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CuPy is an open source library for GPU-accelerated computing with Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them. [3]
A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the t
x 1 = x; x 2 = x 2 for i = k - 2 to 0 do if n i = 0 then x 2 = x 1 * x 2; x 1 = x 1 2 else x 1 = x 1 * x 2; x 2 = x 2 2 return x 1. The algorithm performs a fixed sequence of operations (up to log n): a multiplication and squaring takes place for each bit in the exponent, regardless of the bit's specific value. A similar algorithm for ...
Used in Python 2.3 and up, and Java SE 7. Insertion sorts Insertion sort: determine where the current item belongs in the list of sorted ones, and insert it there; Library sort; Patience sorting; Shell sort: an attempt to improve insertion sort; Tree sort (binary tree sort): build binary tree, then traverse it to create sorted list
Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
CLU is a programming language created at the Massachusetts Institute of Technology (MIT) by Barbara Liskov and her students starting in 1973. [8] While it did not find extensive use, it introduced many features that are used widely now, and is seen as a step in the development of object-oriented programming (OOP).
For example, to multiply 7 and 15 modulo 17 in Montgomery form, again with R = 100, compute the product of 3 and 4 to get 12 as above. The extended Euclidean algorithm implies that 8⋅100 − 47⋅17 = 1, so R′ = 8. Multiply 12 by 8 to get 96 and reduce modulo 17 to get 11. This is the Montgomery form of 3, as expected.