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.
