I need to check is some integer prime in compile time (to put the boolean value as template argument).

I've write code that do it well:

```
#include <type_traits>
namespace impl {
template <int n, long long i>
struct PrimeChecker {
typedef typename std::conditional<
(i * i > n),
std::true_type,
typename std::conditional<
n % i == 0,
std::false_type,
typename PrimeChecker<n, (i * i > n ) ? -1 : i + 1>::type
>::type
>::type type;
};
template <int n>
struct PrimeChecker<n, -1> {
typedef void type;
};
} // namespace impl
template<int n>
struct IsPrime {
typedef typename impl::PrimeChecker<n, 2>::type type;
};
template<>
struct IsPrime<1> : public std::false_type {
};
```

It works for numbers to ~1000000 and fails with error for 10^{9}

```
prog.cpp:15:23: error: template instantiation depth exceeds maximum of 900 (use -ftemplate-depth= to increase the maximum) instantiating ‘struct impl::PrimeChecker<1000000000, 901ll>’
>::type type;
^
prog.cpp:15:23: recursively required from ‘struct impl::PrimeChecker<1000000000, 3ll>’
prog.cpp:15:23: required from ‘struct impl::PrimeChecker<1000000000, 2ll>’
prog.cpp:24:54: required from ‘struct IsPrime<1000000000>’
prog.cpp:32:41: required from here
```

I can't increase the depth limit. Is it somehow possible to decrease depth I use?

**Thing I want to achive**: I need to check is constant prime in compile time **without changing compilation string** with template depth limit 900 and `constexpr`

depth limit 512. (default for my g++). It should work for all positive int32's or at least for numbers up to 10^{9}+9

You can change the space requirement from linear to logarithmic by splitting the range by halves using a divide-and-conquer algorithm. This method uses divide-and-conquer, and only tests odd factors (Live at Coliru):

```
namespace detail {
using std::size_t;
constexpr size_t mid(size_t low, size_t high) {
return (low + high) / 2;
}
// precondition: low*low <= n, high*high > n.
constexpr size_t ceilsqrt(size_t n, size_t low, size_t high) {
return low + 1 >= high
? high
: (mid(low, high) * mid(low, high) == n)
? mid(low, high)
: (mid(low, high) * mid(low, high) < n)
? ceilsqrt(n, mid(low, high), high)
: ceilsqrt(n, low, mid(low, high));
}
// returns ceiling(sqrt(n))
constexpr size_t ceilsqrt(size_t n) {
return n < 3
? n
: ceilsqrt(n, 1, size_t(1) << (std::numeric_limits<size_t>::digits / 2));
}
// returns true if n is divisible by an odd integer in
// [2 * low + 1, 2 * high + 1).
constexpr bool find_factor(size_t n, size_t low, size_t high)
{
return low + 1 >= high
? (n % (2 * low + 1)) == 0
: (find_factor(n, low, mid(low, high))
|| find_factor(n, mid(low, high), high));
}
}
constexpr bool is_prime(std::size_t n)
{
using detail::find_factor;
using detail::ceilsqrt;
return n > 1
&& (n == 2
|| (n % 2 == 1
&& (n == 3
|| !find_factor(n, 1, (ceilsqrt(n) + 1) / 2))));
}
```

EDIT: Use compile-time sqrt to bound search space to ceiling(sqrt(n)), instead of n / 2. Now can compute `is_prime(100000007)`

as desired (and `is_prime(1000000000039ULL)`

for that matter) on Coliru without exploding.

Apologies for the horrible formatting, I still haven't found a comfortable style for C++11's tortured `constexpr`

sub-language.

EDIT: Cleanup code: replace macro with another function, move implementation detail into a detail namespace, steal indentation style from Pablo's answer.