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Yao's method collects in u first those x i that appear to the highest power ; in the next round those with power are collected in u as well etc. The variable y is multiplied h − 1 {\displaystyle h-1} times with the initial u , h − 2 {\displaystyle h-2} times with the next highest powers, and so on.
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m .
Thus, 6.25 = 110.01 in binary, normalised to 1.1001 × 2 2 an even power so the paired bits of the mantissa are 01, while .625 = 0.101 in binary normalises to 1.01 × 2 −1 an odd power so the adjustment is to 10.1 × 2 −2 and the paired bits are 10. Notice that the low order bit of the power is echoed in the high order bit of the pairwise ...
The term RMS power is sometimes erroneously used (e.g., in the audio industry) as a synonym for mean power or average power (it is proportional to the square of the RMS voltage or RMS current in a resistive load). For a discussion of audio power measurements and their shortcomings, see Audio power.
Computing the k th power of a matrix needs k – 1 times the time of a single matrix multiplication, if it is done with the trivial algorithm (repeated multiplication). As this may be very time consuming, one generally prefers using exponentiation by squaring , which requires less than 2 log 2 k matrix multiplications, and is therefore much ...
Kawa is a language framework written in the programming language Java that implements the programming language Scheme, a dialect of Lisp, and can be used to implement other languages to run on the Java virtual machine (JVM). It is a part of the GNU Project.
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KNIME – An open source analytics platform built with Java and Eclipse using modular data pipeline workflows; LabPlot – A free and open-source, cross-platform computer program for interactive scientific plotting, curve fitting, nonlinear regression, data processing and data analysis; LIBSVM – C++ support vector machine libraries