1 /*
2 * Copyright (C) 2016 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 * http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17 #pragma once
18
19 #include <stdint.h>
20 #include <iosfwd>
21 #include <limits>
22 #include <type_traits>
23
24 #ifndef LIKELY
25 #define LIKELY_DEFINED_LOCAL
26 #ifdef __cplusplus
27 # define LIKELY( exp ) (__builtin_expect( !!(exp), true ))
28 # define UNLIKELY( exp ) (__builtin_expect( !!(exp), false ))
29 #else
30 # define LIKELY( exp ) (__builtin_expect( !!(exp), 1 ))
31 # define UNLIKELY( exp ) (__builtin_expect( !!(exp), 0 ))
32 #endif
33 #endif
34
35 #if __cplusplus >= 201402L
36 #define CONSTEXPR constexpr
37 #else
38 #define CONSTEXPR
39 #endif
40
41 namespace android {
42
43 /*
44 * half-float
45 *
46 * 1 5 10
47 * +-+------+------------+
48 * |s|eee.ee|mm.mmmm.mmmm|
49 * +-+------+------------+
50 *
51 * minimum (denormal) value: 2^-24 = 5.96e-8
52 * minimum (normal) value: 2^-14 = 6.10e-5
53 * maximum value: 2-2^-10 = 65504
54 *
55 * Integers between 0 and 2048 can be represented exactly
56 */
57 class half {
58 struct fp16 {
59 uint16_t bits;
fp16fp1660 explicit constexpr fp16() noexcept : bits(0) { }
fp16fp1661 explicit constexpr fp16(uint16_t b) noexcept : bits(b) { }
setSfp1662 void setS(unsigned int s) noexcept { bits = uint16_t((bits & 0x7FFF) | (s<<15)); }
setEfp1663 void setE(unsigned int s) noexcept { bits = uint16_t((bits & 0xE3FF) | (s<<10)); }
setMfp1664 void setM(unsigned int s) noexcept { bits = uint16_t((bits & 0xFC00) | (s<< 0)); }
getSfp1665 constexpr unsigned int getS() const noexcept { return bits >> 15u; }
getEfp1666 constexpr unsigned int getE() const noexcept { return (bits >> 10u) & 0x1Fu; }
getMfp1667 constexpr unsigned int getM() const noexcept { return bits & 0x3FFu; }
68 };
69 struct fp32 {
70 union {
71 uint32_t bits;
72 float fp;
73 };
fp32fp3274 explicit constexpr fp32() noexcept : bits(0) { }
fp32fp3275 explicit constexpr fp32(float f) noexcept : fp(f) { }
setSfp3276 void setS(unsigned int s) noexcept { bits = uint32_t((bits & 0x7FFFFFFF) | (s<<31)); }
setEfp3277 void setE(unsigned int s) noexcept { bits = uint32_t((bits & 0x807FFFFF) | (s<<23)); }
setMfp3278 void setM(unsigned int s) noexcept { bits = uint32_t((bits & 0xFF800000) | (s<< 0)); }
getSfp3279 constexpr unsigned int getS() const noexcept { return bits >> 31u; }
getEfp3280 constexpr unsigned int getE() const noexcept { return (bits >> 23u) & 0xFFu; }
getMfp3281 constexpr unsigned int getM() const noexcept { return bits & 0x7FFFFFu; }
82 };
83
84 public:
half(float v)85 CONSTEXPR half(float v) noexcept : mBits(ftoh(v)) { }
86 CONSTEXPR operator float() const noexcept { return htof(mBits); }
87
getBits()88 uint16_t getBits() const noexcept { return mBits.bits; }
getExponent()89 unsigned int getExponent() const noexcept { return mBits.getE(); }
getMantissa()90 unsigned int getMantissa() const noexcept { return mBits.getM(); }
91
92 private:
93 friend class std::numeric_limits<half>;
94 friend CONSTEXPR half operator"" _hf(long double v);
95
96 enum Binary { binary };
half(Binary,uint16_t bits)97 explicit constexpr half(Binary, uint16_t bits) noexcept : mBits(bits) { }
98 static CONSTEXPR fp16 ftoh(float v) noexcept;
99 static CONSTEXPR float htof(fp16 v) noexcept;
100 fp16 mBits;
101 };
102
ftoh(float v)103 inline CONSTEXPR half::fp16 half::ftoh(float v) noexcept {
104 fp16 out;
105 fp32 in(v);
106 if (UNLIKELY(in.getE() == 0xFF)) { // inf or nan
107 out.setE(0x1F);
108 out.setM(in.getM() ? 0x200 : 0);
109 } else {
110 int e = static_cast<int>(in.getE()) - 127 + 15;
111 if (e >= 0x1F) {
112 // overflow
113 out.setE(0x31); // +/- inf
114 } else if (e <= 0) {
115 // underflow
116 // flush to +/- 0
117 } else {
118 unsigned int m = in.getM();
119 out.setE(uint16_t(e));
120 out.setM(m >> 13);
121 if (m & 0x1000) {
122 // rounding
123 out.bits++;
124 }
125 }
126 }
127 out.setS(in.getS());
128 return out;
129 }
130
htof(half::fp16 in)131 inline CONSTEXPR float half::htof(half::fp16 in) noexcept {
132 fp32 out;
133 if (UNLIKELY(in.getE() == 0x1F)) { // inf or nan
134 out.setE(0xFF);
135 out.setM(in.getM() ? 0x400000 : 0);
136 } else {
137 if (in.getE() == 0) {
138 if (in.getM()) {
139 // TODO: denormal half float, treat as zero for now
140 // (it's stupid because they can be represented as regular float)
141 }
142 } else {
143 int e = static_cast<int>(in.getE()) - 15 + 127;
144 unsigned int m = in.getM();
145 out.setE(uint32_t(e));
146 out.setM(m << 13);
147 }
148 }
149 out.setS(in.getS());
150 return out.fp;
151 }
152
153 inline CONSTEXPR android::half operator"" _hf(long double v) {
154 return android::half(android::half::binary, android::half::ftoh(static_cast<float>(v)).bits);
155 }
156
157 } // namespace android
158
159 namespace std {
160
161 template<> struct is_floating_point<android::half> : public std::true_type {};
162
163 template<>
164 class numeric_limits<android::half> {
165 public:
166 typedef android::half type;
167
168 static constexpr const bool is_specialized = true;
169 static constexpr const bool is_signed = true;
170 static constexpr const bool is_integer = false;
171 static constexpr const bool is_exact = false;
172 static constexpr const bool has_infinity = true;
173 static constexpr const bool has_quiet_NaN = true;
174 static constexpr const bool has_signaling_NaN = false;
175 static constexpr const float_denorm_style has_denorm = denorm_absent;
176 static constexpr const bool has_denorm_loss = true;
177 static constexpr const bool is_iec559 = false;
178 static constexpr const bool is_bounded = true;
179 static constexpr const bool is_modulo = false;
180 static constexpr const bool traps = false;
181 static constexpr const bool tinyness_before = false;
182 static constexpr const float_round_style round_style = round_indeterminate;
183
184 static constexpr const int digits = 11;
185 static constexpr const int digits10 = 3;
186 static constexpr const int max_digits10 = 5;
187 static constexpr const int radix = 2;
188 static constexpr const int min_exponent = -13;
189 static constexpr const int min_exponent10 = -4;
190 static constexpr const int max_exponent = 16;
191 static constexpr const int max_exponent10 = 4;
192
193 inline static constexpr type round_error() noexcept { return android::half(android::half::binary, 0x3800); }
194 inline static constexpr type min() noexcept { return android::half(android::half::binary, 0x0400); }
195 inline static constexpr type max() noexcept { return android::half(android::half::binary, 0x7bff); }
196 inline static constexpr type lowest() noexcept { return android::half(android::half::binary, 0xfbff); }
197 inline static constexpr type epsilon() noexcept { return android::half(android::half::binary, 0x1400); }
198 inline static constexpr type infinity() noexcept { return android::half(android::half::binary, 0x7c00); }
199 inline static constexpr type quiet_NaN() noexcept { return android::half(android::half::binary, 0x7fff); }
200 inline static constexpr type denorm_min() noexcept { return android::half(android::half::binary, 0x0001); }
201 inline static constexpr type signaling_NaN() noexcept { return android::half(android::half::binary, 0x7dff); }
202 };
203
204 } // namespace std
205
206 #ifdef LIKELY_DEFINED_LOCAL
207 #undef LIKELY_DEFINED_LOCAL
208 #undef LIKELY
209 #undef UNLIKELY
210 #endif // LIKELY_DEFINED_LOCAL
211
212 #undef CONSTEXPR
213