Current implementations fail to consider half-float packets, only
half-float scalars. Added specializations for packets on AVX, AVX512 and
NEON. Added tests to `special_packetmath`.
The current `special_functions` tests would fail for half and bfloat16 due to
lack of precision. The NEON tests also fail with precision issues and
due to different handling of `sqrt(inf)`, so special functions bessel, ndtri
have been disabled.
Tested with AVX, AVX512.
This allows the `packetmath` tests to pass for AVX512 on skylake.
Made `half` and `bfloat16` consistent in terms of ops they support.
Note the `log` tests are currently disabled for `bfloat16` since
they fail due to poor precision (they were previously disabled for
`Packet8bf` via test function specialization -- I just removed that
specialization and disabled it in the generic test).
Minimal implementation of AVX `Eigen::half` ops to bring in line
with `bfloat16`. Allows `packetmath_13` to pass.
Also adjusted `bfloat16` packet traits to match the supported set
of ops (e.g. Bessel is not actually implemented).
The AVX half implementation is incomplete, causing the `packetmath_13` test
to fail. This disables the test.
Also refactored the existing AVX implementation to use `bit_cast`
instead of direct access to `.x`.
This change also contains a few minor cleanups:
1. Remove packet op pnot, which is not needed for anything other than pcmp_le_or_nan,
which can be done in other ways.
2. Remove the "HasInsert" enum, which is no longer needed since we removed the
corresponding packet ops.
3. Add faster pselect op for Packet4i when SSE4.1 is supported.
Among other things, this makes the fast transposeInPlace() method available for Matrix<bool>.
Run on ************** (72 X 2994 MHz CPUs); 2020-05-09T10:51:02.372347913-07:00
CPU: Intel Skylake Xeon with HyperThreading (36 cores) dL1:32KB dL2:1024KB dL3:24MB
Benchmark Time(ns) CPU(ns) Iterations
-----------------------------------------------------------------------
BM_TransposeInPlace<float>/4 9.77 9.77 71670320
BM_TransposeInPlace<float>/8 21.9 21.9 31929525
BM_TransposeInPlace<float>/16 66.6 66.6 10000000
BM_TransposeInPlace<float>/32 243 243 2879561
BM_TransposeInPlace<float>/59 844 844 829767
BM_TransposeInPlace<float>/64 933 933 750567
BM_TransposeInPlace<float>/128 3944 3945 177405
BM_TransposeInPlace<float>/256 16853 16853 41457
BM_TransposeInPlace<float>/512 204952 204968 3448
BM_TransposeInPlace<float>/1k 1053889 1053861 664
BM_TransposeInPlace<bool>/4 14.4 14.4 48637301
BM_TransposeInPlace<bool>/8 36.0 36.0 19370222
BM_TransposeInPlace<bool>/16 31.5 31.5 22178902
BM_TransposeInPlace<bool>/32 111 111 6272048
BM_TransposeInPlace<bool>/59 626 626 1000000
BM_TransposeInPlace<bool>/64 428 428 1632689
BM_TransposeInPlace<bool>/128 1677 1677 417377
BM_TransposeInPlace<bool>/256 7126 7126 96264
BM_TransposeInPlace<bool>/512 29021 29024 24165
BM_TransposeInPlace<bool>/1k 116321 116330 6068
This will allow us to define multiple packet types backed by the same vector type, e.g., __m128i.
Use this machanism to define packets for half and clean up the packet op implementations.
This provides a new op that matches std::rint and previous behavior of
pround. Also adds corresponding unsupported/../Tensor op.
Performance is the same as e. g. floor (tested SSE/AVX).
This change re-instates the fast rational approximation of the logistic function for float32 in Eigen (removed in 66f07efeae), but uses the more accurate approximation 1/(1+exp(-1)) ~= exp(x) below -9. The exponential is only calculated on the vectorized path if at least one element in the SIMD input vector is less than -9.
This change also contains a few improvements to speed up the original float specialization of logistic:
- Introduce EIGEN_PREDICT_{FALSE,TRUE} for __builtin_predict and use it to predict that the logistic-only path is most likely (~2-3% speedup for the common case).
- Carefully set the upper clipping point to the smallest x where the approximation evaluates to exactly 1. This saves the explicit clamping of the output (~7% speedup).
The increased accuracy for tanh comes at a cost of 10-20% depending on instruction set.
The benchmarks below repeated calls
u = v.logistic() (u = v.tanh(), respectively)
where u and v are of type Eigen::ArrayXf, have length 8k, and v contains random numbers in [-1,1].
Benchmark numbers for logistic:
Before:
Benchmark Time(ns) CPU(ns) Iterations
-----------------------------------------------------------------
SSE
BM_eigen_logistic_float 4467 4468 155835 model_time: 4827
AVX
BM_eigen_logistic_float 2347 2347 299135 model_time: 2926
AVX+FMA
BM_eigen_logistic_float 1467 1467 476143 model_time: 2926
AVX512
BM_eigen_logistic_float 805 805 858696 model_time: 1463
After:
Benchmark Time(ns) CPU(ns) Iterations
-----------------------------------------------------------------
SSE
BM_eigen_logistic_float 2589 2590 270264 model_time: 4827
AVX
BM_eigen_logistic_float 1428 1428 489265 model_time: 2926
AVX+FMA
BM_eigen_logistic_float 1059 1059 662255 model_time: 2926
AVX512
BM_eigen_logistic_float 673 673 1000000 model_time: 1463
Benchmark numbers for tanh:
Before:
Benchmark Time(ns) CPU(ns) Iterations
-----------------------------------------------------------------
SSE
BM_eigen_tanh_float 2391 2391 292624 model_time: 4242
AVX
BM_eigen_tanh_float 1256 1256 554662 model_time: 2633
AVX+FMA
BM_eigen_tanh_float 823 823 866267 model_time: 1609
AVX512
BM_eigen_tanh_float 443 443 1578999 model_time: 805
After:
Benchmark Time(ns) CPU(ns) Iterations
-----------------------------------------------------------------
SSE
BM_eigen_tanh_float 2588 2588 273531 model_time: 4242
AVX
BM_eigen_tanh_float 1536 1536 452321 model_time: 2633
AVX+FMA
BM_eigen_tanh_float 1007 1007 694681 model_time: 1609
AVX512
BM_eigen_tanh_float 471 471 1472178 model_time: 805
This also adds pset1frombits helper to Packet[24]d.
Makes round ~45% slower for SSE: 1.65µs ± 1% before vs 2.45µs ± 2% after,
stil an order of magnitude faster than scalar version: 33.8µs ± 2%.
- Split SpecialFunctions files in to a separate BesselFunctions file.
In particular add:
- Modified bessel functions of the second kind k0, k1, k0e, k1e
- Bessel functions of the first kind j0, j1
- Bessel functions of the second kind y0, y1
Depending on instruction set, significant speedups are observed for the vectorized path:
log1p wall time is reduced 60-93% (2.5x - 15x speedup)
expm1 wall time is reduced 0-85% (1x - 7x speedup)
The scalar path is slower by 20-30% due to the extra branch needed to handle +infinity correctly.
Full benchmarks measured on Intel(R) Xeon(R) Gold 6154 here: https://bitbucket.org/snippets/rmlarsen/MXBkpM
- no FMA: 1ULP up to 3pi, 2ULP up to sin(25966) and cos(18838), fallback to std::sin/cos for larger inputs
- FMA: 1ULP up to sin(117435.992) and cos(71476.0625), fallback to std::sin/cos for larger inputs
This is a preparation to a change on gebp_traits, where a new template
argument will be introduced to dictate the packet size, so it won't be
bound to the current/max packet size only anymore.
By having packet types defined early on gebp_traits, one has now to
act on packet types, not scalars anymore, for the enum values defined
on that class. One approach for reaching the vectorizable/size
properties one needs there could be getting the packet's scalar again
with unpacket_traits<>, then the size/Vectorizable enum entries from
packet_traits<>. It turns out guards like "#ifndef
EIGEN_VECTORIZE_AVX512" at AVX/PacketMath.h will hide smaller packet
variations of packet_traits<> for some types (and it makes sense to
keep that). In other words, one can't go back to the scalar and create
a new PacketType, as this will always lead to the maximum packet type
for the architecture.
The less costly/invasive solution for that, thus, is to add the
vectorizable info on every unpacket_traits struct as well.