JPH03240826A - Arithmetic unit applying logarithm expressing numerical computing method having scaling function - Google Patents

Abstract

PURPOSE:To use the conversion tables and the addition/subtraction tables as they are and to widen the range of the handling numerical value by providing an input adder between an input conversion tables and a computing element and an output adder between a computing element and an output conversion table respectively. CONSTITUTION:The input data X1,...,Xn on the fixed decimal points are converted into the logarithms via an input conversion table 1 to calculate fj (X1,...,Xn). At the same time, an input adder 2 adds together -K1,...,-Kn and a computing element 3 applying a logarithm expressing numerical computing method performs the due calculation. An output adder 4 adds the proper value, e.g., gj (K1,...,Kn) to the calculation result of the element 3. Then this addition value is converted into the number of fixed decimal points via an output conver sion table 5. Thus, the original output result fj (K1,...,Kn) can be obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial Field of Application) Related to the handling of a wider range of numerical data and the scaling of input and output data in the calculation of numerical data such as image data, acoustic space data, and coordinate data in devices such as computers. .

(Prior art) Logarithmic representation numerical calculation method and fixed point number calculation method using table conversion (for example, literature: Tomio Kurokawa, Tsuyoshi Mizukoshi, "High-speed precise geometric transformation of images - Utilization of logarithmic representation numerical calculation method -
1 Graphics and CAD Symposium Proceedings (Information Processing Society of Japan), pp.

217-226.1989) is very effective in terms of calculation speed. However, when the number of bits for numerical expression is limited, increasing the number of bits to improve calculation precision has the disadvantage that the dynamic range of the numerical value becomes smaller.

Regarding the logarithmic representation numerical calculation method: In the logarithmic representation numerical calculation method, a numerical value is expressed as shown in equation (1).

sdOdl-dmfl-fn (1) Here, s, di, fj are O or 1, S is the numerical sign, and there is a decimal point between part d and part f, so d part is an integer. Part, f part is a minority part.

The base of the logarithm is an implicit value, a number a greater than 1.

Equation (1) represents the value of equation (2).

±ad flexible scaling of data and output data
OdI°°°dmf1°"fn (2) Therefore, dpart and fpart are fixed-point numbers with decimal parts and are exponents of numbers. Therefore, the maximum positive value according to this representation is the minimum positive value Therefore, a number whose absolute value is larger than Equation (3) or smaller than Equation (4) cannot be expressed.

(Problems to be Solved by the Invention) The present invention solves the drawbacks of the conventional method described above, and widens the range of numerical values handled by using the conversion table and addition/subtraction table of the conventional logarithmic expression numerical operation method as they are. The purpose is to The aim is to enter the university at the same time.

(Means and operations for solving the problem) FIG. 1 shows an arithmetic device according to the present invention. The calculation here is to input XI, . . . , Xn and calculate, for example, fj(XI, . . . , Xn). XI...

When calculating Xn), the intermediate result of the calculation may not be able to be expressed within the numerical system used, that is, the range of equation (2) (overflow or underflow). In such a case, the input data XI, , , X
n respectively 2K1. ,, As if divided by 2Kn, - in the input adder (2), respectively.
By adding Kl, . The result is converted to an appropriate value by the output adder in (4), for example, gj
After adding (Kl, , , , Kn), the original output result (fj(K1, , , , Kn)) can be obtained by converting to a fixed-point number using the output conversion table (5).

(Embodiments of the Invention) Example 1 A calculation for drawing an octant using the present invention will be explained. The device is shown in FIG.

8 by calculating fixed decimal points using logarithmic expression numerical arithmetic method
The arc is drawn by directly calculating the circle equation (5). However, if you try to maintain calculation accuracy with a limited word length, you cannot handle very large numbers. In other words, you can't draw a very large circle. for example,
With a word length of 16 bits, a=2゜m24. If n=10, the maximum number that can be represented is 216. Therefore,
According to equation (6), the maximum value of Y is 282256, and a circle with a radius larger than this cannot be drawn.However, as shown in equation (7), if you convert the input values R and X as if they were divided by 25, (In Figure 2, the process of adding K in the input adder (2), in this example, Kl=Kn=K), large R or
In the case of this drawing example of an octant circle, which also allows input of , FIG. 1 is simplified and concretely shown in FIG. 2. Box (1) in Figure 1
to (5) correspond to boxes (1) to (5) in Figure 2, respectively. 5) allows the original result to be obtained. In other words, the result is the same as when overflow or underflow did not occur when calculation was performed using the conventional method. In other words, the accuracy remains unchanged.

In FIG. 1, if boxes (2) and (4) are removed, it becomes a fixed-point pig calculation device using the conventional logarithmic expression numerical arithmetic method. Therefore, there is no need to change the contents of the input conversion table (1), the addition/subtraction table in the arithmetic unit (3) based on the logarithmic expression numerical arithmetic method, and the output conversion table.

Furthermore, an output adder allows the output value to be scaled as required by adding an appropriate value.

Values added by these input adders and output adders (K1, etc.)
does not have to be an integer; it can be a fixed-point number with values below the decimal point.

[Brief explanation of drawings]

FIG. 1 is a block diagram of a computing device according to the present invention, and FIG. 2 is a block diagram of a specific example of a computing device for calculation of drawing a circle. (Effects of the Invention) According to the present invention, when calculating a fixed decimal point number using a logarithmic expression numerical calculation method, a wide range of numerical values can be handled without reducing calculation accuracy (relative accuracy).

Claims (1)

[Claims] 1. In the arithmetic unit (3) using the logarithmic expression numerical arithmetic method,
An input adder (2) is provided between the input conversion table (1) and the arithmetic unit (3), and an output adder (4) is provided between the arithmetic unit (3) and the output conversion table (5). A computing device characterized by