## Abstract

The analysis and modification of numerical programs in the context of

generating and optimizing adjoint code automatically probably ranges among the

technically and theoretically most challenging source transformation algorithms

known today. A complete compiler for the target language (Fortran in our case) is

needed to cover the technical side. This amounts to a mathematically motivated

semantic transformation of the source code that involves the reversal of the flow

of data through the program. Both the arithmetic complexity and the memory

requirement can be substantial for large-scale numerical simulations. Finding the

optimal data-flow reveral schedule turns out to be an NP-complete problem. The

same complexity result applies to other domain-specific peephole optimizations.

In this paper we present a first research prototype of the NAGWare Fortran

compiler with the ability to generate adjoint code automatically. Moreover, we

discuss an approach to generating second-order adjoint code for use in Newtontype algorithms for unconstrained nonlinear optimization. While the focus of this paper is mostly on the compiler issues some information on the mathematical background will be found helpful for motivational purposes

generating and optimizing adjoint code automatically probably ranges among the

technically and theoretically most challenging source transformation algorithms

known today. A complete compiler for the target language (Fortran in our case) is

needed to cover the technical side. This amounts to a mathematically motivated

semantic transformation of the source code that involves the reversal of the flow

of data through the program. Both the arithmetic complexity and the memory

requirement can be substantial for large-scale numerical simulations. Finding the

optimal data-flow reveral schedule turns out to be an NP-complete problem. The

same complexity result applies to other domain-specific peephole optimizations.

In this paper we present a first research prototype of the NAGWare Fortran

compiler with the ability to generate adjoint code automatically. Moreover, we

discuss an approach to generating second-order adjoint code for use in Newtontype algorithms for unconstrained nonlinear optimization. While the focus of this paper is mostly on the compiler issues some information on the mathematical background will be found helpful for motivational purposes

Original language | English |
---|---|

Publisher | RWTH Aachen |

Number of pages | 17 |

Publication status | Published - 2007 |

### Publication series

Name | RWTH Aachen, Dept Comp Science, Technical report |
---|---|

No. | AIB TR 2007-13 |