ef240ae0e91c8f7c763f69885bf61870ee067746
[mesa.git] / src / compiler / nir / nir_opt_algebraic.py
1 #
2 # Copyright (C) 2014 Intel Corporation
3 #
4 # Permission is hereby granted, free of charge, to any person obtaining a
5 # copy of this software and associated documentation files (the "Software"),
6 # to deal in the Software without restriction, including without limitation
7 # the rights to use, copy, modify, merge, publish, distribute, sublicense,
8 # and/or sell copies of the Software, and to permit persons to whom the
9 # Software is furnished to do so, subject to the following conditions:
10 #
11 # The above copyright notice and this permission notice (including the next
12 # paragraph) shall be included in all copies or substantial portions of the
13 # Software.
14 #
15 # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
18 # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
20 # FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
21 # IN THE SOFTWARE.
22 #
23 # Authors:
24 # Jason Ekstrand (jason@jlekstrand.net)
25
26 import nir_algebraic
27
28 # Convenience variables
29 a = 'a'
30 b = 'b'
31 c = 'c'
32 d = 'd'
33
34 # Written in the form (<search>, <replace>) where <search> is an expression
35 # and <replace> is either an expression or a value. An expression is
36 # defined as a tuple of the form ([~]<op>, <src0>, <src1>, <src2>, <src3>)
37 # where each source is either an expression or a value. A value can be
38 # either a numeric constant or a string representing a variable name.
39 #
40 # If the opcode in a search expression is prefixed by a '~' character, this
41 # indicates that the operation is inexact. Such operations will only get
42 # applied to SSA values that do not have the exact bit set. This should be
43 # used by by any optimizations that are not bit-for-bit exact. It should not,
44 # however, be used for backend-requested lowering operations as those need to
45 # happen regardless of precision.
46 #
47 # Variable names are specified as "[#]name[@type][(cond)]" where "#" inicates
48 # that the given variable will only match constants and the type indicates that
49 # the given variable will only match values from ALU instructions with the
50 # given output type, and (cond) specifies an additional condition function
51 # (see nir_search_helpers.h).
52 #
53 # For constants, you have to be careful to make sure that it is the right
54 # type because python is unaware of the source and destination types of the
55 # opcodes.
56 #
57 # All expression types can have a bit-size specified. For opcodes, this
58 # looks like "op@32", for variables it is "a@32" or "a@uint32" to specify a
59 # type and size, and for literals, you can write "2.0@32". In the search half
60 # of the expression this indicates that it should only match that particular
61 # bit-size. In the replace half of the expression this indicates that the
62 # constructed value should have that bit-size.
63
64 optimizations = [
65
66 (('imul', a, '#b@32(is_pos_power_of_two)'), ('ishl', a, ('find_lsb', b))),
67 (('imul', a, '#b@32(is_neg_power_of_two)'), ('ineg', ('ishl', a, ('find_lsb', ('iabs', b))))),
68 (('udiv', a, 1), a),
69 (('idiv', a, 1), a),
70 (('umod', a, 1), 0),
71 (('imod', a, 1), 0),
72 (('udiv', a, '#b@32(is_pos_power_of_two)'), ('ushr', a, ('find_lsb', b))),
73 (('idiv', a, '#b@32(is_pos_power_of_two)'), ('imul', ('isign', a), ('ushr', ('iabs', a), ('find_lsb', b))), 'options->lower_idiv'),
74 (('idiv', a, '#b@32(is_neg_power_of_two)'), ('ineg', ('imul', ('isign', a), ('ushr', ('iabs', a), ('find_lsb', ('iabs', b))))), 'options->lower_idiv'),
75 (('umod', a, '#b(is_pos_power_of_two)'), ('iand', a, ('isub', b, 1))),
76
77 (('fneg', ('fneg', a)), a),
78 (('ineg', ('ineg', a)), a),
79 (('fabs', ('fabs', a)), ('fabs', a)),
80 (('fabs', ('fneg', a)), ('fabs', a)),
81 (('fabs', ('u2f32', a)), ('u2f32', a)),
82 (('iabs', ('iabs', a)), ('iabs', a)),
83 (('iabs', ('ineg', a)), ('iabs', a)),
84 (('~fadd', a, 0.0), a),
85 (('iadd', a, 0), a),
86 (('usadd_4x8', a, 0), a),
87 (('usadd_4x8', a, ~0), ~0),
88 (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
89 (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
90 (('~fadd', ('fneg', a), a), 0.0),
91 (('iadd', ('ineg', a), a), 0),
92 (('iadd', ('ineg', a), ('iadd', a, b)), b),
93 (('iadd', a, ('iadd', ('ineg', a), b)), b),
94 (('~fadd', ('fneg', a), ('fadd', a, b)), b),
95 (('~fadd', a, ('fadd', ('fneg', a), b)), b),
96 (('~fmul', a, 0.0), 0.0),
97 (('imul', a, 0), 0),
98 (('umul_unorm_4x8', a, 0), 0),
99 (('umul_unorm_4x8', a, ~0), a),
100 (('fmul', a, 1.0), a),
101 (('imul', a, 1), a),
102 (('fmul', a, -1.0), ('fneg', a)),
103 (('imul', a, -1), ('ineg', a)),
104 (('~ffma', 0.0, a, b), b),
105 (('~ffma', a, 0.0, b), b),
106 (('~ffma', a, b, 0.0), ('fmul', a, b)),
107 (('ffma', a, 1.0, b), ('fadd', a, b)),
108 (('ffma', 1.0, a, b), ('fadd', a, b)),
109 (('~flrp', a, b, 0.0), a),
110 (('~flrp', a, b, 1.0), b),
111 (('~flrp', a, a, b), a),
112 (('~flrp', 0.0, a, b), ('fmul', a, b)),
113 (('~flrp', a, b, ('b2f', c)), ('bcsel', c, b, a), 'options->lower_flrp32'),
114 (('~flrp', a, 0.0, c), ('fadd', ('fmul', ('fneg', a), c), a)),
115 (('flrp@32', a, b, c), ('fadd', ('fmul', c, ('fsub', b, a)), a), 'options->lower_flrp32'),
116 (('flrp@64', a, b, c), ('fadd', ('fmul', c, ('fsub', b, a)), a), 'options->lower_flrp64'),
117 (('ffract', a), ('fsub', a, ('ffloor', a)), 'options->lower_ffract'),
118 (('~fadd', ('fmul', a, ('fadd', 1.0, ('fneg', ('b2f', c)))), ('fmul', b, ('b2f', c))), ('bcsel', c, b, a), 'options->lower_flrp32'),
119 (('~fadd@32', ('fmul', a, ('fadd', 1.0, ('fneg', c ))), ('fmul', b, c )), ('flrp', a, b, c), '!options->lower_flrp32'),
120 (('~fadd@64', ('fmul', a, ('fadd', 1.0, ('fneg', c ))), ('fmul', b, c )), ('flrp', a, b, c), '!options->lower_flrp64'),
121 (('~fadd', a, ('fmul', ('b2f', c), ('fadd', b, ('fneg', a)))), ('bcsel', c, b, a), 'options->lower_flrp32'),
122 (('~fadd@32', a, ('fmul', c , ('fadd', b, ('fneg', a)))), ('flrp', a, b, c), '!options->lower_flrp32'),
123 (('~fadd@64', a, ('fmul', c , ('fadd', b, ('fneg', a)))), ('flrp', a, b, c), '!options->lower_flrp64'),
124 (('ffma', a, b, c), ('fadd', ('fmul', a, b), c), 'options->lower_ffma'),
125 (('~fadd', ('fmul', a, b), c), ('ffma', a, b, c), 'options->fuse_ffma'),
126
127 # (a * #b + #c) << #d
128 # ((a * #b) << #d) + (#c << #d)
129 # (a * (#b << #d)) + (#c << #d)
130 (('ishl', ('iadd', ('imul', a, '#b'), '#c'), '#d'),
131 ('iadd', ('imul', a, ('ishl', b, d)), ('ishl', c, d))),
132
133 # (a * #b) << #c
134 # a * (#b << #c)
135 (('ishl', ('imul', a, '#b'), '#c'), ('imul', a, ('ishl', b, c))),
136
137 # Comparison simplifications
138 (('~inot', ('flt', a, b)), ('fge', a, b)),
139 (('~inot', ('fge', a, b)), ('flt', a, b)),
140 (('~inot', ('feq', a, b)), ('fne', a, b)),
141 (('~inot', ('fne', a, b)), ('feq', a, b)),
142 (('inot', ('ilt', a, b)), ('ige', a, b)),
143 (('inot', ('ige', a, b)), ('ilt', a, b)),
144 (('inot', ('ieq', a, b)), ('ine', a, b)),
145 (('inot', ('ine', a, b)), ('ieq', a, b)),
146
147 # 0.0 >= b2f(a)
148 # b2f(a) <= 0.0
149 # b2f(a) == 0.0 because b2f(a) can only be 0 or 1
150 # inot(a)
151 (('fge', 0.0, ('b2f', a)), ('inot', a)),
152
153 (('fge', ('fneg', ('b2f', a)), 0.0), ('inot', a)),
154
155 # 0.0 < fabs(a)
156 # fabs(a) > 0.0
157 # fabs(a) != 0.0 because fabs(a) must be >= 0
158 # a != 0.0
159 (('flt', 0.0, ('fabs', a)), ('fne', a, 0.0)),
160
161 (('fmax', ('b2f(is_used_once)', a), ('b2f', b)), ('b2f', ('ior', a, b))),
162 (('fmax', ('fneg(is_used_once)', ('b2f(is_used_once)', a)), ('fneg', ('b2f', b))), ('fneg', ('b2f', ('ior', a, b)))),
163 (('fmin', ('b2f(is_used_once)', a), ('b2f', b)), ('b2f', ('iand', a, b))),
164 (('fmin', ('fneg(is_used_once)', ('b2f(is_used_once)', a)), ('fneg', ('b2f', b))), ('fneg', ('b2f', ('iand', a, b)))),
165
166 # ignore this opt when the result is used by a bcsel or if so we can make
167 # use of conditional modifiers on supported hardware.
168 (('flt(is_not_used_by_conditional)', ('fadd(is_used_once)', a, ('fneg', b)), 0.0), ('flt', a, b)),
169
170 (('fge', ('fneg', ('fabs', a)), 0.0), ('feq', a, 0.0)),
171 (('bcsel', ('flt', b, a), b, a), ('fmin', a, b)),
172 (('bcsel', ('flt', a, b), b, a), ('fmax', a, b)),
173 (('~bcsel', ('fge', a, b), b, a), ('fmin', a, b)),
174 (('~bcsel', ('fge', b, a), b, a), ('fmax', a, b)),
175 (('bcsel', ('inot', a), b, c), ('bcsel', a, c, b)),
176 (('bcsel', a, ('bcsel', a, b, c), d), ('bcsel', a, b, d)),
177 (('bcsel', a, True, 'b@bool'), ('ior', a, b)),
178 (('fmin', a, a), a),
179 (('fmax', a, a), a),
180 (('imin', a, a), a),
181 (('imax', a, a), a),
182 (('umin', a, a), a),
183 (('umax', a, a), a),
184 (('fmin', a, ('fneg', a)), ('fneg', ('fabs', a))),
185 (('imin', a, ('ineg', a)), ('ineg', ('iabs', a))),
186 (('fmin', a, ('fneg', ('fabs', a))), ('fneg', ('fabs', a))),
187 (('imin', a, ('ineg', ('iabs', a))), ('ineg', ('iabs', a))),
188 (('fmin', a, ('fabs', a)), a),
189 (('imin', a, ('iabs', a)), a),
190 (('fmax', a, ('fneg', ('fabs', a))), a),
191 (('imax', a, ('ineg', ('iabs', a))), a),
192 (('fmax', a, ('fabs', a)), ('fabs', a)),
193 (('imax', a, ('iabs', a)), ('iabs', a)),
194 (('fmax', a, ('fneg', a)), ('fabs', a)),
195 (('imax', a, ('ineg', a)), ('iabs', a)),
196 (('~fmin', ('fmax', a, 0.0), 1.0), ('fsat', a), '!options->lower_fsat'),
197 (('~fmax', ('fmin', a, 1.0), 0.0), ('fsat', a), '!options->lower_fsat'),
198 (('fsat', a), ('fmin', ('fmax', a, 0.0), 1.0), 'options->lower_fsat'),
199 (('fsat', ('fsat', a)), ('fsat', a)),
200 (('fmin', ('fmax', ('fmin', ('fmax', a, b), c), b), c), ('fmin', ('fmax', a, b), c)),
201 (('imin', ('imax', ('imin', ('imax', a, b), c), b), c), ('imin', ('imax', a, b), c)),
202 (('umin', ('umax', ('umin', ('umax', a, b), c), b), c), ('umin', ('umax', a, b), c)),
203 (('fmax', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmax', a, b))),
204 (('fmin', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmin', a, b))),
205 (('extract_u8', ('imin', ('imax', a, 0), 0xff), 0), ('imin', ('imax', a, 0), 0xff)),
206 (('~ior', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmax', b, c))),
207 (('~ior', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmin', a, b), c)),
208 (('~ior', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmin', b, c))),
209 (('~ior', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmax', a, b), c)),
210 (('~ior', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmax', b, c))),
211 (('~ior', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmin', a, b), c)),
212 (('~ior', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmin', b, c))),
213 (('~ior', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmax', a, b), c)),
214 (('~iand', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmin', b, c))),
215 (('~iand', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmax', a, b), c)),
216 (('~iand', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmax', b, c))),
217 (('~iand', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmin', a, b), c)),
218 (('~iand', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmin', b, c))),
219 (('~iand', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmax', a, b), c)),
220 (('~iand', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmax', b, c))),
221 (('~iand', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmin', a, b), c)),
222
223 (('ior', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imax', b, c))),
224 (('ior', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imin', a, b), c)),
225 (('ior', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imin', b, c))),
226 (('ior', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imax', a, b), c)),
227 (('ior', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umax', b, c))),
228 (('ior', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umin', a, b), c)),
229 (('ior', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umin', b, c))),
230 (('ior', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umax', a, b), c)),
231 (('iand', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imin', b, c))),
232 (('iand', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imax', a, b), c)),
233 (('iand', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imax', b, c))),
234 (('iand', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imin', a, b), c)),
235 (('iand', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umin', b, c))),
236 (('iand', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umax', a, b), c)),
237 (('iand', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umax', b, c))),
238 (('iand', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umin', a, b), c)),
239
240 # These patterns can result when (a < b || a < c) => (a < min(b, c))
241 # transformations occur before constant propagation and loop-unrolling.
242 (('~flt', a, ('fmax', b, a)), ('flt', a, b)),
243 (('~flt', ('fmin', a, b), a), ('flt', b, a)),
244 (('~fge', a, ('fmin', b, a)), True),
245 (('~fge', ('fmax', a, b), a), True),
246 (('~flt', a, ('fmin', b, a)), False),
247 (('~flt', ('fmax', a, b), a), False),
248
249 (('ilt', a, ('imax', b, a)), ('ilt', a, b)),
250 (('ilt', ('imin', a, b), a), ('ilt', b, a)),
251 (('ige', a, ('imin', b, a)), True),
252 (('ige', ('imax', a, b), a), True),
253 (('ult', a, ('umax', b, a)), ('ult', a, b)),
254 (('ult', ('umin', a, b), a), ('ult', b, a)),
255 (('uge', a, ('umin', b, a)), True),
256 (('uge', ('umax', a, b), a), True),
257
258 (('ilt', '#a', ('imin', '#b', c)), ('iand', ('ilt', a, b), ('ilt', a, c))),
259 (('ilt', ('imax', '#a', b), '#c'), ('iand', ('ilt', a, c), ('ilt', b, c))),
260 (('ige', '#a', ('imax', '#b', c)), ('iand', ('ige', a, b), ('ige', a, c))),
261 (('ige', ('imin', '#a', b), '#c'), ('iand', ('ige', a, c), ('ige', b, c))),
262 (('ult', '#a', ('umin', '#b', c)), ('iand', ('ult', a, b), ('ult', a, c))),
263 (('ult', ('umax', '#a', b), '#c'), ('iand', ('ult', a, c), ('ult', b, c))),
264 (('uge', '#a', ('umax', '#b', c)), ('iand', ('uge', a, b), ('uge', a, c))),
265 (('uge', ('umin', '#a', b), '#c'), ('iand', ('uge', a, c), ('uge', b, c))),
266
267 (('fabs', ('slt', a, b)), ('slt', a, b)),
268 (('fabs', ('sge', a, b)), ('sge', a, b)),
269 (('fabs', ('seq', a, b)), ('seq', a, b)),
270 (('fabs', ('sne', a, b)), ('sne', a, b)),
271 (('slt', a, b), ('b2f', ('flt', a, b)), 'options->lower_scmp'),
272 (('sge', a, b), ('b2f', ('fge', a, b)), 'options->lower_scmp'),
273 (('seq', a, b), ('b2f', ('feq', a, b)), 'options->lower_scmp'),
274 (('sne', a, b), ('b2f', ('fne', a, b)), 'options->lower_scmp'),
275 (('fne', ('fneg', a), a), ('fne', a, 0.0)),
276 (('feq', ('fneg', a), a), ('feq', a, 0.0)),
277 # Emulating booleans
278 (('imul', ('b2i', a), ('b2i', b)), ('b2i', ('iand', a, b))),
279 (('fmul', ('b2f', a), ('b2f', b)), ('b2f', ('iand', a, b))),
280 (('fsat', ('fadd', ('b2f', a), ('b2f', b))), ('b2f', ('ior', a, b))),
281 (('iand', 'a@bool', 1.0), ('b2f', a)),
282 # True/False are ~0 and 0 in NIR. b2i of True is 1, and -1 is ~0 (True).
283 (('ineg', ('b2i@32', a)), a),
284 (('flt', ('fneg', ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
285 (('flt', ('fsub', 0.0, ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
286 # Comparison with the same args. Note that these are not done for
287 # the float versions because NaN always returns false on float
288 # inequalities.
289 (('ilt', a, a), False),
290 (('ige', a, a), True),
291 (('ieq', a, a), True),
292 (('ine', a, a), False),
293 (('ult', a, a), False),
294 (('uge', a, a), True),
295 # Logical and bit operations
296 (('fand', a, 0.0), 0.0),
297 (('iand', a, a), a),
298 (('iand', a, ~0), a),
299 (('iand', a, 0), 0),
300 (('ior', a, a), a),
301 (('ior', a, 0), a),
302 (('ior', a, True), True),
303 (('fxor', a, a), 0.0),
304 (('ixor', a, a), 0),
305 (('ixor', a, 0), a),
306 (('inot', ('inot', a)), a),
307 # DeMorgan's Laws
308 (('iand', ('inot', a), ('inot', b)), ('inot', ('ior', a, b))),
309 (('ior', ('inot', a), ('inot', b)), ('inot', ('iand', a, b))),
310 # Shift optimizations
311 (('ishl', 0, a), 0),
312 (('ishl', a, 0), a),
313 (('ishr', 0, a), 0),
314 (('ishr', a, 0), a),
315 (('ushr', 0, a), 0),
316 (('ushr', a, 0), a),
317 (('iand', 0xff, ('ushr@32', a, 24)), ('ushr', a, 24)),
318 (('iand', 0xffff, ('ushr@32', a, 16)), ('ushr', a, 16)),
319 # Exponential/logarithmic identities
320 (('~fexp2', ('flog2', a)), a), # 2^lg2(a) = a
321 (('~flog2', ('fexp2', a)), a), # lg2(2^a) = a
322 (('fpow', a, b), ('fexp2', ('fmul', ('flog2', a), b)), 'options->lower_fpow'), # a^b = 2^(lg2(a)*b)
323 (('~fexp2', ('fmul', ('flog2', a), b)), ('fpow', a, b), '!options->lower_fpow'), # 2^(lg2(a)*b) = a^b
324 (('~fexp2', ('fadd', ('fmul', ('flog2', a), b), ('fmul', ('flog2', c), d))),
325 ('~fmul', ('fpow', a, b), ('fpow', c, d)), '!options->lower_fpow'), # 2^(lg2(a) * b + lg2(c) + d) = a^b * c^d
326 (('~fexp2', ('fmul', ('flog2', a), 2.0)), ('fmul', a, a)),
327 (('~fexp2', ('fmul', ('flog2', a), 4.0)), ('fmul', ('fmul', a, a), ('fmul', a, a))),
328 (('~fpow', a, 1.0), a),
329 (('~fpow', a, 2.0), ('fmul', a, a)),
330 (('~fpow', a, 4.0), ('fmul', ('fmul', a, a), ('fmul', a, a))),
331 (('~fpow', 2.0, a), ('fexp2', a)),
332 (('~fpow', ('fpow', a, 2.2), 0.454545), a),
333 (('~fpow', ('fabs', ('fpow', a, 2.2)), 0.454545), ('fabs', a)),
334 (('~fsqrt', ('fexp2', a)), ('fexp2', ('fmul', 0.5, a))),
335 (('~frcp', ('fexp2', a)), ('fexp2', ('fneg', a))),
336 (('~frsq', ('fexp2', a)), ('fexp2', ('fmul', -0.5, a))),
337 (('~flog2', ('fsqrt', a)), ('fmul', 0.5, ('flog2', a))),
338 (('~flog2', ('frcp', a)), ('fneg', ('flog2', a))),
339 (('~flog2', ('frsq', a)), ('fmul', -0.5, ('flog2', a))),
340 (('~flog2', ('fpow', a, b)), ('fmul', b, ('flog2', a))),
341 (('~fmul', ('fexp2(is_used_once)', a), ('fexp2(is_used_once)', b)), ('fexp2', ('fadd', a, b))),
342 # Division and reciprocal
343 (('~fdiv', 1.0, a), ('frcp', a)),
344 (('fdiv', a, b), ('fmul', a, ('frcp', b)), 'options->lower_fdiv'),
345 (('~frcp', ('frcp', a)), a),
346 (('~frcp', ('fsqrt', a)), ('frsq', a)),
347 (('fsqrt', a), ('frcp', ('frsq', a)), 'options->lower_fsqrt'),
348 (('~frcp', ('frsq', a)), ('fsqrt', a), '!options->lower_fsqrt'),
349 # Boolean simplifications
350 (('ieq', 'a@bool', True), a),
351 (('ine(is_not_used_by_if)', 'a@bool', True), ('inot', a)),
352 (('ine', 'a@bool', False), a),
353 (('ieq(is_not_used_by_if)', 'a@bool', False), ('inot', 'a')),
354 (('bcsel', a, True, False), a),
355 (('bcsel', a, False, True), ('inot', a)),
356 (('bcsel@32', a, 1.0, 0.0), ('b2f', a)),
357 (('bcsel@32', a, 0.0, 1.0), ('b2f', ('inot', a))),
358 (('bcsel@32', a, -1.0, -0.0), ('fneg', ('b2f', a))),
359 (('bcsel@32', a, -0.0, -1.0), ('fneg', ('b2f', ('inot', a)))),
360 (('bcsel', True, b, c), b),
361 (('bcsel', False, b, c), c),
362 # The result of this should be hit by constant propagation and, in the
363 # next round of opt_algebraic, get picked up by one of the above two.
364 (('bcsel', '#a', b, c), ('bcsel', ('ine', 'a', 0), b, c)),
365
366 (('bcsel', a, b, b), b),
367 (('fcsel', a, b, b), b),
368
369 # Conversions
370 (('i2b', ('b2i', a)), a),
371 (('f2i32', ('ftrunc', a)), ('f2i32', a)),
372 (('f2u32', ('ftrunc', a)), ('f2u32', a)),
373 (('i2b', ('ineg', a)), ('i2b', a)),
374 (('i2b', ('iabs', a)), ('i2b', a)),
375 (('fabs', ('b2f', a)), ('b2f', a)),
376 (('iabs', ('b2i', a)), ('b2i', a)),
377
378 # Packing and then unpacking does nothing
379 (('unpack_64_2x32_split_x', ('pack_64_2x32_split', a, b)), a),
380 (('unpack_64_2x32_split_y', ('pack_64_2x32_split', a, b)), b),
381 (('pack_64_2x32_split', ('unpack_64_2x32_split_x', a),
382 ('unpack_64_2x32_split_y', a)), a),
383
384 # Byte extraction
385 (('ushr', a, 24), ('extract_u8', a, 3), '!options->lower_extract_byte'),
386 (('iand', 0xff, ('ushr', a, 16)), ('extract_u8', a, 2), '!options->lower_extract_byte'),
387 (('iand', 0xff, ('ushr', a, 8)), ('extract_u8', a, 1), '!options->lower_extract_byte'),
388 (('iand', 0xff, a), ('extract_u8', a, 0), '!options->lower_extract_byte'),
389
390 # Word extraction
391 (('ushr', a, 16), ('extract_u16', a, 1), '!options->lower_extract_word'),
392 (('iand', 0xffff, a), ('extract_u16', a, 0), '!options->lower_extract_word'),
393
394 # Subtracts
395 (('~fsub', a, ('fsub', 0.0, b)), ('fadd', a, b)),
396 (('isub', a, ('isub', 0, b)), ('iadd', a, b)),
397 (('ussub_4x8', a, 0), a),
398 (('ussub_4x8', a, ~0), 0),
399 (('fsub', a, b), ('fadd', a, ('fneg', b)), 'options->lower_sub'),
400 (('isub', a, b), ('iadd', a, ('ineg', b)), 'options->lower_sub'),
401 (('fneg', a), ('fsub', 0.0, a), 'options->lower_negate'),
402 (('ineg', a), ('isub', 0, a), 'options->lower_negate'),
403 (('~fadd', a, ('fsub', 0.0, b)), ('fsub', a, b)),
404 (('iadd', a, ('isub', 0, b)), ('isub', a, b)),
405 (('fabs', ('fsub', 0.0, a)), ('fabs', a)),
406 (('iabs', ('isub', 0, a)), ('iabs', a)),
407
408 # Propagate negation up multiplication chains
409 (('fmul', ('fneg', a), b), ('fneg', ('fmul', a, b))),
410 (('imul', ('ineg', a), b), ('ineg', ('imul', a, b))),
411
412 # Propagate constants up multiplication chains
413 (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fmul', ('fmul', a, c), b)),
414 (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('imul', ('imul', a, c), b)),
415 (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fadd', ('fadd', a, c), b)),
416 (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('iadd', ('iadd', a, c), b)),
417
418 # Reassociate constants in add/mul chains so they can be folded together.
419 # For now, we mostly only handle cases where the constants are separated by
420 # a single non-constant. We could do better eventually.
421 (('~fmul', '#a', ('fmul', b, '#c')), ('fmul', ('fmul', a, c), b)),
422 (('imul', '#a', ('imul', b, '#c')), ('imul', ('imul', a, c), b)),
423 (('~fadd', '#a', ('fadd', b, '#c')), ('fadd', ('fadd', a, c), b)),
424 (('~fadd', '#a', ('fneg', ('fadd', b, '#c'))), ('fadd', ('fadd', a, ('fneg', c)), ('fneg', b))),
425 (('iadd', '#a', ('iadd', b, '#c')), ('iadd', ('iadd', a, c), b)),
426
427 # By definition...
428 (('bcsel', ('ige', ('find_lsb', a), 0), ('find_lsb', a), -1), ('find_lsb', a)),
429 (('bcsel', ('ige', ('ifind_msb', a), 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
430 (('bcsel', ('ige', ('ufind_msb', a), 0), ('ufind_msb', a), -1), ('ufind_msb', a)),
431
432 (('bcsel', ('ine', a, 0), ('find_lsb', a), -1), ('find_lsb', a)),
433 (('bcsel', ('ine', a, 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
434 (('bcsel', ('ine', a, 0), ('ufind_msb', a), -1), ('ufind_msb', a)),
435
436 (('bcsel', ('ine', a, -1), ('ifind_msb', a), -1), ('ifind_msb', a)),
437
438 # Misc. lowering
439 (('fmod@32', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod32'),
440 (('fmod@64', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod64'),
441 (('frem', a, b), ('fsub', a, ('fmul', b, ('ftrunc', ('fdiv', a, b)))), 'options->lower_fmod32'),
442 (('uadd_carry@32', a, b), ('b2i', ('ult', ('iadd', a, b), a)), 'options->lower_uadd_carry'),
443 (('usub_borrow@32', a, b), ('b2i', ('ult', a, b)), 'options->lower_usub_borrow'),
444
445 (('bitfield_insert', 'base', 'insert', 'offset', 'bits'),
446 ('bcsel', ('ilt', 31, 'bits'), 'insert',
447 ('bfi', ('bfm', 'bits', 'offset'), 'insert', 'base')),
448 'options->lower_bitfield_insert'),
449
450 (('ibitfield_extract', 'value', 'offset', 'bits'),
451 ('bcsel', ('ilt', 31, 'bits'), 'value',
452 ('ibfe', 'value', 'offset', 'bits')),
453 'options->lower_bitfield_extract'),
454
455 (('ubitfield_extract', 'value', 'offset', 'bits'),
456 ('bcsel', ('ult', 31, 'bits'), 'value',
457 ('ubfe', 'value', 'offset', 'bits')),
458 'options->lower_bitfield_extract'),
459
460 (('extract_i8', a, 'b@32'),
461 ('ishr', ('ishl', a, ('imul', ('isub', 3, b), 8)), 24),
462 'options->lower_extract_byte'),
463
464 (('extract_u8', a, 'b@32'),
465 ('iand', ('ushr', a, ('imul', b, 8)), 0xff),
466 'options->lower_extract_byte'),
467
468 (('extract_i16', a, 'b@32'),
469 ('ishr', ('ishl', a, ('imul', ('isub', 1, b), 16)), 16),
470 'options->lower_extract_word'),
471
472 (('extract_u16', a, 'b@32'),
473 ('iand', ('ushr', a, ('imul', b, 16)), 0xffff),
474 'options->lower_extract_word'),
475
476 (('pack_unorm_2x16', 'v'),
477 ('pack_uvec2_to_uint',
478 ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 65535.0)))),
479 'options->lower_pack_unorm_2x16'),
480
481 (('pack_unorm_4x8', 'v'),
482 ('pack_uvec4_to_uint',
483 ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 255.0)))),
484 'options->lower_pack_unorm_4x8'),
485
486 (('pack_snorm_2x16', 'v'),
487 ('pack_uvec2_to_uint',
488 ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 32767.0)))),
489 'options->lower_pack_snorm_2x16'),
490
491 (('pack_snorm_4x8', 'v'),
492 ('pack_uvec4_to_uint',
493 ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 127.0)))),
494 'options->lower_pack_snorm_4x8'),
495
496 (('unpack_unorm_2x16', 'v'),
497 ('fdiv', ('u2f32', ('vec2', ('extract_u16', 'v', 0),
498 ('extract_u16', 'v', 1))),
499 65535.0),
500 'options->lower_unpack_unorm_2x16'),
501
502 (('unpack_unorm_4x8', 'v'),
503 ('fdiv', ('u2f32', ('vec4', ('extract_u8', 'v', 0),
504 ('extract_u8', 'v', 1),
505 ('extract_u8', 'v', 2),
506 ('extract_u8', 'v', 3))),
507 255.0),
508 'options->lower_unpack_unorm_4x8'),
509
510 (('unpack_snorm_2x16', 'v'),
511 ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec2', ('extract_i16', 'v', 0),
512 ('extract_i16', 'v', 1))),
513 32767.0))),
514 'options->lower_unpack_snorm_2x16'),
515
516 (('unpack_snorm_4x8', 'v'),
517 ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec4', ('extract_i8', 'v', 0),
518 ('extract_i8', 'v', 1),
519 ('extract_i8', 'v', 2),
520 ('extract_i8', 'v', 3))),
521 127.0))),
522 'options->lower_unpack_snorm_4x8'),
523 ]
524
525 def fexp2i(exp, bits):
526 # We assume that exp is already in the right range.
527 if bits == 32:
528 return ('ishl', ('iadd', exp, 127), 23)
529 elif bits == 64:
530 return ('pack_64_2x32_split', 0, ('ishl', ('iadd', exp, 1023), 20))
531 else:
532 assert False
533
534 def ldexp(f, exp, bits):
535 # First, we clamp exp to a reasonable range. The maximum possible range
536 # for a normal exponent is [-126, 127] and, throwing in denormals, you get
537 # a maximum range of [-149, 127]. This means that we can potentially have
538 # a swing of +-276. If you start with FLT_MAX, you actually have to do
539 # ldexp(FLT_MAX, -278) to get it to flush all the way to zero. The GLSL
540 # spec, on the other hand, only requires that we handle an exponent value
541 # in the range [-126, 128]. This implementation is *mostly* correct; it
542 # handles a range on exp of [-252, 254] which allows you to create any
543 # value (including denorms if the hardware supports it) and to adjust the
544 # exponent of any normal value to anything you want.
545 if bits == 32:
546 exp = ('imin', ('imax', exp, -252), 254)
547 elif bits == 64:
548 exp = ('imin', ('imax', exp, -2044), 2046)
549 else:
550 assert False
551
552 # Now we compute two powers of 2, one for exp/2 and one for exp-exp/2.
553 # (We use ishr which isn't the same for -1, but the -1 case still works
554 # since we use exp-exp/2 as the second exponent.) While the spec
555 # technically defines ldexp as f * 2.0^exp, simply multiplying once doesn't
556 # work with denormals and doesn't allow for the full swing in exponents
557 # that you can get with normalized values. Instead, we create two powers
558 # of two and multiply by them each in turn. That way the effective range
559 # of our exponent is doubled.
560 pow2_1 = fexp2i(('ishr', exp, 1), bits)
561 pow2_2 = fexp2i(('isub', exp, ('ishr', exp, 1)), bits)
562 return ('fmul', ('fmul', f, pow2_1), pow2_2)
563
564 optimizations += [
565 (('ldexp@32', 'x', 'exp'), ldexp('x', 'exp', 32), 'options->lower_ldexp'),
566 (('ldexp@64', 'x', 'exp'), ldexp('x', 'exp', 64), 'options->lower_ldexp'),
567 ]
568
569 # Unreal Engine 4 demo applications open-codes bitfieldReverse()
570 def bitfield_reverse(u):
571 step1 = ('ior', ('ishl', u, 16), ('ushr', u, 16))
572 step2 = ('ior', ('ishl', ('iand', step1, 0x00ff00ff), 8), ('ushr', ('iand', step1, 0xff00ff00), 8))
573 step3 = ('ior', ('ishl', ('iand', step2, 0x0f0f0f0f), 4), ('ushr', ('iand', step2, 0xf0f0f0f0), 4))
574 step4 = ('ior', ('ishl', ('iand', step3, 0x33333333), 2), ('ushr', ('iand', step3, 0xcccccccc), 2))
575 step5 = ('ior', ('ishl', ('iand', step4, 0x55555555), 1), ('ushr', ('iand', step4, 0xaaaaaaaa), 1))
576
577 return step5
578
579 optimizations += [(bitfield_reverse('x@32'), ('bitfield_reverse', 'x'))]
580
581 # For any float comparison operation, "cmp", if you have "a == a && a cmp b"
582 # then the "a == a" is redundant because it's equivalent to "a is not NaN"
583 # and, if a is a NaN then the second comparison will fail anyway.
584 for op in ['flt', 'fge', 'feq']:
585 optimizations += [
586 (('iand', ('feq', a, a), (op, a, b)), (op, a, b)),
587 (('iand', ('feq', a, a), (op, b, a)), (op, b, a)),
588 ]
589
590 # Add optimizations to handle the case where the result of a ternary is
591 # compared to a constant. This way we can take things like
592 #
593 # (a ? 0 : 1) > 0
594 #
595 # and turn it into
596 #
597 # a ? (0 > 0) : (1 > 0)
598 #
599 # which constant folding will eat for lunch. The resulting ternary will
600 # further get cleaned up by the boolean reductions above and we will be
601 # left with just the original variable "a".
602 for op in ['flt', 'fge', 'feq', 'fne',
603 'ilt', 'ige', 'ieq', 'ine', 'ult', 'uge']:
604 optimizations += [
605 ((op, ('bcsel', 'a', '#b', '#c'), '#d'),
606 ('bcsel', 'a', (op, 'b', 'd'), (op, 'c', 'd'))),
607 ((op, '#d', ('bcsel', a, '#b', '#c')),
608 ('bcsel', 'a', (op, 'd', 'b'), (op, 'd', 'c'))),
609 ]
610
611
612 # For example, this converts things like
613 #
614 # 1 + mix(0, a - 1, condition)
615 #
616 # into
617 #
618 # mix(1, (a-1)+1, condition)
619 #
620 # Other optimizations will rearrange the constants.
621 for op in ['fadd', 'fmul', 'iadd', 'imul']:
622 optimizations += [
623 ((op, ('bcsel(is_used_once)', a, '#b', c), '#d'), ('bcsel', a, (op, b, d), (op, c, d)))
624 ]
625
626 # This section contains "late" optimizations that should be run before
627 # creating ffmas and calling regular optimizations for the final time.
628 # Optimizations should go here if they help code generation and conflict
629 # with the regular optimizations.
630 before_ffma_optimizations = [
631 # Propagate constants down multiplication chains
632 (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fmul', ('fmul', a, c), b)),
633 (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('imul', ('imul', a, c), b)),
634 (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fadd', ('fadd', a, c), b)),
635 (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('iadd', ('iadd', a, c), b)),
636
637 (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
638 (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
639 (('~fadd', ('fneg', a), a), 0.0),
640 (('iadd', ('ineg', a), a), 0),
641 (('iadd', ('ineg', a), ('iadd', a, b)), b),
642 (('iadd', a, ('iadd', ('ineg', a), b)), b),
643 (('~fadd', ('fneg', a), ('fadd', a, b)), b),
644 (('~fadd', a, ('fadd', ('fneg', a), b)), b),
645 ]
646
647 # This section contains "late" optimizations that should be run after the
648 # regular optimizations have finished. Optimizations should go here if
649 # they help code generation but do not necessarily produce code that is
650 # more easily optimizable.
651 late_optimizations = [
652 # Most of these optimizations aren't quite safe when you get infinity or
653 # Nan involved but the first one should be fine.
654 (('flt', ('fadd', a, b), 0.0), ('flt', a, ('fneg', b))),
655 (('flt', ('fneg', ('fadd', a, b)), 0.0), ('flt', ('fneg', a), b)),
656 (('~fge', ('fadd', a, b), 0.0), ('fge', a, ('fneg', b))),
657 (('~fge', ('fneg', ('fadd', a, b)), 0.0), ('fge', ('fneg', a), b)),
658 (('~feq', ('fadd', a, b), 0.0), ('feq', a, ('fneg', b))),
659 (('~fne', ('fadd', a, b), 0.0), ('fne', a, ('fneg', b))),
660
661 (('~fge', ('fmin(is_used_once)', ('fadd(is_used_once)', a, b), ('fadd', c, d)), 0.0), ('iand', ('fge', a, ('fneg', b)), ('fge', c, ('fneg', d)))),
662
663 (('fdot2', a, b), ('fdot_replicated2', a, b), 'options->fdot_replicates'),
664 (('fdot3', a, b), ('fdot_replicated3', a, b), 'options->fdot_replicates'),
665 (('fdot4', a, b), ('fdot_replicated4', a, b), 'options->fdot_replicates'),
666 (('fdph', a, b), ('fdph_replicated', a, b), 'options->fdot_replicates'),
667
668 (('b2f(is_used_more_than_once)', ('inot', a)), ('bcsel', a, 0.0, 1.0)),
669 (('fneg(is_used_more_than_once)', ('b2f', ('inot', a))), ('bcsel', a, -0.0, -1.0)),
670
671 # we do these late so that we don't get in the way of creating ffmas
672 (('fmin', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmin', a, b))),
673 (('fmax', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmax', a, b))),
674 ]
675
676 print nir_algebraic.AlgebraicPass("nir_opt_algebraic", optimizations).render()
677 print nir_algebraic.AlgebraicPass("nir_opt_algebraic_before_ffma",
678 before_ffma_optimizations).render()
679 print nir_algebraic.AlgebraicPass("nir_opt_algebraic_late",
680 late_optimizations).render()