Search results
Results from the WOW.Com Content Network
Using the complex logarithm in this definition allows the binary logarithm to be extended to the complex numbers. [8] As with other logarithms, the binary logarithm obeys the following equations, which can be used to simplify formulas that combine binary logarithms with multiplication or exponentiation: [9]
Binary logarithms are also used in computer science, where the binary system is ubiquitous; in music theory, where a pitch ratio of two (the octave) is ubiquitous and the number of cents between any two pitches is a scaled version of the binary logarithm, or log 2 times 1200, of the pitch ratio (that is, 100 cents per semitone in conventional ...
In computer science, lg * is often used to indicate the binary iterated logarithm, which iterates the binary logarithm (with base ) instead of the natural logarithm (with base e). Mathematically, the iterated logarithm is well defined for any base greater than e 1 / e ≈ 1.444667 {\displaystyle e^{1/e}\approx 1.444667} , not only for base 2 ...
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
The multiple valued version of log(z) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules. log(z) is the set of complex numbers v which satisfy e v = z; arg(z) is the set of possible values of the arg function applied to z. When k is any integer:
One part of this machine called an "endless spindle" allowed the mechanical expression of the relation = (+), [14] with the aim of extracting the logarithm of a sum as a sum of logarithms. A LNS has been used in the Gravity Pipe ( GRAPE-5 ) special-purpose supercomputer [ 15 ] that won the Gordon Bell Prize in 1999.
Investigators said they had “serious concerns” about “credible reports of sexual assault and other sexual misconduct" by the officers.
From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5 , e = 3 and m = 13 , dividing 5 3 = 125 by 13 leaves a remainder of c = 8 . Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm .