v4: - Added empty s_sincosf_data.c on targets with their own sincosf. - Moved round/converttoint changes in math_private.h to separate patch. 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. 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 On a benchmark with significant use of sincosf the overall speedup is >33%. ChangeLog: 2018-07-06 Wilco Dijkstra Szabolcs Nagy * math/Makefile: Add s_sincosf_data.c. * sysdeps/ia64/fpu/s_sincosf_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h (PREFER_FLOAT_COMPARISON): Define. * 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. --- math/Makefile | 2 +- sysdeps/ia64/fpu/s_sincosf_data.c | 1 + sysdeps/ieee754/flt-32/math_config.h | 3 + sysdeps/ieee754/flt-32/s_sincosf.c | 197 ++++++++++--------------------- sysdeps/ieee754/flt-32/s_sincosf.h | 119 +++++++++++++++++++ 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, 265 insertions(+), 133 deletions(-) create mode 100644 sysdeps/ia64/fpu/s_sincosf_data.c create mode 100644 sysdeps/ieee754/flt-32/s_sincosf_data.c create mode 100644 sysdeps/m68k/m680x0/fpu/s_sincosf_data.c create mode 100644 sysdeps/x86_64/fpu/s_sincosf_data.c