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///
/// @file imath.hpp
/// @brief Integer math functions
///
/// Copyright (C) 2024 Kim Walisch, <kim.walisch@gmail.com>
///
/// This file is distributed under the BSD License. See the COPYING
/// file in the top level directory.
///
#ifndef IMATH_HPP
#define IMATH_HPP
#include <isqrt.hpp>
#include <int128_t.hpp>
#include <stdint.h>
#include <cmath>
#if __cplusplus >= 202002L
#include <bit>
#endif
#if !defined(__has_builtin)
#define __has_builtin(x) 0
#endif
namespace {
inline uint64_t isquare(uint64_t x)
{
return x * x;
}
template <typename A, typename B>
inline A ceil_div(A a, B b)
{
return (A) ((a + b - 1) / b);
}
/// Next power of 2 >= x
template <typename T>
inline T next_power_of_2(T x)
{
#if __cplusplus >= 202002L
using UT = typename pstd::make_unsigned<T>::type;
return std::bit_ceil((UT) x);
#elif __has_builtin(__builtin_clzll)
if (x == 0 || x == 1)
return 1;
static_assert(sizeof(T) <= sizeof(unsigned long long), "Unsupported type, wider than long long!");
auto bits = pstd::numeric_limits<unsigned long long>::digits;
auto shift = bits - __builtin_clzll(x - 1);
return (T) (1ull << shift);
#else
if (x == 0)
return 1;
x--;
using UT = typename pstd::make_unsigned<T>::type;
T bits = pstd::numeric_limits<UT>::digits;
for (T i = 1; i < bits; i += i)
x |= (x >> i);
return ++x;
#endif
}
template <typename T>
inline int ilog(T x)
{
return (int) std::log((double) x);
}
template <typename T>
inline T ilog2(T x)
{
#if __cplusplus >= 202002L
using UT = typename pstd::make_unsigned<T>::type;
auto ux = (UT) x;
ux = (ux > 0) ? ux : 1;
return std::bit_width(ux) - 1;
#elif __has_builtin(__builtin_clzll)
static_assert(sizeof(T) <= sizeof(unsigned long long), "Unsupported type, wider than long long!");
auto bits = pstd::numeric_limits<unsigned long long>::digits;
// Workaround to avoid undefined behavior,
// __builtin_clz(0) is undefined.
x = (x > 0) ? x : 1;
return (T) ((bits - 1) - __builtin_clzll(x));
#else
using UT = typename pstd::make_unsigned<T>::type;
T bits = pstd::numeric_limits<UT>::digits;
T log2 = 0;
for (T i = bits / 2; i > 0; i /= 2)
{
T one = 1;
if (x >= (one << i))
{
x >>= i;
log2 += i;
}
}
return log2;
#endif
}
/// Exponentiation by squaring using template metaprogramming.
/// This code will generate optimal assembly that will be
/// inlined in the calling function. E.g. ipow<16>(x) will
/// generate log2(16) = 4 multiply instructions.
///
template <typename T, int EXP>
struct ipow_helper
{
static T ipow(T x)
{
if (EXP % 2)
return ipow_helper<T, EXP - 1>::ipow(x) * x;
else
{
T res = ipow_helper<T, EXP / 2>::ipow(x);
return res * res;
}
}
};
template <typename T>
struct ipow_helper<T, 0>
{
static T ipow(T)
{
return 1;
}
};
template <int EXP, typename T>
inline T ipow(T base)
{
return ipow_helper<T, EXP>::ipow(base);
}
/// Integer nth root
template <int N, typename T>
inline T iroot(T x)
{
T r;
if (N == 3)
r = (T) std::cbrt((double) x);
else if (N == 4)
r = (T) std::sqrt(std::sqrt((double) x));
else
r = (T) std::pow((double) x, 1.0 / N);
// fix root too large
for (; r > 0; r--)
if (ipow<N - 1>(r) <= x / r)
break;
// fix root too small
while (ipow<N - 1>(r + 1) <= x / (r + 1))
r += 1;
return r;
}
} // namespace
#endif
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