Computer for operations with functions

Within computer engineering and computer science, a computer for operations with (mathematical) functions (unlike the usual computer) operates with functions at the hardware level (i.e. without programming these operations).

A computing machine for operations with functions was presented and developed by Mikhail Kartsev in 1967. Among the operations of this computing machine were the functions addition, subtraction and multiplication, functions comparison, the same operations between a function and a number, finding the function maximum, computing indefinite integral, computing definite integral of derivative of two functions, derivative of two functions, shift of a function along the X-axis etc. By its architecture this computing machine was (using the modern terminology) a vector processor or array processor, a central processing unit (CPU) that implements an instruction set containing instructions that operate on one-dimensional arrays of data called vectors. In it there has been used the fact that many of these operations may be interpreted as the known operation on vectors: addition and subtraction of functions - as addition and subtraction of vectors, computing a definite integral of two functions derivative— as computing the vector product of two vectors, function shift along the X-axis – as vector rotation about axes, etc. In 1966 Khmelnik had proposed a functions coding method, i.e. the functions representation by a "uniform" (for a function as a whole) positional code. And so the mentioned operations with functions are performed as unique computer operations with such codes on a "single" arithmetic unit.

Source:

The positional code of an integer number ${\displaystyle A}$ is a numeral notation of digits ${\displaystyle \alpha }$ in a certain positional number system of the form

Such code may be called "linear". Unlike it a positional code of one-variable ${\displaystyle x}$ function ${\displaystyle F(x)}$ has the form:

and so it is flat and "triangular", as the digits in it comprise a triangle.

The value of the positional number ${\displaystyle A}$ above is that of the sum

where ${\displaystyle \rho }$ is the radix of the said number system. The positional code of a one-variable function correspond to a 'double' code of the form