SU1508209A1 - Rooting device - Google Patents

Abstract

The invention relates to computing. The purpose of the invention is the expansion of the class of tasks by implementing the additional possibility of extracting an arbitrary degree N root. implement the mode of extraction of the root of the Nth degree. 3 il.

Description

00 N9

WITH

F1 (G1

3150

The invention relates to computing and can be used to extract a root of an arbitrary degree N in high-speed specialized computers with data processing in a fixed-point format.

The purpose of the invention is to expand the class of tasks to be solved by ensuring the possibility of extracting the root of the Nth degree.

Figure 1 shows the structural diagram of the device; FIG. 2 is a graph showing the device operation in the extracting root of the n degree; FIG. 3 is a block diagram of the formation of the basic function.

The diagram of FIG. 1 denotes the decoder 1 of the highest unit of the argument code, the shift unit 2, the basic function generation unit 3, the function value memory unit 4 in the i-th approximation area, and the multiplier 5.

The base function generation unit 3 (FIG. 3) forms the memory block 6 of the base function values, block 7. the memory of the slope coefficients of the linear portions of the base function, the multiplier 8 and the adder 9.

To calculate the view function on the i-M plot of the approximation (, 1, ..., n-1; n is the number of bits of the argument code), the ratio

. heh x-; X; -. LH ;, (o

where Xj is the value. the argument corresponding to the beginning of the i-ro site; &X; - length 1 MOT -site of approximation;

(d) () о Jj 4-1 - basic function. In formula (1) with he p; l

X,, 1, ... n-1;

LH; Xj., - X ;; X;

The value с characterizes the change of the argument code inside the approximation area :.

-7 X - X, X - Xj -. city, div, xelx ,, 2xj,

 one.

The area number code is generated by the decoder of the highest unit of the argument code and identifies the cell of the memory block in which the value is stored

g

Yu

15

20

25 30

S

40

-jr.

five

0

five

as well as the magnitude of the shift of the argument required to obtain the normalized value 1. The unit for forming the basis function calculates the value of the function Lf (c) +1, uniform for all the sections, which then will be calculated by the value X; corresponding to this area of approximation.

The device works as follows.

The control input of the device is supplied with a q-bit code that determines the degree N of the extracted root. The code of the argument comes from the information input of the device to the input of the decoder 1, which determines the position of the leftmost unit of the code. If we denote the decimal equivalent of the output code of the 1 M decoder, then, where, I, ..., n-1 is the number of the first left of the bit of the argument code containing the unit.

In this case, the zero code () at the output of the decoder 1 corresponds to the zero segment of the approximation with the initial value of the argument .i ... 00 (FIG. 2) to the code — the first segment with X, 0100 ... 00, etc. The code from the output of the decoder 1 is fed to the address input of the memory block 4, from which the value -JXj corresponding to the 1st segment arriving at the first input of the multiplier 5, counts

In addition, the output code of the decoder 1 is fed to the control input of the shift unit 2, where the corresponding code shift of the argument is made, which is necessary to obtain the normalized value bb 0; 1. For example, if Mj, 0, then in block 2, the shift of the code is zero, the code of the argument is shifted left by one bit, and so on. (n-1) is a bit code defining the normalized - m-value, is fed to the information input of the unit 3 of the basis function formation.

- To calculate the values of the basis function tf (7), you can use any of the known methods. Fig. 3 shows the functional diagram of the unit 3 for the formation of the basic function that implements its piecewise linear approximation. In this case, the basic function (C) on each jth segment

approximation is replaced by a linear function of the form

q (t). (C-Oj),,, i ....,

n

N g; 1

(Jj

K.

. l . l ..

J-j + l

n-p-2

the value of the basis function at the beginning of the J-th approximation area;

the slope factor of the j-ro plot;

the number of high-order bits of the t- code;

For real units of 10 2 shift my

KPI802BP1, tact tact, all right, and 15,

units, dividing the number of linear sections required to provide the required accuracy of calculations. From the control input of the device

and the address inputs of the higher q bits of blocks 6 and 7 of the memory arrive 25

one specifying the degree of N extracted

Orn and defining cell arrays,

which parameters are stored (c-, k :)

corresponding function.

This value N. At the address inputs 30

best h-p-2 bits of blocks 6 and 7

ami is given the code of the elders

ad hocs of the normalized value with

the output of block 2 shift, defining

omer j of the linear region of the approximate formulas

35

The device contains the code of the code arg unified with the input and the shift information, and in the house of the block c is connected to the block it is different for the purpose of resolving the tasks of the Nth scatter i on iM (where, i, i old and the way out

mation base function. In this case, from the output of memory block 7, the code of the slope coefficient K is read, which in multiplier 8 is multiplied by the code of the lower p bits of the value t, the transfer of the body, the output and the second input of which is output from the shift block 2. On, respectively, connected to the output of the multiplier 8, the device is formed and the output of the unit the formation of the K- (-c-), which is summed in the adder 9 with the value of the basic function read from

82096

6 memory block. As a result, on block 3, we obtain an approximate value of the basis function cp (C) j arriving at the second input of the multiplier 5,

at the output of the device, the product X is formed; . .

To implement the decoder 1 senior unit of the code of the argument and block 10 2 shift you can use the LSI

KPI802BP1, which allows performing arithmetic, logical, cyclic left and right shifts in one clock cycle, and also performs operation 15 of determining the code (number) of the first left unit,

Claims (1)

Invention Formula units, 0 five 0 five A device for extracting the root containing the decoder of the highest unit of the argument code, the input of which is connected to the input of the device argument and the information input of the shift unit, and the output - with the control input of the shift unit, the output of which is connected to the information input of the basic function generating unit, characterized in that , in order to expand the class of tasks due to the possibility of extracting the root of the Nth degree, a multiplier and a memory block of function values are entered into it at the iM approximation segment (where, I ,, .. п-1, п is the number of digits and argument), the address input of which is connected to the output of the decoder unit of the elder argument code, while the output - to the first input umnozhini basis function, the address input of which is connected to the control input 45 of the device. QI tchasluk site Q-u plot {| gg; ... oo | Q; O ... QQ -L J. -L 16 in  operations {fj.g L  m ... QQ j z Fie.2 1.0