Logarithmic number system Logarithmic number system A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing. In an LNS, a number, formula_1, is represented by the logarithm, formula_2, of its absolute value as follows: where formula_4 is a bit denoting the sign of formula_1 (formula_6 if formula_7 and formula_8 if formula_9). The number formula_2 is represented by a binary word which usually is in the two's complement format. An LNS can be considered as a floating-point number with the significand being always equal to 1 and a non-integer exponent.
Binary GCD algorithm Binary GCD algorithm The binary GCD algorithm, also known as Stein's algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programmer Josef Stein in 1967, it may have been known in 1st-century China. The algorithm reduces the problem of finding the GCD by repeatedly applying these identities: The algorithm requires O(n) worst-case time, where n is the number of bits in the larger of