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Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = be mod m. From the definition of division, it follows that 0 ≤ c < m . For example, given b = 5, e = 3 and m = 13, dividing 53 = 125 by 13 leaves a remainder of c = 8 .
Modulo. In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the modulus of the operation). Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the ...
This is a list of the instructions that make up the Java bytecode, an abstract machine language that is ultimately executed by the Java virtual machine. [ 1] The Java bytecode is generated from languages running on the Java Platform, most notably the Java programming language . Note that any referenced "value" refers to a 32-bit int as per the ...
The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab using division by N and keeping only the remainder. This division requires quotient digit estimation and ...
Floor function. Ceiling function. In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor (x). Similarly, the ceiling function maps x to the smallest integer greater than or equal to x, denoted ⌈x⌉ or ceil (x).
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.
Step 1 {of topmost APL code entered at left}) 4-5 = -1. Step 2) 3 times -1 = -3. Step 3) Take the floor or lower of 2 and -3 = -3. Step 4) Divide 1 by -3 = -0.3333333333 = final result. An operator may have function or data operands and evaluate to a dyadic or monadic function. Operators have long left scope.
In languages with typed pointers like C, the increment operator steps the pointer to the next item of that type -- increasing the value of the pointer by the size of that type. When a pointer (of the right type) points to any item in an array, incrementing (or decrementing) makes the pointer point to the "next" (or "previous") item of that array.