JPH04229324A - Generation and execution system for error evaluation program - Google Patents

Abstract

PURPOSE:To evaluate the calculation error of a calculation expression in a numeric calculation program for optional input data and analyze the calculation error efficiently. CONSTITUTION:An error evaluation subprogram 6 has a function for evaluating a calculation error due to information absence and a calculation error due to cancelling as to an addition/subtraction pattern according to the numeric data expression of an object computer. A calculation structure analytic part 1 extracts all addition/subtraction patterns included in a calculation expression specified with an evaluation indication statement in the numeric calculation program 4, an error evaluation program generation part 2 generates an error evaluation program 5 for making the error evaluation subprogram 6 evaluates calculation errors of the extracted addition/subtraction patterns, and an error evaluation program execution part 3 translates, merges, and executes the error evaluation program 5 and error evaluation subprogram 6.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to performance evaluation of numerical calculation programs, and more particularly to an error evaluation program generation/execution method for automatically generating and executing a program for evaluating calculation errors in numerical calculation programs.

0002

[Prior Art] Conventionally, in a method for evaluating calculation errors in numerical calculation programs, the entire calculation formula is evaluated by comparing the calculated value with the theoretical value for input data whose theoretical value is known for a certain calculation formula. A method was adopted in which calculation errors were evaluated by humans.

0003

[Problem to be Solved by the Invention] In the method for evaluating calculation errors in the conventional numerical calculation program described above, the calculated value and the theoretical value are compared for input data whose theoretical value is known in advance for a certain calculation formula. Since the calculation error of the entire calculation formula is only evaluated by humans, it is not possible to evaluate the calculation error for arbitrary input data. Does it contribute to the calculation error of the entire degree calculation formula?”
It has the disadvantage that it is not possible to perform calculation error analysis (efficient calculation error analysis).

[0004] In view of the above-mentioned points, an object of the present invention is to provide an error evaluation method that enables evaluation of calculation errors for arbitrary input data and efficient analysis of calculation errors for calculation formulas in a numerical calculation program. The objective is to provide a program generation and execution method.

[0005]

[Means for Solving the Problems] The error evaluation program generation/execution method of the present invention includes an error evaluation subprogram that evaluates calculation errors due to information loss and calculation errors due to digit loss for addition/subtraction patterns according to the numerical data representation of the target computer; A calculation structure analysis section that extracts all addition and subtraction patterns included in the calculation formula specified by the evaluation instruction statement in the numerical calculation program, and a calculation error evaluation subsystem for the addition and subtraction patterns extracted by this calculation structure analysis section. an error evaluation program generation unit that generates an error evaluation program to be evaluated by the program; and an error evaluation program execution unit that translates, combines, and executes the error evaluation program generated by the error evaluation program generation unit and the error evaluation subprogram. has.

[0006]

[Operation] In the error evaluation program generation/execution method of the present invention, the error evaluation subprogram evaluates the calculation error due to information loss and the calculation error due to digit loss with respect to the addition/subtraction pattern according to the numerical data expression of the target computer, and the calculation structure analysis section The error evaluation program generation section extracts all the addition/subtraction patterns included in the calculation formula specified by the evaluation instruction statement in the calculation program, and the error evaluation program generation section generates the calculation errors for the addition/subtraction patterns extracted by the calculation structure analysis section into the error evaluation subprogram. An error evaluation program to be evaluated is generated, and the error evaluation program execution section translates, combines, and executes the error evaluation program generated by the error evaluation program generation section and the above-mentioned error evaluation subprogram.

[0007]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, the present invention will be explained in detail with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of an embodiment of an error evaluation program generation/execution method according to the present invention. The error evaluation program generation/execution method of this embodiment includes a calculation structure analysis section 1, an error evaluation program generation section 2, an error evaluation program execution section 3, a numerical calculation program 4, an error evaluation program 5, and an error evaluation subsystem. It is configured to include a program 6 and evaluation data 7.

FIG. 2 is a diagram showing a part of an example of the numerical calculation program 4 (this numerical calculation program 4 is written in FORTRAN).

FIG. 3 is a diagram showing a part of an example of the error evaluation program 5 (error evaluation program 5 based on the numerical calculation program 4 shown in FIG. 2).

FIG. 4 is a diagram showing a part of an example of the evaluation data 7 (evaluation data 7 for the numerical calculation program 4 shown in FIG. 2).

Next, the operation of the error evaluation program generation/execution system of this embodiment configured as described above will be explained.

As shown in FIG. 2, the numerical calculation program 4
An evaluation instruction sentence ("*ERREST") is inserted immediately before the calculation formula whose calculation error is to be evaluated.

The numerical calculation program 4 into which such evaluation instructions have been inserted is input to the calculation structure analysis section 1.

The calculation structure analysis unit 1 finds the evaluation instruction sentence in the numerical calculation program 4, extracts all the addition and subtraction patterns in the calculation formula following the evaluation instruction sentence according to the order of calculation, and sends them to the error evaluation program generation unit 2. . Here, the addition/subtraction pattern refers to a combination of two terms to be added/subtracted and an addition/subtraction operator, and is a pattern expressed by {term before addition/subtraction, addition/subtraction operator, term after addition/subtraction}. .

The error evaluation program generation unit 2 generates an error evaluation program 5 that causes the error evaluation sub-program 6 to evaluate calculation errors due to missing information and calculation errors due to dropped digits regarding the addition/subtraction pattern sent from the calculation structure analysis unit 1.
generate. Specifically, the CALL statement (“CALL E
RREST (addition/subtraction pattern)), etc., is generated in the error evaluation program 5 (see FIG. 3).

The error evaluation program execution unit 3 translates, combines, and executes the error evaluation program 5 and the error evaluation subprogram 6, and calculates the addition/subtraction pattern in the calculation formula specified by the evaluation instruction statement in the numerical calculation program 4. The evaluation data 7 having the evaluation result of the calculation error is output.

The functions of the error evaluation subprogram 6 executed by the error evaluation program execution section 3 will now be explained.

The error evaluation subprogram 6 expresses numerical data of the computer on which the error evaluation subprogram 6 is executed (hereinafter referred to as the target computer) (in what base system the numerical data is expressed in the target computer and how many significant digits does it have)? Find out if there is one. The method of investigation is as follows.

■ Calculate 2 to the power of n (a positive integer) and find 2n such that the result does not change even if 1 is added to that number. That is, the value of 2n such that 2n and 2n +1 are the same value in the target computer is determined.

[0021] ■ 2n, in order from 1 to 2, 3,
When adding by increasing the value to be added as 4,...,
Find the added value when the addition result becomes a value different from 2n for the first time. Furthermore, when the same addition is continued and the addition result becomes a different value again, the added value is determined, and the difference between the two added values is determined. That is, 2n and 2n +i (i=1, 2
, 3, ...), and further calculate 2n +i and 2n +j (j=i+1, i+2, i+3
,...) is a different value, and find the difference between j and i. With this, it is possible to find out what base system the numerical data is expressed in on the target computer.

[0022] Once you know what base system the numerical data is expressed in (assuming it is K base system here), next calculate the value K to the m (positive integer) power, and multiply that number by 1. Find Km such that the result does not change even if added. That is, m is determined such that Km and Km +1 are the same value in the target computer. This makes it possible to determine the number of effective digits of numerical data on the target computer.

Furthermore, the error evaluation subprogram 6 is configured to express the numerical data examined as described above (in this embodiment,
7-digit hexadecimal system), the following processing (evaluation of calculation errors, etc.) is performed.

(2) The two terms of the addition/subtraction pattern passed as arguments from the error evaluation program 5 are expressed separately into a mantissa part and an exponent part. However, the mantissa part is normalized so that it is smaller than 1 and the first digit of the decimal point is not 0 (
If the term is 0, the exponent and mantissa parts are set to 0). For example, if a term with a decimal value of 4368.0 is passed as an argument, it will be expressed as a hexadecimal number with 7 significant digits and a mantissa and an exponent as shown below. {mantissa part 0.1110000 exponent part 4
}

[0025] When the two terms of the addition/subtraction pattern are compared and the exponent parts are the same, the mantissa part is added or subtracted according to the addition/subtraction operator, and the calculation error due to the dropping of digits from the significant digits of the mantissa part of the calculation result is evaluated.

■ If two terms in an addition/subtraction pattern are compared and the exponent parts are different, the size of the exponent part is adjusted to the larger exponent part, and the mantissa part is added or subtracted according to the addition/subtraction operator to eliminate calculation errors due to dropped digits. Evaluate. Furthermore, a numerical value that is not added or subtracted in one mantissa part by combining the exponent parts is evaluated as a calculation error due to information loss.

■ Convert the calculation errors due to missing digits and calculation errors due to information loss evaluated as described above to decimal numbers according to the numerical data representation of the target computer and output them (based on this output, perform error evaluation. The program execution unit 3 outputs evaluation data 7).

Next, the evaluation of calculation errors by the error evaluation subprogram 6 will be explained below using specific numerical values.

The calculation formula "Y(3) = 2.0" specified in the evaluation instruction statement in the numerical calculation program 4 shown in FIG.
D0*(Y(2) − Y(1)) − C*
The following two addition/subtraction patterns are extracted from "Y(2)". {Y(2),'-',Y(1)} {2.0D0*(Y(2) - Y(1)),'-
',C*Y(2)}

[0030] Here, the numerical data representation of the target computer is "
Consider the evaluation of the calculation error when Y(2) and Y(1) are the following values. Y(2)=1.129918515682220Y(1
)=1.129917442798615

[0031]
■ When the calculation errors Y(2) and Y(1) regarding {Y(2), '-', Y(1)} are expressed in accordance with the numerical data representation of the target computer, the respective values are as follows (``H
” indicates a hexadecimal number). Y(2)=0.1214257H×161Y(1)=0
．． 1214245H×161

[0032] Therefore,
“Y(2) − Y(1)” is as follows. 0.12H×16-4=1.072883605957
031×10-6

Therefore, calculation errors due to missing digits are evaluated as follows. 16-2×16-4=16-6=5.96046447
7539062×10-8

Note that at this time, the calculation error due to information loss is 0.

[0035]■ {2.0D0*(Y(2) −
Calculation error regarding Y(1)), '-', C*Y(2)}

Since C=16, “2.0D0*(
Y(2) − Y(1)) − C*Y(2)” is as follows. 0.00000024H×162 -0.121425
7H x 162

Therefore, calculation errors due to missing digits are evaluated as follows. 16-7×162 =16-5=9.53674316
4062500D-07

Furthermore, calculation errors due to information loss are evaluated as follows. 0.4H×16-5=2.3841857910156
25D-07

FIG. 4 shows the evaluation data 7 (part of the evaluation data 7) having the evaluation results as described above. Note that "ERR" in the figure indicates a calculation error due to missing digits, and "OCH" indicates a calculation error due to missing information.

[0040]

[Effects of the Invention] As explained above, when evaluating the calculation error of a calculation formula in a numerical calculation program, the present invention causes the error evaluation subprogram to evaluate calculation errors regarding all addition/subtraction patterns in a certain calculation formula. By automatically generating and executing the error evaluation program, calculation errors can be evaluated for arbitrary input data, and calculation errors can be efficiently analyzed.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention.

FIG. 2 is a diagram showing a part of an example of the numerical calculation program in FIG. 1;

FIG. 3 is a diagram showing a part of an example of the error evaluation program in FIG. 1;

FIG. 4 is a diagram showing a part of an example of evaluation data in FIG. 1;

[Explanation of symbols]

1. Computational structure analysis department 2 Error evaluation program generation unit 3 Error evaluation program execution unit 4 Numerical calculation program 5 Error evaluation program 6 Error evaluation subprogram 7 Evaluation data

Claims (1)

[Claims] [Claim 1] An error evaluation subprogram that evaluates calculation errors due to information loss and calculation errors due to digit loss according to the numerical data representation of the target computer for addition and subtraction patterns, and a calculation formula specified by an evaluation instruction statement in the numerical calculation program. a calculation structure analysis unit that extracts all included addition and subtraction patterns; and an error evaluation program generation unit that generates an error evaluation program that causes the error evaluation subprogram to evaluate calculation errors for the addition and subtraction patterns extracted by the calculation structure analysis unit. and an error evaluation program execution unit that translates, combines, and executes the error evaluation program generated by the error evaluation program generation unit and the error evaluation subprogram.