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The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. [1] The earliest occurrence in print of the term is thought to be in a 1969 MIT technical report. [2] [3] The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states.
Pairwise summation is the default summation algorithm in NumPy [9] and the Julia technical-computing language, [10] where in both cases it was found to have comparable speed to naive summation (thanks to the use of a large base case).
A designation "flow graph" that includes both the Mason graph and the Coates graph, and a variety of other forms of such graphs [7] appears useful, and agrees with Abrahams and Coverley's and with Henley and Williams' approach. [1] [2] A directed network – also known as a flow network – is a particular type of flow
The first structured method for documenting process flow, the "flow process chart", was introduced by Frank and Lillian Gilbreth in the presentation "Process Charts: First Steps in Finding the One Best Way to do Work", to members of the American Society of Mechanical Engineers (ASME) in 1921. [2]
When that occurs, that number is the GCD of the original two numbers. By reversing the steps or using the extended Euclidean algorithm, the GCD can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each multiplied by an integer (for example, 21 = 5 × 105 + (−2) × 252).
If an adding circuit is to compute the sum of three or more numbers, it can be advantageous to not propagate the carry result. Instead, three-input adders are used, generating two results: a sum and a carry. The sum and the carry may be fed into two inputs of the subsequent 3-number adder without having to wait for propagation of a carry signal.
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