  We describe a new implementation of the elementary transcendental functions
exp, sin, cos, log and atan for variable precision up to approximately 4096
bits. Compared to the MPFR library, we achieve a maximum speedup ranging from a
factor 3 for cos to 30 for atan. Our implementation uses table-based argument
reduction together with rectangular splitting to evaluate Taylor series. We
collect denominators to reduce the number of divisions in the Taylor series,
and avoid overhead by doing all multiprecision arithmetic using the mpn layer
of the GMP library. Our implementation provides rigorous error bounds.
