Numerical precision control and GRACE

The control of the numerical precision of large-scale computations like those generated by the GRACE system for automatic Feynman diagram calculations has become an intrinsic part of those packages. Recently, Hitachi Ltd. has developed in FORTRAN a new library HMLIB for quadruple and octuple precision arithmetic where the number of lost-bits is made available. This library has been tested with success on the 1-loop radiative correction to e+e-→e+e-τ+τ-e+e-→e+e-τ+τ-. It is shown that the approach followed by HMLIB provides an efficient way to track down the source of numerical significance losses and to deliver high-precision results yet minimizing computing time.