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.
6 files changed