JPH0272480A - Mean value arithmetic means - Google Patents

Abstract

PURPOSE:To easily make the error of a mean value into a small value without generating an overflow by dividing a digital numeric value with a prescribed coefficient, and providing two memories which respectively store a quotient value as the result of a division and a remainder value. CONSTITUTION:The digital numeric value is divided by a prescribed coefficient A, the quotient value as the result of the division and the remainder value are allocated to two types of memories 1 and 2, and the added result between the remainder value and the next digital numeric value is divided again by the prescribed coefficient A. Further, the present quotient value and the last quotient value are added to be stored and updated to the first memory 1, the present remainder value is stored and updated to the second memory 2 instead of the last remainder, and the processings are respectively repeated. Thus, the overflow of the memory can be prevented, rounding-up and rounding-off, etc., are not executed even if the value is divided by the prescribed value, the error is not generated at all until the division by means of the total number (n) for the output of the mean value, and the error can be easily suppressed to the small value <= a decimal point.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to an arithmetic method for a digital numerical control device, and particularly to an arithmetic method for preventing overflow of digital numerical values and obtaining a highly accurate average value.

[Conventional technology]

Conventionally, as a method for calculating the average value in a digital numerical control device, there is a method of adding all the digital values and then dividing by the number of all digital values to obtain the average value. When doing so, in some cases, the memory capacity may be exceeded and an overflow may occur, making calculations impossible. In order to prevent this, there is a method of determining the average value by limiting the number of digital numerical values to be added, that is, the number of samplings.

For example, if the number of samplings that does not exceed the memory capacity is , first add the digital values from 1st to 1(th), then divide the number of samples by 0 to obtain the average value, then (k± 1) Add the th digital value and the value obtained by multiplying this average value by <k-1>,
This method calculates the average value by repeating dividing by the number of samples again from the (k+1)th to the last nth digital value.

[Problem to be solved by the invention]

However, according to the arithmetic method described above that adds all the digital numbers and then calculates the average value, in order to ensure a sufficient number of digits and prevent overflow, a large memory capacity is required and the cost is high. Furthermore, the calculation method in which the average value is determined by limiting the number of samples has the problem of poor accuracy.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide an average value calculation method that can prevent memory overflow and suppress errors to a small value below the decimal point in a digital numerical calculation device.

[Means to solve the problem]

The average value calculation method according to the present invention is to divide the sum of the first digital value and the second digital value by a predetermined coefficient, and then divide the value of the quotient of this division result into the first value. After storing the remainder value in a memory and storing the remainder value in a second memory, adding a third digital numerical value and the numerical value stored in the second memory, and dividing the addition result by the predetermined coefficient; The value obtained by adding the quotient value of this division result and the numerical value stored in the first memory is set as the numerical value stored in the first memory, and the stored numerical value is updated, and the value of the remainder is stored in the second memory. The stored numerical value is updated as the numerical value to be stored, and thereafter, the numerical values stored in the first memory and the second memory are sequentially updated in the same manner from the fourth digital numerical value to the nth digital numerical value, The total number n of digital values for the value stored in the first memory updated by the nth digital value
After dividing by, the predetermined coefficient is multiplied, and this multiplication result is added to the value obtained by dividing the numerical value stored in the second memory updated by the n-th digital numerical value by the number n. Features.

[Effect]

According to the average value calculation method according to the present invention, a digital numerical value is divided by a predetermined coefficient, the quotient value and the remainder value of the division result are allocated to two types of memories, and this remainder value and the next digital Divide the addition result with the numerical value again by the predetermined coefficient,
The current quotient value and the previous quotient value are added together and stored and updated in the first memory, and the current remainder value is stored and updated in the second memory instead of the previous remainder. By repeating each, the digital numbers stored in each memory will be those with a small number of digits, so
It is possible to prevent memory overflow that occurs when all digital values are added as they are, as in the past, and even when dividing by a predetermined coefficient, the quotient value and remainder value are assigned to respective memories, and rounding up or down can be avoided. Therefore, no equivalent error occurs until division by the total number n to obtain the average value, and the error from the true average value is determined by the number of significant digits in the memory, so it is easy to add errors to small values below the decimal point. It can be suppressed.

〔Example〕

Next, regarding an embodiment of the average value calculation method according to the present invention,
A detailed description will be given below with reference to the accompanying drawings.

FIG. 1 shows an embodiment of the present invention and shows an overview of the calculation procedure of the average value calculation method. In FIG. 1, ~D is a digital value, n is the number of all digital values,
A is a predetermined coefficient. The predetermined coefficient A is larger than n, preferably a value such that the value of the quotient when the digital numerical value is divided by A is at least one digit smaller, and the value is such that the memory will not overflow even if n values of this quotient are added. For example, a value such as 10' or 104 is a good value to choose. First, add the first digital value D1 and the second digital value D2, and set D and D2 to a value that will not overflow even if you calculate them), and then calculate this addition result by a predetermined coefficient A. Divide. The quotient value of the division result is written to memory 1, and the remainder value is written to memory 2, so there is no need to round up or down.
After adding the third digital value and the remainder value written in the memory 2, division is again performed by the predetermined coefficient A.

The value obtained by adding the current quotient value and the previous quotient value written in the memory 1 is updated to the value X in the memory 1 as the current value. Also, the current remainder value is rewritten as (fiy) in memory 2.

Hereinafter, after repeating the series of calculation steps enclosed by the dashed line 10 until the last digital value, the value in memory 1 is divided by the total number of digital values n, and multiplied by a predetermined coefficient A. , the value in memory 2 is similarly divided by n, and the result of this division is added to the result obtained by multiplying the predetermined coefficient A, the average value of n digital numbers, ~D, is obtained. The obtained average placement and the digital numerical value D1~
The error between the true average value obtained by adding all D and dividing by the total number n (assuming no overflow) is limited only by the number of significant digits in memory 1 and memory 2. If the number of significant digits is sufficiently large, the error can be infinitely close to zero. Therefore, by selecting an appropriate number of significant digits, the error can be easily suppressed to below the decimal point.

FIG. 2 shows the calculation procedure of the average value calculation method according to another embodiment of the present invention. This calculation method eliminates the condition that

In this embodiment, first, the values of memory 1 and memory 2 are set to all zeros as initial fIiXO, yo, respectively. Then, the first digital value D1 and rly of memory 2 are set to zero.

This value is divided by a predetermined coefficient A.

The quotient value is added to the value Xa of memory 1, and a new memory 1 is created.
[Rewrite as [X]. On the other hand, the remainder value is rewritten as y instead of the value y0 in memory 2. From the second digital value D2, the previous value, memory 1
Using value X of , and value y of memory 2, digital numerical value D
The calculation procedure shown by the dashed-dotted line 30 similar to 1.
The process is repeated up to the th digital value. After this, each value in memory 1 and memory 2 is calculated in the same manner as in the embodiment of FIG. 1, and an average value is obtained.

This embodiment differs from the embodiment shown in FIG. 1 only in that memory 1 and memory 2 are initially set to zero.
The same applies to the error in the average value found.

〔Effect of the invention〕

As is clear from the embodiments described above, according to the present invention,
2 memories for dividing a digital numerical value by a predetermined coefficient and storing the quotient value and remainder value of the division result, respectively.
Since the number stored in each memory is divided by the total number, there will be no error until it is divided by the total number, and since the digital numbers handled are small, overflow will not occur. By selecting an appropriate value, it is possible to easily reduce the error in the average value to a small value below the decimal point.

[Brief explanation of the drawing]

FIG. 1 is a block diagram of a calculation procedure showing one embodiment of the average value calculation method according to the present invention, and FIG. 2 is a block diagram of a calculation procedure showing another embodiment of the calculation method of the present invention. 1... Memory (for quotient value) 2... Memory (for remainder value) 10... Repeat calculation procedure 20... Initial value calculation procedure 30... Repeat calculation procedure DI to D1...・Digital numerical value n... Number of digital numerical values A... Predetermined coefficient X o + 'j'... Initial value (zero) X... Numerical value in memory 1 y... Numerical value in memory 2

Claims (1)

[Claims] (1) Divide the sum of the first digital value and the second digital value by a predetermined coefficient,
After storing the quotient value of this division result in the first memory and storing the remainder value in the second memory, the third digital value and the value stored in the second memory are added. , divide the addition result by the predetermined coefficient, and update the stored numerical value by adding the quotient value of this division result and the numerical value stored in the first memory as a numerical value stored in the first memory. At the same time, the value of the remainder is stored in the second memory and the stored numerical value is updated, and from the fourth digital numerical value to the nth digital numerical value, the first memory and the second digital numerical value are stored in the same manner. The numerical values stored in the memory are updated sequentially, and the total number n of digital numerical values is calculated for the numerical value stored in the first memory updated by the nth digital numerical value.
After dividing by, the predetermined coefficient is multiplied, and this multiplication result is added to the value obtained by dividing the numerical value stored in the second memory updated by the n-th digital numerical value by the number n. Features an average value calculation method.