- 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
Commit c53eececb0
introduced AVX512 support for complex numbers but required
avx512dq to build. Commit 1d683ae2f5
fixed some but not, it would seem all,
of the hard avx512dq dependencies. Build failures are still evident on
Eigen and TensorFlow when compiling with just avx512f and no avx512dq
using gcc 7.3. Looking at the code there does indeed seem to be a problem.
Commit c53eececb0
calls avx512dq intrinsics directly, e.g, _mm512_extractf32x8_ps
and _mm512_and_ps. This commit fixes the issue by replacing the direct
intrinsic calls with the various wrapper functions that are safe to use on
avx512f only builds.
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The patch works by altering the gebp lhs packing routines to also
consider ½ and ¼ packet lenght rows when packing, besides the original
whole package and row-by-row attempts. Finally, gebp itself will try
to fit a fraction of a packet at a time if:
i) ½ and/or ¼ packets are available for the current context (e.g. AVX2
and SSE-sized SIMD register for x86)
ii) The matrix's height is favorable to it (it may be it's too small
in that dimension to take full advantage of the current/maximum
packet width or it may be the case that last rows may take
advantage of smaller packets before gebp goes row-by-row)
This helps mitigate huge slowdowns one had on AVX512 builds when
compared to AVX2 ones, for some dimensions. Gains top at an extra 1x
in throughput. This patch is a complement to changeset 4ad359237a
.
Since packing is changed, Eigen users which would go for very
low-level API usage, like TensorFlow, will have to be adapted to work
fine with the changes.
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.
- cleanup noise in imaginary part of real roots
- take into account the magnitude of the derivative to check roots.
- use <= instead of < at appropriate places
