JPH04348424A - Integer division system - Google Patents

Abstract

PURPOSE:To improve the division executing speed by attaining a dividing operation just with the addition/subtraction operations of the comparatively low accuracy and a bit shift operation. CONSTITUTION:The quotient p is obtained from an equation p=>>a.(x+1+>=r.x/2**m])/2**m], where x shows a dividend (positive value) with y showing a divisor (positive odd number), n showing the accuracy of the dividend (maximum value of dividend =2**n-1), a showing a reciporcal of the divisor (=>=2**m/y] and m>=n-1, and r showing the remainder (=2**n-a.y) obtained when the reciprocal of the divisor is calculated. Thus a dividing operation is carried out at a high speed. Then the value with which r is equal to an exponent of 2 for m, and >=r.x/2**m] is calculated just with extraction of several head bits of x.

Description

[Detailed description of the invention]

0001

[Field of Industrial Application] The present invention relates to information processing, and particularly to RISC (Reduced Instruction Set Computer).
The present invention relates to a method for quickly executing a division operation on a computer that does not have multiplication/division instructions, such as on-set computers.

0002

[Prior Art] Conventionally, as a technique related to integer division,
”Integer Multiplication and Division on the Hp Prination Architecture: Integer Multiplica
tion and Division on the
HP Precision Architecture
“Communication of the ACM: Co.
communications of the ACM, v.
ol14, no. 10, oct. 1987, pp. 90
-99. In this document, division is realized by calculating the reciprocal of the divisor in advance and multiplying the value obtained by adding 1 to the dividend by the reciprocal of the divisor. However, in some divisor cases, higher precision calculations are required than in other cases, which has the disadvantage of reducing the execution speed of division.

0003

[Problem to be solved by the invention] In the above conventional technology,
There is a problem in that some divisor cases require higher precision calculations than other cases.

An object of the present invention is to realize a division operation with the same precision in the case of the divisor as in other cases,
The purpose is to improve the execution speed of division.

[0005]

[Means for Solving the Problems] The above object is achieved by correcting the dividend with an appropriate value before multiplying the dividend by the reciprocal of the divisor.

That is, when each symbol is defined as follows, x: Dividend (value is positive) y: Divisor (value is a positive odd number) n: Precision of dividend (maximum value of dividend = 2) **n-1
) a: Reciprocal of divisor (=[2**m/y] where m≧
n-1) r: Remainder when calculating the reciprocal of the divisor (=2**n-
a・y) The quotient P is P = [a・(x+1+[r・x/2**m
])/2**m] (Equation 1).

From this equation, the above-mentioned prior art is a technology for a specific case when r=1, and the present invention
This can be seen as a more generalized version.

The value of m is determined as follows.

(1) When m=n, if r is a power of 2, then
Calculate "Equation 1" with m=n.

(2) When m=n, if r is not a power of 2, then m=n+1, . ．． ．． n+k (however, k=[log
2 y]), find the value of r for r
1 is found first).

(3) If r does not become a power of 2 in the above range, then in the same range, (r/2**(m-n+
1) Calculate "Equation 1" for m that satisfies <1.

(4) When m=n-1, if r is a power of 2, then when 2**(n-1)>x≧0, m=n-1 and the calculation of "Equation 1" is performed.

2**(n-1)+(yr)>x
When ≧2**(n-1), the quotient p is set to a.

[0014] 2**n> x ≧2**(n-1)
+(yr-r), then x to 2**(n-1)+(y
-r), and after performing the calculation of "Equation 1" with m=n-1, a+1 is added to the quotient p.

[0015]

[Table 1]

[0016] The present invention is not applicable to cases where none of the above conditions are satisfied, but as shown in Table 1, when n = 32, the cases where y is 43 or less are not applicable are 25 and 41 cases only.

[0017]

[Operation] In the explanation in the previous section, both the dividend and the divisor are positive, and the divisor is limited to odd numbers. However, in the case of a negative number, it is sufficient to first convert it to a positive value and then perform the calculation, and then adjust the sign. Furthermore, in the case where the divisor is an even number, the method described in the previous section may be applied after dividing the dividend by 2.

In the operation of “Math 1”, [r・x/2*
*m] can be realized by extracting the first log2 r bits of x. However, when r=1, there is no need to do anything. Further, the multiplication of a and the subsequent truncation operation can be realized by a combination of a bit shift instruction and an addition/subtraction instruction, making it possible to perform a high-speed division operation as a whole.

[0019] The precision required for the calculation of "Math 1" is as follows (1
), (x+1+[r・x/2**m]) is n+1 bits, a
is n-k bits, so the whole number 1 is 2・n-
It becomes k+1 bits.

In the case of (2) and (3) above, (x+1+[
r. **m]
) is small, 2·n bits are sufficient for the entire equation 1.

From the above, for all cases, n=
If n=32, 64-bit double-precision arithmetic is sufficient, and if n=16, 32-bit single-precision arithmetic is sufficient.

[0022]

[Example] An example of the present invention is shown below. In this embodiment, the case of item number (4) in the section of means of the invention is taken as an example. FIG. 1 is a flowchart of an integer division program when the precision of the dividend is 16 bits and the divisor is 13. The numbers on the right side of Figure 1 indicate that the value of x is (FFFD)1
6 shows the value of each variable at each step. Note that all numerical values in FIG. 1 are expressed in hexadecimal.

In steps 1, 2, and 3, the range of values of the dividend is examined.

Step 4 is 2**(n-1)+(y-
r)> x ≧2**(n-1),
The reciprocal of the divisor itself is the result.

In step 5, the value of [r·x/2**m] is determined.

The value of the reciprocal a (9D8)16 is (((40)
It can be expressed as 16-1)*5)*8, so step 6,
7, 8, 9, and 10, calculate the product of this value and x. Note that in step 10, the final multiplication by 8 and division by 2**15 are executed at the same time. In step 11, the reciprocal +1 is added to correct the quotient. This completes the division by the divisor 13.

[0027]

According to the present invention, a division operation can be completed only by addition/subtraction and bit shift operations with relatively low precision, so that high-speed division can be realized. That is, whereas the conventional technique required double-precision calculations in each step of 6, 7, 8, 9, and 10, in this method, single-precision calculations are sufficient.

[Brief explanation of drawings]

FIG. 1 is a flowchart of an integer division program when the precision of the dividend is 16 bits and the divisor is 13;

Claims (1)

[Claims] 1. An integer division method characterized in that, in integer division, when the divisor is a predetermined constant, the quotient is determined by correcting the dividend using only addition, subtraction, and bit shift operations.