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@@ -1,219 +0,0 @@
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-#pragma once
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-
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-#include <cstdint>
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-#include <cstddef>
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-#include <cstring>
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-#include <base/extended_types.h>
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-
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-
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-/// Allows to check the internals of IEEE-754 floating point number.
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-
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-template <typename T> struct FloatTraits;
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-
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-template <>
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-struct FloatTraits<float>
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-{
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- using UInt = uint32_t;
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- static constexpr size_t bits = 32;
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- static constexpr size_t exponent_bits = 8;
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- static constexpr size_t mantissa_bits = bits - exponent_bits - 1;
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-};
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-
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-template <>
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-struct FloatTraits<double>
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-{
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- using UInt = uint64_t;
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- static constexpr size_t bits = 64;
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- static constexpr size_t exponent_bits = 11;
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- static constexpr size_t mantissa_bits = bits - exponent_bits - 1;
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-};
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-
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-
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-/// x = sign * (2 ^ normalized_exponent) * (1 + mantissa * 2 ^ -mantissa_bits)
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-/// x = sign * (2 ^ normalized_exponent + mantissa * 2 ^ (normalized_exponent - mantissa_bits))
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-template <typename T>
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-struct DecomposedFloat
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-{
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- using Traits = FloatTraits<T>;
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-
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- explicit DecomposedFloat(T x)
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- {
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- memcpy(&x_uint, &x, sizeof(x));
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- }
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-
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- typename Traits::UInt x_uint;
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-
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- bool isNegative() const
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- {
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- return x_uint >> (Traits::bits - 1);
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- }
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-
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- /// Returns 0 for both +0. and -0.
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- int sign() const
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- {
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- return (exponent() == 0 && mantissa() == 0)
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- ? 0
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- : (isNegative()
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- ? -1
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- : 1);
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- }
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-
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- uint16_t exponent() const
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- {
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- return (x_uint >> (Traits::mantissa_bits)) & (((1ull << (Traits::exponent_bits + 1)) - 1) >> 1);
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- }
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-
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- int16_t normalizedExponent() const
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- {
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- return int16_t(exponent()) - ((1ull << (Traits::exponent_bits - 1)) - 1);
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- }
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-
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- uint64_t mantissa() const
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- {
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- return x_uint & ((1ull << Traits::mantissa_bits) - 1);
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- }
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-
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- int64_t mantissaWithSign() const
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- {
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- return isNegative() ? -mantissa() : mantissa();
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- }
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-
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- /// NOTE Probably floating point instructions can be better.
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- bool isIntegerInRepresentableRange() const
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- {
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- return x_uint == 0
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- || (normalizedExponent() >= 0 /// The number is not less than one
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- /// The number is inside the range where every integer has exact representation in float
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- && normalizedExponent() <= static_cast<int16_t>(Traits::mantissa_bits)
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- /// After multiplying by 2^exp, the fractional part becomes zero, means the number is integer
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- && ((mantissa() & ((1ULL << (Traits::mantissa_bits - normalizedExponent())) - 1)) == 0));
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- }
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-
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-
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- /// Compare float with integer of arbitrary width (both signed and unsigned are supported). Assuming two's complement arithmetic.
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- /// This function is generic, big integers (128, 256 bit) are supported as well.
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- /// Infinities are compared correctly. NaNs are treat similarly to infinities, so they can be less than all numbers.
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- /// (note that we need total order)
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- /// Returns -1, 0 or 1.
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- template <typename Int>
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- int compare(Int rhs) const
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- {
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- if (rhs == 0)
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- return sign();
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-
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- /// Different signs
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- if (isNegative() && rhs > 0)
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- return -1;
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- if (!isNegative() && rhs < 0)
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- return 1;
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-
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- /// Fractional number with magnitude less than one
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- if (normalizedExponent() < 0)
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- {
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- if (!isNegative())
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- return rhs > 0 ? -1 : 1;
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- else
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- return rhs >= 0 ? -1 : 1;
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- }
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-
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- /// The case of the most negative integer
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- if constexpr (is_signed_v<Int>)
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- {
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- if (rhs == std::numeric_limits<Int>::lowest())
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- {
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- assert(isNegative());
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-
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- if (normalizedExponent() < static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>))
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- return 1;
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- if (normalizedExponent() > static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>))
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- return -1;
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-
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- if (mantissa() == 0)
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- return 0;
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- else
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- return -1;
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- }
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- }
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-
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- /// Too large number: abs(float) > abs(rhs). Also the case with infinities and NaN.
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- if (normalizedExponent() >= static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>))
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- return isNegative() ? -1 : 1;
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-
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- using UInt = std::conditional_t<(sizeof(Int) > sizeof(typename Traits::UInt)), make_unsigned_t<Int>, typename Traits::UInt>;
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- UInt uint_rhs = rhs < 0 ? -rhs : rhs;
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-
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- /// Smaller octave: abs(rhs) < abs(float)
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- /// FYI, TIL: octave is also called "binade", https://en.wikipedia.org/wiki/Binade
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- if (uint_rhs < (static_cast<UInt>(1) << normalizedExponent()))
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- return isNegative() ? -1 : 1;
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-
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- /// Larger octave: abs(rhs) > abs(float)
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- if (normalizedExponent() + 1 < static_cast<int16_t>(8 * sizeof(Int) - is_signed_v<Int>)
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- && uint_rhs >= (static_cast<UInt>(1) << (normalizedExponent() + 1)))
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- return isNegative() ? 1 : -1;
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-
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- /// The same octave
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- /// uint_rhs == 2 ^ normalizedExponent + mantissa * 2 ^ (normalizedExponent - mantissa_bits)
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-
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- bool large_and_always_integer = normalizedExponent() >= static_cast<int16_t>(Traits::mantissa_bits);
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-
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- UInt a = large_and_always_integer
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- ? static_cast<UInt>(mantissa()) << (normalizedExponent() - Traits::mantissa_bits)
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- : static_cast<UInt>(mantissa()) >> (Traits::mantissa_bits - normalizedExponent());
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-
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- UInt b = uint_rhs - (static_cast<UInt>(1) << normalizedExponent());
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-
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- if (a < b)
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- return isNegative() ? 1 : -1;
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- if (a > b)
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- return isNegative() ? -1 : 1;
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-
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- /// Float has no fractional part means that the numbers are equal.
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- if (large_and_always_integer || (mantissa() & ((1ULL << (Traits::mantissa_bits - normalizedExponent())) - 1)) == 0)
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- return 0;
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- else
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- /// Float has fractional part means its abs value is larger.
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- return isNegative() ? -1 : 1;
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- }
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-
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-
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- template <typename Int>
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- bool equals(Int rhs) const
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- {
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- return compare(rhs) == 0;
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- }
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-
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- template <typename Int>
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- bool notEquals(Int rhs) const
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- {
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- return compare(rhs) != 0;
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- }
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-
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- template <typename Int>
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- bool less(Int rhs) const
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- {
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- return compare(rhs) < 0;
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- }
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-
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- template <typename Int>
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- bool greater(Int rhs) const
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- {
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- return compare(rhs) > 0;
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- }
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-
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- template <typename Int>
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- bool lessOrEquals(Int rhs) const
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- {
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- return compare(rhs) <= 0;
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- }
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-
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- template <typename Int>
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- bool greaterOrEquals(Int rhs) const
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- {
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- return compare(rhs) >= 0;
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- }
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-};
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-
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-
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-using DecomposedFloat64 = DecomposedFloat<double>;
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-using DecomposedFloat32 = DecomposedFloat<float>;
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