JPH01295367A - Interpolation system for trigonometrical function - Google Patents

Abstract

PURPOSE:To shorten the arithmetic interpolation processing time by using a Taylor's expansion, addressing a data table to read out the differential coefficient of each member of said expansion, and applying the non-inversion or inversion to the relevant code. CONSTITUTION:A data table part 1 is prepared together with an address generating part 2, a bit inverting part 3 set between both parts 1 and 2, a code inverting part 4, and an arithmetic part 5. The data read out of the part 1 and undergone the non-inversion or inversion of its code via the par 4 is supplied to the part 5 for calculation of a Taylor's expansion. Thus it is possible to obtain the differential coefficients of each member of said expansion just by addressing the part 1 and changing the data code. Then the interpolation processing time is shortened.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to an interpolation method for trigonometric functions, and particularly to an interpolation method for trigonometric functions characterized by a correspondence method between differentiation of trigonometric functions and addressing nosing of a data table.

[Conventional technology]

Conventionally, the interpolation method for trigonometric functions has been a method in which interpolation is performed using values in a data table located before and after the value to be determined, such as by the Lagranche interpolation method.

For example, in the interpolation of a sine function, the third-order Lagranche interpolation formula for the sine function is y+ (Xo+ΔX) = sinx.

・ ・ ・■ s 1nx-,, s 1nxe, s inx,, s
inx.

was interpolated by substituting . However, as shown in Figure 3, x0+ΔX is the desired point, x-1+ x6+ xI+ x
2 is a point 5inx- corresponding to the address of the table near the desired point, each with an interval of Δ.

s 1nxo, s 1nxl, and s 1nx2 are values stored in the data table. The value obtained by interpolation is )'3(XO+ΔX).

[Problem to be solved by the invention]

The conventional interpolation method described above uses a Lagranche interpolation formula, etc., and performs interpolation by substituting the values in the data table before and after the desired value into the Lagranche interpolation formula. 1. The higher the value, the more times the data table is referenced and the more times the calculations are performed. There was a problem that the interpolation process took a long time.

For example, first-order Lagranche interpolation method of sine function% formula% The third-order Lagranche interpolation formula is the above formula 0.

Therefore, compared to formula ■, formula 0 requires 5i data to be substituted.
nx, which increases by 5inx-1. That is, as the order becomes higher as in the 0 expression, the number of types of data to be substituted increases, and as a result, the number of times data is introduced and the number of operations increases.

In order to solve the above-mentioned problems, an object of the present invention is to provide interpolation of trigonometric functions in which the interpolation processing time is shortened by utilizing Taylor expansion and the law between its differential coefficients for addressing data tables, etc. The goal is to provide a method.

[Means to solve the problem]

The trigonometric function interpolation method of the present invention includes: a data table section that stores trigonometric function values in a predetermined range as data; an address signal generation section that sends an address signal for reading required data to the data table section; A bit inverting unit that is provided between an address signal generating unit and a data table unit and non-inverting or inverting bits of the address signal; and a code that non-inverting or inverting the sign of data read from the data table unit. an inverting unit; and an arithmetic unit that takes data read from the data table unit and whose sign is not inverted or inverted by the sign inverting unit as a differential coefficient of each term and calculates a Taylor expansion formula of a trigonometric function. It is characterized by

〔Example〕

Next, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing a trigonometric function interpolation method according to an embodiment of the present invention.

As shown in FIG. 1, the trigonometric function interpolation method includes a data table section 1, an address signal generation section 2, a bit inversion section 3 provided between the address signal generation section 2 and the data table section 1, and , a sign inverting section 4, and an arithmetic section 5.

The data table section 1 stores required data.
Here, the value of 5inxk is stored as data. The value of this 5inx is the angle O ~ as shown in Figure 2.
It is the value of the sine function given at each point of n equal divisions between π/2 (rad). However, when 0≦≦n-1, Xk 7 ((2+1)/2n)·π/2. Note that, from the properties of the sine function and the cosine function, the value of 5inxlO at the point of X is equal to the value of cos x, -. Similarly, at the point Xk**, S j n
Xk+1 = COS x, -1<-g.

” At the point −2 to −Xn−, S 1 n Xn−
-2=COS Xk*I, 51 n at the point of -1 to Xn-1'=C05X11.

The address signal generating section 2 generates and outputs an address signal corresponding to read data in order to read required data from the data table section 1. This address signal generating section 2 is connected to the data table section 1 via a bit inverting section 3.

The bit inversion unit 3 includes a direct path 3a that directly connects the address signal of the address signal generation unit 2 to the data table unit 1;
Bit inversion circuit 3b that inverts the bits of the address signal
and a switching section 3C that switches between the direct path 3a and the bit inversion circuit 3b. The bit inverting circuit 3b inverts the bit of the address signal and inverts the bit of the address signal.
It has a function of reading the value of s xk from the data table unit 1.

Since only the sine function value is stored in the data table section 1 and the cosine function value is not stored, the 5inXn-
1° (using the relationship of o s
This is because it is necessary to read out a sine function value that is equivalent to the cosine function value. In other words, if n=2''' is set, the inversion of 1 for bit O in the binary representation of the address signal becomes n-
Since it matches the binary representation of -1, 5lnXn- becomes -
1, that is, data of cos XI() is read from the data table section 1.

The sign inversion unit 4 is provided between the data table unit l and the calculation unit 5, and has a direct path 4a that directly connects the data 5inx or cos xk read from the data table unit 1 to the calculation unit 5; Data 5inxk or co
a sign inverting circuit 4b which inverts the sign of s It is composed of

The arithmetic unit 5 calculates the formula 5in(
x,,+Δx)=s inx,+Δx・cosxk−□
(Δx)"5inx1゜■ 1□(Δx)'3cosxk...■ In order to perform this operation, a direct path 5a, a negative multiplier 5b, a quadratic multiplier 5c, and a cubic The multiplier 5d, these direct paths 5a and the multipliers 5b to 5
and an adder 5e that adds the results of c. The direct path 5a is a path for directly sending the data of 5inxk, which is the 0th order term of the equation (2) above, to the addition section 5e. The -order multiplier 5b has the function of multiplying the data of cos The third-order multiplier 5d has a function of multiplying the third-order term (-cosx, ) by ΔX three times and by 1/6.

Next, the operation of this embodiment will be explained.

The address signal from the address signal generating section 2 is inputted to the data table section 1 via the direct path 3a connected to the data table section 1 by the switching section 3c of the bit inverting section 3, , is read out as data.

This 5inxA signal is input to the calculation section 5 via the direct path 4a connected to the calculation section 5 by the switching section 4C of the sign inversion section 4.

In addition, when reading the value of cos The signal k is input to the bit inversion circuit 3b. The address signal input to the bit inverting circuit 3b is outputted from the bit inverting circuit 3b as -1 in the address signal n- by a bit inverting effect, and from the data table section 1, s inX, - in -l =
(Read the value of o s Xk. This co s Xk
The signal is sent to the arithmetic unit 5 by the switching unit 4c of the sign inverting unit 4.
The signal is input to the arithmetic unit 5 via a direct path 4a connected to the .

Furthermore, -5inx and -cos xk are calculated by the calculation unit 5.
If you want to input 5inxk and cos
The signal is sent to the calculation unit 5 by the switching unit 4c of the sign inverting unit
This is performed by inputting the signal to the sign inverting circuit 4b connected to the sign inverting circuit 4b. The -5inxk and -cosxk signals whose sign has been inverted by the sign inverting circuit 4b are input to the arithmetic unit 5.

5inxk entered into the calculation unit 5 as described above.

The signals cosx, -s inx, -CO3Xk are sequentially transmitted through the direct path 5a, -th multiplier 5b, and secondary multiplier 5.
c, is input to the cubic multiplier 5d, multiplied by the multipliers 5b to 5d, and then input to the adder 5e and added.

That is, the Taylor expansion equation shown in equation (2) above is calculated.

As explained above, the trigonometric function interpolation method according to the present embodiment allows the differential coefficient of each term of the Taylor expansion formula to be obtained by simply changing the addressing and data sign of the data table section 1, and as a result, the data table Data can also be read out from the unit 1 only twice, 5 inx and s in x, so that the speed of arithmetic processing can be increased.

In addition, in this example, an example is shown in which the formula for the Taylor expansion of the sine function is calculated by dividing it into cubic terms as shown in (■) above, but the purpose is not limited to this, and the calculation is It is clear that by increasing the computational power of section 5, it is possible to calculate terms of any order.

Also, the Taylor expansion formula up to the third order term of the cosine function is cos
(x, +Δx) = cosx, -Δxsinxk−-(Δ
x)”・cosx.

+-(Δx)'-5inxk Therefore, when calculating the interpolation of the cosine function, C03Xh (0≦≦n 1.
It is clear that if the value of Xm = ((2 + 1)/2n) · ff/2) is stored, it can be determined using a method similar to the method described above.

〔Effect of the invention〕

As explained above, in the interpolation method of trigonometric functions, the present invention uses a Taylor expansion formula, reads out the data of the differential coefficient of each term by addressing the data table, and also non-inverts or inverts the sign. , all the differential coefficients of each term can be found, so
The number of interpolation calculations is small, and as a result, the interpolation calculation processing time can be reduced.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing a trigonometric function interpolation method according to an embodiment of the present invention, FIG. 2 is a diagram showing data stored in the data table section used in FIG. 1, and FIG. 3 is a conventional FIG. 3 is a diagram showing an interpolation method. 1...Data table unit 2...Address signal generation unit 3...Bit inversion unit 4...Sign inversion unit 5...Arithmetic unit agent Patent attorney Iwa Yoshiyuki Sa

Claims (1)

[Claims] (1) A data table section that stores trigonometric function values in a predetermined range as data, an address signal generation section that sends an address signal to read the required data to this data table section, and these address signal generation sections and the data table. a bit inversion section that is provided between the data table section and non-inverts or inverts the bits of the address signal; a sign inversion section that non-inverts or inverts the sign of the data read from the data table section; A trigonometric function characterized by comprising: an arithmetic unit that calculates a Taylor expansion formula of a trigonometric function by taking data read from the unit and whose sign is not inverted or inverted by the sign inverting unit as a differential coefficient of each term. interpolation method.