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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 divisor.
Computing the remainder then consists of subtracting multiples of the generator polynomial (). This is just like decimal long division, but even simpler because the only possible multiples at each step are 0 and 1, and the subtractions borrow "from infinity" instead of reducing the upper digits. Because we do not care about the quotient, there ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Zero-copy programming techniques can be used when exchanging data within a user space process (i.e. between two or more threads, etc.) and/or between two or more processes (see also producer–consumer problem) and/or when data has to be accessed / copied / moved inside kernel space or between a user space process and kernel space portions of operating systems (OS).
The remainder, as defined above, is called the least positive remainder or simply the remainder. [2] The integer a is either a multiple of d, or lies in the interval between consecutive multiples of d, namely, q⋅d and (q + 1)d (for positive q). In some occasions, it is convenient to carry out the division so that a is as close to an integral ...
Divide the highest term of the remainder by the highest term of the divisor (x 2 ÷ x = x). Place the result (+x) below the bar. x 2 has been divided leaving no remainder, and can therefore be marked as used. The result x is then multiplied by the second term in the divisor −3 = −3x. Determine the partial remainder by subtracting 0x − ...
Thus t, or, more exactly, the remainder of the division of t by n, is the multiplicative inverse of a modulo n. To adapt the extended Euclidean algorithm to this problem, one should remark that the Bézout coefficient of n is not needed, and thus does not need to be computed.
In Linux, Copy Control discs are easily accessed through cdparanoia or any other software that uses it, such as the KDE "audiocd:/" service. In Mac OS X , these discs are easily accessed through iTunes and QuickTime (When a CDDA track is dragged to a folder other than the CD, QuickTime automatically converts it to AIFF , which is a lossless PCM ...