// Copyright (c) 2015-2016 The Khronos Group Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#ifndef SOURCE_UTIL_HEX_FLOAT_H_
#define SOURCE_UTIL_HEX_FLOAT_H_
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstdint>
#include <iomanip>
#include <limits>
#include <sstream>
#include <vector>
#include "source/util/bitutils.h"
#ifndef __GNUC__
#define GCC_VERSION 0
#else
#define GCC_VERSION \
(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
#endif
namespace spvtools {
namespace utils {
class Float16 {
public:
Float16(uint16_t v) : val(v) {}
Float16() = default;
static bool isNan(const Float16& val) {
return ((val.val & 0x7C00) == 0x7C00) && ((val.val & 0x3FF) != 0);
}
// Returns true if the given value is any kind of infinity.
static bool isInfinity(const Float16& val) {
return ((val.val & 0x7C00) == 0x7C00) && ((val.val & 0x3FF) == 0);
}
Float16(const Float16& other) { val = other.val; }
uint16_t get_value() const { return val; }
// Returns the maximum normal value.
static Float16 max() { return Float16(0x7bff); }
// Returns the lowest normal value.
static Float16 lowest() { return Float16(0xfbff); }
private:
uint16_t val;
};
// To specialize this type, you must override uint_type to define
// an unsigned integer that can fit your floating point type.
// You must also add a isNan function that returns true if
// a value is Nan.
template <typename T>
struct FloatProxyTraits {
using uint_type = void;
};
template <>
struct FloatProxyTraits<float> {
using uint_type = uint32_t;
static bool isNan(float f) { return std::isnan(f); }
// Returns true if the given value is any kind of infinity.
static bool isInfinity(float f) { return std::isinf(f); }
// Returns the maximum normal value.
static float max() { return std::numeric_limits<float>::max(); }
// Returns the lowest normal value.
static float lowest() { return std::numeric_limits<float>::lowest(); }
// Returns the value as the native floating point format.
static float getAsFloat(const uint_type& t) { return BitwiseCast<float>(t); }
// Returns the bits from the given floating pointer number.
static uint_type getBitsFromFloat(const float& t) {
return BitwiseCast<uint_type>(t);
}
// Returns the bitwidth.
static uint32_t width() { return 32u; }
};
template <>
struct FloatProxyTraits<double> {
using uint_type = uint64_t;
static bool isNan(double f) { return std::isnan(f); }
// Returns true if the given value is any kind of infinity.
static bool isInfinity(double f) { return std::isinf(f); }
// Returns the maximum normal value.
static double max() { return std::numeric_limits<double>::max(); }
// Returns the lowest normal value.
static double lowest() { return std::numeric_limits<double>::lowest(); }
// Returns the value as the native floating point format.
static double getAsFloat(const uint_type& t) {
return BitwiseCast<double>(t);
}
// Returns the bits from the given floating pointer number.
static uint_type getBitsFromFloat(const double& t) {
return BitwiseCast<uint_type>(t);
}
// Returns the bitwidth.
static uint32_t width() { return 64u; }
};
template <>
struct FloatProxyTraits<Float16> {
using uint_type = uint16_t;
static bool isNan(Float16 f) { return Float16::isNan(f); }
// Returns true if the given value is any kind of infinity.
static bool isInfinity(Float16 f) { return Float16::isInfinity(f); }
// Returns the maximum normal value.
static Float16 max() { return Float16::max(); }
// Returns the lowest normal value.
static Float16 lowest() { return Float16::lowest(); }
// Returns the value as the native floating point format.
static Float16 getAsFloat(const uint_type& t) { return Float16(t); }
// Returns the bits from the given floating pointer number.
static uint_type getBitsFromFloat(const Float16& t) { return t.get_value(); }
// Returns the bitwidth.
static uint32_t width() { return 16u; }
};
// Since copying a floating point number (especially if it is NaN)
// does not guarantee that bits are preserved, this class lets us
// store the type and use it as a float when necessary.
template <typename T>
class FloatProxy {
public:
using uint_type = typename FloatProxyTraits<T>::uint_type;
// Since this is to act similar to the normal floats,
// do not initialize the data by default.
FloatProxy() = default;
// Intentionally non-explicit. This is a proxy type so
// implicit conversions allow us to use it more transparently.
FloatProxy(T val) { data_ = FloatProxyTraits<T>::getBitsFromFloat(val); }
// Intentionally non-explicit. This is a proxy type so
// implicit conversions allow us to use it more transparently.
FloatProxy(uint_type val) { data_ = val; }
// This is helpful to have and is guaranteed not to stomp bits.
FloatProxy<T> operator-() const {
return static_cast<uint_type>(data_ ^
(uint_type(0x1) << (sizeof(T) * 8 - 1)));
}
// Returns the data as a floating point value.
T getAsFloat() const { return FloatProxyTraits<T>::getAsFloat(data_); }
// Returns the raw data.
uint_type data() const { return data_; }
// Returns a vector of words suitable for use in an Operand.
std::vector<uint32_t> GetWords() const {
std::vector<uint32_t> words;
if (FloatProxyTraits<T>::width() == 64) {
FloatProxyTraits<double>::uint_type d = data();
words.push_back(static_cast<uint32_t>(d));
words.push_back(static_cast<uint32_t>(d >> 32));
} else {
words.push_back(static_cast<uint32_t>(data()));
}
return words;
}
// Returns true if the value represents any type of NaN.
bool isNan() { return FloatProxyTraits<T>::isNan(getAsFloat()); }
// Returns true if the value represents any type of infinity.
bool isInfinity() { return FloatProxyTraits<T>::isInfinity(getAsFloat()); }
// Returns the maximum normal value.
static FloatProxy<T> max() {
return FloatProxy<T>(FloatProxyTraits<T>::max());
}
// Returns the lowest normal value.
static FloatProxy<T> lowest() {
return FloatProxy<T>(FloatProxyTraits<T>::lowest());
}
private:
uint_type data_;
};
template <typename T>
bool operator==(const FloatProxy<T>& first, const FloatProxy<T>& second) {
return first.data() == second.data();
}
// Reads a FloatProxy value as a normal float from a stream.
template <typename T>
std::istream& operator>>(std::istream& is, FloatProxy<T>& value) {
T float_val;
is >> float_val;
value = FloatProxy<T>(float_val);
return is;
}
// This is an example traits. It is not meant to be used in practice, but will
// be the default for any non-specialized type.
template <typename T>
struct HexFloatTraits {
// Integer type that can store this hex-float.
using uint_type = void;
// Signed integer type that can store this hex-float.
using int_type = void;
// The numerical type that this HexFloat represents.
using underlying_type = void;
// The type needed to construct the underlying type.
using native_type = void;
// The number of bits that are actually relevant in the uint_type.
// This allows us to deal with, for example, 24-bit values in a 32-bit
// integer.
static const uint32_t num_used_bits = 0;
// Number of bits that represent the exponent.
static const uint32_t num_exponent_bits = 0;
// Number of bits that represent the fractional part.
static const uint32_t num_fraction_bits = 0;
// The bias of the exponent. (How much we need to subtract from the stored
// value to get the correct value.)
static const uint32_t exponent_bias = 0;
};
// Traits for IEEE float.
// 1 sign bit, 8 exponent bits, 23 fractional bits.
template <>
struct HexFloatTraits<FloatProxy<float>> {
using uint_type = uint32_t;
using int_type = int32_t;
using underlying_type = FloatProxy<float>;
using native_type = float;
static const uint_type num_used_bits = 32;
static const uint_type num_exponent_bits = 8;
static const uint_type num_fraction_bits = 23;
static const uint_type exponent_bias = 127;
};
// Traits for IEEE double.
// 1 sign bit, 11 exponent bits, 52 fractional bits.
template <>
struct HexFloatTraits<FloatProxy<double>> {
using uint_type = uint64_t;
using int_type = int64_t;
using underlying_type = FloatProxy<double>;
using native_type = double;
static const uint_type num_used_bits = 64;
static const uint_type num_exponent_bits = 11;
static const uint_type num_fraction_bits = 52;
static const uint_type exponent_bias = 1023;
};
// Traits for IEEE half.
// 1 sign bit, 5 exponent bits, 10 fractional bits.
template <>
struct HexFloatTraits<FloatProxy<Float16>> {
using uint_type = uint16_t;
using int_type = int16_t;
using underlying_type = uint16_t;
using native_type = uint16_t;
static const uint_type num_used_bits = 16;
static const uint_type num_exponent_bits = 5;
static const uint_type num_fraction_bits = 10;
static const uint_type exponent_bias = 15;
};
enum class round_direction {
kToZero,
kToNearestEven,
kToPositiveInfinity,
kToNegativeInfinity,
max = kToNegativeInfinity
};
// Template class that houses a floating pointer number.
// It exposes a number of constants based on the provided traits to
// assist in interpreting the bits of the value.
template <typename T, typename Traits = HexFloatTraits<T>>
class HexFloat {
public:
using uint_type = typename Traits::uint_type;
using int_type = typename Traits::int_type;
using underlying_type = typename Traits::underlying_type;
using native_type = typename Traits::native_type;
explicit HexFloat(T f) : value_(f) {}
T value() const { return value_; }
void set_value(T f) { value_ = f; }
// These are all written like this because it is convenient to have
// compile-time constants for all of these values.
// Pass-through values to save typing.
static const uint32_t num_used_bits = Traits::num_used_bits;
static const uint32_t exponent_bias = Traits::exponent_bias;
static const uint32_t num_exponent_bits = Traits::num_exponent_bits;
static const uint32_t num_fraction_bits = Traits::num_fraction_bits;
// Number of bits to shift left to set the highest relevant bit.
static const uint32_t top_bit_left_shift = num_used_bits - 1;
// How many nibbles (hex characters) the fractional part takes up.
static const uint32_t fraction_nibbles = (num_fraction_bits + 3) / 4;
// If the fractional part does not fit evenly into a hex character (4-bits)
// then we have to left-shift to get rid of leading 0s. This is the amount
// we have to shift (might be 0).
static const uint32_t num_overflow_bits =
fraction_nibbles * 4 - num_fraction_bits;
// The representation of the fraction, not the actual bits. This
// includes the leading bit that is usually implicit.
static const uint_type fraction_represent_mask =
SetBits<uint_type, 0, num_fraction_bits + num_overflow_bits>::get;
// The topmost bit in the nibble-aligned fraction.
static const uint_type fraction_top_bit =
uint_type(1) << (num_fraction_bits + num_overflow_bits - 1);
// The least significant bit in the exponent, which is also the bit
// immediately to the left of the significand.
static const uint_type first_exponent_bit = uint_type(1)
<< (num_fraction_bits);
// The mask for the encoded fraction. It does not include the
// implicit bit.
static const uint_type fraction_encode_mask =
SetBits<uint_type, 0, num_fraction_bits>::get;
// The bit that is used as a sign.
static const uint_type sign_mask = uint_type(1) << top_bit_left_shift;
// The bits that represent the exponent.
static const uint_type exponent_mask =
SetBits<uint_type, num_fraction_bits, num_exponent_bits>::get;
// How far left the exponent is shifted.
static const uint32_t exponent_left_shift = num_fraction_bits;
// How far from the right edge the fraction is shifted.
static const uint32_t fraction_right_shift =
static_cast<uint32_t>(sizeof(uint_type) * 8) - num_fraction_bits;
// The maximum representable unbiased exponent.
static const int_type max_exponent =
(exponent_mask >> num_fraction_bits) - exponent_bias;
// The minimum representable exponent for normalized numbers.
static const int_type min_exponent = -static_cast<int_type>(exponent_bias);
// Returns the bits associated with the value.
uint_type getBits() const { return value_.data(); }
// Returns the bits associated with the value, without the leading sign bit.
uint_type getUnsignedBits() const {
return static_cast<uint_type>(value_.data() & ~sign_mask);
}
// Returns the bits associated with the exponent, shifted to start at the
// lsb of the type.
const uint_type getExponentBits() const {
return static_cast<uint_type>((getBits() & exponent_mask) >>
num_fraction_bits);
}
// Returns the exponent in unbiased form. This is the exponent in the
// human-friendly form.
const int_type getUnbiasedExponent() const {
return static_cast<int_type>(getExponentBits() - exponent_bias);
}
// Returns just the significand bits from the value.
const uint_type getSignificandBits() const {
return getBits() & fraction_encode_mask;
}
// If the number was normalized, returns the unbiased exponent.
// If the number was denormal, normalize the exponent first.
const int_type getUnbiasedNormalizedExponent() const {
if ((getBits() & ~sign_mask) == 0) { // special case if everything is 0
return 0;
}
int_type exp = getUnbiasedExponent();
if (exp == min_exponent) { // We are in denorm land.
uint_type significand_bits = getSignificandBits();
while ((significand_bits & (first_exponent_bit >> 1)) == 0) {
significand_bits = static_cast<uint_type>(significand_bits << 1);
exp = static_cast<int_type>(exp - 1);
}
significand_bits &= fraction_encode_mask;
}
return exp;
}
// Returns the signficand after it has been normalized.
const uint_type getNormalizedSignificand() const {
int_type unbiased_exponent = getUnbiasedNormalizedExponent();
uint_type significand = getSignificandBits();
for (int_type i = unbiased_exponent; i <= min_exponent; ++i) {
significand = static_cast<uint_type>(significand << 1);
}
significand &= fraction_encode_mask;
return significand;
}
// Returns true if this number represents a negative value.
bool isNegative() const { return (getBits() & sign_mask) != 0; }
// Sets this HexFloat from the individual components.
// Note this assumes EVERY significand is normalized, and has an implicit
// leading one. This means that the only way that this method will set 0,
// is if you set a number so denormalized that it underflows.
// Do not use this method with raw bits extracted from a subnormal number,
// since subnormals do not have an implicit leading 1 in the significand.
// The significand is also expected to be in the
// lowest-most num_fraction_bits of the uint_type.
// The exponent is expected to be unbiased, meaning an exponent of
// 0 actually means 0.
// If underflow_round_up is set, then on underflow, if a number is non-0
// and would underflow, we round up to the smallest denorm.
void setFromSignUnbiasedExponentAndNormalizedSignificand(
bool negative, int_type exponent, uint_type significand,
bool round_denorm_up) {
bool significand_is_zero = significand == 0;
if (exponent <= min_exponent) {
// If this was denormalized, then we have to shift the bit on, meaning
// the significand is not zero.
significand_is_zero = false;
significand |= first_exponent_bit;
significand = static_cast<uint_type>(significand >> 1);
}
while (exponent < min_exponent) {
significand = static_cast<uint_type>(significand >> 1);
++exponent;
}
if (exponent == min_exponent) {
if (significand == 0 && !significand_is_zero && round_denorm_up) {
significand = static_cast<uint_type>(0x1);
}
}
uint_type new_value = 0;
if (negative) {
new_value = static_cast<uint_type>(new_value | sign_mask);
}
exponent = static_cast<int_type>(exponent + exponent_bias);
assert(exponent >= 0);
// put it all together
exponent = static_cast<uint_type>((exponent << exponent_left_shift) &
exponent_mask);
significand = static_cast<uint_type>(significand & fraction_encode_mask);
new_value = static_cast<uint_type>(new_value | (exponent | significand));
value_ = T(new_value);
}
// Increments the significand of this number by the given amount.
// If this would spill the significand into the implicit bit,
// carry is set to true and the significand is shifted to fit into
// the correct location, otherwise carry is set to false.
// All significands and to_increment are assumed to be within the bounds
// for a valid significand.
static uint_type incrementSignificand(uint_type significand,
uint_type to_increment, bool* carry) {
significand = static_cast<uint_type>(significand + to_increment);
*carry = false;
if (significand & first_exponent_bit) {
*carry = true;
// The implicit 1-bit will have carried, so we should zero-out the
// top bit and shift back.
significand = static_cast<uint_type>(significand & ~first_exponent_bit);
significand = static_cast<uint_type>(significand >> 1);
}
return significand;
}
#if GCC_VERSION == 40801
// These exist because MSVC throws warnings on negative right-shifts
// even if they are not going to be executed. Eg:
// constant_number < 0? 0: constant_number
// These convert the negative left-shifts into right shifts.
template <int_type N>
struct negatable_left_shift {
static uint_type val(uint_type val) {
if (N > 0) {
return static_cast<uint_type>(val << N);
} else {
return static_cast<uint_type>(val >> N);
}
}
};
template <int_type N>
struct negatable_right_shift {
static uint_type val(uint_type val) {
if (N > 0) {
return static_cast<uint_type>(val >> N);
} else {
return static_cast<uint_type>(val << N);
}
}
};
#else
// These exist because MSVC throws warnings on negative right-shifts
// even if they are not going to be executed. Eg:
// constant_number < 0? 0: constant_number
// These convert the negative left-shifts into right shifts.
template <int_type N, typename enable = void>
struct negatable_left_shift {
static uint_type val(uint_type val) {
return static_cast<uint_type>(val >> -N);
}
};
template <int_type N>
struct negatable_left_shift<N, typename std::enable_if<N >= 0>::type> {
static uint_type val(uint_type val) {
return static_cast<uint_type>(val << N);
}
};
template <int_type N, typename enable = void>
struct negatable_right_shift {
static uint_type val(uint_type val) {
return static_cast<uint_type>(val << -N);
}
};
template <int_type N>
struct negatable_right_shift<N, typename std::enable_if<N >= 0>::type> {
static uint_type val(uint_type val) {
return static_cast<uint_type>(val >> N);
}
};
#endif
// Returns the significand, rounded to fit in a significand in
// other_T. This is shifted so that the most significant
// bit of the rounded number lines up with the most significant bit
// of the returned significand.
template <typename other_T>
typename other_T::uint_type getRoundedNormalizedSignificand(
round_direction dir, bool* carry_bit) {
using other_uint_type = typename other_T::uint_type;
static const int_type num_throwaway_bits =
static_cast<int_type>(num_fraction_bits) -
static_cast<int_type>(other_T::num_fraction_bits);
static const uint_type last_significant_bit =
(num_throwaway_bits < 0)
? 0
: negatable_left_shift<num_throwaway_bits>::val(1u);
static const uint_type first_rounded_bit =
(num_throwaway_bits < 1)
? 0
: negatable_left_shift<num_throwaway_bits - 1>::val(1u);
static const uint_type throwaway_mask_bits =
num_throwaway_bits > 0 ? num_throwaway_bits : 0;
static const uint_type throwaway_mask =
SetBits<uint_type, 0, throwaway_mask_bits>::get;
*carry_bit = false;
other_uint_type out_val = 0;
uint_type significand = getNormalizedSignificand();
// If we are up-casting, then we just have to shift to the right location.
if (num_throwaway_bits <= 0) {
out_val = static_cast<other_uint_type>(significand);
uint_type shift_amount = static_cast<uint_type>(-num_throwaway_bits);
out_val = static_cast<other_uint_type>(out_val << shift_amount);
return out_val;
}
// If every non-representable bit is 0, then we don't have any casting to
// do.
if ((significand & throwaway_mask) == 0) {
return static_cast<other_uint_type>(
negatable_right_shift<num_throwaway_bits>::val(significand));
}
bool round_away_from_zero = false;
// We actually have to narrow the significand here, so we have to follow the
// rounding rules.
switch (dir) {
case round_direction::kToZero:
break;
case round_direction::kToPositiveInfinity:
round_away_from_zero = !isNegative();
break;
case round_direction::kToNegativeInfinity:
round_away_from_zero = isNegative();
break;
case round_direction::kToNearestEven:
// Have to round down, round bit is 0
if ((first_rounded_bit & significand) == 0) {
break;
}
if (((significand & throwaway_mask) & ~first_rounded_bit) != 0) {
// If any subsequent bit of the rounded portion is non-0 then we round
// up.
round_away_from_zero = true;
break;
}
// We are exactly half-way between 2 numbers, pick even.
if ((significand & last_significant_bit) != 0) {
// 1 for our last bit, round up.
round_away_from_zero = true;
break;
}
break;
}
if (round_away_from_zero) {
return static_cast<other_uint_type>(
negatable_right_shift<num_throwaway_bits>::val(incrementSignificand(
significand, last_significant_bit, carry_bit)));
} else {
return static_cast<other_uint_type>(
negatable_right_shift<num_throwaway_bits>::val(significand));
}
}
// Casts this value to another HexFloat. If the cast is widening,
// then round_dir is ignored. If the cast is narrowing, then
// the result is rounded in the direction specified.
// This number will retain Nan and Inf values.
// It will also saturate to Inf if the number overflows, and
// underflow to (0 or min depending on rounding) if the number underflows.
template <typename other_T>
void castTo(other_T& other, round_direction round_dir) {
other = other_T(static_cast<typename other_T::native_type>(0));
bool negate = isNegative();
if (getUnsignedBits() == 0) {
if (negate) {
other.set_value(-other.value());
}
return;
}
uint_type significand = getSignificandBits();
bool carried = false;
typename other_T::uint_type rounded_significand =
getRoundedNormalizedSignificand<other_T>(round_dir, &carried);
int_type exponent = getUnbiasedExponent();
if (exponent == min_exponent) {
// If we are denormal, normalize the exponent, so that we can encode
// easily.
exponent = static_cast<int_type>(exponent + 1);
for (uint_type check_bit = first_exponent_bit >> 1; check_bit != 0;
check_bit = static_cast<uint_type>(check_bit >> 1)) {
exponent = static_cast<int_type>(exponent - 1);
if (check_bit & significand) break;
}
}
bool is_nan =
(getBits() & exponent_mask) == exponent_mask && significand != 0;
bool is_inf =
!is_nan &&
((exponent + carried) > static_cast<int_type>(other_T::exponent_bias) ||
(significand == 0 && (getBits() & exponent_mask) == exponent_mask));
// If we are Nan or Inf we should pass that through.
if (is_inf) {
other.set_value(typename other_T::underlying_type(
static_cast<typename other_T::uint_type>(
(negate ? other_T::sign_mask : 0) | other_T::exponent_mask)));
return;
}
if (is_nan) {
typename other_T::uint_type shifted_significand;
shifted_significand = static_cast<typename other_T::uint_type>(
negatable_left_shift<
static_cast<int_type>(other_T::num_fraction_bits) -
static_cast<int_type>(num_fraction_bits)>::val(significand));
// We are some sort of Nan. We try to keep the bit-pattern of the Nan
// as close as possible. If we had to shift off bits so we are 0, then we
// just set the last bit.
other.set_value(typename other_T::underlying_type(
static_cast<typename other_T::uint_type>(
(negate ? other_T::sign_mask : 0) | other_T::exponent_mask |
(shifted_significand == 0 ? 0x1 : shifted_significand))));
return;
}
bool round_underflow_up =
isNegative() ? round_dir == round_direction::kToNegativeInfinity
: round_dir == round_direction::kToPositiveInfinity;
using other_int_type = typename other_T::int_type;
// setFromSignUnbiasedExponentAndNormalizedSignificand will
// zero out any underflowing value (but retain the sign).
other.setFromSignUnbiasedExponentAndNormalizedSignificand(
negate, static_cast<other_int_type>(exponent), rounded_significand,
round_underflow_up);
return;
}
private:
T value_;
static_assert(num_used_bits ==
Traits::num_exponent_bits + Traits::num_fraction_bits + 1,
"The number of bits do not fit");
static_assert(sizeof(T) == sizeof(uint_type), "The type sizes do not match");
};
// Returns 4 bits represented by the hex character.
inline uint8_t get_nibble_from_character(int character) {
const char* dec = "0123456789";
const char* lower = "abcdef";
const char* upper = "ABCDEF";
const char* p = nullptr;
if ((p = strchr(dec, character))) {
return static_cast<uint8_t>(p - dec);
} else if ((p = strchr(lower, character))) {
return static_cast<uint8_t>(p - lower + 0xa);
} else if ((p = strchr(upper, character))) {
return static_cast<uint8_t>(p - upper + 0xa);
}
assert(false && "This was called with a non-hex character");
return 0;
}
// Outputs the given HexFloat to the stream.
template <typename T, typename Traits>
std::ostream& operator<<(std::ostream& os, const HexFloat<T, Traits>& value) {
using HF = HexFloat<T, Traits>;
using uint_type = typename HF::uint_type;
using int_type = typename HF::int_type;
static_assert(HF::num_used_bits != 0,
"num_used_bits must be non-zero for a valid float");
static_assert(HF::num_exponent_bits != 0,
"num_exponent_bits must be non-zero for a valid float");
static_assert(HF::num_fraction_bits != 0,
"num_fractin_bits must be non-zero for a valid float");
const uint_type bits = value.value().data();
const char* const sign = (bits & HF::sign_mask) ? "-" : "";
const uint_type exponent = static_cast<uint_type>(
(bits & HF::exponent_mask) >> HF::num_fraction_bits);
uint_type fraction = static_cast<uint_type>((bits & HF::fraction_encode_mask)
<< HF::num_overflow_bits);
const bool is_zero = exponent == 0 && fraction == 0;
const bool is_denorm = exponent == 0 && !is_zero;
// exponent contains the biased exponent we have to convert it back into
// the normal range.
int_type int_exponent = static_cast<int_type>(exponent - HF::exponent_bias);
// If the number is all zeros, then we actually have to NOT shift the
// exponent.
int_exponent = is_zero ? 0 : int_exponent;
// If we are denorm, then start shifting, and decreasing the exponent until
// our leading bit is 1.
if (is_denorm) {
while ((fraction & HF::fraction_top_bit) == 0) {
fraction = static_cast<uint_type>(fraction << 1);
int_exponent = static_cast<int_type>(int_exponent - 1);
}
// Since this is denormalized, we have to consume the leading 1 since it
// will end up being implicit.
fraction = static_cast<uint_type>(fraction << 1); // eat the leading 1
fraction &= HF::fraction_represent_mask;
}
uint_type fraction_nibbles = HF::fraction_nibbles;
// We do not have to display any trailing 0s, since this represents the
// fractional part.
while (fraction_nibbles > 0 && (fraction & 0xF) == 0) {
// Shift off any trailing values;
fraction = static_cast<uint_type>(fraction >> 4);
--fraction_nibbles;
}
const auto saved_flags = os.flags();
const auto saved_fill = os.fill();
os << sign << "0x" << (is_zero ? '0' : '1');
if (fraction_nibbles) {
// Make sure to keep the leading 0s in place, since this is the fractional
// part.
os << "." << std::setw(static_cast<int>(fraction_nibbles))
<< std::setfill('0') << std::hex << fraction;
}
os << "p" << std::dec << (int_exponent >= 0 ? "+" : "") << int_exponent;
os.flags(saved_flags);
os.fill(saved_fill);
return os;
}
// Returns true if negate_value is true and the next character on the
// input stream is a plus or minus sign. In that case we also set the fail bit
// on the stream and set the value to the zero value for its type.
template <typename T, typename Traits>
inline bool RejectParseDueToLeadingSign(std::istream& is, bool negate_value,
HexFloat<T, Traits>& value) {
if (negate_value) {
auto next_char = is.peek();
if (next_char == '-' || next_char == '+') {
// Fail the parse. Emulate standard behaviour by setting the value to
// the zero value, and set the fail bit on the stream.
value = HexFloat<T, Traits>(typename HexFloat<T, Traits>::uint_type{0});
is.setstate(std::ios_base::failbit);
return true;
}
}
return false;
}
// Parses a floating point number from the given stream and stores it into the
// value parameter.
// If negate_value is true then the number may not have a leading minus or
// plus, and if it successfully parses, then the number is negated before
// being stored into the value parameter.
// If the value cannot be correctly parsed or overflows the target floating
// point type, then set the fail bit on the stream.
// TODO(dneto): Promise C++11 standard behavior in how the value is set in
// the error case, but only after all target platforms implement it correctly.
// In particular, the Microsoft C++ runtime appears to be out of spec.
template <typename T, typename Traits>
inline std::istream& ParseNormalFloat(std::istream& is, bool negate_value,
HexFloat<T, Traits>& value) {
if (RejectParseDueToLeadingSign(is, negate_value, value)) {
return is;
}
T val;
is >> val;
if (negate_value) {
val = -val;
}
value.set_value(val);
// In the failure case, map -0.0 to 0.0.
if (is.fail() && value.getUnsignedBits() == 0u) {
value = HexFloat<T, Traits>(typename HexFloat<T, Traits>::uint_type{0});
}
if (val.isInfinity()) {
// Fail the parse. Emulate standard behaviour by setting the value to
// the closest normal value, and set the fail bit on the stream.
value.set_value((value.isNegative() | negate_value) ? T::lowest()
: T::max());
is.setstate(std::ios_base::failbit);
}
return is;
}
// Specialization of ParseNormalFloat for FloatProxy<Float16> values.
// This will parse the float as it were a 32-bit floating point number,
// and then round it down to fit into a Float16 value.
// The number is rounded towards zero.
// If negate_value is true then the number may not have a leading minus or
// plus, and if it successfully parses, then the number is negated before
// being stored into the value parameter.
// If the value cannot be correctly parsed or overflows the target floating
// point type, then set the fail bit on the stream.
// TODO(dneto): Promise C++11 standard behavior in how the value is set in
// the error case, but only after all target platforms implement it correctly.
// In particular, the Microsoft C++ runtime appears to be out of spec.
template <>
inline std::istream&
ParseNormalFloat<FloatProxy<Float16>, HexFloatTraits<FloatProxy<Float16>>>(
std::istream& is, bool negate_value,
HexFloat<FloatProxy<Float16>, HexFloatTraits<FloatProxy<Float16>>>& value) {
// First parse as a 32-bit float.
HexFloat<FloatProxy<float>> float_val(0.0f);
ParseNormalFloat(is, negate_value, float_val);
// Then convert to 16-bit float, saturating at infinities, and
// rounding toward zero.
float_val.castTo(value, round_direction::kToZero);
// Overflow on 16-bit behaves the same as for 32- and 64-bit: set the
// fail bit and set the lowest or highest value.
if (Float16::isInfinity(value.value().getAsFloat())) {
value.set_value(value.isNegative() ? Float16::lowest() : Float16::max());
is.setstate(std::ios_base::failbit);
}
return is;
}
// Reads a HexFloat from the given stream.
// If the float is not encoded as a hex-float then it will be parsed
// as a regular float.
// This may fail if your stream does not support at least one unget.
// Nan values can be encoded with "0x1.<not zero>p+exponent_bias".
// This would normally overflow a float and round to
// infinity but this special pattern is the exact representation for a NaN,
// and therefore is actually encoded as the correct NaN. To encode inf,
// either 0x0p+exponent_bias can be specified or any exponent greater than
// exponent_bias.
// Examples using IEEE 32-bit float encoding.
// 0x1.0p+128 (+inf)
// -0x1.0p-128 (-inf)
//
// 0x1.1p+128 (+Nan)
// -0x1.1p+128 (-Nan)
//
// 0x1p+129 (+inf)
// -0x1p+129 (-inf)
template <typename T, typename Traits>
std::istream& operator>>(std::istream& is, HexFloat<T, Traits>& value) {
using HF = HexFloat<T, Traits>;
using uint_type = typename HF::uint_type;
using int_type = typename HF::int_type;
value.set_value(static_cast<typename HF::native_type>(0.f));
if (is.flags() & std::ios::skipws) {
// If the user wants to skip whitespace , then we should obey that.
while (std::isspace(is.peek())) {
is.get();
}
}
auto next_char = is.peek();
bool negate_value = false;
if (next_char != '-' && next_char != '0') {
return ParseNormalFloat(is, negate_value, value);
}
if (next_char == '-') {
negate_value = true;
is.get();
next_char = is.peek();
}
if (next_char == '0') {
is.get(); // We may have to unget this.
auto maybe_hex_start = is.peek();
if (maybe_hex_start != 'x' && maybe_hex_start != 'X') {
is.unget();
return ParseNormalFloat(is, negate_value, value);
} else {
is.get(); // Throw away the 'x';
}
} else {
return ParseNormalFloat(is, negate_value, value);
}
// This "looks" like a hex-float so treat it as one.
bool seen_p = false;
bool seen_dot = false;
uint_type fraction_index = 0;
uint_type fraction = 0;
int_type exponent = HF::exponent_bias;
// Strip off leading zeros so we don't have to special-case them later.
while ((next_char = is.peek()) == '0') {
is.get();
}
bool is_denorm =
true; // Assume denorm "representation" until we hear otherwise.
// NB: This does not mean the value is actually denorm,
// it just means that it was written 0.
bool bits_written = false; // Stays false until we write a bit.
while (!seen_p && !seen_dot) {
// Handle characters that are left of the fractional part.
if (next_char == '.') {
seen_dot = true;
} else if (next_char == 'p') {
seen_p = true;
} else if (::isxdigit(next_char)) {
// We know this is not denormalized since we have stripped all leading
// zeroes and we are not a ".".
is_denorm = false;
int number = get_nibble_from_character(next_char);
for (int i = 0; i < 4; ++i, number <<= 1) {
uint_type write_bit = (number & 0x8) ? 0x1 : 0x0;
if (bits_written) {
// If we are here the bits represented belong in the fractional
// part of the float, and we have to adjust the exponent accordingly.
fraction = static_cast<uint_type>(
fraction |
static_cast<uint_type>(
write_bit << (HF::top_bit_left_shift - fraction_index++)));
exponent = static_cast<int_type>(exponent + 1);
}
bits_written |= write_bit != 0;
}
} else {
// We have not found our exponent yet, so we have to fail.
is.setstate(std::ios::failbit);
return is;
}
is.get();
next_char = is.peek();
}
bits_written = false;
while (seen_dot && !seen_p) {
// Handle only fractional parts now.
if (next_char == 'p') {
seen_p = true;
} else if (::isxdigit(next_char)) {
int number = get_nibble_from_character(next_char);
for (int i = 0; i < 4; ++i, number <<= 1) {
uint_type write_bit = (number & 0x8) ? 0x01 : 0x00;
bits_written |= write_bit != 0;
if (is_denorm && !bits_written) {
// Handle modifying the exponent here this way we can handle
// an arbitrary number of hex values without overflowing our
// integer.
exponent = static_cast<int_type>(exponent - 1);
} else {
fraction = static_cast<uint_type>(
fraction |
static_cast<uint_type>(
write_bit << (HF::top_bit_left_shift - fraction_index++)));
}
}
} else {
// We still have not found our 'p' exponent yet, so this is not a valid
// hex-float.
is.setstate(std::ios::failbit);
return is;
}
is.get();
next_char = is.peek();
}
bool seen_sign = false;
int8_t exponent_sign = 1;
int_type written_exponent = 0;
while (true) {
if ((next_char == '-' || next_char == '+')) {
if (seen_sign) {
is.setstate(std::ios::failbit);
return is;
}
seen_sign = true;
exponent_sign = (next_char == '-') ? -1 : 1;
} else if (::isdigit(next_char)) {
// Hex-floats express their exponent as decimal.
written_exponent = static_cast<int_type>(written_exponent * 10);
written_exponent =
static_cast<int_type>(written_exponent + (next_char - '0'));
} else {
break;
}
is.get();
next_char = is.peek();
}
written_exponent = static_cast<int_type>(written_exponent * exponent_sign);
exponent = static_cast<int_type>(exponent + written_exponent);
bool is_zero = is_denorm && (fraction == 0);
if (is_denorm && !is_zero) {
fraction = static_cast<uint_type>(fraction << 1);
exponent = static_cast<int_type>(exponent - 1);
} else if (is_zero) {
exponent = 0;
}
if (exponent <= 0 && !is_zero) {
fraction = static_cast<uint_type>(fraction >> 1);
fraction |= static_cast<uint_type>(1) << HF::top_bit_left_shift;
}
fraction = (fraction >> HF::fraction_right_shift) & HF::fraction_encode_mask;
const int_type max_exponent =
SetBits<uint_type, 0, HF::num_exponent_bits>::get;
// Handle actual denorm numbers
while (exponent < 0 && !is_zero) {
fraction = static_cast<uint_type>(fraction >> 1);
exponent = static_cast<int_type>(exponent + 1);
fraction &= HF::fraction_encode_mask;
if (fraction == 0) {
// We have underflowed our fraction. We should clamp to zero.
is_zero = true;
exponent = 0;
}
}
// We have overflowed so we should be inf/-inf.
if (exponent > max_exponent) {
exponent = max_exponent;
fraction = 0;
}
uint_type output_bits = static_cast<uint_type>(
static_cast<uint_type>(negate_value ? 1 : 0) << HF::top_bit_left_shift);
output_bits |= fraction;
uint_type shifted_exponent = static_cast<uint_type>(
static_cast<uint_type>(exponent << HF::exponent_left_shift) &
HF::exponent_mask);
output_bits |= shifted_exponent;
T output_float(output_bits);
value.set_value(output_float);
return is;
}
// Writes a FloatProxy value to a stream.
// Zero and normal numbers are printed in the usual notation, but with
// enough digits to fully reproduce the value. Other values (subnormal,
// NaN, and infinity) are printed as a hex float.
template <typename T>
std::ostream& operator<<(std::ostream& os, const FloatProxy<T>& value) {
auto float_val = value.getAsFloat();
switch (std::fpclassify(float_val)) {
case FP_ZERO:
case FP_NORMAL: {
auto saved_precision = os.precision();
os.precision(std::numeric_limits<T>::max_digits10);
os << float_val;
os.precision(saved_precision);
} break;
default:
os << HexFloat<FloatProxy<T>>(value);
break;
}
return os;
}
template <>
inline std::ostream& operator<<<Float16>(std::ostream& os,
const FloatProxy<Float16>& value) {
os << HexFloat<FloatProxy<Float16>>(value);
return os;
}
} // namespace utils
} // namespace spvtools
#endif // SOURCE_UTIL_HEX_FLOAT_H_