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  2. Modular exponentiation - Wikipedia

    en.wikipedia.org/wiki/Modular_exponentiation

    For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8. Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m).

  3. Shunting yard algorithm - Wikipedia

    en.wikipedia.org/wiki/Shunting_yard_algorithm

    In computer science, the shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation.It can produce either a postfix notation string, also known as reverse Polish notation (RPN), or an abstract syntax tree (AST). [1]

  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. Exponentiation by squaring - Wikipedia

    en.wikipedia.org/wiki/Exponentiation_by_squaring

    Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For semigroups for which additive notation is commonly used, like elliptic curves used in cryptography , this method is also referred to as double-and-add .

  6. Primitive recursive function - Wikipedia

    en.wikipedia.org/wiki/Primitive_recursive_function

    Exponentiation and primality testing are primitive recursive. Given primitive recursive functions e {\displaystyle e} , f {\displaystyle f} , g {\displaystyle g} , and h {\displaystyle h} , a function that returns the value of g {\displaystyle g} when e ≤ f {\displaystyle e\leq f} and the value of h {\displaystyle h} otherwise is primitive ...

  7. Operator-precedence parser - Wikipedia

    en.wikipedia.org/wiki/Operator-precedence_parser

    In computer science, an operator-precedence parser is a bottom-up parser that interprets an operator-precedence grammar.For example, most calculators use operator-precedence parsers to convert from the human-readable infix notation relying on order of operations to a format that is optimized for evaluation such as Reverse Polish notation (RPN).

  8. Arbitrary-precision arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

    In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system.

  9. Hyperoperation - Wikipedia

    en.wikipedia.org/wiki/Hyperoperation

    The concepts of successor, addition, multiplication and exponentiation are all hyperoperations; the successor operation (producing x + 1 from x) is the most primitive, the addition operator specifies the number of times 1 is to be added to itself to produce a final value, multiplication specifies the number of times a number is to be added to ...

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