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  2. Saturation arithmetic - Wikipedia

    en.wikipedia.org/wiki/Saturation_arithmetic

    Saturation arithmetic for integers has also been implemented in software for a number of programming languages including C, C++, such as the GNU Compiler Collection, [2] LLVM IR, and Eiffel. Support for saturation arithmetic is included as part of the C++26 Standard Library. This helps programmers anticipate and understand the effects of ...

  3. Binary multiplier - Wikipedia

    en.wikipedia.org/wiki/Binary_multiplier

    The method is slow, however, as it involves many intermediate additions. These additions are time-consuming. Faster multipliers may be engineered in order to do fewer additions; a modern processor can multiply two 64-bit numbers with 6 additions (rather than 64), and can do several steps in parallel. [citation needed]

  4. 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 ...

  5. Wallace tree - Wikipedia

    en.wikipedia.org/wiki/Wallace_tree

    Multiply each bit of one of the arguments, by each bit of the other. Reduce the number of partial products to two by layers of full and half adders . Group the wires in two numbers, and add them with a conventional adder.

  6. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    To form the product of two 8-bit integers, for example, the digital device forms the sum and difference, looks both quantities up in a table of squares, takes the difference of the results, and divides by four by shifting two bits to the right. For 8-bit integers the table of quarter squares will have 2 9 −1=511 entries (one entry for the ...

  7. Bitwise operation - Wikipedia

    en.wikipedia.org/wiki/Bitwise_operation

    In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits.It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor.

  8. Integer overflow - Wikipedia

    en.wikipedia.org/wiki/Integer_overflow

    The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...

  9. 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 ...