JP3074910B2 - Division device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a division device, and more particularly to a division device for obtaining a quotient and a remainder of many digits by using an approximate division result between upper blocks.

[0002]

2. Description of the Related Art Consider a case where positive integers A and N are given in a general-purpose computer and a system using a general-purpose microprocessor, etc., and a remainder and a quotient are obtained by executing A / N division. For example, A and N are written to the corresponding memory, and A and N correspond to A and N respectively.
i, Nj (0≤i≤m-1, 0≤j≤n-1, n≤m) divided into m or n blocks,

(Equation 6) Where Ai and Nj are each represented by an integer from 0 to r-1 using r as a radix. In the conventional method, if there is only an operation means for dividing two blocks by one block, after initializing i = m−1 and q = 0,

(Equation 7) Seeking a quotient

(Equation 8) Is repeated while reducing i. However,

(Equation 9) Represents the largest integer not exceeding x, and x‖y is r × x + y
Represents Examples of the conventional division device include, for example, “Hiroshi Hagiwara, Computer Science, 2, Asakura Shoten, pp. 135-174”, “HWANG, High-speed Computer Computing System,” published by Modern Science Co., Ltd. And so on.

[0003]

In the above prior art, A
It is necessary to judge the case where is negative, which hinders speeding up of division. An object of the present invention is to improve such a problem and to provide a division device suitable for speeding up arithmetic processing.

[0004]

In order to achieve the above object, the dividing apparatus of the present invention performs the calculations shown in the above equations (3) and (4) starting from i = m-1 as in the prior art. This is repeatedly performed while reducing the number of digits of A and reducing i, and is characterized by using a quotient Q expressed by the following equation (5).

(Equation 10) That is, in a dividing device having a memory and an ALU, positive integers A and N are given, and a quotient and a remainder, which are the largest integers not exceeding A / N, are obtained.
q is written to the memory area, A and N are Ai, Nj (0 ≦
i ≦ m−1, 0 ≦ j ≦ n−1, n ≦ m) and is divided into m or n parts, expressed by the above equation (1), and r
Ai, Nj are represented by integers from 0 to r−1, and when r / 2 ≦ Nn−1, m−1 is stored in i and 0 is stored in q to initialize. And if the upper digit Ai of A is Nn-1 + 1 or more,

[Equation 11] A second step of subtracting A from A and accumulating 1 in q;
The quotient Q is obtained by dividing the high-order digit r × Ai + Ai-1 of N by a divisor obtained by adding 1 to the high-order digit Nn-1 of N,

(Equation 12) Is subtracted from A, and q is updated by r × q + Q. Again, the upper digit r × Ai + Ai−1 of A is changed to the upper digit N of N.
A fourth step of obtaining a quotient Q obtained by dividing the divisor by adding 1 to n-1 and, if Q = 0, subtracting the value of equation (6) from A and updating q by q + Q, and the upper digit of A Ai-1 is Nn-1 + 1
Only in the above cases,

(Equation 13) A fifth step of subtracting 1 from A and updating q by q + 1, a sixth step of subtracting 1 from i, a seventh step of returning to the third step if i> n−1, and i> n
If −1 and A <N, an eighth step in which q is a quotient and A is a remainder, and i is not i> n−1 and A <N
If it is not N, the process is characterized by performing a process having a ninth step of subtracting N from A, adding 1 to q, and returning to the eighth step.

[0005]

In the present invention, in order to obtain the quotient Q, if the divisor Q for executing the above equation (5) is used,

[Equation 14] Therefore, A generated by the above equation (3) using Q generated by using the equation (5) is always guaranteed to be positive. Because, equations (3), (5),
From (9),

(Equation 15) Therefore, processing such as condition determination accompanying the handling of a negative value is unnecessary, and the division processing can be sped up.

[0006]

An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a flowchart showing the processing of the division device according to one embodiment of the present invention, and FIG. 2 is a configuration diagram showing the main parts of the division device according to one embodiment of the present invention. In FIG.
Reference numeral 21 denotes a memory area for storing the quotients A and N and intermediate progresses i and q, and reference numeral 22 denotes an arithmetic logic unit (ALU) for realizing addition, multiplication, and division in block units. In the division device of the present embodiment, the division process is performed by the procedure shown in FIG. 1 by the memory area 21, the ALU 22, and the control means (not shown in FIG. 2) for performing a series of processes related to the division.

Next, the procedure of the division process will be described with reference to FIG. In this embodiment, positive integers A and N are given.
The quotient and the remainder, which are the largest integers not exceeding / N, are obtained.
N, i, and q are written to the memory area 21, and A and N
i, Nj (0 ≦ i ≦ m−1, 0 ≦ j ≦ n−1, n ≦ m) divided into m or n parts and represented by the above formula (1) . Also, r is a radix, and Ai, Nj
Is represented by an integer from 0 to r-1, and r /
It is assumed that 2 ≦ Nn−1 (101). When m blocks are required to represent the integer A, m-1 is stored in i and 0 is stored in q to initialize (102).
When Ai ≧ Nn-1 + 1, the value of the above equation (6) is subtracted from A, and 1 is stored in q (104). Then, a quotient Q is obtained by dividing the upper digit r × Ai + Ai−1 of A by the divisor obtained by adding 1 to the upper digit Nn−1 of N, and subtracting the value of the above equation (7) from A,
q is updated by r × q + Q (105). Then again, A
Is obtained by dividing the high-order digit r × Ai + Ai-1 of N by a divisor obtained by adding 1 to the high-order digit Nn-1 of N. If Q = 0 is not obtained, the value of the equation (7) is subtracted from A, and q + Q gives q Is updated (10
6) In step 107, if Ai-1 ≧ Nn-1 + 1, the value of the above equation (8) is subtracted from A, and q is updated by q + 1 (108). Then, subtract 1 from i (10
9). As a result, if i is greater than n-1, (11
0), returning to step 105, if i is not greater than n-1, proceed to the next step. In the next step 111, if A <N, q is output as a quotient and A as a remainder (113). If A <N is not satisfied, N is subtracted from A and 1 is added to q (112).
It is checked whether or not <N (111).

Here, a specific example will be given to show the calculation method of this embodiment. In this embodiment, “965432 ÷ 562”
1 will be described to obtain “quotient 171 remainder 4241”. First, radix r = 10 (decimal system), and the data structure is A = A ₅ ‖A ₄ ‖A ₃ ‖A ₂ ‖A ₁ ‖A ₀ = 9‖6‖5‖4‖3‖2 N = It is assumed that N ₃ ‖N ₂ ‖N ₁ ‖N ₀ = 5‖6‖2‖1. Since there is no risk of misunderstanding in the decimal system, the separator ‖ is omitted below. As a result, division processing is performed in the following order (1) to (8). (1) i = 6-1 = 5, q = 0 (2) From A ₅ = 9> N ₃ + 1 = 6,

(Equation 16) q = 1 (3) Q = 40/6 "= 6

[Equation 17] q = 10 × 1 + 6 = 16 (4) Q = 0/6/6 ”= 1

(Equation 18) q = 16 + 1 = 17 (5) Since A ₄ = 0 <N ₃ + 1 = 6, A and q remain as they are. (6) i = 5-1 = 4 (7) Returning to (3) from 4> 3. (3) Q = 09/6 "= 1

[Equation 19] q = 10 × 17 + 1 = 171 (4) Q = 04/6 ”= 0, A and q remain as they are. (5) Since A ₃ = 4 <N ₃ + 1 = 6, A and q remain as they are. (6) i = 3-1 = 2 (7) i = 3 (8) From A = 4241 <N = 5621, the quotient q = 17
1. The remainder A = 4241 is output as a result. In the case of radix 10 as in the present embodiment, the most significant block of N must be 5 or more. However, in actual use, since r is a power of 2, shifting N and setting the most significant bit to 1 Just start.

[0009]

According to the present invention, it is possible to eliminate the processing involved in handling negative values, and to obtain a quotient and remainder of many digits by using an approximate division result between upper blocks. This makes it possible to speed up the division process.

[0010]

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a process of a division device according to an embodiment of the present invention.

FIG. 2 is a configuration diagram illustrating a part of a division device according to an embodiment of the present invention.

[Explanation of symbols]

 21 Memory area 22 ALU

Claims (1)

(57) [Claims] 1. A dividing apparatus comprising an ALU, a divisor, a dividend, and a memory area for accumulating progress information.
The ALU is controlled, given positive integers A and N, obtaining a quotient and a remainder that are the largest integers not exceeding A / N, writing the A, N and intermediate progresses i and q to the memory area, , N
Are Ai, Nj (0≤i≤m-1, 0≤j≤n-1, n≤
m) divided into m or n parts shown by And each Ai, Nj is represented by an integer from 0 to r-1 using r as a radix. When r / 2≤Nn-1, m-1 is stored in i and 0 is stored in q. The first step of initialization and only if the upper digit Ai of A is greater than or equal to Nn-1 + 1, A second step of subtracting A from A and accumulating 1 in q;
The quotient Q is obtained by dividing the high-order digit r × Ai + Ai-1 of N by the divisor obtained by adding 1 to the high-order digit Nn-1 of N, and Is subtracted from A, and q is updated by r × q + Q. Again, the upper digit r × Ai + Ai−1 of A is changed to the upper digit N of N.
The quotient Q obtained by dividing by 1 to the divisor obtained by adding 1 to n-1 is obtained. Is subtracted from A, and q is updated by q + Q, and only when the upper digit Ai-1 of A is Nn-1 + 1 or more, A fifth step of subtracting 1 from A and updating q by q + 1, a sixth step of subtracting 1 from i, a seventh step of returning to the third step if i> n−1, and i> n
If −1 and A <N, an eighth step in which q is a quotient and A is a remainder, and i is not i> n−1 and A <N
A ninth step of subtracting N from A, adding 1 to q, and returning to the eighth step if the value is not N;