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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).
Duff realized that to handle cases where count is not divisible by eight, the assembly programmer's technique of jumping into the loop body could be implemented by interlacing the structures of a switch statement and a loop, putting the switch's case labels at the points of the loop body that correspond to the remainder of count/8: [1]
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.
The reciprocal function y = 1 / x . As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
The long division may begin with a non-zero remainder. The remainder is generally computed using an -bit shift register holding the current remainder, while message bits are added and reduction modulo () is performed. Normal division initializes the shift register to zero, but it may instead be initialized to a non-zero value.
Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of Python 2. [37] Python consistently ranks as one of the most popular programming languages, and has gained widespread use in the machine learning community. [38] [39] [40] [41]
In the next step, b(x) is divided by r 0 (x) yielding a remainder r 1 (x) = x 2 + x + 2. Finally, dividing r 0 ( x ) by r 1 ( x ) yields a zero remainder, indicating that r 1 ( x ) is the greatest common divisor polynomial of a ( x ) and b ( x ) , consistent with their factorization.
To maximise computation speed, an intermediate remainder can be calculated by first computing the CRC of the message modulo a sparse polynomial which is a multiple of the CRC polynomial. For CRC-32, the polynomial x 123 + x 111 + x 92 + x 84 + x 64 + x 46 + x 23 + 1 has the property that its terms (feedback taps) are at least 8 positions apart ...