JPS62280935A - Program processing system - Google Patents

Abstract

PURPOSE:To improve the quality of calculated results by impressing a sientific and technical programming language capable of handling a four-dimensional numeric on a compiler capable of analyzing. CONSTITUTION:A source program 1 including newly expressed source program language 1a is inputted to a compiler 2. A vocabulary analysis part 3, a syntax analysis part 4 and a processing part 5 for giving meaning in the compiler 2 are equipped with corresponding processing means 3a-5a. What the vocabulary analysis part 3 hands in to the syntax analysis part 4 in the compiler 2 is a token string, and what the syntax analysis part 4 does to the processing part 5 for giving meaning is an analysis tree. The corresponding processing means 3a-5a sequentially process the source program. As a result, the programming language can be easily produced and the time required for compiling can be shortened.

Description

[Detailed Description of the Invention] 3. Detailed Description of the Invention [Summary] rFORTRAN that can handle up to quaternions and has improved descriptive performance
This is a program processing system in which a source program written in a language such as J is input to a compiler, each part is equipped with a corresponding processing means for the compiler, and intermediate code is generated as a result of processing.

[Field of Industrial Application] The present invention relates to a processing system that inputs a source program written in a language such as "rFORTRAN" which can handle up to quaternions when performing scientific and technical calculations using an electronic computer.

Although scientific and technological programming languages such as rFORTRANJ can handle complex numbers as numerical expressions, they cannot easily handle quaternions, and there has been a need to develop a method for doing so.

[Prior Art] It is well known that arithmetic processing is performed on an electronic computer via a compiler using a language such as rFORTRANJ, which is suitable for scientific and technical calculations. rFORTRAN is a language system that organizes the procedures involved in processes such as arithmetic calculations into a form that is similar to everyday expressions, and has become an international standard language.

In addition to arithmetic operations and character processing, rFORTRANJ allows logical operations and complex number operations. We program by converting theories and models commonly used in computational processing into scalar representations.

On the other hand, it has been found that it is effective to use a "quaternion" for calculations such as expressing and determining the attitude of an artificial satellite, or for calculating coordinate rotation. "Quaternion" is a number system that is an extension of complex numbers, and when expressed as q, it can be defined as follows.

Stone = χ + ξl + ηj + ζ = χ1q (Here, i and j represent three-dimensional orthogonal bases.) The four arithmetic operations of quaternions are as follows. That is, the sum 'Ql'' q2
−(χ1+χ2)+(ξ, +ξ2)i+(η, +η,)
j + (ζ, +ζ2) k difference: mackerel - 12 = (χ1 - χ2) +
(ξ1−ξ2) 1+(η, −η2)j+(ζ,−ζyu) k product: ql・q2=[χ, χ2−(ξ1ξ2+η1η
2+ζ, ζ2)]+ [χ, ξ2+ χ2ξ1+ η
1 ξ2− η2ζ1ko i+[χ1η2+η1χ2
+ζ,ξ2−ζ2ξ1]j+[χ,ζ2+χ2ζ1+ξ
, η2−ξ2η, ] k=(χ1χ2 'Qj”1
2〉"χiqz""zoq, + q+ x (12
~・-(1) where q, , q2> represent a scalar product, and q and xq2 represent a vector product. Equation (1) is derived assuming that the following relationship exists between the bases denoted by i, j, and i.

Therefore quaternions are not commutative.

Inverse: 1=qn(N (q))2 Coordinate rotation matrix corresponding to the quaternion q of norm-1 Conventional r
In creating the FORTRANJ programming language, it has been predicted and studied that if quaternions are treated as defined numbers, the effect on the processing performance of the processor will be small.

[Problems to be Solved by the Invention] As mentioned above, when performing complex number operations using the rFORTRANJ language, the theory is expressed in scalar form, so naturally, when dealing with quaternions, conversion work is required. At that time, the quaternion representation was purposely changed to a scalar representation, which had the disadvantage that errors were likely to occur during the conversion process, and it took extra time to check the boograms. For example rFOR
A program using "TRAN" is shown in FIG. 9th
The figure shows a main routine and a subroutine for multiplication, which required a total of 22 steps, excluding comments.

[Means for Solving the Problems] The present invention provides a means for extending the programming language so as to facilitate the "quaternion operation" as defined above, and creates a new expression for the programming language. shall be. FIG. 1 is a diagram showing the basic configuration of the present invention, and 1 in FIG. 1 indicates a source program such as rFORTRANJ. In the present invention, a portion that allows new expression is indicated by hunting and indicated as 1a. That is, it is expressed as a source program including the declaration bones of the quaternion, its arithmetic expressions, substitutions, and built-in functions.

Next, the source program 1 including the new expression programming language 1a is input to the compiler 2 having the following configuration. The word parsing section 3, syntactic analysis section 4, and meaning processing section 5 in the compiler 2 include means 3a and 4a for correspondingly processing the source program.

5a. In the compiler 2, what is passed from the word party analysis section 3 to the syntax analysis section 4 is a token string, and what is passed from the syntax analysis section 4 to the semantic processing section 5 is called a parse tree.

[Operation] Expand programming language creation to enable quaternion operations, and input the resulting source program to a compiler. At this time, the compiler sequentially processes the source program in the word parsing section, syntactic analysis section, and meaning processing section in the corresponding processing means 3.4a and 5a, respectively.

As a result, it is easy to create a programming language, and processing by a compiler can be completed in a short time.

[Embodiment] (1) Regarding the programming language Regarding the rFORTRANJ language, a quaternary distributed type is added as a data type in addition to the conventional character type, logical type, complex number type, and double precision real number type. Quaternary distributed data occupies 16 bytes of storage space. (As defined above, the scalar part is 4 bytes, and the vector part is 4 bytes each).

Next, when adding a quaternion constant in the form of a complex constant extension, the quaternion constant is defined in the programming language (0,866, 0,
5,0,5,0,5).

Next, define the type declaration statement. The rFORTRANJ type declaration statement generally has the following format.

type [1m (,] ko, name
[, name - Here r typeJ is the following type specification, so here rQUA'TERN1ON
Add J. The conventional type specification is INTEGERLOGI
CAL REAL DOUBLE-PRECISIO
NCOMPLEX CHARACTIER.

When type is QUATERN ION, the format Niokel m specifies the length, so 16 name indicates the variable name or function name of the quaternary distributed type.

Also, the arithmetic operator used for the four arithmetic operations on quaternions is + addition −Subtraction * Multiplication / (division) and ** (power) are not used.

When talking about arithmetic statements, rFORTRAN
j is written as y=e, where y is a variable name to which a value is assigned, and e is an arithmetic expression. Here, y is allowed to be an arithmetic expression of a four-dimensional distributed operation. In addition, the following three types of built-in functions are prepared as built-in functions.

Norm value: NLM (Q) - Calculate the norm of quaternion Q Conjugate: C0NJ (Q) - Calculate the co-casting number of quaternion Q Inverse: INVQ (Q), - Inverse of quaternion Q (2 )
The syntax of a programming language when dealing with quaternions is as follows.

B. Definition of constants: <C0N5TANT> → <INTEGER><RE
AL>-...-<QUATERNION><QtlATERNION>→ “ (“ <RE
AL＞”, ”(REAL＞”.

"<REAL>", "<REAL>") "Here," indicates a non-terminal symbol, and " indicates a terminal symbol.

Mouth, type declaration, <TYPE>→” INTEGER”
“IIEAL” C0MPLEX” “QUATERNIO”
N” “LOGICAL” “DOUBLE PRECIS
ION” “CHARACTER” c, arithmetic expression <ARIT
)l-OP>-<ARITH><ARIT)I-QU
AT><ARITH-QUAT>→<Q><Q>→<Q>"+"<T><Q>→<T><Q>→<Q>"-"<T><T>→<T ＞“Book”＜F＞ ＜T＞→＜F＞ ＜F＞→”(”＜g＞”)11 ＜F＞ →＜QLIATERNION＞
<QVAL><QBUILD-IN> 21 Assignment statement: <ARITH-^SS IGNMENT> → Conventional one <QVAL>-'<ARITH-QUAT> E1Mi included function: (QBUILD-IN>-"NLM'"C”<F>
If the arithmetic grammar of quaternions is G, then G = (V, J, V, S, P), where the set of nonterminal symbols VN = (S, Q, T, F)
Set of terminal symbols ■A” (qttj−>*, (3))
The starting symbol is S, and the set of production rules is P. The syntax of the four arithmetic operations on quaternions can be defined by the following production rules.

S→Q#1 Q-hQ+T#2 Q-Ta2 Q-Q-Ta2 Q→-Ta5 T-4T*F#6 T→F#7 F→ (Q) # 8F= C
1t #9 (3) Processing in the compiler FIG. 2 shows an example of a program expressed as a quaternion, in which quaternion multiplication is performed. 21, which is written using only two steps and knobs, can perform the same processing as the program shown in FIG. 9 of the prior art described above.

Operation of the 8-word snow analysis section The block diagram shown in FIG. 3 is a diagram showing a part of the structure of the compiler. So-called source progera Lf) < Q
tlATERNION (Q1*Q2)*(0,0,%
, V'4) is input using a quaternion arithmetic expression written in rFORTRANJ. The word analysis unit 41 looks at the initial quaternion declaration statement of the program and learns from the reserved word table 31 in the various information tables 30 that a quaternion has been input, and then reads the variable name table 32 and constants. The reference position of Table 33 will be referred to in a limited manner. And the word spirit analysis department 41
examines the character string of the input program character by character, and creates variable name table 3.
Code id written in the column corresponding to Ql from 2,
1 is taken out as a "token", and the token string obtained by repeating it is input to the syntax analysis unit 42. In other words, this token is a token string of quaternion constants, variables, and built-in functions.

Operation of the syntactic analysis unit The syntactic analysis unit 42 inputs the above-mentioned token string, analyzes which part of the program corresponds to which rule of the grammar, and generates an analysis tree as a result. Figure 4 is L
An example using the R parser method is shown below. In FIG. 4, 43 is a syntax analysis table whose contents are calculated based on production rules that define quaternion operations. 44 is a stack, 45 is an input register, and 46 is a driver routine program. When analyzing the arithmetic expression % expression %), first assume that there is one look-ahead symbol since L R (11).The symbol scanned by the "head" shown in FIG. 4 is the look-ahead symbol.

The driver routine program searches the syntax analysis table 43 for the next operation to be performed based on the pair of the symbol Sm at the head of the stack 44 and the symbol ai read ahead by the head, and based on the information G, pops the button on the stack 44. and move the head left and right to proceed with parsing.

The algorithm of the driver routine is A, V, AhO.
Author: “Pr1nciple of Compiler”
Design'' (published by DDison-Wesley).

FIG. 5 is a diagram showing a specific example of a syntax analysis table 43 as one of the correspondence processing means added according to the present invention, and FIG. 6 is a diagram showing an example of a parse tree obtained by syntax analysis. It is.

In FIG. 5, the top stay of the stack 44) Sm and the symbol ai of the token string at the position currently being scanned by the head are read, and the corresponding (Sm, ai) is executed in the action column of FIG. . If Sj here, for example, qt (indicates that the quaternion has arrived)
When the stack is 6 with the paddle, it becomes S7, so perform the "shift" operation, push ai and 5j to the stack, and move the head one place to the right. If action (S m.

When ai) is rj, for example, a reduction operation is performed when r3 in the column ). Reduction operation refers to finding production rules from the terminal symbols of a given quaternion. When the rule for production rule number j is A-β (where the length of β is r), find SmGOTOC3m r, A) from the GOTO part of the parsing table and calculate the shape (5OX1S1X2S2-- Xm-r Sm-rA)
S, at at, +---an 4).

Specifically, if you pop 2r symbols from the top of the stack (β"
This means that it has transitioned to Go. Therefore, using the syntax analysis table 45, the state S corresponding to A is found in the GOTO portion of state Sm-t, and AS is pushed onto the stack. (
Therefore, the parser has transitioned to state S). Furthermore, when the action (Sm, ai) is accept, the syntactic analysis is completed. When the action (Sm, at) is an error, an error recovery routine is called.

The syntax tree shown in FIG. 6 is therefore given the lower qt, #9. The production rule #7 means replacing qt with F (#9) and replacing F with T (#7). By repeating these, the production rule is #
It can be seen that they are recognized in the order 9-97-#1 and a syntax tree is obtained.

C. Processing of semantics For the parse tree obtained by the syntactic analysis described above, the semantics corresponding to each production rule (# numbers listed on pages 10 to 11) that make up the parse tree can be added by activating an action. Generate intermediate code. For example, as an example of a processing execution method, meaning is assigned to an arithmetic expression of a quaternion based on a "syntax direction conversion method." FIG. 8 shows a comparison table of the production rules and action numbers used for the meaning processing. For example, for a subsequence W of a quaternion, the LR parser is A-
When recognizing XYZ -=w, the parser process shown in Figure 4 pops up three stacks in the stack immediately before reduction shown in Figure 7 and reduces XYZ to A, but
Immediately before this, the action number α attached to the A-XYZ rule is executed to give meaning. In FIG. 7, the stack immediately after reduction is shown to the right of the thick arrow. In FIG. 8, the operation symbols ■, e, and ■ mean that + and -1* on the left side of each equation described on pages 3 and 4 are replaced, respectively, and the corresponding right side is calculated. Further, LEXVAL is a value consisting of a quaternion recognized in the lightning analysis and has the attribute of a quaternion. For example, in Figure 8, VAL (TOP)
= VAL (TOP) 0VAL (TOP-2
) means to add the value at the top of the stack and the value at the second level from the top and replace it with the value at the top to obtain a meaningful intermediate code.

[Effects of the Invention] Thus, according to the present invention, a system that can easily process quaternions can be created by applying a scientific and technological programming language that handles quaternions to a compiler that can analyze and process quaternions. It has gained. Therefore, when performing complex scientific and technical calculations, it becomes easier to create a source list than before, which reduces errors and makes it easier to find errors when checking later. Therefore, it has the effect of improving the quality of calculation results.

[Brief explanation of drawings]

Figure 1 is a diagram showing the principle configuration of the present invention, Figure 2 is an example of a program expressed as a quaternion, Figure 3 is a diagram showing a part of the configuration in a compiler, and Figure 4 is the syntax in Figure 1. Analysis method in the analysis section Figure 5 shows the syntax analysis table, Figure 6 shows an example of the parse tree obtained by syntax analysis, and Figure 7
The figure shows a processing table with meaning, FIG. 8 shows a change in the stack, and FIG. 9 shows a program using conventional rFORTRANJ. 1.-Source program 1a...Part including the expression of the present invention 2.--Compiler 3.-Double analysis section 4.Syntax analysis section 5.Semantic processing for processing sections 3a, 4a, 5a, -4a Means for each part Patent applicant Fujitsu Ltd. agent Patent attorney Eisuke Suzuki Figure 1 Four-gen kudzuri shishi leg view 1 Wami moon bow 1 Gu bow Figure 2 Construction diagram of Konnozuira (-8μ) Figure 3 LR ( f) Parser Figure 4 Figure 5 Figure 1 (4H) 9 Example of a tree Figure 6

Claims (1)

[Claims] A source program (1) is input to a compiler (2) comprising a lexical analysis unit (3), a syntactic analysis unit (4), and a meaning processing unit (5), and the source program (1) is processed. Intermediate code (6)
In the program processing system that generates A program processing system characterized by comprising means (3a), (4a), and (5a) for correspondingly processing a source program including the quaternion declaration statement.