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In computing, Verbose mode is an option available in many computer operating systems and programming languages that provides additional details as to what the computer is doing and what drivers and software it is loading during startup or in programming it would produce detailed output for diagnostic purposes thus makes a program easier to debug.
Let be a cyclic group of order , and given ,, and a partition =, let : be the map = {and define maps : and : by (,) = {() + (,) = {+ ()input: a: a generator of G b: an element of G output: An integer x such that a x = b, or failure Initialise i ← 0, a 0 ← 0, b 0 ← 0, x 0 ← 1 ∈ G loop i ← i + 1 x i ← f(x i−1), a i ← g(x i−1, a i−1), b i ← h(x i−1, b i−1) x 2i−1 ← ...
(The conversion to log form is expensive, but is only incurred once.) Multiplication arises from calculating the probability that multiple independent events occur: the probability that all independent events of interest occur is the product of all these events' probabilities. Accuracy. The use of log probabilities improves numerical stability ...
RetroArch is a free and open-source, cross-platform frontend for emulators, game engines, video games, media players and other applications. It is the reference implementation of the libretro API , [ 2 ] [ 3 ] designed to be fast, lightweight, portable and without dependencies. [ 4 ]
The name comes from the fact that in complex analysis, () = /; here / is a typical example of a 1-form on the complex numbers C with a logarithmic pole at the origin. Differential forms such as d z / z {\displaystyle dz/z} make sense in a purely algebraic context, where there is no analog of the logarithm function.
Many style guides advise against excessive verbosity. While it may be rhetorically useful [1] verbose parts in communications are sometimes referred to as "fluff" or "fuzz". [17] For instance, William Strunk, an American professor of English advised in 1918 to "Use the active voice: Put statements in positive form; Omit needless words." [18]
In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logarithmic number of fixed-size integers . [ 1 ]
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.