intmath.hh

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#ifndef __BASE_INTMATH_HH__
#define __BASE_INTMATH_HH__
 
#include <cassert>
#include <cstdint>
#include <type_traits>
#include <utility>
 
#include "base/bitfield.hh"
 
namespace gem5
{
 
template <class T>
static constexpr std::enable_if_t<std::is_integral<T>::value, int>
floorLog2(T x)
{
    assert(x > 0);
 
    // A guaranteed unsigned version of x.
    uint64_t ux = (typename std::make_unsigned<T>::type)x;
 
    int y = 0;
    constexpr auto ts = sizeof(T);
 
    if (ts >= 8 && (ux & 0xffffffff00000000ULL)) { y += 32; ux >>= 32; }
    if (ts >= 4 && (ux & 0x00000000ffff0000ULL)) { y += 16; ux >>= 16; }
    if (ts >= 2 && (ux & 0x000000000000ff00ULL)) { y +=  8; ux >>=  8; }
    if (ux & 0x00000000000000f0ULL) { y +=  4; ux >>=  4; }
    if (ux & 0x000000000000000cULL) { y +=  2; ux >>=  2; }
    if (ux & 0x0000000000000002ULL) { y +=  1; }
 
    return y;
}
 
template <class T>
static constexpr int
ceilLog2(const T& n)
{
    assert(n > 0);
    if (n == 1)
        return 0;
 
    return floorLog2(n - (T)1) + 1;
}
 
template <class T>
static constexpr bool
isPowerOf2(const T& n)
{
    // If n is non-zero, and subtracting one borrows all the way to the MSB
    // and flips all bits, then this is a power of 2.
    return n && !(n & (n - 1));
}
 
template <class T, class U>
static constexpr T
divCeil(const T& a, const U& b)
{
    return (a + b - 1) / b;
}
 
template <typename T>
static constexpr std::enable_if_t<sizeof(T) <= sizeof(uint32_t)>
mulUnsigned(std::make_unsigned_t<T> &high, std::make_unsigned_t<T> &low,
            std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b)
{
    uint64_t product = (uint64_t)val_a * (uint64_t)val_b;
    low = product;
    high = (product >> (sizeof(low) * 8));
};
 
template <typename T>
static constexpr std::enable_if_t<sizeof(T) <= sizeof(uint32_t)>
mulSigned(std::make_signed_t<T> &high, std::make_signed_t<T> &low,
          std::make_signed_t<T> val_a, std::make_signed_t<T> val_b)
{
    uint64_t product = (int64_t)val_a * (int64_t)val_b;
    low = product;
    high = (product >> (sizeof(low) * 8));
};
 
template <typename T>
static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)>
mulUnsignedManual(std::make_unsigned_t<T> &high, std::make_unsigned_t<T> &low,
                  std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b)
{
    low = val_a * val_b;
 
    uint64_t A = (uint32_t)(val_a >> 32);
    uint64_t a = (uint32_t)val_a;
    uint64_t B = (uint32_t)(val_b >> 32);
    uint64_t b = (uint32_t)val_b;
 
    uint64_t c1 = 0, c2 = 0; // Carry between place values.
    uint64_t ab = a * b, Ab = A * b, aB = a * B, AB = A * B;
 
    c1 = (uint32_t)(ab >> 32);
 
    // Be careful to avoid overflow.
    c2 = (c1 >> 1) + (Ab >> 1) + (aB >> 1);
    c2 += ((c1 & 0x1) + (Ab & 0x1) + (aB & 0x1)) >> 1;
    c2 >>= 31;
 
    high = AB + c2;
}
 
template <typename T>
static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)>
mulUnsigned(std::make_unsigned_t<T> &high, std::make_unsigned_t<T> &low,
            std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b)
{
#ifdef __SIZEOF_INT128__
    __uint128_t val = (__uint128_t)val_a * (__uint128_t)val_b;
    low = val;
    high = (val >> 64);
#else
    mulUnsignedManual<T>(high, low, val_a, val_b);
#endif
}
 
template <typename T>
static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)>
mulSignedManual(std::make_signed_t<T> &high, std::make_signed_t<T> &low,
                std::make_signed_t<T> val_a, std::make_signed_t<T> val_b)
{
    uint64_t u_high = 0, u_low = 0;
    mulUnsigned<T>(u_high, u_low, val_a, val_b);
 
    if (val_a < 0)
        u_high -= val_b;
    if (val_b < 0)
        u_high -= val_a;
 
    high = u_high;
    low = u_low;
}
 
template <typename T>
static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)>
mulSigned(std::make_signed_t<T> &high, std::make_signed_t<T> &low,
          std::make_signed_t<T> val_a, std::make_signed_t<T> val_b)
{
#ifdef __SIZEOF_INT128__
    __int128_t val = (__int128_t)val_a * (__int128_t)val_b;
    low = val;
    high = (val >> 64);
#else
    mulSignedManual<T>(high, low, val_a, val_b);
#endif
}
 
template <typename T>
static constexpr std::pair<std::make_unsigned_t<T>, std::make_unsigned_t<T>>
mulUnsigned(std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b)
{
    std::make_unsigned_t<T> hi{}, low{};
    mulUnsigned<T>(hi, low, val_a, val_b);
    return {hi, low};
};
 
template <typename T>
static constexpr std::pair<std::make_signed_t<T>, std::make_signed_t<T>>
mulSigned(std::make_signed_t<T> val_a, std::make_signed_t<T> val_b)
{
    std::make_signed_t<T> hi{}, low{};
    mulSigned<T>(hi, low, val_a, val_b);
    return {hi, low};
};
 
template <class T, class U>
static constexpr T
roundUp(const T& val, const U& align)
{
    assert(isPowerOf2(align));
    T mask = (T)align - 1;
    return (val + mask) & ~mask;
}
 
template <class T, class U>
static constexpr T
roundDown(const T& val, const U& align)
{
    assert(isPowerOf2(align));
    T mask = (T)align - 1;
    return val & ~mask;
}
 
static constexpr int
log2i(int value)
{
    assert(isPowerOf2(value) && value > 0);
    return ctz32(value);
}
 
} // namespace gem5
 
#endif // __BASE_INTMATH_HH__