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A trigonometric function calculation method and device based on interval division and CORDIC

A technology of trigonometric functions and calculation methods, applied in calculation, electrical digital data processing, digital data processing components, etc., can solve problems such as limited angle coverage, long cycle iterations, and low calculation accuracy, so as to save raw materials and The effect of energy consumption, reducing the number of iterations, and improving computational efficiency

Inactive Publication Date: 2019-05-28
CHINA ELECTRONIS TECH INSTR CO LTD
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0004] However, there are still deficiencies in the traditional algorithm, such as limited angle coverage, too long loop iterations, and low calculation accuracy, resulting in a decrease in calculation efficiency, which is increasingly unable to meet the dual requirements of speed and accuracy.
Secondly, due to the higher requirements for precision, the number of iterations required will inevitably increase, and the hardware implementation structure will become more complex, thereby reducing the speed of the entire iterative process. To solve this problem, people start from the algorithm itself to analyze and improve it.
In 2005, Maharatna proposed the SF CORDIC algorithm without scaling gain based on the first approximation theorem of sine series. Each cycle iteration of the algorithm is controlled by the binary complement of the corresponding bit of the initial rotation angle instead of the sign bit of the angle data path. Control so that there is no data dependence between different loop iterations. Although the SF CORDIC algorithm eliminates the scaling compensation logic and angle data path, it still has shortcomings such as too many loop iterations and low calculation accuracy.
The ARC algorithm reduces the complexity of the hardware structure, but the flow station series has not been improved

Method used

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  • A trigonometric function calculation method and device based on interval division and CORDIC
  • A trigonometric function calculation method and device based on interval division and CORDIC
  • A trigonometric function calculation method and device based on interval division and CORDIC

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Experimental program
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Effect test

Embodiment 1

[0075] This embodiment discloses a trigonometric function calculation method based on interval division and CORDIC, such as Figure 3-4 shown, including the following steps:

[0076] Step 1: Input any angle θ, and map it to the interval (0,2π) according to the periodicity of the trigonometric function;

[0077] The specific method is to divide the angle by 2π and take the remainder, that is, θ MOD1 = mod(θ,2π);

[0078] Step 2: Divide a periodic interval into 8 equal parts according to the symmetry of trigonometric functions, and divide θ MOD1 Mapped to the interval (0, π / 4);

[0079] The specific operation is to set θ MOD1 Divide by π / 4 to get the quotient θ ceil =ceil(θ MOD1 ,π / 4) and the remainder θ MOD2 =MOD(θ MOD1 ,π / 4);

[0080] Step 3: Divide the interval (0, π / 4) into 2 k parts, the angular range of each interval is The starting angle of each interval is

[0081]

[0082] Step 4: Because the angle of each iteration loop is tan -1 2 -n , so the rotatio...

Embodiment 2

[0103] The purpose of this embodiment is to provide a computing device.

[0104] A computing device comprising a memory and a processor,

[0105] The memory on the memory is pre-stored: interval (0, π / 4)2 k The trigonometric function value of the initial angle of each angle interval obtained by equal division, and a computer program that can run on a processor, when the processor executes the program, it realizes:

[0106] Receive the angle to be solved, map the angle to the periodic interval (0, 2π), and obtain the first mapped angle;

[0107] Mapping the first mapping angle to the interval (0, π / 4) to obtain a second mapping angle;

[0108] judging the angle interval to which the second mapping angle belongs in the interval (0, π / 4);

[0109] According to the starting angle of the angle interval, starting from the kth iteration, the trigonometric function calculation is performed based on the CODIC algorithm;

[0110] Based on the calculation result, the trigonometric fu...

Embodiment 3

[0113] The purpose of this embodiment is to provide a computer-readable storage medium.

[0114] A computer-readable storage medium having the interval (0, π / 4)2 stored thereon k The trigonometric function value of the initial angle of each angle interval obtained by equal division, and a computer program, the following steps are performed when the program is executed by the processor:

[0115] Receive the angle to be solved, map the angle to the periodic interval (0, 2π), and obtain the first mapped angle;

[0116] Mapping the first mapping angle to the interval (0, π / 4) to obtain a second mapping angle;

[0117] judging the angle interval to which the second mapping angle belongs in the interval (0, π / 4);

[0118] According to the starting angle of the angle interval, starting from the kth iteration, the trigonometric function calculation is performed based on the CODIC algorithm;

[0119] Based on the calculation result, the trigonometric function value of the angle to b...

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Abstract

The invention discloses a trigonometric function calculation method and a trigonometric function calculation device based on interval division and CORDIC. The method comprises the following steps: carrying out octasection on periodic intervals (0, 2pi); carrying out 2k equal division on the intervals (0,pi / 4), and obtaining an initial angle of each angle interval; calculating a trigonometric function value of a starting angle of each interval, and storing the trigonometric function value; receiving an angle to be solved, and mapping the angle to a period interval (0, 2pi) to obtain a first mapping angle; Mapping the first mapping angle to an interval (0,pi / 4) to obtain a second mapping angle; judging an angle interval to which the second mapping angle belongs in an interval (0,pi / 4); Executing trigonometric function calculation based on a CODIC algorithm from the kth iteration according to the initial angle of the angle interval; And based on a calculation result, correcting to obtaina trigonometric function value of the angle to be solved. According to the method, the lookup table method and the CORDIC iterative computation method are combined, the number of iterations can be reduced, meanwhile, the computation efficiency is improved, and computation resources are saved.

Description

technical field [0001] The disclosure belongs to the technical field of digital signal processing, and in particular relates to a trigonometric function calculation method and device based on interval division and CORDIC. Background technique [0002] Traditional arbitrary waveform generators use direct frequency synthesis (DDS) to generate digital signals of the required frequency. There are two methods for generating digital waveforms in the DDS module. One is to use a look-up table to generate amplitudes corresponding to different phases. It is to directly calculate the amplitude of the phase according to the current phase. The method of using the lookup table needs to store a large amount of waveform data in advance. When the data of a certain phase is needed, the stored waveform is addressed to find the corresponding amplitude. This method requires a large memory space, and the large-capacity ROM has high Disadvantages of power consumption, high cost, and low reliabili...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F7/548
Inventor 刘庆刘宇腾友伟朱卫国逄锦昊吴恒奎
Owner CHINA ELECTRONIS TECH INSTR CO LTD