ClickHouse/base/common/DecomposedFloat.h
Alexey Milovidov 3b2f897f3a Fix UBSan
2021-05-09 02:25:36 +03:00

217 lines
6.3 KiB
C++

#pragma once
#include <cstdint>
#include <cstddef>
#include <cstring>
#include <common/extended_types.h>
/// Allows to check the internals of IEEE-754 floating point number.
template <typename T> struct FloatTraits;
template <>
struct FloatTraits<float>
{
using UInt = uint32_t;
static constexpr size_t bits = 32;
static constexpr size_t exponent_bits = 8;
static constexpr size_t mantissa_bits = bits - exponent_bits - 1;
};
template <>
struct FloatTraits<double>
{
using UInt = uint64_t;
static constexpr size_t bits = 64;
static constexpr size_t exponent_bits = 11;
static constexpr size_t mantissa_bits = bits - exponent_bits - 1;
};
/// x = sign * (2 ^ normalized_exponent) * (1 + mantissa * 2 ^ -mantissa_bits)
/// x = sign * (2 ^ normalized_exponent + mantissa * 2 ^ (normalized_exponent - mantissa_bits))
template <typename T>
struct DecomposedFloat
{
using Traits = FloatTraits<T>;
DecomposedFloat(T x)
{
memcpy(&x_uint, &x, sizeof(x));
}
typename Traits::UInt x_uint;
bool is_negative() const
{
return x_uint >> (Traits::bits - 1);
}
/// Returns 0 for both +0. and -0.
int sign() const
{
return (exponent() == 0 && mantissa() == 0)
? 0
: (is_negative()
? -1
: 1);
}
uint16_t exponent() const
{
return (x_uint >> (Traits::mantissa_bits)) & (((1ull << (Traits::exponent_bits + 1)) - 1) >> 1);
}
int16_t normalized_exponent() const
{
return int16_t(exponent()) - ((1ull << (Traits::exponent_bits - 1)) - 1);
}
uint64_t mantissa() const
{
return x_uint & ((1ull << Traits::mantissa_bits) - 1);
}
int64_t mantissa_with_sign() const
{
return is_negative() ? -mantissa() : mantissa();
}
/// NOTE Probably floating point instructions can be better.
bool is_integer_in_representable_range() const
{
return x_uint == 0
|| (normalized_exponent() >= 0 /// The number is not less than one
/// The number is inside the range where every integer has exact representation in float
&& normalized_exponent() <= static_cast<int16_t>(Traits::mantissa_bits)
/// After multiplying by 2^exp, the fractional part becomes zero, means the number is integer
&& ((mantissa() & ((1ULL << (Traits::mantissa_bits - normalized_exponent())) - 1)) == 0));
}
/// Compare float with integer of arbitrary width (both signed and unsigned are supported). Assuming two's complement arithmetic.
/// Infinities are compared correctly. NaNs are treat similarly to infinities, so they can be less than all numbers.
/// (note that we need total order)
template <typename Int>
int compare(Int rhs)
{
if (rhs == 0)
return sign();
/// Different signs
if (is_negative() && rhs > 0)
return -1;
if (!is_negative() && rhs < 0)
return 1;
/// Fractional number with magnitude less than one
if (normalized_exponent() < 0)
{
if (!is_negative())
return rhs > 0 ? -1 : 1;
else
return rhs >= 0 ? -1 : 1;
}
/// The case of the most negative integer
if constexpr (is_signed_v<Int>)
{
if (rhs == std::numeric_limits<Int>::lowest())
{
assert(is_negative());
if (normalized_exponent() < static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>))
return 1;
if (normalized_exponent() > static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>))
return -1;
if (mantissa() == 0)
return 0;
else
return -1;
}
}
/// Too large number: abs(float) > abs(rhs). Also the case with infinities and NaN.
if (normalized_exponent() >= static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>))
return is_negative() ? -1 : 1;
using UInt = make_unsigned_t<Int>;
UInt uint_rhs = rhs < 0 ? -rhs : rhs;
/// Smaller octave: abs(rhs) < abs(float)
if (uint_rhs < (static_cast<UInt>(1) << normalized_exponent()))
return is_negative() ? -1 : 1;
/// Larger octave: abs(rhs) > abs(float)
if (normalized_exponent() + 1 < static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>)
&& uint_rhs >= (static_cast<UInt>(1) << (normalized_exponent() + 1)))
return is_negative() ? 1 : -1;
/// The same octave
/// uint_rhs == 2 ^ normalized_exponent + mantissa * 2 ^ (normalized_exponent - mantissa_bits)
bool large_and_always_integer = normalized_exponent() >= static_cast<int16_t>(Traits::mantissa_bits);
typename Traits::UInt a = large_and_always_integer
? mantissa() << (normalized_exponent() - Traits::mantissa_bits)
: mantissa() >> (Traits::mantissa_bits - normalized_exponent());
typename Traits::UInt b = uint_rhs - (static_cast<UInt>(1) << normalized_exponent());
if (a < b)
return is_negative() ? 1 : -1;
if (a > b)
return is_negative() ? -1 : 1;
/// Float has no fractional part means that the numbers are equal.
if (large_and_always_integer || (mantissa() & ((1ULL << (Traits::mantissa_bits - normalized_exponent())) - 1)) == 0)
return 0;
else
/// Float has fractional part means its abs value is larger.
return is_negative() ? -1 : 1;
}
template <typename Int>
bool equals(Int rhs)
{
return compare(rhs) == 0;
}
template <typename Int>
bool notEquals(Int rhs)
{
return compare(rhs) != 0;
}
template <typename Int>
bool less(Int rhs)
{
return compare(rhs) < 0;
}
template <typename Int>
bool greater(Int rhs)
{
return compare(rhs) > 0;
}
template <typename Int>
bool lessOrEquals(Int rhs)
{
return compare(rhs) <= 0;
}
template <typename Int>
bool greaterOrEquals(Int rhs)
{
return compare(rhs) >= 0;
}
};
using DecomposedFloat64 = DecomposedFloat<double>;
using DecomposedFloat32 = DecomposedFloat<float>;