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Complex arithmetic using the float complex and double complex primitive data types was added in the C99 standard, via the _Complex keyword and complex convenience macro. In C++, complex arithmetic can be performed using the complex number class, but the two methods are not code-compatible.
Any floating-point type can be modified with complex, and is then defined as a pair of floating-point numbers. Note that C99 and C++ do not implement complex numbers in a code-compatible way – the latter instead provides the class std:: complex. All operations on complex numbers are defined in the <complex.h> header.
The JScience library has a Complex number class. The JAS library allows the use of complex numbers. Netlib has a complex number class for Java. javafastcomplex also adds complex number support for Java; jcomplexnumber is a project on implementation of complex number in Java. JLinAlg includes complex numbers with arbitrary precision.
Here is a very simple program in re2c (example.re). It checks that all input arguments are hexadecimal numbers. The code for re2c is enclosed in comments /*!re2c ... */, all the rest is plain C code. See the official re2c website for more complex examples. [23]
It supports integer, floating point (single and double precision), complex numbers, and a subset of trigonometric and statistics functions. Dense and sparse matrices are supported. [ 2 ] Various matrix decompositions are provided through optional integration with Linear Algebra PACKage ( LAPACK ), Automatically Tuned Linear Algebra Software ...
Integer addition, for example, can be performed as a single machine instruction, and some offer specific instructions to process sequences of characters with a single instruction. [7] But the choice of primitive data type may affect performance, for example it is faster using SIMD operations and data types to operate on an array of floats.
(A variant of this can also be used to multiply complex numbers quickly.) Done recursively, this has a time complexity of (). Splitting numbers into more than two parts results in Toom-Cook multiplication; for example, using three parts results in the Toom-3 algorithm. Using many parts can set the exponent arbitrarily close to 1, but the ...
For example, one can add N numbers either by a simple loop that adds each datum to a single variable, or by a D&C algorithm called pairwise summation that breaks the data set into two halves, recursively computes the sum of each half, and then adds the two sums. While the second method performs the same number of additions as the first and pays ...