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Rapid calculation method and system of high-order derivable function based on probability calculation

A technology of probability calculation and fast calculation, applied in the direction of complex mathematical operations, etc., can solve the problems of complex conversion of function calculation, large number of iterations, and large amount of calculation, and achieve the effect of reducing the amount of calculation, low computational complexity, and low complexity

Active Publication Date: 2019-08-06
GUANGXI UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, the calculation and conversion of each function is complicated, and when calculating at the same time, the number of iterations is large, and the amount of calculation is still relatively large.

Method used

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  • Rapid calculation method and system of high-order derivable function based on probability calculation
  • Rapid calculation method and system of high-order derivable function based on probability calculation
  • Rapid calculation method and system of high-order derivable function based on probability calculation

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Effect test

Embodiment 1

[0051] A fast calculation method of a higher-order derivative function based on probability calculation, which includes the following steps:

[0052] A. Transform the input higher-order derivable functions (such as trigonometric functions, exponential functions, logarithmic functions, etc.) into probability calculation polynomials, use the parameters of each term as control points, and obtain the steps of the control point group;

[0053] B. A step of performing normalization processing on each control point in the control point group to obtain a corresponding mapping value group.

[0054] C. A step of binarizing the data in the mapping value group and the data of the externally input node group, and converting to obtain the corresponding first binary string group and the second binary string group.

[0055] D. The step of demultiplexing the first binary string based on the second binary string to obtain a probability value group. It is realized by a multiplexer.

[0056] E....

Embodiment 2

[0058] A fast calculation method of a higher-order derivative function based on probability calculation, which includes the following steps:

[0059] A. The step of transforming the input higher-order derivable function into a probability calculation polynomial to obtain a control point group.

[0060] Step A is implemented in two steps, the first step A-1: ​​convert the higher-order derivable function into Maclaurin series:

[0061] The higher-order derivable function can be transformed into the following Maclaurin series at 0:

[0062] f(x)≈f(0)+f'(0)x+(f″(0) / 2!)x 2 +...+(f (n) (0) / n! )x n (1)

[0063] Order A 0 =f(0),A 1 =f'(0),A 2 =f″(0) / 2!,...,A n = f (n) (0)

[0064] There is f(x)≈A 0 +A 1 x+A 2 x 2 +A 3 x 3 +......+A n x n (2)

[0065] Express the right side part of formula (2) in Maclaurin series as follows:

[0066] P(x)=A 0 +A 1 x+A 2 x 2 +A 3 x 3 +......+A n x n (3)

[0067] The larger the degree n of McLaughlin's series, the closer...

Embodiment 3

[0099] Such as figure 1 As shown, this embodiment discloses a fast calculation system for high-order derivable functions based on probability calculation, which includes sequentially connected function transformation modules, normalization processing modules, binarization processing modules, probability calculation modules and data The decoding module, the function transformation module includes a function input end, one input end of the binarization processing module is connected to the normalization processing module, and also includes a node input end.

[0100] The function calculation module is used to transform the input high-order derivable function into a probability calculation polynomial, and output the corresponding control point group B i (i=0,1,2...n);

[0101] The normalization processing module is used to control the received control point group B i (i=0,1,2...n) perform normalization processing, and output the corresponding mapping value group GB i (i=1,2...n...

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Abstract

The invention discloses a rapid calculation method and system of a high-order derivable function based on probability calculation. The method comprises the following steps: converting the function, normalizing the control point group, and binarizing the mapping value group and the input node group, obtaining a first binary string group and a second binary string group, performing multipath gatingon the first binary string group based on the second binary string group by using a probability calculation method to obtain a probability value group, and randomly decoding the probability value group. The system comprises a function transformation module, a normalization processing module, a binarization processing module, a probability calculation module and a data decoding module which are sequentially connected, the function transformation module receives a function, and the binarization processing module receives a node group. The high-order derivable function can be rapidly calculated through a simple structure, the system complexity is low, the calculation amount is small, and the calculation time is short.

Description

technical field [0001] The invention relates to the field of computer-aided analysis, in particular to a method and system for rapidly calculating high-order derivable functions by using a probability calculation method. Background technique [0002] Traditionally, to calculate high-order derivable functions such as trigonometric functions, look-up table method, polynomial expansion or approximation methods are generally used on hardware, and a large number of floating-point operations are bound to be involved in the calculation process. Using these methods to calculate these functions will be very difficult. Based on this, Voider proposed the CORDIC (Coordinate Rotational Digital Computer) algorithm in the design of the American aviation control system in 1959. The algorithm is calculated in different forms (such as circular mode, hyperbolic mode, linear mode, etc.) including multiplication, division, square root, sine, cosine, arctangent, vector rotation (ie, complex multi...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/15
CPCG06F17/15
Inventor 邱佳琪王海峰
Owner GUANGXI UNIV