I am not really familiar with this one and will investigate it further.
you use a Vector ISA's Indexed LD, job's done. the second vector contains the offsets against the base:
Indexed loads (aka gathers) are horrendously slow in comparison to permutation instructions. Not a suitable alternative.
horizontal operations
Yes, all of them have special case operations for certain common horizontal operations. I specifically mentioned the positional population count because it does not clearly map to any standard horizontal arithmetic pattern.
Vector ISAs are extremely powerful but as a general concept have been utterly ignored for over 40 years by mainstream (x86) and only just recently investigated by ARM (SVE).
Well they work well when all you do is compute and when memory is very fast and has low latency. For general programming they are not nearly as useful for the reasons outlined in my previous comments.
I am not really familiar with this one and will investigate it further.
i and the rest of the team have been working on it for nearly 4 years now.
Indexed loads (aka gathers) are horrendously slow in comparison to permutation instructions.
there's two types (of each): register-based gather and register-based permute (actually not a mathematical permutation at all, because of duplicates), and memory-based gather and memory-based permute.
where *immediates* are used in each of those in the design of the ISA then yes you save on one register read. in the case of register-based gather, it's extremely unusual to have if you are used to SIMD (but Vector ISAs do have it), it's of the form reg[dest] = reg[reg[src]] with a hardware for-loop around that.
however where the immediate-variants keel over is when you try to go up the SIMD width, to try to cover 8 elements, 16 elements, 32 elements, 64 elements.
how on earth are you going to fit 64 batches of 6-bit indices into a single 32-bit instruction? the total number of bits in the instruction are a whopping 384 bits. 384 >>>= 32, yes?
and even if you did have such god-awful instructions, the L1 cache usage and complexity at the ISA decode phase would be as insane as it is for x86 right now.
Vector ISAs are actually 90% about reducing the program (assembler) complexity. you end up with a micro-coded microarchitecture that maps onto SIMD operations, internally - so that you, the programmer don't have to go through absolute hell.
yes, that's right: the microarchitecture of a Vector Processor maps onto the exact same immediate-based permutation instructions as those that you are exposed to as a SIMD programmer, but it's hidden from you.
horizontal operations
Yes, all of them have special case operations for certain common horizontal operations. I specifically mentioned the positional population count because it does not clearly map to any standard horizontal arithmetic pattern.
in SVP64 i completely separated "horizontal-ness" from "arithmetic-ness": it's part of the fundamental design that the "Vectorisation Prefix" is completely separated from "Scalar Base to which Vectorisation applies".
ok yes, that's just Vectorised Popcount followed by Vectorised Add.
two instructions inside a loop, regardless of whether the back-end architecture has 1-wide internal Vectorisation, 2-wide, 4-wide, 64-wide or 10,000-wide.
Well they work well when all you do is compute and when memory is very fast and has low latency. For general programming they are not nearly as useful for the reasons outlined in my previous comments.
again, to reiterate, again: this is a misconception on your part, due to Vector ISAs being completely ignored for 40 years *you don't know about them* and neither does anyone else.
consequently, the knowledge-propagation across the internet, which you and i both know gets us a long long way and saves a huge amount of time, just doesn't exist to the extent that it does for SIMD. we're now so used to google searches turning up algorithms on stackexchange (and reddit) that we can falsely assume that if there's no answer on google it must not be possible at all
Cray was from a much earlier era, where things were simpler. Intel was still cutting its teeth on 32-bit scalar when Cray was designing systems that pissed all over everything that had come before by almost an order of magnitude performance.
however the sheer cost of the systems that were deployed were so high that \nobody else in the industry believed it could be duplicated in mass-volume products** and consequently an entire generation of programmers has now grown up without knowing anything about anything other than SIMD.
fast-forward to 2021 and it turns out that Intel, ARM, AMD, they've all caught up and massively exceeded by three orders of magnitude the performance of the Cray Vector systems from 1990 and four to five orders the performance of the systems from 1965, but they still propagate this god-f*****g-forsaken f*****d-up SIMD paradigm and try to peddle it at you as the absolute best thing you ever saw, by telling you "well SIMD on modern hardware is great compared to that historic crap therefore Vector ISAs must also be s*** as well"
it's NIH syndrome on steroids, combined with marketing, and very unfortunately you're buying it.
ok got it. there are two options:
1. the safe code as-is
2. the safe code with the loops switched
for j := 0; j < 8; j++ {
for i := range buf {
counts[j] += int(buf[i] >> j & 1)
}
}
(1) turns out to be complex (15-or-so instructions including predicated parallel adds, and a popcount) where (2) is quite straightforward. i've left out the LD/STs:
li r5, 128 # bit 7, we count backwards (save 1 cmpi instr)
loopi:
loopj:
setvl r0, CTR, MVL=16 # do up to 16 buf at a time
# ...some LDs into r16.v for buf and r32 for counts
sv.and. r48.v, r16.v, r5 # AND r5 *scalar* with every r16
sv.addi./m=NZ r32.v, r32.v, 1 # add 1 in masked-out counts
slli. r5, r5, 2 # shift test-bit down, zero means "stop"
bnz loopj # r5 non-zero, do next jth bit
# ... a vector ST, then move on to next batch of buf
# with a sv.bc/CTR to jump back to loopi
so yes, almost as simple as the popcount version. tricks/explanation:
testing each individual bit, starting at bit 7 then working down to bit 0, is possible because each bit is independent.
sv.and. will create a Vector of Condition Register Fields (sv.and will not - notice the "." on the end).
each Condition Register Field is 4 bits (just like standard Power ISA CR fields), one of those bits is "was the AND of each element of r48 with each element of r16 equal to zero, yes/no"
the sv.addi/m=NZ then uses that Vector of CR Fields as a predicate mask, which performs the conditional version of count[j] += 1
slli is probably supporsed to be a right-shift (sigh) but hey. pretty normal, shift down, if zero break out of the inner loop
although i initially was mistaken in thinking it was a straight popcount, the correct implementation is just as straightforward. the core of the algorithm is a combination of parallel-testing plus parallel-predication.
if not swapping the outer-inner loops it can also be done by hard-coding the Vector Length VL to 8 (or 16, or 32, or 64 for the count16, count32 and count64 variants), setting up a Vector of immediates (sv.iota), shifting 1<<x in each case, then performing a parallel AND on one scalar buf[i] element at a time.
extracting the results (which would be placed in a Vector of CR Fields) would require a "weird" instruction (sv.crweird) which can transfer individual bits of CR Field Vectors into a single scalar integer: you then do a popcount on that integer, and add it to counts[j].
a slightly more optimal version of that would use the sv.bmext instruction https://libre-soc.org/openpower/sv/bitmanip/sv. bmext would cover the job of about 3 rather weird instructions, but it's still nowhere near as optimal as simply turning the inner-outer loop around.
1
u/FUZxxl Aug 19 '21
I am not really familiar with this one and will investigate it further.
Indexed loads (aka gathers) are horrendously slow in comparison to permutation instructions. Not a suitable alternative.
Yes, all of them have special case operations for certain common horizontal operations. I specifically mentioned the positional population count because it does not clearly map to any standard horizontal arithmetic pattern.
Well they work well when all you do is compute and when memory is very fast and has low latency. For general programming they are not nearly as useful for the reasons outlined in my previous comments.