]> sourceware.org Git - newlib-cygwin.git/commit
Improve performance of sinf/cosf/sincosf
authorWilco Dijkstra <Wilco.Dijkstra@arm.com>
Mon, 18 Jun 2018 17:59:37 +0000 (17:59 +0000)
committerCorinna Vinschen <corinna@vinschen.de>
Tue, 19 Jun 2018 07:44:28 +0000 (09:44 +0200)
commitfca80a9d1b3fa6620cdaccec6b726eef1a6530a1
tree7a64a4ce10e95213c13b888b38be7ac3618ceb24
parent9dd3c3b0ad176683e2c004cb1c734588b63e59d7
Improve performance of sinf/cosf/sincosf

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.

Simple benchmark showing 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:
2018-06-18  Wilco Dijkstra  <wdijkstr@arm.com>

        * newlib/libm/common/Makefile.in: Regenerated.
        * newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
        sincosf.h, sincosf_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/cosf.c: New file.
        * newlib/libm/common/sinf.c: Likewise.
        * newlib/libm/common/sincosf.h: Likewise.
        * newlib/libm/common/sincosf.c: Likewise.
        * newlib/libm/common/sincosf_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.

--
newlib/libm/common/Makefile.am
newlib/libm/common/Makefile.in
newlib/libm/common/cosf.c [new file with mode: 0644]
newlib/libm/common/math_config.h
newlib/libm/common/sincosf.c [new file with mode: 0644]
newlib/libm/common/sincosf.h [new file with mode: 0644]
newlib/libm/common/sincosf_data.c [new file with mode: 0644]
newlib/libm/common/sinf.c [new file with mode: 0644]
newlib/libm/math/sf_cos.c
newlib/libm/math/sf_sin.c
newlib/libm/math/wf_sincos.c
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