D. Knuth, The Art of Computer Programming, Vol II: Seminumerical Algorithms, (1973). Home/Search Document Not in Database Summary Related Articles |
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Efficient and Exact Quantum Compression and Molecular Scale O° K.. - Reif (Correct)
....carry added algorithm. ffl Reversible Multiplication. see also Vedral, Barenco, Ekert [VBE96] Given N bit numbers x; y, we can reversibly compute the function: x; y) x; xy) in M(N) O(N log N log log N) reversible steps by use of the Schonhagen Strassen multiplication algorithm (see Knuth [K73]) On Making Reversible Functions Bijective. In a number of cases, we will required not only to reversibly compute a function f(x) but also if the function bijective (e.g. the SCHUMACHER function) we further require that we do not retain on output any record of the initial state, nor of the ....
.... log(2x) O(1) Let f(x) x log(x=e) Gamma 1 2 log(2x) and let its inverse function be f Gamma1 (y) The inverse x = f Gamma1 (y) can be approximately computed up to the required log x bits in time O(N log 2 N log log N) by the Newton iteration methods of Brent and Kung (see Knuth [K73]) and this computation can easily be made reversible. Hence we compute the factorial of x i for each i where jij O(1) We output that x = x i such that ( x i) y: This has cost O(1) times the cost O(N log 2 N log log N) of the forward computation of factorial, and hence has cost ....
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D. Knuth, The Art of Computer Programming, Vol II: Seminumerical Algorithms, (1973).
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