# The random number generator

(57) Abstract:

The invention relates to specialized tools computer engineering and is intended for use in stochastic computing devices. The aim of the invention is to expand the functional capabilities of the device due to the formation of random samples from the distribution of the product of two uniformly distributed random numbers. The objective is achieved by the fact that the random number generator, containing five blocks of multiplication, the adder, a memory block of coefficients, the random number generator and the control unit, inputs of the subtraction unit, three unit, block squaring, block cubing, the random number generator is used to generate the sampling distribution of the product of two uniformly distributed random numbers. 1 Il. The invention relates to computer technology and can be used to generate samples according to the law of distribution of the product of two uniformly distributed random numbers.The known device for generating random numbers [1 and 2].Of the known devices is the closest to the technical with the OK memory coefficients, the random number generator and the control unit.The disadvantage of this device is the narrow scope of its application due to the lack of opportunities to generate random samples under the law of distribution to generate random samples under the law of distribution of the product of two uniformly distributed random numbers.The aim of the invention is to expand the functionality of the device by generating samples from the distribution of the product of two uniformly distributed random numbers.The objective is achieved by the fact that the random number generator, containing five blocks of multiplication, the adder, a memory block of coefficients, the random number generator and the control unit, inputs of the subtraction unit, three unit, block squaring, block cubing and excluded four block multiplication, and the first output unit 1 unit (see the drawing) is connected with the installation inputs the random number generator 2, the subtracting unit 4, block 5, 8, 9 division, unit 6 squaring block 7 of cubing, block 10 summation, unit 11 multiplication, the second output unit 1 control is connected with the control of shadaloo 4 subtraction, the fourth output unit 1 control connected to control inputs of block 5 of division, unit 6 squaring block 7 of cubing, the fifth output of the unit 1 control connected to control inputs of the blocks 8, 9 division, sixth output unit 1 control is connected with the control input of the summation block 10, the seventh output of the unit 1 control is connected with the control unit 11 of the multiplication, the output of the random number generator connected to the first information input of the subtracting unit 4, the first output unit 3 memory connected with the second information input unit 4 subtraction, the second output unit 3 memory connected with the second information input unit 5 of the division, the third output unit 3 memory connected with the second information input unit 8 division, the fourth output unit 3 memory connected with the second information input unit 9 division, fifth exit block 3 memory connected to the fourth information input unit 10 summation, the sixth and seventh outputs of block 3 of memory are connected respectively with the second and third information input unit 11 multiplication, the output of the subtraction unit is connected to the first information input unit 5 division with the information input unit 6 squaring and block 7 of cubing, vivatrat connected to the first information input unit 8 division the output of block 7 of cubing is connected with the first information input unit 9 division output unit 8 division connected with the second information input unit 10 summation, the output of block 9 of division is connected with the third information input unit 10 summation, the output of summation block 10 is connected to the first information input unit 11 multiplication, the output of block 11 of the multiplication is output.Functional diagram of the random number generator, which allows sampling on the distribution of the product of two uniformly distributed random variables, represented in the drawing.The invention follows from the following considerations.Let there be independent random variables X_{1}and X

_{2}with a uniform probability density

f(X

_{1}) = 1/a, 0X

_{1}a,

f(X

_{2}) = 1/b, 0X

_{2}b.To find the density distribution of the product of two random variables we will use are known from probability theory formula

< / BR>

Taking into account the uniform distribution of X

_{1}and X

_{2}'ll get:

< / BR>

In the change of variable Z = Y/X

_{2}and integration can be obtained

< / BR>

therefore, the modeling algorithm can be found on the basis of operator handling of series C. Lee (martsenko L. A. and Panov Century Century Methods of military-scientific research in the development and testing of weapons. The USSR Ministry of defense, 1981, 280 S.).Using the conversion operator

< / BR>

you can find the value of the coefficients of the series

< / BR>

This number of members is determined with sufficient accuracy.Then to simulate the numbers on the law of distribution of the product of two uniformly distributed random variables can be used a number of

< / BR>

where

k

_{1}= 2 Ln 2 = 1,386;

k

_{2}= Ln

^{3}2 = of 0.333;

;

F

_{0}(y) = 1/2 (Ln2 + 1) = 0,847 - the value of the anchor point

is a uniformly distributed random number in the interval (0,1).The generator in the simulation of random numbers obeying the law of distribution of the product of two uniformly distributed random variables, as follows. Before you begin in block 3 of memory are incremented F(y), k

_{1}, k

_{2}, k

_{3}, 0,5, a, b.When power runs the unit 1 control.The first clock pulse output 1 unit 1 control initialises the random number generator 2, the subtracting unit 4, block 5, 8, 9 division, unit 6, the squaring unit 7 construction in ku is rawsome inputs the random number generator 2, unit 3 memory and initiates their work. From exit 8 of the random number generator 2 random number is fed to the first information input unit 4 subtraction. Output 9 of block 3 of memory is F

_{0}(y) is supplied to the second information input of the subtracting unit 4, exit 10, 11, 12 number of k

_{1}, k

_{2}, k

_{3}on the second information inputs respectively of blocks 5, 8, 9 division, exit 13 number of 0.5 on the fourth information input unit 10 summation of the outputs 14, 15 numbers a and b are respectively the second and third information input unit 11 of the multiplication.The third clock pulse of unit 1 control is fed to the control input of block 3 subtraction and initiates its work. From the output of block 3 subtracting the number - F

_{0}(y) is fed to the first information input unit 5 of the division, the information input unit 6 squaring unit 7 construction in cubicThe fourth clock pulse unit 1 control is fed to the control inputs of block 5 of division, unit 6 squaring block 7 of cubing and initiates their work. From the output of block 5 division number [ - F

_{0}(y)]/k

_{1}served on a first information input unit 10 summation. From the output of block 6 squaring the number [ - F

_{0}(y)]

^{3}goes to the first information input unit 9 division.The fifth clock pulse of unit 1 control is fed to the control inputs of blocks 8, 9 division and initiates their work. From the output of the unit 8 dividing number [ - F

_{0}(y)]

^{2}/k

_{2}supplied to the second information input unit 10 summation. From the output unit 9 division number [ - F

_{0}(y)]

^{3}/k

_{3}comes on the third information input unit 10 summation.The sixth clock pulse unit 1 control is fed to the control input of the summation block 10 and initiates its work. From the output of the summation block 10 number

,

served on a first information input unit 11 of the multiplication.The seventh clock pulse unit 1 control is fed to the control input unit 11 multiplication and initiates its work. From the output of block 11 multiplying the number of

< / BR>

output device. The random number generator containing the memory block, the block subtraction, summation block, the block multiplication, and the control unit, the first output of which is connected to the inputs of the read sensor of random numbers and the memory block, the second output control unit connected to synchronou block subtraction, the first and second information is Amati, the third and fourth outputs of the control unit is connected to the state clock inputs of the summation block and block multiplication, the first information input connected to the output of the summation block, characterized in that it introduced blocks divide, squarer and block cubing, the output of which is connected to the first information input of the first unit, the second information input of which is connected to the second output of the memory block, the third output of which is connected to the first information input of the second unit, the second information input and information inputs Quad and block cubing is connected to the output of the subtraction unit, the output of the Quad and the fourth output of the memory block are connected to information inputs of the third unit, engraved which engraved the first unit is connected to the third output of the control unit, the fourth output of which is connected to the state clock inputs of the Quad, block cubing and the second unit, the output of which, the fifth output of the memory block and the outputs of the first and third blocks dividing connected to the information input unit summation, engraved of which is connected to the fifth output control unit, the sixth output of which padmam outputs of the memory block, the generator output is the output of block multiplication.

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