1========================== 2Auto-Vectorization in LLVM 3========================== 4 5.. contents:: 6 :local: 7 8LLVM has two vectorizers: The :ref:`Loop Vectorizer <loop-vectorizer>`, 9which operates on Loops, and the :ref:`SLP Vectorizer 10<slp-vectorizer>`. These vectorizers 11focus on different optimization opportunities and use different techniques. 12The SLP vectorizer merges multiple scalars that are found in the code into 13vectors while the Loop Vectorizer widens instructions in loops 14to operate on multiple consecutive iterations. 15 16Both the Loop Vectorizer and the SLP Vectorizer are enabled by default. 17 18.. _loop-vectorizer: 19 20The Loop Vectorizer 21=================== 22 23Usage 24----- 25 26The Loop Vectorizer is enabled by default, but it can be disabled 27through clang using the command line flag: 28 29.. code-block:: console 30 31 $ clang ... -fno-vectorize file.c 32 33Command line flags 34^^^^^^^^^^^^^^^^^^ 35 36The loop vectorizer uses a cost model to decide on the optimal vectorization factor 37and unroll factor. However, users of the vectorizer can force the vectorizer to use 38specific values. Both 'clang' and 'opt' support the flags below. 39 40Users can control the vectorization SIMD width using the command line flag "-force-vector-width". 41 42.. code-block:: console 43 44 $ clang -mllvm -force-vector-width=8 ... 45 $ opt -loop-vectorize -force-vector-width=8 ... 46 47Users can control the unroll factor using the command line flag "-force-vector-unroll" 48 49.. code-block:: console 50 51 $ clang -mllvm -force-vector-unroll=2 ... 52 $ opt -loop-vectorize -force-vector-unroll=2 ... 53 54Features 55-------- 56 57The LLVM Loop Vectorizer has a number of features that allow it to vectorize 58complex loops. 59 60Loops with unknown trip count 61^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 62 63The Loop Vectorizer supports loops with an unknown trip count. 64In the loop below, the iteration ``start`` and ``finish`` points are unknown, 65and the Loop Vectorizer has a mechanism to vectorize loops that do not start 66at zero. In this example, 'n' may not be a multiple of the vector width, and 67the vectorizer has to execute the last few iterations as scalar code. Keeping 68a scalar copy of the loop increases the code size. 69 70.. code-block:: c++ 71 72 void bar(float *A, float* B, float K, int start, int end) { 73 for (int i = start; i < end; ++i) 74 A[i] *= B[i] + K; 75 } 76 77Runtime Checks of Pointers 78^^^^^^^^^^^^^^^^^^^^^^^^^^ 79 80In the example below, if the pointers A and B point to consecutive addresses, 81then it is illegal to vectorize the code because some elements of A will be 82written before they are read from array B. 83 84Some programmers use the 'restrict' keyword to notify the compiler that the 85pointers are disjointed, but in our example, the Loop Vectorizer has no way of 86knowing that the pointers A and B are unique. The Loop Vectorizer handles this 87loop by placing code that checks, at runtime, if the arrays A and B point to 88disjointed memory locations. If arrays A and B overlap, then the scalar version 89of the loop is executed. 90 91.. code-block:: c++ 92 93 void bar(float *A, float* B, float K, int n) { 94 for (int i = 0; i < n; ++i) 95 A[i] *= B[i] + K; 96 } 97 98 99Reductions 100^^^^^^^^^^ 101 102In this example the ``sum`` variable is used by consecutive iterations of 103the loop. Normally, this would prevent vectorization, but the vectorizer can 104detect that 'sum' is a reduction variable. The variable 'sum' becomes a vector 105of integers, and at the end of the loop the elements of the array are added 106together to create the correct result. We support a number of different 107reduction operations, such as addition, multiplication, XOR, AND and OR. 108 109.. code-block:: c++ 110 111 int foo(int *A, int *B, int n) { 112 unsigned sum = 0; 113 for (int i = 0; i < n; ++i) 114 sum += A[i] + 5; 115 return sum; 116 } 117 118We support floating point reduction operations when `-ffast-math` is used. 119 120Inductions 121^^^^^^^^^^ 122 123In this example the value of the induction variable ``i`` is saved into an 124array. The Loop Vectorizer knows to vectorize induction variables. 125 126.. code-block:: c++ 127 128 void bar(float *A, float* B, float K, int n) { 129 for (int i = 0; i < n; ++i) 130 A[i] = i; 131 } 132 133If Conversion 134^^^^^^^^^^^^^ 135 136The Loop Vectorizer is able to "flatten" the IF statement in the code and 137generate a single stream of instructions. The Loop Vectorizer supports any 138control flow in the innermost loop. The innermost loop may contain complex 139nesting of IFs, ELSEs and even GOTOs. 140 141.. code-block:: c++ 142 143 int foo(int *A, int *B, int n) { 144 unsigned sum = 0; 145 for (int i = 0; i < n; ++i) 146 if (A[i] > B[i]) 147 sum += A[i] + 5; 148 return sum; 149 } 150 151Pointer Induction Variables 152^^^^^^^^^^^^^^^^^^^^^^^^^^^ 153 154This example uses the "accumulate" function of the standard c++ library. This 155loop uses C++ iterators, which are pointers, and not integer indices. 156The Loop Vectorizer detects pointer induction variables and can vectorize 157this loop. This feature is important because many C++ programs use iterators. 158 159.. code-block:: c++ 160 161 int baz(int *A, int n) { 162 return std::accumulate(A, A + n, 0); 163 } 164 165Reverse Iterators 166^^^^^^^^^^^^^^^^^ 167 168The Loop Vectorizer can vectorize loops that count backwards. 169 170.. code-block:: c++ 171 172 int foo(int *A, int *B, int n) { 173 for (int i = n; i > 0; --i) 174 A[i] +=1; 175 } 176 177Scatter / Gather 178^^^^^^^^^^^^^^^^ 179 180The Loop Vectorizer can vectorize code that becomes a sequence of scalar instructions 181that scatter/gathers memory. 182 183.. code-block:: c++ 184 185 int foo(int *A, int *B, int n, int k) { 186 for (int i = 0; i < n; ++i) 187 A[i*7] += B[i*k]; 188 } 189 190Vectorization of Mixed Types 191^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 192 193The Loop Vectorizer can vectorize programs with mixed types. The Vectorizer 194cost model can estimate the cost of the type conversion and decide if 195vectorization is profitable. 196 197.. code-block:: c++ 198 199 int foo(int *A, char *B, int n, int k) { 200 for (int i = 0; i < n; ++i) 201 A[i] += 4 * B[i]; 202 } 203 204Global Structures Alias Analysis 205^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 206 207Access to global structures can also be vectorized, with alias analysis being 208used to make sure accesses don't alias. Run-time checks can also be added on 209pointer access to structure members. 210 211Many variations are supported, but some that rely on undefined behaviour being 212ignored (as other compilers do) are still being left un-vectorized. 213 214.. code-block:: c++ 215 216 struct { int A[100], K, B[100]; } Foo; 217 218 int foo() { 219 for (int i = 0; i < 100; ++i) 220 Foo.A[i] = Foo.B[i] + 100; 221 } 222 223Vectorization of function calls 224^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 225 226The Loop Vectorize can vectorize intrinsic math functions. 227See the table below for a list of these functions. 228 229+-----+-----+---------+ 230| pow | exp | exp2 | 231+-----+-----+---------+ 232| sin | cos | sqrt | 233+-----+-----+---------+ 234| log |log2 | log10 | 235+-----+-----+---------+ 236|fabs |floor| ceil | 237+-----+-----+---------+ 238|fma |trunc|nearbyint| 239+-----+-----+---------+ 240| | | fmuladd | 241+-----+-----+---------+ 242 243The loop vectorizer knows about special instructions on the target and will 244vectorize a loop containing a function call that maps to the instructions. For 245example, the loop below will be vectorized on Intel x86 if the SSE4.1 roundps 246instruction is available. 247 248.. code-block:: c++ 249 250 void foo(float *f) { 251 for (int i = 0; i != 1024; ++i) 252 f[i] = floorf(f[i]); 253 } 254 255Partial unrolling during vectorization 256^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 257 258Modern processors feature multiple execution units, and only programs that contain a 259high degree of parallelism can fully utilize the entire width of the machine. 260The Loop Vectorizer increases the instruction level parallelism (ILP) by 261performing partial-unrolling of loops. 262 263In the example below the entire array is accumulated into the variable 'sum'. 264This is inefficient because only a single execution port can be used by the processor. 265By unrolling the code the Loop Vectorizer allows two or more execution ports 266to be used simultaneously. 267 268.. code-block:: c++ 269 270 int foo(int *A, int *B, int n) { 271 unsigned sum = 0; 272 for (int i = 0; i < n; ++i) 273 sum += A[i]; 274 return sum; 275 } 276 277The Loop Vectorizer uses a cost model to decide when it is profitable to unroll loops. 278The decision to unroll the loop depends on the register pressure and the generated code size. 279 280Performance 281----------- 282 283This section shows the the execution time of Clang on a simple benchmark: 284`gcc-loops <http://llvm.org/viewvc/llvm-project/test-suite/trunk/SingleSource/UnitTests/Vectorizer/>`_. 285This benchmarks is a collection of loops from the GCC autovectorization 286`page <http://gcc.gnu.org/projects/tree-ssa/vectorization.html>`_ by Dorit Nuzman. 287 288The 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. 289The Y-axis shows the time in msec. Lower is better. The last column shows the geomean of all the kernels. 290 291.. image:: gcc-loops.png 292 293And Linpack-pc with the same configuration. Result is Mflops, higher is better. 294 295.. image:: linpack-pc.png 296 297.. _slp-vectorizer: 298 299The SLP Vectorizer 300================== 301 302Details 303------- 304 305The goal of SLP vectorization (a.k.a. superword-level parallelism) is 306to combine similar independent instructions 307into vector instructions. Memory accesses, arithmetic operations, comparison 308operations, PHI-nodes, can all be vectorized using this technique. 309 310For example, the following function performs very similar operations on its 311inputs (a1, b1) and (a2, b2). The basic-block vectorizer may combine these 312into vector operations. 313 314.. code-block:: c++ 315 316 void foo(int a1, int a2, int b1, int b2, int *A) { 317 A[0] = a1*(a1 + b1)/b1 + 50*b1/a1; 318 A[1] = a2*(a2 + b2)/b2 + 50*b2/a2; 319 } 320 321The SLP-vectorizer processes the code bottom-up, across basic blocks, in search of scalars to combine. 322 323Usage 324------ 325 326The SLP Vectorizer is enabled by default, but it can be disabled 327through clang using the command line flag: 328 329.. code-block:: console 330 331 $ clang -fno-slp-vectorize file.c 332 333LLVM has a second basic block vectorization phase 334which is more compile-time intensive (The BB vectorizer). This optimization 335can be enabled through clang using the command line flag: 336 337.. code-block:: console 338 339 $ clang -fslp-vectorize-aggressive file.c 340 341