// 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 LIBSPIRV_UTIL_HEX_FLOAT_H_ #define LIBSPIRV_UTIL_HEX_FLOAT_H_ #include <cassert> #include <cctype> #include <cmath> #include <cstdint> #include <iomanip> #include <limits> #include <sstream> #if defined(_MSC_VER) && _MSC_VER < 1800 namespace std { bool isnan(double f) { return ::_isnan(f) != 0; } bool isinf(double f) { return ::_finite(f) == 0; } } #endif #include "bitutils.h" namespace spvutils { class Float16 { public: Float16(uint16_t v) : val(v) {} Float16() {} 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 { typedef void uint_type; }; template <> struct FloatProxyTraits<float> { typedef uint32_t uint_type; 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(); } }; template <> struct FloatProxyTraits<double> { typedef uint64_t uint_type; 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(); } }; template <> struct FloatProxyTraits<Float16> { typedef uint16_t uint_type; 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(); } }; // 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: typedef typename FloatProxyTraits<T>::uint_type uint_type; // Since this is to act similar to the normal floats, // do not initialize the data by default. FloatProxy() {} // Intentionally non-explicit. This is a proxy type so // implicit conversions allow us to use it more transparently. FloatProxy(T val) { data_ = BitwiseCast<uint_type>(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 BitwiseCast<T>(data_); } // Returns the raw data. uint_type data() const { return data_; } // 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. typedef void uint_type; // Signed integer type that can store this hex-float. typedef void int_type; // The numerical type that this HexFloat represents. typedef void underlying_type; // The type needed to construct the underlying type. typedef void native_type; // 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>> { typedef uint32_t uint_type; typedef int32_t int_type; typedef FloatProxy<float> underlying_type; typedef float native_type; 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>> { typedef uint64_t uint_type; typedef int64_t int_type; typedef FloatProxy<double> underlying_type; typedef double native_type; 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>> { typedef uint16_t uint_type; typedef int16_t int_type; typedef uint16_t underlying_type; typedef uint16_t native_type; 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 round_direction { kRoundToZero, kRoundToNearestEven, kRoundToPositiveInfinity, kRoundToNegativeInfinity }; // 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: typedef typename Traits::uint_type uint_type; typedef typename Traits::int_type int_type; typedef typename Traits::underlying_type underlying_type; typedef typename Traits::native_type 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 = spvutils::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 = spvutils::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 = spvutils::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 spvutils::BitwiseCast<uint_type>(value_); } // Returns the bits associated with the value, without the leading sign bit. uint_type getUnsignedBits() const { return static_cast<uint_type>(spvutils::BitwiseCast<uint_type>(value_) & ~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_ = BitwiseCast<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; } // 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 <typename int_type> uint_type negatable_left_shift(int_type N, uint_type val) { if(N >= 0) return val << N; return val >> -N; } template <typename int_type> uint_type negatable_right_shift(int_type N, uint_type val) { if(N >= 0) return val >> N; return val << -N; } // 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) { typedef typename other_T::uint_type other_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, 1u); static const uint_type first_rounded_bit = (num_throwaway_bits < 1) ? 0 : negatable_left_shift(num_throwaway_bits - 1, 1u); static const uint_type throwaway_mask_bits = num_throwaway_bits > 0 ? num_throwaway_bits : 0; static const uint_type throwaway_mask = spvutils::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, 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 kRoundToZero: break; case kRoundToPositiveInfinity: round_away_from_zero = !isNegative(); break; case kRoundToNegativeInfinity: round_away_from_zero = isNegative(); break; case kRoundToNearestEven: // 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, incrementSignificand( significand, last_significant_bit, carry_bit))); } else { return static_cast<other_uint_type>( negatable_right_shift(num_throwaway_bits, 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(BitwiseCast<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), 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(BitwiseCast<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 == kRoundToNegativeInfinity : round_dir == kRoundToPositiveInfinity; typedef typename other_T::int_type other_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) { typedef HexFloat<T, Traits> HF; typedef typename HF::uint_type uint_type; typedef typename HF::int_type 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 = spvutils::BitwiseCast<uint_type>(value.value()); 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, kRoundToZero); // 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 = spvutils::BitwiseCast<T>(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>::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; } } #endif // LIBSPIRV_UTIL_HEX_FLOAT_H_