1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
|
//===--- Float16bits.cpp - supports 2-byte floats ------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file implements f16 and bf16 to support the compilation and execution
// of programs using these types.
//
//===----------------------------------------------------------------------===//
#include "mlir/ExecutionEngine/Float16bits.h"
#ifdef MLIR_FLOAT16_DEFINE_FUNCTIONS // We are building this library
#include <cmath>
#include <cstring>
namespace {
// Union used to make the int/float aliasing explicit so we can access the raw
// bits.
union Float32Bits {
uint32_t u;
float f;
};
const uint32_t kF32MantiBits = 23;
const uint32_t kF32HalfMantiBitDiff = 13;
const uint32_t kF32HalfBitDiff = 16;
const Float32Bits kF32Magic = {113 << kF32MantiBits};
const uint32_t kF32HalfExpAdjust = (127 - 15) << kF32MantiBits;
// Constructs the 16 bit representation for a half precision value from a float
// value. This implementation is adapted from Eigen.
uint16_t float2half(float floatValue) {
const Float32Bits inf = {255 << kF32MantiBits};
const Float32Bits f16max = {(127 + 16) << kF32MantiBits};
const Float32Bits denormMagic = {((127 - 15) + (kF32MantiBits - 10) + 1)
<< kF32MantiBits};
uint32_t signMask = 0x80000000u;
uint16_t halfValue = static_cast<uint16_t>(0x0u);
Float32Bits f;
f.f = floatValue;
uint32_t sign = f.u & signMask;
f.u ^= sign;
if (f.u >= f16max.u) {
const uint32_t halfQnan = 0x7e00;
const uint32_t halfInf = 0x7c00;
// Inf or NaN (all exponent bits set).
halfValue = (f.u > inf.u) ? halfQnan : halfInf; // NaN->qNaN and Inf->Inf
} else {
// (De)normalized number or zero.
if (f.u < kF32Magic.u) {
// The resulting FP16 is subnormal or zero.
//
// Use a magic value to align our 10 mantissa bits at the bottom of the
// float. As long as FP addition is round-to-nearest-even this works.
f.f += denormMagic.f;
halfValue = static_cast<uint16_t>(f.u - denormMagic.u);
} else {
uint32_t mantOdd =
(f.u >> kF32HalfMantiBitDiff) & 1; // Resulting mantissa is odd.
// Update exponent, rounding bias part 1. The following expressions are
// equivalent to `f.u += ((unsigned int)(15 - 127) << kF32MantiBits) +
// 0xfff`, but without arithmetic overflow.
f.u += 0xc8000fffU;
// Rounding bias part 2.
f.u += mantOdd;
halfValue = static_cast<uint16_t>(f.u >> kF32HalfMantiBitDiff);
}
}
halfValue |= static_cast<uint16_t>(sign >> kF32HalfBitDiff);
return halfValue;
}
// Converts the 16 bit representation of a half precision value to a float
// value. This implementation is adapted from Eigen.
float half2float(uint16_t halfValue) {
const uint32_t shiftedExp =
0x7c00 << kF32HalfMantiBitDiff; // Exponent mask after shift.
// Initialize the float representation with the exponent/mantissa bits.
Float32Bits f = {
static_cast<uint32_t>((halfValue & 0x7fff) << kF32HalfMantiBitDiff)};
const uint32_t exp = shiftedExp & f.u;
f.u += kF32HalfExpAdjust; // Adjust the exponent
// Handle exponent special cases.
if (exp == shiftedExp) {
// Inf/NaN
f.u += kF32HalfExpAdjust;
} else if (exp == 0) {
// Zero/Denormal?
f.u += 1 << kF32MantiBits;
f.f -= kF32Magic.f;
}
f.u |= (halfValue & 0x8000) << kF32HalfBitDiff; // Sign bit.
return f.f;
}
const uint32_t kF32BfMantiBitDiff = 16;
// Constructs the 16 bit representation for a bfloat value from a float value.
// This implementation is adapted from Eigen.
uint16_t float2bfloat(float floatValue) {
if (std::isnan(floatValue))
return std::signbit(floatValue) ? 0xFFC0 : 0x7FC0;
Float32Bits floatBits;
floatBits.f = floatValue;
uint16_t bfloatBits;
// Least significant bit of resulting bfloat.
uint32_t lsb = (floatBits.u >> kF32BfMantiBitDiff) & 1;
uint32_t roundingBias = 0x7fff + lsb;
floatBits.u += roundingBias;
bfloatBits = static_cast<uint16_t>(floatBits.u >> kF32BfMantiBitDiff);
return bfloatBits;
}
// Converts the 16 bit representation of a bfloat value to a float value. This
// implementation is adapted from Eigen.
float bfloat2float(uint16_t bfloatBits) {
Float32Bits floatBits;
floatBits.u = static_cast<uint32_t>(bfloatBits) << kF32BfMantiBitDiff;
return floatBits.f;
}
} // namespace
f16::f16(float f) : bits(float2half(f)) {}
bf16::bf16(float f) : bits(float2bfloat(f)) {}
std::ostream &operator<<(std::ostream &os, const f16 &f) {
os << half2float(f.bits);
return os;
}
std::ostream &operator<<(std::ostream &os, const bf16 &d) {
os << bfloat2float(d.bits);
return os;
}
bool operator==(const f16 &f1, const f16 &f2) { return f1.bits == f2.bits; }
bool operator==(const bf16 &f1, const bf16 &f2) { return f1.bits == f2.bits; }
// Mark these symbols as weak so they don't conflict when compiler-rt also
// defines them.
#define ATTR_WEAK
#ifdef __has_attribute
#if __has_attribute(weak) && !defined(__MINGW32__) && !defined(__CYGWIN__) && \
!defined(_WIN32)
#undef ATTR_WEAK
#define ATTR_WEAK __attribute__((__weak__))
#endif
#endif
#if defined(__x86_64__) || defined(_M_X64)
// On x86 bfloat16 is passed in SSE registers. Since both float and __bf16
// are passed in the same register we can use the wider type and careful casting
// to conform to x86_64 psABI. This only works with the assumption that we're
// dealing with little-endian values passed in wider registers.
// Ideally this would directly use __bf16, but that type isn't supported by all
// compilers.
using BF16ABIType = float;
#else
// Default to uint16_t if we have nothing else.
using BF16ABIType = uint16_t;
#endif
// Provide a float->bfloat conversion routine in case the runtime doesn't have
// one.
extern "C" BF16ABIType ATTR_WEAK __truncsfbf2(float f) {
uint16_t bf = float2bfloat(f);
// The output can be a float type, bitcast it from uint16_t.
BF16ABIType ret = 0;
std::memcpy(&ret, &bf, sizeof(bf));
return ret;
}
// Provide a double->bfloat conversion routine in case the runtime doesn't have
// one.
extern "C" BF16ABIType ATTR_WEAK __truncdfbf2(double d) {
// This does a double rounding step, but it's precise enough for our use
// cases.
return __truncsfbf2(static_cast<float>(d));
}
// Provide these to the CRunner with the local float16 knowledge.
extern "C" void printF16(uint16_t bits) {
f16 f;
std::memcpy(&f, &bits, sizeof(f16));
std::cout << f;
}
extern "C" void printBF16(uint16_t bits) {
bf16 f;
std::memcpy(&f, &bits, sizeof(bf16));
std::cout << f;
}
#endif // MLIR_FLOAT16_DEFINE_FUNCTIONS
|
