JPH0285923A - Function value calculating device - Google Patents

Abstract

PURPOSE:To shorten the calculating time by performing the calculation of a trigonometric function with the addition, subtraction and multiplication only and with no division. CONSTITUTION:A 1st memory means 101 stores the value of a sine function and/or the value of a cosine function against the value within one cycle. While a 2nd memory means 102 stores the information corresponding to the input value in a format of floating decimals including the data on an exponential part and a mantissa part. Then a calculation means 103 obtains the corresponding value of a sine function and/or a cosine function against the input value by reference to a 2nd recording means in response to the corresponding mantissa and exponential part data and by reference to a 1st recording medium based on the mantissa part data. The value of the sine or cosine function is calculated to the input value with use of a formula for n-fold angle (n: an integer) of a trigonometric function against the value of the sine or cosine function and the exponential part data. Thus the values of sine and cosine functions can be obtained with the addition, subtraction and multiplication only. In such a way, a desired trigonometric function is obtained in a short time.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Field of Application] The present invention relates to a function value calculation device, and particularly to a function value calculation device suitable for calculating trigonometric functions.

[Prior Art] Numerical calculations regarding specific functions, such as trigonometric functions, are one of the basic functions essential for calculations in electronic computers and the like.

In an electronic computer, in order to calculate the value of a trigonometric function corresponding to a given input value, it is necessary to calculate π for any input value.
Calculations are performed by taking the modulo.

FIG. 6 is a flowchart showing an example of a processing procedure for calculating the value of a trigonometric function (in this case, a sine function (y=sin x)) by taking the modulo.

First, in step 561, a predetermined value is input. Next, by performing the operation in step S62, X becomes -
It is converted to π/2≦X≦π/2. In step 562, the function "cint" is used to round off the decimal point when converting the value of X/π to an integer value. Next, in step S63, the value of y is determined by substituting the value of X using Macrolin expansion or the like. Then, if the value of t is an odd number in step S64,
y”-y (step 565), y-sin
The value of x is found.

By looking at such processing steps, −π/2≦X
The value of sin X can be determined in the range of ≦π/2.

Originally, the sine function is a function with a period of 2π, so -
Range other than π/2≦X≦π/2, that is, −π≦X≦
In order to find the range of π and O≦X≦2π, it is necessary to change the sign of the sine function.

In any case, in the conventional function value calculation device, it is necessary to take the modulo of π in order to obtain a trigonometric function for a predetermined value. Therefore, division was essential in the process of taking the modulo of the argument.

However, the execution time for division in a multiprocessor unit (MPU) or digital signal processor (OSP) is usually many times longer than the execution time for addition, subtraction, and multiplication, which creates the problem that the calculation time increases accordingly. was. Such an increase in calculation time simply means that the throughput of MPti or DSP is reduced.

[Problems to be Solved by the Invention] Therefore, an object of the present invention is to solve the conventional problems and to solve the problems by calculating trigonometric functions using only addition, subtraction, and multiplication without performing division. It is an object of the present invention to provide a function value calculation device that requires less time and does not reduce the throughput of the calculation device.

[Means for Solving the Problems] In order to achieve the above object, the present invention provides a function value calculation device that outputs a sine function value and a cosine function value of an input value, as shown in FIG. The first storage means 101 stores the values of the sine function and/or the cosine function for values within one period, and the information corresponding to the input value is a floating point number having exponent data and mantissa data. With reference to the second storage means 102 stored in the format of the input value, the mantissa data is stored in correspondence with the corresponding mantissa data and exponent data. , the value of the sine function and/or the value of the sine function are determined with reference to the first recording means, and the n times angle ( However, by applying the formula (n is an integer),
It is characterized by comprising a calculation means 103 for calculating a value of a sine function or a value of a cosine function for the input value.

[Function] According to the present invention, there is no need to take the modulo of π for any value, and the values of the sine function and cosine function can be calculated only by addition, subtraction, and multiplication, so the calculation time is short. desired 3
An angular function is obtained.

[Example] The present invention will be explained in detail below.

Example 1 To find the value of the sine function or the value of the cosine function, use the following double angle formula for trigonometric functions: %Formula%.

Here, floating point numbers are expressed in the following format inside the multiprocessor unit (MPU). That is, x-(-1)" x 1.F x 2@(1), where S is the sign part, e is the exponent part, and 1.
F corresponds to the mantissa part, 1. The value of F ranges from -2 to 2.

The floating point format described above is
It is stored in the format shown in Figure 2.

In the above equation (1), dividing X by 2 is equivalent to subtracting 1 from the exponent part e.

Based on the above, this embodiment will be specifically described below.

FIG. 3 is a block diagram showing an embodiment of the function value calculation device of the present invention. 31 is a function calculator that calculates a sine function value and/or a cosine function value for values from -π to π, 32 is a central processing unit (CPU) that controls the entire function value calculation device, and 33 is (: Built into Pt133,
This is a read-only memory (ROM) in which programs and the like corresponding to the processing procedure described later with reference to FIG. 4 are stored. 34 is a calculation processing device that performs calculation processing in accordance with the instructions of the CPt 132, and 35 is a random access memory (RAM) provided with registers and the like for storing numerical values entered manually during calculation.

FIG. 4 is a flowchart showing an example of the processing procedure of the function value calculation device of the present invention.

First, in step 541, 1 of the floating point representation of
．． F is stored in register A in RAM 35, and the exponent part e is stored in register B in RAM 35.

Here, the value stored in register A, namely 1.
F is in the range from -2 to 2, so naturally it is from -π to π
It is within the range of Therefore, −
The value of the sine function and/or the value of the cosine function can be determined for values between 2 and 2.

Next, in step 542, the calculation processing unit 34 stores 5in (A) in the register C, and cos (
A) is stored in register D. In step S43, the calculation processing device calculates 2XCXD and 2XD"-1 and stores them in register E and register F, respectively.

In step S44, the value of B is subtracted by 1 and the value of B is
Put it as. In step S45, it is determined whether the value of B is greater than 0 or not. In step S45,
When it is determined that B>O, in step 546, the values stored in register E and register F are calculated as register C and register D, respectively, and the process returns to step S43. Following the same procedure, the value of the sine function and/or the value of the cosine function can be determined.

In step S45, if B≦0, step S47
Then, when 5in(x), the value of E is repeated, and when cos (x), the value of F is repeated, and the process ends.

In this embodiment, the following formulas are used to calculate the values of the sine function and cosine function. According to the double angle formula of trigonometric functions, when x'''nxa (+, + n - integer value).Here, [] represents the Gaussian symbol, and inside the multiprocessor unit, A floating point number is expressed by x= (-1)X1.F X2@ as in the first embodiment.

The present embodiment is almost the same as the block diagram of the function value calculation device of the first embodiment, but this embodiment does not have the register E and the register F.

FIG. 5 is a flowchart showing an example of another processing procedure of the function value calculation device of the present invention.

For x''nxa, the sign part S, the exponent part e, and the mantissa part 1.F are determined by itself.

First, in step S51, the mantissa of the floating point representation of X is stored in register A of the RAM 35, and the exponent part 2@ is stored in register B of the RAM 35.

Here, register A&: the stored value, i.e. 1
．． Since F is in the range from -2 to 2*, it is naturally in the range from -π to π. Therefore, the function calculator 31 can calculate the values of the sine function and the cosine function corresponding to values from -2 to 2.

Next, in step 552, the function value calculator
Store in(^) in register C and store cos(A) in register D. is calculated in step S53. In this way, the value of a predetermined sine function and cosine function can be calculated using the double angle formula.

In each of the above embodiments, the values of the sine function and the cosine function for input values from -π to π stored in the function calculator 31 can be calculated based on values from -π/2 to π/2. can. That is, values from π/2 to π/2 can be determined by macrolin expansion or the like. y-sin for values from −π to −π/2
It can be found from (x+π), and from π/2
Values up to can be determined by y-sin (x-π).

In this way, values within one period can be determined.

Here, if the value of 5in(x) is found first, cos(x
)-sin(x+π/2)-sin(yc/2-x
It can be obtained from J.

Furthermore, jan (x) can be obtained from tan (x) sin (x)/cos (ear).

[Effects of the Invention] As explained above, according to the present invention, it is not necessary to take the modulo of π for any value, and it is possible to calculate the value of a sine function and the value of a cosine function only by addition, subtraction, and multiplication. Therefore, it has the advantage that a desired trigonometric function can be obtained in a short calculation time.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing an example of the basic configuration of a function value calculation device of the present invention, Fig. 2 is an explanatory diagram showing a situation in which floating point numbers are stored in a central processing unit, and Fig. 3 is a function value calculation device of the present invention. A block diagram showing an embodiment of the calculation device; FIG. 4 is a flowchart showing an example of the processing procedure of the function value calculation device of the present invention; FIG. 5 is a flowchart showing an example of the processing procedure of the function value calculation device of the invention; FIG. 6 is a flowchart showing a conventional processing procedure for calculating a sine function. 101... First storage means, 102... Second storage means, 103... Calculation means, 31-... Function calculator, 32... Central processing unit (CPU), 33... ROM. 34... Computation processing device, 35... RAM. A block showing the beginning of the opening, the breaking of the value needle, and the month of disaster. Diagram 3
Figure 3 is a flowchart showing one member of the ring.

Claims (1)

[Claims] 1) A function value calculation device that outputs a sine function value and a cosine function value of an input value, wherein the sine function value and/or the cosine function value for values within one period are stored. a second storage means in which information corresponding to the input value is stored in a floating point format having exponent data and mantissa data; The value of the sine function and/or the sine function is determined by referring to the first recording means based on the corresponding mantissa data and exponent data. The value of the sine function for the input value or A function value calculation device comprising: calculation means for calculating a value of a cosine function.