JPH0764766A - Maximum and minimum value calculating method for parallel computer - Google Patents

Abstract

PURPOSE:To calculate maximum and minimum values in the parallel computer which consciously handles not only maximum and minimum values but also the value of an index to obtain the same result as a sequential computer. CONSTITUTION:Values of array elements as objects are compared with each other; and if they are equal to each other, index values are compared with each other, and the smaller index value is taken. That is, stages L1 to L9 where portions in charge of respective parts are individually calculated and a tournament processing is called and tournament processings (function global) L10 to L14 are equal to conventional procedure, but processings L29 to L30 executed in the case of equal inputs in functions to be subjected to maximum value comparison are different from conventional procedure. The minimum value is obtained in the same manner. Another way to take the larger index value in the case of equal inputs can be easily selected. This method is easily transformed that a parameter designates which of the larger index value and the smaller index value should be taken in the case of equal input values.

Description

Detailed Description of the Invention

[0001]

[Industrial application] In numerical calculation, an operation for obtaining an index indicating the maximum or minimum value of an array element and the position of that element is often used.

A parallel computer is one of the computers for high-speed arithmetic. The present invention relates to a method of calculating a maximum value / minimum value using a parallel computer.

[0003]

2. Description of the Related Art A tournament method is known as a method for obtaining a maximum value or a minimum value at high speed using a parallel computer. In a parallel computer, the target numerical value group (array element) is distributed to each processor, and the maximum value (minimum value) is allocated to each processor.
Then, the maximum value (minimum value) between the maximum values (minimum values) of each processor is calculated. The process of obtaining the maximum value (minimum value) of the values distributed by each processor is naturally performed in parallel. Even in the subsequent step of obtaining the maximum value (minimum value) between the maximum values (minimum values) of each processor, a tournament method is used to operate a plurality of processors in parallel as much as possible.

FIG. 3 is an explanatory diagram of the configuration of a parallel computer. A large number of processor elements PE are arranged in parallel and are connected by a network n. The figure shows an example in which 8 × 8 processor elements (hereinafter referred to as processors) are connected by a two-dimensional torus network. FIG. 4 is a diagram showing the concept of a tournament method operation performed in such a parallel computer. Each processor (its value) is paired in pairs, and one processor transfers one value from another processor to obtain a larger value (or smaller value) of them. The results are again paired in pairs, and the operation of ... Is repeated, and finally one value is obtained as the solution, that is, the maximum value (or minimum value). Figure 4
In (A), at the first time, processors 0 and 1, 2 and 3, 4 and 5, 6 and 7, ... Are paired, and processors 1, 3, 5, and
7, ... Sends data to the processors 0, 2, 4, 6 ,. Next, the processors 0 and 2, 4 and 6, ... Are paired, and the processors 2, 6 ... Send data to the processors 0, 4 ,. Next, the processors 0 and 4, ... Are paired, and so on (represented by) is repeated, and finally the maximum value as the final result is obtained in the processor 0.

FIG. 4B shows an example of a program in which the above tournament processing is described as a function in the pseudo C language. In this example, it is assumed that the number of processors is 2 ⁿ and the processor-specific numbers (machine numbers) are set in the variable pid. Each processor sets the target value of the tournament processing and its index to myData and myIndex, and when this program is executed respectively, finally pi
The result is obtained in myData and myIndex of the d = 0th processor. In addition, send is a function that transfers a message, and sends the second and third arguments to the processor indicated by the first argument,
recv is a function that receives a message, and receives the message sent to you by send. The calculation function is a part that calls a function for calculation such as “comparison of maximum values” and “comparison of minimum values”.

When performing maximum value calculation, etc., the processor
An index indicating the position of the element on the array is treated as being associated with the element. That is, the two sets of elements are compared and the resulting values are associated with their index values. Accordingly, the index value associated with the value remaining (winning) as a result of the comparison also survives, and the finally remaining maximum value (or minimum value) and the index value associated therewith are obtained as a solution. As a result, it is possible to know which position in the array the maximum value (or the minimum value) is, and which processor has the maximum value (or the minimum value), and it becomes an index for the subsequent calculation.

By the way, when two values to be compared are equal, which index value is to be taken is not well known. This is because if the maximum value or the minimum value is correct, the index value itself is secondary.

FIG. 2 shows a sequential maximum value program and a conventional maximum value calculation program. The sequential program of (A) is a program that examines the elements of the array a from 1 to N, and obtains the largest value as x and the index value at that time as i, which is written for a sequential computer. Is.

In (B), the same processing is written for a parallel computer. First, find the maximum value and its index for the element of a in charge of each processor (L1 to L
8). Next, the function global (L
Call 9) to find the maximum value and its index among the maximum values calculated by each processor. here,
The function global is the one shown in FIG. 4B. The first argument x is a variable that gives the data to be compared, the second argument i is the variable that gives its index value, and the third argument & x is set by each processor. A variable that returns the maximum value (minimum value) of x as a result, and the fourth argument & i is a variable that is returned as an index associated with it. All processors do this.

The resulting values of x, whether sequential or parallel, are always the same. However, the index value i at that time may be different. Each processor is a function global
This is a case where there are a plurality of items having the same x set as the first argument of. In the sequential program, L3 in FIG.
Due to the nature of the conditional branch shown in, the smallest index value is adopted as the final result. On the other hand, in a parallel type program, the size comparison between processors is performed by parallel processing by a tournament method, so it is not guaranteed that the one with the smallest index value will be adopted depending on the allocation of elements to the processor. As a result, when a program originally written for serial processing is rewritten for a parallel computer by such a method, different results may be obtained. Also, when parallelized programs are executed with different numbers of processors, the data assigned to each processor changes, so the results may differ.

[0011]

When a program developed for an ordinary sequential computer is parallelized for a parallel computer, the index value may differ from the result obtained by the sequential computer. Further, in a parallel computer, when the number of processors is different, the resulting index value may be different. This may result in subtle differences in the final result. Such a situation makes it difficult to determine whether the program is operating correctly or has been correctly parallelized. That is, there is a result compatibility problem.

According to the present invention, not only the maximum value / minimum value but also the index value are consciously handled so that the same result as that of the serial type can be obtained. The purpose is to realize the calculation method.

[0013]

FIG. 1 shows a program according to an embodiment of the present invention. Like the functions L29 to L32 that compare the maximum values shown in L20 to L35 in the figure, the processing that considers the magnitude relationship of the index values is performed.

According to a first aspect of the present invention, the values of the target array elements are compared in the operation of obtaining the maximum value or the minimum value of the array elements and the index value indicating the position of the array element by the tournament method. At the same time, when the values are equal, the index values are compared and the smaller index value is taken.

According to a second aspect of the present invention, in the above calculation, the index values are compared and the index value having the larger value is taken. According to a third aspect of the present invention, in the calculation of the preceding two terms, the index values are compared, and it is determined by a predetermined parameter whether the larger index value or the smaller index value is taken. This is the case.

When the operation target is a multidimensional array, each index is a one-dimensional array having the number of elements corresponding to the number of dimensions of the multidimensional array to be operated. As described in claim 4, when the comparison values to be calculated are equal, the solution is achieved by comparing the element values of those index arrays in a lexicographical manner (also referred to as a dictionary order).

[0017]

According to the first aspect or the second aspect, it is possible to guarantee that the result is always the same even if the number of processors of the parallel computer changes.

According to the third aspect, when the serial program is parallelized, the index value can be used properly depending on the determination condition of the original loop. For example, in the example of FIG. 2 (A), the determination condition is if (a [j] <= x) goto L100 ;, so the smaller index value may be set. If the determination condition is if (a [j] <x) goto L100 ;, the one with the larger index value may be set. In the above example, if the loops are in descending order, the one with the larger index value,
This can be handled by setting the smaller one.

The same applies to the case where a multidimensional array is to be operated, except that the comparison is performed lexicographically because the index is a one-dimensional array. By doing so, the index value can be uniquely determined when the maximum value / minimum value operation is performed by the parallel computer. Therefore, it is possible to guarantee the compatibility of results regardless of the number of processors and the compatibility of results with the sequential type.

[0020]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows a subroutine for obtaining the maximum value as one embodiment of the present invention. In this example, when the input values are the same, the smaller index value is used.

The steps of individually calculating the charge of L1 to L9 and calling the tournament processing and the tournament processing of L10 to L14 (function global) itself are the same as in the conventional case. Shown in L29 to L32 in the function that compares the maximum values,
The processing when the inputs are equal is the main part of the method of the present invention.

It goes without saying that the same can be done when obtaining the minimum value. If the input values are the same, it is possible to easily take the larger index value. Also, it goes without saying that it is easy to make a modification such that when the input values are the same, the parameter with the larger index value or the smaller index value is designated by a parameter.

The array to be operated is not limited to one dimension and may be multidimensional. In that case, the indexes are also arrays, so the arrays of indexes are compared in a lexicographical order to determine the magnitude relationship.

The elements of the array need not be numerical values, but may be character strings. In this case as well, the magnitude relationship may be determined by comparing in a lexicographical order.

[0025]

As described above, according to the present invention, the compatibility of the solution with the sequential program can be guaranteed when the operations for obtaining the maximum value and the minimum value are parallelized. Also, when executing a parallelized program, it can be guaranteed that the solution does not change regardless of the number of processors. Such a property is important for ensuring that the parallelized program is correctly converted without impairing the meaning of the original program.

[Brief description of drawings]

FIG. 1 is a diagram showing a main part of a program according to an embodiment of the present invention.

FIG. 2 is a diagram showing an example of a conventional maximum value calculation program.

FIG. 3 is an explanatory diagram of a configuration of a parallel computer.

FIG. 4 is an explanatory diagram of tournament processing.

[Explanation of symbols]

PE Processor (Element) n Network between processors

Claims (4)

[Claims] 1. In a parallel computer, in a calculation for obtaining a maximum value or a minimum value of an array element and an index value indicating the position of the array element by a tournament method, the values of the target array element are compared, When the values are equal, the index values are compared and the smaller index value is taken.
Minimum value calculation method. 2. The maximum / minimum value calculation method according to claim 1, wherein the index values are compared and the index value with the larger value is taken. 3. The index value is compared, and whether the index value having a larger value or the index value having a smaller value is determined by a predetermined parameter is set. The maximum / minimum value calculation method according to item 2. 4. The maximum / minimum value calculation method according to claim 1, wherein the element values of the index array are compared in a lexicographical order in the case of a multidimensional array.