Add <sincosf_poly.h> and include it in s_sincosf.h to allow vectorized
sincosf_poly. Add x86 sincosf_poly.h to vectorize sincosf_poly. On
Broadwell, bench-sincosf shows:
Before After Improvement
max 160.273 114.198 40%
min 6.25 5.625 11%
mean 13.0325 10.6462 22%
Vectorized sincosf_poly shows
Before After Improvement
max 138.653 114.198 21%
min 5.004 5.625 -11%
mean 11.5934 10.6462 9%
Tested on x86-64 and i686 as well as with build-many-glibcs.py.
* sysdeps/ieee754/flt-32/s_sincosf.h: Include <sincosf_poly.h>.
(sincos_t, sincosf_poly, sinf_poly): Moved to ...
* sysdeps/ieee754/flt-32/sincosf_poly.h: Here. New file.
* sysdeps/x86/fpu/s_sincosf_data.c: New file.
* sysdeps/x86/fpu/sincosf_poly.h: Likewise.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include
<sysdeps/ieee754/flt-32/s_sincosf.c>.
The second patch improves performance of sinf and cosf using the same
algorithms and polynomials. The returned values are identical to sincosf
for the same input. ULP definitions for AArch64 and x64 are updated.
sinf/cosf througput gains on Cortex-A72:
* |x| < 0x1p-12 : 1.2x
* |x| < M_PI_4 : 1.8x
* |x| < 2 * M_PI: 1.7x
* |x| < 120.0 : 2.3x
* |x| < Inf : 3.0x
* NEWS: Mention sinf, cosf, sincosf.
* sysdeps/aarch64/libm-test-ulps: Update ULP for sinf, cosf, sincosf.
* sysdeps/x86_64/fpu/libm-test-ulps: Update ULP for sinf and cosf.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Add definitions of
constants rather than including generic sincosf.h.
* sysdeps/x86_64/fpu/s_sincosf_data.c: Remove.
* sysdeps/ieee754/flt-32/s_cosf.c (cosf): Rewrite.
* sysdeps/ieee754/flt-32/s_sincosf.h (reduced_sin): Remove.
(reduced_cos): Remove.
(sinf_poly): New function.
* sysdeps/ieee754/flt-32/s_sinf.c (sinf): Rewrite.
This patch is a complete rewrite of sincosf. The new version is
significantly faster, as well as simple and accurate.
The worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23 over
all 4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
sincosf throughput gains on Cortex-A72:
* |x| < 0x1p-12 : 1.6x
* |x| < M_PI_4 : 1.7x
* |x| < 2 * M_PI: 1.5x
* |x| < 120.0 : 1.8x
* |x| < Inf : 2.3x
* math/Makefile: Add s_sincosf_data.c.
* sysdeps/ia64/fpu/s_sincosf_data.c: New file.
* sysdeps/ieee754/flt-32/s_sincosf.h (abstop12): Add new function.
(sincosf_poly): Likewise.
(reduce_small): Likewise.
(reduce_large): Likewise.
* sysdeps/ieee754/flt-32/s_sincosf.c (sincosf): Rewrite.
* sysdeps/ieee754/flt-32/s_sincosf_data.c: New file with sincosf data.
* sysdeps/m68k/m680x0/fpu/s_sincosf_data.c: New file.
* sysdeps/x86_64/fpu/s_sincosf_data.c: New file.
