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.
ea5c662c62 Improve performance of sincosf
ChangeLog | 14 +++
math/Makefile | 2 +-
sysdeps/ia64/fpu/s_sincosf_data.c | 1 +
sysdeps/ieee754/flt-32/s_sincosf.c | 196 ++++++++++---------------------
sysdeps/ieee754/flt-32/s_sincosf.h | 118 +++++++++++++++++++
sysdeps/ieee754/flt-32/s_sincosf_data.c | 74 ++++++++++++
sysdeps/m68k/m680x0/fpu/s_sincosf_data.c | 1 +
sysdeps/x86_64/fpu/s_sincosf_data.c | 1 +
8 files changed, 274 insertions(+), 133 deletions(-)