Abstract   We present a new version of TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding mixed derivatives. The new version fixes a potentially serious bug in the code for exponential-related functions that could corrupt the imaginary parts of derivatives, as well as being compatible with a wider range of compilers.    Program summary   Title of program:  TaylUR   Catalogue identifier:  ADXR_v2_0   Program summary URL:   http://cpc.cs.qub.ac.uk/summaries/ADXR_v2_0    Program obtainable from:  CPC Program Library, Queen's University of Belfast, N. Ireland   Licensing provisions:  none   Programming language used:  Fortran 95   Computer:  Any computer with a conforming Fortran 95 compiler   Operating system:  Any system with a conforming Fortran 95 compiler   No. of lines in distributed program, including test data, etc.:  6548   No. of bytes in distributed program, including test data, etc.:  17 468   Catalogue identifier of previous version:  ADXR_v1_0   Journal reference of previous version:  Comput. Phys. Comm. 174 (2006) 569–576   Does the new version supersede the previous version?:  yes   Distribution format: tar.gz   Nature of problem:  Problems that require potentially high orders of derivatives with respect to some variables or derivatives of complex-valued functions, such as, e.g., expansions of Feynman diagrams in particle masses in perturbative Quantum Field Theory.   Solution method:  Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type  taylor , which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faa di Bruno's formula.   Reasons for the new version:  The previous version [G.M. von Hippel, TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 174 (2006) 569–576] contained a potentially serious bug in the functions overloading the exponential-related intrinsics ( EXP ,  LOG ,  SIN ,  COS ,  TAN ,  SINH ,  COSH ,  TANH ), which could corrupt the imaginary parts of derivatives. It also contained some features which caused it to crash when compiled with certain compilers (notably the NAG and Lahey/Fujitsu compilers).   Summary of revisions:  The bug in the exponential-related intrinsics has been corrected. A number of additional changes have been made to the code to enable better compatibility with a greater range of compilers, including the NAG and Lahey/Fujitsu compilers. Users of some of these compilers may have to define  useintrinsic  as a preprocessor symbol when compiling TaylUR.   Restrictions:  Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders.   Unusual features:  No mixed higher-order derivatives are computed. The complex conjugation operation assumes all independent variables to be real.   Running time:  The running time of TaylUR operations depends linearly on the number of variables. Its dependence on the Taylor expansion order varies from linear (for linear operations) through quadratic (for multiplication) to exponential (for elementary function calls).
['G. M. Von Hippel']
New version announcement for TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95