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
|
# Copyright 2010 Luca Barbieri
#
# Permission is hereby granted, free of charge, to any person obtaining
# a copy of this software and associated documentation files (the
# "Software"), to deal in the Software without restriction, including
# without limitation the rights to use, copy, modify, merge, publish,
# distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so, subject to
# the following conditions:
#
# The above copyright notice and this permission notice (including the
# next paragraph) shall be included in all copies or substantial
# portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
# IN NO EVENT SHALL THE COPYRIGHT OWNER(S) AND/OR ITS SUPPLIERS BE
# LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
# OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
# WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
#
# *************************************************************************
# The code is a reimplementation of the algorithm in
# www.fox-toolkit.org/ftp/fasthalffloatconversion.pdf
# "Fast Half Float Conversions" by Jeroen van der Zijp, Nov 2008
#
# The table contents have been slightly changed so that the exponent
# bias is now in the exponent table instead of the mantissa table (mostly
# for cosmetic reasons, and because it theoretically allows a variant
# that flushes denormal to zero but uses a mantissa table with 24-bit
# entries).
#
# The tables are also constructed slightly differently.
#
# Note that using a 64K * 4 table is a terrible idea since it will not fit
# in the L1 cache and will massively pollute the L2 cache as well
#
# These should instead fit in the L1 cache.
#
# TODO: we could use a denormal bias table instead of the mantissa/offset
# tables: this would reduce the L1 cache usage from 8704 to 2304 bytes
# but would involve more computation
#
# Note however that if denormals are never encountered, the L1 cache usage
# is only about 4608 bytes anyway.
table_index = None
table_length = None
def begin(t, n, l):
global table_length
global table_index
table_index = 0
table_length = l
print
print "const " + t + " " + n + "[" + str(l) + "] = {"
def value(v):
global table_index
table_index += 1
print "\t" + hex(v) + ","
def end():
global table_length
global table_index
print "};"
assert table_index == table_length
print "/* This file is autogenerated by u_half.py. Do not edit directly. */"
print "#include \"util/u_half.h\""
begin("uint32_t", "util_half_to_float_mantissa_table", 2048)
# zero
value(0)
# denormals
for i in xrange(1, 1024):
m = i << 13
e = 0
# normalize number
while (m & 0x00800000) == 0:
e -= 0x00800000;
m <<= 1;
m &= ~0x00800000;
e += 0x38800000;
value(m | e)
# normals
for i in xrange(1024, 2048):
value((i - 1024) << 13)
end()
begin("uint32_t", "util_half_to_float_exponent_table", 64)
# positive zero or denormals
value(0)
# positive numbers
for i in xrange(1, 31):
value(0x38000000 + (i << 23))
# positive infinity/NaN
value(0x7f800000)
# negative zero or denormals
value(0x80000000)
# negative numbers
for i in range(33, 63):
value(0xb8000000 + ((i - 32) << 23))
# negative infinity/NaN
value(0xff800000)
end()
begin("uint32_t", "util_half_to_float_offset_table", 64)
# positive zero or denormals
value(0)
# positive normals
for i in range(1, 32):
value(1024)
# negative zero or denormals
value(0)
# negative normals
for i in xrange(33, 64):
value(1024)
end()
begin("uint16_t", "util_float_to_half_base_table", 512)
for sign in (0, 0x8000):
# very small numbers mapping to zero
for i in xrange(-127, -24):
value(sign | 0)
# small numbers mapping to denormals
for i in xrange(-24, -14):
value(sign | (0x400 >> (-14 -i)))
# normal numbers
for i in xrange(-14, 16):
value(sign | ((i + 15) << 10))
# large numbers mapping to infinity
for i in xrange(16, 128):
value(sign | 0x7c00)
# infinity and NaNs
value(sign | 0x7c00)
end()
begin("uint8_t", "util_float_to_half_shift_table", 512)
for sign in (0, 0x8000):
# very small numbers mapping to zero
for i in xrange(-127, -24):
value(24)
# small numbers mapping to denormals
for i in xrange(-24, -14):
value(-1 - i)
# normal numbers
for i in xrange(-14, 16):
value(13)
# large numbers mapping to infinity
for i in xrange(16, 128):
value(24)
# infinity and NaNs
value(13)
end()
|
