Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
1999-04-01
2002-12-10
Ngo, Chuong Dinh (Department: 2124)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
C708S497000
Reexamination Certificate
active
06493738
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to an apparatus and method used for rounding that is necessary for analyses, measurements, investigations, and so on. More particularly, the invention relates to an apparatus and method for performing rounding processing according to significant digits or a rounding interval.
DESCRIPTION OF PRIOR ART
Generally, rounding processing typified by rounding off has enjoyed wide acceptance. Examples include reorganization of experimental data and accounting processes. Many rounding processes are prepared as functions in high-level languages and data-processing software. A user can obtain rounded a numerical value by specifying a numerical value and a digit place to be processed.
FIG. 14
illustrates processing performed using a conventional rounding function. First, a user enters a numerical value x to be processed and a digit place p to be processed (step
601
). If the digit place p to be processed is the place of 100, for example, p is −2. If an integer should be derived, p is 0. If the digit place is the third decimal place, p is +3. Then, the digits in the successive digit places of the given numerical value x are stored in turn in memory (step
602
). A digit in the digit place immediately to the right of the specified digit place p is read from the memory (step
603
). A decision is made as to whether the digit is equal to or greater than 5 (step
604
). If the result of the decision is YES (i.e., the numerical value is equal to or greater than 5), rounding up is performed (step
605
). If the result of the decision is NO, rounding down is performed (step
606
). In this way, the conventional conditional branching processing using a function takes out only one digit from digits in plural digit places. Then, a conditional branch is effected.
The prior art technique described above has the following problems.
(1) It is impossible to specify the processed digit place by significant digits.
Spreadsheet software programs presently available on the market do not have the concept that the processed digit place is specified by significant digits. If a digit place to be processed is counted from the leftmost digit place and specified, other conditional branching processing is necessary so that the processed digit place is specified by significant digits across a decimal point, as long as the prior art conditional branching processing is performed (i.e., only one digit is taken from plural digit places and a decision is made). For example, where 0.0000234 should be rounded to two significant digits, if this numerical value is counted as it is, then the digit in the third decimal place will be taken and a rounding process will be performed. Therefore, digits are taken in turn from the leftmost digit place and counted. A decision is made as to whether each taken digit is 0 or not. If it is 0, this digit place is not counted. In this way, conditional branching processing is needed. Furthermore, where a rounding process is executed with four significant digits, if the numerical value is 30200, “0” in the fourth digit place, “0” in the second digit place, and “0” in the first digit place all need to be counted. In the case of 0.34502, “0” in the first digit place(the most significant digit) is not counted. However, “0” in the fourth decimal place and so on must be counted. Therefore, more conditional branches are necessary.
Where the prior art processing sequence as described above is used, if the digit to be rounded is specified by significant digits, very complicated processing inevitably takes place. For this reason, the prior art function does not make it possible to specify a digit place by significant digits. Furthermore, any spreadsheet software capable of specifying a desired digit place by a significant number is not available.
(2) Rounding processing directly using a rounding interval cannot be performed.
Rounding using a rounding interval is based on ISO (International Standards Organization) 31-0:1992(E), appendix B, “Guide to the rounding of numbers”. Rounding using a rounding interval is to replace a given numerical value by a numerical value selected from a sequence of integral multiples of a chosen rounding interval. For instance, where the rounding interval is 0.1, 12.849 is rounded to 12.8 and 13.451 is rounded to 13.5. Where the rounding interval is 10, 1284.9 is rounded to 1280, and 1345.1 is rounded to 1350. Accordingly, in rounding processing using a rounding interval, what is entered first is not the processed digit place but a rounding interval. However, spreadsheet software programs currently available on the market do not have the concept that rounding is performed based on a rounding interval. Hence, it has been impossible to perform a rounding process by directly entering a rounding interval. Therefore, in order to perform the prior art rounding process using a rounding interval, additional processing for converting the rounding interval to the processed digit place is necessary. This complicates the processing, and the processing time is prolonged.
(3) It is impossible to cope with JIS (Japanese Industrial Standard).
Where simple rounding off is used, the result is biased according to the numerical values contained in the data. Therefore, rounding for correcting the biased result and minimizing the round-off error is necessary. JIS stipulates a rounding method for that purpose. Many materials submitted to the public agencies have numerical values that must be rounded in accordance with JIS.
FIG. 15
illustrates a rounding method stipulated by JIS, Z8401. Fundamentally, a round-off process is performed, and the remaining 5 is sorted. Where a numerical value is rounded to a numerical value having n significant digits, a digit in the (n+1)th place and less significant digits are reorganized as follows.
(a) Where a digit in the (n+1)th digit place or a less significant digit is less than half of 1 unit in the nth digit place, the digit is dropped.
(b) Where a digit in the (n+1)th digit place or a less significant digit is in excess of half of 1 unit in the nth digit place, the digit in the nth digit place is increased by 1 unit.
(c) Where the digit in the (n+1)th place or a less significant digit is equal to half of 1 unit in the nth digit place, the following processes (i) and (ii) are carried out.
(i) If the digit in the nth digit place is 0, 2, 4, 6, or 8, the digit is dropped.
(ii) If the digit in the nth digit place is 1, 3, 5, 7, or 9, the digit in the nth place is increased by 1 unit.
Significant digits are counted from the place of the most significant digit that is nonzero. This rounding must be performed in one stage. For example, if 5.346 is rounded to two significant digits by this method, then 5.3 results. If the rounding is done in two stages, the numerical value is rounded to 5.35 in the first stage and to 5.4 in the second stage.
The processing is conducted in the sequence in the manner described below. First, the number of digits is judged (step
701
). A decision is made as to whether the digit in the (n+1)th digit place is 6 or more (step
702
). If the digit is 6 or more, the digit in the nth digit place is increased by 1. The digit in the (n+1)th place and less significant digits are dropped (step
706
). For example, if 13.461 is rounded to three significant digits, 13.5 results.
Then, a decision is made as to whether the digit in the (n+1)th digit place is 4 or less (step
703
). If it is 4 or less, the digit in the (n+1)th place and less significant digits are dropped (step
707
). For example, if 12.849 is rounded to three significant digits, 12.8 is derived.
If the digit in the (n+1)th place is neither equal to or greater than 6 nor equal to or less than 4, i.e., the digit in the (n+1)th digit place is 5, a decision is made as to whether the digit in the (n+2)th place and less significant digits are all 0 (step
704
). If the digit in the (n+2)th place and less significant digits contain nonzero numeral or numeral
Data Action Co., Ltd.
Knobbe Martens Olson & Bear LLP
Ngo Chuong Dinh
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