Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
SIAM Journal on Scientific Computing
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Efficient derivative computations in neutron scattering via interface contraction
Proceedings of the 2002 ACM symposium on Applied computing
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Explicit Loop Scheduling in OpenMP for Parallel Automatic Differentiation
HPCS '02 Proceedings of the 16th Annual International Symposium on High Performance Computing Systems and Applications
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For functions given in the form of a computer program, automatic differentiation is an efficient technique to accurately evaluate the derivatives of that function. Starting from a given computer program, automatic differentiation generates another program for the evaluation of the original function and its derivatives in a fully mechanical way. While the efficiency of this black box approach is already high as compared to numerical differentiation based on divided differences, automatic differentiation can be applied even more efficiently by taking into account high-level knowledge about the given computer program. We show that, in the case where the function involves a Fourier transform, the degree of parallelism in the program generated by automatic differentiation can be increased leading to a rich set of automatic parallelization strategies that are not available when employing a black box automatic parallelization approach. Experiments of the new automatic parallelization approach are reported on a SunFire 6800 server using up to 20 processors.