JPS58178478A - Arithmetic device for inverse trigonometric function - Google Patents

Abstract

PURPOSE:To shorten an arithmetic time by rotating a point on an orthogonal coordinates until its X and Y components attain to alpha, and finding sin<-1>alpha and cos<-1>alpha from the angle of rotation. CONSTITUTION:A vector (1,0) on an (x) axis is rotated by tan<-1>1/1(=45 deg.). The angle of rotation is decreased successively in the order of tan<-1>1/2, tan<-1>1/4, tan<-1>1/8...tan<-1>1/2n. Further, when the (y) component after the rotation is greater than alpha, clockwise rotation is performed next and when the (y) component is smaller than alpha to the contrary, counterclockwise rotation is performed. The angle of rotation approximating alpha is an angle to be found. The X and Y components after the rotation are stored in an X register 5 and a Y register 6. The contents of both registers 5 and 6 are inputted to a 1/2<n> arithmetic device, where they are processed to find the X and Y components after the rotation. This operation is repeated.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an inverse trigonometric function calculation device that calculates an angle by digitally calculating an inverse trigonometric function using a wiring logic method.

Conventionally, this type of calculation has been performed using software on a program-storing digital computer, using the inverse trigonometric function Sinα
, Cos ct%Tanα, and when calculating the angle, an approximate expression is used and a series calculation is performed using software.

However, conventional software-based calculations take a long processing time and are not suitable for calculating inverse trigonometric functions in real time.

This invention was made to speed up the calculation time of inverse trigonometric functions, and instead of using software calculations using a program control method, the X component or Y component obtained by rotating a point (Rho) on orthogonal coordinates is Sinα respectively
It is an object of the present invention to provide an inverse trigonometric function calculation device that rotates until α of Cooα and α of Cooα, and obtains Sinα Cos'P using this rotation angle.

An embodiment of the present invention will be described below with reference to the drawings. 1st
In the figure, (1) is an external device such as a program-controlled computer or a data processing device, (2) is data α input from the external device (1) to this device, and (3) is n·1 Tan 1/8. 5in (n-Tan 1./8 people c
os(n@Tan V8)(n:Q, l, 2.
-++, m, m: integer], 5in45", etc., and set the constant based on the command of the controller (8) as B.
A constant generator that outputs to the path circle, (4) is input terminal A.

Addition and subtraction devices that add or subtract values input to B, +51, +61, and +7109 are X registers, X registers, angle registers, and α registers that temporarily store the outputs of the addition and subtraction devices (4), respectively, and (8) is a sign register. Addition/subtraction device (4
) to add or subtract, and also to the constant generator (
Specify the constant to be output for 3), and also specify the constant 16 to be described later.
a controller that specifies the value of n for the n arithmetic unit (9), (
9) multiplies the contents of X register (5) or X register (6) by 1/2n? Arithmetic unit, (l [is X register (
5) is multiplied by Vf by the V2ri arithmetic unit (9), and αυ is the X register (6
02 is the input data α(
2) Add/subtract the constant from the constant generator (3), the contents of the X register, or the contents of the Y register (Iυ)
B bus (so-called pass line) that transfers to input terminal B of
, 03 is the data output from the addition/subtraction device (4) to the X register (5), X register (6), and angle register (7).
, or the α register (C bus, u4 that transfers to
an A bus that transfers the contents of the register (5), the contents of the X register (6), or the contents of the angle register (7) to the input terminal A of the addition/subtraction device (4) and the 1/211 arithmetic device (9); (161 is a code register that temporarily stores the code bit output from the addition/subtraction device (4).

Next, the operation will be explained.

As shown in Figure 2(a), the polar coordinate value 1 is expressed as (k
, θ), and this value is expressed as (x, a) in orthogonal coordinates. Hereinafter, x1 is assumed to be within the second quadrant. 1(
= l, - is expressed as (1, 0), and in the case of calculating θ = Sin'α, if the value of vector (1, 0) is rotated until the Y component becomes ba, then the angle of rotation is the angle θ It is.

In the case of calculating θ=Cosα, if the value of vector (1, 0) is rotated until the X component becomes α, the rotation angle is the angle − to be found. If zl is in another quadrant, it can be easily calculated from θ obtained assuming that it is in the second quadrant.

Generally speaking, to rotate the value 1 by an angle r, the second rotation is performed on multiple planes.
It is only necessary to take the product of zl(a, b) shown in FIG.

! x-Tomix-Tomis-(x-)-yi)(a-1-bi
) = x・a−y−b+1(x−b+y−ri (1)
This odor is shown in FIG. 2(c).

FIG. 5 shows the rotation angle r and the value of 11 after rotation by selecting the values of λ and b such that R〒b2 =1 in equation (1), and where n is an integer.

The basic calculation method for 5in-1α will be explained.

First, the vector (1,0) on the X axis is Tan-
' Rotate by 1/1 (-45°). Then, the first rotation angle is 'ran-''l/2, Tan-11/4, Tan
``1/8, ・, Tan4Vt.If the Y component after rotation is larger than α, the next rotation direction will be clockwise, and conversely, if the Y component is smaller than α, the next rotation direction will be is counterclockwise, and gradually change the y component to α
get closer to Part 1: Coefficient 2f in calculation during rotation
A method is adopted in which the error caused by this is made as small as possible even without performing the /2 operation. In addition, if α is larger than vH, the calculation 9O−(JO5α can be performed, so Si
Consider up to 45 as the 4 outputs of nα.

Coefficient 2) Rotation angle where the L arm is close to 1, e.g. Tan '1
Select /8 and use this angle to divide the 45° angle. Then, by comparing α with the constant shown in FIG. 6, it is verified in which category the obtained angle Sin α falls. Next, the usage shown in that category is Tan 1/16, T Feng L/32. ...,
The rotation angle is made smaller as Tan l/2n, and the rotation angle when it approaches α is used as the angle to be determined.

Next, the operation of the inverse trigonometric function arithmetic device according to the present invention will be explained using FIG.'S1 in conjunction with FIG.

Since Sinα and C0IIα are found by the same =S, Si
nα will be described below.

[Step 1] Data α(2) from the external device (1) is placed on the B bus I2 and input to the input end B of the addition/subtraction device (4). On the other hand, the A bus I is set to 0, and O is input to the input terminal A of the addition/subtraction device (4). From the controller (8) to the addition/subtraction device (4
) by giving an addition command and calculating 0+α, the C bus becomes 0.
α appears in 3. In this way, the data α(2) of the external device is placed on the C bus row, and is stored by applying a read pulse to the α register a-.

Next, the contents of α register u51 are transferred to the A bus (14), and B1
From the constant generator (3) to the constant C in Figure 6
Place SX and input to terminals A and B of addition/subtraction device (4). A subtraction command B-A is given to the adding/subtracting device (4) from the control 41''8), and a command of Cl1l-α is given, and if this result is positive, it is in the first category in Fig. 6. Recognize.

In the same way, check which category α is in. If it is in the first category, put the constant from the constant generator (3) in Figure 6 onto the B bus @, and set the value α to σ register 0.
In the same way as in 51, it is stored in the angle register (7). Similarly, the constant &Xt + Yt in FIG. 6 is generated from the constant generator (3) and stored in the X register +51 and the Y register (6), respectively.

[Step 2] Put the contents of the X register (5) on the A bus I and input it to the Vt transfer device (9).

The controller (8) inputs 40 fm as the value of n to the arithmetic unit (9).
), and the output multiplied by l/2 is given to the X registor (1
Give a read pulse to 1 and store it. As a result, the value (1/2)·X shown in FIG. 3 is stored in the X Luzisk 1G. 1 of Y register (6) in the same way
Multiply the valley by 1/24+n and store the result in Y Luzisk a1. As a result, the value (1/24+n)·Y shown in FIG. 3 is stored in the Y register U.

The contents of the Y register (6) are placed on the A bus 141, and the contents of the α register 09 are placed on the B bus IJB, and each is input to terminals A and H of the adder/subtractor (4). and,
A subtraction command A-B is issued from the controller (8), and the sign register (1al) stores the sign register (1al) to store the sign register (1al).
are placed on the B bus t12 and input to terminals A and H of the adder/subtractor (4), respectively. On the other hand, control a4+81 issues an addition command if the content of sign register 1e is positive, and subtracts if it is negative! # Give the command to the addition/subtraction device (4). The output of the adder/subtractor (4) appears on the C bus (13) Ic, which is read into the X register (5) and stored with a value given to it. From this point, in Figure 3, if the value of Y-α is positive, then X + (1/
24+”)・Y Null value ζ negative t, U” −(1/2””
) ”Y?, (Le value force (XL/Jister (5) is stored.If the value of Y-α is positive, -
(1/4”)・x-4-y value, if negative, Tan)/
24+" is one rotation, and the X component and Y component after the rotation are stored in the X register (5) and Y register (6), respectively. Here, the rotation angle is -n-11/24+n
The reason for this is that in step 1, the input value d is divided into seven divisions I by Tan 1/8 as shown in FIG.

[Step 3] Save the contents of the angle register (7) to A node I.
At the same time, select Tan-11/24+n based on the command from the constant generator (3) and the controller (8) and place it on B/chair @, and then select the terminal A of the addition/subtraction device (4). , B
1 is input ('t'L). On the other hand, the controller (8) gives a subtraction command to the addition/subtraction device (4) if the sign of the sign register 0e is positive, and an addition command if it is negative. Output force 4 G appears on chair 03, which is stored by giving a read pulse to the angle register (7th position). Through this calculation, if the value of Y-α in Figure 9α3 is positive, θ-T
an v24+n, and if it is negative, θ+Tan l/4+n is executed, and the result is stored in the angle register (7).

Step 2 and step 3 are calculated as n = O# m (m H
If you repeat until the angle register (7) is S in
−'α value is stored. Cos in Figure 4 in the same way
As shown in the flowchart for α operation (Co5-1
α can be found.

In the above embodiment, repeated operations are executed using the same hardware, but hardware with the same structure may also be arranged in a pipelined manner. This is particularly effective when coming from 1). In addition, in the above embodiment, the calculation was repeated until n = 9 to m and ended, but in the case of Sin α on the way from n = 9 to m, if the value of Y - α becomes 0,
Further, in the case of Co5ct, the process may be terminated when the value of X-α becomes O. In addition, in the above embodiment, the external device (
Although data α is inputted from step 1), it may also be incorporated as a subroutine processing device in a program storage type digital computer.

As described above, according to the present invention, since the device is constituted by standard digital circuits such as an addition/subtraction device capable of addition and subtraction, an arithmetic device capable of multiplying by 1/2n, and a register, the device can be made at low cost. The circuit configuration is simple,
Since the number of repeated calculations is small and the accuracy is sufficiently improved if n is about 7, the calculation speed is orders of magnitude faster than when calculation is performed using software.

[Brief explanation of drawings]

FIG. 1 is a block diagram of an inverse trigonometric function calculation device according to an embodiment of the present invention, FIG. 2 is a diagram for explaining the embodiment of FIG. 1, and FIG. The flowchart to be executed, Figure 4 is C in Figure 1.
A flowchart diagram for executing the owα calculation, 'I45' shows the rotation angle r and the ! after rotation! FIG. 6 is a diagram representing a value of 1, and FIG. 6 is a diagram representing a constant at the start of an operation and an angle corresponding thereto. (4)... Force arithmetic unit M, (5+...X register, (6)...Y register xp, +7) -...Angle VV di xp
, 191-1/2" tA Jl' device 1, IIJ...
・X register, (''D...Y register, uto...sign register, (3)...constant generator 4, (8)...controller. Agent Shin Kuzuno - 1st ml Fig. 4

Claims (1)

[Claims] (1) An addition/subtraction device that adds or subtracts two inputs and outputs the operation result and its sign, x and Y registers that temporarily store the x and y components of orthogonal coordinates of the output of the addition and subtraction device, respectively; The angle register that temporarily stores the angle among the outputs of the adder/subtractor and the contents of the X register or Y register mentioned above are divided by 1/! n times (nz Q,
l, 2, m, m! m: integer) 1/!
n arithmetic device, an /,n The contents of the above Y register are converted to L by the n arithmetic unit.
A Y register that temporarily stores the result multiplied by /2n, a constant generator that generates a series of constants for the input value α, and a series of constants for the value of n above, and (Y In the case of Cosα calculation, the sign of the operation result is (contents of X register - input value α), and (contents of X register - manual value σ
), and a controller that controls the operation of each circuit according to the output of the sign register and the value of n, and the controller controls the contents of the X register and the Y/register. The contents of the Y register and the contents of the X register are input to the adder/subtracter to perform addition or subtraction, and the result of the operation is stored in the X register. The result of the calculation is stored in the Y register, and the contents of the angle register and the angle constant selectively output from the constant generator for the value of n are input to the addition/subtraction device to perform addition or subtraction, and the result of the calculation is is stored in the angle register, and the above operation is repeated from Hw Q to nm to obtain Sin.
An inverse trigonometric function calculation device characterized in that it calculates α or Cow cl.