[PATCH] Improve performance of sinf/cosf/sincosf
Corinna Vinschen
vinschen@redhat.com
Mon Jun 18 12:28:00 GMT 2018
On Jun 8 12:49, Wilco Dijkstra wrote:
> This patch is a complete rewrite of sinf, cosf and sincosf. The new version
> is significantly faster, as well as simple and accurate.
> The worst-case ULP is 0.56072, maximum relative error is 0.5303p-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 - on some targets this may
> be slow, so this can be configured to use floating point comparisons.
>
> 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.
>
> The speedup factor on AArch64 for various ranges:
>
> range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
> range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
> range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
> range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
> range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
> range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
>
>
> ChangeLog:
> 2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
>
> * newlib/libm/common/Makefile.in: Regenerated.
> * newlib/libm/common/Makefile.am: Add sf_sin.c, sf_cos.c, sf_sincos.c
> sf_sincos.h, sf_sincos_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
> * newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
> roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
> eval_as_double, likely, unlikely.
> * newlib/libm/common/sf_cos.c: New file.
> * newlib/libm/common/sf_sin.c: Likewise.
> * newlib/libm/common/sf_sincos.h: Likewise.
> * newlib/libm/common/sf_sincos.c: Likewise.
> * newlib/libm/common/sf_sincos_data.c: Likewise.
> * newlib/libm/math/sf_cos.c: Add #if to build conditionally.
> * newlib/libm/math/sf_sin.c: Likewise.
> * newlib/libm/math/wf_sincos.c: Likewise.
I tested this patch on Cygwin and it breaks the build:
ld: Cannot export cosf: symbol not defined
ld: Cannot export sinf: symbol not defined
x86_64-pc-cygwin/newlib/libm/libm.a(lib_a-ccosf.o): In function `ccosf':
newlib/libm/complex/ccosf.c:46: undefined reference to `sinf'
newlib/libm/complex/ccosf.c:46:(.text+0x6e): relocation truncated to fit: R_X86_64_PC32 against undefined symbol `sinf'
newlib/libm/complex/ccosf.c:46: undefined reference to `cosf'
[etc]
Somehow sinf and cosf disappeard...
Corinna
--
Corinna Vinschen
Cygwin Maintainer
Red Hat
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