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wmath_primes.hpp
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wmath_primes.hpp
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#ifndef WMATH_PRIMES_H
#define WMATH_PRIMES_H
#include "wmath_forward.hpp"
namespace wmath{
/* depends on a good potentiation with modulus reduction
template <typename T>
typename std::enable_if<std::is_integral<T>::value,bool>::type
miller_rabin(
const T& n,
const T& a
)
{
if (n%2==0) return 0;
auto d = n-1;
// if there was a count trailing zeros intrinsic I'd use that instead
while (d&1u) d>>=1;
const auto r = pow_mod(a,d,n);
return (r==n-1)||(r==1);
}
*/
/* deterministic miller-rabin, probably not worth it
Input: n > 1, an odd integer to be tested for primality
Output: “composite” if n is composite, “prime” otherwise
write n as 2r·d + 1 with d odd (by factoring out powers of 2 from n − 1)
WitnessLoop: for all a in the range [2, min(n−2, ⌊2(ln n)2⌋)]:
x ← ad mod n
if x = 1 or x = n − 1 then
continue WitnessLoop
repeat r − 1 times:
x ← x2 mod n
if x = n − 1 then
continue WitnessLoop
return “composite”
return “prime”
*/
/*
is_prime(const T& n) {
// miller rabin with 2 3 sufficient below 1373653
// miller rabin with 31 73 sufficient below 9080191
// miller rabin with 2 3 5 sufficient below 25326001
// miller rabin with 2 13 23 1662803 below 1122004669633
// miller rabin with 2 3 5 7 11 below 2152302898747
// 2 3 5 7 11 13 17 19 23 29 31 37 below 318'665'857'834'031'151'167'461
}
*/
template <typename T>
typename std::enable_if<std::is_integral<T>::value,bool>::type
constexpr is_prime(const T& n) {
if (n<2) return false;
if (n%2 ==0) return n==2;
if (n%3 ==0) return n==3;
if (n%5 ==0) return n==5;
if (n<49) return true;
const T m = n%30;
switch(m) {
case 1:
case 7:
case 11:
case 13:
case 17:
case 19:
case 23:
case 29:
break;
default:
return false;
}
for (T i=7;i*i<=n;i+=2){
if (n%i==0) return false;
}
return true;
}
template <typename T>
typename std::enable_if<std::is_integral<T>::value,vector<T>>::type
const prime_factorization(const T& n){
if (n<2) return {};
if (n%2 ==0){
T m = n/2;
while (m%2==0) m/=2;
auto v = prime_factorization(m);
v.push_back(2);
return v;
}
if (n%3 ==0){
T m = n/3;
while (m%3==0) m/=3;
auto v = prime_factorization(m);
v.push_back(3);
return v;
}
if (n%5 ==0){
T m = n/5;
while (m%5==0) m/=5;
auto v = prime_factorization(m);
v.push_back(5);
return v;
}
for (size_t k=7,i=1;k*k<=n;){
if (n%k==0){
T m = n/k;
while (m%k==0) m/=k;
auto v = prime_factorization(m);
v.push_back(k);
return v;
}
switch(i){
case 0: k+=6; i=1; break; // 1
case 1: k+=4; i=2; break; // 7
case 2: k+=2; i=3; break; //11
case 3: k+=4; i=4; break; //13
case 4: k+=2; i=5; break; //17
case 5: k+=4; i=6; break; //19
case 6: k+=6; i=7; break; //23
case 7: k+=2; i=0; break; //29
}
}
return {n};
}
template <typename T>
typename std::enable_if<std::is_unsigned<T>::value,T>::type
constexpr largest_prime(const T& i=0);
template <>
uint8_t constexpr largest_prime(const uint8_t& i){
switch (i){
case 0:
return 251;
case 1:
return 241;
case 2:
return 239;
case 3:
return 233;
default:
return 1;
}
}
template <>
uint16_t constexpr largest_prime(const uint16_t& i){
switch (i){
case 0:
return uint16_t(0)-uint16_t(15);
case 1:
return uint16_t(0)-uint16_t(17);
case 2:
return uint16_t(0)-uint16_t(39);
case 3:
return uint16_t(0)-uint16_t(57);
default:
return 1;
}
}
template <>
uint32_t constexpr largest_prime(const uint32_t& i){
switch (i){
case 0:
return uint32_t(0)-uint32_t(5);
case 1:
return uint32_t(0)-uint32_t(17);
case 2:
return uint32_t(0)-uint32_t(65);
case 3:
return uint32_t(0)-uint32_t(99);
default:
return 1;
}
}
template <>
uint64_t constexpr largest_prime(const uint64_t& i){
switch (i){
case 0:
return uint64_t(0)-uint64_t(59);
case 1:
return uint64_t(0)-uint64_t(83);
case 2:
return uint64_t(0)-uint64_t(95);
case 3:
return uint64_t(0)-uint64_t(179);
default:
return 1;
}
}
template <typename T>
typename std::enable_if<std::is_unsigned<T>::value,T>::type
constexpr random_prime(const T& i=0);
template <>
uint8_t constexpr random_prime(const uint8_t& i){
uint8_t primes[] = {127u,
131u,
251u,
223u,
191u,
193u,
47u,
97u};
return primes[i];
}
template <>
uint16_t constexpr random_prime(const uint16_t& i){
uint16_t primes[] = {42307u,
52313u,
51307u,
11317u,
60317u,
60337u,
60037u,
30137u};
return primes[i];
}
template <>
uint32_t constexpr random_prime(const uint32_t& i){
uint32_t primes[] = {4184867191u,
4184864197u,
4184411197u,
3184410197u,
2184200197u,
728033399u,
1061068399u,
3183208117u};
return primes[i];
}
template <>
uint64_t constexpr random_prime(const uint64_t& i){
uint64_t primes[] = {15112557877901478707ul,
18446744073709503907ul,
5819238023569667969ul,
17457704070697003907ul,
14023704271282629773ul,
15457704070697023907ul,
12023704271182029287ul,
10023704271182029357ul,
8023704271998834967ul};
return primes[i];
}
}
#endif // WMATH_PRIMES_H