The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
All Algebraic Functions Can Be Computed Fast
Journal of the ACM (JACM)
The Area-Time Complexity of Binary Multiplication
Journal of the ACM (JACM)
Computer Arithmetic: Logic and Design
Computer Arithmetic: Logic and Design
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Functions Equivalent to Integer Multiplication
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Area-Time Optimal VLSI Networks for Computing Integer Multiplications and Discrete Fourier Transform
Proceedings of the 8th Colloquium on Automata, Languages and Programming
The Classifikation of Problems which have Fast Parallel Algorithms
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Comparison of arithmetic functions with respect to boolean circuit depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Numerical Methods
Optimal size integer division circuits
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Private collaborative forecasting and benchmarking
Proceedings of the 2004 ACM workshop on Privacy in the electronic society
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Methods are presented for finding reductions between the computations of certain arithmetic functions that preserve asymptotic Boolean complexities (circuit depth or size). They can be used to show, for example, that all nonlinear algebraic functions are as difficult as integer multiplication with respect to circuit size. As a consequence, any lower or upper bound (e.g., O(n log n log log n)) for one of them applies to the whole class. It is also shown that, with respect to depth and size simultaneously, multiplication is reducible to any nonlinear and division to any nonpolynomial algebraic function.