SPIRV-Tools/source/util/hex_float.h

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2016-01-07 18:44:22 +00:00
// 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>
Pull out the number parsing logic Pull out the number parsing logic from AssemblyContext::binaryEncodeNumericLiteral() to utilities. The new utility function: `ParseAndEncodeNumber()` now accepts: * number text to parse * number type * a emit function, which is a function which will be called with each parsed uint32 word. * a pointer to std::string to be overwritten with error messages. (pass nullptr if expect no error message) and returns: * an enum result type to indicate the status Type/Structs moved to utility: * template<typename T> class ClampToZeroIfUnsignedType New type: * enum EncodeNumberStatus: success or error code * NumberType: hold the number type information for the number to be parsed. * several helper functions are also added for NumberType. Functions moved to utility: * Helpers: * template<typename T> checkRangeAndIfHexThenSignExtend() -> CheckRangeAndIfHex....() * Interfaces: * template<typename T> parseNumber() -> ParseNumber() * binaryEncodeIntegerLiteral() -> ParseAndEncodeIntegerNumber() * binaryEncodeFloatingPointLiteral() -> ParseAndEncodeFloatingPointNumber() * binaryEncodeNumericLiteral() -> ParseAndEncodeNumber() Tests added/moved to test/ParseNumber.cpp, including tests for: * ParseNumber(): This is moved from TextToBinary.cpp to ParseNumber.cpp * ParseAndEncodeIntegerNumber(): New added * ParseAndEncodeFloatingPointNumber(): New added * ParseAndEncodeNumber(): New added Note that the error messages are kept almost the same as before, but they may be inappropriate for an utility function. Those will be fixed in another CL.
2016-09-01 18:27:04 +00:00
#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 = static_cast<T>(0.0);
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);
}
}
2016-01-06 19:43:55 +00:00
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();
}
// Finished reading the part preceding any '.' or 'p'.
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();
}
// Finished reading the part preceding 'p'.
// In hex floats syntax, the binary exponent is required.
bool seen_sign = false;
int8_t exponent_sign = 1;
bool seen_written_exponent_digits = false;
int_type written_exponent = 0;
while (true) {
if (!seen_written_exponent_digits &&
(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)) {
seen_written_exponent_digits = true;
// 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();
}
if (!seen_written_exponent_digits) {
// Binary exponent had no digits.
is.setstate(std::ios::failbit);
return is;
}
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();
hex_float: Use max_digits10 for the float precision CPPreference.com has this description of digits10: “The value of std::numeric_limits<T>::digits10 is the number of base-10 digits that can be represented by the type T without change, that is, any number with this many significant decimal digits can be converted to a value of type T and back to decimal form, without change due to rounding or overflow.” This means that any number with this many digits can be represented accurately in the corresponding type. A change in any digit in a number after that may or may not cause it a different bitwise representation. Therefore this isn’t necessarily enough precision to accurately represent the value in text. Instead we need max_digits10 which has the following description: “The value of std::numeric_limits<T>::max_digits10 is the number of base-10 digits that are necessary to uniquely represent all distinct values of the type T, such as necessary for serialization/deserialization to text.” The patch includes a test case in hex_float_test which tries to do a round-robin conversion of a number that requires more than 6 decimal places to be accurately represented. This would fail without the patch. Sadly this also breaks a bunch of other tests. Some of the tests in hex_float_test use ldexp and then compare it with a value which is not the same as the one returned by ldexp but instead is the value rounded to 6 decimals. Others use values that are not evenly representable as a binary floating fraction but then happened to generate the same value when rounded to 6 decimals. Where the actual value didn’t seem to matter these have been changed with different values that can be represented as a binary fraction.
2018-03-30 23:35:45 +00:00
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_