JP3194080B2 - Fraction processing device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a fraction processing device required for analysis, measurement, investigation and the like. More particularly, it relates to a numerical rounding capable rounding apparatus in accordance with the digit specification and JIS standards by significant digits.

[0002]

2. Description of the Related Art In general, fraction processing represented by rounding is widely performed, and examples thereof include organizing experimental data and accounting processing. The process of rounding is often provided as a function in high-level languages and data processing software, and the user can obtain the rounded number by specifying the numerical value and the position of the digit to be processed. It is.

FIG. 6 shows processing performed by a conventional rounding function. First, the user inputs a numerical value x to be processed and a digit position p to be processed (step S601). For example, the position p of the digit to be processed is specified as -2 for hundreds, 0 for integers, and +3 for the third decimal place. Next, given numerical value x
Is stored in a memory for each digit (step S602), and the numerical value of the digit immediately to the right of the designated digit position p is obtained from the memory (step S603), and it is determined whether the numerical value is 5 or more. (Step S604). When the result of the determination is 5 or more, a round-up process is performed (step S60).
5) If it is not 5 or more, a truncation process is performed (step S606). As described above, the conditional branch processing performed by the conventional function is performed by extracting only one digit from a plurality of digits and performing the conditional branch processing.

[0004]

However, the prior art has the following problems.

(1) The digits to be processed cannot be designated by the number of significant digits Currently, spreadsheet software currently on the market does not originally have the concept of designating the digits to be processed by significant digits.

In addition, even if the designated digit is processed by counting from the highest digit, the conventional conditional branching process, that is, a process of taking out only one of a plurality of digits and performing a discriminating process is performed. As far as the procedure is concerned, other conditional branch processing is required so that the number of significant digits can be specified across the decimal point. For example, when rounding off with 0.0000234 as two significant digits, if the count is made as it is, the third decimal place is taken in and rounded. for that reason,
Count while taking in numerical values in order from the highest digit,
It is determined whether or not the fetched number is 0, and if it is 0, a conditional branching process is required such that the digit is not counted. In addition, for example, in the case of rounding off to four significant figures, if the numerical value is 30,200, all of the thousands place, the tens place, and the ones place must be counted. If it is 34502, the first-place zero is not counted, but the fourth-place zero and the like must be counted, so more conditional branch processing is required.

As described above, according to the conventional processing procedure, when the digits to be subjected to the fraction processing are specified by the number of significant digits, the processing must be very complicated. For this reason, the conventional function does not permit designating digits with significant figures, and there is no spreadsheet software capable of designating digits with significant figures.

It is a first object of the present invention to provide fraction processing software capable of designating a digit to be processed as a fraction with the concept of a significant digit.

(2) Inapplicability to JIS standard With simple rounding, the result is biased by the number of data, so fraction processing for correcting the bias, that is, rounding is required. The JIS standard defines a rounding method for that purpose. For example, in the case of materials to be submitted to public offices, it is often necessary to round a numerical value in accordance with the JIS standard.

FIG. 7 shows a rounding method defined by the JIS standard (Z8401). This basically rounds off,
The remaining 5 is subjected to a sorting process. (N + 1) to round a number to a number with n significant digits
The numbers below the first digit are arranged as follows. (A) If the value of the (n + 1) th digit or less is less than 1/2 of one unit of the nth digit, it is truncated. (B) If the value of the (n + 1) th digit or less exceeds 1/2 of one unit of the nth digit, the nth digit is increased by one unit. (C) When the numerical value of the (n + 1) th digit or less is 1/2 of one unit of the nth digit, the following (i) and (ii) are performed. (i) If the value of the n-th digit is 0, 2, 4, 6, or 8, round down. (ii) If the n-th digit is 1, 3, 5, 7, 9
Increase the nth digit by one unit.

The significant digits are counted from the highest non-zero digit. This rounding must be performed in one step. For example, if 5.346 is rounded to two significant figures by this method, it becomes 5.3. If this is divided into two stages, it will be 5.35 in the first stage and 5.4 in the second stage.

As a processing procedure, first, it is determined whether the number in the (n + 1) th digit is 6 or more (step S702). If it is 6 or more, the nth digit is incremented by 1 and the (n + 1) th and subsequent digits are discarded. (Step S706). For example, if accordingly 13.4 6 1 than rounded to three significant digits, 1
3.5.

Next, it is determined whether or not the number in the (n + 1) th digit is 4 or less (step S703), and if it is 4 or less, the digits after the (n + 1) th digit are discarded (step S70).
7). For example, if the rounding 12.8 4 9 to three significant figures, and 12.8.

If the (n + 1) th digit is neither 6 or more, nor 4 or less, that is, if the (n + 1) th digit is 5, n +
It is determined whether or not all the digits after the second digit are 0 (step S704).
The digit is increased by one, and the digits after the (n + 1) th digit are discarded (step S706). For example, if accordingly the rounding 13.4 51 three significant figures, and 13.5.

On the other hand, if all the digits after the (n + 2) th digit are 0, it is determined whether the nth digit is an even number or an odd number (step S705). As a result, if the n-th digit is an even number, the digits after the (n + 1) -th digit are truncated (step S).
707). For example, 11. If 450 is rounded to three significant figures, it is 11.4. Conversely, if the n-th digit is an odd number, the n-th digit is incremented by 1 and the digits after the (n + 1) -th digit are discarded (step S706). For example, 12. 75
If 0 is rounded to three significant digits, it is 12.8.

However, if a numerical value required for discrimination is extracted for each digit and treated as one numerical value as in the conditional branching process performed by the conventional rounding function, the conditional branching process in step S704 in FIG. Therefore, as shown in FIG. 8, a number of conditional branch processes (steps S804 to S807) are required.

In this part, it is determined that the (n + 1) th digit is 5, and the lower digits are 0000000.... In such a processing procedure, all digits must be determined.

For example, if the digit lower than the digit to be rounded is 500
In the case of 00001, rounding up must be performed according to the JIS standard. When a human makes a judgment by eye, it is immediately apparent that there is a digit other than 0 in the lower digit, but when a computer is used, the method of judgment becomes a problem. In the conventional processing for discriminating each digit, it is discriminated whether the n + 2 digit is 0, and the n + 3 digit is 0.
And the n + 4 digit is determined to be 0, and so on, until the least significant digit is determined. If there is no 0 at all after the n + 2 digit, or if any digit other than 0 is found in any digit It is determined whether there is. Since each digit is sequentially discriminated, the final discrimination cannot be made until after many branching processes.

Furthermore, considering the number of digits that can be calculated by today's computers, the number of conditional branch processing is expected to be enormous. Therefore, in the conventional procedure, it is necessary to limit the number of digits of the numerical value to be processed much more than the processing capability of the computer itself, and to reduce the number of necessary conditional branch processes. For this reason, even if it is softened,
The calculation has to be performed at a level considerably lower than the computing power of the computer, the processing range is narrow, and it cannot be commercially available. Thus, JIS (Z84)
Software that can perform numerical rounding based on 01) has not been developed or put into practical use.

A second object of the present invention is to provide fraction processing software capable of rounding a numerical value according to JIS standard (Z8401).

[0021]

According to a first aspect of the present invention, there is provided a fraction processing apparatus comprising: an input means for inputting a value x before a fraction processing and a significant digit number n; and an n storage means for storing the entered significant digit number n. And the numerical value x input by the input means is A × 10
^{When a} is expressed in the form of a (where A does not include 0 in the least significant digit and the original numerical value is multiplied by ^a power of 10 ^a such that a number other than 0 does not exist below the decimal point) Integer part exponent calculating means for calculating the integer A and exponent a; exponent part storing means for storing the exponent a calculated by the integer part exponent calculating means; and integer A calculated by the integer part exponent calculating means And an integer A stored in the integer part storage means and a significant figure n stored in the n storage means, and the integer A is rounded to n significant figures to calculate an integer B. Fraction processing means, a digit restoring means for calculating B × 10 ^a using the integer B calculated by the fraction processing means and the exponent a stored in the exponent part storage means, and an operation result by the digit restoring means is effective. Output means for outputting an n-digit number.

According to a second aspect of the present invention, in the fraction processing device according to the first aspect, the fraction processing means converts the numerical value of the integer A from the (n + 1) th digit after the integer A stored in the integer part storage means. Take out as one numerical value, the numerical value is 5
And a fifth determining means for determining whether or not the integer A is equal to 5. If the five determining means determines that the value obtained by adding one after the (n + 1) th digit is equal to 5, the nth digit of the integer A is divided by 2, and the remainder is calculated. Is an odd number discriminating means for discriminating whether or not is 0, and a value obtained by the fifth discriminating means from the (n + 1) th digit to one is 5
When it is determined that the remainder is not equal to, the rounding-off determination means for determining whether or not the value of the (n + 1) th digit of the integer A is 5 or more, and the remainder is determined to be 0 by the even-odd number determination means. Case, and n +
When it is determined that the first digit is not greater than or equal to 5, when the remainder is not 0 by the truncation processing means for calculating the integer B by truncating the value after the (n + 1) th digit, And n is determined by the
And a round-up processing means for calculating an integer B by incrementing the n-th digit by 1 and discarding the value after the (n + 1) -th digit when it is determined that the + 1st digit is 5 or more. It is.

[0023] The fraction processing device according to claim 3 is an integer A
Processing to calculate the integer B by performing a rounding on the number of significant digits n
A device for converting the value after the (n + 1) th digit of the integer A into one
Take out as a number and determine if the number is equal to 5
5 discriminating means, and the (n + 1) th digit or more by the 5 discriminating means.
If it is determined that the numerical value of one descending is equal to 5,
Divide the n-th digit of the integer A by 2 to determine whether the remainder is 0 or not.
The different even / odd discriminating means and n +
Determines that the value after the first digit is 1 is not equal to 5
When the value of the (n + 1) th digit of the integer A is 5 or more,
Rounding determining means for determining whether or not
When the determination unit determines that the remainder is 0, and
The n + 1 digit is not more than 5 by the rounding discrimination means.
If it is determined that the
Truncation processing means for calculating an integer B
If the number discriminating means determines that the remainder is not 0,
And the n + 1 digit is 5 or more by the rounding discrimination means.
When it is determined that the n-th digit is increased by one and the (n + 1) -th digit
Round-up processing to calculate integer B by truncating subsequent values
Means.

[0024] The fraction processing device according to claim 4, wherein the integer A
To calculate the integer B by performing a rounding on the nth digit from the top
A processing device, wherein the numerical value after the (n + 1) th digit of the integer A is 1
And extract whether it is equal to 5
5 discriminating means for discriminating, and n + 1 digits by the 5 discriminating means
When it is determined that the number after the first is equal to 5
Divides the n-th digit of the integer A by 2, and determines whether the remainder is 0
And odd number discriminating means for discriminating
If the number after the (n + 1) th digit is 1 is not equal to 5,
If it is determined, the value of the (n + 1) th digit of the integer A is 5 or more
A round-off determining means for determining whether or not
If the odd number discriminating means determines that the remainder is 0,
And the n + 1 digit is 5 or more by the rounding discrimination means.
If it is determined that there is no
A truncation processing means for calculating an integer B by discarding,
If the odd number discriminating means determines that the remainder is not 0,
And the (n + 1) th digit is 5 or more by the rounding discrimination means.
If it is determined to be above, the nth digit is increased by 1 and n +
Rounding up to calculate integer B by truncating the first and subsequent digits
And processing means.

[0025]

Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a block diagram showing an embodiment of a fraction processing device according to the present invention. The devices are an input device 1, a storage device 3, a ROM 5, a CP
U6, a storage device 7, a display device 12, and a printing device 13 are provided.

The input device 1 is provided with a numeric keypad 2 for inputting significant figures.
Send to The storage device 3 has a calculation / measurement result storage area 4 in which numerical data such as measurement results of experiments and the like and calculation results are stored in advance. The numerical data stored in the calculation / measurement result storage area 4 is sent to the CPU 6 and subjected to fraction processing.

The ROM 5 stores a program for performing fraction processing, and the CPU 6 performs operations such as calculation, reading, and writing according to the program. In this embodiment, the program is stored in the ROM 5. However, the RAM is used instead of the ROM, and the program recorded on a recording medium such as a floppy disk, a hard disk, or a magneto-optical disk is read into the RAM. Can also.

The storage device 7 has a numerical value storage area 8 before rounding,
The CPU 6 includes an integer part storage area 9, an exponent part storage area 10, and a rounded numerical value storage area 11. When the CPU 6 performs processing, these storage areas are used as needed. The pre-rounding numerical value storage area 8 stores numerical values to be processed among the numerical data stored in the calculation / measurement result storage area 4 of the storage device 3. The integer part storage area 9 stores a numerical value of the integer part when the numerical value stored in the pre-rounding numerical value storage area 8 is represented by an exponent, and the exponent part storage area 10 stores an exponent. The rounded numerical value storage area 11 stores the numerical value after performing the fraction processing, and can read out the numerical value and display the processing result on a display device 12 such as a CRT, and a printing device 13 such as a laser printer. Can also be output.

FIG. 2 shows a processing procedure in the case where the truncation process is performed with n significant digits according to the present invention. First, the numerical value x to be processed and the number of significant digits n are input (step S20).
1). The numerical value to be processed may be one of the data stored in the calculation / measurement result storage area 4, but may be directly input by the operator. The input numerical value x before processing is stored in the numerical value storage area 8 before rounding.

Next, the numerical value x before processing is divided into an integer part A and an exponent part, and x = A × 10 ^a (A does not include 0 in the least significant digit,
In addition, the original numerical value is represented by a product of ^a power of 10 and ^a so that a number other than 0 does not exist below the decimal point.
And a are calculated (step S202). For example, if x is 0.00021, then it is 21 × 10 ^-5 , so A
Is 21 and a is -5, and if x is 320100,
Since it is 3201 × 10 ² , A is 3201 and a is 2.

The integer A and index a thus calculated are stored in the storage device 7 (steps S203, S203).
204). The exponent a is stored in the exponent part storage area 10,
The integer A is stored in the integer part storage area 9 for each digit. For example, when the integer part A is 3201, 3, 2,
0, 1 and the numerical value of each digit are stored separately. In step S205, the numerical value of each digit after the (n + 1) th digit counted from the highest digit of each digit of the integer A is rewritten to 0. At this stage, since the numerical value after the truncation processing is stored in the integer part storage area 9 for each digit, step S206
Then, the value stored for each digit is converted into one numerical value. For example, the numerical value stored for each digit as 3, 2, 0, 0 is 3
It is converted to the number 200.

Steps S204 to S206 are portions for performing the truncation processing, and the truncation processing can be performed using various conventional processing in addition to the processing shown in the figure.

[0033] Finally, by reading the index a stored in the exponent part storage area 10 (step S207), by performing the multiplication between the integer part and exponent part 10 ^a after the truncation, truncation The result is calculated (step S208). The calculated truncation result is stored in the numerical value storage area 11 after rounding and is output to the display device 12, the printing device 13, an external storage medium or the like as needed (step S209).

Here, 0.205 is truncated to two significant figures according to the flowchart shown in FIG. First, in step S201, 0.
205 is input, and 2 is input as the number of significant digits n.
In step S202, 0.205 is separated into an integer part and an exponent part, and becomes 205 × 10 ⁻³ .

In step S203, the index a is -3.
Is stored in the exponent part storage area 10. Step S20
In 4, the integer part A 205 is divided into 2, 0, and 5 and stored in the integer part storage area 9 in order. Step S20
In 5, the number corresponding to the (n + 1) th digit or more, that is, the digit after the third digit, is rewritten to 0. In this case, the last 5 is rewritten to 0. In step S206, the sequence of numbers in the integer part storage area 9 that has become 2, 0, 0 is converted to a numerical value of 200. Then, in step S207, a numerical value of -3 stored in the exponent part storage area 10 is extracted, and in step S208, 200 × 10 ^-3 is calculated, and a rounded result of 0.20 is obtained.

FIG. 3 shows a processing procedure in the case where a round-up process is performed by designating a digit with a significant digit according to the present invention. As in the case of the truncation process (FIG. 2), a numerical value x to be processed and the number of significant digits n are input (step S30).
1), separating the numerical value x to an integer part A and the exponent part 10 ^a (step S302), and stores the index a in the exponent part storage area 10 (step S303).

Steps S304 to S311 are an example of rounding-up processing for the integer part A.
Various conventional means other than the processing method shown in the figure can be used. In the round-up processing shown in FIG. 3, first, the integer part A is stored in the integer part storage area 9 for each digit (step S304). Then, of the integer part A stored for each digit, only the number of each digit corresponding to the (n + 1) th digit and thereafter is restored to the original value and converted into one numerical value (step S305). It is determined whether this numerical value is 1 or more (step S306). If not, the process proceeds to step S311 without performing the round-up process. This numerical value, that is, n +
When the value obtained by returning the first and subsequent digits to one number is 1 or more, the rewriting process from step S307 to S310 is performed.

In step S307, n is set from the highest digit to n.
Convert up to the first digit and convert it to a single number. And
One is added to the numerical value up to the n-th digit (step S30).
8) Store again in the integer part storage area 9 for each digit (step S310). Next, of the respective digits of the integer part A stored for each digit, each numerical value corresponding to the (n + 1) th digit and thereafter is set to 0.
(Step S310).

After such processing, each digit of the integer part storage area 9 is taken out and returned to one numerical value (step S311). At step S312, the index a is retrieved which is stored in the exponent part storage area 10, in step S313, the multiplication of the round-up process integer part and 10 ^a is performed. Then, the calculation result is output in the same manner as in the case of FIG. 2 (step S314).

Here, 1270400 is rounded up to two significant figures according to the processing procedure according to the present invention. First, in step S301, 1270 is set as a numerical value x.
400, 2 is input as a significant figure n. 12704
00 is 12704 × 10 ² , so the integer part A is 1
2704, the index a becomes 2. Therefore, 2 is stored in the exponent part storage area 10 (step S303), and the numbers 1, 2, 7, 0, and 4 are sequentially stored in the integer part storage area 9 (step S304).

In step S305, after the (n + 1) th digit,
That is, the numbers 7, 4, and 0 after the third digit are extracted and converted into one numerical value 740. Since this numerical value is 1 or more, the process proceeds to step S307 (step S30).
6). In step S307, numerical values up to the n-th digit of the integer part A, that is, numerical values 1 and 2 up to the second digit are extracted and converted into one numerical value 12. In step S308, 1 is added to this numerical value to become 13.

Then, it is stored again for each digit in the integer part storage area 9 (step S309). After such processing, 1, 3, 7, 4, 0 is stored in the integer part storage area 9.
Are stored in order. Then, n +
Numerical values 7, 4, 0 corresponding to the first and subsequent digits, that is, the third and subsequent digits
Are respectively rewritten to 0 (step S310), and the numerical values of the integer part storage area 9 are 1, 3, 0, 0, 0.
If this is returned to one numerical value, it becomes 13000 (step S311).

Finally, 2 is extracted from the exponent part storage area 10 (step S312), and multiplication of 13000 × 10 ² is executed (step S313), and the operation result 13
00000 is output (step S314).

FIG. 4 shows a processing procedure for rounding off by designating the number of significant digits according to the present invention.
Rounding that can be specified by the number of significant digits can be executed by combining the round-down procedure shown in FIG. 2 and the round-up procedure shown in FIG.

In steps S401 to S404, the numerical value x is divided into an integer part A and an exponent part ^10a and stored in the respective storage areas 9 and 10 as in the case of FIGS. Then, at step S405, n +
The numerical value of the first digit is taken out from the integer part storage area 9 and it is determined whether or not it is 5 or more. The number in the (n + 1) th digit is 5.
When it is determined that the above is the case, the round-up processing is performed (Step S406), and when it is determined that the number is not more than 5, the round-down processing is performed (Step S40).
7). The round-down process and the round-up process are shown in FIGS. 2 and 3 (steps S204 to S206 in FIG. 2, steps S304 to S311 in FIG. 3).
In addition, various commonly used means can be applied.

[0046] In the case of FIGS. 2 and 3 and are made operational to multiply the exponent 10 ^a in the same manner, the operation result is outputted (steps S408 S410).

FIG. 5 shows significant figures n according to the JIS standard.
It is a flowchart which shows the processing procedure at the time of performing numerical value rounding by a digit. First, the numerical value x before rounding and the number of significant digits n are input (step S501). The pre-rounding value x is stored in the pre-rounding value storage area 8. Next, the value x before rounding is converted to an integer part A.
A × 10 ^a is calculated to divide the data into the exponent part 10 ^a (step S 502), the exponent a is stored in the exponent part storage area 10 (step S 503), and the integer part A is stored for each digit in the integer part storage area. 9 (step S504). In the integer part A, the value after the (n + 1) th digit is returned to one numerical value again (step S505). That is, by doing in this way, it is divided into the highest digit to the n-th digit and the n + 1-th digit and thereafter, and the n + 1-th digit and thereafter are extracted as one numerical value.

Then, an operation of dividing the numerical value after the (n + 1) th digit by 5 is performed, and it is determined whether or not the result of the division is 1 (step S506). Thus, in the present invention,
In particular, divided rounding before numerical value x to the integer part A and the exponent 10 ^a,
Further, by performing an operation of dividing the (n + 1) th digit and subsequent digits of the integer part A by 5, it has been determined that it has been difficult to round the value according to the JIS standard in the past. That is, if the (n + 1) th digit is 5, the n + 2 digits It is possible to make substantially the same determination as whether or not all of the eyes are 0.

That is, conventionally, the case where the numerical value of the (n + 1) th digit or less corresponds to exactly 5 (the least significant digit where a number other than 0 appears in the digits constituting the numerical value is 5) has been the most problematic. In the present invention, the numerical value x before rounding is represented by an exponent and its integer part is taken. Therefore, in such a case, the first place of the integer part A is always 5. Since the n-th digit is the tens place of the integer part A, after the process of step S505, n + 1
5 will be extracted as the numerical value after the first digit. Therefore, if it is determined whether the result obtained by dividing the number obtained after the (n + 1) th digit by 5 is 1 or not, the least significant digit of the value x before rounding is 5 and this digit is n + 1 digits You can extract cases that correspond to your eyes.

For example, 0.0125 is set to J in two significant figures.
When performing rounding numerical by IS standard, when dividing this number to an integer part A and the exponent 10 ^a, since it is 125 × 10 ^-4, A is 125, a becomes -4. If 125 is divided into the n-th digit (in this case, the second digit) and the (n + 1) -th digit (in this case, the third digit), it is separated into 12 and 5. Then, when the number 5 after the (n + 1) th digit is divided by 5, the calculation result is 1
Becomes

Meanwhile, when performing rounding numerical by JIS standard two significant figures to 0.0125001, Dividing this number to an integer part A and the exponent 10 ^a, 125001 × 1
Because it is 0 ^-7, A is 125001, a becomes -7.
Then, if 125001 is divided into the second and third digits and thereafter, it is separated into 12 and 5001. However, 50
Even if 01 is divided by 5, the operation result is not 1, so in this case, ordinary rounding may be performed.

In step S506, the value after the (n + 1) th digit is set to 5
When it is determined that the calculation result obtained by dividing by 1 is 1, the n-th digit of the integer part A stored for each digit is read,
It is determined whether the number is even or odd. This means that the n-th digit is 2
It is determined based on whether the remainder when divided by is 0 (step S507).

If the remainder is determined to be 0 in step S507, that is, if the value of the n-th digit is an even number, the truncation processing shown in FIG.
06) or other commonly used truncation processing is performed (step S508). If it is determined in step S507 that the remainder is not 0, that is, if the n-th digit is an odd number, the round-up processing shown in FIG. 3 (steps S304 to S311) or another commonly used round-up The process is performed (Step S509).

In step S506, the value after the (n + 1) th digit is set to 5
If it is determined that the calculation result obtained by dividing by is not 1,
Normal rounding processing is performed (steps S510 and S510).
509, S511). In step S506, the case where the (n + 1) th digit is 5 and the value after the (n + 2) th digit is 0 is distinguished. In other cases, if the normal rounding processing is performed, it is possible to comply with the JIS standard. First, n +
The numerical value of the first digit is read out, and it is determined whether or not the numerical value is 5 or more (step S510). If the numerical value of the (n + 1) th digit is 5 or more, a round-up process is performed (step S5).
09), if the value of the (n + 1) th digit is not 5 or more, that is, if it is 4 or less, a truncation process is performed (step S511).

In this way, the integer part A is rounded. Then, the retrieved indices a from the exponent part storage area 10 (step S512), multiplication of the rounded integer portion and exponent portion 10 ^a is executed (step S51
3) The result is output to a storage device, a display device, a printing device, etc. (step S514).

Here, when the processing of FIG. 5 is performed in the above-described example (0.0125 is two significant figures, and 0.0125001 is two significant figures), how the numerical values from input to output are changed. Change.

First, in the case of 0.0125, 125 × 1
Since it is 0 ^-4 , the integer part A is 125 and the index a is -4. Therefore, -4 is written in the exponent part storage area 10 (step S503). As for the integer part A, numerical values of 1, 2, and 5 are written in the integer part storage area 9 for each digit (step S504).

When the digits after the (n + 1) th digit, ie, the digits after the third digit, of the integer part A are returned to one numerical value, 5 is extracted (step S505). When this 5 is divided by 5 (step S506), the result of the operation is 1, so the process of step S507 is performed. In this case, the n-th digit, that is, the numerical value of the second digit is 2, and the remainder is 0 when divided by 2. Therefore, the process proceeds to step S508,
That is, the numerical values after the third digit are truncated. Then, the processing result becomes 120.

Then, -4 stored in the exponent part storage area 10 is read out (step S512), and 120 is read out.
An operation of × 10 ^-4 is executed (step S513),
0.012 is output as the calculation result (step S5)
14).

Next, in the case of 0.0125001, 12
Since it is 5001 × 10 ⁻⁷ , the integer part A is 125001,
The index a is -7. Therefore, -7 is written in the exponent part storage area 10 (step S503). For the integer part A, the integer part storage area 9 stores each digit,
Each numerical value of 1, 2, 5, 0, 0, 1 is written (step S504).

When the digits after the (n + 1) th digit of the integer part A, ie, the digits after the third digit, are returned to one numerical value, 5001 is extracted (step S505). When this 5001 is divided by 5 (step S506), the result of the operation is not 1, so the process of step S510 is performed. in this case,
Since the value of the (n + 1) th digit, that is, the third digit, is 5, the flow advances to step S509 to perform a round-up process. Then, the processing result becomes 130,000.

Then, -7 stored in the exponent part storage area 10 is read out (step S512), and 130 is read out.
The calculation of 000 × 10 ⁻⁷ is executed (step S51).
3), 0.013 is output as the calculation result (step S514).

In the above description, in order to avoid a misunderstanding regarding the number of digits, in step S506, the n + 1th and subsequent digits are set to 1
Is divided by 5 to determine whether the result of the operation is 1 or not. However, even if it is determined whether the numerical value obtained by subtracting 1 from the (n + 1) th digit is 5 or not. Good.

[0064]

According to the processing procedure of the present invention, since the numerical value before processing is separated into an integer part and an exponent part, the digit to be subjected to the fraction processing can be designated by the number of significant digits.

When the numerical value rounding specified by the JIS standard is performed in the processing procedure according to the present invention, the numerical value before processing is separated into an integer part and an exponent part, and the integer part after the (n + 1) th digit of the integer part is converted into one numerical value. And divide this number by five. Therefore, it can be determined by a very small number of conditional branch processes whether or not the case where the (n + 1) th digit is 5 and it is the least significant digit other than 0 that appears in each digit is applicable. The processing can be speeded up and the program creation can be facilitated.

Further, since the processing procedure of the present invention performs processing regardless of the number of digits that can be processed by a computer, it can be applied to a computer having a large number of digits to be processed. This means that software processing can be performed irrespective of the processing capability of the computer, and the processing procedure according to the present invention can be applied in various fields for performing fraction processing. The following are examples of application fields of the present invention.

1. EXCEL, Lotus 1-2-3, Sanshiro, etc. can be cited as spreadsheet software as a function.

2. Incorporation into analysis / measurement / calculation software Such software includes software for determining the concentration of nitrogen oxides, software for determining the concentration of chemical components, and the like.

3. Examples of such a device to be incorporated into an analysis / measurement device include an electrochemical analysis device, a photochemical analysis device, an electromagnetic analysis device, a separation analysis device, and a thermal analysis device.

4. Incorporate in physical quantity / physical property measuring equipment This includes physical quantity / physical property measuring instrument, temperature / humidity / dew point meter,
Includes photometric and colorimetric devices.

5. Incorporate in special equipment For example, development-related equipment, bio-related equipment, agriculture, forestry, fisheries,
It can also be incorporated into livestock related equipment, weather observation equipment, ocean observation equipment, and the like.

6. International standard ISO9000 and ISO14
For example, it can be incorporated into test, measurement and monitoring hardware, test, measurement and monitoring software, and the like.

[Brief description of the drawings]

FIG. 1 is a block diagram showing one embodiment of a fraction processing device according to the present invention.

FIG. 2 is a flowchart illustrating an example of a processing procedure according to the present invention when performing truncation processing with n significant figures.

FIG. 3 is a flowchart illustrating an example of a processing procedure according to the present invention when performing round-up processing with n significant digits.

FIG. 4 is a flowchart illustrating an example of a processing procedure according to the present invention when performing rounding processing with n significant figures.

FIG. 5 is a flowchart illustrating an example of a processing procedure according to the present invention in a case where a numerical value is rounded to n significant figures according to the JIS standard.

FIG. 6 is a flowchart showing a conventional processing procedure when performing rounding.

FIG. 7 is a flowchart in a case where numerical value rounding specified in JIS standard is processed by a computer using a conventional processing procedure.

FIG. 8 is a flowchart in a case where a computer performs a rounding of a numerical value defined in the JIS standard by using a conventional processing procedure.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Input device 2 Numeric keypad 3 Storage device 4 Calculation / measurement result storage area 5 ROM 6 CPU 7 Storage device 8 Numerical value storage area before rounding 9 Integer part storage area 10 Exponential part storage area 11 Numerical value storage area after rounding 12 Display device 13 Printing device

Claims (4)

(57) [Claims] 1. An input means for inputting a numerical value x before a rounding process and a significant digit n, an n storage means for storing the entered significant digit n, and a numerical value x input by the input means being A × ^10a form (the original number is a power of 10 so that A does not contain 0 in the least significant digit and there are no non-zero digits after the decimal point)
Integer a exponent part calculating means for calculating an integer A and an exponent a when expressed by a product of 0 ^a ), and an exponent part storing means for storing the exponent a calculated by the integer part exponent calculating means. An integer part storage means for storing the integer A calculated by the integer part exponent operation means; and an integer A using the integer A stored in the integer part storage means and the significant figure n stored in the n storage means. A fraction processing means for calculating an integer B by performing a fraction processing on n significant figures; and calculating B × 10 ^a using the integer B calculated by the fraction processing means and the exponent a stored in the exponent part storage means. A fraction processing device comprising: digit restoring means; and output means for outputting the operation result of the digit restoring means as n significant digits. 2. The fraction processing unit extracts a numerical value after the (n + 1) th digit of the integer A stored in the integer part storing unit as one numerical value, and determines whether the numerical value is equal to 5. Means for determining whether the n-th digit of the integer A is 2
Even and odd number discriminating means for discriminating whether or not the remainder is 0; and when the number discriminating from the (n + 1) th digit to one is not equal to 5, n +
A rounding discriminating means for discriminating whether or not the first digit value is 5 or more; and a case where the remainder is discriminated to be 0 by the even / odd discriminating means, and a case where the n + 1th digit is 5 or more by the rounding discriminating means. If it is determined that the remainder is not zero, the truncation processing means for truncating the numerical value after the (n + 1) th digit to calculate the integer B, and the case where the remainder is determined to be not 0 by the even / odd determination means, and the rounding determination means a round-up processing means for calculating an integer B by incrementing the n-th digit by 1 and discarding a numerical value after the (n + 1) -th digit when it is determined that the (n + 1) -th digit is 5 or more. Item 4. The fraction processing device according to Item 1. 3. An integer A obtained by fractionally processing an integer A with the number of significant digits n.
A fraction processing device for calculating B, which takes a numerical value from the (n + 1) th digit of the integer A as one numerical value.
5 determining means for determining whether the numerical value is equal to 5
And a numerical value in which the number after the (n + 1) th digit is set to one by the 5 discriminating means.
Is determined to be equal to 5, the n-th digit of the integer A is changed to 2
Even odd number discrimination to determine whether the remainder is 0
Means and a numerical value in which the number after the (n + 1) th digit is set to one by the 5 discriminating means.
Is determined not to be equal to 5, then n +
Rounding to determine if the first digit is greater than 5
The remainder is determined to be 0 by the determination means and the even / odd determination means.
And the (n + 1) th digit is determined by the rounding discrimination means.
If it is determined that it is not 5 or more,
Truncation processing means for calculating an integer B by truncating a numerical value
If the remainder is not 0 determined by the even-odd judging means
And the (n + 1) th digit is determined by the rounding discrimination means.
If it is determined that it is 5 or more, the n-th digit is increased by 1.
Calculate the integer B by truncating the value after the (n + 1) th digit
And a lifting processing means.
Equipment. 4. An integer A is rounded to the nth digit from the highest order.
A fraction processing device for calculating an integer B, which takes a numerical value after the (n + 1) th digit of the integer A as one numerical value.
5 determining means for determining whether the numerical value is equal to 5
And a numerical value in which the number after the (n + 1) th digit is set to one by the 5 discriminating means.
Is determined to be equal to 5, the n-th digit of the integer A is changed to 2
Even odd number discrimination to determine whether the remainder is 0
Means and a numerical value in which the number after the (n + 1) th digit is set to one by the 5 discriminating means.
Is determined not to be equal to 5, then n +
Rounding to determine if the first digit is greater than 5
The remainder is determined to be 0 by the determination means and the even / odd determination means.
And the (n + 1) th digit is determined by the rounding discrimination means.
If it is determined that it is not 5 or more,
Truncation processing means for calculating an integer B by truncating a numerical value
If the remainder is not 0 determined by the even-odd judging means
And the (n + 1) th digit is determined by the rounding discrimination means.
If it is determined that it is 5 or more, the n-th digit is increased by 1.
Calculate the integer B by truncating the value after the (n + 1) th digit
And a lifting processing means.
Equipment.