Read e-book online 2D-Discontinuity Detection from Scattered Data PDF

By Rossini M.

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Thus we can write c(i) = (p(i) AND c ( i - D ) OR g ( i ) . We evaluate this recurrence using parallel prefix, where the associative operation is a 2-by-2 Boolean matrix multiplication ( c(i) \ _ fp(i) AND c{i - 1) OR g(i) \ [T)-{ _fp« ~\F T T]{ 9(i)\(c{i-l)\ ) T J = c(i) • c(» -1) *... * c(i) * c(o) * (^ ) where c(-l) = F. The Boolean matrix multiplication is associative, because AND and OR satisfy the same associative and distributive laws as multiplication and addition. This algorithm is called carry look-ahead.

For example, consider the division of 90 by 9 viewed as 8 bit numbers. 90 is given by 01011010 and 9 is given by 00001001 in binary representation. Then 011011010 -00001001 1111011111011010 + 00001001 111110000|11010 + 00001001 11111001111010 + 00001001 1111110011010 + 00001001 000000100110 00001001 111110111|0 + 00001001 000000000| 00001001 11110111 + 00001001 00000000 -> n e g a t i v e -> 0 -> n e g a t i v e -> 0 -> negative -> 0 -> n e g a t i v e -> 0 -> p o s i t i v e -> 1 -> negative -> 0 -> p o s i t i v e -> 1 -> negative -> 0 Remainder The least significant bit is computed last.

For n even, the set of bent functions is the set of functions / : {0,1}™ —> {0,1} such that \Wf(w)\ = 2% Vii)e{0,l}" Find all bent functions for n — 2 and n = 4. Solution 21. We identify x with an integer y(x) £ Z according to y(x) = x0 + 2xx + • • • + 2"- 1 :r n _ 1 and similarly for w. , 2™ — 1 for w and x. The function / is represented as an element of {0,1} 2 ". ,2n-l. The following C++ program finds all bent functions for n = 2. The value for const size_t n should be changed to 4 to find all the bent functions for n = 4.

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2D-Discontinuity Detection from Scattered Data by Rossini M.

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