nir: Implement optional b2f->iand lowering
[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
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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 import itertools
28
29 # Convenience variables
30 a = 'a'
31 b = 'b'
32 c = 'c'
33 d = 'd'
34
35 # Written in the form (<search>, <replace>) where <search> is an expression
36 # and <replace> is either an expression or a value. An expression is
37 # defined as a tuple of the form ([~]<op>, <src0>, <src1>, <src2>, <src3>)
38 # where each source is either an expression or a value. A value can be
39 # either a numeric constant or a string representing a variable name.
40 #
41 # If the opcode in a search expression is prefixed by a '~' character, this
42 # indicates that the operation is inexact. Such operations will only get
43 # applied to SSA values that do not have the exact bit set. This should be
44 # used by by any optimizations that are not bit-for-bit exact. It should not,
45 # however, be used for backend-requested lowering operations as those need to
46 # happen regardless of precision.
47 #
48 # Variable names are specified as "[#]name[@type][(cond)]" where "#" inicates
49 # that the given variable will only match constants and the type indicates that
50 # the given variable will only match values from ALU instructions with the
51 # given output type, and (cond) specifies an additional condition function
52 # (see nir_search_helpers.h).
53 #
54 # For constants, you have to be careful to make sure that it is the right
55 # type because python is unaware of the source and destination types of the
56 # opcodes.
57 #
58 # All expression types can have a bit-size specified. For opcodes, this
59 # looks like "op@32", for variables it is "a@32" or "a@uint32" to specify a
60 # type and size, and for literals, you can write "2.0@32". In the search half
61 # of the expression this indicates that it should only match that particular
62 # bit-size. In the replace half of the expression this indicates that the
63 # constructed value should have that bit-size.
64
65 optimizations = [
66
67 (('imul', a, '#b@32(is_pos_power_of_two)'), ('ishl', a, ('find_lsb', b))),
68 (('imul', a, '#b@32(is_neg_power_of_two)'), ('ineg', ('ishl', a, ('find_lsb', ('iabs', b))))),
69 (('udiv', a, 1), a),
70 (('idiv', a, 1), a),
71 (('umod', a, 1), 0),
72 (('imod', a, 1), 0),
73 (('udiv', a, '#b@32(is_pos_power_of_two)'), ('ushr', a, ('find_lsb', b))),
74 (('idiv', a, '#b@32(is_pos_power_of_two)'), ('imul', ('isign', a), ('ushr', ('iabs', a), ('find_lsb', b))), 'options->lower_idiv'),
75 (('idiv', a, '#b@32(is_neg_power_of_two)'), ('ineg', ('imul', ('isign', a), ('ushr', ('iabs', a), ('find_lsb', ('iabs', b))))), 'options->lower_idiv'),
76 (('umod', a, '#b(is_pos_power_of_two)'), ('iand', a, ('isub', b, 1))),
77
78 (('fneg', ('fneg', a)), a),
79 (('ineg', ('ineg', a)), a),
80 (('fabs', ('fabs', a)), ('fabs', a)),
81 (('fabs', ('fneg', a)), ('fabs', a)),
82 (('fabs', ('u2f32', a)), ('u2f32', a)),
83 (('iabs', ('iabs', a)), ('iabs', a)),
84 (('iabs', ('ineg', a)), ('iabs', a)),
85 (('~fadd', a, 0.0), a),
86 (('iadd', a, 0), a),
87 (('usadd_4x8', a, 0), a),
88 (('usadd_4x8', a, ~0), ~0),
89 (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
90 (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
91 (('~fadd', ('fneg', a), a), 0.0),
92 (('iadd', ('ineg', a), a), 0),
93 (('iadd', ('ineg', a), ('iadd', a, b)), b),
94 (('iadd', a, ('iadd', ('ineg', a), b)), b),
95 (('~fadd', ('fneg', a), ('fadd', a, b)), b),
96 (('~fadd', a, ('fadd', ('fneg', a), b)), b),
97 (('~fmul', a, 0.0), 0.0),
98 (('imul', a, 0), 0),
99 (('umul_unorm_4x8', a, 0), 0),
100 (('umul_unorm_4x8', a, ~0), a),
101 (('fmul', a, 1.0), a),
102 (('imul', a, 1), a),
103 (('fmul', a, -1.0), ('fneg', a)),
104 (('imul', a, -1), ('ineg', a)),
105 (('~ffma', 0.0, a, b), b),
106 (('~ffma', a, 0.0, b), b),
107 (('~ffma', a, b, 0.0), ('fmul', a, b)),
108 (('ffma', a, 1.0, b), ('fadd', a, b)),
109 (('ffma', 1.0, a, b), ('fadd', a, b)),
110 (('~flrp', a, b, 0.0), a),
111 (('~flrp', a, b, 1.0), b),
112 (('~flrp', a, a, b), a),
113 (('~flrp', 0.0, a, b), ('fmul', a, b)),
114 (('~flrp', a, b, ('b2f', c)), ('bcsel', c, b, a), 'options->lower_flrp32'),
115 (('~flrp', a, 0.0, c), ('fadd', ('fmul', ('fneg', a), c), a)),
116 (('flrp@32', a, b, c), ('fadd', ('fmul', c, ('fsub', b, a)), a), 'options->lower_flrp32'),
117 (('flrp@64', a, b, c), ('fadd', ('fmul', c, ('fsub', b, a)), a), 'options->lower_flrp64'),
118 (('ffract', a), ('fsub', a, ('ffloor', a)), 'options->lower_ffract'),
119 (('~fadd', ('fmul', a, ('fadd', 1.0, ('fneg', ('b2f', c)))), ('fmul', b, ('b2f', c))), ('bcsel', c, b, a), 'options->lower_flrp32'),
120 (('~fadd@32', ('fmul', a, ('fadd', 1.0, ('fneg', c ))), ('fmul', b, c )), ('flrp', a, b, c), '!options->lower_flrp32'),
121 (('~fadd@64', ('fmul', a, ('fadd', 1.0, ('fneg', c ))), ('fmul', b, c )), ('flrp', a, b, c), '!options->lower_flrp64'),
122 (('~fadd', a, ('fmul', ('b2f', c), ('fadd', b, ('fneg', a)))), ('bcsel', c, b, a), 'options->lower_flrp32'),
123 (('~fadd@32', a, ('fmul', c , ('fadd', b, ('fneg', a)))), ('flrp', a, b, c), '!options->lower_flrp32'),
124 (('~fadd@64', a, ('fmul', c , ('fadd', b, ('fneg', a)))), ('flrp', a, b, c), '!options->lower_flrp64'),
125 (('ffma', a, b, c), ('fadd', ('fmul', a, b), c), 'options->lower_ffma'),
126 (('~fadd', ('fmul', a, b), c), ('ffma', a, b, c), 'options->fuse_ffma'),
127
128 (('fdot4', ('vec4', a, b, c, 1.0), d), ('fdph', ('vec3', a, b, c), d)),
129 (('fdot4', ('vec4', a, 0.0, 0.0, 0.0), b), ('fmul', a, b)),
130 (('fdot4', ('vec4', a, b, 0.0, 0.0), c), ('fdot2', ('vec2', a, b), c)),
131 (('fdot4', ('vec4', a, b, c, 0.0), d), ('fdot3', ('vec3', a, b, c), d)),
132
133 (('fdot3', ('vec3', a, 0.0, 0.0), b), ('fmul', a, b)),
134 (('fdot3', ('vec3', a, b, 0.0), c), ('fdot2', ('vec2', a, b), c)),
135
136 # (a * #b + #c) << #d
137 # ((a * #b) << #d) + (#c << #d)
138 # (a * (#b << #d)) + (#c << #d)
139 (('ishl', ('iadd', ('imul', a, '#b'), '#c'), '#d'),
140 ('iadd', ('imul', a, ('ishl', b, d)), ('ishl', c, d))),
141
142 # (a * #b) << #c
143 # a * (#b << #c)
144 (('ishl', ('imul', a, '#b'), '#c'), ('imul', a, ('ishl', b, c))),
145
146 # Comparison simplifications
147 (('~inot', ('flt', a, b)), ('fge', a, b)),
148 (('~inot', ('fge', a, b)), ('flt', a, b)),
149 (('~inot', ('feq', a, b)), ('fne', a, b)),
150 (('~inot', ('fne', a, b)), ('feq', a, b)),
151 (('inot', ('ilt', a, b)), ('ige', a, b)),
152 (('inot', ('ige', a, b)), ('ilt', a, b)),
153 (('inot', ('ieq', a, b)), ('ine', a, b)),
154 (('inot', ('ine', a, b)), ('ieq', a, b)),
155
156 # 0.0 >= b2f(a)
157 # b2f(a) <= 0.0
158 # b2f(a) == 0.0 because b2f(a) can only be 0 or 1
159 # inot(a)
160 (('fge', 0.0, ('b2f', a)), ('inot', a)),
161
162 (('fge', ('fneg', ('b2f', a)), 0.0), ('inot', a)),
163
164 (('~flt', ('fadd', a, b), a), ('flt', b, 0.0)),
165 (('~fge', ('fadd', a, b), a), ('fge', b, 0.0)),
166 (('~feq', ('fadd', a, b), a), ('feq', b, 0.0)),
167 (('~fne', ('fadd', a, b), a), ('fne', b, 0.0)),
168
169 # Cannot remove the addition from ilt or ige due to overflow.
170 (('ieq', ('iadd', a, b), a), ('ieq', b, 0)),
171 (('ine', ('iadd', a, b), a), ('ine', b, 0)),
172
173 # fmin(-b2f(a), b) >= 0.0
174 # -b2f(a) >= 0.0 && b >= 0.0
175 # -b2f(a) == 0.0 && b >= 0.0 -b2f can only be 0 or -1, never >0
176 # b2f(a) == 0.0 && b >= 0.0
177 # a == False && b >= 0.0
178 # !a && b >= 0.0
179 #
180 # The fge in the second replacement is not a typo. I leave the proof that
181 # "fmin(-b2f(a), b) >= 0 <=> fmin(-b2f(a), b) == 0" as an exercise for the
182 # reader.
183 (('fge', ('fmin', ('fneg', ('b2f', a)), b), 0.0), ('iand', ('inot', a), ('fge', b, 0.0))),
184 (('feq', ('fmin', ('fneg', ('b2f', a)), b), 0.0), ('iand', ('inot', a), ('fge', b, 0.0))),
185
186 (('feq', ('b2f', a), 0.0), ('inot', a)),
187 (('fne', ('b2f', a), 0.0), a),
188 (('ieq', ('b2i', a), 0), ('inot', a)),
189 (('ine', ('b2i', a), 0), a),
190
191 # 0.0 < fabs(a)
192 # fabs(a) > 0.0
193 # fabs(a) != 0.0 because fabs(a) must be >= 0
194 # a != 0.0
195 (('flt', 0.0, ('fabs', a)), ('fne', a, 0.0)),
196
197 (('fmax', ('b2f(is_used_once)', a), ('b2f', b)), ('b2f', ('ior', a, b))),
198 (('fmax', ('fneg(is_used_once)', ('b2f(is_used_once)', a)), ('fneg', ('b2f', b))), ('fneg', ('b2f', ('ior', a, b)))),
199 (('fmin', ('b2f(is_used_once)', a), ('b2f', b)), ('b2f', ('iand', a, b))),
200 (('fmin', ('fneg(is_used_once)', ('b2f(is_used_once)', a)), ('fneg', ('b2f', b))), ('fneg', ('b2f', ('iand', a, b)))),
201
202 # fmin(b2f(a), b)
203 # bcsel(a, fmin(b2f(a), b), fmin(b2f(a), b))
204 # bcsel(a, fmin(b2f(True), b), fmin(b2f(False), b))
205 # bcsel(a, fmin(1.0, b), fmin(0.0, b))
206 #
207 # Since b is a constant, constant folding will eliminate the fmin and the
208 # fmax. If b is > 1.0, the bcsel will be replaced with a b2f.
209 (('fmin', ('b2f', a), '#b'), ('bcsel', a, ('fmin', b, 1.0), ('fmin', b, 0.0))),
210
211 (('flt', ('fadd(is_used_once)', a, ('fneg', b)), 0.0), ('flt', a, b)),
212
213 (('fge', ('fneg', ('fabs', a)), 0.0), ('feq', a, 0.0)),
214 (('~bcsel', ('flt', b, a), b, a), ('fmin', a, b)),
215 (('~bcsel', ('flt', a, b), b, a), ('fmax', a, b)),
216 (('~bcsel', ('fge', a, b), b, a), ('fmin', a, b)),
217 (('~bcsel', ('fge', b, a), b, a), ('fmax', a, b)),
218 (('bcsel', ('inot', a), b, c), ('bcsel', a, c, b)),
219 (('bcsel', a, ('bcsel', a, b, c), d), ('bcsel', a, b, d)),
220 (('bcsel', a, True, 'b@bool'), ('ior', a, b)),
221 (('fmin', a, a), a),
222 (('fmax', a, a), a),
223 (('imin', a, a), a),
224 (('imax', a, a), a),
225 (('umin', a, a), a),
226 (('umax', a, a), a),
227 (('fmin', a, ('fneg', a)), ('fneg', ('fabs', a))),
228 (('imin', a, ('ineg', a)), ('ineg', ('iabs', a))),
229 (('fmin', a, ('fneg', ('fabs', a))), ('fneg', ('fabs', a))),
230 (('imin', a, ('ineg', ('iabs', a))), ('ineg', ('iabs', a))),
231 (('fmin', a, ('fabs', a)), a),
232 (('imin', a, ('iabs', a)), a),
233 (('fmax', a, ('fneg', ('fabs', a))), a),
234 (('imax', a, ('ineg', ('iabs', a))), a),
235 (('fmax', a, ('fabs', a)), ('fabs', a)),
236 (('imax', a, ('iabs', a)), ('iabs', a)),
237 (('fmax', a, ('fneg', a)), ('fabs', a)),
238 (('imax', a, ('ineg', a)), ('iabs', a)),
239 (('~fmin', ('fmax', a, 0.0), 1.0), ('fsat', a), '!options->lower_fsat'),
240 (('~fmax', ('fmin', a, 1.0), 0.0), ('fsat', a), '!options->lower_fsat'),
241 (('fsat', a), ('fmin', ('fmax', a, 0.0), 1.0), 'options->lower_fsat'),
242 (('fsat', ('fsat', a)), ('fsat', a)),
243 (('fmin', ('fmax', ('fmin', ('fmax', a, b), c), b), c), ('fmin', ('fmax', a, b), c)),
244 (('imin', ('imax', ('imin', ('imax', a, b), c), b), c), ('imin', ('imax', a, b), c)),
245 (('umin', ('umax', ('umin', ('umax', a, b), c), b), c), ('umin', ('umax', a, b), c)),
246 (('fmax', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmax', a, b))),
247 (('fmin', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmin', a, b))),
248 (('extract_u8', ('imin', ('imax', a, 0), 0xff), 0), ('imin', ('imax', a, 0), 0xff)),
249 (('~ior', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmax', b, c))),
250 (('~ior', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmin', a, b), c)),
251 (('~ior', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmin', b, c))),
252 (('~ior', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmax', a, b), c)),
253 (('~ior', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmax', b, c))),
254 (('~ior', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmin', a, b), c)),
255 (('~ior', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmin', b, c))),
256 (('~ior', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmax', a, b), c)),
257 (('~iand', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmin', b, c))),
258 (('~iand', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmax', a, b), c)),
259 (('~iand', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmax', b, c))),
260 (('~iand', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmin', a, b), c)),
261 (('~iand', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmin', b, c))),
262 (('~iand', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmax', a, b), c)),
263 (('~iand', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmax', b, c))),
264 (('~iand', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmin', a, b), c)),
265
266 (('ior', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imax', b, c))),
267 (('ior', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imin', a, b), c)),
268 (('ior', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imin', b, c))),
269 (('ior', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imax', a, b), c)),
270 (('ior', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umax', b, c))),
271 (('ior', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umin', a, b), c)),
272 (('ior', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umin', b, c))),
273 (('ior', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umax', a, b), c)),
274 (('iand', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imin', b, c))),
275 (('iand', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imax', a, b), c)),
276 (('iand', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imax', b, c))),
277 (('iand', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imin', a, b), c)),
278 (('iand', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umin', b, c))),
279 (('iand', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umax', a, b), c)),
280 (('iand', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umax', b, c))),
281 (('iand', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umin', a, b), c)),
282
283 # These patterns can result when (a < b || a < c) => (a < min(b, c))
284 # transformations occur before constant propagation and loop-unrolling.
285 (('~flt', a, ('fmax', b, a)), ('flt', a, b)),
286 (('~flt', ('fmin', a, b), a), ('flt', b, a)),
287 (('~fge', a, ('fmin', b, a)), True),
288 (('~fge', ('fmax', a, b), a), True),
289 (('~flt', a, ('fmin', b, a)), False),
290 (('~flt', ('fmax', a, b), a), False),
291
292 (('ilt', a, ('imax', b, a)), ('ilt', a, b)),
293 (('ilt', ('imin', a, b), a), ('ilt', b, a)),
294 (('ige', a, ('imin', b, a)), True),
295 (('ige', ('imax', a, b), a), True),
296 (('ult', a, ('umax', b, a)), ('ult', a, b)),
297 (('ult', ('umin', a, b), a), ('ult', b, a)),
298 (('uge', a, ('umin', b, a)), True),
299 (('uge', ('umax', a, b), a), True),
300
301 (('ilt', '#a', ('imin', '#b', c)), ('iand', ('ilt', a, b), ('ilt', a, c))),
302 (('ilt', ('imax', '#a', b), '#c'), ('iand', ('ilt', a, c), ('ilt', b, c))),
303 (('ige', '#a', ('imax', '#b', c)), ('iand', ('ige', a, b), ('ige', a, c))),
304 (('ige', ('imin', '#a', b), '#c'), ('iand', ('ige', a, c), ('ige', b, c))),
305 (('ult', '#a', ('umin', '#b', c)), ('iand', ('ult', a, b), ('ult', a, c))),
306 (('ult', ('umax', '#a', b), '#c'), ('iand', ('ult', a, c), ('ult', b, c))),
307 (('uge', '#a', ('umax', '#b', c)), ('iand', ('uge', a, b), ('uge', a, c))),
308 (('uge', ('umin', '#a', b), '#c'), ('iand', ('uge', a, c), ('uge', b, c))),
309
310 (('fabs', ('slt', a, b)), ('slt', a, b)),
311 (('fabs', ('sge', a, b)), ('sge', a, b)),
312 (('fabs', ('seq', a, b)), ('seq', a, b)),
313 (('fabs', ('sne', a, b)), ('sne', a, b)),
314 (('slt', a, b), ('b2f', ('flt', a, b)), 'options->lower_scmp'),
315 (('sge', a, b), ('b2f', ('fge', a, b)), 'options->lower_scmp'),
316 (('seq', a, b), ('b2f', ('feq', a, b)), 'options->lower_scmp'),
317 (('sne', a, b), ('b2f', ('fne', a, b)), 'options->lower_scmp'),
318 (('fne', ('fneg', a), a), ('fne', a, 0.0)),
319 (('feq', ('fneg', a), a), ('feq', a, 0.0)),
320 # Emulating booleans
321 (('imul', ('b2i', a), ('b2i', b)), ('b2i', ('iand', a, b))),
322 (('fmul', ('b2f', a), ('b2f', b)), ('b2f', ('iand', a, b))),
323 (('fsat', ('fadd', ('b2f', a), ('b2f', b))), ('b2f', ('ior', a, b))),
324 (('iand', 'a@bool', 1.0), ('b2f', a), '!options->lower_b2f'),
325 # True/False are ~0 and 0 in NIR. b2i of True is 1, and -1 is ~0 (True).
326 (('ineg', ('b2i@32', a)), a),
327 (('flt', ('fneg', ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
328 (('flt', ('fsub', 0.0, ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
329 # Comparison with the same args. Note that these are not done for
330 # the float versions because NaN always returns false on float
331 # inequalities.
332 (('ilt', a, a), False),
333 (('ige', a, a), True),
334 (('ieq', a, a), True),
335 (('ine', a, a), False),
336 (('ult', a, a), False),
337 (('uge', a, a), True),
338 # Logical and bit operations
339 (('fand', a, 0.0), 0.0),
340 (('iand', a, a), a),
341 (('iand', a, ~0), a),
342 (('iand', a, 0), 0),
343 (('ior', a, a), a),
344 (('ior', a, 0), a),
345 (('ior', a, True), True),
346 (('fxor', a, a), 0.0),
347 (('ixor', a, a), 0),
348 (('ixor', a, 0), a),
349 (('inot', ('inot', a)), a),
350 # DeMorgan's Laws
351 (('iand', ('inot', a), ('inot', b)), ('inot', ('ior', a, b))),
352 (('ior', ('inot', a), ('inot', b)), ('inot', ('iand', a, b))),
353 # Shift optimizations
354 (('ishl', 0, a), 0),
355 (('ishl', a, 0), a),
356 (('ishr', 0, a), 0),
357 (('ishr', a, 0), a),
358 (('ushr', 0, a), 0),
359 (('ushr', a, 0), a),
360 (('iand', 0xff, ('ushr@32', a, 24)), ('ushr', a, 24)),
361 (('iand', 0xffff, ('ushr@32', a, 16)), ('ushr', a, 16)),
362 # Exponential/logarithmic identities
363 (('~fexp2', ('flog2', a)), a), # 2^lg2(a) = a
364 (('~flog2', ('fexp2', a)), a), # lg2(2^a) = a
365 (('fpow', a, b), ('fexp2', ('fmul', ('flog2', a), b)), 'options->lower_fpow'), # a^b = 2^(lg2(a)*b)
366 (('~fexp2', ('fmul', ('flog2', a), b)), ('fpow', a, b), '!options->lower_fpow'), # 2^(lg2(a)*b) = a^b
367 (('~fexp2', ('fadd', ('fmul', ('flog2', a), b), ('fmul', ('flog2', c), d))),
368 ('~fmul', ('fpow', a, b), ('fpow', c, d)), '!options->lower_fpow'), # 2^(lg2(a) * b + lg2(c) + d) = a^b * c^d
369 (('~fexp2', ('fmul', ('flog2', a), 2.0)), ('fmul', a, a)),
370 (('~fexp2', ('fmul', ('flog2', a), 4.0)), ('fmul', ('fmul', a, a), ('fmul', a, a))),
371 (('~fpow', a, 1.0), a),
372 (('~fpow', a, 2.0), ('fmul', a, a)),
373 (('~fpow', a, 4.0), ('fmul', ('fmul', a, a), ('fmul', a, a))),
374 (('~fpow', 2.0, a), ('fexp2', a)),
375 (('~fpow', ('fpow', a, 2.2), 0.454545), a),
376 (('~fpow', ('fabs', ('fpow', a, 2.2)), 0.454545), ('fabs', a)),
377 (('~fsqrt', ('fexp2', a)), ('fexp2', ('fmul', 0.5, a))),
378 (('~frcp', ('fexp2', a)), ('fexp2', ('fneg', a))),
379 (('~frsq', ('fexp2', a)), ('fexp2', ('fmul', -0.5, a))),
380 (('~flog2', ('fsqrt', a)), ('fmul', 0.5, ('flog2', a))),
381 (('~flog2', ('frcp', a)), ('fneg', ('flog2', a))),
382 (('~flog2', ('frsq', a)), ('fmul', -0.5, ('flog2', a))),
383 (('~flog2', ('fpow', a, b)), ('fmul', b, ('flog2', a))),
384 (('~fmul', ('fexp2(is_used_once)', a), ('fexp2(is_used_once)', b)), ('fexp2', ('fadd', a, b))),
385 # Division and reciprocal
386 (('~fdiv', 1.0, a), ('frcp', a)),
387 (('fdiv', a, b), ('fmul', a, ('frcp', b)), 'options->lower_fdiv'),
388 (('~frcp', ('frcp', a)), a),
389 (('~frcp', ('fsqrt', a)), ('frsq', a)),
390 (('fsqrt', a), ('frcp', ('frsq', a)), 'options->lower_fsqrt'),
391 (('~frcp', ('frsq', a)), ('fsqrt', a), '!options->lower_fsqrt'),
392 # Boolean simplifications
393 (('ieq', 'a@bool', True), a),
394 (('ine(is_not_used_by_if)', 'a@bool', True), ('inot', a)),
395 (('ine', 'a@bool', False), a),
396 (('ieq(is_not_used_by_if)', 'a@bool', False), ('inot', 'a')),
397 (('bcsel', a, True, False), a),
398 (('bcsel', a, False, True), ('inot', a)),
399 (('bcsel@32', a, 1.0, 0.0), ('b2f', a)),
400 (('bcsel@32', a, 0.0, 1.0), ('b2f', ('inot', a))),
401 (('bcsel@32', a, -1.0, -0.0), ('fneg', ('b2f', a))),
402 (('bcsel@32', a, -0.0, -1.0), ('fneg', ('b2f', ('inot', a)))),
403 (('bcsel', True, b, c), b),
404 (('bcsel', False, b, c), c),
405 (('bcsel', a, ('b2f(is_used_once)', b), ('b2f', c)), ('b2f', ('bcsel', a, b, c))),
406 # The result of this should be hit by constant propagation and, in the
407 # next round of opt_algebraic, get picked up by one of the above two.
408 (('bcsel', '#a', b, c), ('bcsel', ('ine', 'a', 0), b, c)),
409
410 (('bcsel', a, b, b), b),
411 (('fcsel', a, b, b), b),
412
413 # Conversions
414 (('i2b', ('b2i', a)), a),
415 (('i2b', 'a@bool'), a),
416 (('f2i32', ('ftrunc', a)), ('f2i32', a)),
417 (('f2u32', ('ftrunc', a)), ('f2u32', a)),
418 (('i2b', ('ineg', a)), ('i2b', a)),
419 (('i2b', ('iabs', a)), ('i2b', a)),
420 (('fabs', ('b2f', a)), ('b2f', a)),
421 (('iabs', ('b2i', a)), ('b2i', a)),
422
423 # Packing and then unpacking does nothing
424 (('unpack_64_2x32_split_x', ('pack_64_2x32_split', a, b)), a),
425 (('unpack_64_2x32_split_y', ('pack_64_2x32_split', a, b)), b),
426 (('pack_64_2x32_split', ('unpack_64_2x32_split_x', a),
427 ('unpack_64_2x32_split_y', a)), a),
428
429 # Byte extraction
430 (('ushr', a, 24), ('extract_u8', a, 3), '!options->lower_extract_byte'),
431 (('iand', 0xff, ('ushr', a, 16)), ('extract_u8', a, 2), '!options->lower_extract_byte'),
432 (('iand', 0xff, ('ushr', a, 8)), ('extract_u8', a, 1), '!options->lower_extract_byte'),
433 (('iand', 0xff, a), ('extract_u8', a, 0), '!options->lower_extract_byte'),
434
435 # Word extraction
436 (('ushr', a, 16), ('extract_u16', a, 1), '!options->lower_extract_word'),
437 (('iand', 0xffff, a), ('extract_u16', a, 0), '!options->lower_extract_word'),
438
439 # Subtracts
440 (('~fsub', a, ('fsub', 0.0, b)), ('fadd', a, b)),
441 (('isub', a, ('isub', 0, b)), ('iadd', a, b)),
442 (('ussub_4x8', a, 0), a),
443 (('ussub_4x8', a, ~0), 0),
444 (('fsub', a, b), ('fadd', a, ('fneg', b)), 'options->lower_sub'),
445 (('isub', a, b), ('iadd', a, ('ineg', b)), 'options->lower_sub'),
446 (('fneg', a), ('fsub', 0.0, a), 'options->lower_negate'),
447 (('ineg', a), ('isub', 0, a), 'options->lower_negate'),
448 (('~fadd', a, ('fsub', 0.0, b)), ('fsub', a, b)),
449 (('iadd', a, ('isub', 0, b)), ('isub', a, b)),
450 (('fabs', ('fsub', 0.0, a)), ('fabs', a)),
451 (('iabs', ('isub', 0, a)), ('iabs', a)),
452
453 # Propagate negation up multiplication chains
454 (('fmul', ('fneg', a), b), ('fneg', ('fmul', a, b))),
455 (('imul', ('ineg', a), b), ('ineg', ('imul', a, b))),
456
457 # Propagate constants up multiplication chains
458 (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fmul', ('fmul', a, c), b)),
459 (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('imul', ('imul', a, c), b)),
460 (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fadd', ('fadd', a, c), b)),
461 (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('iadd', ('iadd', a, c), b)),
462
463 # Reassociate constants in add/mul chains so they can be folded together.
464 # For now, we mostly only handle cases where the constants are separated by
465 # a single non-constant. We could do better eventually.
466 (('~fmul', '#a', ('fmul', b, '#c')), ('fmul', ('fmul', a, c), b)),
467 (('imul', '#a', ('imul', b, '#c')), ('imul', ('imul', a, c), b)),
468 (('~fadd', '#a', ('fadd', b, '#c')), ('fadd', ('fadd', a, c), b)),
469 (('~fadd', '#a', ('fneg', ('fadd', b, '#c'))), ('fadd', ('fadd', a, ('fneg', c)), ('fneg', b))),
470 (('iadd', '#a', ('iadd', b, '#c')), ('iadd', ('iadd', a, c), b)),
471
472 # By definition...
473 (('bcsel', ('ige', ('find_lsb', a), 0), ('find_lsb', a), -1), ('find_lsb', a)),
474 (('bcsel', ('ige', ('ifind_msb', a), 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
475 (('bcsel', ('ige', ('ufind_msb', a), 0), ('ufind_msb', a), -1), ('ufind_msb', a)),
476
477 (('bcsel', ('ine', a, 0), ('find_lsb', a), -1), ('find_lsb', a)),
478 (('bcsel', ('ine', a, 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
479 (('bcsel', ('ine', a, 0), ('ufind_msb', a), -1), ('ufind_msb', a)),
480
481 (('bcsel', ('ine', a, -1), ('ifind_msb', a), -1), ('ifind_msb', a)),
482
483 # Misc. lowering
484 (('fmod@32', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod32'),
485 (('fmod@64', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod64'),
486 (('frem', a, b), ('fsub', a, ('fmul', b, ('ftrunc', ('fdiv', a, b)))), 'options->lower_fmod32'),
487 (('uadd_carry@32', a, b), ('b2i', ('ult', ('iadd', a, b), a)), 'options->lower_uadd_carry'),
488 (('usub_borrow@32', a, b), ('b2i', ('ult', a, b)), 'options->lower_usub_borrow'),
489
490 (('bitfield_insert', 'base', 'insert', 'offset', 'bits'),
491 ('bcsel', ('ilt', 31, 'bits'), 'insert',
492 ('bfi', ('bfm', 'bits', 'offset'), 'insert', 'base')),
493 'options->lower_bitfield_insert'),
494
495 (('ibitfield_extract', 'value', 'offset', 'bits'),
496 ('bcsel', ('ilt', 31, 'bits'), 'value',
497 ('ibfe', 'value', 'offset', 'bits')),
498 'options->lower_bitfield_extract'),
499
500 (('ubitfield_extract', 'value', 'offset', 'bits'),
501 ('bcsel', ('ult', 31, 'bits'), 'value',
502 ('ubfe', 'value', 'offset', 'bits')),
503 'options->lower_bitfield_extract'),
504
505 (('extract_i8', a, 'b@32'),
506 ('ishr', ('ishl', a, ('imul', ('isub', 3, b), 8)), 24),
507 'options->lower_extract_byte'),
508
509 (('extract_u8', a, 'b@32'),
510 ('iand', ('ushr', a, ('imul', b, 8)), 0xff),
511 'options->lower_extract_byte'),
512
513 (('extract_i16', a, 'b@32'),
514 ('ishr', ('ishl', a, ('imul', ('isub', 1, b), 16)), 16),
515 'options->lower_extract_word'),
516
517 (('extract_u16', a, 'b@32'),
518 ('iand', ('ushr', a, ('imul', b, 16)), 0xffff),
519 'options->lower_extract_word'),
520
521 (('pack_unorm_2x16', 'v'),
522 ('pack_uvec2_to_uint',
523 ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 65535.0)))),
524 'options->lower_pack_unorm_2x16'),
525
526 (('pack_unorm_4x8', 'v'),
527 ('pack_uvec4_to_uint',
528 ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 255.0)))),
529 'options->lower_pack_unorm_4x8'),
530
531 (('pack_snorm_2x16', 'v'),
532 ('pack_uvec2_to_uint',
533 ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 32767.0)))),
534 'options->lower_pack_snorm_2x16'),
535
536 (('pack_snorm_4x8', 'v'),
537 ('pack_uvec4_to_uint',
538 ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 127.0)))),
539 'options->lower_pack_snorm_4x8'),
540
541 (('unpack_unorm_2x16', 'v'),
542 ('fdiv', ('u2f32', ('vec2', ('extract_u16', 'v', 0),
543 ('extract_u16', 'v', 1))),
544 65535.0),
545 'options->lower_unpack_unorm_2x16'),
546
547 (('unpack_unorm_4x8', 'v'),
548 ('fdiv', ('u2f32', ('vec4', ('extract_u8', 'v', 0),
549 ('extract_u8', 'v', 1),
550 ('extract_u8', 'v', 2),
551 ('extract_u8', 'v', 3))),
552 255.0),
553 'options->lower_unpack_unorm_4x8'),
554
555 (('unpack_snorm_2x16', 'v'),
556 ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec2', ('extract_i16', 'v', 0),
557 ('extract_i16', 'v', 1))),
558 32767.0))),
559 'options->lower_unpack_snorm_2x16'),
560
561 (('unpack_snorm_4x8', 'v'),
562 ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec4', ('extract_i8', 'v', 0),
563 ('extract_i8', 'v', 1),
564 ('extract_i8', 'v', 2),
565 ('extract_i8', 'v', 3))),
566 127.0))),
567 'options->lower_unpack_snorm_4x8'),
568 ]
569
570 invert = {'feq': 'fne', 'fne': 'feq', 'fge': 'flt', 'flt': 'fge' }
571
572 for left, right in list(itertools.combinations(invert.keys(), 2)) + zip(invert.keys(), invert.keys()):
573 optimizations.append((('inot', ('ior(is_used_once)', (left, a, b), (right, c, d))),
574 ('iand', (invert[left], a, b), (invert[right], c, d))))
575 optimizations.append((('inot', ('iand(is_used_once)', (left, a, b), (right, c, d))),
576 ('ior', (invert[left], a, b), (invert[right], c, d))))
577
578 def fexp2i(exp, bits):
579 # We assume that exp is already in the right range.
580 if bits == 32:
581 return ('ishl', ('iadd', exp, 127), 23)
582 elif bits == 64:
583 return ('pack_64_2x32_split', 0, ('ishl', ('iadd', exp, 1023), 20))
584 else:
585 assert False
586
587 def ldexp(f, exp, bits):
588 # First, we clamp exp to a reasonable range. The maximum possible range
589 # for a normal exponent is [-126, 127] and, throwing in denormals, you get
590 # a maximum range of [-149, 127]. This means that we can potentially have
591 # a swing of +-276. If you start with FLT_MAX, you actually have to do
592 # ldexp(FLT_MAX, -278) to get it to flush all the way to zero. The GLSL
593 # spec, on the other hand, only requires that we handle an exponent value
594 # in the range [-126, 128]. This implementation is *mostly* correct; it
595 # handles a range on exp of [-252, 254] which allows you to create any
596 # value (including denorms if the hardware supports it) and to adjust the
597 # exponent of any normal value to anything you want.
598 if bits == 32:
599 exp = ('imin', ('imax', exp, -252), 254)
600 elif bits == 64:
601 exp = ('imin', ('imax', exp, -2044), 2046)
602 else:
603 assert False
604
605 # Now we compute two powers of 2, one for exp/2 and one for exp-exp/2.
606 # (We use ishr which isn't the same for -1, but the -1 case still works
607 # since we use exp-exp/2 as the second exponent.) While the spec
608 # technically defines ldexp as f * 2.0^exp, simply multiplying once doesn't
609 # work with denormals and doesn't allow for the full swing in exponents
610 # that you can get with normalized values. Instead, we create two powers
611 # of two and multiply by them each in turn. That way the effective range
612 # of our exponent is doubled.
613 pow2_1 = fexp2i(('ishr', exp, 1), bits)
614 pow2_2 = fexp2i(('isub', exp, ('ishr', exp, 1)), bits)
615 return ('fmul', ('fmul', f, pow2_1), pow2_2)
616
617 optimizations += [
618 (('ldexp@32', 'x', 'exp'), ldexp('x', 'exp', 32), 'options->lower_ldexp'),
619 (('ldexp@64', 'x', 'exp'), ldexp('x', 'exp', 64), 'options->lower_ldexp'),
620 ]
621
622 # Unreal Engine 4 demo applications open-codes bitfieldReverse()
623 def bitfield_reverse(u):
624 step1 = ('ior', ('ishl', u, 16), ('ushr', u, 16))
625 step2 = ('ior', ('ishl', ('iand', step1, 0x00ff00ff), 8), ('ushr', ('iand', step1, 0xff00ff00), 8))
626 step3 = ('ior', ('ishl', ('iand', step2, 0x0f0f0f0f), 4), ('ushr', ('iand', step2, 0xf0f0f0f0), 4))
627 step4 = ('ior', ('ishl', ('iand', step3, 0x33333333), 2), ('ushr', ('iand', step3, 0xcccccccc), 2))
628 step5 = ('ior', ('ishl', ('iand', step4, 0x55555555), 1), ('ushr', ('iand', step4, 0xaaaaaaaa), 1))
629
630 return step5
631
632 optimizations += [(bitfield_reverse('x@32'), ('bitfield_reverse', 'x'))]
633
634 # For any float comparison operation, "cmp", if you have "a == a && a cmp b"
635 # then the "a == a" is redundant because it's equivalent to "a is not NaN"
636 # and, if a is a NaN then the second comparison will fail anyway.
637 for op in ['flt', 'fge', 'feq']:
638 optimizations += [
639 (('iand', ('feq', a, a), (op, a, b)), (op, a, b)),
640 (('iand', ('feq', a, a), (op, b, a)), (op, b, a)),
641 ]
642
643 # Add optimizations to handle the case where the result of a ternary is
644 # compared to a constant. This way we can take things like
645 #
646 # (a ? 0 : 1) > 0
647 #
648 # and turn it into
649 #
650 # a ? (0 > 0) : (1 > 0)
651 #
652 # which constant folding will eat for lunch. The resulting ternary will
653 # further get cleaned up by the boolean reductions above and we will be
654 # left with just the original variable "a".
655 for op in ['flt', 'fge', 'feq', 'fne',
656 'ilt', 'ige', 'ieq', 'ine', 'ult', 'uge']:
657 optimizations += [
658 ((op, ('bcsel', 'a', '#b', '#c'), '#d'),
659 ('bcsel', 'a', (op, 'b', 'd'), (op, 'c', 'd'))),
660 ((op, '#d', ('bcsel', a, '#b', '#c')),
661 ('bcsel', 'a', (op, 'd', 'b'), (op, 'd', 'c'))),
662 ]
663
664
665 # For example, this converts things like
666 #
667 # 1 + mix(0, a - 1, condition)
668 #
669 # into
670 #
671 # mix(1, (a-1)+1, condition)
672 #
673 # Other optimizations will rearrange the constants.
674 for op in ['fadd', 'fmul', 'iadd', 'imul']:
675 optimizations += [
676 ((op, ('bcsel(is_used_once)', a, '#b', c), '#d'), ('bcsel', a, (op, b, d), (op, c, d)))
677 ]
678
679 # This section contains "late" optimizations that should be run before
680 # creating ffmas and calling regular optimizations for the final time.
681 # Optimizations should go here if they help code generation and conflict
682 # with the regular optimizations.
683 before_ffma_optimizations = [
684 # Propagate constants down multiplication chains
685 (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fmul', ('fmul', a, c), b)),
686 (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('imul', ('imul', a, c), b)),
687 (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fadd', ('fadd', a, c), b)),
688 (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('iadd', ('iadd', a, c), b)),
689
690 (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
691 (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
692 (('~fadd', ('fneg', a), a), 0.0),
693 (('iadd', ('ineg', a), a), 0),
694 (('iadd', ('ineg', a), ('iadd', a, b)), b),
695 (('iadd', a, ('iadd', ('ineg', a), b)), b),
696 (('~fadd', ('fneg', a), ('fadd', a, b)), b),
697 (('~fadd', a, ('fadd', ('fneg', a), b)), b),
698 ]
699
700 # This section contains "late" optimizations that should be run after the
701 # regular optimizations have finished. Optimizations should go here if
702 # they help code generation but do not necessarily produce code that is
703 # more easily optimizable.
704 late_optimizations = [
705 # Most of these optimizations aren't quite safe when you get infinity or
706 # Nan involved but the first one should be fine.
707 (('flt', ('fadd', a, b), 0.0), ('flt', a, ('fneg', b))),
708 (('flt', ('fneg', ('fadd', a, b)), 0.0), ('flt', ('fneg', a), b)),
709 (('~fge', ('fadd', a, b), 0.0), ('fge', a, ('fneg', b))),
710 (('~fge', ('fneg', ('fadd', a, b)), 0.0), ('fge', ('fneg', a), b)),
711 (('~feq', ('fadd', a, b), 0.0), ('feq', a, ('fneg', b))),
712 (('~fne', ('fadd', a, b), 0.0), ('fne', a, ('fneg', b))),
713
714 (('~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)))),
715
716 (('fdot2', a, b), ('fdot_replicated2', a, b), 'options->fdot_replicates'),
717 (('fdot3', a, b), ('fdot_replicated3', a, b), 'options->fdot_replicates'),
718 (('fdot4', a, b), ('fdot_replicated4', a, b), 'options->fdot_replicates'),
719 (('fdph', a, b), ('fdph_replicated', a, b), 'options->fdot_replicates'),
720
721 (('b2f(is_used_more_than_once)', ('inot', a)), ('bcsel', a, 0.0, 1.0)),
722 (('fneg(is_used_more_than_once)', ('b2f', ('inot', a))), ('bcsel', a, -0.0, -1.0)),
723
724 # we do these late so that we don't get in the way of creating ffmas
725 (('fmin', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmin', a, b))),
726 (('fmax', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmax', a, b))),
727
728 # Lowered for backends without a dedicated b2f instruction
729 (('b2f@32', a), ('iand', a, 1.0), 'options->lower_b2f'),
730 ]
731
732 print nir_algebraic.AlgebraicPass("nir_opt_algebraic", optimizations).render()
733 print nir_algebraic.AlgebraicPass("nir_opt_algebraic_before_ffma",
734 before_ffma_optimizations).render()
735 print nir_algebraic.AlgebraicPass("nir_opt_algebraic_late",
736 late_optimizations).render()