autovectorization of outer loop

I have the following C++ code that evaluates a Chebyshev polynomial using Clenshaw’s algorithm

void cheby_eval(double coeffs,int n,double xs,double ys,int m)
{
#pragma omp simd
for (int i=0;i<m;i++){
double x = xs[i];
double u0=0,u1=0,u2=0;
for (int k=n;k>=0;k–){
u2 = u1;
u1 = u0;
u0 = 2
x
u1-u2+coeffs[k];
}
ys[i] = 0.5
(coeffs[0]+u0-u2);
}
}

I’m hoping for an autovectorization of the outer loop so that the inner loop operates on vectors.

When compiled with

clang++ -O3 -march=haswell -Rpass-analysis=loop-vectorize -S chebyshev.cc

using clang++ 3.8.1-23, no vectorization happens and I get the message

chebyshev.cc:19:18: remark: loop not vectorized: cannot identify array bounds
[-Rpass-analysis=loop-vectorize]
ys[i] = 0.5*(coeffs[0]+u0-u2);
^
chebyshev.cc:21:1: remark: loop not vectorized: value that could not be
identified as reduction is used outside the loop
[-Rpass-analysis=loop-vectorize]

On the same code icc vectorizes the outer loop as expected.

I was wondering if there are small ways in which I can change my code to help LLVM’s autovectorizer to succeed. I would also appreciate any pointers to documentation or LLVM source that can help me better understand how autovectorization of outer loops works.

Regards,
Jyotirmoy Bhattacharya

PS. The interesting part of icc’s assembler output is

…B1.4: # Preds …B1.8 …B1.3
xorl %r15d, %r15d #14.5
xorl %ebx, %ebx #14.21
testq %rsi, %rsi #14.21
vmovupd (%rdx,%r9,8), %ymm3 #12.16
vxorpd %ymm5, %ymm5, %ymm5 #13.14
vmovdqa %ymm1, %ymm4 #13.19
vmovdqa %ymm1, %ymm2 #13.24
jl …B1.8 # Prob 2% #14.21

…B1.5: # Preds …B1.4
vaddpd %ymm3, %ymm3, %ymm3 #17.14

…B1.6: # Preds …B1.6 …B1.5
vmovapd %ymm4, %ymm2 #20.3
incq %r15 #14.5
vmovapd %ymm5, %ymm4 #20.3
vfmsub213pd %ymm2, %ymm3, %ymm5 #17.19
vbroadcastsd (%r11,%rbx,8), %ymm6 #17.22
decq %rbx
vaddpd %ymm5, %ymm6, %ymm5 #17.22
cmpq %r10, %r15 #14.5
jb …B1.6 # Prob 82% #14.5

…B1.8: # Preds …B1.6 …B1.4
vbroadcastsd (%rdi), %ymm3 #19.18
vaddpd %ymm3, %ymm5, %ymm4 #19.28
vsubpd %ymm2, %ymm4, %ymm2 #19.31
vmulpd %ymm2, %ymm0, %ymm5 #19.31
vmovupd %ymm5, (%rcx,%r9,8) #19.5
addq $4, %r9 #11.3
cmpq %r8, %r9 #11.3
jb …B1.4 # Prob 82% #11

help me better understand how autovectorization of outer loops works.

LLVM’s loop vectorizer currently handles innermost loops only.

I’m hoping for an autovectorization of the outer loop so that the inner loop operates on vectors.

We share that hope and are working to achieve it: http://lists.llvm.org/pipermail/llvm-dev/2016-September/105057.html, but it will take some time. See https://reviews.llvm.org/D28975 and https://reviews.llvm.org/D32871. Thanks for the use-case.

I was wondering if there are small ways in which I can change my code to help LLVM’s autovectorizer to succeed.

If a doubly-nested loop can be interchanged such that the inner loop becomes vectorizable, it may help.

Ayal.