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/*
* Copyright (C) 2016 The Android Open Source Project
*
* 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.
*/
#pragma once
#include <stdint.h>
#include <iosfwd>
#include <limits>
#include <type_traits>
#ifndef LIKELY
#define LIKELY_DEFINED_LOCAL
#ifdef __cplusplus
# define LIKELY( exp ) (__builtin_expect( !!(exp), true ))
# define UNLIKELY( exp ) (__builtin_expect( !!(exp), false ))
#else
# define LIKELY( exp ) (__builtin_expect( !!(exp), 1 ))
# define UNLIKELY( exp ) (__builtin_expect( !!(exp), 0 ))
#endif
#endif
#if __cplusplus >= 201402L
#define CONSTEXPR constexpr
#else
#define CONSTEXPR
#endif
namespace android {
/*
* half-float
*
* 1 5 10
* +-+------+------------+
* |s|eee.ee|mm.mmmm.mmmm|
* +-+------+------------+
*
* minimum (denormal) value: 2^-24 = 5.96e-8
* minimum (normal) value: 2^-14 = 6.10e-5
* maximum value: 2-2^-10 = 65504
*
* Integers between 0 and 2048 can be represented exactly
*/
class half {
struct fp16 {
uint16_t bits;
explicit constexpr fp16() noexcept : bits(0) { }
explicit constexpr fp16(uint16_t b) noexcept : bits(b) { }
void setS(unsigned int s) noexcept { bits = uint16_t((bits & 0x7FFF) | (s<<15)); }
void setE(unsigned int s) noexcept { bits = uint16_t((bits & 0xE3FF) | (s<<10)); }
void setM(unsigned int s) noexcept { bits = uint16_t((bits & 0xFC00) | (s<< 0)); }
constexpr unsigned int getS() const noexcept { return bits >> 15u; }
constexpr unsigned int getE() const noexcept { return (bits >> 10u) & 0x1Fu; }
constexpr unsigned int getM() const noexcept { return bits & 0x3FFu; }
};
struct fp32 {
union {
uint32_t bits;
float fp;
};
explicit constexpr fp32() noexcept : bits(0) { }
explicit constexpr fp32(float f) noexcept : fp(f) { }
void setS(unsigned int s) noexcept { bits = uint32_t((bits & 0x7FFFFFFF) | (s<<31)); }
void setE(unsigned int s) noexcept { bits = uint32_t((bits & 0x807FFFFF) | (s<<23)); }
void setM(unsigned int s) noexcept { bits = uint32_t((bits & 0xFF800000) | (s<< 0)); }
constexpr unsigned int getS() const noexcept { return bits >> 31u; }
constexpr unsigned int getE() const noexcept { return (bits >> 23u) & 0xFFu; }
constexpr unsigned int getM() const noexcept { return bits & 0x7FFFFFu; }
};
public:
CONSTEXPR half(float v) noexcept : mBits(ftoh(v)) { }
CONSTEXPR operator float() const noexcept { return htof(mBits); }
uint16_t getBits() const noexcept { return mBits.bits; }
unsigned int getExponent() const noexcept { return mBits.getE(); }
unsigned int getMantissa() const noexcept { return mBits.getM(); }
private:
friend class std::numeric_limits<half>;
friend CONSTEXPR half operator"" _hf(long double v);
enum Binary { binary };
explicit constexpr half(Binary, uint16_t bits) noexcept : mBits(bits) { }
static CONSTEXPR fp16 ftoh(float v) noexcept;
static CONSTEXPR float htof(fp16 v) noexcept;
fp16 mBits;
};
inline CONSTEXPR half::fp16 half::ftoh(float v) noexcept {
fp16 out;
fp32 in(v);
if (UNLIKELY(in.getE() == 0xFF)) { // inf or nan
out.setE(0x1F);
out.setM(in.getM() ? 0x200 : 0);
} else {
int e = static_cast<int>(in.getE()) - 127 + 15;
if (e >= 0x1F) {
// overflow
out.setE(0x31); // +/- inf
} else if (e <= 0) {
// underflow
// flush to +/- 0
} else {
unsigned int m = in.getM();
out.setE(uint16_t(e));
out.setM(m >> 13);
if (m & 0x1000) {
// rounding
out.bits++;
}
}
}
out.setS(in.getS());
return out;
}
inline CONSTEXPR float half::htof(half::fp16 in) noexcept {
fp32 out;
if (UNLIKELY(in.getE() == 0x1F)) { // inf or nan
out.setE(0xFF);
out.setM(in.getM() ? 0x400000 : 0);
} else {
if (in.getE() == 0) {
if (in.getM()) {
// TODO: denormal half float, treat as zero for now
// (it's stupid because they can be represented as regular float)
}
} else {
int e = static_cast<int>(in.getE()) - 15 + 127;
unsigned int m = in.getM();
out.setE(uint32_t(e));
out.setM(m << 13);
}
}
out.setS(in.getS());
return out.fp;
}
inline CONSTEXPR android::half operator"" _hf(long double v) {
return android::half(android::half::binary, android::half::ftoh(static_cast<float>(v)).bits);
}
} // namespace android
namespace std {
template<> struct is_floating_point<android::half> : public std::true_type {};
template<>
class numeric_limits<android::half> {
public:
typedef android::half type;
static constexpr const bool is_specialized = true;
static constexpr const bool is_signed = true;
static constexpr const bool is_integer = false;
static constexpr const bool is_exact = false;
static constexpr const bool has_infinity = true;
static constexpr const bool has_quiet_NaN = true;
static constexpr const bool has_signaling_NaN = false;
static constexpr const float_denorm_style has_denorm = denorm_absent;
static constexpr const bool has_denorm_loss = true;
static constexpr const bool is_iec559 = false;
static constexpr const bool is_bounded = true;
static constexpr const bool is_modulo = false;
static constexpr const bool traps = false;
static constexpr const bool tinyness_before = false;
static constexpr const float_round_style round_style = round_indeterminate;
static constexpr const int digits = 11;
static constexpr const int digits10 = 3;
static constexpr const int max_digits10 = 5;
static constexpr const int radix = 2;
static constexpr const int min_exponent = -13;
static constexpr const int min_exponent10 = -4;
static constexpr const int max_exponent = 16;
static constexpr const int max_exponent10 = 4;
inline static constexpr type round_error() noexcept { return android::half(android::half::binary, 0x3800); }
inline static constexpr type min() noexcept { return android::half(android::half::binary, 0x0400); }
inline static constexpr type max() noexcept { return android::half(android::half::binary, 0x7bff); }
inline static constexpr type lowest() noexcept { return android::half(android::half::binary, 0xfbff); }
inline static constexpr type epsilon() noexcept { return android::half(android::half::binary, 0x1400); }
inline static constexpr type infinity() noexcept { return android::half(android::half::binary, 0x7c00); }
inline static constexpr type quiet_NaN() noexcept { return android::half(android::half::binary, 0x7fff); }
inline static constexpr type denorm_min() noexcept { return android::half(android::half::binary, 0x0001); }
inline static constexpr type signaling_NaN() noexcept { return android::half(android::half::binary, 0x7dff); }
};
} // namespace std
#ifdef LIKELY_DEFINED_LOCAL
#undef LIKELY_DEFINED_LOCAL
#undef LIKELY
#undef UNLIKELY
#endif // LIKELY_DEFINED_LOCAL
#undef CONSTEXPR
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