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Some languages specifically targeted towards numerical computing such as Julia might have the concept of loop fusion built into it at a high level, where the compiler will notice adjacent elementwise operations and fuse them into a single loop. Currently, to achieve the same syntax in general purpose
95:
data dependencies that require an intermediate allocation to store the results). If loop fusion is able to remove redundant allocations, performance increases can be large. Otherwise, there is a more complex trade-off between data locality, instruction-level parallelism, and loop overhead (branching,
1442:
functions must pessimistically allocate arrays to store their results, since they do not know what context they will be called from. This issue can be avoided in C++ by using a different syntax that does not rely on the compiler to remove unnecessary temporary allocations (e.g., using functions and
91:. This is possible when there are no data dependencies between the bodies of the two loops (this is in stark contrast to the other main benefit of loop fusion described above, which only presents itself when there
1601:
36:
is broken into multiple loops over the same index range with each taking only a part of the original loop's body. The goal is to break down a large loop body into smaller ones to achieve better utilization of
80:
within each loop. One of the main benefits of loop fusion is that it allows temporary allocations to be avoided, which can lead to huge performance gains in numerical computing languages such as
87:
Other benefits of loop fusion are that it avoids the overhead of the loop control structures, and also that it allows the loop body to be parallelized by the processor by taking advantage of
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when doing elementwise operations on arrays (however, Julia's loop fusion is not technically a compiler optimization, but a syntactic guarantee of the language).
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11.1, this loop fusion and redundant allocation removal does not occur - even on the highest optimization level.
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All of these steps are individually possible. Even step four is possible despite the fact that functions like
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88:
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81:
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2016:
1940:
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incrementing, etc.) that may make loop fusion, loop fission, or neither, the preferable optimization.
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Remove the unused stores into the temporary arrays (can use a register or stack variable instead).
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1948:
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76:, two loops may actually perform better than one loop because, for example, there is increased
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29:
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The
Compiler Design Handbook: Optimizations and Machine Code Generation, Second Edition
1369:
However, the above example unnecessarily allocates a temporary array for the result of
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with a single one. Loop fusion does not always improve run-time speed. On some
2122:
77:
1235:// Print the result out - just to make sure the optimizer doesn't remove
986:// it would be unwieldy to define all possible overloaded math operations as
983:// Similarly, we can define an overload for the sin() function. In practice,
1517:
Optimizing
Compilers for Modern Architectures: A Dependence-based Approach
827:// Declare an overloaded addition operator as a free friend function (this
1810:
1727:
1422:
so that they can remove unused allocations from the code. However, as of
1414:
have global side effects, since some compilers hardcode symbols such as
1890:
830:// syntax defines operator+ as a free function that is a friend of this
1539:
548:// Factory method to produce an array over an integer range (the upper
1984:
1373:. A more efficient implementation would allocate a single array for
989:// friends inside the class like this, but this is just an example.
1676:
1651:
1626:
1381:
in a single loop. To optimize this, a C++ compiler would need to:
833:// class, despite it appearing as a member function declaration).
378:% Create an array of numbers from 0 to 999 (range is inclusive)
1169:// Here, we perform the same computation as the MATLAB example
1423:
414:
408:% Take the sine of x (element-wise) and add 4 to each element
488:// Internal constructor that produces an uninitialized array
1540:
Steven
Muchnick; Muchnick and Associates (15 August 1997).
1514:
1484:
1533:
551:// bound is exclusive, unlike MATLAB's ranges).
45:that can split a task into multiple tasks for each
1541:
1238:// everything (if it's smart enough to do so).
1478:
2120:
1652:"Compiler Explorer - C++ (x86-64 clang 12.0.0)"
1627:"Compiler Explorer - C++ (x86-64 clang 12.0.0)"
1897:Induction variable recognition and elimination
1485:Y.N. Srikant; Priti Shankar (3 October 2018).
1743:
350:
1677:"Compiler Explorer - C++ (x86-64 gcc 11.1)"
1577:"More Dots: Syntactic Loop Fusion in Julia"
1443:overloads for in-place operations, such as
417:by using function and operator overloading:
1757:
1750:
1736:
1515:Kennedy, Ken & Allen, Randy. (2001).
1510:
1508:
41:. This optimization is most efficient in
1931:Sparse conditional constant propagation
1574:
1544:Advanced Compiler Design Implementation
2121:
1575:Johnson, Steven G. (21 January 2017).
1505:
1402:Remove the unused allocation and free.
1731:
413:You could achieve the same syntax in
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1624:
355:Consider the following MATLAB code:
13:
1396:Fuse the loops into a single loop.
14:
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1881:Common subexpression elimination
1701:"Functions · The Julia Language"
2022:Compile-time function execution
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1:
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89:instruction-level parallelism
2001:Interprocedural optimization
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2052:Profile-guided optimization
2017:Bounds-checking elimination
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1253:"The result is: "
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1816:Loop-invariant code motion
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2009:
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1796:Automatic parallelization
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719:// Basic array operations
351:Example in C++ and MATLAB
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1434:languages like C++, the
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68:which replaces multiple
1801:Automatic vectorization
2129:Compiler optimizations
1949:Instruction scheduling
1926:Global value numbering
1902:Live-variable analysis
1831:Loop nest optimization
1759:Compiler optimizations
2078:Control-flow analysis
2073:Array-access analysis
2027:Dead-code elimination
1985:Tail-call elimination
1954:Instruction selection
1778:Local value numbering
1773:Peephole optimization
62:compiler optimization
43:multi-core processors
39:locality of reference
30:compiler optimization
2108:Value range analysis
2032:Expression templates
1876:Available expression
1461:Expression templates
2088:Dependence analysis
1959:Register allocation
1851:Software pipelining
1548:. Morgan Kaufmann.
1519:. Morgan Kaufmann.
1466:Loop transformation
66:loop transformation
2083:Data-flow analysis
2047:Partial evaluation
1856:Strength reduction
1806:Induction variable
1705:docs.julialang.org
203:is equivalent to:
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1964:Rematerialization
1555:978-1-55860-320-2
1498:978-1-4200-4383-9
26:loop distribution
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2098:Pointer analysis
2037:Inline expansion
1907:Use-define chain
1886:Constant folding
1846:Loop unswitching
1826:Loop interchange
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18:computer science
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2093:Escape analysis
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1941:Code generation
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1675:Godbolt, Matt.
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1650:Godbolt, Matt.
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1766:Basic block
1681:godbolt.org
1656:godbolt.org
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1385:Inline the
54:loop fusion
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1973:Functional
1891:Dead store
1710:2021-06-25
1686:2021-06-25
1661:2021-06-25
1636:2021-06-25
1611:2021-06-25
1472:References
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470:unique_ptr
1866:Data-flow
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