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In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.
When performed with a single rounding, it is called a fused multiply–add (FMA) or fused multiply–accumulate (FMAC). Modern computers may contain a dedicated MAC, consisting of a multiplier implemented in combinational logic followed by an adder and an accumulator register that stores the result. The output of the register is fed back to one ...
Consider a dynamic array that grows in size as more elements are added to it, such as ArrayList in Java or std::vector in C++. If we started out with a dynamic array of size 4, we could push 4 elements onto it, and each operation would take constant time. Yet pushing a fifth element onto that array would take longer as the array would have to ...
The FMA instruction set is an extension to the 128 and 256-bit Streaming SIMD Extensions instructions in the x86 microprocessor instruction set to perform fused multiply–add (FMA) operations. [1]
Implicit iteration is also partially supported by C++ through the use of standard function templates, such as std::for_each(), std::copy() and std::accumulate(). When used they must be initialized with existing iterators, usually begin and end, that define the range over which iteration occurs. But no explicit iterator object is subsequently ...
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
It is, however, preferable to use an algorithm from the C++ Standard Library for such tasks. [1] [2] [3] The member function erase can be used to delete an element from a collection, but for containers which are based on an array, such as vector, all elements after the deleted element have to be moved forward to avoid "gaps" in the collection ...
[10] [11] vector<bool> does not meet the requirements for a C++ Standard Library container. For instance, a container<T>::reference must be a true lvalue of type T. This is not the case with vector<bool>::reference, which is a proxy class convertible to bool. [12] Similarly, the vector<bool>::iterator does not yield a bool& when dereferenced.