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diff --git a/docs/Vectorizers.rst b/docs/Vectorizers.rst new file mode 100644 index 0000000..e2d3667 --- /dev/null +++ b/docs/Vectorizers.rst @@ -0,0 +1,338 @@ +========================== +Auto-Vectorization in LLVM +========================== + +.. contents:: + :local: + +LLVM has two vectorizers: The :ref:`Loop Vectorizer <loop-vectorizer>`, +which operates on Loops, and the :ref:`Basic Block Vectorizer +<bb-vectorizer>`, which optimizes straight-line code. These vectorizers +focus on different optimization opportunities and use different techniques. +The BB vectorizer merges multiple scalars that are found in the code into +vectors while the Loop Vectorizer widens instructions in the original loop +to operate on multiple consecutive loop iterations. + +.. _loop-vectorizer: + +The Loop Vectorizer +=================== + +Usage +----- + +LLVM's Loop Vectorizer is now available and will be useful for many people. +It is not enabled by default, but can be enabled through clang using the +command line flag: + +.. code-block:: console + + $ clang -fvectorize -O3 file.c + +If the ``-fvectorize`` flag is used then the loop vectorizer will be enabled +when running with ``-O3``, ``-O2``. When ``-Os`` is used, the loop vectorizer +will only vectorize loops that do not require a major increase in code size. + +We plan to enable the Loop Vectorizer by default as part of the LLVM 3.3 release. + +Command line flags +^^^^^^^^^^^^^^^^^^ + +The loop vectorizer uses a cost model to decide on the optimal vectorization factor +and unroll factor. However, users of the vectorizer can force the vectorizer to use +specific values. Both 'clang' and 'opt' support the flags below. + +Users can control the vectorization SIMD width using the command line flag "-force-vector-width". + +.. code-block:: console + + $ clang -mllvm -force-vector-width=8 ... + $ opt -loop-vectorize -force-vector-width=8 ... + +Users can control the unroll factor using the command line flag "-force-vector-unroll" + +.. code-block:: console + + $ clang -mllvm -force-vector-unroll=2 ... + $ opt -loop-vectorize -force-vector-unroll=2 ... + +Features +-------- + +The LLVM Loop Vectorizer has a number of features that allow it to vectorize +complex loops. + +Loops with unknown trip count +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The Loop Vectorizer supports loops with an unknown trip count. +In the loop below, the iteration ``start`` and ``finish`` points are unknown, +and the Loop Vectorizer has a mechanism to vectorize loops that do not start +at zero. In this example, 'n' may not be a multiple of the vector width, and +the vectorizer has to execute the last few iterations as scalar code. Keeping +a scalar copy of the loop increases the code size. + +.. code-block:: c++ + + void bar(float *A, float* B, float K, int start, int end) { + for (int i = start; i < end; ++i) + A[i] *= B[i] + K; + } + +Runtime Checks of Pointers +^^^^^^^^^^^^^^^^^^^^^^^^^^ + +In the example below, if the pointers A and B point to consecutive addresses, +then it is illegal to vectorize the code because some elements of A will be +written before they are read from array B. + +Some programmers use the 'restrict' keyword to notify the compiler that the +pointers are disjointed, but in our example, the Loop Vectorizer has no way of +knowing that the pointers A and B are unique. The Loop Vectorizer handles this +loop by placing code that checks, at runtime, if the arrays A and B point to +disjointed memory locations. If arrays A and B overlap, then the scalar version +of the loop is executed. + +.. code-block:: c++ + + void bar(float *A, float* B, float K, int n) { + for (int i = 0; i < n; ++i) + A[i] *= B[i] + K; + } + + +Reductions +^^^^^^^^^^ + +In this example the ``sum`` variable is used by consecutive iterations of +the loop. Normally, this would prevent vectorization, but the vectorizer can +detect that 'sum' is a reduction variable. The variable 'sum' becomes a vector +of integers, and at the end of the loop the elements of the array are added +together to create the correct result. We support a number of different +reduction operations, such as addition, multiplication, XOR, AND and OR. + +.. code-block:: c++ + + int foo(int *A, int *B, int n) { + unsigned sum = 0; + for (int i = 0; i < n; ++i) + sum += A[i] + 5; + return sum; + } + +We support floating point reduction operations when `-ffast-math` is used. + +Inductions +^^^^^^^^^^ + +In this example the value of the induction variable ``i`` is saved into an +array. The Loop Vectorizer knows to vectorize induction variables. + +.. code-block:: c++ + + void bar(float *A, float* B, float K, int n) { + for (int i = 0; i < n; ++i) + A[i] = i; + } + +If Conversion +^^^^^^^^^^^^^ + +The Loop Vectorizer is able to "flatten" the IF statement in the code and +generate a single stream of instructions. The Loop Vectorizer supports any +control flow in the innermost loop. The innermost loop may contain complex +nesting of IFs, ELSEs and even GOTOs. + +.. code-block:: c++ + + int foo(int *A, int *B, int n) { + unsigned sum = 0; + for (int i = 0; i < n; ++i) + if (A[i] > B[i]) + sum += A[i] + 5; + return sum; + } + +Pointer Induction Variables +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +This example uses the "accumulate" function of the standard c++ library. This +loop uses C++ iterators, which are pointers, and not integer indices. +The Loop Vectorizer detects pointer induction variables and can vectorize +this loop. This feature is important because many C++ programs use iterators. + +.. code-block:: c++ + + int baz(int *A, int n) { + return std::accumulate(A, A + n, 0); + } + +Reverse Iterators +^^^^^^^^^^^^^^^^^ + +The Loop Vectorizer can vectorize loops that count backwards. + +.. code-block:: c++ + + int foo(int *A, int *B, int n) { + for (int i = n; i > 0; --i) + A[i] +=1; + } + +Scatter / Gather +^^^^^^^^^^^^^^^^ + +The Loop Vectorizer can vectorize code that becomes a sequence of scalar instructions +that scatter/gathers memory. + +.. code-block:: c++ + + int foo(int *A, int *B, int n, int k) { + for (int i = 0; i < n; ++i) + A[i*7] += B[i*k]; + } + +Vectorization of Mixed Types +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The Loop Vectorizer can vectorize programs with mixed types. The Vectorizer +cost model can estimate the cost of the type conversion and decide if +vectorization is profitable. + +.. code-block:: c++ + + int foo(int *A, char *B, int n, int k) { + for (int i = 0; i < n; ++i) + A[i] += 4 * B[i]; + } + +Global Structures Alias Analysis +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Access to global structures can also be vectorized, with alias analysis being +used to make sure accesses don't alias. Run-time checks can also be added on +pointer access to structure members. + +Many variations are supported, but some that rely on undefined behaviour being +ignored (as other compilers do) are still being left un-vectorized. + +.. code-block:: c++ + + struct { int A[100], K, B[100]; } Foo; + + int foo() { + for (int i = 0; i < 100; ++i) + Foo.A[i] = Foo.B[i] + 100; + } + +Vectorization of function calls +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The Loop Vectorize can vectorize intrinsic math functions. +See the table below for a list of these functions. + ++-----+-----+---------+ +| pow | exp | exp2 | ++-----+-----+---------+ +| sin | cos | sqrt | ++-----+-----+---------+ +| log |log2 | log10 | ++-----+-----+---------+ +|fabs |floor| ceil | ++-----+-----+---------+ +|fma |trunc|nearbyint| ++-----+-----+---------+ +| | | fmuladd | ++-----+-----+---------+ + +The loop vectorizer knows about special instructions on the target and will +vectorize a loop containing a function call that maps to the instructions. For +example, the loop below will be vectorized on Intel x86 if the SSE4.1 roundps +instruction is available. + +.. code-block:: c++ + + void foo(float *f) { + for (int i = 0; i != 1024; ++i) + f[i] = floorf(f[i]); + } + +Partial unrolling during vectorization +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Modern processors feature multiple execution units, and only programs that contain a +high degree of parallelism can fully utilize the entire width of the machine. +The Loop Vectorizer increases the instruction level parallelism (ILP) by +performing partial-unrolling of loops. + +In the example below the entire array is accumulated into the variable 'sum'. +This is inefficient because only a single execution port can be used by the processor. +By unrolling the code the Loop Vectorizer allows two or more execution ports +to be used simultaneously. + +.. code-block:: c++ + + int foo(int *A, int *B, int n) { + unsigned sum = 0; + for (int i = 0; i < n; ++i) + sum += A[i]; + return sum; + } + +The Loop Vectorizer uses a cost model to decide when it is profitable to unroll loops. +The decision to unroll the loop depends on the register pressure and the generated code size. + +Performance +----------- + +This section shows the the execution time of Clang on a simple benchmark: +`gcc-loops <http://llvm.org/viewvc/llvm-project/test-suite/trunk/SingleSource/UnitTests/Vectorizer/>`_. +This benchmarks is a collection of loops from the GCC autovectorization +`page <http://gcc.gnu.org/projects/tree-ssa/vectorization.html>`_ by Dorit Nuzman. + +The chart below compares GCC-4.7, ICC-13, and Clang-SVN with and without loop vectorization at -O3, tuned for "corei7-avx", running on a Sandybridge iMac. +The Y-axis shows the time in msec. Lower is better. The last column shows the geomean of all the kernels. + +.. image:: gcc-loops.png + +And Linpack-pc with the same configuration. Result is Mflops, higher is better. + +.. image:: linpack-pc.png + +.. _bb-vectorizer: + +The Basic Block Vectorizer +========================== + +Usage +------ + +The Basic Block Vectorizer is not enabled by default, but it can be enabled +through clang using the command line flag: + +.. code-block:: console + + $ clang -fslp-vectorize file.c + +Details +------- + +The goal of basic-block vectorization (a.k.a. superword-level parallelism) is +to combine similar independent instructions within simple control-flow regions +into vector instructions. Memory accesses, arithemetic operations, comparison +operations and some math functions can all be vectorized using this technique +(subject to the capabilities of the target architecture). + +For example, the following function performs very similar operations on its +inputs (a1, b1) and (a2, b2). The basic-block vectorizer may combine these +into vector operations. + +.. code-block:: c++ + + int foo(int a1, int a2, int b1, int b2) { + int r1 = a1*(a1 + b1)/b1 + 50*b1/a1; + int r2 = a2*(a2 + b2)/b2 + 50*b2/a2; + return r1 + r2; + } + + |
