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1079 lines
39 KiB
C
1079 lines
39 KiB
C
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// Copyright (c) 2015-2016 The Khronos Group Inc.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef LIBSPIRV_UTIL_HEX_FLOAT_H_
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#define LIBSPIRV_UTIL_HEX_FLOAT_H_
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#include <cassert>
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#include <cctype>
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#include <cmath>
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#include <cstdint>
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#include <iomanip>
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#include <limits>
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#include <sstream>
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#if defined(_MSC_VER) && _MSC_VER < 1800
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namespace std {
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bool isnan(double f)
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{
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return ::_isnan(f) != 0;
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}
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bool isinf(double f)
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{
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return ::_finite(f) == 0;
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}
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}
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#endif
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#include "bitutils.h"
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namespace spvutils {
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class Float16 {
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public:
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Float16(uint16_t v) : val(v) {}
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Float16() {}
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static bool isNan(const Float16& val) {
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return ((val.val & 0x7C00) == 0x7C00) && ((val.val & 0x3FF) != 0);
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}
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// Returns true if the given value is any kind of infinity.
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static bool isInfinity(const Float16& val) {
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return ((val.val & 0x7C00) == 0x7C00) && ((val.val & 0x3FF) == 0);
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}
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Float16(const Float16& other) { val = other.val; }
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uint16_t get_value() const { return val; }
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// Returns the maximum normal value.
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static Float16 max() { return Float16(0x7bff); }
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// Returns the lowest normal value.
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static Float16 lowest() { return Float16(0xfbff); }
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private:
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uint16_t val;
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};
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// To specialize this type, you must override uint_type to define
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// an unsigned integer that can fit your floating point type.
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// You must also add a isNan function that returns true if
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// a value is Nan.
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template <typename T>
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struct FloatProxyTraits {
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typedef void uint_type;
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};
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template <>
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struct FloatProxyTraits<float> {
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typedef uint32_t uint_type;
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static bool isNan(float f) { return std::isnan(f); }
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// Returns true if the given value is any kind of infinity.
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static bool isInfinity(float f) { return std::isinf(f); }
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// Returns the maximum normal value.
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static float max() { return std::numeric_limits<float>::max(); }
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// Returns the lowest normal value.
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static float lowest() { return std::numeric_limits<float>::lowest(); }
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};
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template <>
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struct FloatProxyTraits<double> {
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typedef uint64_t uint_type;
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static bool isNan(double f) { return std::isnan(f); }
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// Returns true if the given value is any kind of infinity.
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static bool isInfinity(double f) { return std::isinf(f); }
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// Returns the maximum normal value.
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static double max() { return std::numeric_limits<double>::max(); }
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// Returns the lowest normal value.
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static double lowest() { return std::numeric_limits<double>::lowest(); }
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};
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template <>
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struct FloatProxyTraits<Float16> {
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typedef uint16_t uint_type;
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static bool isNan(Float16 f) { return Float16::isNan(f); }
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// Returns true if the given value is any kind of infinity.
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static bool isInfinity(Float16 f) { return Float16::isInfinity(f); }
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// Returns the maximum normal value.
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static Float16 max() { return Float16::max(); }
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// Returns the lowest normal value.
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static Float16 lowest() { return Float16::lowest(); }
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};
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// Since copying a floating point number (especially if it is NaN)
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// does not guarantee that bits are preserved, this class lets us
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// store the type and use it as a float when necessary.
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template <typename T>
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class FloatProxy {
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public:
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typedef typename FloatProxyTraits<T>::uint_type uint_type;
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// Since this is to act similar to the normal floats,
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// do not initialize the data by default.
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FloatProxy() {}
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// Intentionally non-explicit. This is a proxy type so
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// implicit conversions allow us to use it more transparently.
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FloatProxy(T val) { data_ = BitwiseCast<uint_type>(val); }
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// Intentionally non-explicit. This is a proxy type so
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// implicit conversions allow us to use it more transparently.
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FloatProxy(uint_type val) { data_ = val; }
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// This is helpful to have and is guaranteed not to stomp bits.
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FloatProxy<T> operator-() const {
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return static_cast<uint_type>(data_ ^
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(uint_type(0x1) << (sizeof(T) * 8 - 1)));
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}
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// Returns the data as a floating point value.
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T getAsFloat() const { return BitwiseCast<T>(data_); }
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// Returns the raw data.
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uint_type data() const { return data_; }
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// Returns true if the value represents any type of NaN.
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bool isNan() { return FloatProxyTraits<T>::isNan(getAsFloat()); }
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// Returns true if the value represents any type of infinity.
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bool isInfinity() { return FloatProxyTraits<T>::isInfinity(getAsFloat()); }
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// Returns the maximum normal value.
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static FloatProxy<T> max() {
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return FloatProxy<T>(FloatProxyTraits<T>::max());
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}
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// Returns the lowest normal value.
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static FloatProxy<T> lowest() {
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return FloatProxy<T>(FloatProxyTraits<T>::lowest());
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}
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private:
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uint_type data_;
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};
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template <typename T>
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bool operator==(const FloatProxy<T>& first, const FloatProxy<T>& second) {
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return first.data() == second.data();
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}
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// Reads a FloatProxy value as a normal float from a stream.
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template <typename T>
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std::istream& operator>>(std::istream& is, FloatProxy<T>& value) {
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T float_val;
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is >> float_val;
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value = FloatProxy<T>(float_val);
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return is;
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}
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// This is an example traits. It is not meant to be used in practice, but will
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// be the default for any non-specialized type.
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template <typename T>
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struct HexFloatTraits {
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// Integer type that can store this hex-float.
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typedef void uint_type;
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// Signed integer type that can store this hex-float.
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typedef void int_type;
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// The numerical type that this HexFloat represents.
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typedef void underlying_type;
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// The type needed to construct the underlying type.
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typedef void native_type;
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// The number of bits that are actually relevant in the uint_type.
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// This allows us to deal with, for example, 24-bit values in a 32-bit
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// integer.
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static const uint32_t num_used_bits = 0;
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// Number of bits that represent the exponent.
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static const uint32_t num_exponent_bits = 0;
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// Number of bits that represent the fractional part.
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static const uint32_t num_fraction_bits = 0;
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// The bias of the exponent. (How much we need to subtract from the stored
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// value to get the correct value.)
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static const uint32_t exponent_bias = 0;
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};
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// Traits for IEEE float.
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// 1 sign bit, 8 exponent bits, 23 fractional bits.
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template <>
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struct HexFloatTraits<FloatProxy<float>> {
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typedef uint32_t uint_type;
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typedef int32_t int_type;
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typedef FloatProxy<float> underlying_type;
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typedef float native_type;
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static const uint_type num_used_bits = 32;
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static const uint_type num_exponent_bits = 8;
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static const uint_type num_fraction_bits = 23;
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static const uint_type exponent_bias = 127;
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};
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// Traits for IEEE double.
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// 1 sign bit, 11 exponent bits, 52 fractional bits.
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template <>
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struct HexFloatTraits<FloatProxy<double>> {
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typedef uint64_t uint_type;
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typedef int64_t int_type;
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typedef FloatProxy<double> underlying_type;
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typedef double native_type;
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static const uint_type num_used_bits = 64;
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static const uint_type num_exponent_bits = 11;
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static const uint_type num_fraction_bits = 52;
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static const uint_type exponent_bias = 1023;
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};
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// Traits for IEEE half.
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// 1 sign bit, 5 exponent bits, 10 fractional bits.
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template <>
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struct HexFloatTraits<FloatProxy<Float16>> {
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typedef uint16_t uint_type;
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typedef int16_t int_type;
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typedef uint16_t underlying_type;
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typedef uint16_t native_type;
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static const uint_type num_used_bits = 16;
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static const uint_type num_exponent_bits = 5;
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static const uint_type num_fraction_bits = 10;
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static const uint_type exponent_bias = 15;
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};
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enum round_direction {
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kRoundToZero,
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kRoundToNearestEven,
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kRoundToPositiveInfinity,
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kRoundToNegativeInfinity
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};
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// Template class that houses a floating pointer number.
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// It exposes a number of constants based on the provided traits to
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// assist in interpreting the bits of the value.
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template <typename T, typename Traits = HexFloatTraits<T>>
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class HexFloat {
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public:
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typedef typename Traits::uint_type uint_type;
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typedef typename Traits::int_type int_type;
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typedef typename Traits::underlying_type underlying_type;
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typedef typename Traits::native_type native_type;
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explicit HexFloat(T f) : value_(f) {}
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T value() const { return value_; }
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void set_value(T f) { value_ = f; }
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// These are all written like this because it is convenient to have
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// compile-time constants for all of these values.
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// Pass-through values to save typing.
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static const uint32_t num_used_bits = Traits::num_used_bits;
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static const uint32_t exponent_bias = Traits::exponent_bias;
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static const uint32_t num_exponent_bits = Traits::num_exponent_bits;
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static const uint32_t num_fraction_bits = Traits::num_fraction_bits;
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// Number of bits to shift left to set the highest relevant bit.
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static const uint32_t top_bit_left_shift = num_used_bits - 1;
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// How many nibbles (hex characters) the fractional part takes up.
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static const uint32_t fraction_nibbles = (num_fraction_bits + 3) / 4;
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// If the fractional part does not fit evenly into a hex character (4-bits)
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// then we have to left-shift to get rid of leading 0s. This is the amount
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// we have to shift (might be 0).
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static const uint32_t num_overflow_bits =
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fraction_nibbles * 4 - num_fraction_bits;
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// The representation of the fraction, not the actual bits. This
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// includes the leading bit that is usually implicit.
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static const uint_type fraction_represent_mask =
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spvutils::SetBits<uint_type, 0,
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num_fraction_bits + num_overflow_bits>::get;
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// The topmost bit in the nibble-aligned fraction.
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static const uint_type fraction_top_bit =
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uint_type(1) << (num_fraction_bits + num_overflow_bits - 1);
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// The least significant bit in the exponent, which is also the bit
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// immediately to the left of the significand.
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static const uint_type first_exponent_bit = uint_type(1)
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<< (num_fraction_bits);
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// The mask for the encoded fraction. It does not include the
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// implicit bit.
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static const uint_type fraction_encode_mask =
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spvutils::SetBits<uint_type, 0, num_fraction_bits>::get;
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// The bit that is used as a sign.
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static const uint_type sign_mask = uint_type(1) << top_bit_left_shift;
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// The bits that represent the exponent.
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static const uint_type exponent_mask =
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spvutils::SetBits<uint_type, num_fraction_bits, num_exponent_bits>::get;
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// How far left the exponent is shifted.
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static const uint32_t exponent_left_shift = num_fraction_bits;
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// How far from the right edge the fraction is shifted.
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static const uint32_t fraction_right_shift =
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static_cast<uint32_t>(sizeof(uint_type) * 8) - num_fraction_bits;
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// The maximum representable unbiased exponent.
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static const int_type max_exponent =
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(exponent_mask >> num_fraction_bits) - exponent_bias;
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// The minimum representable exponent for normalized numbers.
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static const int_type min_exponent = -static_cast<int_type>(exponent_bias);
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// Returns the bits associated with the value.
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uint_type getBits() const { return spvutils::BitwiseCast<uint_type>(value_); }
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// Returns the bits associated with the value, without the leading sign bit.
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uint_type getUnsignedBits() const {
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return static_cast<uint_type>(spvutils::BitwiseCast<uint_type>(value_) &
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~sign_mask);
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}
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// Returns the bits associated with the exponent, shifted to start at the
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// lsb of the type.
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const uint_type getExponentBits() const {
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return static_cast<uint_type>((getBits() & exponent_mask) >>
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num_fraction_bits);
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}
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// Returns the exponent in unbiased form. This is the exponent in the
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// human-friendly form.
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const int_type getUnbiasedExponent() const {
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return static_cast<int_type>(getExponentBits() - exponent_bias);
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}
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// Returns just the significand bits from the value.
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const uint_type getSignificandBits() const {
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return getBits() & fraction_encode_mask;
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}
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// If the number was normalized, returns the unbiased exponent.
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// If the number was denormal, normalize the exponent first.
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const int_type getUnbiasedNormalizedExponent() const {
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if ((getBits() & ~sign_mask) == 0) { // special case if everything is 0
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return 0;
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}
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int_type exp = getUnbiasedExponent();
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if (exp == min_exponent) { // We are in denorm land.
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uint_type significand_bits = getSignificandBits();
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while ((significand_bits & (first_exponent_bit >> 1)) == 0) {
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significand_bits = static_cast<uint_type>(significand_bits << 1);
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exp = static_cast<int_type>(exp - 1);
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}
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significand_bits &= fraction_encode_mask;
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}
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return exp;
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}
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// Returns the signficand after it has been normalized.
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const uint_type getNormalizedSignificand() const {
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int_type unbiased_exponent = getUnbiasedNormalizedExponent();
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uint_type significand = getSignificandBits();
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for (int_type i = unbiased_exponent; i <= min_exponent; ++i) {
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significand = static_cast<uint_type>(significand << 1);
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}
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significand &= fraction_encode_mask;
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return significand;
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}
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// Returns true if this number represents a negative value.
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bool isNegative() const { return (getBits() & sign_mask) != 0; }
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// Sets this HexFloat from the individual components.
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// Note this assumes EVERY significand is normalized, and has an implicit
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// leading one. This means that the only way that this method will set 0,
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// is if you set a number so denormalized that it underflows.
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// Do not use this method with raw bits extracted from a subnormal number,
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// since subnormals do not have an implicit leading 1 in the significand.
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// The significand is also expected to be in the
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// lowest-most num_fraction_bits of the uint_type.
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// The exponent is expected to be unbiased, meaning an exponent of
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// 0 actually means 0.
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// If underflow_round_up is set, then on underflow, if a number is non-0
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// and would underflow, we round up to the smallest denorm.
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void setFromSignUnbiasedExponentAndNormalizedSignificand(
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bool negative, int_type exponent, uint_type significand,
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bool round_denorm_up) {
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bool significand_is_zero = significand == 0;
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if (exponent <= min_exponent) {
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// If this was denormalized, then we have to shift the bit on, meaning
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// the significand is not zero.
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significand_is_zero = false;
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significand |= first_exponent_bit;
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||
|
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_
|