rpcs3/Utilities/types.h

#pragma once

#ifdef _MSC_VER
#include <intrin.h>
#else
#include <x86intrin.h>
#endif
#include <immintrin.h>
#include <emmintrin.h>

#include <cstdint>
#include <cstddef>
#include <cstring>
#include <type_traits>
#include <utility>
#include <chrono>
#include <limits>
#include <array>

// Assume little-endian
#define IS_LE_MACHINE 1
#define IS_BE_MACHINE 0

#ifndef __has_builtin
	#define __has_builtin(x) 0
#endif

#ifdef _MSC_VER

#define ASSUME(...) __assume(__VA_ARGS__) // MSVC __assume ignores side-effects
#define LIKELY
#define UNLIKELY
#define SAFE_BUFFERS __declspec(safebuffers)
#define NEVER_INLINE __declspec(noinline)
#define FORCE_INLINE __forceinline
#define RESTRICT __restrict

#else // not _MSC_VER

#ifdef __clang__
#if defined(__has_builtin) && __has_builtin(__builtin_assume)
#pragma clang diagnostic ignored "-Wassume" // ignore the clang "side-effects ignored" warning
#define ASSUME(...) __builtin_assume(!!(__VA_ARGS__)) // __builtin_assume (supported by modern clang) ignores side-effects
#endif
#endif

#ifndef ASSUME // gcc and old clang
#define ASSUME(...) do { if (!(__VA_ARGS__)) __builtin_unreachable(); } while (0)  // note: the compiler will generate code to evaluate "cond" if the expression is opaque
#endif

#define LIKELY(...) __builtin_expect(!!(__VA_ARGS__), 1)
#define UNLIKELY(...) __builtin_expect(!!(__VA_ARGS__), 0)
#define SAFE_BUFFERS
#define NEVER_INLINE __attribute__((noinline))
#define FORCE_INLINE __attribute__((always_inline)) inline
#define RESTRICT __restrict__

#endif // _MSC_VER

#define CHECK_SIZE(type, size) static_assert(sizeof(type) == size, "Invalid " #type " type size")
#define CHECK_ALIGN(type, align) static_assert(alignof(type) == align, "Invalid " #type " type alignment")
#define CHECK_MAX_SIZE(type, size) static_assert(sizeof(type) <= size, #type " type size is too big")
#define CHECK_SIZE_ALIGN(type, size, align) CHECK_SIZE(type, size); CHECK_ALIGN(type, align)

// Variant pattern matching helper
#define MATCH(arg, ...) constexpr(std::is_same_v<std::decay_t<decltype(arg)>, __VA_ARGS__>)

#define CONCATENATE_DETAIL(x, y) x ## y
#define CONCATENATE(x, y) CONCATENATE_DETAIL(x, y)

#define STRINGIZE_DETAIL(x) #x ""
#define STRINGIZE(x) STRINGIZE_DETAIL(x)

#define HERE "\n(in file " __FILE__ ":" STRINGIZE(__LINE__) ")"

#define DECLARE(...) decltype(__VA_ARGS__) __VA_ARGS__

#define STR_CASE(...) case __VA_ARGS__: return #__VA_ARGS__


#define ASSERT(...) do { if(!(__VA_ARGS__)) fmt::raw_error("Assertion failed: " STRINGIZE(__VA_ARGS__) HERE); } while(0)

#if defined(_DEBUG) || defined(_AUDIT)
#define AUDIT(...) ASSERT(__VA_ARGS__)
#else
#define AUDIT(...) ((void)0)
#endif

#if defined(__cpp_lib_bit_cast) && (__cpp_lib_bit_cast >= 201806L)
#include <bit>
#else
namespace std
{
	template <class To, class From, typename = std::enable_if_t<sizeof(To) == sizeof(From)>>
	constexpr To bit_cast(const From& from) noexcept
	{
		static_assert(sizeof(To) == sizeof(From), "std::bit_cast<>: incompatible type size");

		To result;
		std::memcpy(&result, &from, sizeof(From));
		return result;
	}
}
#endif

using schar  = signed char;
using uchar  = unsigned char;
using ushort = unsigned short;
using uint   = unsigned int;
using ulong  = unsigned long;
using ullong = unsigned long long;
using llong  = long long;

#if __APPLE__
using uptr = std::uint64_t;
#else
using uptr = std::uintptr_t;
#endif

using u8  = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;

using s8  = std::int8_t;
using s16 = std::int16_t;
using s32 = std::int32_t;
using s64 = std::int64_t;

using steady_clock = std::conditional<
    std::chrono::high_resolution_clock::is_steady,
    std::chrono::high_resolution_clock, std::chrono::steady_clock>::type;

// Get unsigned integral type from type size
template<size_t N>
struct get_int_impl
{
};

template<>
struct get_int_impl<sizeof(u8)>
{
    using type = u8;
};

template<>
struct get_int_impl<sizeof(u16)>
{
    using type = u16;
};

template<>
struct get_int_impl<sizeof(u32)>
{
    using type = u32;
};

template<>
struct get_int_impl<sizeof(u64)>
{
    using type = u64;
};

template <size_t N>
using get_int_t = typename get_int_impl<N>::type;

namespace gsl
{
	using std::byte;
}

// Formatting helper, type-specific preprocessing for improving safety and functionality
template <typename T, typename = void>
struct fmt_unveil;

template <typename Arg>
using fmt_unveil_t = typename fmt_unveil<Arg>::type;

struct fmt_type_info;

namespace fmt
{
	template <typename... Args>
	const fmt_type_info* get_type_info();
}

template <typename T, std::size_t Align = alignof(T), std::size_t Size = sizeof(T)>
struct se_storage;

template <typename T, bool Se = true, std::size_t Align = alignof(T)>
class se_t;

template <typename T>
class atomic_t;

// Extract T::simple_type if available, remove cv qualifiers
template <typename T, typename = void>
struct simple_type_helper
{
	using type = typename std::remove_cv<T>::type;
};

template <typename T>
struct simple_type_helper<T, std::void_t<typename T::simple_type>>
{
	using type = typename T::simple_type;
};

template <typename T>
using simple_t = typename simple_type_helper<T>::type;

// Bool type equivalent
class b8
{
	u8 m_value;

public:
	b8() = default;

	constexpr b8(bool value)
		: m_value(value)
	{
	}

	constexpr operator bool() const
	{
		return m_value != 0;
	}
};

#ifndef _MSC_VER
using u128 = __uint128_t;
using s128 = __int128_t;
#else

// Unsigned 128-bit integer implementation (TODO)
struct alignas(16) u128
{
	u64 lo, hi;

	u128() = default;

	constexpr u128(u64 l)
		: lo(l)
		, hi(0)
	{
	}

	friend u128 operator+(const u128& l, const u128& r)
	{
		u128 value;
		_addcarry_u64(_addcarry_u64(0, r.lo, l.lo, &value.lo), r.hi, l.hi, &value.hi);
		return value;
	}

	friend u128 operator+(const u128& l, u64 r)
	{
		u128 value;
		_addcarry_u64(_addcarry_u64(0, r, l.lo, &value.lo), l.hi, 0, &value.hi);
		return value;
	}

	friend u128 operator+(u64 l, const u128& r)
	{
		u128 value;
		_addcarry_u64(_addcarry_u64(0, r.lo, l, &value.lo), 0, r.hi, &value.hi);
		return value;
	}

	friend u128 operator-(const u128& l, const u128& r)
	{
		u128 value;
		_subborrow_u64(_subborrow_u64(0, r.lo, l.lo, &value.lo), r.hi, l.hi, &value.hi);
		return value;
	}

	friend u128 operator-(const u128& l, u64 r)
	{
		u128 value;
		_subborrow_u64(_subborrow_u64(0, r, l.lo, &value.lo), 0, l.hi, &value.hi);
		return value;
	}

	friend u128 operator-(u64 l, const u128& r)
	{
		u128 value;
		_subborrow_u64(_subborrow_u64(0, r.lo, l, &value.lo), r.hi, 0, &value.hi);
		return value;
	}

	u128 operator+() const
	{
		return *this;
	}

	u128 operator-() const
	{
		u128 value;
		_subborrow_u64(_subborrow_u64(0, lo, 0, &value.lo), hi, 0, &value.hi);
		return value;
	}

	u128& operator++()
	{
		_addcarry_u64(_addcarry_u64(0, 1, lo, &lo), 0, hi, &hi);
		return *this;
	}

	u128 operator++(int)
	{
		u128 value = *this;
		_addcarry_u64(_addcarry_u64(0, 1, lo, &lo), 0, hi, &hi);
		return value;
	}

	u128& operator--()
	{
		_subborrow_u64(_subborrow_u64(0, 1, lo, &lo), 0, hi, &hi);
		return *this;
	}

	u128 operator--(int)
	{
		u128 value = *this;
		_subborrow_u64(_subborrow_u64(0, 1, lo, &lo), 0, hi, &hi);
		return value;
	}

	u128 operator~() const
	{
		u128 value;
		value.lo = ~lo;
		value.hi = ~hi;
		return value;
	}

	friend u128 operator&(const u128& l, const u128& r)
	{
		u128 value;
		value.lo = l.lo & r.lo;
		value.hi = l.hi & r.hi;
		return value;
	}

	friend u128 operator|(const u128& l, const u128& r)
	{
		u128 value;
		value.lo = l.lo | r.lo;
		value.hi = l.hi | r.hi;
		return value;
	}

	friend u128 operator^(const u128& l, const u128& r)
	{
		u128 value;
		value.lo = l.lo ^ r.lo;
		value.hi = l.hi ^ r.hi;
		return value;
	}

	u128& operator+=(const u128& r)
	{
		_addcarry_u64(_addcarry_u64(0, r.lo, lo, &lo), r.hi, hi, &hi);
		return *this;
	}

	u128& operator+=(uint64_t r)
	{
		_addcarry_u64(_addcarry_u64(0, r, lo, &lo), 0, hi, &hi);
		return *this;
	}

	u128& operator&=(const u128& r)
	{
		lo &= r.lo;
		hi &= r.hi;
		return *this;
	}

	u128& operator|=(const u128& r)
	{
		lo |= r.lo;
		hi |= r.hi;
		return *this;
	}

	u128& operator^=(const u128& r)
	{
		lo ^= r.lo;
		hi ^= r.hi;
		return *this;
	}
};

// Signed 128-bit integer implementation (TODO)
struct alignas(16) s128
{
	u64 lo;
	s64 hi;

	s128() = default;

	constexpr s128(s64 l)
		: hi(l >> 63)
		, lo(l)
	{
	}

	constexpr s128(u64 l)
		: hi(0)
		, lo(l)
	{
	}
};
#endif

CHECK_SIZE_ALIGN(u128, 16, 16);
CHECK_SIZE_ALIGN(s128, 16, 16);

using f32 = float;
using f64 = double;

union alignas(2) f16
{
	u16 _u16;
	u8 _u8[2];

	explicit f16(u16 raw)
	{
		_u16 = raw;
	}

	explicit operator f32() const
	{
		// See http://stackoverflow.com/a/26779139
		// The conversion doesn't handle NaN/Inf
		u32 raw = ((_u16 & 0x8000) << 16) |             // Sign (just moved)
		          (((_u16 & 0x7c00) + 0x1C000) << 13) | // Exponent ( exp - 15 + 127)
		          ((_u16 & 0x03FF) << 13);              // Mantissa

		return std::bit_cast<f32>(raw);
	}
};

CHECK_SIZE_ALIGN(f16, 2, 2);

template <typename T, typename = std::enable_if_t<std::is_integral<T>::value>>
constexpr T align(const T& value, ullong align)
{
	return static_cast<T>((value + (align - 1)) & ~(align - 1));
}

template <typename T, typename T2>
inline u32 offset32(T T2::*const mptr)
{
#ifdef _MSC_VER
	return std::bit_cast<u32>(mptr);
#elif __GNUG__
	return std::bit_cast<std::size_t>(mptr);
#else
	static_assert(sizeof(mptr) == 0, "Unsupported pointer-to-member size");
#endif
}

template <typename T>
struct offset32_array
{
	static_assert(std::is_array<T>::value, "Invalid pointer-to-member type (array expected)");

	template <typename Arg>
	static inline u32 index32(const Arg& arg)
	{
		return u32{sizeof(std::remove_extent_t<T>)} * static_cast<u32>(arg);
	}
};

template <typename T, std::size_t N>
struct offset32_array<std::array<T, N>>
{
	template <typename Arg>
	static inline u32 index32(const Arg& arg)
	{
		return u32{sizeof(T)} * static_cast<u32>(arg);
	}
};

template <typename Arg>
struct offset32_detail;

template <typename T, typename T2, typename Arg, typename... Args>
inline u32 offset32(T T2::*const mptr, const Arg& arg, const Args&... args)
{
	return offset32_detail<Arg>::offset32(mptr, arg, args...);
}

template <typename Arg>
struct offset32_detail
{
	template <typename T, typename T2, typename... Args>
	static inline u32 offset32(T T2::*const mptr, const Arg& arg, const Args&... args)
	{
		return ::offset32(mptr, args...) + offset32_array<T>::index32(arg);
	}
};

template <typename T3, typename T4>
struct offset32_detail<T3 T4::*>
{
	template <typename T, typename T2, typename... Args>
	static inline u32 offset32(T T2::*const mptr, T3 T4::*const mptr2, const Args&... args)
	{
		return ::offset32(mptr) + ::offset32(mptr2, args...);
	}
};

// Helper function, used by ""_u16, ""_u32, ""_u64
constexpr u8 to_u8(char c)
{
	return static_cast<u8>(c);
}

// Convert 2-byte string to u16 value like reinterpret_cast does
constexpr u16 operator""_u16(const char* s, std::size_t length)
{
	return length != 2 ? throw s :
#if IS_LE_MACHINE == 1
		to_u8(s[1]) << 8 | to_u8(s[0]);
#endif
}

// Convert 4-byte string to u32 value like reinterpret_cast does
constexpr u32 operator""_u32(const char* s, std::size_t length)
{
	return length != 4 ? throw s :
#if IS_LE_MACHINE == 1
		to_u8(s[3]) << 24 | to_u8(s[2]) << 16 | to_u8(s[1]) << 8 | to_u8(s[0]);
#endif
}

// Convert 8-byte string to u64 value like reinterpret_cast does
constexpr u64 operator""_u64(const char* s, std::size_t length)
{
	return length != 8 ? throw s :
#if IS_LE_MACHINE == 1
		static_cast<u64>(to_u8(s[7]) << 24 | to_u8(s[6]) << 16 | to_u8(s[5]) << 8 | to_u8(s[4])) << 32 | to_u8(s[3]) << 24 | to_u8(s[2]) << 16 | to_u8(s[1]) << 8 | to_u8(s[0]);
#endif
}

namespace fmt
{
	[[noreturn]] void raw_error(const char* msg);
	[[noreturn]] void raw_verify_error(const char* msg, const fmt_type_info* sup, u64 arg);
	[[noreturn]] void raw_narrow_error(const char* msg, const fmt_type_info* sup, u64 arg);
}

struct verify_func
{
	template <typename T>
	bool operator()(T&& value) const
	{
		if (std::forward<T>(value))
		{
			return true;
		}

		return false;
	}
};

template <uint N>
struct verify_impl
{
	const char* cause;

	template <typename T>
	auto operator,(T&& value) const
	{
		// Verification (can be safely disabled)
		if (!verify_func()(std::forward<T>(value)))
		{
			fmt::raw_verify_error(cause, nullptr, N);
		}

		return verify_impl<N + 1>{cause};
	}
};

// Verification helper, checks several conditions delimited with comma operator
inline auto verify(const char* cause)
{
	return verify_impl<0>{cause};
}

// Verification helper (returns value or lvalue reference, may require to use verify_move instead)
template <typename F = verify_func, typename T>
inline T verify(const char* cause, T&& value, F&& pred = F())
{
	if (!pred(std::forward<T>(value)))
	{
		using unref = std::remove_const_t<std::remove_reference_t<T>>;
		fmt::raw_verify_error(cause, fmt::get_type_info<fmt_unveil_t<unref>>(), fmt_unveil<unref>::get(value));
	}

	return std::forward<T>(value);
}

// Verification helper (must be used in return expression or in place of std::move)
template <typename F = verify_func, typename T>
inline std::remove_reference_t<T>&& verify_move(const char* cause, T&& value, F&& pred = F())
{
	if (!pred(std::forward<T>(value)))
	{
		using unref = std::remove_const_t<std::remove_reference_t<T>>;
		fmt::raw_verify_error(cause, fmt::get_type_info<fmt_unveil_t<unref>>(), fmt_unveil<unref>::get(value));
	}

	return std::move(value);
}

// narrow() function details
template <typename From, typename To = void, typename = void>
struct narrow_impl
{
	// Temporarily (diagnostic)
	static_assert(std::is_void<To>::value, "narrow_impl<> specialization not found");

	// Returns true if value cannot be represented in type To
	static constexpr bool test(const From& value)
	{
		// Unspecialized cases (including cast to void) always considered narrowing
		return true;
	}
};

// Unsigned to unsigned narrowing
template <typename From, typename To>
struct narrow_impl<From, To, std::enable_if_t<std::is_unsigned<From>::value && std::is_unsigned<To>::value>>
{
	static constexpr bool test(const From& value)
	{
		return sizeof(To) < sizeof(From) && static_cast<To>(value) != value;
	}
};

// Signed to signed narrowing
template <typename From, typename To>
struct narrow_impl<From, To, std::enable_if_t<std::is_signed<From>::value && std::is_signed<To>::value>>
{
	static constexpr bool test(const From& value)
	{
		return sizeof(To) < sizeof(From) && static_cast<To>(value) != value;
	}
};

// Unsigned to signed narrowing
template <typename From, typename To>
struct narrow_impl<From, To, std::enable_if_t<std::is_unsigned<From>::value && std::is_signed<To>::value>>
{
	static constexpr bool test(const From& value)
	{
		return sizeof(To) <= sizeof(From) && value > (static_cast<std::make_unsigned_t<To>>(-1) >> 1);
	}
};

// Signed to unsigned narrowing (I)
template <typename From, typename To>
struct narrow_impl<From, To, std::enable_if_t<std::is_signed<From>::value && std::is_unsigned<To>::value && sizeof(To) >= sizeof(From)>>
{
	static constexpr bool test(const From& value)
	{
		return value < static_cast<From>(0);
	}
};

// Signed to unsigned narrowing (II)
template <typename From, typename To>
struct narrow_impl<From, To, std::enable_if_t<std::is_signed<From>::value && std::is_unsigned<To>::value && sizeof(To) < sizeof(From)>>
{
	static constexpr bool test(const From& value)
	{
		return static_cast<std::make_unsigned_t<From>>(value) > static_cast<To>(-1);
	}
};

// Simple type enabled (TODO: allow for To as well)
template <typename From, typename To>
struct narrow_impl<From, To, std::void_t<typename From::simple_type>>
	: narrow_impl<simple_t<From>, To>
{
};

template <typename To = void, typename From, typename = decltype(static_cast<To>(std::declval<From>()))>
inline To narrow(const From& value, const char* msg = nullptr)
{
	// Narrow check
	if (narrow_impl<From, To>::test(value))
	{
		// Pack value as formatting argument
		fmt::raw_narrow_error(msg, fmt::get_type_info<fmt_unveil_t<From>>(), fmt_unveil<From>::get(value));
	}

	return static_cast<To>(value);
}

// Returns u32 size() for container
template <typename CT, typename = decltype(static_cast<u32>(std::declval<CT>().size()))>
inline u32 size32(const CT& container, const char* msg = nullptr)
{
	return narrow<u32>(container.size(), msg);
}

// Returns u32 size for an array
template <typename T, std::size_t Size>
constexpr u32 size32(const T (&)[Size], const char* msg = nullptr)
{
	return static_cast<u32>(Size);
}

// Simplified hash algorithm for pointers. May be used in std::unordered_(map|set).
template <typename T, std::size_t Align = alignof(T)>
struct pointer_hash
{
	std::size_t operator()(T* ptr) const
	{
		return reinterpret_cast<std::uintptr_t>(ptr) / Align;
	}
};

template <typename T, std::size_t Shift = 0>
struct value_hash
{
	std::size_t operator()(T value) const
	{
		return static_cast<std::size_t>(value) >> Shift;
	}
};

// Contains value of any POD type with fixed size and alignment. TT<> is the type converter applied.
// For example, `simple_t` may be used to remove endianness.
template <template <typename> class TT, std::size_t S, std::size_t A = S>
struct alignas(A) any_pod
{
	alignas(A) std::byte data[S];

	any_pod() = default;

	template <typename T, typename T2 = TT<T>, typename = std::enable_if_t<std::is_pod<T2>::value && sizeof(T2) == S && alignof(T2) <= A>>
	any_pod(const T& value)
	{
		reinterpret_cast<T2&>(data) = value;
	}

	template <typename T, typename T2 = TT<T>, typename = std::enable_if_t<std::is_pod<T2>::value && sizeof(T2) == S && alignof(T2) <= A>>
	T2& as()
	{
		return reinterpret_cast<T2&>(data);
	}

	template <typename T, typename T2 = TT<T>, typename = std::enable_if_t<std::is_pod<T2>::value && sizeof(T2) == S && alignof(T2) <= A>>
	const T2& as() const
	{
		return reinterpret_cast<const T2&>(data);
	}
};

using any16 = any_pod<simple_t, sizeof(u16)>;
using any32 = any_pod<simple_t, sizeof(u32)>;
using any64 = any_pod<simple_t, sizeof(u64)>;

struct cmd64 : any64
{
	struct pair_t
	{
		any32 arg1;
		any32 arg2;
	};

	cmd64() = default;

	template <typename T>
	cmd64(const T& value)
		: any64(value)
	{
	}

	template <typename T1, typename T2>
	cmd64(const T1& arg1, const T2& arg2)
		: any64(pair_t{arg1, arg2})
	{
	}

	explicit operator bool() const
	{
		return as<u64>() != 0;
	}

	// TODO: compatibility with std::pair/std::tuple?

	template <typename T>
	decltype(auto) arg1()
	{
		return as<pair_t>().arg1.as<T>();
	}

	template <typename T>
	decltype(auto) arg1() const
	{
		return as<const pair_t>().arg1.as<const T>();
	}

	template <typename T>
	decltype(auto) arg2()
	{
		return as<pair_t>().arg2.as<T>();
	}

	template <typename T>
	decltype(auto) arg2() const
	{
		return as<const pair_t>().arg2.as<const T>();
	}
};

static_assert(sizeof(cmd64) == 8 && std::is_pod<cmd64>::value, "Incorrect cmd64 type");

// Error code type (return type), implements error reporting. Could be a template.
struct error_code
{
	// Use fixed s32 type for now
	s32 value;

	error_code() = default;

	// Implementation must be provided specially
	static s32 error_report(const fmt_type_info* sup, u64 arg, const fmt_type_info* sup2, u64 arg2);

	// Helper type
	enum class not_an_error : s32
	{
		__not_an_error // SFINAE marker
	};

	// __not_an_error tester
	template<typename ET, typename = void>
	struct is_error : std::integral_constant<bool, std::is_enum<ET>::value || std::is_integral<ET>::value>
	{
	};

	template<typename ET>
	struct is_error<ET, std::enable_if_t<sizeof(ET::__not_an_error) != 0>> : std::false_type
	{
	};

	// Common constructor
	template<typename ET>
	error_code(const ET& value)
		: value(static_cast<s32>(value))
	{
		if constexpr(is_error<ET>::value)
		{
			this->value = error_report(fmt::get_type_info<fmt_unveil_t<ET>>(), fmt_unveil<ET>::get(value), nullptr, 0);
		}
	}

	// Error constructor (2 args)
	template<typename ET, typename T2>
	error_code(const ET& value, const T2& value2)
		: value(error_report(fmt::get_type_info<fmt_unveil_t<ET>>(), fmt_unveil<ET>::get(value), fmt::get_type_info<fmt_unveil_t<T2>>(), fmt_unveil<T2>::get(value2)))
	{
	}

	operator s32() const
	{
		return value;
	}
};

// Helper function for error_code
template <typename T>
constexpr FORCE_INLINE error_code::not_an_error not_an_error(const T& value)
{
	return static_cast<error_code::not_an_error>(static_cast<s32>(value));
}

// Synchronization helper (cache-friendly busy waiting)
inline void busy_wait(std::size_t cycles = 3000)
{
	const u64 s = __rdtsc();
	do _mm_pause(); while (__rdtsc() - s < cycles);
}

// TODO: Remove when moving to c++20
template <typename T>
inline constexpr uintmax_t floor2(T value)
{
	value >>= 1;

	for (uintmax_t i = 0;; i++, value >>= 1)
	{
		if (value == 0)
		{
			return i;
		}
	}
}

template <typename T>
inline constexpr uintmax_t ceil2(T value)
{
	const uintmax_t ispow2 = value & (value - 1); // if power of 2 the result is 0

	value >>= 1;

	for (uintmax_t i = 0;; i++, value >>= 1)
	{
		if (value == 0)
		{
			return i + std::min<uintmax_t>(ispow2, 1);
		}
	}
}