/* * 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 #include #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 * * * 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(, le_zero, lt_zero) * | bcsel(, eq_zero, lt_zero) * | bcsel(, le_zero, eq_zero) * | bcsel(, lt_zero, le_zero) * | bcsel(, lt_zero, eq_zero) * | bcsel(, eq_zero, le_zero) * | bcsel(, le_zero, le_zero) * ; * * lt_zero: bcsel(, lt_zero, lt_zero) * ; * * ge_zero: bcsel(, ge_zero, ge_zero) * | bcsel(, ge_zero, gt_zero) * | bcsel(, ge_zero, eq_zero) * | bcsel(, gt_zero, ge_zero) * | bcsel(, eq_zero, ge_zero) * ; * * gt_zero: bcsel(, gt_zero, gt_zero) * ; * * ne_zero: bcsel(, ne_zero, gt_zero) * | bcsel(, ne_zero, lt_zero) * | bcsel(, gt_zero, lt_zero) * | bcsel(, gt_zero, ne_zero) * | bcsel(, lt_zero, ne_zero) * | bcsel(, lt_zero, gt_zero) * | bcsel(, ne_zero, ne_zero) * ; * * eq_zero: bcsel(, 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)); }