JP2753922B2 - Fixed-point division method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a fixed-point division method performed in a fixed-point decimal data format.

[0002]

2. Description of the Related Art As a conventional fixed-point division method, an operation method disclosed in Japanese Patent Application Laid-Open No. 50-10046 is known. The division method disclosed herein uses the dividend as a numerator,
Put the divisors in the denominator respectively, make the denominator close to 1 while multiplying the numerator and denominator by the same number, find the value of the numerator when the denominator approaches 1, as an approximate quotient, and calculate the approximate quotient, dividend, and divisor. This method is used to find the remainder.

Hereinafter, a specific example of this conventional fixed-point division method will be described. Here, the fixed-point decimal data format is 8 bits for the integer part and 4 bits for the decimal part, and the dividend and divisor are 1011.011 and 10.1, respectively, in binary notation. First, the dividend (1011.011) is set in the numerator and the divisor (10.1) is set in the denominator, and both the numerator and denominator are successively multiplied by 0.01 and 0.001 to bring the denominator close to 1. Such a calculation process will be described below.

[0004]

(Equation 1)

Then, the value of the numerator when the denominator approaches 1
(100.01) is obtained as an approximate quotient. Next, as shown below, the remainder is obtained by subtracting the product of the approximate quotient and the divisor from the dividend. Approximate quotient × divisor = 100.01 × 10.1 = 1010.101 1011.011−110.101 = 0.11 remainder approximate quotient = 100.01 remainder = 0.11 Fixed-point division is performed by correcting the approximate quotient and the remainder thus obtained.

[0006]

In the above-described conventional fixed-point division method, first, the dividend and the divisor are respectively set in the numerator and the denominator, and the denominator is reduced to 1 while multiplying the numerator and the denominator by the same number. A series of processing to find the approximate quotient by approaching, subtract the value obtained by multiplying the obtained approximate quotient by the divisor from the dividend, find the remainder, and correct the approximate quotient using the approximate quotient and the remainder to obtain the correct quotient Therefore, there is a problem that the processing is complicated and takes a long time.

[0007] The present invention has been made in view of such circumstances, and an object of the present invention is to perform fixed-point division at high speed simply by using dividend shift processing and integer division.
An object of the present invention is to provide a fixed-point division method capable of obtaining a quotient obtained by truncating a value less than the fixed-point precision in a short time.

Another object of the present invention is to provide a fixed-point division method capable of obtaining, in a short time, a quotient rounded up to the fixed-point precision or rounded down to a fixed-point precision.

[0009]

According to a first aspect of the present invention, there is provided a fixed-point division method, wherein a data size is L + 2M bits.
With respect to the dividend and the divisor, which are fixed-point data in which M bits are represented by a fraction part and L bits are represented by an integer part from the LSB, the dividend is first shifted to the MSB side by M bits, and the shifted dividend and It is characterized in that the original divisor is regarded as integer data and subjected to integer division to obtain a quotient obtained by truncating a value below a fixed-point precision.

The fixed-point division method according to the second invention of the present application is the method according to the first invention, wherein a remainder is obtained at the time of integer division, and 1 or 0 is added to the LSB of the quotient according to the obtained value of the remainder. It is characterized in that a quotient obtained by rounding up below the precision of the fixed point is obtained.

The fixed-point division method according to the third invention of the present application is the first invention, wherein the remainder is also obtained at the time of integer division, and the value obtained by shifting the obtained remainder by one bit to the MSB side is compared with the divisor. Accordingly, by adding 1 or 0 to the LSB of the quotient, a quotient obtained by rounding off less than the precision of the fixed point is obtained.

[0012]

According to the fixed-point division method of the first invention, after the dividend is shifted to the MSB side by the number of bits of the decimal part, integer division is performed using the dividend and the divisor, ignoring the decimal point. If the original dividend and the divisor are simply subjected to integer division without shifting the dividend, the quotient after the decimal point is truncated and only the quotient of the integer part alone is obtained. In the present invention, since the dividend is shifted by the number of bits (the number of digits) of the fractional part and then the integer division is performed, a quotient obtained by discarding less than the fixed-point precision of the same format as the dividend and the divisor is obtained.

In the fixed-point division method according to the second or third aspect of the present invention, a remainder is obtained in integer division, and a quotient is processed according to the obtained remainder. In this way, a quotient obtained by rounding up the precision of the fixed point or rounding down the precision of the fixed point is obtained in the same format as the dividend and the divisor.

[0014]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be specifically described with reference to the drawings showing the embodiments.

FIG. 1 is a flowchart showing the procedure of the fixed-point division method according to the present invention. First, the size of the data
From the LSB, dividends and divisors, which are fixed-point data in which M bits are represented by a decimal part and L bits are represented by an integer part, are input from the LSB (step S1).
Next, the dividend is set to the MSB side by M bits (for the number of digits of the decimal part).
Shift only (step S2). The shifted dividend and the original divisor are both regarded as integers (step S3). Then, a quotient is obtained by performing integer division using the dividend and the divisor regarded as integers (step S4).

Next, a specific example of division using the present invention will be described. FIG. 2 is a data flow diagram showing a specific example of the present invention, and FIG. 3 is a data flow diagram in a comparative example of the present invention. Here, the data size is 16 bits, the fixed-point decimal data format is 8 bits for the integer part and 4 bits for the decimal part, and the dividend and divisor are each expressed in binary notation.
11.011, 10.1 First, a comparative example in which integer division is performed without shifting the dividend will be described with reference to FIG. 3, and then, an example of the present invention will be described with reference to FIG.

The dividend (00001011.0110) and the divisor (0000001
0.1000), the decimal point is ignored for these dividends and divisors, and the integer data of the dividend (00001011011
0), Get integer data of divisor (000000101000). Integer division is performed using each obtained integer data, and the quotient (0000
00000100) and the remainder (000000001.0110). In such a procedure of the comparative example, the format of the quotient is only the integer part, and furthermore, only the quotient obtained by truncating the decimal part is obtained, and the quotient having the same precision as the original dividend and divisor cannot be obtained.

On the other hand, in the present invention (see FIG. 2),
Given the dividend (00001011.0110) and the divisor (00000010.1000), the dividend is shifted to the MSB side by M (4) bits (the number of digits of the decimal part) to obtain dividend data (00001011.01100000) padded with zeros. Next, with respect to the dividend data and the original divisor, the decimal point is ignored and the dividend integer data (0000101101100000) and the divisor integer data (0000
00101000). Integer division is performed using each of the obtained integer data to obtain a quotient (00000100.1000) and a remainder (00000000.0).
010). According to such a procedure of the present invention, it is possible to obtain a quotient in which the precision less than the fixed point is truncated in the same format as the given dividend and divisor.

In the above-described embodiment, an example has been described in which a quotient obtained by rounding down the precision of the fixed point is rounded down. It is also possible to obtain a quotient rounded to the nearest. Hereinafter, each of these examples will be described.

FIG. 4 is a flowchart showing a processing procedure of another embodiment of the present invention (an example of obtaining a quotient obtained by rounding up the precision below the fixed point). First, in the same manner as the processing procedure of the above-described embodiment (the flowchart shown in FIG. 1), the quotient of the integer division and the remainder are obtained (step S11). Then, it is determined whether or not the obtained remainder is 0 (step
S12). If the obtained remainder is other than 0, 1 is added to the LSB of the obtained quotient (step S13) to obtain a new quotient (step S14). If the obtained remainder is 0, the quotient obtained without adding anything is used as a new quotient (step
S14). By performing the above processing, it is possible to obtain a quotient obtained by rounding up the precision below the fixed point in the same format as the given dividend and divisor.

FIG. 5 is a flowchart showing a processing procedure of still another embodiment of the present invention (an example of obtaining a quotient obtained by rounding off the precision of a fixed point). First, the quotient of the integer division and the remainder are obtained in the same manner as the processing procedure of the above-described embodiment (the flowchart shown in FIG. 1) (step S2).
1). Then, the obtained remainder is shifted by one bit to the MSB side (step S22). The magnitude of the remainder after the shift and the divisor are compared (step S23). If the remainder after the shift is equal to or greater than the divisor, 1 is added to the LSB of the obtained quotient (step S24) to obtain a new quotient (step S25). If the remainder after the shift is less than the divisor, the quotient obtained without adding anything is used as a new quotient (step S25). By performing the above processing, it is possible to obtain a quotient in which the precision less than the fixed-point precision is rounded off in the same format as the given dividend and divisor. In this embodiment, when the remainder after the shift is equal to the divisor, 1 is added to the LSB of the obtained quotient, but this is an example.
It goes without saying that the condition of this processing may be changed according to the condition of rounding.

[0022]

As described above, in the fixed-point division method of the first invention, since the quotient is obtained by using the dividend shift processing and the integer division, the fixed-point division can be performed at a high speed, and the precision of the fixed-point is improved. It is possible to obtain a quotient in which a fraction is rounded off in a short time.

In the fixed-point division method according to the second or third invention, the quotient and the remainder are obtained in the same manner as in the first invention, and the quotient obtained is processed according to the value of the remainder. It is possible to obtain a quotient obtained by rounding up the precision below the decimal point or a quotient obtained by rounding down the precision below the fixed point.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a processing procedure of an embodiment of a fixed-point division method according to the present invention.

FIG. 2 is a data flow diagram showing a specific example of a fixed-point division method of the present invention.

FIG. 3 is a data flow diagram showing a specific example in a comparative example of the fixed-point division method of the present invention.

FIG. 4 is a flowchart showing a processing procedure of another embodiment of the fixed-point division method of the present invention.

FIG. 5 is a flowchart showing a processing procedure of still another embodiment of the fixed-point division method of the present invention.

Claims (3)

(57) [Claims] 1. A method for performing division by a dividend and a divisor in which an integer part and a decimal part are represented by a bit string, wherein the dividend is shifted to its MSB side by the number of bits of the decimal part, and the shifted dividend and the divisor are shifted. A fixed-point division method wherein integers are regarded as integers and integer division is performed to obtain a quotient obtained by truncating a value less than a fixed-point precision. 2. The method according to claim 1, further comprising: obtaining a remainder when performing the integer division, processing a quotient obtained by rounding down the precision of the fixed point according to the obtained remainder, and obtaining a quotient obtained by rounding up the precision of the fixed point. The fixed-point division method according to claim 1, wherein 3. A quotient obtained by rounding off a precision less than a fixed-point precision according to a result obtained by processing the obtained remainder. 2. The method according to claim 1, wherein the division is performed.