Difference between revisions of "Vectorization"

From Lazarus wiki
Jump to navigationJump to search
(Minor updates)
Line 18: Line 18:
 
   SetLength(Output, Length(Input1));
 
   SetLength(Output, Length(Input1));
  
   for X := 0 to Length(Input1) do
+
   for X := 0 to Length(Input1) - 1 do
 
   begin
 
   begin
 
     Output[X] := Input1[X] * Input2[X];
 
     Output[X] := Input1[X] * Input2[X];

Revision as of 19:43, 13 December 2017

An editor has declared this article to be a stub, meaning that it needs more information. Can you help out and add some? If you have some useful information, you can help the Free Pascal Wiki by clicking on the edit box on the left and expanding this page.

This page has been set up as a collaboration and design spec for the proposal to include vectorisation support in the x86 and x86_64 variant of the Free Pascal Compiler (using SSE or AVX to reduce the number of instructions, and hence the execution speed, required to encode functionality). Eventually this page can be converted into a guide to the optimizer once vectorization is at least partially supported.

CuriousKit (talk) 22:52, 11 December 2017 (CET)

Vector Types

As of 12 December 2017, only static arrays of Singles or Doubles are considered vector types, but they are unaligned unless enforced by additional compiler directives. Dynamic arrays and pointers to Singles or Doubles are currently not considered to be vectors.

Loop Optimization

Coupled with loop unrolling, it is possible to theoretically reduce the number of cycles by a factor of 4 or 8, depending on if SSE2 or AVX2 is used. It depends on the code contained within the loop, but if it utilises only relatively simple arithmetic and pointer movement (e.g. reading and writing sequentially from and to an array), then it might be vectorised with relative ease.

For example:

var
  Input1, Input2, Output: array of Cardinal; X: Integer;

begin
  assert(Length(Input1) = Length(Input2));
  SetLength(Output, Length(Input1));

  for X := 0 to Length(Input1) - 1 do
  begin
    Output[X] := Input1[X] * Input2[X];
  end;
end;

While the size of the inputs is not immediately known, it can be seen that the array sizes do not change within the loop and hence Length(Input1) is constant. Visualising how the compiler might evaluate the code, it could be internally changed to the following:

var
  Input1, Input2, Output: array of Cardinal; X, ArrayLen: Integer;

begin
  assert(Length(Input1) = Length(Input2));
  SetLength(Output, Length(Input1));

  ArrayLen := Length(Input1) div 4;

  for X := 0 to ArrayLen - 1 do
  begin
    Output[4 * X] :=     Input1[4 * X] *     Input2[4 * X];
    Output[4 * X + 1] := Input1[4 * X + 1] * Input2[4 * X + 1];
    Output[4 * X + 2] := Input1[4 * X + 2] * Input2[4 * X + 2];
    Output[4 * X + 3] := Input1[4 * X + 3] * Input2[4 * X + 3];
  end;

  { Handle leftover array entries individually (count = Length(Input1) mod 4)) }
end;

As such, the 4 statements in the converted for-loop can be easily assembled into SSE2 opcodes (although PMULLD is SSE4.1), even with potentially unaligned memory. For example:

  LEA  R8,  Output[0]
  LEA  R9,  Input1[0]
  LEA  R10, Input2[0]

  MOV  ECX, ArrayLen
  XOR  RBX, RBX
  TEST ECX, ECX
  JZ   @LoopExit

@VectorisedLoop:
  MOVDQU  XMM0, [R9+RBX*4]
  PMULLD  XMM0, [R10+RBX*4]
  MOVDQU  [R8*RBX*4], XMM0

  INC  RBX
  DEC  ECX
  JNZ  @VectorisedLoop
@LoopExit:

Further optimisations can be achieved by, for example, performing two reads, multiplies and writes per loop cycle, taking advantage of the fact that modern processors have more than one SIMD port to send instructions to.