Halide
Associativity.h
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1 #ifndef HALIDE_ASSOCIATIVITY_H
2 #define HALIDE_ASSOCIATIVITY_H
3 
4 /** \file
5  *
6  * Methods for extracting an associative operator from a Func's update definition
7  * if there is any and computing the identity of the associative operator.
8  */
9 #include <string>
10 #include <vector>
11 
12 #include "AssociativeOpsTable.h"
13 #include "Expr.h"
14 
15 namespace Halide {
16 namespace Internal {
17 
18 /**
19  * Represent the equivalent associative op of an update definition.
20  * For example, the following associative Expr, min(f(x), g(r.x) + 2),
21  * where f(x) is the self-recurrence term, is represented as:
22  \code
23  AssociativeOp assoc(
24  AssociativePattern(min(x, y), +inf, true),
25  {Replacement("x", f(x))},
26  {Replacement("y", g(r.x) + 2)},
27  true
28  );
29  \endcode
30  *
31  * 'pattern' contains the list of equivalent binary/unary operators (+ identities)
32  * for each Tuple element in the update definition. 'pattern' also contains
33  * a boolean that indicates if the op is also commutative. 'xs' and 'ys'
34  * contain the corresponding definition of each variable in the list of
35  * binary operators.
36  *
37  * For unary operator, 'xs' is not set, i.e. it will be a pair of empty string
38  * and undefined Expr: {"", Expr()}. 'pattern' will only contain the 'y' term in
39  * this case. For example, min(g(r.x), 4), will be represented as:
40  \code
41  AssociativeOp assoc(
42  AssociativePattern(y, 0, false),
43  {Replacement("", Expr())},
44  {Replacement("y", min(g(r.x), 4))},
45  true
46  );
47  \endcode
48  *
49  * Self-assignment, f(x) = f(x), will be represented as:
50  \code
51  AssociativeOp assoc(
52  AssociativePattern(x, 0, true),
53  {Replacement("x", f(x))},
54  {Replacement("", Expr())},
55  true
56  );
57  \endcode
58  * For both unary operator and self-assignment cases, the identity does not
59  * matter. It can be anything.
60  */
61 struct AssociativeOp {
62  struct Replacement {
63  /** Variable name that is used to replace the expr in 'op'. */
64  std::string var;
66 
67  Replacement() = default;
68  Replacement(const std::string &var, Expr expr)
69  : var(var), expr(std::move(expr)) {
70  }
71 
72  bool operator==(const Replacement &other) const {
73  return (var == other.var) && equal(expr, other.expr);
74  }
75  bool operator!=(const Replacement &other) const {
76  return !(*this == other);
77  }
78  };
79 
80  /** List of pairs of binary associative op and its identity. */
82  std::vector<Replacement> xs;
83  std::vector<Replacement> ys;
84  bool is_associative = false;
85 
86  AssociativeOp() = default;
88  : pattern(size), xs(size), ys(size) {
89  }
90  AssociativeOp(const AssociativePattern &p, const std::vector<Replacement> &xs,
91  const std::vector<Replacement> &ys, bool is_associative)
93  }
94 
95  bool associative() const {
96  return is_associative;
97  }
98  bool commutative() const {
99  return pattern.is_commutative;
100  }
101  size_t size() const {
102  return pattern.size();
103  }
104 };
105 
106 /**
107  * Given an update definition of a Func 'f', determine its equivalent
108  * associative binary/unary operator if there is any. 'is_associative'
109  * indicates if the operation was successfuly proven as associative.
110  */
111 AssociativeOp prove_associativity(
112  const std::string &f, std::vector<Expr> args, std::vector<Expr> exprs);
113 
114 void associativity_test();
115 
116 } // namespace Internal
117 } // namespace Halide
118 
119 #endif
Halide::Internal::associativity_test
void associativity_test()
Halide::Internal::AssociativeOp::Replacement::expr
Expr expr
Definition: Associativity.h:65
Halide::Internal::AssociativeOp::AssociativeOp
AssociativeOp(const AssociativePattern &p, const std::vector< Replacement > &xs, const std::vector< Replacement > &ys, bool is_associative)
Definition: Associativity.h:90
Halide::Internal::AssociativeOp::commutative
bool commutative() const
Definition: Associativity.h:98
Halide::Internal::AssociativeOp
Represent the equivalent associative op of an update definition.
Definition: Associativity.h:61
Halide::Internal::AssociativeOp::size
size_t size() const
Definition: Associativity.h:101
Halide::Internal::AssociativeOp::AssociativeOp
AssociativeOp()=default
Halide::Internal::AssociativeOp::is_associative
bool is_associative
Definition: Associativity.h:84
Halide
This file defines the class FunctionDAG, which is our representation of a Halide pipeline,...
Definition: AbstractGenerator.h:19
Halide::LinkageType::Internal
@ Internal
Not visible externally, similar to 'static' linkage in C.
Halide::Internal::prove_associativity
AssociativeOp prove_associativity(const std::string &f, std::vector< Expr > args, std::vector< Expr > exprs)
Given an update definition of a Func 'f', determine its equivalent associative binary/unary operator ...
Halide::Internal::AssociativeOp::Replacement::var
std::string var
Variable name that is used to replace the expr in 'op'.
Definition: Associativity.h:64
Halide::Internal::AssociativeOp::Replacement::operator!=
bool operator!=(const Replacement &other) const
Definition: Associativity.h:75
Halide::Internal::AssociativeOp::Replacement::Replacement
Replacement(const std::string &var, Expr expr)
Definition: Associativity.h:68
Expr.h
Halide::Internal::equal
bool equal(const RDom &bounds0, const RDom &bounds1)
Return true if bounds0 and bounds1 represent the same bounds.
Halide::Internal::AssociativePattern::size
size_t size() const
Definition: AssociativeOpsTable.h:64
Halide::Internal::AssociativeOp::ys
std::vector< Replacement > ys
Definition: Associativity.h:83
Halide::Internal::AssociativeOp::associative
bool associative() const
Definition: Associativity.h:95
Halide::Internal::AssociativePattern::is_commutative
bool is_commutative
Indicate if the associative op is also commutative.
Definition: AssociativeOpsTable.h:37
Halide::Internal::AssociativeOp::Replacement::Replacement
Replacement()=default
AssociativeOpsTable.h
Halide::Internal::AssociativeOp::Replacement
Definition: Associativity.h:62
Halide::Internal::AssociativePattern
Represent an associative op with its identity.
Definition: AssociativeOpsTable.h:31
Halide::Expr
A fragment of Halide syntax.
Definition: Expr.h:257
Halide::Internal::AssociativeOp::Replacement::operator==
bool operator==(const Replacement &other) const
Definition: Associativity.h:72
Halide::Internal::AssociativeOp::xs
std::vector< Replacement > xs
Definition: Associativity.h:82
Halide::Internal::AssociativeOp::AssociativeOp
AssociativeOp(size_t size)
Definition: Associativity.h:87
Halide::Internal::AssociativeOp::pattern
AssociativePattern pattern
List of pairs of binary associative op and its identity.
Definition: Associativity.h:81