src/compiler/nir/nir_range_analysis.c

   1 /*
   2  * Copyright © 2018 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 #include <math.h>
  24 #include <float.h>
  25 #include "nir.h"
  26 #include "nir_range_analysis.h"
  27 #include "util/hash_table.h"
  28
  29 /**
  30  * Analyzes a sequence of operations to determine some aspects of the range of
  31  * the result.
  32  */
  33
  34 static bool
  35 is_not_zero(enum ssa_ranges r)
  36 {
  37    return r == gt_zero || r == lt_zero || r == ne_zero;
  38 }
  39
  40 static void *
  41 pack_data(const struct ssa_result_range r)
  42 {
  43    return (void *)(uintptr_t)(r.range | r.is_integral << 8);
  44 }
  45
  46 static struct ssa_result_range
  47 unpack_data(const void *p)
  48 {
  49    const uintptr_t v = (uintptr_t) p;
  50
  51    return (struct ssa_result_range){v & 0xff, (v & 0x0ff00) != 0};
  52 }
  53
  54 static struct ssa_result_range
  55 analyze_constant(const struct nir_alu_instr *instr, unsigned src)
  56 {
  57    uint8_t swizzle[4] = { 0, 1, 2, 3 };
  58
  59    /* If the source is an explicitly sized source, then we need to reset
  60     * both the number of components and the swizzle.
  61     */
  62    const unsigned num_components = nir_ssa_alu_instr_src_components(instr, src);
  63
  64    for (unsigned i = 0; i < num_components; ++i)
  65       swizzle[i] = instr->src[src].swizzle[i];
  66
  67    const nir_load_const_instr *const load =
  68       nir_instr_as_load_const(instr->src[src].src.ssa->parent_instr);
  69
  70    struct ssa_result_range r = { unknown, false };
  71
  72    switch (nir_op_infos[instr->op].input_types[src]) {
  73    case nir_type_float: {
  74       double min_value = DBL_MAX;
  75       double max_value = -DBL_MAX;
  76       bool any_zero = false;
  77       bool all_zero = true;
  78
  79       r.is_integral = true;
  80
  81       for (unsigned i = 0; i < num_components; ++i) {
  82          const double v = nir_const_value_as_float(load->value[swizzle[i]],
  83                                                    load->def.bit_size);
  84
  85          if (floor(v) != v)
  86             r.is_integral = false;
  87
  88          any_zero = any_zero || (v == 0.0);
  89          all_zero = all_zero && (v == 0.0);
  90          min_value = MIN2(min_value, v);
  91          max_value = MAX2(max_value, v);
  92       }
  93
  94       assert(any_zero >= all_zero);
  95       assert(isnan(max_value) || max_value >= min_value);
  96
  97       if (all_zero)
  98          r.range = eq_zero;
  99       else if (min_value > 0.0)
 100          r.range = gt_zero;
 101       else if (min_value == 0.0)
 102          r.range = ge_zero;
 103       else if (max_value < 0.0)
 104          r.range = lt_zero;
 105       else if (max_value == 0.0)
 106          r.range = le_zero;
 107       else if (!any_zero)
 108          r.range = ne_zero;
 109       else
 110          r.range = unknown;
 111
 112       return r;
 113    }
 114
 115    case nir_type_int:
 116    case nir_type_bool: {
 117       int64_t min_value = INT_MAX;
 118       int64_t max_value = INT_MIN;
 119       bool any_zero = false;
 120       bool all_zero = true;
 121
 122       for (unsigned i = 0; i < num_components; ++i) {
 123          const int64_t v = nir_const_value_as_int(load->value[swizzle[i]],
 124                                                   load->def.bit_size);
 125
 126          any_zero = any_zero || (v == 0);
 127          all_zero = all_zero && (v == 0);
 128          min_value = MIN2(min_value, v);
 129          max_value = MAX2(max_value, v);
 130       }
 131
 132       assert(any_zero >= all_zero);
 133       assert(max_value >= min_value);
 134
 135       if (all_zero)
 136          r.range = eq_zero;
 137       else if (min_value > 0)
 138          r.range = gt_zero;
 139       else if (min_value == 0)
 140          r.range = ge_zero;
 141       else if (max_value < 0)
 142          r.range = lt_zero;
 143       else if (max_value == 0)
 144          r.range = le_zero;
 145       else if (!any_zero)
 146          r.range = ne_zero;
 147       else
 148          r.range = unknown;
 149
 150       return r;
 151    }
 152
 153    case nir_type_uint: {
 154       bool any_zero = false;
 155       bool all_zero = true;
 156
 157       for (unsigned i = 0; i < num_components; ++i) {
 158          const uint64_t v = nir_const_value_as_uint(load->value[swizzle[i]],
 159                                                     load->def.bit_size);
 160
 161          any_zero = any_zero || (v == 0);
 162          all_zero = all_zero && (v == 0);
 163       }
 164
 165       assert(any_zero >= all_zero);
 166
 167       if (all_zero)
 168          r.range = eq_zero;
 169       else if (any_zero)
 170          r.range = ge_zero;
 171       else
 172          r.range = gt_zero;
 173
 174       return r;
 175    }
 176
 177    default:
 178       unreachable("Invalid alu source type");
 179    }
 180 }
 181
 182 #ifndef NDEBUG
 183 #define ASSERT_TABLE_IS_COMMUTATIVE(t)                        \
 184    do {                                                       \
 185       for (unsigned r = 0; r < ARRAY_SIZE(t); r++) {          \
 186          for (unsigned c = 0; c < ARRAY_SIZE(t[0]); c++)      \
 187             assert(t[r][c] == t[c][r]);                       \
 188       }                                                       \
 189    } while (false)
 190
 191 #define ASSERT_TABLE_IS_DIAGONAL(t)                           \
 192    do {                                                       \
 193       for (unsigned r = 0; r < ARRAY_SIZE(t); r++)            \
 194          assert(t[r][r] == r);                                \
 195    } while (false)
 196 #else
 197 #define ASSERT_TABLE_IS_COMMUTATIVE(t)
 198 #define ASSERT_TABLE_IS_DIAGONAL(t)
 199 #endif
 200
 201 /**
 202  * Short-hand name for use in the tables in analyze_expression.  If this name
 203  * becomes a problem on some compiler, we can change it to _.
 204  */
 205 #define _______ unknown
 206
 207 /**
 208  * Analyze an expression to determine the range of its result
 209  *
 210  * The end result of this analysis is a token that communicates something
 211  * about the range of values.  There's an implicit grammar that produces
 212  * tokens from sequences of literal values, other tokens, and operations.
 213  * This function implements this grammar as a recursive-descent parser.  Some
 214  * (but not all) of the grammar is listed in-line in the function.
 215  */
 216 static struct ssa_result_range
 217 analyze_expression(const nir_alu_instr *instr, unsigned src,
 218                    struct hash_table *ht)
 219 {
 220    if (!instr->src[src].src.is_ssa)
 221       return (struct ssa_result_range){unknown, false};
 222
 223    if (nir_src_is_const(instr->src[src].src))
 224       return analyze_constant(instr, src);
 225
 226    if (instr->src[src].src.ssa->parent_instr->type != nir_instr_type_alu)
 227       return (struct ssa_result_range){unknown, false};
 228
 229    const struct nir_alu_instr *const alu =
 230        nir_instr_as_alu(instr->src[src].src.ssa->parent_instr);
 231
 232    struct hash_entry *he = _mesa_hash_table_search(ht, alu);
 233    if (he != NULL)
 234       return unpack_data(he->data);
 235
 236    struct ssa_result_range r = {unknown, false};
 237
 238    /* ge_zero: ge_zero + ge_zero
 239     *
 240     * gt_zero: gt_zero + eq_zero
 241     *        | gt_zero + ge_zero
 242     *        | eq_zero + gt_zero   # Addition is commutative
 243     *        | ge_zero + gt_zero   # Addition is commutative
 244     *        | gt_zero + gt_zero
 245     *        ;
 246     *
 247     * le_zero: le_zero + le_zero
 248     *
 249     * lt_zero: lt_zero + eq_zero
 250     *        | lt_zero + le_zero
 251     *        | eq_zero + lt_zero   # Addition is commutative
 252     *        | le_zero + lt_zero   # Addition is commutative
 253     *        | lt_zero + lt_zero
 254     *        ;
 255     *
 256     * eq_zero: eq_zero + eq_zero
 257     *
 258     * All other cases are 'unknown'.
 259     */
 260    static const enum ssa_ranges fadd_table[last_range + 1][last_range + 1] = {
 261       /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
 262       /* unknown */ { _______, _______, _______, _______, _______, _______, _______ },
 263       /* lt_zero */ { _______, lt_zero, lt_zero, _______, _______, _______, lt_zero },
 264       /* le_zero */ { _______, lt_zero, le_zero, _______, _______, _______, le_zero },
 265       /* gt_zero */ { _______, _______, _______, gt_zero, gt_zero, _______, gt_zero },
 266       /* ge_zero */ { _______, _______, _______, gt_zero, ge_zero, _______, ge_zero },
 267       /* ne_zero */ { _______, _______, _______, _______, _______, ne_zero, ne_zero },
 268       /* eq_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
 269    };
 270
 271    ASSERT_TABLE_IS_COMMUTATIVE(fadd_table);
 272    ASSERT_TABLE_IS_DIAGONAL(fadd_table);
 273
 274    /* ge_zero: ge_zero * ge_zero
 275     *        | ge_zero * gt_zero
 276     *        | ge_zero * eq_zero
 277     *        | le_zero * lt_zero
 278     *        | lt_zero * le_zero  # Multiplication is commutative
 279     *        | le_zero * le_zero
 280     *        | gt_zero * ge_zero  # Multiplication is commutative
 281     *        | eq_zero * ge_zero  # Multiplication is commutative
 282     *        | a * a              # Left source == right source
 283     *        ;
 284     *
 285     * gt_zero: gt_zero * gt_zero
 286     *        | lt_zero * lt_zero
 287     *        ;
 288     *
 289     * le_zero: ge_zero * le_zero
 290     *        | ge_zero * lt_zero
 291     *        | lt_zero * ge_zero  # Multiplication is commutative
 292     *        | le_zero * ge_zero  # Multiplication is commutative
 293     *        | le_zero * gt_zero
 294     *        ;
 295     *
 296     * lt_zero: lt_zero * gt_zero
 297     *        | gt_zero * lt_zero  # Multiplication is commutative
 298     *        ;
 299     *
 300     * ne_zero: ne_zero * gt_zero
 301     *        | ne_zero * lt_zero
 302     *        | gt_zero * ne_zero  # Multiplication is commutative
 303     *        | lt_zero * ne_zero  # Multiplication is commutative
 304     *        | ne_zero * ne_zero
 305     *        ;
 306     *
 307     * eq_zero: eq_zero * <any>
 308     *          <any> * eq_zero    # Multiplication is commutative
 309     *
 310     * All other cases are 'unknown'.
 311     */
 312    static const enum ssa_ranges fmul_table[last_range + 1][last_range + 1] = {
 313       /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
 314       /* unknown */ { _______, _______, _______, _______, _______, _______, eq_zero },
 315       /* lt_zero */ { _______, gt_zero, ge_zero, lt_zero, le_zero, ne_zero, eq_zero },
 316       /* le_zero */ { _______, ge_zero, ge_zero, le_zero, le_zero, _______, eq_zero },
 317       /* gt_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
 318       /* ge_zero */ { _______, le_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
 319       /* ne_zero */ { _______, ne_zero, _______, ne_zero, _______, ne_zero, eq_zero },
 320       /* eq_zero */ { eq_zero, eq_zero, eq_zero, eq_zero, eq_zero, eq_zero, eq_zero }
 321    };
 322
 323    ASSERT_TABLE_IS_COMMUTATIVE(fmul_table);
 324
 325    static const enum ssa_ranges fneg_table[last_range + 1] = {
 326    /* unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
 327       _______, gt_zero, ge_zero, lt_zero, le_zero, ne_zero, eq_zero
 328    };
 329
 330
 331    switch (alu->op) {
 332    case nir_op_b2f32:
 333    case nir_op_b2i32:
 334       r = (struct ssa_result_range){ge_zero, alu->op == nir_op_b2f32};
 335       break;
 336
 337    case nir_op_bcsel: {
 338       const struct ssa_result_range left = analyze_expression(alu, 1, ht);
 339       const struct ssa_result_range right = analyze_expression(alu, 2, ht);
 340
 341       /* If either source is a constant load that is not zero, punt.  The type
 342        * will always be uint regardless of the actual type.  We can't even
 343        * decide if the value is non-zero because -0.0 is 0x80000000, and that
 344        * will (possibly incorrectly) be considered non-zero.
 345        */
 346       /* FINISHME: We could do better, but it would require having the expected
 347        * FINISHME: type passed in.
 348        */
 349       if ((nir_src_is_const(alu->src[1].src) && left.range != eq_zero) ||
 350           (nir_src_is_const(alu->src[2].src) && right.range != eq_zero)) {
 351          return (struct ssa_result_range){unknown, false};
 352       }
 353
 354       r.is_integral = left.is_integral && right.is_integral;
 355
 356       /* le_zero: bcsel(<any>, le_zero, lt_zero)
 357        *        | bcsel(<any>, eq_zero, lt_zero)
 358        *        | bcsel(<any>, le_zero, eq_zero)
 359        *        | bcsel(<any>, lt_zero, le_zero)
 360        *        | bcsel(<any>, lt_zero, eq_zero)
 361        *        | bcsel(<any>, eq_zero, le_zero)
 362        *        | bcsel(<any>, le_zero, le_zero)
 363        *        ;
 364        *
 365        * lt_zero: bcsel(<any>, lt_zero, lt_zero)
 366        *        ;
 367        *
 368        * ge_zero: bcsel(<any>, ge_zero, ge_zero)
 369        *        | bcsel(<any>, ge_zero, gt_zero)
 370        *        | bcsel(<any>, ge_zero, eq_zero)
 371        *        | bcsel(<any>, gt_zero, ge_zero)
 372        *        | bcsel(<any>, eq_zero, ge_zero)
 373        *        ;
 374        *
 375        * gt_zero: bcsel(<any>, gt_zero, gt_zero)
 376        *        ;
 377        *
 378        * ne_zero: bcsel(<any>, ne_zero, gt_zero)
 379        *        | bcsel(<any>, ne_zero, lt_zero)
 380        *        | bcsel(<any>, gt_zero, lt_zero)
 381        *        | bcsel(<any>, gt_zero, ne_zero)
 382        *        | bcsel(<any>, lt_zero, ne_zero)
 383        *        | bcsel(<any>, lt_zero, gt_zero)
 384        *        | bcsel(<any>, ne_zero, ne_zero)
 385        *        ;
 386        *
 387        * eq_zero: bcsel(<any>, eq_zero, eq_zero)
 388        *        ;
 389        *
 390        * All other cases are 'unknown'.
 391        *
 392        * The ranges could be tightened if the range of the first source is
 393        * known.  However, opt_algebraic will (eventually) elminiate the bcsel
 394        * if the condition is known.
 395        */
 396       static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
 397          /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
 398          /* unknown */ { _______, _______, _______, _______, _______, _______, _______ },
 399          /* lt_zero */ { _______, lt_zero, le_zero, ne_zero, _______, ne_zero, le_zero },
 400          /* le_zero */ { _______, le_zero, le_zero, _______, _______, _______, le_zero },
 401          /* gt_zero */ { _______, ne_zero, _______, gt_zero, ge_zero, ne_zero, ge_zero },
 402          /* ge_zero */ { _______, _______, _______, ge_zero, ge_zero, _______, ge_zero },
 403          /* ne_zero */ { _______, ne_zero, _______, ne_zero, _______, ne_zero, _______ },
 404          /* eq_zero */ { _______, le_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
 405       };
 406
 407       ASSERT_TABLE_IS_COMMUTATIVE(table);
 408       ASSERT_TABLE_IS_DIAGONAL(table);
 409
 410       r.range = table[left.range][right.range];
 411       break;
 412    }
 413
 414    case nir_op_i2f32:
 415    case nir_op_u2f32:
 416       r = analyze_expression(alu, 0, ht);
 417
 418       r.is_integral = true;
 419
 420       if (r.range == unknown && alu->op == nir_op_u2f32)
 421          r.range = ge_zero;
 422
 423       break;
 424
 425    case nir_op_fabs:
 426       r = analyze_expression(alu, 0, ht);
 427
 428       switch (r.range) {
 429       case unknown:
 430       case le_zero:
 431       case ge_zero:
 432          r.range = ge_zero;
 433          break;
 434
 435       case lt_zero:
 436       case gt_zero:
 437       case ne_zero:
 438          r.range = gt_zero;
 439          break;
 440
 441       case eq_zero:
 442          break;
 443       }
 444
 445       break;
 446
 447    case nir_op_fadd: {
 448       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 449       const struct ssa_result_range right = analyze_expression(alu, 1, ht);
 450
 451       r.is_integral = left.is_integral && right.is_integral;
 452       r.range = fadd_table[left.range][right.range];
 453       break;
 454    }
 455
 456    case nir_op_fexp2:
 457       r = (struct ssa_result_range){gt_zero, analyze_expression(alu, 0, ht).is_integral};
 458       break;
 459
 460    case nir_op_fmax: {
 461       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 462       const struct ssa_result_range right = analyze_expression(alu, 1, ht);
 463
 464       r.is_integral = left.is_integral && right.is_integral;
 465
 466       /* gt_zero: fmax(gt_zero, *)
 467        *        | fmax(*, gt_zero)        # Treat fmax as commutative
 468        *        ;
 469        *
 470        * ge_zero: fmax(ge_zero, ne_zero)
 471        *        | fmax(ge_zero, lt_zero)
 472        *        | fmax(ge_zero, le_zero)
 473        *        | fmax(ge_zero, eq_zero)
 474        *        | fmax(ne_zero, ge_zero)  # Treat fmax as commutative
 475        *        | fmax(lt_zero, ge_zero)  # Treat fmax as commutative
 476        *        | fmax(le_zero, ge_zero)  # Treat fmax as commutative
 477        *        | fmax(eq_zero, ge_zero)  # Treat fmax as commutative
 478        *        | fmax(ge_zero, ge_zero)
 479        *        ;
 480        *
 481        * le_zero: fmax(le_zero, lt_zero)
 482        *        | fmax(lt_zero, le_zero)  # Treat fmax as commutative
 483        *        | fmax(le_zero, le_zero)
 484        *        ;
 485        *
 486        * lt_zero: fmax(lt_zero, lt_zero)
 487        *        ;
 488        *
 489        * ne_zero: fmax(ne_zero, lt_zero)
 490        *        | fmax(lt_zero, ne_zero)  # Treat fmax as commutative
 491        *        | fmax(ne_zero, ne_zero)
 492        *        ;
 493        *
 494        * eq_zero: fmax(eq_zero, le_zero)
 495        *        | fmax(eq_zero, lt_zero)
 496        *        | fmax(le_zero, eq_zero)  # Treat fmax as commutative
 497        *        | fmax(lt_zero, eq_zero)  # Treat fmax as commutative
 498        *        | fmax(eq_zero, eq_zero)
 499        *        ;
 500        *
 501        * All other cases are 'unknown'.
 502        */
 503       static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
 504          /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
 505          /* unknown */ { _______, _______, _______, gt_zero, ge_zero, _______, _______ },
 506          /* lt_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
 507          /* le_zero */ { _______, le_zero, le_zero, gt_zero, ge_zero, _______, eq_zero },
 508          /* gt_zero */ { gt_zero, gt_zero, gt_zero, gt_zero, gt_zero, gt_zero, gt_zero },
 509          /* ge_zero */ { ge_zero, ge_zero, ge_zero, gt_zero, ge_zero, ge_zero, ge_zero },
 510          /* ne_zero */ { _______, ne_zero, _______, gt_zero, ge_zero, ne_zero, _______ },
 511          /* eq_zero */ { _______, eq_zero, eq_zero, gt_zero, ge_zero, _______, eq_zero }
 512       };
 513
 514       /* Treat fmax as commutative. */
 515       ASSERT_TABLE_IS_COMMUTATIVE(table);
 516       ASSERT_TABLE_IS_DIAGONAL(table);
 517
 518       r.range = table[left.range][right.range];
 519       break;
 520    }
 521
 522    case nir_op_fmin: {
 523       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 524       const struct ssa_result_range right = analyze_expression(alu, 1, ht);
 525
 526       r.is_integral = left.is_integral && right.is_integral;
 527
 528       /* lt_zero: fmin(lt_zero, *)
 529        *        | fmin(*, lt_zero)        # Treat fmin as commutative
 530        *        ;
 531        *
 532        * le_zero: fmin(le_zero, ne_zero)
 533        *        | fmin(le_zero, gt_zero)
 534        *        | fmin(le_zero, ge_zero)
 535        *        | fmin(le_zero, eq_zero)
 536        *        | fmin(ne_zero, le_zero)  # Treat fmin as commutative
 537        *        | fmin(gt_zero, le_zero)  # Treat fmin as commutative
 538        *        | fmin(ge_zero, le_zero)  # Treat fmin as commutative
 539        *        | fmin(eq_zero, le_zero)  # Treat fmin as commutative
 540        *        | fmin(le_zero, le_zero)
 541        *        ;
 542        *
 543        * ge_zero: fmin(ge_zero, gt_zero)
 544        *        | fmin(gt_zero, ge_zero)  # Treat fmin as commutative
 545        *        | fmin(ge_zero, ge_zero)
 546        *        ;
 547        *
 548        * gt_zero: fmin(gt_zero, gt_zero)
 549        *        ;
 550        *
 551        * ne_zero: fmin(ne_zero, gt_zero)
 552        *        | fmin(gt_zero, ne_zero)  # Treat fmin as commutative
 553        *        | fmin(ne_zero, ne_zero)
 554        *        ;
 555        *
 556        * eq_zero: fmin(eq_zero, ge_zero)
 557        *        | fmin(eq_zero, gt_zero)
 558        *        | fmin(ge_zero, eq_zero)  # Treat fmin as commutative
 559        *        | fmin(gt_zero, eq_zero)  # Treat fmin as commutative
 560        *        | fmin(eq_zero, eq_zero)
 561        *        ;
 562        *
 563        * All other cases are 'unknown'.
 564        */
 565       static const enum ssa_ranges table[last_range + 1][last_range + 1] = {
 566          /* left\right   unknown  lt_zero  le_zero  gt_zero  ge_zero  ne_zero  eq_zero */
 567          /* unknown */ { _______, lt_zero, le_zero, _______, _______, _______, _______ },
 568          /* lt_zero */ { lt_zero, lt_zero, lt_zero, lt_zero, lt_zero, lt_zero, lt_zero },
 569          /* le_zero */ { le_zero, lt_zero, le_zero, le_zero, le_zero, le_zero, le_zero },
 570          /* gt_zero */ { _______, lt_zero, le_zero, gt_zero, ge_zero, ne_zero, eq_zero },
 571          /* ge_zero */ { _______, lt_zero, le_zero, ge_zero, ge_zero, _______, eq_zero },
 572          /* ne_zero */ { _______, lt_zero, le_zero, ne_zero, _______, ne_zero, _______ },
 573          /* eq_zero */ { _______, lt_zero, le_zero, eq_zero, eq_zero, _______, eq_zero }
 574       };
 575
 576       /* Treat fmin as commutative. */
 577       ASSERT_TABLE_IS_COMMUTATIVE(table);
 578       ASSERT_TABLE_IS_DIAGONAL(table);
 579
 580       r.range = table[left.range][right.range];
 581       break;
 582    }
 583
 584    case nir_op_fmul: {
 585       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 586       const struct ssa_result_range right = analyze_expression(alu, 1, ht);
 587
 588       r.is_integral = left.is_integral && right.is_integral;
 589
 590       /* x * x => ge_zero */
 591       if (left.range != eq_zero && nir_alu_srcs_equal(alu, alu, 0, 1)) {
 592          /* x * x => ge_zero or gt_zero depending on the range of x. */
 593          r.range = is_not_zero(left.range) ? gt_zero : ge_zero;
 594       } else if (left.range != eq_zero && nir_alu_srcs_negative_equal(alu, alu, 0, 1)) {
 595          /* -x * x => le_zero or lt_zero depending on the range of x. */
 596          r.range = is_not_zero(left.range) ? lt_zero : le_zero;
 597       } else
 598          r.range = fmul_table[left.range][right.range];
 599
 600       break;
 601    }
 602
 603    case nir_op_frcp:
 604       r = (struct ssa_result_range){analyze_expression(alu, 0, ht).range, false};
 605       break;
 606
 607    case nir_op_mov:
 608       r = analyze_expression(alu, 0, ht);
 609       break;
 610
 611    case nir_op_fneg:
 612       r = analyze_expression(alu, 0, ht);
 613
 614       r.range = fneg_table[r.range];
 615       break;
 616
 617    case nir_op_fsat:
 618       r = analyze_expression(alu, 0, ht);
 619
 620       switch (r.range) {
 621       case le_zero:
 622       case lt_zero:
 623          r.range = eq_zero;
 624          r.is_integral = true;
 625          break;
 626
 627       case eq_zero:
 628          assert(r.is_integral);
 629       case gt_zero:
 630       case ge_zero:
 631          /* The fsat doesn't add any information in these cases. */
 632          break;
 633
 634       case ne_zero:
 635       case unknown:
 636          /* Since the result must be in [0, 1], the value must be >= 0. */
 637          r.range = ge_zero;
 638          break;
 639       }
 640       break;
 641
 642    case nir_op_fsign:
 643       r = (struct ssa_result_range){analyze_expression(alu, 0, ht).range, true};
 644       break;
 645
 646    case nir_op_fsqrt:
 647    case nir_op_frsq:
 648       r = (struct ssa_result_range){ge_zero, false};
 649       break;
 650
 651    case nir_op_ffloor: {
 652       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 653
 654       r.is_integral = true;
 655
 656       if (left.is_integral || left.range == le_zero || left.range == lt_zero)
 657          r.range = left.range;
 658       else if (left.range == ge_zero || left.range == gt_zero)
 659          r.range = ge_zero;
 660       else if (left.range == ne_zero)
 661          r.range = unknown;
 662
 663       break;
 664    }
 665
 666    case nir_op_fceil: {
 667       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 668
 669       r.is_integral = true;
 670
 671       if (left.is_integral || left.range == ge_zero || left.range == gt_zero)
 672          r.range = left.range;
 673       else if (left.range == le_zero || left.range == lt_zero)
 674          r.range = le_zero;
 675       else if (left.range == ne_zero)
 676          r.range = unknown;
 677
 678       break;
 679    }
 680
 681    case nir_op_ftrunc: {
 682       const struct ssa_result_range left = analyze_expression(alu, 0, ht);
 683
 684       r.is_integral = true;
 685
 686       if (left.is_integral)
 687          r.range = left.range;
 688       else if (left.range == ge_zero || left.range == gt_zero)
 689          r.range = ge_zero;
 690       else if (left.range == le_zero || left.range == lt_zero)
 691          r.range = le_zero;
 692       else if (left.range == ne_zero)
 693          r.range = unknown;
 694
 695       break;
 696    }
 697
 698    case nir_op_flt:
 699    case nir_op_fge:
 700    case nir_op_feq:
 701    case nir_op_fne:
 702    case nir_op_ilt:
 703    case nir_op_ige:
 704    case nir_op_ieq:
 705    case nir_op_ine:
 706    case nir_op_ult:
 707    case nir_op_uge:
 708       /* Boolean results are 0 or -1. */
 709       r = (struct ssa_result_range){le_zero, false};
 710       break;
 711
 712    case nir_op_ffma: {
 713       const struct ssa_result_range first = analyze_expression(alu, 0, ht);
 714       const struct ssa_result_range second = analyze_expression(alu, 1, ht);
 715       const struct ssa_result_range third = analyze_expression(alu, 2, ht);
 716
 717       r.is_integral = first.is_integral && second.is_integral &&
 718                       third.is_integral;
 719
 720       enum ssa_ranges fmul_range;
 721
 722       if (first.range != eq_zero && nir_alu_srcs_equal(alu, alu, 0, 1)) {
 723          /* x * x => ge_zero or gt_zero depending on the range of x. */
 724          fmul_range = is_not_zero(first.range) ? gt_zero : ge_zero;
 725       } else if (first.range != eq_zero && nir_alu_srcs_negative_equal(alu, alu, 0, 1)) {
 726          /* -x * x => le_zero or lt_zero depending on the range of x. */
 727          fmul_range = is_not_zero(first.range) ? lt_zero : le_zero;
 728       } else
 729          fmul_range = fmul_table[first.range][second.range];
 730
 731       r.range = fadd_table[fmul_range][third.range];
 732       break;
 733    }
 734
 735    case nir_op_flrp: {
 736       const struct ssa_result_range first = analyze_expression(alu, 0, ht);
 737       const struct ssa_result_range second = analyze_expression(alu, 1, ht);
 738       const struct ssa_result_range third = analyze_expression(alu, 2, ht);
 739
 740       r.is_integral = first.is_integral && second.is_integral &&
 741                       third.is_integral;
 742
 743       /* Decompose the flrp to first + third * (second + -first) */
 744       const enum ssa_ranges inner_fadd_range =
 745          fadd_table[second.range][fneg_table[first.range]];
 746
 747       const enum ssa_ranges fmul_range =
 748          fmul_table[third.range][inner_fadd_range];
 749
 750       r.range = fadd_table[first.range][fmul_range];
 751       break;
 752    }
 753
 754    default:
 755       r = (struct ssa_result_range){unknown, false};
 756       break;
 757    }
 758
 759    if (r.range == eq_zero)
 760       r.is_integral = true;
 761
 762    _mesa_hash_table_insert(ht, alu, pack_data(r));
 763    return r;
 764 }
 765
 766 #undef _______
 767
 768 struct ssa_result_range
 769 nir_analyze_range(const nir_alu_instr *instr, unsigned src)
 770 {
 771    struct hash_table *ht = _mesa_pointer_hash_table_create(NULL);
 772
 773    const struct ssa_result_range r = analyze_expression(instr, src, ht);
 774
 775    _mesa_hash_table_destroy(ht, NULL);
 776
 777    return r;
 778 }