The previous implementations produced garbage values if the exponent did
not fit within the exponent bits. See #2131 for a complete discussion,
and !375 for other possible implementations.
Here we implement the 4-factor version. See `pldexp_impl` in
`GenericPacketMathFunctions.h` for a full description.
The SSE `pcmp*` methods were moved down since `pcmp_le<Packet4i>`
requires `por`.
Left as a "TODO" is to delegate to a faster version if we know the
exponent does fit within the exponent bits.
Fixes#2131.
I ran some testing (comparing to `std::pow(double(x), double(y)))` for `x` in the set of all (positive) floats in the interval `[std::sqrt(std::numeric_limits<float>::min()), std::sqrt(std::numeric_limits<float>::max())]`, and `y` in `{2, sqrt(2), -sqrt(2)}` I get the following error statistics:
```
max_rel_error = 8.34405e-07
rms_rel_error = 2.76654e-07
```
If I widen the range to all normal float I see lower accuracy for arguments where the result is subnormal, e.g. for `y = sqrt(2)`:
```
max_rel_error = 0.666667
rms = 6.8727e-05
count = 1335165689
argmax = 2.56049e-32, 2.10195e-45 != 1.4013e-45
```
which seems reasonable, since these results are subnormals with only couple of significant bits left.
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).
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.
