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  2. GNU Multiple Precision Arithmetic Library - Wikipedia

    en.wikipedia.org/wiki/GNU_Multiple_Precision...

    GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. [3] There are no practical limits to the precision except the ones implied by the available memory (operands may be of up to 2 32 −1 bits on 32-bit machines and 2 37 ...

  3. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    In arbitrary-precision arithmetic, it is common to use long multiplication with the base set to 2 w, where w is the number of bits in a word, for multiplying relatively small numbers. To multiply two numbers with n digits using this method, one needs about n 2 operations.

  4. Booth's multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Booth's_multiplication...

    Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. [1] Booth's algorithm is of interest in the study of computer ...

  5. Arbitrary-precision arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

    For multiplication, the most straightforward algorithms used for multiplying numbers by hand (as taught in primary school) require (N 2) operations, but multiplication algorithms that achieve O(N log(N) log(log(N))) complexity have been devised, such as the Schönhage–Strassen algorithm, based on fast Fourier transforms, and there are also ...

  6. Integer overflow - Wikipedia

    en.wikipedia.org/wiki/Integer_overflow

    For example, in the language Rust, while functionality is provided to give users choice and control, the behavior for basic use of mathematic operators is naturally fixed; however, this fixed behavior differs between a program built in 'debug' mode and one built in 'release' mode. [9] In C, unsigned integer overflow is defined to wrap around ...

  7. Saturation arithmetic - Wikipedia

    en.wikipedia.org/wiki/Saturation_arithmetic

    Saturation arithmetic is a version of arithmetic in which all operations, such as addition and multiplication, are limited to a fixed range between a minimum and maximum value. If the result of an operation is greater than the maximum, it is set (" clamped ") to the maximum; if it is below the minimum, it is clamped to the minimum.

  8. Schönhage–Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Schönhage–Strassen...

    This section has a simplified version of the algorithm, showing how to compute the product of two natural numbers ,, modulo a number of the form +, where = is some fixed number. The integers a , b {\displaystyle a,b} are to be divided into D = 2 k {\displaystyle D=2^{k}} blocks of M {\displaystyle M} bits, so in practical implementations, it is ...

  9. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.