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Fastest s16 summation reduction of a q register

Josh Bleecher Snyder
Note: This was originally posted on 26th April 2011 at http://forums.arm.com

Hi,

I've got a NEON q register filled with 8 signed 16 bit ints. I'd like to calculate the sum across all of them as quickly as possible. The result should ultimately be a 16 bit int (overflow will not occur due to external constraints). Here are a few possibilities:

(1) Add pairwise twice, then do a scalar addition:

int32x4_t pairwiseAddedOnce = vpaddlq_s16(vec);
int64x2_t pairwiseAddedTwice = vpaddlq_s32(pairwiseAddedOnce);
int16_t sum = (int16_t)(vgetq_lane_s64(pairwiseAddedTwice, 0) + vgetq_lane_s64(pairwiseAddedTwice, 1));

(2) Add high and low d registers, then add pairwise twice:

int16x4_t addedDRegisters = vadd_s16(vget_low_s16(vec), vget_high_s16(vec));
int32x2_t pairwiseAddedOnce = vpaddl_s16(addedDRegisters);
int64x1_t pairwiseAddedTwice = vpaddl_s32(pairwiseAddedOnce);
int16_t sum = (int16_t)vget_lane_s64(pairwiseAddedTwice, 0);

(3) Add pairwise twice, then do an integer narrow, then another pairwise addition:

int32x4_t pairwiseAddedOnce = vpaddlq_s16(vec);
int64x2_t pairwiseAddedTwice = vpaddlq_s32(pairwiseAddedOnce);
int32x2_t narrowed = vmovn_s64(pairwiseAddedTwice);
int64x1_t pairwiseAddedThrice = vpaddl_s32(narrowed);
int16_t sum = (int16_t)vget_lane_s64(pairwiseAddedThrice, 0);

There are many, many other ways to do this (pairwise once, integer narrow, pairwise twice; or pairwise once, add high and low d registers, pairwise again; or cut out to scalar addition at some earlier point, etc.).

Which one of the many possibilities is most efficient? And what's a good way for me to figure this out for myself next time (either a good way to measure effectively or how I ought to reason it through)?

Thanks!

Josh

P.S. In case it matters, I'm writing in Xcode 4, for iOS, targeting armv7, using LLVM+gcc4.2.
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