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Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.. Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in ...
The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general. A general algorithm for computing log b a in finite groups G is to raise b to larger and larger powers k until the desired a is found.
The discrete logarithm algorithm and the factoring algorithm are instances of the period-finding algorithm, and all three are instances of the hidden subgroup problem. On a quantum computer, to factor an integer N {\displaystyle N} , Shor's algorithm runs in polynomial time , meaning the time taken is polynomial in log N {\displaystyle \log ...
Logarithm; Matrix multiplication algorithm; Mental calculation; Number-theoretic transform; Prosthaphaeresis; Slide rule; Trachtenberg system; Residue number system § Multiplication for another fast multiplication algorithm, specially efficient when many operations are done in sequence, such as in linear algebra; Wallace tree
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{*}} where q {\displaystyle q} is a prime, index calculus leads to a family of algorithms adapted to finite fields and to ...