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
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
|
# Copyright (C) 2020 Arm Limited or its affiliates. All rights reserved.
#
# SPDX-License-Identifier: Apache-2.0
#
# 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
#
# 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.
# Description:
# Unit tests for fixed point math
import numpy as np
import pytest
from ethosu.vela import fp_math
from ethosu.vela import scaling
from ethosu.vela.softmax import SoftMax
# Turn off black formatting for EXP_LUT to keep it compact
# fmt: off
EXP_LUT = [
0x000011c9, 0x000012b8, 0x000013b4, 0x000014bd, 0x000015d4, 0x000016fa, 0x0000182f, 0x00001975,
0x00001acb, 0x00001c34, 0x00001daf, 0x00001f3f, 0x000020e3, 0x0000229e, 0x00002470, 0x0000265a,
0x0000285e, 0x00002a7d, 0x00002cb9, 0x00002f13, 0x0000318c, 0x00003427, 0x000036e5, 0x000039c8,
0x00003cd1, 0x00004004, 0x00004361, 0x000046ec, 0x00004aa6, 0x00004e93, 0x000052b4, 0x0000570d,
0x00005ba1, 0x00006072, 0x00006583, 0x00006ada, 0x00007077, 0x00007661, 0x00007c9a, 0x00008327,
0x00008a0c, 0x0000914d, 0x000098f1, 0x0000a0fb, 0x0000a971, 0x0000b259, 0x0000bbb9, 0x0000c597,
0x0000cffa, 0x0000dae9, 0x0000e66b, 0x0000f288, 0x0000ff48, 0x00010cb3, 0x00011ad3, 0x000129b1,
0x00013957, 0x000149d0, 0x00015b26, 0x00016d65, 0x0001809b, 0x000194d2, 0x0001aa1a, 0x0001c080,
0x0001d814, 0x0001f0e4, 0x00020b03, 0x00022681, 0x00024371, 0x000261e7, 0x000281f7, 0x0002a3b5,
0x0002c73b, 0x0002ec9e, 0x000313f8, 0x00033d64, 0x000368fd, 0x000396e1, 0x0003c72e, 0x0003fa05,
0x00042f89, 0x000467dd, 0x0004a326, 0x0004e18e, 0x0005233d, 0x00056861, 0x0005b126, 0x0005fdbf,
0x00064e5f, 0x0006a33c, 0x0006fc8e, 0x00075a93, 0x0007bd89, 0x000825b3, 0x00089356, 0x000906bd,
0x00098035, 0x000a000f, 0x000a86a2, 0x000b1447, 0x000ba95f, 0x000c464e, 0x000ceb7c, 0x000d9959,
0x000e505a, 0x000f10f9, 0x000fdbb9, 0x0010b120, 0x001191c0, 0x00127e2f, 0x0013770b, 0x00147cfc,
0x001590b2, 0x0016b2e7, 0x0017e45d, 0x001925e1, 0x001a784c, 0x001bdc81, 0x001d536f, 0x001ede14,
0x00207d77, 0x002232af, 0x0023fee4, 0x0025e349, 0x0027e125, 0x0029f9ce, 0x002c2ead, 0x002e813e,
0x0030f30f, 0x003385c7, 0x00363b1f, 0x003914e9, 0x003c1510, 0x003f3d97, 0x004290a1, 0x00461066,
0x0049bf41, 0x004d9fad, 0x0051b444, 0x0055ffc3, 0x005a850f, 0x005f4730, 0x0064495a, 0x00698eeb,
0x006f1b6c, 0x0074f299, 0x007b185f, 0x008190de, 0x00886074, 0x008f8bae, 0x00971762, 0x009f08a2,
0x00a764c2, 0x00b03164, 0x00b9746e, 0x00c3341b, 0x00cd76fa, 0x00d843ed, 0x00e3a23b, 0x00ef9983,
0x00fc31d2, 0x010973a0, 0x011767d1, 0x012617cf, 0x01358d70, 0x0145d31c, 0x0156f3c1, 0x0168fadf,
0x017bf4a0, 0x018fedb6, 0x01a4f394, 0x01bb145a, 0x01d25ee1, 0x01eae2e5, 0x0204b0c8, 0x021fd9ed,
0x023c7091, 0x025a87f9, 0x027a343d, 0x029b8ac5, 0x02bea1ee, 0x02e3914d, 0x030a71c2, 0x03335d4e,
0x035e6f8d, 0x038bc56a, 0x03bb7d57, 0x03edb77c, 0x04229573, 0x045a3ae4, 0x0494cd29, 0x04d2739e,
0x051357c7, 0x0557a519, 0x059f8997, 0x05eb358d, 0x063adbcc, 0x068eb1ff, 0x06e6f049, 0x0743d21b,
0x07a595d9, 0x080c7d29, 0x0878cd66, 0x08eacf1a, 0x0962cf07, 0x09e11dcc, 0x0a661032, 0x0af1ffea,
0x0b854a9a, 0x0c20536f, 0x0cc3828e, 0x0d6f4584, 0x0e241040, 0x0ee25bb0, 0x0faaa7f2, 0x107d7b9e,
0x115b64be, 0x1244f787, 0x133ad1c6, 0x143d9885, 0x154df999, 0x166cac7a, 0x179a70d5, 0x18d81262,
0x1a266657, 0x1b864d4c, 0x1cf8b43e, 0x1e7e9316, 0x2018f0b9, 0x21c8e0b1, 0x238f851d, 0x256e1046,
0x2765c287, 0x2977ef55, 0x2ba5fab4, 0x2df15b8a, 0x305b9d83, 0x32e65ea3, 0x35935539, 0x38644d75,
0x3b5b2b74, 0x3e79eea7, 0x41c2addc, 0x45379f60, 0x48db159c, 0x4caf81fa, 0x50b7797f, 0x54f5af2b,
0x596cfe46, 0x5e2066e8, 0x631310c8, 0x684852d8, 0x6dc3a909, 0x7388c43d, 0x799b84b7, 0x7fffffff,
]
# fmt: on
def test_saturating_rounding_mul():
i32info = np.iinfo(np.int32)
i16info = np.iinfo(np.int16)
# Saturation
assert fp_math.saturating_rounding_mul32(i32info.min, i32info.min) == i32info.max
assert fp_math.saturating_rounding_mul32(i32info.min, i32info.max) == -i32info.max
assert fp_math.saturating_rounding_mul32(i32info.max, i32info.min) == -i32info.max
assert fp_math.saturating_rounding_mul16(i16info.min, i16info.min) == i16info.max
assert fp_math.saturating_rounding_mul16(i16info.min, i16info.max) == -i16info.max
assert fp_math.saturating_rounding_mul16(i16info.max, i16info.min) == -i16info.max
# Multiply by zero
assert fp_math.saturating_rounding_mul32(0, fp_math.from_float(1.0)) == 0
assert fp_math.saturating_rounding_mul32(0, fp_math.from_float(-1.0)) == 0
assert fp_math.saturating_rounding_mul32(fp_math.from_float(1.0), 0) == 0
assert fp_math.saturating_rounding_mul32(fp_math.from_float(-1.0), 0) == 0
assert fp_math.saturating_rounding_mul16(0, i16info.max) == 0
assert fp_math.saturating_rounding_mul16(0, i16info.min) == 0
assert fp_math.saturating_rounding_mul16(i16info.max, 0) == 0
assert fp_math.saturating_rounding_mul16(i16info.min, 0) == 0
# Multiply positive/negative
assert fp_math.saturating_rounding_mul32(fp_math.from_float(1.0), fp_math.from_float(1.0)) == fp_math.from_float(
1.0, 5 + 5
)
assert fp_math.saturating_rounding_mul32(fp_math.from_float(-1.0), fp_math.from_float(1.0)) == fp_math.from_float(
-1.0, 5 + 5
)
assert fp_math.saturating_rounding_mul32(fp_math.from_float(1.0), fp_math.from_float(-1.0)) == fp_math.from_float(
-1.0, 5 + 5
)
assert fp_math.saturating_rounding_mul32(fp_math.from_float(-1.0), fp_math.from_float(-1.0)) == fp_math.from_float(
1.0, 5 + 5
)
# Rounding
assert fp_math.saturating_rounding_mul32(fp_math.from_float(16.0), 1) == 1
assert fp_math.saturating_rounding_mul32(fp_math.from_float(-16.0), 1) == 0
assert fp_math.saturating_rounding_mul32(fp_math.from_float(16.0) - 1, 1) == 0
assert fp_math.saturating_rounding_mul32(fp_math.from_float(-16.0) - 1, 1) == -1
assert fp_math.saturating_rounding_mul16(fp_math.from_float(16.0, 21), 1) == 1
assert fp_math.saturating_rounding_mul16(fp_math.from_float(-16.0, 21), 1) == 0
assert fp_math.saturating_rounding_mul16(fp_math.from_float(16.0, 21) - 1, 1) == 0
assert fp_math.saturating_rounding_mul16(fp_math.from_float(-16.0, 21) - 1, 1) == -1
def test_shift_left():
i32info = np.iinfo(np.int32)
i16info = np.iinfo(np.int16)
assert fp_math.shift_left32(1, i32info.bits) == i32info.max
assert fp_math.shift_left32(-1, i32info.bits) == i32info.min
assert fp_math.shift_left32(1, i32info.bits - 2) == (i32info.max + 1) / 2
assert fp_math.shift_left32(-1, i32info.bits - 2) == i32info.min // 2
assert fp_math.shift_left16(1, i16info.bits) == i16info.max
assert fp_math.shift_left16(-1, i16info.bits) == i16info.min
assert fp_math.shift_left16(1, i16info.bits - 2) == (i16info.max + 1) / 2
assert fp_math.shift_left16(-1, i16info.bits - 2) == i16info.min // 2
assert fp_math.shift_left32(fp_math.from_float(1.0), 5) == i32info.max
assert fp_math.shift_left32(fp_math.from_float(-1.0), 5) == i32info.min
assert fp_math.shift_left32(fp_math.from_float(1.0), 4) == 16 * fp_math.from_float(1.0)
assert fp_math.shift_left32(fp_math.from_float(-1.0), 4) == 16 * fp_math.from_float(-1.0)
assert fp_math.shift_left16(fp_math.from_float(1.0, 21), 5) == i16info.max
assert fp_math.shift_left16(fp_math.from_float(-1.0, 21), 5) == i16info.min
assert fp_math.shift_left16(fp_math.from_float(1.0, 21), 4) == 16 * fp_math.from_float(1.0, 21)
assert fp_math.shift_left16(fp_math.from_float(-1.0, 21), 4) == 16 * fp_math.from_float(-1.0, 21)
with pytest.raises(AssertionError):
fp_math.shift_left32(1, -1)
fp_math.shift_left16(1, -1)
def test_rounding_divide_by_pot():
# No remainder division
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0), 26) == 1
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0), 26) == -1
# Remainder rounding the result away from zero
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0), 27) == -1
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0), 27) == 1
# Remainder smaller than threshold to round the result away from zero
# Positive and negative edge cases
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0) - 1, 27) == 0
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0) + 1, 27) == 0
# Far from the edge
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0), 28) == 0
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0), 28) == 0
# Regular division - no remainder
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0), 4) == fp_math.from_float(1.0 / 16)
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0), 4) == fp_math.from_float(-1.0 / 16)
# Rounding/no rounding edge cases
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0) + (1 << 3) - 1, 4) == fp_math.from_float(1.0 / 16)
assert fp_math.rounding_divide_by_pot(fp_math.from_float(1.0) + (1 << 3), 4) == fp_math.from_float(1.0 / 16) + 1
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0) - (1 << 3) + 1, 4) == fp_math.from_float(-1.0 / 16)
assert fp_math.rounding_divide_by_pot(fp_math.from_float(-1.0) - (1 << 3), 4) == fp_math.from_float(-1.0 / 16) - 1
def test_saturating_rounding_multiply_by_pot():
i32info = np.iinfo(np.int32)
assert fp_math.saturating_rounding_multiply_by_pot(fp_math.from_float(1.0), 5) == i32info.max
assert fp_math.saturating_rounding_multiply_by_pot(fp_math.from_float(-1.0), 5) == i32info.min
assert fp_math.saturating_rounding_multiply_by_pot(fp_math.from_float(1.0) - 1, 5) == i32info.max - 32 + 1
assert fp_math.saturating_rounding_multiply_by_pot(fp_math.from_float(-1.0) + 1, 5) == -i32info.max + 32 - 1
assert fp_math.saturating_rounding_multiply_by_pot(fp_math.from_float(1.0), 4) == fp_math.from_float(1.0 * 16)
assert fp_math.saturating_rounding_multiply_by_pot(fp_math.from_float(-1.0), 4) == fp_math.from_float(-1.0 * 16)
def test_rescale():
assert fp_math.rescale(5, 0, fp_math.from_float(1.0)) == fp_math.from_float(1.0, 0)
assert fp_math.rescale(5, 10, fp_math.from_float(1.0)) == fp_math.from_float(1.0, 10)
assert fp_math.rescale(5, 0, fp_math.from_float(-1.0)) == fp_math.from_float(-1.0, 0)
assert fp_math.rescale(5, 10, fp_math.from_float(-1.0)) == fp_math.from_float(-1.0, 10)
assert fp_math.rescale(5, 4, fp_math.from_float(32.0)) == fp_math.from_float(32.0, 4)
assert fp_math.rescale(5, 6, fp_math.from_float(32.0)) == fp_math.from_float(32.0, 6)
assert fp_math.rescale(5, 4, fp_math.from_float(-32.0)) == fp_math.from_float(-32.0, 4)
assert fp_math.rescale(5, 6, fp_math.from_float(-32.0)) == fp_math.from_float(-32.0, 6)
assert fp_math.rescale(5, 4, fp_math.from_float(31.9)) == fp_math.from_float(31.9, 4)
assert fp_math.rescale(5, 6, fp_math.from_float(31.9)) == fp_math.from_float(31.9, 6)
assert fp_math.rescale(5, 4, fp_math.from_float(-31.9)) == fp_math.from_float(-31.9, 4)
assert fp_math.rescale(5, 6, fp_math.from_float(-31.9)) == fp_math.from_float(-31.9, 6)
def test_exp():
sm = SoftMax(None)
for (expected, actual) in zip(EXP_LUT, sm.generate_exp_table(1.0, np.float32(0.05123165))):
assert actual == expected
multiply_test_data = [
(0, 0, 0),
(0, 0.7, 0),
(0, 55.8, 0),
(6, 0.3, 2),
(200, 0, 0),
(1, 1, 1),
(1, 0.1, 0),
(1, 3.49, 3),
(1, 3.51, 4),
(27, 1, 27),
(13, 0.9, 12),
(3, 21.2, 64),
(1000, 2000, 2000000),
(32767, 32767, 32767 * 32767), # extreme values
]
@pytest.mark.parametrize("x, factor, expected", multiply_test_data)
def test_multiply_by_quantized_multiplier(x, factor, expected):
scale, shift = scaling.quantise_scale(factor)
assert fp_math.multiply_by_quantized_multiplier(x, scale, shift) == expected
assert fp_math.multiply_by_quantized_multiplier(-x, scale, shift) == -expected
assert fp_math.multiply_by_quantized_multiplier(x, -scale, shift) == -expected
assert fp_math.multiply_by_quantized_multiplier(-x, -scale, shift) == expected
def test_multiply_by_quantized_multiplier_int16_limits():
# Tests min/max limits of foreseen practical usage of multiply_by_quantized_multiplier
# for the purpose of calculating LUTs
for x in [-32768, 32767]:
for y in [-32768, 32767]:
scale, shift = scaling.quantise_scale(y)
assert fp_math.multiply_by_quantized_multiplier(x, scale, shift) == x * y
|
