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A non-extra pixel interpolation NPI is introduced for efficient image upscaling purposes. The NPI algorithm uses extended-triangular and linear scaling functions to match the pixel coordinates. The triangular function uses a modulo-operator with only two variables representing image pixels and scaling ratio. Every two variables of the linear scaling function represent the source/destination image pixels and scaling ratio. The traditional ceil function is used to round off non-integer pixel coordinates. The circshift and padarray functions are used to circularly shift the elements in array output by k -amount in each dimension and pad elements of the d th columns/rows by g-padsize in the shifted array, respectively. The k , d and g values are determined with respect to integer scaling ratios by a vector of n -elements. The Exactness, Peak Signal-to-Noise Ratio, Signal-to-Noise Ratio and Discrete Fourier Transform techniques were used for objective evaluation purposes. Experiments demonstrated comparable results as well as the need for further researches. [ABSTRACT FROM AUTHOR]

Let be an integer. Denote by the multiplicative order of modulo integer . We prove that there is a positive constant such that if , then where It was known for in [P. Kurlberg and C. Pomerance, On a problem of Arnold: The average multiplicative order of a given integer, Algebra Number Theory 7 (2013) 981-999] in which they refer to [F. Luca and I. E. Shparlinski, Average multiplicative orders of elements modulo , Acta Arith. 109(4) (2003) 387-411. [ABSTRACT FROM AUTHOR]

It is shown that a diminished-1 adder, with minor modifications, can be also used for the modulo 2n + 1 addition of two n-bit operands in the weighted representation, if the sum of its input operands is decreased by one. This modified diminished-1 adder can perform n-bit modulo 2n + 1 addition in less area and time than solutions that are based on the use of binary adders and/or weighted modulo 2n + 1 adders. Therefore, it can be applied effectively to all weighted modulo 2n + 1 arithmetic components that finally derive two n-bit addends. A small number of weighted arithmetic components have in the past adopted such a scheme without presenting this general theory. By applying this idea, we propose novel multi-operand modulo 2n + 1 adders (MOMAs) and residue generators (RGs). Experimental results indicate that the resulting arithmetic components offer significant savings in delay, implementation area and average power consumption compared to the currently most efficient solutions. [ABSTRACT FROM AUTHOR]