JPH01259420A - Trigonometric function arithmetic unit - Google Patents

Abstract

PURPOSE:To reduce the capacity of a data table and quickly perform arithmetic operation by using since or cosine values of equal angles, by which a prescribed angle is equally divided into (n), and sine or cosine values calculated by approximation to calculate the value of the trigonometric function in accordance with the addition theorem. CONSTITUTION:At least since or cosine values of equal angles by which the prescribed angle is divided into (n) are stored in a storage means, and at least two equal angles nearest to an input argument are selected by the storage means. Sine or cosine values of values obtained by subtracting equal angles from the argument are calculated by approximation, and sine or cosine values of selected equal angles and sine or cosine values calculated by approximation are used to calculate the value of the trigonometric function by four rules of arithmetic in accordance with the addition theorem of the trigonometric function. Thus, the trigonometric function value of high precision is calculated with a small storage area and a small quantity of calculation.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Application in Business A] The present invention relates to a trigonometric function calculation device that receives arguments and trigonometric functions to be sought and calculates the trigonometric functions.

[Prior Art] When calculating a trigonometric function such as a sine value or a cosine value corresponding to a given argument using a calculator, conventionally, the sine value or cosine value corresponding to the argument is stored in a storage area such as a table in advance. I memorized them and used them to perform calculations. Also,
When such a table is not used, methods such as approximation using rational function expressions have been used.

[Problems to be Solved by the Invention] However, if the former table reference method is used to calculate trigonometric functions and the accuracy is to be improved, a huge amount of storage space is required. On the other hand, when trying to improve accuracy using the latter approximation method, there is a drawback that the amount of calculation increases and the calculation time becomes longer.

The present invention has been made in view of the above conventional example, and an object of the present invention is to provide a trigonometric function calculation device that can calculate highly accurate trigonometric function values with a small storage area and a small amount of calculation.

[Means for Solving the Problems] In order to achieve the above object, the trigonometric function calculation device of the present invention has the following configuration. That is, it is a trigonometric function calculation device that calculates a designated trigonometric function in accordance with an input argument, and a storage means that stores at least a sine value or a cosine value of an angle obtained by dividing a predetermined angle into n equal parts. , selection means for selecting at least two of the equidistant angles closest to the argument, and means for calculating, by an approximation method, a small sine or cosine value obtained by subtracting the equidistant angle from the argument; Calculating means for calculating the value of the trigonometric function by addition, subtraction, multiplication, and division according to the addition theorem of the trigonometric function using the sine value or cosine value of the equidistant angle and the sine value or cosine value calculated by approximation.

[Operation] In the above configuration, at least the sine value or cosine value of an equal angle obtained by dividing a predetermined angle into n equal parts is stored in the storage means, and at least two equal angles closest to the input argument are stored. Choose from the means.

Calculate the sine or cosine value of the value obtained by subtracting the equal angle from the argument using an approximation method, and use the sine or cosine value of the selected equal angle and the sine or cosine value calculated by the approximation. , operates to calculate the value of a trigonometric function by addition, subtraction, multiplication, and division according to the addition theorem of trigonometric functions.

[Embodiments] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[Description of the arithmetic device (FIG. 1)] FIG. 1 is a block diagram showing a schematic configuration of the arithmetic device of the embodiment.

In the figure, 10 is a control unit equipped with a CPU such as a microprocessor, and the CPU is stored in a program ROMII and outputs various control signals according to the control program shown in the flowchart of FIG. 2 to control the entire device. It is carried out. A table ROM 12 stores sine values and cosine values, which will be described later, and is referenced when calculating trigonometric functions.

Reference numeral 13 denotes an input section for inputting arguments, the type of trigonometric function desired (sine, cosine, or tangent), etc., and is composed of, for example, a keyboard. Reference numeral 14 denotes an output unit for displaying and outputting calculation results, and is comprised of, for example, a display such as an LED or CRT, a printer, or the like. Reference numeral 15 denotes an arithmetic unit that performs calculations of addition, subtraction, multiplication, and division, and based on the sine value, cosine value, etc. given from the control unit 10, multiplies and adds these values, and outputs the results to the control unit 10.

[Description of calculation method (Figs. 2 and 3)] Fig. 2 is a flowchart of a control program for calculating the sine value in the arithmetic unit of the embodiment. The process starts when the type of trigonometric function to be calculated is specified.

First, in step S1, the argument X and the type of trigonometric function to be obtained (sin) are input from the input unit 13, and the process proceeds to step S2.

In this example, if the argument X=a+b, then sin (X)
= sin (a) ・cos (b) + cos (a
) 1s t n From the addition theorem of (b), s in
This is to find the value of (X).

Table ROM 12 (7) Table 121 contains values obtained by dividing 2π into n equal parts (from the smallest to a O+a I+a 2
+..., aN-1) are stored. Note that these 80 to a N-1 are values in radians.

Therefore, in step S2, from the argument X, al≦X<a+
++ Determine al and a l+1.

FIG. 3 is a diagram showing a specific example of the table 121 of these a, and 31 shows an example of the numerical values of a obtained by dividing 2π into four, and the corresponding sine and cosine values. Note that although the sine value and cosine value are shown here with two digits below the decimal point, in reality, more digits are set to increase accuracy.

Here, al is determined as a value obtained by dividing 2π (=about 6.28 in radians) into four equal parts. Therefore, a o-0,
00,a 1-1.57. a 2-3.14.
a 3-4.71.

Therefore, now in step S1, X=2 and 5i are used as arguments.
When the calculation of nX is instructed, in step S2, a, then at ==1.57, a 141 and a2=
3.14 is encountered (at≦2×a2).

In this way, in step S3, b=2-1.57=0.
43 and sin from table ROM12.
Read the values of (1, 57) and cos (1, 57),
Let A=sin (1, 57) B-cos (f, 57), respectively.

Next, in step S4, 5in(b) and cos(b) are approximated using an approximation equation based on Macrolin expansion.

This uses the following expansion formula, and for C up to n=3 and for D up to n
=2, and find the values of C and D from C=-b+b'/6-b5/120 D=1-b''+b'/24.

In step S5, these values A to D are output to the arithmetic unit 15 to calculate AxD+BxC, and the result is s i
It is output to the output unit 14 as the calculation result of n (X).

By doing this, for example, if we provide a table of radian values for 2π (up to 2 digits after the decimal point), π = 3.14
, a total of 629 tables are required, whereas according to this embodiment, the number of tables for a is 4 (4/629 tables 1
/157) will be sufficient.

This Macrolin expansion is the simplest approximation formula for sine and cosine, and high accuracy can be obtained near "0", but "0"
The error increases as it moves away from ``.'' In this example, this expansion formula is used for the minute part ``X-a'', so very good accuracy can be obtained with a small number of terms (n = about 2 or 3). It has the advantage of being

Furthermore, for an argument X greater than or equal to π/2, π/2<X<
For π, sin (X) − sin (π/2−X
)π<X<3yr/2, sin (X)−sin
(X-π/2)3π/2<X<2a, sin
By using the relational expression (X) ・-5in (2π-X), the amount of sine and cosine values stored in the table ROM 12 does not need to be up to 2π, but can be reduced to 1/2π.
4 will suffice.

Furthermore, from the relationship cos (X) = sin (yr/2 - /2.

In addition, although this embodiment has been explained so as to have only sine values, it is also possible to have a table of only cosine values due to the relationship cos (X) = sin (π/2-X). Of course.

As explained above, according to this embodiment, the amount of data in the conventional table ROM can be significantly reduced, and calculations using approximate expressions can be accomplished with a small number of terms using only addition, subtraction and multiplication, so the time required for calculations is reduced. It has the effect of requiring far less.

[Effects of the Invention] As described above, according to the present invention, the amount of data tables such as sine values and cosine values can be reduced, and trigonometric function calculations can be performed at high speed.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of the arithmetic unit of the embodiment, FIG. 2 is a flowchart for calculating the sine value of the embodiment, and FIG. 3 is a diagram showing a specific example of the table 121 in the embodiment. In the figure, 10...control unit, 11...program ROM
, 12...Table ROM, 13...Input section, 14
. . . output section, 15 . . . arithmetic unit, 121 . . . table. Figure 1 Figure 2

Claims (3)

[Claims] (1) A trigonometric function calculation device that calculates specified trigonometric functions in accordance with input arguments, and has a memory that stores at least the sine value or cosine value of an angle divided into n equal parts of a predetermined angle. means for selecting at least two of the equal angles closest to the argument; and means for calculating, by an approximation method, a sine or cosine value of a value obtained by subtracting the equal angle from the argument; calculation means for calculating the value of the trigonometric function by addition, subtraction, multiplication, and division according to the addition theorem of the trigonometric function, using the sine value or cosine value of the equisecting angle and the sine value or cosine value calculated by approximation; A trigonometric function calculation device comprising: (2) The trigonometric function calculation device according to claim 1, wherein the predetermined angle is an angle that is an integral multiple of π/2. (3) The trigonometric function calculation device according to claim 1, wherein the approximation method is an approximation method using Maclaurin expansion.