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====Elementary and special functions==== {{further|Special functions}} * [[Computing π|Computation of π]]: ** [[Borwein's algorithm]]: an algorithm to calculate the value of 1/π ** [[Gauss–Legendre algorithm]]: computes the digits of [[pi]] ** [[Chudnovsky algorithm]]: a fast method for calculating the digits of π ** [[Bailey–Borwein–Plouffe formula]]: (BBP formula) a spigot algorithm for the computation of the nth binary digit of π * [[Division algorithm]]s: for computing quotient and/or remainder of two numbers ** [[Long division]] ** [[Restoring division]] ** [[Non-restoring division]] ** [[SRT division]] ** [[Newton–Raphson division]]: uses [[Newton's method]] to find the [[Multiplicative inverse|reciprocal]] of D, and multiply that reciprocal by N to find the final quotient Q. ** [[Goldschmidt division]] * Hyperbolic and Trigonometric Functions: ** [[BKM algorithm]]: computes [[Elementary function (differential algebra)|elementary functions]] using a table of logarithms ** [[CORDIC]]: computes hyperbolic and trigonometric functions using a table of arctangents * Exponentiation: ** [[Addition-chain exponentiation]]: exponentiation by positive integer powers that requires a minimal number of multiplications ** [[Exponentiating by squaring]]: an algorithm used for the fast computation of [[Arbitrary-precision arithmetic|large integer]] powers of a number * [[Montgomery reduction]]: an algorithm that allows [[modular arithmetic]] to be performed efficiently when the modulus is large * [[Multiplication algorithm]]s: fast multiplication of two numbers ** [[Booth's multiplication algorithm]]: a multiplication algorithm that multiplies two signed binary numbers in two's complement notation ** [[Fürer's algorithm]]: an integer multiplication algorithm for very large numbers possessing a very low [[Computational complexity theory|asymptotic complexity]] ** [[Karatsuba algorithm]]: an efficient procedure for multiplying large numbers ** [[Schönhage–Strassen algorithm]]: an asymptotically fast multiplication algorithm for large integers ** [[Toom–Cook multiplication]]: (Toom3) a multiplication algorithm for large integers * [[Multiplicative inverse#Algorithms|Multiplicative inverse Algorithms]]: for computing a number's multiplicative inverse (reciprocal). ** [[Newton's method#Multiplicative inverses of numbers and power series|Newton's method]] * [[Rounding functions]]: the classic ways to round numbers * [[Spigot algorithm]]: a way to compute the value of a [[mathematical constant]] without knowing preceding digits * Square and Nth root of a number: ** [[Alpha max plus beta min algorithm]]: an approximation of the square-root of the sum of two squares ** [[Methods of computing square roots]] ** [[Nth root algorithm|''n''th root algorithm]] * Summation: ** [[Binary splitting]]: a [[Divide and conquer algorithm|divide and conquer]] technique which speeds up the numerical evaluation of many types of series with rational terms ** [[Kahan summation algorithm]]: a more accurate method of summing floating-point numbers * [[Unrestricted algorithm]]
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