nir: lower fexp2(fmul(flog2(a), 2)) to fmul(a, a)
[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', ('inot', a), b, c), ('bcsel', a, c, b)),
174 (('bcsel', a, ('bcsel', a, b, c), d), ('bcsel', a, b, d)),
175 (('bcsel', a, True, 'b@bool'), ('ior', a, b)),
176 (('fmin', a, a), a),
177 (('fmax', a, a), a),
178 (('imin', a, a), a),
179 (('imax', a, a), a),
180 (('umin', a, a), a),
181 (('umax', a, a), a),
182 (('fmin', a, ('fneg', a)), ('fneg', ('fabs', a))),
183 (('imin', a, ('ineg', a)), ('ineg', ('iabs', a))),
184 (('fmin', a, ('fneg', ('fabs', a))), ('fneg', ('fabs', a))),
185 (('imin', a, ('ineg', ('iabs', a))), ('ineg', ('iabs', a))),
186 (('fmin', a, ('fabs', a)), a),
187 (('imin', a, ('iabs', a)), a),
188 (('fmax', a, ('fneg', ('fabs', a))), a),
189 (('imax', a, ('ineg', ('iabs', a))), a),
190 (('fmax', a, ('fabs', a)), ('fabs', a)),
191 (('imax', a, ('iabs', a)), ('iabs', a)),
192 (('fmax', a, ('fneg', a)), ('fabs', a)),
193 (('imax', a, ('ineg', a)), ('iabs', a)),
194 (('~fmin', ('fmax', a, 0.0), 1.0), ('fsat', a), '!options->lower_fsat'),
195 (('~fmax', ('fmin', a, 1.0), 0.0), ('fsat', a), '!options->lower_fsat'),
196 (('fsat', a), ('fmin', ('fmax', a, 0.0), 1.0), 'options->lower_fsat'),
197 (('fsat', ('fsat', a)), ('fsat', a)),
198 (('fmin', ('fmax', ('fmin', ('fmax', a, b), c), b), c), ('fmin', ('fmax', a, b), c)),
199 (('imin', ('imax', ('imin', ('imax', a, b), c), b), c), ('imin', ('imax', a, b), c)),
200 (('umin', ('umax', ('umin', ('umax', a, b), c), b), c), ('umin', ('umax', a, b), c)),
201 (('fmax', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmax', a, b))),
202 (('fmin', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmin', a, b))),
203 (('extract_u8', ('imin', ('imax', a, 0), 0xff), 0), ('imin', ('imax', a, 0), 0xff)),
204 (('~ior', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmax', b, c))),
205 (('~ior', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmin', a, b), c)),
206 (('~ior', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmin', b, c))),
207 (('~ior', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmax', a, b), c)),
208 (('~ior', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmax', b, c))),
209 (('~ior', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmin', a, b), c)),
210 (('~ior', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmin', b, c))),
211 (('~ior', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmax', a, b), c)),
212 (('~iand', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmin', b, c))),
213 (('~iand', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmax', a, b), c)),
214 (('~iand', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmax', b, c))),
215 (('~iand', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmin', a, b), c)),
216 (('~iand', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmin', b, c))),
217 (('~iand', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmax', a, b), c)),
218 (('~iand', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmax', b, c))),
219 (('~iand', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmin', a, b), c)),
220
221 (('ior', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imax', b, c))),
222 (('ior', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imin', a, b), c)),
223 (('ior', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imin', b, c))),
224 (('ior', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imax', a, b), c)),
225 (('ior', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umax', b, c))),
226 (('ior', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umin', a, b), c)),
227 (('ior', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umin', b, c))),
228 (('ior', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umax', a, b), c)),
229 (('iand', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imin', b, c))),
230 (('iand', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imax', a, b), c)),
231 (('iand', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imax', b, c))),
232 (('iand', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imin', a, b), c)),
233 (('iand', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umin', b, c))),
234 (('iand', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umax', a, b), c)),
235 (('iand', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umax', b, c))),
236 (('iand', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umin', a, b), c)),
237
238 # These patterns can result when (a < b || a < c) => (a < min(b, c))
239 # transformations occur before constant propagation and loop-unrolling.
240 (('~flt', a, ('fmax', b, a)), ('flt', a, b)),
241 (('~flt', ('fmin', a, b), a), ('flt', b, a)),
242 (('~fge', a, ('fmin', b, a)), True),
243 (('~fge', ('fmax', a, b), a), True),
244 (('~flt', a, ('fmin', b, a)), False),
245 (('~flt', ('fmax', a, b), a), False),
246
247 (('ilt', a, ('imax', b, a)), ('ilt', a, b)),
248 (('ilt', ('imin', a, b), a), ('ilt', b, a)),
249 (('ige', a, ('imin', b, a)), True),
250 (('ige', ('imax', a, b), a), True),
251 (('ult', a, ('umax', b, a)), ('ult', a, b)),
252 (('ult', ('umin', a, b), a), ('ult', b, a)),
253 (('uge', a, ('umin', b, a)), True),
254 (('uge', ('umax', a, b), a), True),
255
256 (('ilt', '#a', ('imin', '#b', c)), ('iand', ('ilt', a, b), ('ilt', a, c))),
257 (('ilt', ('imax', '#a', b), '#c'), ('iand', ('ilt', a, c), ('ilt', b, c))),
258 (('ige', '#a', ('imax', '#b', c)), ('iand', ('ige', a, b), ('ige', a, c))),
259 (('ige', ('imin', '#a', b), '#c'), ('iand', ('ige', a, c), ('ige', b, c))),
260 (('ult', '#a', ('umin', '#b', c)), ('iand', ('ult', a, b), ('ult', a, c))),
261 (('ult', ('umax', '#a', b), '#c'), ('iand', ('ult', a, c), ('ult', b, c))),
262 (('uge', '#a', ('umax', '#b', c)), ('iand', ('uge', a, b), ('uge', a, c))),
263 (('uge', ('umin', '#a', b), '#c'), ('iand', ('uge', a, c), ('uge', b, c))),
264
265 (('fabs', ('slt', a, b)), ('slt', a, b)),
266 (('fabs', ('sge', a, b)), ('sge', a, b)),
267 (('fabs', ('seq', a, b)), ('seq', a, b)),
268 (('fabs', ('sne', a, b)), ('sne', a, b)),
269 (('slt', a, b), ('b2f', ('flt', a, b)), 'options->lower_scmp'),
270 (('sge', a, b), ('b2f', ('fge', a, b)), 'options->lower_scmp'),
271 (('seq', a, b), ('b2f', ('feq', a, b)), 'options->lower_scmp'),
272 (('sne', a, b), ('b2f', ('fne', a, b)), 'options->lower_scmp'),
273 (('fne', ('fneg', a), a), ('fne', a, 0.0)),
274 (('feq', ('fneg', a), a), ('feq', a, 0.0)),
275 # Emulating booleans
276 (('imul', ('b2i', a), ('b2i', b)), ('b2i', ('iand', a, b))),
277 (('fmul', ('b2f', a), ('b2f', b)), ('b2f', ('iand', a, b))),
278 (('fsat', ('fadd', ('b2f', a), ('b2f', b))), ('b2f', ('ior', a, b))),
279 (('iand', 'a@bool', 1.0), ('b2f', a)),
280 # True/False are ~0 and 0 in NIR. b2i of True is 1, and -1 is ~0 (True).
281 (('ineg', ('b2i@32', a)), a),
282 (('flt', ('fneg', ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
283 (('flt', ('fsub', 0.0, ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
284 # Comparison with the same args. Note that these are not done for
285 # the float versions because NaN always returns false on float
286 # inequalities.
287 (('ilt', a, a), False),
288 (('ige', a, a), True),
289 (('ieq', a, a), True),
290 (('ine', a, a), False),
291 (('ult', a, a), False),
292 (('uge', a, a), True),
293 # Logical and bit operations
294 (('fand', a, 0.0), 0.0),
295 (('iand', a, a), a),
296 (('iand', a, ~0), a),
297 (('iand', a, 0), 0),
298 (('ior', a, a), a),
299 (('ior', a, 0), a),
300 (('ior', a, True), True),
301 (('fxor', a, a), 0.0),
302 (('ixor', a, a), 0),
303 (('ixor', a, 0), a),
304 (('inot', ('inot', a)), a),
305 # DeMorgan's Laws
306 (('iand', ('inot', a), ('inot', b)), ('inot', ('ior', a, b))),
307 (('ior', ('inot', a), ('inot', b)), ('inot', ('iand', a, b))),
308 # Shift optimizations
309 (('ishl', 0, a), 0),
310 (('ishl', a, 0), a),
311 (('ishr', 0, a), 0),
312 (('ishr', a, 0), a),
313 (('ushr', 0, a), 0),
314 (('ushr', a, 0), a),
315 (('iand', 0xff, ('ushr@32', a, 24)), ('ushr', a, 24)),
316 (('iand', 0xffff, ('ushr@32', a, 16)), ('ushr', a, 16)),
317 # Exponential/logarithmic identities
318 (('~fexp2', ('flog2', a)), a), # 2^lg2(a) = a
319 (('~flog2', ('fexp2', a)), a), # lg2(2^a) = a
320 (('fpow', a, b), ('fexp2', ('fmul', ('flog2', a), b)), 'options->lower_fpow'), # a^b = 2^(lg2(a)*b)
321 (('~fexp2', ('fmul', ('flog2', a), b)), ('fpow', a, b), '!options->lower_fpow'), # 2^(lg2(a)*b) = a^b
322 (('~fexp2', ('fadd', ('fmul', ('flog2', a), b), ('fmul', ('flog2', c), d))),
323 ('~fmul', ('fpow', a, b), ('fpow', c, d)), '!options->lower_fpow'), # 2^(lg2(a) * b + lg2(c) + d) = a^b * c^d
324 (('~fexp2', ('fmul', ('flog2', a), 2.0)), ('fmul', a, a)),
325 (('~fexp2', ('fmul', ('flog2', a), 4.0)), ('fmul', ('fmul', a, a), ('fmul', a, a))),
326 (('~fpow', a, 1.0), a),
327 (('~fpow', a, 2.0), ('fmul', a, a)),
328 (('~fpow', a, 4.0), ('fmul', ('fmul', a, a), ('fmul', a, a))),
329 (('~fpow', 2.0, a), ('fexp2', a)),
330 (('~fpow', ('fpow', a, 2.2), 0.454545), a),
331 (('~fpow', ('fabs', ('fpow', a, 2.2)), 0.454545), ('fabs', a)),
332 (('~fsqrt', ('fexp2', a)), ('fexp2', ('fmul', 0.5, a))),
333 (('~frcp', ('fexp2', a)), ('fexp2', ('fneg', a))),
334 (('~frsq', ('fexp2', a)), ('fexp2', ('fmul', -0.5, a))),
335 (('~flog2', ('fsqrt', a)), ('fmul', 0.5, ('flog2', a))),
336 (('~flog2', ('frcp', a)), ('fneg', ('flog2', a))),
337 (('~flog2', ('frsq', a)), ('fmul', -0.5, ('flog2', a))),
338 (('~flog2', ('fpow', a, b)), ('fmul', b, ('flog2', a))),
339 (('~fmul', ('fexp2(is_used_once)', a), ('fexp2(is_used_once)', b)), ('fexp2', ('fadd', a, b))),
340 # Division and reciprocal
341 (('~fdiv', 1.0, a), ('frcp', a)),
342 (('fdiv', a, b), ('fmul', a, ('frcp', b)), 'options->lower_fdiv'),
343 (('~frcp', ('frcp', a)), a),
344 (('~frcp', ('fsqrt', a)), ('frsq', a)),
345 (('fsqrt', a), ('frcp', ('frsq', a)), 'options->lower_fsqrt'),
346 (('~frcp', ('frsq', a)), ('fsqrt', a), '!options->lower_fsqrt'),
347 # Boolean simplifications
348 (('ieq', 'a@bool', True), a),
349 (('ine(is_not_used_by_if)', 'a@bool', True), ('inot', a)),
350 (('ine', 'a@bool', False), a),
351 (('ieq(is_not_used_by_if)', 'a@bool', False), ('inot', 'a')),
352 (('bcsel', a, True, False), a),
353 (('bcsel', a, False, True), ('inot', a)),
354 (('bcsel@32', a, 1.0, 0.0), ('b2f', a)),
355 (('bcsel@32', a, 0.0, 1.0), ('b2f', ('inot', a))),
356 (('bcsel@32', a, -1.0, -0.0), ('fneg', ('b2f', a))),
357 (('bcsel@32', a, -0.0, -1.0), ('fneg', ('b2f', ('inot', a)))),
358 (('bcsel', True, b, c), b),
359 (('bcsel', False, b, c), c),
360 # The result of this should be hit by constant propagation and, in the
361 # next round of opt_algebraic, get picked up by one of the above two.
362 (('bcsel', '#a', b, c), ('bcsel', ('ine', 'a', 0), b, c)),
363
364 (('bcsel', a, b, b), b),
365 (('fcsel', a, b, b), b),
366
367 # Conversions
368 (('i2b', ('b2i', a)), a),
369 (('f2i32', ('ftrunc', a)), ('f2i32', a)),
370 (('f2u32', ('ftrunc', a)), ('f2u32', a)),
371 (('i2b', ('ineg', a)), ('i2b', a)),
372 (('i2b', ('iabs', a)), ('i2b', a)),
373 (('fabs', ('b2f', a)), ('b2f', a)),
374 (('iabs', ('b2i', a)), ('b2i', a)),
375
376 # Packing and then unpacking does nothing
377 (('unpack_64_2x32_split_x', ('pack_64_2x32_split', a, b)), a),
378 (('unpack_64_2x32_split_y', ('pack_64_2x32_split', a, b)), b),
379 (('pack_64_2x32_split', ('unpack_64_2x32_split_x', a),
380 ('unpack_64_2x32_split_y', a)), a),
381
382 # Byte extraction
383 (('ushr', a, 24), ('extract_u8', a, 3), '!options->lower_extract_byte'),
384 (('iand', 0xff, ('ushr', a, 16)), ('extract_u8', a, 2), '!options->lower_extract_byte'),
385 (('iand', 0xff, ('ushr', a, 8)), ('extract_u8', a, 1), '!options->lower_extract_byte'),
386 (('iand', 0xff, a), ('extract_u8', a, 0), '!options->lower_extract_byte'),
387
388 # Word extraction
389 (('ushr', a, 16), ('extract_u16', a, 1), '!options->lower_extract_word'),
390 (('iand', 0xffff, a), ('extract_u16', a, 0), '!options->lower_extract_word'),
391
392 # Subtracts
393 (('~fsub', a, ('fsub', 0.0, b)), ('fadd', a, b)),
394 (('isub', a, ('isub', 0, b)), ('iadd', a, b)),
395 (('ussub_4x8', a, 0), a),
396 (('ussub_4x8', a, ~0), 0),
397 (('fsub', a, b), ('fadd', a, ('fneg', b)), 'options->lower_sub'),
398 (('isub', a, b), ('iadd', a, ('ineg', b)), 'options->lower_sub'),
399 (('fneg', a), ('fsub', 0.0, a), 'options->lower_negate'),
400 (('ineg', a), ('isub', 0, a), 'options->lower_negate'),
401 (('~fadd', a, ('fsub', 0.0, b)), ('fsub', a, b)),
402 (('iadd', a, ('isub', 0, b)), ('isub', a, b)),
403 (('fabs', ('fsub', 0.0, a)), ('fabs', a)),
404 (('iabs', ('isub', 0, a)), ('iabs', a)),
405
406 # Propagate negation up multiplication chains
407 (('fmul', ('fneg', a), b), ('fneg', ('fmul', a, b))),
408 (('imul', ('ineg', a), b), ('ineg', ('imul', a, b))),
409
410 # Propagate constants up multiplication chains
411 (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fmul', ('fmul', a, c), b)),
412 (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('imul', ('imul', a, c), b)),
413 (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fadd', ('fadd', a, c), b)),
414 (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('iadd', ('iadd', a, c), b)),
415
416 # Reassociate constants in add/mul chains so they can be folded together.
417 # For now, we mostly only handle cases where the constants are separated by
418 # a single non-constant. We could do better eventually.
419 (('~fmul', '#a', ('fmul', b, '#c')), ('fmul', ('fmul', a, c), b)),
420 (('imul', '#a', ('imul', b, '#c')), ('imul', ('imul', a, c), b)),
421 (('~fadd', '#a', ('fadd', b, '#c')), ('fadd', ('fadd', a, c), b)),
422 (('~fadd', '#a', ('fneg', ('fadd', b, '#c'))), ('fadd', ('fadd', a, ('fneg', c)), ('fneg', b))),
423 (('iadd', '#a', ('iadd', b, '#c')), ('iadd', ('iadd', a, c), b)),
424
425 # By definition...
426 (('bcsel', ('ige', ('find_lsb', a), 0), ('find_lsb', a), -1), ('find_lsb', a)),
427 (('bcsel', ('ige', ('ifind_msb', a), 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
428 (('bcsel', ('ige', ('ufind_msb', a), 0), ('ufind_msb', a), -1), ('ufind_msb', a)),
429
430 (('bcsel', ('ine', a, 0), ('find_lsb', a), -1), ('find_lsb', a)),
431 (('bcsel', ('ine', a, 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
432 (('bcsel', ('ine', a, 0), ('ufind_msb', a), -1), ('ufind_msb', a)),
433
434 (('bcsel', ('ine', a, -1), ('ifind_msb', a), -1), ('ifind_msb', a)),
435
436 # Misc. lowering
437 (('fmod@32', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod32'),
438 (('fmod@64', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod64'),
439 (('frem', a, b), ('fsub', a, ('fmul', b, ('ftrunc', ('fdiv', a, b)))), 'options->lower_fmod32'),
440 (('uadd_carry@32', a, b), ('b2i', ('ult', ('iadd', a, b), a)), 'options->lower_uadd_carry'),
441 (('usub_borrow@32', a, b), ('b2i', ('ult', a, b)), 'options->lower_usub_borrow'),
442
443 (('bitfield_insert', 'base', 'insert', 'offset', 'bits'),
444 ('bcsel', ('ilt', 31, 'bits'), 'insert',
445 ('bfi', ('bfm', 'bits', 'offset'), 'insert', 'base')),
446 'options->lower_bitfield_insert'),
447
448 (('ibitfield_extract', 'value', 'offset', 'bits'),
449 ('bcsel', ('ilt', 31, 'bits'), 'value',
450 ('ibfe', 'value', 'offset', 'bits')),
451 'options->lower_bitfield_extract'),
452
453 (('ubitfield_extract', 'value', 'offset', 'bits'),
454 ('bcsel', ('ult', 31, 'bits'), 'value',
455 ('ubfe', 'value', 'offset', 'bits')),
456 'options->lower_bitfield_extract'),
457
458 (('extract_i8', a, 'b@32'),
459 ('ishr', ('ishl', a, ('imul', ('isub', 3, b), 8)), 24),
460 'options->lower_extract_byte'),
461
462 (('extract_u8', a, 'b@32'),
463 ('iand', ('ushr', a, ('imul', b, 8)), 0xff),
464 'options->lower_extract_byte'),
465
466 (('extract_i16', a, 'b@32'),
467 ('ishr', ('ishl', a, ('imul', ('isub', 1, b), 16)), 16),
468 'options->lower_extract_word'),
469
470 (('extract_u16', a, 'b@32'),
471 ('iand', ('ushr', a, ('imul', b, 16)), 0xffff),
472 'options->lower_extract_word'),
473
474 (('pack_unorm_2x16', 'v'),
475 ('pack_uvec2_to_uint',
476 ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 65535.0)))),
477 'options->lower_pack_unorm_2x16'),
478
479 (('pack_unorm_4x8', 'v'),
480 ('pack_uvec4_to_uint',
481 ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 255.0)))),
482 'options->lower_pack_unorm_4x8'),
483
484 (('pack_snorm_2x16', 'v'),
485 ('pack_uvec2_to_uint',
486 ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 32767.0)))),
487 'options->lower_pack_snorm_2x16'),
488
489 (('pack_snorm_4x8', 'v'),
490 ('pack_uvec4_to_uint',
491 ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 127.0)))),
492 'options->lower_pack_snorm_4x8'),
493
494 (('unpack_unorm_2x16', 'v'),
495 ('fdiv', ('u2f32', ('vec2', ('extract_u16', 'v', 0),
496 ('extract_u16', 'v', 1))),
497 65535.0),
498 'options->lower_unpack_unorm_2x16'),
499
500 (('unpack_unorm_4x8', 'v'),
501 ('fdiv', ('u2f32', ('vec4', ('extract_u8', 'v', 0),
502 ('extract_u8', 'v', 1),
503 ('extract_u8', 'v', 2),
504 ('extract_u8', 'v', 3))),
505 255.0),
506 'options->lower_unpack_unorm_4x8'),
507
508 (('unpack_snorm_2x16', 'v'),
509 ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec2', ('extract_i16', 'v', 0),
510 ('extract_i16', 'v', 1))),
511 32767.0))),
512 'options->lower_unpack_snorm_2x16'),
513
514 (('unpack_snorm_4x8', 'v'),
515 ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec4', ('extract_i8', 'v', 0),
516 ('extract_i8', 'v', 1),
517 ('extract_i8', 'v', 2),
518 ('extract_i8', 'v', 3))),
519 127.0))),
520 'options->lower_unpack_snorm_4x8'),
521 ]
522
523 def fexp2i(exp, bits):
524 # We assume that exp is already in the right range.
525 if bits == 32:
526 return ('ishl', ('iadd', exp, 127), 23)
527 elif bits == 64:
528 return ('pack_64_2x32_split', 0, ('ishl', ('iadd', exp, 1023), 20))
529 else:
530 assert False
531
532 def ldexp(f, exp, bits):
533 # First, we clamp exp to a reasonable range. The maximum possible range
534 # for a normal exponent is [-126, 127] and, throwing in denormals, you get
535 # a maximum range of [-149, 127]. This means that we can potentially have
536 # a swing of +-276. If you start with FLT_MAX, you actually have to do
537 # ldexp(FLT_MAX, -278) to get it to flush all the way to zero. The GLSL
538 # spec, on the other hand, only requires that we handle an exponent value
539 # in the range [-126, 128]. This implementation is *mostly* correct; it
540 # handles a range on exp of [-252, 254] which allows you to create any
541 # value (including denorms if the hardware supports it) and to adjust the
542 # exponent of any normal value to anything you want.
543 if bits == 32:
544 exp = ('imin', ('imax', exp, -252), 254)
545 elif bits == 64:
546 exp = ('imin', ('imax', exp, -2044), 2046)
547 else:
548 assert False
549
550 # Now we compute two powers of 2, one for exp/2 and one for exp-exp/2.
551 # (We use ishr which isn't the same for -1, but the -1 case still works
552 # since we use exp-exp/2 as the second exponent.) While the spec
553 # technically defines ldexp as f * 2.0^exp, simply multiplying once doesn't
554 # work with denormals and doesn't allow for the full swing in exponents
555 # that you can get with normalized values. Instead, we create two powers
556 # of two and multiply by them each in turn. That way the effective range
557 # of our exponent is doubled.
558 pow2_1 = fexp2i(('ishr', exp, 1), bits)
559 pow2_2 = fexp2i(('isub', exp, ('ishr', exp, 1)), bits)
560 return ('fmul', ('fmul', f, pow2_1), pow2_2)
561
562 optimizations += [
563 (('ldexp@32', 'x', 'exp'), ldexp('x', 'exp', 32)),
564 (('ldexp@64', 'x', 'exp'), ldexp('x', 'exp', 64)),
565 ]
566
567 # Unreal Engine 4 demo applications open-codes bitfieldReverse()
568 def bitfield_reverse(u):
569 step1 = ('ior', ('ishl', u, 16), ('ushr', u, 16))
570 step2 = ('ior', ('ishl', ('iand', step1, 0x00ff00ff), 8), ('ushr', ('iand', step1, 0xff00ff00), 8))
571 step3 = ('ior', ('ishl', ('iand', step2, 0x0f0f0f0f), 4), ('ushr', ('iand', step2, 0xf0f0f0f0), 4))
572 step4 = ('ior', ('ishl', ('iand', step3, 0x33333333), 2), ('ushr', ('iand', step3, 0xcccccccc), 2))
573 step5 = ('ior', ('ishl', ('iand', step4, 0x55555555), 1), ('ushr', ('iand', step4, 0xaaaaaaaa), 1))
574
575 return step5
576
577 optimizations += [(bitfield_reverse('x@32'), ('bitfield_reverse', 'x'))]
578
579 # For any float comparison operation, "cmp", if you have "a == a && a cmp b"
580 # then the "a == a" is redundant because it's equivalent to "a is not NaN"
581 # and, if a is a NaN then the second comparison will fail anyway.
582 for op in ['flt', 'fge', 'feq']:
583 optimizations += [
584 (('iand', ('feq', a, a), (op, a, b)), (op, a, b)),
585 (('iand', ('feq', a, a), (op, b, a)), (op, b, a)),
586 ]
587
588 # Add optimizations to handle the case where the result of a ternary is
589 # compared to a constant. This way we can take things like
590 #
591 # (a ? 0 : 1) > 0
592 #
593 # and turn it into
594 #
595 # a ? (0 > 0) : (1 > 0)
596 #
597 # which constant folding will eat for lunch. The resulting ternary will
598 # further get cleaned up by the boolean reductions above and we will be
599 # left with just the original variable "a".
600 for op in ['flt', 'fge', 'feq', 'fne',
601 'ilt', 'ige', 'ieq', 'ine', 'ult', 'uge']:
602 optimizations += [
603 ((op, ('bcsel', 'a', '#b', '#c'), '#d'),
604 ('bcsel', 'a', (op, 'b', 'd'), (op, 'c', 'd'))),
605 ((op, '#d', ('bcsel', a, '#b', '#c')),
606 ('bcsel', 'a', (op, 'd', 'b'), (op, 'd', 'c'))),
607 ]
608
609
610 # For example, this converts things like
611 #
612 # 1 + mix(0, a - 1, condition)
613 #
614 # into
615 #
616 # mix(1, (a-1)+1, condition)
617 #
618 # Other optimizations will rearrange the constants.
619 for op in ['fadd', 'fmul', 'iadd', 'imul']:
620 optimizations += [
621 ((op, ('bcsel(is_used_once)', a, '#b', c), '#d'), ('bcsel', a, (op, b, d), (op, c, d)))
622 ]
623
624 # This section contains "late" optimizations that should be run before
625 # creating ffmas and calling regular optimizations for the final time.
626 # Optimizations should go here if they help code generation and conflict
627 # with the regular optimizations.
628 before_ffma_optimizations = [
629 # Propagate constants down multiplication chains
630 (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fmul', ('fmul', a, c), b)),
631 (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('imul', ('imul', a, c), b)),
632 (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fadd', ('fadd', a, c), b)),
633 (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('iadd', ('iadd', a, c), b)),
634
635 (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
636 (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
637 (('~fadd', ('fneg', a), a), 0.0),
638 (('iadd', ('ineg', a), a), 0),
639 (('iadd', ('ineg', a), ('iadd', a, b)), b),
640 (('iadd', a, ('iadd', ('ineg', a), b)), b),
641 (('~fadd', ('fneg', a), ('fadd', a, b)), b),
642 (('~fadd', a, ('fadd', ('fneg', a), b)), b),
643 ]
644
645 # This section contains "late" optimizations that should be run after the
646 # regular optimizations have finished. Optimizations should go here if
647 # they help code generation but do not necessarily produce code that is
648 # more easily optimizable.
649 late_optimizations = [
650 # Most of these optimizations aren't quite safe when you get infinity or
651 # Nan involved but the first one should be fine.
652 (('flt', ('fadd', a, b), 0.0), ('flt', a, ('fneg', b))),
653 (('flt', ('fneg', ('fadd', a, b)), 0.0), ('flt', ('fneg', a), b)),
654 (('~fge', ('fadd', a, b), 0.0), ('fge', a, ('fneg', b))),
655 (('~fge', ('fneg', ('fadd', a, b)), 0.0), ('fge', ('fneg', a), b)),
656 (('~feq', ('fadd', a, b), 0.0), ('feq', a, ('fneg', b))),
657 (('~fne', ('fadd', a, b), 0.0), ('fne', a, ('fneg', b))),
658
659 (('~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)))),
660
661 (('fdot2', a, b), ('fdot_replicated2', a, b), 'options->fdot_replicates'),
662 (('fdot3', a, b), ('fdot_replicated3', a, b), 'options->fdot_replicates'),
663 (('fdot4', a, b), ('fdot_replicated4', a, b), 'options->fdot_replicates'),
664 (('fdph', a, b), ('fdph_replicated', a, b), 'options->fdot_replicates'),
665
666 (('b2f(is_used_more_than_once)', ('inot', a)), ('bcsel', a, 0.0, 1.0)),
667 (('fneg(is_used_more_than_once)', ('b2f', ('inot', a))), ('bcsel', a, -0.0, -1.0)),
668
669 # we do these late so that we don't get in the way of creating ffmas
670 (('fmin', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmin', a, b))),
671 (('fmax', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmax', a, b))),
672 ]
673
674 print nir_algebraic.AlgebraicPass("nir_opt_algebraic", optimizations).render()
675 print nir_algebraic.AlgebraicPass("nir_opt_algebraic_before_ffma",
676 before_ffma_optimizations).render()
677 print nir_algebraic.AlgebraicPass("nir_opt_algebraic_late",
678 late_optimizations).render()