89 // 1. The division is even, so try next potential prime.
90 // 2. The i > sqrt(n), in which case n is prime.
91 // It is known a-priori that n is not divisible by 2, 3, 5 or 7,
92 // so don't test those (j == 5 -> divide by 11 first). And the
93 // potential primes start with 211, so don't test against the last
94 // small prime.
95 for (size_t j = 5; j < N - 1; ++j) {
96 const std::size_t p = small_primes[j];
97 const std::size_t q = n / p;
98 if (q < p)
99 return n;
100 if (n == q * p)
101 goto next;
102 }
103 // n wasn't divisible by small primes, try potential primes
104 {
105 size_t i = 211;
106 while (true) {
107 for (auto inc : increments) {
108 i += inc;
109 std::size_t q = n / i;
110 if (q < i)
111 return n;
112 if (n == q * i)
113 goto next;
114 }
115
116 // This will loop i to the next "plane" of potential primes
117 i += 2;
118 }
119 }
120 next:
121 // n is not prime. Increment n to next potential prime.
122 if (++in == M) {
123 ++k0;
124 in = 0;
125 }
126 n = L * k0 + indices[in];
127 }
128}
129
130_LIBCPP_END_NAMESPACE_STD
131