[Llvm-bgq-discuss] QPX SLEEF (a SIMD math library)

[Hal Finkel]

Hello everyone,

I've completed an initial port of Naoki Shibata's SLEEF (SIMD Library for Evaluating Elementary Functions) to the BG/Q. For our purposes, the library is an open-source (public domain) alternative to libmass_simd. Most functions are slower than libmass_simd, but tend to be more accurate, and handle corner cases (and infinitys, nans, etc.) better than libmass_simd (and are still much faster than computing 4 x the scalar function).

You don't need any special compiler flags to use the library with bgclang. To use with bgxlc, add: -I/home/projects/llvm/sleef/include -L/home/projects/llvm/sleef/lib -lsleef

With either compiler, you'll need to: #include <qpxmath.h>

The following functions are provided:
vector4double xldexp(vector4double x, const int *q);
void xilogb(vector4double d, int *l);

vector4double xsin(vector4double d);
vector4double xcos(vector4double d);
void xsincos(vector4double d, vector4double *ds, vector4double *dc);
vector4double xtan(vector4double d);
vector4double xasin(vector4double s);
vector4double xacos(vector4double s);
vector4double xatan(vector4double s);
vector4double xatan2(vector4double y, vector4double x);
vector4double xlog(vector4double d);
vector4double xexp(vector4double d);
vector4double xpow(vector4double x, vector4double y);

vector4double xsinh(vector4double d);
vector4double xcosh(vector4double d);
vector4double xtanh(vector4double d);
vector4double xasinh(vector4double s);
vector4double xacosh(vector4double s);
vector4double xatanh(vector4double s);

vector4double xcbrt(vector4double d);

vector4double xexp2(vector4double a);
vector4double xexp10(vector4double a);
vector4double xexpm1(vector4double a);
vector4double xlog10(vector4double a);
vector4double xlog1p(vector4double a);

vector4double xsin_u1(vector4double d);
vector4double xcos_u1(vector4double d);
void xsincos_u1(vector4double d, vector4double *ds, vector4double *dc);
vector4double xtan_u1(vector4double d);
vector4double xasin_u1(vector4double s);
vector4double xacos_u1(vector4double s);
vector4double xatan_u1(vector4double s);
vector4double xatan2_u1(vector4double y, vector4double x);
vector4double xlog_u1(vector4double d);
vector4double xcbrt_u1(vector4double d);

plus single precision versions (which are named like the double-precision variants but have an 'f' as a suffix like this):
...
vector4double xsinf(vector4double d);
vector4double xcosf(vector4double d);
...
vector4double xsinf_u1(vector4double d);
vector4double xcosf_u1(vector4double d);
...

I've attached a file (sleef-vs-mass-simd.txt) showing cycle counts for all of the SLEEF functions, the corresponding libmass_simd functions, and 4 x the cost of the reference libm function. I've also attached a file (sleef-max-error.txt) showing the maximum error (in ULPs) for all of the SLEEF functions. The error can be compared to those for the corresponding libmass_simd functions documented here: http://www-01.ibm.com/support/docview.wss?uid=swg27006978

For convenience, if you define QPXMATH_MASS_SIMD_FUNCTIONS before including the qpxmath.h header, aliases will also be defined for libmass_simd function names (sind4, etc.). Note, however, that libmass_simd provides some functions not (yet) provided here. Also, SLEEF provides vectorized ldexp and ilogb functions (which libmass_simd does not provide).

The patches to SLEEF are available in the llvm-bgq archives (https://trac.alcf.anl.gov/projects/llvm-bgq/), and the source code will compile with bgxlc as well (it is C + bgxlc-style intrinsics). The performance when compiling with bgclang is *much* better, however, so I recommend that you use bgclang (and, at ALCF, you can use my build as detailed above). Regardless, the same libraries can be used from either compiler. SLEEF itself is from: http://shibatch.sourceforge.net/

 -Hal

-- 
Hal Finkel
Assistant Computational Scientist
Leadership Computing Facility
Argonne National Laboratory
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