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Merged
merged 35 commits into from
Apr 26, 2020
Merged

Spin-weighted spherical harmonics and refactored use of SIMD #43

merged 35 commits into from
Apr 26, 2020

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MikaelSlevinsky
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New features in this PR:

  • Support for spin-weighted spherical harmonic transforms. They are orthonormalized in L^2, with the complex Fourier series as longitudinal basis and with complex coefficients.
  • Three new functions (x2 for float/double) for Horner's rule and Clenshaw's algorithm for Chebyshev series and for orthogonal polynomial series as well.

Improvements in this PR:

  • The code is now designed with a cross-compiler in mind. For performance-critical tasks, SIMD is hidden from the user interface and instead is dispatched based on CPU ID. This allows a cross-compiler to include functions with more advanced SIMD than legal for the host computer, but a runtime check ensures that only the best SIMD level is dispatched (closes Do not declare backups if Intel instruction sets are not available #12 and Use runtime checks to dispatch on SIMD #41).
  • The computational kernels for the spherical/triangular/disk harmonics are refactored to not only use the correct types of registers, but also help the compiler maximize throughput. This relies on a property of Givens rotations that two adjacent rotations commute if they do not act on the same rows. This property allows one to re-order the Givens rotations to increase the ratio of computation to memory loads/stores. The computational kernels and execute drivers are largely generated by a macro, which means the code may already be prepared for AVX-1024 when the instruction sets are available in GCC. Part of this is the introduction of the ft_simd struct to store a bit-field of a variety of SIMD extensions.
  • The real-to-real FFTW routines now use fftw_execute_dft_r2c and fftw_execute_dft_r2c instead of FFTW_R2HC and FFTW_HC2R-type real-to-real transforms to avoid a global transpose of the data.
  • The performance benchmark timings were not scaling as O(n3) because one needs to call a function a few times, typically at least twice, before peak performance is realized. These are now updated and the macro FT_TIME helps to bring this support system-wide.

New Examples in this PR:

  • spinweighted.c is a basic tutorial on how to use spin-weighted spherical harmonic transforms.

Releases no longer trigger the attachment of binaries, as compilation with -march=native may fail on a host computer.

@MikaelSlevinsky
start vectorized recurrence summation
2c3bf3d 
The template for Horner's rule is:

ft_horner(n, c, incc, m, x, f)

For Clenshaw's algorithm, it's

ft_clenshaw(n, c, incc, m, x, f)

The coefficients have stride incc, but the points and the output array must be contiguous.

The points and output pointers may be aliased so that in-place evaluation can work with one array for x and f.

The design is as follows:
1. Find the native SIMD flags on the machine that is compiling the code.
2. Define as many internal functions using the highest level of SIMD with SIMD flags. Otherwise, define fallbacks.
3. Define the exported functions with SIMD dispatch based on GCC's cpuid.

This approach allows one to cross-compile and generate optimal code for machines that are as good as the cross compiler. It also allows the code to be callable from machines that are newer than the cross compiler (in case the cross compiler is not state-of-the-art) due to the fallbacks, though newer SIMD is not accessible.
@MikaelSlevinsky
attempt to fix appveyor
6b10664
@MikaelSlevinsky
attempt to fix linux builds
8b5047e 
The reported error is:

/usr/bin/ld: /tmp/ccuNTFaV.o: relocation R_X86_64_PC32 against undefined symbol `memset@@GLIBC_2.2.5' can not be used when making a shared object; recompile with -fPIC
500/usr/bin/ld: final link failed: Bad value
@MikaelSlevinsky
windows fix bis
99d46df
@MikaelSlevinsky
link too?
0785e0a
@MikaelSlevinsky
add tests for AVX512F
e79da25 
apparently, linux build machines already have it
@MikaelSlevinsky
check SIMD checks
720988b
@MikaelSlevinsky
AVX512F is an extended feature, which needs to be checked with __get_…
5218346 
…cpuid_count(7, ...)
@MikaelSlevinsky
attempt cpuid
74e031a
@MikaelSlevinsky
fix spacing
17b8307
@MikaelSlevinsky
temporarily remove the recurrence module
0fc3695
@MikaelSlevinsky
separate assembly from source in an attempt to get library flags clos…
e900e57 
…er to source?
@MikaelSlevinsky
flatten the directory tree?
7176171
@MikaelSlevinsky
specify the assembly wihout *
864ac1e
@MikaelSlevinsky
gotta pump up those levels
7b0eaa4
@MikaelSlevinsky
Le commencement du grand dérangement
9b21c11
@MikaelSlevinsky
double4 => double8
75fbfe0
@MikaelSlevinsky
restore all drivers tests
42a43ce
@MikaelSlevinsky
make the addition theorem work for any degree-n Legendre polynomial
01d2400 
not just degree 4
@MikaelSlevinsky
cleanup execute_sph and kernel_sph
0cd54fc
@MikaelSlevinsky
does this hack fix the bug?
4739a3b
@MikaelSlevinsky
fftw_execute_r2r => fftw_execute_dft_c2r
deaaea7 
The dft_c2r obviates the need for a global transpose (in colswap) outside the fftw call. Instead, it requires setting and extracting some data from fftw_complex arrays.
@MikaelSlevinsky
complex.h is apparently not always loaded in cblas.h
a75dcb9
@MikaelSlevinsky
add spin-weighted spherical harmonic transforms!
3603fd8
@MikaelSlevinsky
try to remove most warnings across gcc versions & platforms
ca9595e 
up error tolerance for triangular transforms for Windows
@MikaelSlevinsky
ok better fix
daf7bfa
@MikaelSlevinsky
revert fix
44cfc8a 
no warning in gcc-8 is a warning in gcc-7 and vice versa
@MikaelSlevinsky
refactor disk harmonic drivers!
6e3e33b
@MikaelSlevinsky
remove commented code
7d95c54
@MikaelSlevinsky
finish cleaning up test_drivers and test_fftw
13dfcb0
@MikaelSlevinsky MikaelSlevinsky merged commit decaec0 into master Apr 26, 2020
@MikaelSlevinsky MikaelSlevinsky deleted the feat-recurrence-simd branch April 26, 2020 15:29
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Do not declare backups if Intel instruction sets are not available
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@MikaelSlevinsky