A practical algorithm for exact array dependence analysis
Communications of the ACM
Computing large sparse Jacobian matrices using automatic differentiation
SIAM Journal on Scientific Computing
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A unified approach to global program optimization
POPL '73 Proceedings of the 1st annual ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Dependence Analysis for Supercomputing
Dependence Analysis for Supercomputing
Adjoining independent computations
Automatic differentiation of algorithms
The Power Test for Data Dependence
IEEE Transactions on Parallel and Distributed Systems
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Preprocessing for quadratic programming
Mathematical Programming: Series A and B
Representation-independent program analysis
PASTE '05 Proceedings of the 6th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
"To be recorded" analysis in reverse-mode automatic differentiation
Future Generation Computer Systems
OpenAD/F: A Modular Open-Source Tool for Automatic Differentiation of Fortran Codes
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.00 |
Linearity analysis determines which variables depend on which other variables and whether the dependence is linear or nonlinear. One of the many applications of this analysis is determining whether a loop involves only linear loop-carried dependences and therefore the adjoint of the loop may be reversed and fused with the computation of the original function. This paper specifies the data-flow equations that compute linearity analysis. In addition, the paper describes using linearity analysis with array dependence analysis to determine whether a loop-carried dependence is linear or nonlinear.