Improve performance of sinf/cosf/sincosf

Here is the correct patch with both filenames and int cast fixed:

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:
2018-05-18  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.

--

3 files changed, 7 insertions, 0 deletions

diff --git a/newlib/libm/math/sf_cos.c b/newlib/libm/math/sf_cos.c
index 4c0a9a5..8cb0eb0 100644
--- a/newlib/libm/math/sf_cos.c
+++ b/newlib/libm/math/sf_cos.c
@@ -14,6 +14,7 @@
  */
 
 #include "fdlibm.h"
+#if __OBSOLETE_MATH
 
 #ifdef __STDC__
 static const float one=1.0;
@@ -66,3 +67,4 @@ static float one=1.0;
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/math/sf_sin.c b/newlib/libm/math/sf_sin.c
index da81845..c3ec6e2 100644
--- a/newlib/libm/math/sf_sin.c
+++ b/newlib/libm/math/sf_sin.c
@@ -14,6 +14,7 @@
  */
 
 #include "fdlibm.h"
+#if __OBSOLETE_MATH
 
 #ifdef __STDC__
 	float sinf(float x)
@@ -60,3 +61,4 @@
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */
diff --git a/newlib/libm/math/wf_sincos.c b/newlib/libm/math/wf_sincos.c
index 477c604..69eb922 100644
--- a/newlib/libm/math/wf_sincos.c
+++ b/newlib/libm/math/wf_sincos.c
@@ -1,6 +1,8 @@
 /* sincos -- currently no more efficient than two separate calls to
    sin and cos. */
 #include "fdlibm.h"
+#if __OBSOLETE_MATH
+
 #include <errno.h>
 
 #ifdef __STDC__
@@ -31,3 +33,4 @@
   *cosx = cosf((float) x);
 }
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */