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CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
The logarithm keys (LOG for base 10 and LN for base e) on a TI-83 Plus graphing calculator. Logarithms are easy to compute in some cases, such as log 10 (1000) = 3. In general, logarithms can be calculated using power series or the arithmetic–geometric mean, or be retrieved from a precalculated logarithm table that provides a fixed precision.
The iterated logarithm is closely related to the generalized logarithm function used in symmetric level-index arithmetic. The additive persistence of a number , the number of times someone must replace the number by the sum of its digits before reaching its digital root , is O ( log ∗ n ) {\displaystyle O(\log ^{*}n)} .
The discrete logarithm is just the inverse operation. For example, consider the equation 3 k ≡ 13 (mod 17). From the example above, one solution is k = 4, but it is not the only solution. Since 3 16 ≡ 1 (mod 17)—as follows from Fermat's little theorem—it also follows that if n is an integer then 3 4+16n ≡ 3 4 × (3 16) n ≡ 13 × 1 n ...
Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the discrete logarithms of small primes, computes them by a linear algebra procedure and finally expresses the desired discrete ...
The discrete logarithm problem in a finite field consists of solving the equation = for ,, a prime number and an integer. The function f : F p n → F p n , a ↦ a x {\displaystyle f:\mathbb {F} _{p^{n}}\to \mathbb {F} _{p^{n}},a\mapsto a^{x}} for a fixed x ∈ N {\displaystyle x\in \mathbb {N} } is a one-way function used in cryptography .
Of great interest in number theory is the growth rate of the prime-counting function. [3] [4] It was conjectured in the end of the 18th century by Gauss and by Legendre to be approximately where log is the natural logarithm, in the sense that / =
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, ...