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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
106:
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,
1453:
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
102:. 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
1612:
47:
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
91:
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
98:
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
95:
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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99:
2011:
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17:
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2027:
1951:
1826:
107:
incrementing, etc.) that may make loop fusion, loop fission, or neither, the preferable optimization.
1806:
1711:
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Remove the unused stores into the temporary arrays (can use a register or stack variable instead).
1811:
1438:
1959:
1936:
1912:
1841:
87:, two loops may actually perform better than one loop because, for example, there is increased
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40:
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8:
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1969:
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The
Compiler Design Handbook: Optimizations and Machine Code Generation, Second Edition
1380:
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
2133:
88:
1246:// Print the result out - just to make sure the optimizer doesn't remove
997:// it would be unwieldy to define all possible overloaded math operations as
994:// Similarly, we can define an overload for the sin() function. In practice,
1528:
Optimizing
Compilers for Modern Architectures: A Dependence-based Approach
838:// Declare an overloaded addition operator as a free friend function (this
1821:
1738:
1433:
so that they can remove unused allocations from the code. However, as of
1425:
have global side effects, since some compilers hardcode symbols such as
1901:
841:// syntax defines operator+ as a free function that is a friend of this
1550:
559:// Factory method to produce an array over an integer range (the upper
1995:
1384:. A more efficient implementation would allocate a single array for
1000:// friends inside the class like this, but this is just an example.
1687:
1662:
1637:
1392:
in a single loop. To optimize this, a C++ compiler would need to:
844:// class, despite it appearing as a member function declaration).
389:% Create an array of numbers from 0 to 999 (range is inclusive)
1180:// Here, we perform the same computation as the MATLAB example
1434:
425:
419:% Take the sine of x (element-wise) and add 4 to each element
499:// Internal constructor that produces an uninitialized array
1551:
Steven
Muchnick; Muchnick and Associates (15 August 1997).
1525:
1495:
1544:
562:// bound is exclusive, unlike MATLAB's ranges).
56:that can split a task into multiple tasks for each
1552:
1249:// everything (if it's smart enough to do so).
1489:
2131:
1663:"Compiler Explorer - C++ (x86-64 clang 12.0.0)"
1638:"Compiler Explorer - C++ (x86-64 clang 12.0.0)"
1908:Induction variable recognition and elimination
1496:Y.N. Srikant; Priti Shankar (3 October 2018).
1754:
361:
1688:"Compiler Explorer - C++ (x86-64 gcc 11.1)"
1588:"More Dots: Syntactic Loop Fusion in Julia"
1454:overloads for in-place operations, such as
428:by using function and operator overloading:
1768:
1761:
1747:
1526:Kennedy, Ken & Allen, Randy. (2001).
1521:
1519:
52:. This optimization is most efficient in
1942:Sparse conditional constant propagation
1585:
1555:Advanced Compiler Design Implementation
14:
2132:
1586:Johnson, Steven G. (21 January 2017).
1516:
1413:Remove the unused allocation and free.
1742:
424:You could achieve the same syntax in
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1635:
366:Consider the following MATLAB code:
24:
1407:Fuse the loops into a single loop.
25:
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1892:Common subexpression elimination
1712:"Functions · The Julia Language"
2033:Compile-time function execution
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13:
1:
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100:instruction-level parallelism
2012:Interprocedural optimization
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2063:Profile-guided optimization
2028:Bounds-checking elimination
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1264:"The result is: "
10:
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1827:Loop-invariant code motion
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2020:
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1807:Automatic parallelization
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730:// Basic array operations
362:Example in C++ and MATLAB
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1445:languages like C++, the
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79:which replaces multiple
1812:Automatic vectorization
2140:Compiler optimizations
1960:Instruction scheduling
1937:Global value numbering
1913:Live-variable analysis
1842:Loop nest optimization
1770:Compiler optimizations
2089:Control-flow analysis
2084:Array-access analysis
2038:Dead-code elimination
1996:Tail-call elimination
1965:Instruction selection
1789:Local value numbering
1784:Peephole optimization
73:compiler optimization
54:multi-core processors
50:locality of reference
41:compiler optimization
2119:Value range analysis
2043:Expression templates
1887:Available expression
1472:Expression templates
2099:Dependence analysis
1970:Register allocation
1862:Software pipelining
1559:. Morgan Kaufmann.
1530:. Morgan Kaufmann.
1477:Loop transformation
77:loop transformation
2094:Data-flow analysis
2058:Partial evaluation
1867:Strength reduction
1817:Induction variable
1716:docs.julialang.org
214:is equivalent to:
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1975:Rematerialization
1566:978-1-55860-320-2
1509:978-1-4200-4383-9
37:loop distribution
16:(Redirected from
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2109:Pointer analysis
2048:Inline expansion
1918:Use-define chain
1897:Constant folding
1857:Loop unswitching
1837:Loop interchange
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2104:Escape analysis
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1734:Loop fission
1719:. Retrieved
1715:
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62:
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33:loop fission
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1904:elimination
1822:Loop fusion
1777:Basic block
1692:godbolt.org
1667:godbolt.org
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1437:12.0.0 and
1396:Inline the
65:loop fusion
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1984:Functional
1902:Dead store
1721:2021-06-25
1697:2021-06-25
1672:2021-06-25
1647:2021-06-25
1622:2021-06-25
1483:References
1456:operator+=
481:unique_ptr
1877:Data-flow
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2134:Category
1879:analysis
1466:See also
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