Groups   113 of 99+      julia-users › SIMD long inner expression 3 posts by 3 authors      Chris Rackauckas    Feb 4   Hi, I am trying to optimize a code which just adds a bunch of things. My first instinct was to unravel the loops and run it as SIMD, like so:  dx   1 400 addprocs 3  imin   -6 jmin   -2   Some SIMD  time res    sync  parallel  +  for i   imin:dx:0   tmp   0   for j jmin:dx:0     ans   0      simd for k 1:24        inbounds ans +  coefs k   i  powz k     j  poww k        end     tmp +  abs ans  1   end   tmp end res   res  12  length imin:dx:0  length jmin:dx:0    println res  Mathematica gives 2.98   Coefficients arrays posted at the bottom for completeness . On a 4 core i7 this runs in  4.68 seconds. I was able to beat this by optimizing the power calculations like so:     Full unravel  time res    sync  parallel  +  for i   imin:dx:0   tmp   0   isq2   i i; isq3   i isq2; isq4   isq2 isq2; isq5   i isq4   isq6   isq4 isq2; isq7   i isq6; isq8   isq4 isq4   for j jmin:dx:0     jsq2   j j; jsq4   jsq2 jsq2; jsq6   jsq2 jsq4; jsq8   jsq4 jsq4      inbounds tmp +  abs coefs 1   jsq2  + coefs 2   jsq4  + coefs 3   jsq6  + coefs 4   jsq8  + coefs 5   i  + coefs 6   i   jsq2  + coefs 7   i   jsq4  + coefs 8   i   jsq6  +     coefs 9   isq2  + coefs 10   isq2   jsq2  + coefs 11   isq2   jsq4  + coefs 12   isq2   jsq6  + coefs 13   isq3  + coefs 14   isq3   jsq2  + coefs 15   isq3   jsq4  +     coefs 16   isq4  + coefs 17   isq4   jsq2  + coefs 18   isq4   jsq4  + coefs 19   isq5  + coefs 20   isq5   jsq2  + coefs 21   isq6  + coefs 22   isq6   jsq2  +     coefs 23   isq7  + coefs 24   isq8   1   end   tmp end res   res  12  length imin:dx:0  length jmin:dx:0    println res  Mathematica gives 2.98  This is the best version and gets  1.83 seconds  FYI it bets a version where I distributed out by isq . However, when I put this into a function and call it with  code_llvm, I get:  define -jl_value_t   julia_simdCheck_3161     top:    0   alloca  8 x -jl_value_t  , align 8    .sub   getelementptr inbounds  8 x -jl_value_t     0, i64 0, i64 0    1   getelementptr  8 x -jl_value_t     0, i64 0, i64 2    2   getelementptr  8 x -jl_value_t     0, i64 0, i64 3   store -jl_value_t  inttoptr  i64 12 to -jl_value_t  , -jl_value_t    .sub, align 8    3   getelementptr  8 x -jl_value_t     0, i64 0, i64 1    4   load -jl_value_t    -jl_pgcstack, align 8    .c   bitcast -jl_value_t    4 to -jl_value_t    store -jl_value_t   .c, -jl_value_t    3, align 8   store -jl_value_t    .sub, -jl_value_t    -jl_pgcstack, align 8   store -jl_value_t  null, -jl_value_t    1, align 8   store -jl_value_t  null, -jl_value_t    2, align 8    5   getelementptr  8 x -jl_value_t     0, i64 0, i64 4   store -jl_value_t  null, -jl_value_t    5, align 8    6   getelementptr  8 x -jl_value_t     0, i64 0, i64 5   store -jl_value_t  null, -jl_value_t    6, align 8    7   getelementptr  8 x -jl_value_t     0, i64 0, i64 6   store -jl_value_t  null, -jl_value_t    7, align 8    8   getelementptr  8 x -jl_value_t     0, i64 0, i64 7   store -jl_value_t  null, -jl_value_t    8, align 8    9   call -jl_value_t   julia_sync_begin_535     store -jl_value_t  inttoptr  i64 2274649264 to -jl_value_t  , -jl_value_t    2, align 8    10   load -jl_value_t   -jl_value_t , -jl_value_t  , i32    inttoptr  i64 2274649264 to -jl_value_t   -jl_value_t , -jl_value_t  , i32    , align 16    11   load -jl_value_t   inttoptr  i64 2212282536 to -jl_value_t   , align 8   store -jl_value_t   11, -jl_value_t    5, align 8    12   load -jl_value_t   inttoptr  i64 2197909240 to -jl_value_t   , align 8   store -jl_value_t   12, -jl_value_t    6, align 8    13   load -jl_value_t   inttoptr  i64 2197909288 to -jl_value_t   , align 8   store -jl_value_t   13, -jl_value_t    7, align 8    14   load -jl_value_t   inttoptr  i64 2212418552 to -jl_value_t   , align 8   store -jl_value_t   14, -jl_value_t    8, align 8    15   call -jl_value_t   10 -jl_value_t  inttoptr  i64 2274649264 to -jl_value_t  , -jl_value_t    5, i32 4    store -jl_value_t   15, -jl_value_t    1, align 8   call void  julia_sync_end_541      16   load -jl_value_t    3, align 8    17   getelementptr inbounds -jl_value_t   16, i64 0, i32 0   store -jl_value_t    17, -jl_value_t    -jl_pgcstack, align 8   ret -jl_value_t   15    This shows me that the llvm is not auto-vectorizing the inner part. Is there a way to tell the llvm to SIMD vectorize the big summation in this more optimized form?  For completeness, here are the coefficient arrays  note: coefs should be treated as variable. In principle those zeros could change so there's no manual optimizing to be done there :  coefs  Vector Float64, 24 1.3333333333333328 0.16666666666666669 0.0 0.0 2.0 2.333333333333335 0.06250000000000001 0.0 2.0 1.1666666666666659 0.019097222222222224 0.0 1.0 3.469446951953614e-18 0.0 0.25 0.010416666666666666 0.0 0.0 0.0 0.0 0.0 0.0 0.0  powz Vector Float64, 24 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 4.0 4.0 4.0 5.0 5.0 6.0 6.0 7.0 8.0  poww  Vector Float64, 24  2.0 4.0 6.0 8.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 0.0 2.0 4.0 0.0 2.0 0.0 2.0 0.0 0.0     alan souza    Feb 4   Hi. I think that the number of variables in the inner loop  is too high and the compiler can't vectorize the code because of a insufficient number of available registers  see wik i- Register_allocation   and even if the compiler could vectorize this loop the speedup will be at best of two times for SSE code  Could you use float32 . I believe that can be easier to the compiler if split your computation  calculate the arrays with powers, pointwise multiplication and finally a reduction .      Erik Schnetter    Feb 4   Chris   To get good performance, you need to put your code into a function.  You seem to be evaluating it directly at the REPL -- this will be  slow. See the  Performance Tips  in the manual.   The LLVM code you see is not your kernel code. Instead, it contains a   call  statement, presumably to a function that contains all the code  in the  parallel region. You can try creating a function for your  actual kernel, which goes from  tmp   0  to  tmp  near the bottom, and  running   code_llvm  on it.   -erik   --  Erik Schnetter  schn... gmail.com   http:  www.perimeterinstitute.ca personal eschnetter