> On Thursday, September 30, 2021, 01:25:02 PM EDT, <luke-tier...@uiowa.edu> > wrote: > >> On Thu, 30 Sep 2021, brodie gaslam via R-devel wrote: >> >> André, >> >> I'm not an R core member, but happen to have looked a little bit at this >> issue myself. I've seen similar things on Skylake and Coffee Lake 2 >> (9700, one generation past your latest) too. I think it would make sense >> to have some handling of this, although I would want to show the trade-off >> with performance impacts on CPUs that are not affected by this, and on >> vectors that don't actually have NAs and similar. I think the performance >> impact is likely to be small so long as branch prediction is active, but >> since branch prediction is involved you might need to check with different >> ratios of NAs (not for your NA bailout branch, but for e.g. interaction >> of what you add and the existing `na.rm=TRUE` logic). > > I would want to see realistic examples where this matters, not > microbenchmarks, before thinking about complicating the code. Not all > but most cases where sum(x) returns NaN/NA would eventually result in > an error; getting to the error faster is not likely to be useful.
That's a very good point, and I'll admit I did not consider it sufficiently. There are examples such as `rowSums`/`colSums` where some rows/columns evaluate to NA thus the result is still contains meaningful data. By extension, any loop that applies `sum` to list elements where some might contain NAs, and others not. `tapply` or any other group based aggregation come to mind. > My understanding is that arm64 does not support proper long doubles > (they are the same as regular doubles). Mine is the same. > So code using long doubles isn't getting the hoped-for improved > precision. Since that architecture is becoming more common we should > probably be looking at replacing uses of long doubles with better > algorithms that can work with regular doubles, e.g Kahan summation or > variants for sum. This is probably the bigger issue. If the future is ARM/AMD, the value of Intel x87-only optimizations becomes questionable. More generally is the question of whether to completely replace long double with algorithmic precision methods, at a cost of performance on systems that do support hardware long doubles (Intel or otherwise), or whether both code pathways are kept and selected at compile time. Or maybe the aggregation functions gain a low-precision flag for simple double precision accumulation. I'm curious to look at the performance and precision implications of e.g. Kahan summation if no one has done that yet. Some quick poking around shows people using processor specific intrinsics to take advantage of advanced multi-element instructions, but I imagine R would not want to do that. Assuming others have not done this already, I will have a look and report back. >> Since we're on the topic I want to point out that the default NA in R >> starts off as a signaling NA: >> >> example(numToBits) # for `bitC` >> bitC(NA_real_) >> ## [1] 0 11111111111 | >>0000000000000000000000000000000000000000011110100010 >> bitC(NA_real_ + 0) >> ## [1] 0 11111111111 | >>1000000000000000000000000000000000000000011110100010 >> >> Notice the leading bit of the significant starts off as zero, which marks >> it as a signaling NA, but becomes 1, i.e. non-signaling, after any >> operation[2]. >> >> This is meaningful because the mere act of loading a signaling NA into the >> x87 FPU is sufficient to trigger the slowdowns, even if the NA is not >> actually used in arithmetic operations. This happens sometimes under some >> optimization levels. I don't now of any benefit of starting off with a >> signaling NA, especially since the encoding is lost pretty much as soon as >> it is used. If folks are interested I can provide patch to turn the NA >> quiet by default. > > In principle this might be a good idea, but the current bit pattern is > unfortunately baked into a number of packages and documents on > internals, as well as serialized objects. The work needed to sort that > out is probably not worth the effort. One reason why we might not need to sort this out is precisely the instability shown above. Anything that relies on the signaling bit set to a particular value will behave differently with `NA_real_` vs `NA_real_ + x`. `R_IsNA` only checks the lower word, so it doesn't care about the signaling bit or the 19 subsequent ones. Anything that does likely has unpredictable behavior **currently**. Similarly, the documentation[1] only specifies the low word: > On such platforms NA is represented by the NaN value with low-word 0x7a2 > (1954 in decimal). This is consistent with the semantics of `R_IsNA`. > It also doesn't seem to affect the performance issue here since > setting b[1] <- NA_real_ + 0 produces the same slowdown (at least on > my current Intel machine). The subtlety here is that the slowdown happens by merely loading the signaling NaN onto the X87 FPU. Consider the following: x <- t(1:1e7+1L) system.time(rowSums(x)) ## user system elapsed ## 1.685 0.007 1.693 If we apply the following patch to make NA_REAL quiet: Index: src/main/arithmetic.c =================================================================== --- src/main/arithmetic.c (revision 80996) +++ src/main/arithmetic.c (working copy) @@ -117,7 +117,7 @@ /* The gcc shipping with Fedora 9 gets this wrong without * the volatile declaration. Thanks to Marc Schwartz. */ volatile ieee_double x; - x.word[hw] = 0x7ff00000; + x.word[hw] = 0x7ff80000; x.word[lw] = 1954; return x.value; } We get a ~25x speedup: x <- t(1:1e7+1L) system.time(rowSums(x)) ## user system elapsed ## 0.068 0.000 0.068 This despite no NAs anywhere in sight. I observe the slow behavior on both Skylake, Coffee Lake 2 and others, across different OSes, so long as the -O2 compilation flag is used. This likely happens because the compiler tries to prepare for the `keepNA` branch in[1]: case INTSXP: { int *ix = INTEGER(x) + (R_xlen_t)n*j; for (cnt = 0, sum = 0., i = 0; i < n; i++, ix++) if (*ix != NA_INTEGER) {cnt++; sum += *ix;} else if (keepNA) {sum = NA_REAL; break;} break; } by loading an NA_REAL into the FPU. At least that was my interpretation of the following machine code (dumped from src/main/array.o). I barely understand ASM, but it looks like 9bd4 loads R_NaReal, and this happens before the test for NA at 9be8: case LGLSXP: # looks like INTSXP/LGLSXP branches collapsed { int *ix = LOGICAL(x) + (R_xlen_t)n * j; 9bc8: 4d 01 e3 add r11,r12 for (R_xlen_t i = 0; i < n; i++, ra++, ix++) 9bcb: 48 85 db test rbx,rbx 9bce: 0f 8e fc fe ff ff jle 9ad0 <do_colsum+0x260> if (keepNA) { if (*ix != NA_LOGICAL) *ra += *ix; else *ra = NA_REAL; 9bd4: dd 05 00 00 00 00 fld QWORD PTR [rip+0x0] # 9bda <do_colsum+0x36a> 9bd6: R_X86_64_PC32 R_NaReal-0x4 9bda: 48 8b 95 60 ff ff ff mov rdx,QWORD PTR [rbp-0xa0] for (R_xlen_t i = 0; i < n; i++, ra++, ix++) 9be1: 31 c0 xor eax,eax 9be3: eb 2c jmp 9c11 <do_colsum+0x3a1> 9be5: 0f 1f 00 nop DWORD PTR [rax] if (*ix != NA_LOGICAL) *ra += *ix; 9be8: 45 39 d0 cmp r8d,r10d 9beb: 74 5b je 9c48 <do_colsum+0x3d8> 9bed: 44 89 85 78 ff ff ff mov DWORD PTR [rbp-0x88],r8d 9bf4: db 85 78 ff ff ff fild DWORD PTR [rbp-0x88] 9bfa: db 2a fld TBYTE PTR [rdx] 9bfc: de c1 faddp st(1),st 9bfe: db 3a fstp TBYTE PTR [rdx] ... SNIP 9c48: db 3a fstp TBYTE PTR [rdx] 9c4a: db 2a fld TBYTE PTR [rdx] 9c4c: eb b2 jmp 9c00 <do_colsum+0x390> If no NA_LOGICAL (NA_INTEGER) are encountered, the NaN is not used. However, it is always loaded, and for signaling NaNs this alone appears to switch the FPU to turtle mode. But more important than whether I can interpret ASM correctly (dubious), simply changing the NA_REAL value to be of the quiet variety dramatically improves performance of `rowSums` with integers. Ironically, this doesn't happen with the REALSXP branch because that one relies on NaN propagation in the FPU so doesn't load the NA_REAL for the early-break case when it encounters one. Of course if it does encounter a NaN, quiet or not, we get a slowdown. Compiling with -O3 also fixes this. Bad performance of `rowSums` on integers alone is not really that big a deal given the output is numeric, and that's why I never reported this despite having known about it for a while. But André's e-mail pushed me into saying something about it. There is a risk that code relies on the full bit pattern of NA_REAL, but I think those are probably broken currently since the signaling bit is even more unstable than the general payload bits. Best, B. [1]: https://github.com/r-devel/r-svn/blob/6891db49680629427e3d5927053531b8fa5d8ee3/src/main/array.c#L1939 [2]: https://cran.r-project.org/doc/manuals/r-release/R-data.html#Special-values > Best, > > luke > > >> >> Best, >> >> B. >> >> [1]: >> https://randomascii.wordpress.com/2012/05/20/thats-not-normalthe-performance-of-odd-floats/ >> [2]: https://en.wikipedia.org/wiki/NaN#Encoding >> >> >> >> >> >>> On Thursday, September 30, 2021, 06:52:59 AM EDT, GILLIBERT, Andre >>> <andre.gillib...@chu-rouen.fr> wrote: >>> >>> Dear R developers, >>> >>> By default, R uses the "long double" data type to get extra precision for >>> intermediate computations, with a small performance tradeoff. >>> >>> Unfortunately, on all Intel x86 computers I have ever seen, long doubles >>> (implemented in the x87 FPU) are extremely slow whenever a special >>> representation (NA, NaN or infinities) is used; probably because it >>> triggers poorly optimized microcode in the CPU firmware. A function such as >>> sum() becomes more than hundred times slower! >>> Test code: >>> a=runif(1e7);system.time(for(i in 1:100)sum(a)) >>> b=a;b[1]=NA;system.time(sum(b)) >>> >>> The slowdown factors are as follows on a few intel CPU: >>> >>> 1) Pentium Gold G5400 (Coffee Lake, 8th generation) with R 64 bits : >>> 140 times slower with NA >>> >>> 2) Pentium G4400 (Skylake, 6th generation) with R 64 bits : 150 times >>> slower with NA >>> >>> 3) Pentium G3220 (Haswell, 4th generation) with R 64 bits : 130 times >>> slower with NA >>> >>> 4) Celeron J1900 (Atom Silvermont) with R 64 bits : 45 times slower >>> with NA >>> >>> I do not have access to more recent Intel CPUs, but I doubt that it has >>> improved much. >>> >>> Recent AMD CPUs have no significant slowdown. >>> There is no significant slowdown on Intel CPUs (more recent than Sandy >>> Bridge) for 64 bits floating point calculations based on SSE2. Therefore, >>> operators using doubles, such as '+' are unaffected. >>> >>> I do not know whether recent ARM CPUs have slowdowns on FP64... Maybe >>> somebody can test. >>> >>> Since NAs are not rare in real-life, I think that it would worth an extra >>> check in functions based on long doubles, such as sum(). The check for >>> special representations do not necessarily have to be done at each >>> iteration for cumulative functions. >>> If you are interested, I can write a bunch of patches to fix the main >>> functions using long doubles: cumsum, cumprod, sum, prod, rowSums, colSums, >>> matrix multiplication (matprod="internal"). >>> >>> What do you think of that? >>> >>> -- >>> Sincerely >>> Andr� GILLIBERT >>> >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> R-devel@r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-devel >>> >> >> ______________________________________________ >> R-devel@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-devel > >> > > -- > Luke Tierney > Ralph E. Wareham Professor of Mathematical Sciences > University of Iowa Phone: 319-335-3386 > Department of Statistics and Fax: 319-335-3017 > Actuarial Science > 241 Schaeffer Hall email: luke-tier...@uiowa.edu > Iowa City, IA 52242 WWW: http://www.stat.uiowa.edu > > ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel