Advances in Computers, Vol. 31 by Marshall C. Yovits

By Marshall C. Yovits

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42 Associative Operations n = half nonnegative(n); if (zero(n)) return a; return power accumulate positive(a, op(a, a), n, op); } Since we know that an+m = anam, a0 must evaluate to the identity element for the operation op. 1 Floating-point multiplication and addition are not associative, so they may give different results when they are used as the operation for power and power left associated; establish whether power or power left associated gives a more accurate result for raising a floating-point number to an integral power.

Consider the distance d from fast to slow at the top of the loop when slow first enters the cycle: 0 ≤ d < c. If d = 0, the procedure terminates. Otherwise the distance from fast to slow decreases by 1 on each iteration. Therefore the procedure always terminates; when it terminates, slow has moved a total of h + d steps. The following procedure determines whether an orbit is terminating: template requires(Transformation(F) && UnaryPredicate(P) && Domain(F) == Domain(P)) bool terminating(const Domain(F)& x, F f, P p) Elements of Programming.

Any other use requires prior written consent from the copyright owner. Unauthorized use, reproduction and/or distribution are strictly prohibited and violate applicable laws. All rights reserved. = I(0)) { r = op(r, a); if (n == I(1)) return r; } else if (n == I(0)) return r; a = op(a, a); n = n / I(2); } } The recursion invariant becomes the loop invariant. Elements of Programming. com, Chris Nehren Copyright © 2009 Pearson Education, Inc.. This download file is made available for personal use only and is subject to the Terms of Service.

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