JPH01109428A - Trigonometric function arithmetic unit - Google Patents

Abstract

PURPOSE:To calculate a highly accurate trigonometric function value with a small quantity of a storing area and a small calculation quantity by dividing a given argument into a prescribed equally divided angle, using the sine value or cosine value of the divided equally divided angle and adding, subtracting, multiplying and dividing in accordance with the addition theorem of the trigonometric function. CONSTITUTION:In a table 121 of a table ROM 12, for example, a sine value and a cosine value to values a0-aN-1 to (n)-equally-divide 2pi are stored and the sine value and the cosine value to values b0-bM-1 to (m)-equally-divide further (a) are stored in a table 122. A control part 10 determines a1 which becomes a1<=X<a1+1 from an argument X inputted from an input part 13 and bj which becomes bj<=b<j+1 for b=x-a1, reads the sine value and the cosine value for ai and bj from the table ROM 12, outputs these values to a computing element 15, executes the calculation with the addition theorem and outputs the result to an output part 14. Thus, the data quantity of the table ROM can be reduced and a short operation time can be sufficient.

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, when calculating trigonometric functions using the former table reference method and attempting to improve its accuracy, a huge amount of storage space is required. On the other hand, if the latter approximation method were used to improve accuracy, the amount of calculation would increase, resulting in a longer calculation time.

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 specified trigonometric function in response to an input argument, the device comprising: a first equal dividing angle obtained by dividing a predetermined angle into n equal parts;
a storage means for storing at least a sine value or a cosine value of each of second equal angles obtained by further dividing the first equal angle into m equal parts; a dividing means for dividing, and a 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 divided first and second equal angles. Be prepared.

[Operation] In the above configuration, at least the sine value of each of the first equal dividing angle obtained by dividing the predetermined angle into n equal parts and the second equal dividing angle obtained by further dividing the first equal dividing angle into m equal parts. One of the cosine values is stored in a storage means.

Divide the given argument into the first and second equal angles, and divide the first and '! Using the sine value or cosine value of the equidistant angle J2, it operates to calculate the value of the 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 the 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 unit for inputting arguments, the type of trigonometric function desired (sine, cosine, or tangent), etc., and is comprised 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 a sine value in the calculation device of the embodiment. The process starts when the type of trigonometric function to be used 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)
xsin (a)-cos (b)+cos (a)
−s i n (b) From the addition theorem, sin (X
).

The table 121 of the table ROM 12 contains values obtained by dividing 2π into n equal parts (from the smallest to a Or a In a 2
+...+aN-1), and the table 122 stores the sine and cosine values for the values obtained by further dividing a into m equal parts (smaller glass, b,... bM-1). and cosine value are stored. In addition, these a0 to a N-
11b o Nb M-1 is a value in radians.

Therefore, in step S2, from the argument X, al≦X<at
++ for al and bxx-ai, bj
≦1) <1) Determine bj that satisfies J*I.

FIG. 3 is a diagram showing numerical examples of these a and b, where 30 shows a numerical example of a, and 31 shows a numerical example of b.

Here, we assume 2π (= about 6.28 in radians), and 2π
a is determined by dividing the value into four equal parts. Therefore, a
oso, oo, a, -1,57,a 2-3.14
°a becomes -4,71. In addition, b is the interval of a ``1,''
57" is further divided into 157 equal parts, b o = o, ol, b r , -0,02, b z
"o, 03. +*+.

b, s, -1,58.

Therefore, now in step S1, X=2 and 5i are used as arguments.
When the calculation of nX is instructed, in step S2, ai
As such, a,=1.57 is selected (a+≦2×a,)
, and bJ is b-2-1,57=0.43, so bJ2
is selected.

In this way, in step S3, the sine and cosine values for al+b42, sin (1, 57), cos (1, 5
7), the values of sin (0, 43) and cos (0, 43) are read from the table ROM 12, and each is Aws in (1, 57) B=cos (1, 57) C-s in (0, 43) Let D=cos (0,43).

In step S4, these AND values 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 a table of radian values for 2π (up to two digits after the decimal point) is provided, a total of 629 tables would be required as π = 3.14, but according to this embodiment, the number of tables for a is is 4, and the number of tables in b is 15.
7, a total of 161 tables (161/629 to 1/4
) will be sufficient.

Furthermore, for an argument X greater than or equal to π/2, re/2
< X < tt: Then, 5in(X)・51n(yr
/2-X)tt < X < 3 π/2, si
n (X) ・-5In (X-7! /2)3π/
For 2<X<2π, 51n(X)-sin(2yr-X
) By using the relational expression, table ROM
The amount of sine and cosine values to be stored in 12 does not need to be up to 2π, and can be 1/4 of that.

Furthermore, cos (X) ms in (π/2−
From the relationship of
The data amount of M can be further reduced to 1/2.

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 from the relationship cos (X) = sin (tt /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 since calculations can be accomplished only by addition, subtraction and multiplication, the time required for calculations is also much shorter. effective.

[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 device 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 values of a and b that can be used in the embodiment. be. In the figure, t o--control unit, 11- program RO
M112...Table ROM, 13...Input section, 1
4--Output section, 15--Arithmetic section. Figure 1 Figure 2 Figure 3

Claims (2)

[Claims] (1) A trigonometric function calculation device that calculates a specified trigonometric function in response to an input argument, the device comprising: a first equal dividing angle obtained by dividing a predetermined angle into n equal parts, and the first equal dividing angle. storage means for storing at least the sine value or cosine value of each of the second equal angles obtained by further dividing the angle into m equal parts; and a dividing means for dividing the argument into the first and second equal angles; 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 divided first and second equal angles. A trigonometric function calculation device. (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.