JP2000347870A - Method for linearizing nonlinear index expression based on value profile - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the applicability of the optimization of a loop including an array reference having a nonlinear index expression. SOLUTION: By this linearizing method, a language processing system 20 adds a value profile acquisition code of a variable as a nonlinear coefficient in some nonlinear index expression in some array having values set in a loop of a source program 10 to the source program 10, finds a nonlinear coefficient value profile 60 obtained by executing an object program generated from the source program, and uses the profile to linearlize the nonlinear index expression in the loop of the source program 10.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the technology of a language processing system (Language Processor) for a computer program, and more particularly to efficient optimization in a case where a subscript expression of an array in a loop is nonlinear. And a non-linear subscript type linearization method based on a value profile suitable for.

[0002]

2. Description of the Related Art In a language processing system, at the time of compilation, various optimizations are performed in order to improve the execution performance of a program. Each optimization cannot be applied unconditionally, and many optimizations such as loop parallelization and loop invariant movement are hindered by dependencies between array reference points in the program.

[0003] The dependency is described in "William Pugh, A Practical
Algorithm for Exact Array Dependence Analysis, CAC
M Vol.35, No.8, pp.102-114, ACM, August 1992 ”, the subscript expression of the array in the loop is a linear expression for the loop control variable, that is, the loop control variable. Strict analysis is possible if it can be expressed by an expression obtained by adding a constant to the sum of terms multiplied by a constant.

If a term that cannot be expressed by a constant times the loop control variable is a loop invariant, a condition for having a dependency is expressed by a condition on the value of the loop invariant. It is possible.

According to the truth or false of this condition, the compiler generates a code for executing either unoptimized code or optimized code. If this condition is not satisfied, the optimized code is executed. Performance is improved. Such program conversion is called two-versioning.

Hereinafter, such a conventional technique will be described with reference to FIGS. FIG. 12 is an explanatory diagram showing an example of a source program to be compiled conventionally, FIG. 13 is an explanatory diagram showing an example of a dependency equation in the source program in FIG. 12, and FIG. FIG. 9 is an explanatory diagram showing an example of a target program obtained by optimization.

In the prior art, a condition for generating a dependency between array reference points is represented by a dependency equation. If there is a solution in the dependency equation, there is a dependency, and if there is no solution, there is no dependency. Among the dependence equations for the dependence between the array reference points in the loop in the source program shown in FIG.
Only one, as shown in FIG.

In the equation shown in FIG. 13, "I1" and "I2"
Are "A (I)" and "A (I + M)" in the second line of FIG.
Represents the value of the loop control variable I at the time when each is referred to. From these equations, when variables other than the variable M, which is a loop invariant, are eliminated by, for example, the Motzkin variable elimination method, the condition “−99 <= M <= 99” is obtained. Dependencies only occur if this condition is true.

If there is no dependency between the array reference points in the loop, the loop can be parallelized, so that the target program as shown in FIG. 14 can be generated by the two versions. Accordingly, when the condition of “−99 <= M <= 99” is not satisfied, the parallelized loop of rows 6 to 8 in FIG. 14 is executed, and the execution performance is improved. However, the loop starting with DOALL represents a parallel loop, the language processing system is a preprocessor, and the target program is represented in the same format as the source program.

However, in such a conventional technique, when the subscript expression of the array is "non-linear", the dependency cannot be calculated, and even the condition for two versions cannot be obtained. For example, two array references “A (I * IX1)” and “A (I * IX1)” in the source program to be processed according to the present invention shown in FIG.
2 + M) ”is as shown in FIG.

In FIG. 7, the first expression “I1 * IX1 = I2 * IX
“2 + M” is nonlinear because the coefficients for the loop control variable values “I1” and “I2” are not constants but variables “IX1” and “IX2”. Hereinafter, when the coefficient of the loop control variable is other than a constant, the coefficient is referred to as a non-linear coefficient.

Since the above-mentioned prior art cannot handle a non-linear equation, the dependence cannot be calculated from the dependence equation shown in FIG. Further, since the calculation of the condition for the two versions can be handled only when the dependent equation is linear, the two versions cannot be implemented.

[0013]

The problem to be solved is that in the prior art, when the subscript expression of the array is non-linear, the dependency cannot be calculated, and the condition for the two versions is not obtained. It is not even possible to ask for it.

An object of the present invention is to solve the problems of the prior art and to improve the applicability of optimization to a loop including an array reference having a non-linear subscript expression. The purpose of the present invention is to provide an equation linearization method.

[0015]

To achieve the above object, the present invention provides a method for linearizing a non-linear index based on a value profile, comprising the steps of: The execution time history (value profile) of the value of the variable is obtained, and the subscript is linearized by replacing the variable with, for example, the most frequent value.

That is, first, the loop control variable is set in any of the non-linear subscript expressions in any of the arrays in which a value may be set in the loop to cause a dependency between reference points in the loop. Is added before execution of a loop in a source program to be optimized, for acquiring a profile of a value that the variable can take at the time of execution for a variable that becomes a non-linear coefficient.

Next, a target program is generated from the source program to which the code is added, and the profile of the actual value of the nonlinear coefficient is obtained by executing the target program. Then, the subscript expression is linearized by replacing the nonlinear coefficient in the loop with the obtained actual value.

As a result, the dependency analysis technique can be applied, the subscript expression can be linearized for a loop including an array reference having a non-linear subscript expression, and the dependency analysis accuracy can be improved and two-version application can be performed. Possible and the applicability of the optimization is improved.

[0019]

Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 1 is a block diagram showing an example of a functional configuration for executing a processing procedure of a nonlinear subscript linearization method based on a value profile according to the present invention.
FIG. 2 is a block diagram showing a hardware configuration of the system in FIG.

In FIG. 2, reference numeral 1 denotes a CRT (Cathode Ray).
Display device that displays and outputs characters and images,
Reference numeral 1 denotes an input device which is composed of a keyboard and a mouse for inputting instructions from an operator, 3 is an external storage device which is composed of an HDD (Hard Disk Drive) or the like and stores a large amount of data and programs, and 4 is a CPU (Central Processing Unit). ) And an information processing apparatus having a main memory and performing computer processing by a storage program method, 5 is an optical disk as a recording medium on which programs and data according to the processing procedure of the present invention are recorded, and 6 is an instruction from the information processing apparatus Is a driving device that reads out data and programs in the optical disk 5 to be stored in the external storage device 3 based on.

The information processing device 4 constitutes a language processing system comprising the respective processing units shown in FIG. 1 by loading data and programs from the optical disk 5 stored in the external storage device 3 into the main memory. In FIG. 1, reference numeral 10 denotes a source program to be optimized, which includes a loop shown in FIG. 6, and reference numeral 20 denotes a language processing system that performs processing according to the present invention.

The language processing system 20 comprises a non-linear coefficient value profile acquisition code addition processing section 30, a target program generation processing section 40, a non-linear subscript type linearization processing section 70, and an optimization processing section 90. Is input, the non-linear coefficient value profile acquisition purpose program 50 is output.

By executing this in the execution processing unit 55, a nonlinear coefficient value profile 60 is obtained. When both the nonlinear coefficient value profile 60 and the source program 10 are input, the language processing system 20 outputs the final target program 95 after linearizing and optimizing the nonlinear suffix.

Note that the source program 10 has a "Fortra
n ”and“ C ”, the target program 50 and the target program 95 for acquiring a nonlinear coefficient value profile are machine instructions in a compiler, and“ Fortra ”in a preprocessor.
A programming language such as "n" or "C".

Hereinafter, the source program 10 is called "Fortra
n ", and the objective program 50 and the objective program 95 for obtaining a nonlinear coefficient value profile are programs described in" Fortran ",
The operation of the language processor 20 when the language processor 20 is a preprocessor will be described. It should be noted that, among the processing units constituting the language processing system 20, the non-linear coefficient value profile acquisition code addition processing unit 30 and the non-linear subscript type linearization processing unit 70
Performs the processing according to the present invention, and the other processing units are known technologies.

The non-linear coefficient value profile acquisition code addition processing unit 30 may input the source program 10 and generate a dependency between reference points in the loop by setting values in the loop in the source program 10. Code for acquiring a profile of the value of a variable that becomes a non-linear coefficient of a loop control variable in any of the non-linear subscript expressions of any of the arrays having a possibility at the time of execution
Is added to the source program 10. The details of the processing of the non-linear coefficient value profile acquisition code addition processing section 30 will be described later with reference to FIG.

The target program generation processing section 40 generates a target program for the program output from the nonlinear coefficient value profile acquisition code addition processing section 30.
As a result, the non-linear coefficient value profile acquisition purpose program 50 is generated.

The non-linear coefficient value profile acquisition purpose program 50 is actually executed by the execution processing unit 55,
The actual value of the nonlinear coefficient obtained by the instruction code added by the nonlinear coefficient value profile acquisition code addition processing unit 30 is acquired as the nonlinear coefficient value profile 60.

FIG. 3 is an explanatory diagram showing an example of the content of the nonlinear coefficient profile in FIG. Basically, in the linearization method in this example, it is sufficient to obtain statistical information on the value of a variable that becomes a nonlinear coefficient in the loop,
In the language processing system 20 of the present example shown in FIG. 1, all values of variables that become nonlinear coefficients in the loop are output immediately before this loop.

Various statistical information can all be obtained from the nonlinear coefficient profile 60. In order to reduce the overhead of acquiring a value profile of a variable serving as a nonlinear coefficient, a processing procedure in which only necessary statistical information is calculated and output at the end of the program may be considered.

In FIG. 1, a non-linear subscript type linearization processing unit 70 receives a non-linear coefficient value profile 60 and a source program 10, and based on the non-linear coefficient value profile 60, calculates a non-linear coefficient in a loop in the source program 10. Linearize the non-linear subscript expression by replacing it with the actual value determined at runtime. The details of the processing performed by the nonlinear subscript-type linearization processing unit 70 will be described later with reference to FIG.

The optimization processing unit 90 performs optimization such as parallelization and loop invariant movement on the output program from the non-linear subscript type linearization processing unit 70. Here, the dependency analysis and the two-versioning, which are conventional techniques, are applied to the loop including the subscript expression linearized by the nonlinear subscript expression linearization processing unit 70 to optimize the source program 10. Since it can be performed, the applicability of the optimization is improved as compared with the related art.

Then, the target program generation processing unit 40
Generates a target program for the program optimized by the optimization processing unit 90, and generates a target program 95. As described above, the nonlinear suffix included in the source program 10 is linearized, and the conventional dependency analysis and two-versioning can be applied. Therefore, the applicability of the optimization is improved more than before, and the objective program 95 Performance is improved.

Next, the details of the processing of the nonlinear coefficient value profile acquisition code addition processing section 30 will be described with reference to FIG. 4, and the details of the processing of the nonlinear subscript type linearization processing section 70 will be described with reference to FIG. FIG. 4 is a flowchart showing an example of the processing operation of the nonlinear coefficient value profile acquisition code addition processing section in FIG.

In step 31, the leading loop in the input source program 10 of FIG. 1 is set to L. If there is no loop in the source program 10, L is assumed to be empty. In step 32, it is determined whether or not L is empty. If this is true (TRUE), the process ends, and if false (FALSE), the process proceeds to step 35. In step 35, a set NLV of variables that become non-linear coefficients by any non-linear subscript expression in any of the arrays whose values are set in the loop L is obtained.

In step 36, a WRITE statement for writing the line number at the head of the loop L and the variable name and value of each variable in the NLV is inserted immediately before the loop L. It is assumed that the output format of the WRITE statement conforms to the nonlinear coefficient value profile 60 shown in FIG. In step 37, the loop following the loop L is newly set to L. However, the source program 10
If there is no loop next to the loop L, L is assumed to be empty.

With the above processing, the nonlinear coefficient value profile acquisition code addition processing unit 30 in FIG. 1 sets the values in all the loops in the source program 10 in the loops, thereby setting the reference points in the loops. A non-linear coefficient value profile 60 in the form shown in FIG. 3 is output for a variable that becomes a non-linear coefficient of a loop control variable in any of the non-linear subscript expressions in any of the arrays that may cause a dependency between the two. Is added immediately before the loop.

FIG. 5 is a flowchart showing an example of the processing operation of the non-linear subscript type linearization processing section in FIG.
In step 71, the input source program 1 of FIG.
Let L be the first loop in 0. If there is no loop in the source program 10, L is assumed to be empty. In step 72, it is determined whether L is empty. If this is true, the process ends. If false, the process proceeds to step 73.

In step 73, the information on the loop L in the nonlinear coefficient value profile 60 of FIG. 1 is totaled using the first line number of the loop L as a key, and the combination NLVAL of the most frequent variable values is obtained. In step 74, N
Create an IF statement that is conditional on the combination of the variable values indicated by LVAL, and create a loop on the THEN side that replaces the value of the variable in L with the variable value indicated by NLVAL to linearize the nonlinear subscript expression. Then, a copy of the loop L is created on the ELSE side, and the loop L is replaced with the IF statement created here.

In step 75, the loop following the loop L is newly set to L. However, the source program 10
If there is no loop next to the loop L, L is assumed to be empty. By the above processing, the non-linear subscripting linearization processing unit 70 in FIG. 1 performs the non-linear subscripting on all the loops in the source program 10 when the value of the variable serving as the non-linear coefficient matches the most frequent combination. Two-versioning is performed in which a loop in which the character expression is linearized is executed. In the loop in which the non-linearized subscript expression is linearized in this manner, the dependency analysis and the 2
Since versioning can be performed, applicability of optimization is improved.

Next, the operation of the language processing system 20 in FIG. 1 will be described using a specific example of a source program. FIG. 6 is an explanatory diagram showing a part of the source program in FIG. Although omitted in FIG. 6, it is assumed that the source program 10 of FIG. 1 includes program portions other than those shown in this example, and that the program portion shown in the example of FIG. 6 is executed several times. I do.

The source program of the present example includes a loop whose first line number is 1, and in the loop there is an array A in which a value is set, and a variable which becomes a nonlinear coefficient in the nonlinear subscript expression of the array A Are "IX1" and "IX2", and their dependent equations are as shown in FIG.

FIG. 7 is an explanatory diagram showing an example of a dependency equation for the source program shown in FIG. In FIG.
The first expression “I1 * IX1 = I2 * IX2 + M” is a constant for the loop control variable values “I1” and “I2” which is not a constant but a variable “IX”.
1 ”and“ IX2 ”, so it is non-linear. Since the non-linear equation cannot be handled by the conventional technique, the dependence cannot be calculated from the dependence equation shown in FIG. Also, the calculation of the condition for the two versions can be handled only when the dependent equation is linear.
Versioning is also not possible.

On the other hand, in the present example, the processing in the nonlinear coefficient value profile acquisition code addition processing unit 30 and the target program generation processing unit 40 in the language processing system 20 in FIG. As the coefficient value profile acquisition purpose program 50, a program as shown in FIG. 8 is generated.

FIG. 8 is an explanatory diagram showing a specific example of the objective program for obtaining a nonlinear coefficient value profile in FIG. In this example, “LOOP
(1) "and a WRITE statement (first line) for outputting the variable names and the variable values of the variables" IX1 "and" IX2 "to be non-linear coefficients are inserted immediately before the loop.

When such an object program (50) for obtaining a nonlinear coefficient value profile is executed by the execution processing unit 55 in FIG. 1, a nonlinear coefficient value profile 60 as shown in FIG. 9 is generated. However, it is assumed that the values of “IX1” and “IX2” have been changed by an operation in a program portion not shown in FIG.

FIG. 9 is an explanatory diagram showing a specific example of the nonlinear coefficient value profile in FIG. Variable names "IX1" and "IX2" in the loop whose line number is "1" at the beginning of the loop
Is output as the variable value “1”. The language processing system 20 of FIG. 1 converts the nonlinear coefficient value profile 60 and the source program 10 of FIG. 6 into the program shown in FIG.

FIG. 10 is an explanatory diagram showing a specific example of a program output from the non-linear subscript type linearization processing unit in FIG. In FIG. 10, row 1 indicates that “IX1 =
This is an IF statement conditional on "1" and "IX2 = 1", and THEN
In the loop of rows 2 to 4 on the side, the values of “IX1” and “IX2” are replaced with “1” and “1”, respectively, and the array subscript expression is linearized. The ELSE side is a copy of the original loop shown in FIG.

In the optimization by the optimization processing unit 90 in FIG. 1, existing dependency analysis and two-version conversion for the linear subscript are performed. This is the same as the source program example of FIG. 12 shown in the description of the conventional technology, and is converted into the same as the target program of FIG. 14, which is the target program after the source program of FIG. Thus, the target program has the form shown in FIG.

FIG. 11 is an explanatory diagram showing a specific example of a target program generated by the language processing system in FIG. Lines 2 to 10 in FIG. 11 are portions obtained by performing two versions and optimizing the loop of lines 2 to 4 in FIG.

As described above with reference to FIGS. 1 to 11, in the non-linear subscript type linearization method based on the value profile by the language processing system 20 according to the present embodiment, a value is first set in a loop. For any variable that may cause a dependency between the reference points in the loop, the variable that becomes the non-linear coefficient of the loop control variable in any non-linear subscript expression will A code (command statement) for acquiring a profile at the time of execution is added to a source program to be optimized, and a target program is generated from the source program to which the code is added. Next, the profile of the actual value of the nonlinear coefficient is obtained by executing the target program. Then, the subscript expression is linearized by replacing the nonlinear coefficient in the loop with the obtained actual value.

As described above, the execution history (value profile) of the variable that becomes the nonlinear coefficient of the loop control variable in the nonlinear suffix of the array reference in the loop is acquired, and for example, the value of the most frequently used value is obtained. Linearizing subscripts by substituting variables makes it possible to apply dependency analysis technology, linearizing subscript expressions for loops containing array references with nonlinear subscript expressions, and analyzing dependencies. It is possible to improve accuracy and apply two versions, and the applicability of optimization is improved.

The present invention is not limited to the examples described with reference to FIGS. 1 to 11, and can be variously modified without departing from the gist thereof. For example, in the example shown in FIG. 1, the optimization processing unit 90 optimizes the program after the linearization of the non-linear subscripts, but outputs the program without optimization, and the actual optimization is performed by another language processing system. It may be that it is carried out in.

Further, in this example, only the linearization for the most frequent combination of the variable values serving as the non-linear coefficients is performed.
Linearization may be performed on combinations of values other than the most frequent ones, or linearization may be performed on all combinations of values to determine applicability of optimization.

Further, when the applicability of optimization is determined by linearizing all combinations of values, this result is not used directly in optimization, but as a part of program tuning support, It is also conceivable to present the applicability of optimization to Thereby, even when the profile of the nonlinear coefficient value changes due to the input data of the program, it is possible to prompt the insertion of the user instruction so that the optimization can be applied.

[0056]

According to the present invention, even when the subscript expression of the array is non-linear, the dependence can be calculated, the condition for two-version can be obtained, and the array reference having the non-linear subscript expression can be obtained. The applicability of the optimization to the loop including is improved, and for example, by applying to the parallelization of the program, the parallelization function of the distributed processing system can be enhanced.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an example of a functional configuration for executing a processing procedure of a non-linear subscript type linearization method based on a value profile according to the present invention.

FIG. 2 is a block diagram illustrating a hardware configuration of the system in FIG. 1;

FIG. 3 is an explanatory diagram showing a content example of a nonlinear coefficient profile in FIG. 1;

FIG. 4 is a flowchart illustrating an example of a processing operation of a nonlinear coefficient value profile acquisition code addition processing unit in FIG. 1;

FIG. 5 is a flowchart illustrating an example of a processing operation of a nonlinear subscript-type linearization processing unit in FIG. 1;

FIG. 6 is an explanatory diagram showing a part of the source program in FIG. 1;

FIG. 7 is an explanatory diagram showing an example of a dependency equation for the source program shown in FIG. 6;

FIG. 8 is an explanatory diagram showing a specific example of a target program for acquiring a nonlinear coefficient value profile in FIG. 1;

FIG. 9 is an explanatory diagram showing a specific example of a nonlinear coefficient value profile in FIG. 1;

FIG. 10 is an explanatory diagram showing a specific example of a program output from the nonlinear subscript linearization processing unit in FIG. 1;

FIG. 11 is an explanatory diagram showing a specific example of a target program generated by the language processing system in FIG. 1;

FIG. 12 is an explanatory diagram showing an example of a source program to be compiled conventionally.

FIG. 13 is an explanatory diagram showing an example of a dependency equation in the source program in FIG.

14 is an explanatory diagram showing an example of a target program obtained by optimizing the source program in FIG.

[Explanation of symbols]

1: display device, 2: input device, 3: external storage device, 4:
Information processing device, 5: optical disk, 6: drive device, 10:
Source program, 20: Language processing system, 30: Non-linear coefficient value profile acquisition code addition processing unit, 40: Object program generation processing unit, 50: Object program for non-linear coefficient value profile acquisition, 55: Execution processing unit, 60: Non-linear relation Numerical profile, 70: Non-linear subscript type linearization processing unit, 90: Optimization processing unit, 95: Objective program.

Claims (1)

[Claims] 1. A method for linearizing a non-linear subscript expression in a language processing system for generating a target program from a source program, wherein the non-linear subscript expression of an array in which a value is set in a loop in the source program. Adding an instruction code for acquiring a history (value profile) of a value at the time of execution of a variable serving as a nonlinear coefficient to the source program; and generating a target program from the source program to which the instruction code is added. Executing the objective program to obtain a value profile of a variable serving as a non-linear coefficient obtained by the instruction code; and linearizing a non-linear subscript expression in the loop using the value profile. A non-linear subscripted linearization method based on a value profile.