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# Auto-Vectorization in LLVM

- The Loop Vectorizer
  - Usage
    - Command line flags
  - Features
    - Loops with unknown trip count
    - Runtime Checks of Pointers
    - Reductions
    - Inductions
    - If Conversion
    - Pointer Induction Variables
    - Reverse Iterators
    - Scatter / Gather
    - Vectorization of Mixed Types
    - Global Structures Alias Analysis
    - Vectorization of function calls
    - Partial unrolling during vectorization
  - Performance
- The SLP Vectorizer
  - Details
  - Usage

LLVM has two vectorizers: The Loop Vectorizer, which operates on Loops, and the SLP Vectorizer, which optimizes straight-line code. These vectorizers focus on different optimization opportunities and use different techniques. The SLP 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.

## The Loop Vectorizer

### Usage

LLVM’s Loop Vectorizer is now enabled by default for -O3. We plan to enable parts of the Loop Vectorizer on -O2 and -Os in future releases. The vectorizer can be disabled using the command line:

    $ clang ... -fno-vectorize  file.c

#### 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”.

    $ 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”

    $ 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.

    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.

    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.

    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.

    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.

    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.

    int baz(int *A, int n) {
      return std::accumulate(A, A + n, 0);
    }

#### Reverse Iterators

The Loop Vectorizer can vectorize loops that count backwards.

    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.

    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.

    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.

    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.

    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.

    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. This benchmarks is a collection of loops from the GCC autovectorization page 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.

And Linpack-pc with the same configuration. Result is Mflops, higher is better.

## The SLP Vectorizer

### Details

The goal of SLP 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.

    void foo(int a1, int a2, int b1, int b2, int *A) {
      A[0] = a1*(a1 + b1)/b1 + 50*b1/a1;
      A[1] = a2*(a2 + b2)/b2 + 50*b2/a2;
    }

The SLP-vectorizer has two phases, bottom-up, and top-down. The top-down vectorization phase is more aggressive, but takes more time to run.

### Usage

The SLP Vectorizer is not enabled by default, but it can be enabled through clang using the command line flag:

    $ clang -fslp-vectorize file.c

LLVM has a second basic block vectorization phase which is more compile-time intensive (The BB vectorizer). This optimization can be enabled through clang using the command line flag:

    $ clang -fslp-vectorize-aggressive file.c

The SLP vectorizer is in early development stages but can already vectorize and accelerate many programs in the LLVM test suite.

Benchmark Name | Gain
--- | ---
Misc/flops-7 | -32.70%
Misc/matmul_f64_4x4 | -23.23%
Olden/power | -21.45%
Misc/flops-4 | -14.90%
ASC_Sequoia/AMGmk | -13.85%
TSVC/LoopRerolling-flt | -11.76%
Misc/flops-6 | -9.70%
Misc/flops-5 | -8.54%
Misc/flops | -8.12%
TSVC/NodeSplitting-dbl | -6.96%
Misc-C++/sphereflake | -6.74%
Ptrdist/yacr2 | -6.31%

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