summaryrefslogtreecommitdiff
path: root/src/compiler/nir/nir_range_analysis.c
blob: d38bcc0b0407635629b0be2600ed58eeaa988ea3 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
/*
 * Copyright © 2018 Intel Corporation
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice (including the next
 * paragraph) shall be included in all copies or substantial portions of the
 * Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
 * IN THE SOFTWARE.
 */
#include <math.h>
#include <float.h>
#include "nir.h"
#include "nir_range_analysis.h"
#include "util/hash_table.h"

/**
 * Analyzes a sequence of operations to determine some aspects of the range of
 * the result.
 */

static bool
is_not_negative(enum ssa_ranges r)
{
   return r == gt_zero || r == ge_zero || r == eq_zero;
}

static void *
pack_data(const struct ssa_result_range r)
{
   return (void *)(uintptr_t)(r.range | r.is_integral << 8);
}

static struct ssa_result_range
unpack_data(const void *p)
{
   const uintptr_t v = (uintptr_t) p;

   return (struct ssa_result_range){v & 0xff, (v & 0x0ff00) != 0};
}

static void *
pack_key(const struct nir_alu_instr *instr, nir_alu_type type)
{
   uintptr_t type_encoding;
   uintptr_t ptr = (uintptr_t) instr;

   /* The low 2 bits have to be zero or this whole scheme falls apart. */
   assert((ptr & 0x3) == 0);

   /* NIR is typeless in the sense that sequences of bits have whatever
    * meaning is attached to them by the instruction that consumes them.
    * However, the number of bits must match between producer and consumer.
    * As a result, the number of bits does not need to be encoded here.
    */
   switch (nir_alu_type_get_base_type(type)) {
   case nir_type_int:   type_encoding = 0; break;
   case nir_type_uint:  type_encoding = 1; break;
   case nir_type_bool:  type_encoding = 2; break;
   case nir_type_float: type_encoding = 3; break;
   default: unreachable("Invalid base type.");
   }

   return (void *)(ptr | type_encoding);
}

static nir_alu_type
nir_alu_src_type(const nir_alu_instr *instr, unsigned src)
{
   return nir_alu_type_get_base_type(nir_op_infos[instr->op].input_types[src]) |
          nir_src_bit_size(instr->src[src].src);
}

static struct ssa_result_range
analyze_constant(const struct nir_alu_instr *instr, unsigned src,
                 nir_alu_type use_type)
{
   uint8_t swizzle[4] = { 0, 1, 2, 3 };

   /* If the source is an explicitly sized source, then we need to reset
    * both the number of components and the swizzle.
    */
   const unsigned num_components = nir_ssa_alu_instr_src_components(instr, src);

   for (unsigned i = 0; i < num_components; ++i)
      swizzle[i] = instr->src[src].swizzle[i];

   const nir_load_const_instr *const load =
      nir_instr_as_load_const(instr->src[src].src.ssa->parent_instr);

   struct ssa_result_range r = { unknown, false };

   switch (nir_alu_type_get_base_type(use_type)) {
   case nir_type_float: {
      double min_value = DBL_MAX;
      double max_value = -DBL_MAX;
      bool any_zero = false;
      bool all_zero = true;

      r.is_integral = true;

      for (unsigned i = 0; i < num_components; ++i) {
         const double v = nir_const_value_as_float(load->value[swizzle[i]],
                                                   load->def.bit_size);

         if (floor(v) != v)
            r.is_integral = false;

         any_zero = any_zero || (v == 0.0);
         all_zero = all_zero && (v == 0.0);
         min_value = MIN2(min_value, v);
         max_value = MAX2(max_value, v);
      }

      assert(any_zero >= all_zero);
      assert(isnan(max_value) || max_value >= min_value);

      if (all_zero)
         r.range = eq_zero;
      else if (min_value > 0.0)
         r.range = gt_zero;
      else if (min_value == 0.0)
         r.range = ge_zero;
      else if (max_value < 0.0)
         r.range = lt_zero;
      else if (max_value == 0.0)
         r.range = le_zero;
      else if (!any_zero)
         r.range = ne_zero;
      else
         r.range = unknown;

      return r;
   }

   case nir_type_int:
   case nir_type_bool: {
      int64_t min_value = INT_MAX;
      int64_t max_value = INT_MIN;
      bool any_zero = false;
      bool all_zero = true;

      for (unsigned i = 0; i < num_components; ++i) {
         const int64_t v = nir_const_value_as_int(load->value[swizzle[i]],
                                                  load->def.bit_size);

         any_zero = any_zero || (v == 0);
         all_zero = all_zero && (v == 0);
         min_value = MIN2(min_value, v);
         max_value = MAX2(max_value, v);
      }

      assert(any_zero >= all_zero);
      assert(max_value >= min_value);

      if (all_zero)
         r.range = eq_zero;
      else if (min_value > 0)
         r.range = gt_zero;
      else if (min_value == 0)
         r.range = ge_zero;
      else if (max_value < 0)
         r.range = lt_zero;
      else if (max_value == 0)
         r.range = le_zero;
      else if (!any_zero)
         r.range = ne_zero;
      else
         r.range = unknown;

      return r;
   }

   case nir_type_uint: {
      bool any_zero = false;
      bool all_zero = true;

      for (unsigned i = 0; i < num_components; ++i) {
         const uint64_t v = nir_const_value_as_uint(load->value[swizzle[i]],
                                                    load->def.bit_size);

         any_zero = any_zero || (v == 0);
         all_zero = all_zero && (v == 0);
      }

      assert(any_zero >= all_zero);

      if (all_zero)
         r.range = eq_zero;
      else if (any_zero)
         r.range = ge_zero;
      else
         r.range = gt_zero;

      return r;
   }

   default:
      unreachable("Invalid alu source type");
   }
}

/**
 * Short-hand name for use in the tables in analyze_expression.  If this name
 * becomes a problem on some compiler, we can change it to _.
 */
#define _______ unknown


/* MSVC doesn't have C99's _Pragma() */
#ifdef _MSC_VER
#define _Pragma(x)
#endif


#ifndef NDEBUG
#define ASSERT_TABLE_IS_COMMUTATIVE(t)                        \
   do {                                                       \
      static bool first = true;                               \
      if (first) {                                            \
         first = false;                                       \
         _Pragma("GCC unroll 7")                              \
         for (unsigned r = 0; r < ARRAY_SIZE(t); r++) {       \
            _Pragma("GCC unroll 7")                           \
            for (unsigned c = 0; c < ARRAY_SIZE(t[0]); c++)   \
               assert(t[r][c] == t[c][r]);                    \
         }                                                    \
      }                                                       \
   } while (false)

#define ASSERT_TABLE_IS_DIAGONAL(t)                           \
   do {                                                       \
      static bool first = true;                               \
      if (first) {                                            \
         first = false;                                       \
         _Pragma("GCC unroll 7")                              \
         for (unsigned r = 0; r < ARRAY_SIZE(t); r++)         \
            assert(t[r][r] == r);                             \
      }                                                       \
   } while (false)

static enum ssa_ranges
union_ranges(enum ssa_ranges a, enum ssa_ranges b)
{
   static const enum ssa_ranges union_table[last_range + 1][last_range + 1] = {
      /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
      /* unknown */ { _______, _______, _______, _______, _______, _______, _______ },
      /* lt_zero */ { _______, lt_zero, le_zero, ne_zero, _______, ne_zero, le_zero },
      /* le_zero */ { _______, le_zero, le_zero, _______, _______, _______, le_zero },
      /* gt_zero */ { _______, ne_zero, _______, gt_zero, ge_zero, ne_zero, ge_zero },
      /* ge_zero */ { _______, _______, _______, ge_zero, ge_zero, _______, ge_zero },
      /* ne_zero */ { _______, ne_zero, _______, ne_zero, _______, ne_zero, _______ },
      /* eq_zero */ { _______, le_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
   };

   ASSERT_TABLE_IS_COMMUTATIVE(union_table);
   ASSERT_TABLE_IS_DIAGONAL(union_table);

   return union_table[a][b];
}

/* Verify that the 'unknown' entry in each row (or column) of the table is the
 * union of all the other values in the row (or column).
 */
#define ASSERT_UNION_OF_OTHERS_MATCHES_UNKNOWN_2_SOURCE(t)              \
   do {                                                                 \
      static bool first = true;                                         \
      if (first) {                                                      \
         first = false;                                                 \
         _Pragma("GCC unroll 7")                                        \
         for (unsigned i = 0; i < last_range; i++) {                    \
            enum ssa_ranges col_range = t[i][unknown + 1];              \
            enum ssa_ranges row_range = t[unknown + 1][i];              \
                                                                        \
            _Pragma("GCC unroll 5")                                     \
            for (unsigned j = unknown + 2; j < last_range; j++) {       \
               col_range = union_ranges(col_range, t[i][j]);            \
               row_range = union_ranges(row_range, t[j][i]);            \
            }                                                           \
                                                                        \
            assert(col_range == t[i][unknown]);                         \
            assert(row_range == t[unknown][i]);                         \
         }                                                              \
      }                                                                 \
   } while (false)

/* For most operations, the union of ranges for a strict inequality and
 * equality should be the range of the non-strict inequality (e.g.,
 * union_ranges(range(op(lt_zero), range(op(eq_zero))) == range(op(le_zero)).
 *
 * Does not apply to selection-like opcodes (bcsel, fmin, fmax, etc.).
 */
#define ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_1_SOURCE(t) \
   do {                                                                 \
      assert(union_ranges(t[lt_zero], t[eq_zero]) == t[le_zero]);       \
      assert(union_ranges(t[gt_zero], t[eq_zero]) == t[ge_zero]);       \
   } while (false)

#define ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_2_SOURCE(t) \
   do {                                                                 \
      static bool first = true;                                         \
      if (first) {                                                      \
         first = false;                                                 \
         _Pragma("GCC unroll 7")                                        \
         for (unsigned i = 0; i < last_range; i++) {                    \
            assert(union_ranges(t[i][lt_zero], t[i][eq_zero]) == t[i][le_zero]); \
            assert(union_ranges(t[i][gt_zero], t[i][eq_zero]) == t[i][ge_zero]); \
            assert(union_ranges(t[lt_zero][i], t[eq_zero][i]) == t[le_zero][i]); \
            assert(union_ranges(t[gt_zero][i], t[eq_zero][i]) == t[ge_zero][i]); \
         }                                                              \
      }                                                                 \
   } while (false)

/* Several other unordered tuples span the range of "everything."  Each should
 * have the same value as unknown: (lt_zero, ge_zero), (le_zero, gt_zero), and
 * (eq_zero, ne_zero).  union_ranges is already commutative, so only one
 * ordering needs to be checked.
 *
 * Does not apply to selection-like opcodes (bcsel, fmin, fmax, etc.).
 *
 * In cases where this can be used, it is unnecessary to also use
 * ASSERT_UNION_OF_OTHERS_MATCHES_UNKNOWN_*_SOURCE.  For any range X,
 * union_ranges(X, X) == X.  The disjoint ranges cover all of the non-unknown
 * possibilities, so the union of all the unions of disjoint ranges is
 * equivalent to the union of "others."
 */
#define ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_1_SOURCE(t)            \
   do {                                                                 \
      assert(union_ranges(t[lt_zero], t[ge_zero]) == t[unknown]);       \
      assert(union_ranges(t[le_zero], t[gt_zero]) == t[unknown]);       \
      assert(union_ranges(t[eq_zero], t[ne_zero]) == t[unknown]);       \
   } while (false)

#define ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_2_SOURCE(t)            \
   do {                                                                 \
      static bool first = true;                                         \
      if (first) {                                                      \
         first = false;                                                 \
         _Pragma("GCC unroll 7")                                        \
         for (unsigned i = 0; i < last_range; i++) {                    \
            assert(union_ranges(t[i][lt_zero], t[i][ge_zero]) ==        \
                   t[i][unknown]);                                      \
            assert(union_ranges(t[i][le_zero], t[i][gt_zero]) ==        \
                   t[i][unknown]);                                      \
            assert(union_ranges(t[i][eq_zero], t[i][ne_zero]) ==        \
                   t[i][unknown]);                                      \
                                                                        \
            assert(union_ranges(t[lt_zero][i], t[ge_zero][i]) ==        \
                   t[unknown][i]);                                      \
            assert(union_ranges(t[le_zero][i], t[gt_zero][i]) ==        \
                   t[unknown][i]);                                      \
            assert(union_ranges(t[eq_zero][i], t[ne_zero][i]) ==        \
                   t[unknown][i]);                                      \
         }                                                              \
      }                                                                 \
   } while (false)

#else
#define ASSERT_TABLE_IS_COMMUTATIVE(t)
#define ASSERT_TABLE_IS_DIAGONAL(t)
#define ASSERT_UNION_OF_OTHERS_MATCHES_UNKNOWN_2_SOURCE(t)
#define ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_1_SOURCE(t)
#define ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_2_SOURCE(t)
#define ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_1_SOURCE(t)
#define ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_2_SOURCE(t)
#endif

/**
 * Analyze an expression to determine the range of its result
 *
 * The end result of this analysis is a token that communicates something
 * about the range of values.  There's an implicit grammar that produces
 * tokens from sequences of literal values, other tokens, and operations.
 * This function implements this grammar as a recursive-descent parser.  Some
 * (but not all) of the grammar is listed in-line in the function.
 */
static struct ssa_result_range
analyze_expression(const nir_alu_instr *instr, unsigned src,
                   struct hash_table *ht, nir_alu_type use_type)
{
   /* Ensure that the _Pragma("GCC unroll 7") above are correct. */
   STATIC_ASSERT(last_range + 1 == 7);

   if (!instr->src[src].src.is_ssa)
      return (struct ssa_result_range){unknown, false};

   if (nir_src_is_const(instr->src[src].src))
      return analyze_constant(instr, src, use_type);

   if (instr->src[src].src.ssa->parent_instr->type != nir_instr_type_alu)
      return (struct ssa_result_range){unknown, false};

   const struct nir_alu_instr *const alu =
       nir_instr_as_alu(instr->src[src].src.ssa->parent_instr);

   /* Bail if the type of the instruction generating the value does not match
    * the type the value will be interpreted as.  int/uint/bool can be
    * reinterpreted trivially.  The most important cases are between float and
    * non-float.
    */
   if (alu->op != nir_op_mov && alu->op != nir_op_bcsel) {
      const nir_alu_type use_base_type =
         nir_alu_type_get_base_type(use_type);
      const nir_alu_type src_base_type =
         nir_alu_type_get_base_type(nir_op_infos[alu->op].output_type);

      if (use_base_type != src_base_type &&
          (use_base_type == nir_type_float ||
           src_base_type == nir_type_float)) {
         return (struct ssa_result_range){unknown, false};
      }
   }

   struct hash_entry *he = _mesa_hash_table_search(ht, pack_key(alu, use_type));
   if (he != NULL)
      return unpack_data(he->data);

   struct ssa_result_range r = {unknown, false};

   /* ge_zero: ge_zero + ge_zero
    *
    * gt_zero: gt_zero + eq_zero
    *        | gt_zero + ge_zero
    *        | eq_zero + gt_zero   # Addition is commutative
    *        | ge_zero + gt_zero   # Addition is commutative
    *        | gt_zero + gt_zero
    *        ;
    *
    * le_zero: le_zero + le_zero
    *
    * lt_zero: lt_zero + eq_zero
    *        | lt_zero + le_zero
    *        | eq_zero + lt_zero   # Addition is commutative
    *        | le_zero + lt_zero   # Addition is commutative
    *        | lt_zero + lt_zero
    *        ;
    *
    * ne_zero: eq_zero + ne_zero
    *        | ne_zero + eq_zero   # Addition is commutative
    *        ;
    *
    * eq_zero: eq_zero + eq_zero
    *        ;
    *
    * All other cases are 'unknown'.  The seeming odd entry is (ne_zero,
    * ne_zero), but that could be (-5, +5) which is not ne_zero.
    */
   static const enum ssa_ranges fadd_table[last_range + 1][last_range + 1] = {
      /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
      /* unknown */ { _______, _______, _______, _______, _______, _______, _______ },
      /* lt_zero */ { _______, lt_zero, lt_zero, _______, _______, _______, lt_zero },
      /* le_zero */ { _______, lt_zero, le_zero, _______, _______, _______, le_zero },
      /* gt_zero */ { _______, _______, _______, gt_zero, gt_zero, _______, gt_zero },
      /* ge_zero */ { _______, _______, _______, gt_zero, ge_zero, _______, ge_zero },
      /* ne_zero */ { _______, _______, _______, _______, _______, _______, ne_zero },
      /* eq_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
   };

   ASSERT_TABLE_IS_COMMUTATIVE(fadd_table);
   ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_2_SOURCE(fadd_table);
   ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_2_SOURCE(fadd_table);

   /* Due to flush-to-zero semanatics of floating-point numbers with very
    * small mangnitudes, we can never really be sure a result will be
    * non-zero.
    *
    * ge_zero: ge_zero * ge_zero
    *        | ge_zero * gt_zero
    *        | ge_zero * eq_zero
    *        | le_zero * lt_zero
    *        | lt_zero * le_zero  # Multiplication is commutative
    *        | le_zero * le_zero
    *        | gt_zero * ge_zero  # Multiplication is commutative
    *        | eq_zero * ge_zero  # Multiplication is commutative
    *        | a * a              # Left source == right source
    *        | gt_zero * gt_zero
    *        | lt_zero * lt_zero
    *        ;
    *
    * le_zero: ge_zero * le_zero
    *        | ge_zero * lt_zero
    *        | lt_zero * ge_zero  # Multiplication is commutative
    *        | le_zero * ge_zero  # Multiplication is commutative
    *        | le_zero * gt_zero
    *        | lt_zero * gt_zero
    *        | gt_zero * lt_zero  # Multiplication is commutative
    *        ;
    *
    * eq_zero: eq_zero * <any>
    *          <any> * eq_zero    # Multiplication is commutative
    *
    * All other cases are 'unknown'.
    */
   static const enum ssa_ranges fmul_table[last_range + 1][last_range + 1] = {
      /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
      /* unknown */ { _______, _______, _______, _______, _______, _______, eq_zero },
      /* lt_zero */ { _______, ge_zero, ge_zero, le_zero, le_zero, _______, eq_zero },
      /* le_zero */ { _______, ge_zero, ge_zero, le_zero, le_zero, _______, eq_zero },
      /* gt_zero */ { _______, le_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
      /* ge_zero */ { _______, le_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
      /* ne_zero */ { _______, _______, _______, _______, _______, _______, eq_zero },
      /* eq_zero */ { eq_zero, eq_zero, eq_zero, eq_zero, eq_zero, eq_zero, eq_zero }
   };

   ASSERT_TABLE_IS_COMMUTATIVE(fmul_table);
   ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_2_SOURCE(fmul_table);
   ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_2_SOURCE(fmul_table);

   static const enum ssa_ranges fneg_table[last_range + 1] = {
   /* unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
      _______, gt_zero, ge_zero, lt_zero, le_zero, ne_zero, eq_zero
   };

   ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_1_SOURCE(fneg_table);
   ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_1_SOURCE(fneg_table);


   switch (alu->op) {
   case nir_op_b2f32:
   case nir_op_b2i32:
      r = (struct ssa_result_range){ge_zero, alu->op == nir_op_b2f32};
      break;

   case nir_op_bcsel: {
      const struct ssa_result_range left =
         analyze_expression(alu, 1, ht, use_type);
      const struct ssa_result_range right =
         analyze_expression(alu, 2, ht, use_type);

      r.is_integral = left.is_integral && right.is_integral;

      /* le_zero: bcsel(<any>, le_zero, lt_zero)
       *        | bcsel(<any>, eq_zero, lt_zero)
       *        | bcsel(<any>, le_zero, eq_zero)
       *        | bcsel(<any>, lt_zero, le_zero)
       *        | bcsel(<any>, lt_zero, eq_zero)
       *        | bcsel(<any>, eq_zero, le_zero)
       *        | bcsel(<any>, le_zero, le_zero)
       *        ;
       *
       * lt_zero: bcsel(<any>, lt_zero, lt_zero)
       *        ;
       *
       * ge_zero: bcsel(<any>, ge_zero, ge_zero)
       *        | bcsel(<any>, ge_zero, gt_zero)
       *        | bcsel(<any>, ge_zero, eq_zero)
       *        | bcsel(<any>, gt_zero, ge_zero)
       *        | bcsel(<any>, eq_zero, ge_zero)
       *        ;
       *
       * gt_zero: bcsel(<any>, gt_zero, gt_zero)
       *        ;
       *
       * ne_zero: bcsel(<any>, ne_zero, gt_zero)
       *        | bcsel(<any>, ne_zero, lt_zero)
       *        | bcsel(<any>, gt_zero, lt_zero)
       *        | bcsel(<any>, gt_zero, ne_zero)
       *        | bcsel(<any>, lt_zero, ne_zero)
       *        | bcsel(<any>, lt_zero, gt_zero)
       *        | bcsel(<any>, ne_zero, ne_zero)
       *        ;
       *
       * eq_zero: bcsel(<any>, eq_zero, eq_zero)
       *        ;
       *
       * All other cases are 'unknown'.
       *
       * The ranges could be tightened if the range of the first source is
       * known.  However, opt_algebraic will (eventually) elminiate the bcsel
       * if the condition is known.
       */
      static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
         /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
         /* unknown */ { _______, _______, _______, _______, _______, _______, _______ },
         /* lt_zero */ { _______, lt_zero, le_zero, ne_zero, _______, ne_zero, le_zero },
         /* le_zero */ { _______, le_zero, le_zero, _______, _______, _______, le_zero },
         /* gt_zero */ { _______, ne_zero, _______, gt_zero, ge_zero, ne_zero, ge_zero },
         /* ge_zero */ { _______, _______, _______, ge_zero, ge_zero, _______, ge_zero },
         /* ne_zero */ { _______, ne_zero, _______, ne_zero, _______, ne_zero, _______ },
         /* eq_zero */ { _______, le_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
      };

      ASSERT_TABLE_IS_COMMUTATIVE(table);
      ASSERT_TABLE_IS_DIAGONAL(table);
      ASSERT_UNION_OF_OTHERS_MATCHES_UNKNOWN_2_SOURCE(table);

      r.range = table[left.range][right.range];
      break;
   }

   case nir_op_i2f32:
   case nir_op_u2f32:
      r = analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      r.is_integral = true;

      if (r.range == unknown && alu->op == nir_op_u2f32)
         r.range = ge_zero;

      break;

   case nir_op_fabs:
      r = analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      switch (r.range) {
      case unknown:
      case le_zero:
      case ge_zero:
         r.range = ge_zero;
         break;

      case lt_zero:
      case gt_zero:
      case ne_zero:
         r.range = gt_zero;
         break;

      case eq_zero:
         break;
      }

      break;

   case nir_op_fadd: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range right =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));

      r.is_integral = left.is_integral && right.is_integral;
      r.range = fadd_table[left.range][right.range];
      break;
   }

   case nir_op_fexp2: {
      /* If the parameter might be less than zero, the mathematically result
       * will be on (0, 1).  For sufficiently large magnitude negative
       * parameters, the result will flush to zero.
       */
      static const enum ssa_ranges table[last_range + 1] = {
      /* unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
         ge_zero, ge_zero, ge_zero, gt_zero, gt_zero, ge_zero, gt_zero
      };

      r = analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_1_SOURCE(table);
      ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_1_SOURCE(table);

      r.is_integral = r.is_integral && is_not_negative(r.range);
      r.range = table[r.range];
      break;
   }

   case nir_op_fmax: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range right =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));

      r.is_integral = left.is_integral && right.is_integral;

      /* gt_zero: fmax(gt_zero, *)
       *        | fmax(*, gt_zero)        # Treat fmax as commutative
       *        ;
       *
       * ge_zero: fmax(ge_zero, ne_zero)
       *        | fmax(ge_zero, lt_zero)
       *        | fmax(ge_zero, le_zero)
       *        | fmax(ge_zero, eq_zero)
       *        | fmax(ne_zero, ge_zero)  # Treat fmax as commutative
       *        | fmax(lt_zero, ge_zero)  # Treat fmax as commutative
       *        | fmax(le_zero, ge_zero)  # Treat fmax as commutative
       *        | fmax(eq_zero, ge_zero)  # Treat fmax as commutative
       *        | fmax(ge_zero, ge_zero)
       *        ;
       *
       * le_zero: fmax(le_zero, lt_zero)
       *        | fmax(lt_zero, le_zero)  # Treat fmax as commutative
       *        | fmax(le_zero, le_zero)
       *        ;
       *
       * lt_zero: fmax(lt_zero, lt_zero)
       *        ;
       *
       * ne_zero: fmax(ne_zero, lt_zero)
       *        | fmax(lt_zero, ne_zero)  # Treat fmax as commutative
       *        | fmax(ne_zero, ne_zero)
       *        ;
       *
       * eq_zero: fmax(eq_zero, le_zero)
       *        | fmax(eq_zero, lt_zero)
       *        | fmax(le_zero, eq_zero)  # Treat fmax as commutative
       *        | fmax(lt_zero, eq_zero)  # Treat fmax as commutative
       *        | fmax(eq_zero, eq_zero)
       *        ;
       *
       * All other cases are 'unknown'.
       */
      static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
         /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
         /* unknown */ { _______, _______, _______, gt_zero, ge_zero, _______, _______ },
         /* lt_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
         /* le_zero */ { _______, le_zero, le_zero, gt_zero, ge_zero, _______, eq_zero },
         /* gt_zero */ { gt_zero, gt_zero, gt_zero, gt_zero, gt_zero, gt_zero, gt_zero },
         /* ge_zero */ { ge_zero, ge_zero, ge_zero, gt_zero, ge_zero, ge_zero, ge_zero },
         /* ne_zero */ { _______, ne_zero, _______, gt_zero, ge_zero, ne_zero, _______ },
         /* eq_zero */ { _______, eq_zero, eq_zero, gt_zero, ge_zero, _______, eq_zero }
      };

      /* Treat fmax as commutative. */
      ASSERT_TABLE_IS_COMMUTATIVE(table);
      ASSERT_TABLE_IS_DIAGONAL(table);
      ASSERT_UNION_OF_OTHERS_MATCHES_UNKNOWN_2_SOURCE(table);

      r.range = table[left.range][right.range];
      break;
   }

   case nir_op_fmin: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range right =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));

      r.is_integral = left.is_integral && right.is_integral;

      /* lt_zero: fmin(lt_zero, *)
       *        | fmin(*, lt_zero)        # Treat fmin as commutative
       *        ;
       *
       * le_zero: fmin(le_zero, ne_zero)
       *        | fmin(le_zero, gt_zero)
       *        | fmin(le_zero, ge_zero)
       *        | fmin(le_zero, eq_zero)
       *        | fmin(ne_zero, le_zero)  # Treat fmin as commutative
       *        | fmin(gt_zero, le_zero)  # Treat fmin as commutative
       *        | fmin(ge_zero, le_zero)  # Treat fmin as commutative
       *        | fmin(eq_zero, le_zero)  # Treat fmin as commutative
       *        | fmin(le_zero, le_zero)
       *        ;
       *
       * ge_zero: fmin(ge_zero, gt_zero)
       *        | fmin(gt_zero, ge_zero)  # Treat fmin as commutative
       *        | fmin(ge_zero, ge_zero)
       *        ;
       *
       * gt_zero: fmin(gt_zero, gt_zero)
       *        ;
       *
       * ne_zero: fmin(ne_zero, gt_zero)
       *        | fmin(gt_zero, ne_zero)  # Treat fmin as commutative
       *        | fmin(ne_zero, ne_zero)
       *        ;
       *
       * eq_zero: fmin(eq_zero, ge_zero)
       *        | fmin(eq_zero, gt_zero)
       *        | fmin(ge_zero, eq_zero)  # Treat fmin as commutative
       *        | fmin(gt_zero, eq_zero)  # Treat fmin as commutative
       *        | fmin(eq_zero, eq_zero)
       *        ;
       *
       * All other cases are 'unknown'.
       */
      static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
         /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
         /* unknown */ { _______, lt_zero, le_zero, _______, _______, _______, _______ },
         /* lt_zero */ { lt_zero, lt_zero, lt_zero, lt_zero, lt_zero, lt_zero, lt_zero },
         /* le_zero */ { le_zero, lt_zero, le_zero, le_zero, le_zero, le_zero, le_zero },
         /* gt_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
         /* ge_zero */ { _______, lt_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
         /* ne_zero */ { _______, lt_zero, le_zero, ne_zero, _______, ne_zero, _______ },
         /* eq_zero */ { _______, lt_zero, le_zero, eq_zero, eq_zero, _______, eq_zero }
      };

      /* Treat fmin as commutative. */
      ASSERT_TABLE_IS_COMMUTATIVE(table);
      ASSERT_TABLE_IS_DIAGONAL(table);
      ASSERT_UNION_OF_OTHERS_MATCHES_UNKNOWN_2_SOURCE(table);

      r.range = table[left.range][right.range];
      break;
   }

   case nir_op_fmul: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range right =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));

      r.is_integral = left.is_integral && right.is_integral;

      /* x * x => ge_zero */
      if (left.range != eq_zero && nir_alu_srcs_equal(alu, alu, 0, 1)) {
         /* Even if x > 0, the result of x*x can be zero when x is, for
          * example, a subnormal number.
          */
         r.range = ge_zero;
      } else if (left.range != eq_zero && nir_alu_srcs_negative_equal(alu, alu, 0, 1)) {
         /* -x * x => le_zero. */
         r.range = le_zero;
      } else
         r.range = fmul_table[left.range][right.range];

      break;
   }

   case nir_op_frcp:
      r = (struct ssa_result_range){
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0)).range,
         false
      };
      break;

   case nir_op_mov:
      r = analyze_expression(alu, 0, ht, use_type);
      break;

   case nir_op_fneg:
      r = analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      r.range = fneg_table[r.range];
      break;

   case nir_op_fsat:
      r = analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      switch (r.range) {
      case le_zero:
      case lt_zero:
         r.range = eq_zero;
         r.is_integral = true;
         break;

      case eq_zero:
         assert(r.is_integral);
      case gt_zero:
      case ge_zero:
         /* The fsat doesn't add any information in these cases. */
         break;

      case ne_zero:
      case unknown:
         /* Since the result must be in [0, 1], the value must be >= 0. */
         r.range = ge_zero;
         break;
      }
      break;

   case nir_op_fsign:
      r = (struct ssa_result_range){
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0)).range,
         true
      };
      break;

   case nir_op_fsqrt:
   case nir_op_frsq:
      r = (struct ssa_result_range){ge_zero, false};
      break;

   case nir_op_ffloor: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      r.is_integral = true;

      if (left.is_integral || left.range == le_zero || left.range == lt_zero)
         r.range = left.range;
      else if (left.range == ge_zero || left.range == gt_zero)
         r.range = ge_zero;
      else if (left.range == ne_zero)
         r.range = unknown;

      break;
   }

   case nir_op_fceil: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      r.is_integral = true;

      if (left.is_integral || left.range == ge_zero || left.range == gt_zero)
         r.range = left.range;
      else if (left.range == le_zero || left.range == lt_zero)
         r.range = le_zero;
      else if (left.range == ne_zero)
         r.range = unknown;

      break;
   }

   case nir_op_ftrunc: {
      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));

      r.is_integral = true;

      if (left.is_integral)
         r.range = left.range;
      else if (left.range == ge_zero || left.range == gt_zero)
         r.range = ge_zero;
      else if (left.range == le_zero || left.range == lt_zero)
         r.range = le_zero;
      else if (left.range == ne_zero)
         r.range = unknown;

      break;
   }

   case nir_op_flt:
   case nir_op_fge:
   case nir_op_feq:
   case nir_op_fne:
   case nir_op_ilt:
   case nir_op_ige:
   case nir_op_ieq:
   case nir_op_ine:
   case nir_op_ult:
   case nir_op_uge:
      /* Boolean results are 0 or -1. */
      r = (struct ssa_result_range){le_zero, false};
      break;

   case nir_op_fpow: {
      /* Due to flush-to-zero semanatics of floating-point numbers with very
       * small mangnitudes, we can never really be sure a result will be
       * non-zero.
       *
       * NIR uses pow() and powf() to constant evaluate nir_op_fpow.  The man
       * page for that function says:
       *
       *    If y is 0, the result is 1.0 (even if x is a NaN).
       *
       * gt_zero: pow(*, eq_zero)
       *        | pow(eq_zero, lt_zero)   # 0^-y = +inf
       *        | pow(eq_zero, le_zero)   # 0^-y = +inf or 0^0 = 1.0
       *        ;
       *
       * eq_zero: pow(eq_zero, gt_zero)
       *        ;
       *
       * ge_zero: pow(gt_zero, gt_zero)
       *        | pow(gt_zero, ge_zero)
       *        | pow(gt_zero, lt_zero)
       *        | pow(gt_zero, le_zero)
       *        | pow(gt_zero, ne_zero)
       *        | pow(gt_zero, unknown)
       *        | pow(ge_zero, gt_zero)
       *        | pow(ge_zero, ge_zero)
       *        | pow(ge_zero, lt_zero)
       *        | pow(ge_zero, le_zero)
       *        | pow(ge_zero, ne_zero)
       *        | pow(ge_zero, unknown)
       *        | pow(eq_zero, ge_zero)  # 0^0 = 1.0 or 0^+y = 0.0
       *        | pow(eq_zero, ne_zero)  # 0^-y = +inf or 0^+y = 0.0
       *        | pow(eq_zero, unknown)  # union of all other y cases
       *        ;
       *
       * All other cases are unknown.
       *
       * We could do better if the right operand is a constant, integral
       * value.
       */
      static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
         /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
         /* unknown */ { _______, _______, _______, _______, _______, _______, gt_zero },
         /* lt_zero */ { _______, _______, _______, _______, _______, _______, gt_zero },
         /* le_zero */ { _______, _______, _______, _______, _______, _______, gt_zero },
         /* gt_zero */ { ge_zero, ge_zero, ge_zero, ge_zero, ge_zero, ge_zero, gt_zero },
         /* ge_zero */ { ge_zero, ge_zero, ge_zero, ge_zero, ge_zero, ge_zero, gt_zero },
         /* ne_zero */ { _______, _______, _______, _______, _______, _______, gt_zero },
         /* eq_zero */ { ge_zero, gt_zero, gt_zero, eq_zero, ge_zero, ge_zero, gt_zero },
      };

      const struct ssa_result_range left =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range right =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));

      ASSERT_UNION_OF_DISJOINT_MATCHES_UNKNOWN_2_SOURCE(table);
      ASSERT_UNION_OF_EQ_AND_STRICT_INEQ_MATCHES_NONSTRICT_2_SOURCE(table);

      r.is_integral = left.is_integral && right.is_integral &&
                      is_not_negative(right.range);
      r.range = table[left.range][right.range];
      break;
   }

   case nir_op_ffma: {
      const struct ssa_result_range first =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range second =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));
      const struct ssa_result_range third =
         analyze_expression(alu, 2, ht, nir_alu_src_type(alu, 2));

      r.is_integral = first.is_integral && second.is_integral &&
                      third.is_integral;

      enum ssa_ranges fmul_range;

      if (first.range != eq_zero && nir_alu_srcs_equal(alu, alu, 0, 1)) {
         /* See handling of nir_op_fmul for explanation of why ge_zero is the
          * range.
          */
         fmul_range = ge_zero;
      } else if (first.range != eq_zero && nir_alu_srcs_negative_equal(alu, alu, 0, 1)) {
         /* -x * x => le_zero */
         fmul_range = le_zero;
      } else
         fmul_range = fmul_table[first.range][second.range];

      r.range = fadd_table[fmul_range][third.range];
      break;
   }

   case nir_op_flrp: {
      const struct ssa_result_range first =
         analyze_expression(alu, 0, ht, nir_alu_src_type(alu, 0));
      const struct ssa_result_range second =
         analyze_expression(alu, 1, ht, nir_alu_src_type(alu, 1));
      const struct ssa_result_range third =
         analyze_expression(alu, 2, ht, nir_alu_src_type(alu, 2));

      r.is_integral = first.is_integral && second.is_integral &&
                      third.is_integral;

      /* Decompose the flrp to first + third * (second + -first) */
      const enum ssa_ranges inner_fadd_range =
         fadd_table[second.range][fneg_table[first.range]];

      const enum ssa_ranges fmul_range =
         fmul_table[third.range][inner_fadd_range];

      r.range = fadd_table[first.range][fmul_range];
      break;
   }

   default:
      r = (struct ssa_result_range){unknown, false};
      break;
   }

   if (r.range == eq_zero)
      r.is_integral = true;

   _mesa_hash_table_insert(ht, pack_key(alu, use_type), pack_data(r));
   return r;
}

#undef _______

struct ssa_result_range
nir_analyze_range(struct hash_table *range_ht,
                  const nir_alu_instr *instr, unsigned src)
{
   return analyze_expression(instr, src, range_ht,
                             nir_alu_src_type(instr, src));
}