SU465630A1 - Device for calculating the inverse hyperbolic tangent - Google Patents

Description

one

The invention relates to the field of digital computing and can be used for the computation of elementary functions, in particular, in specialized binary digital computers with a fixed occupation.

A device for calculating the inverse hyperbolic tangepsis is known, which contains three cumulative shifts, their registers, three subtractors, a pseudo-partial unit and a control unit. The outputs of the lower triggers of the first, second and third cumulative shift registers are connected respectively with the first inputs of the first, second and third adders-subtractors, and the outputs of the adders-subtractors with counting inputs of the senior triggers of the corresponding cumulative shift registers. The output of the senior trigger of the first cumulative shift register is connected with the input of the pseudo-partial block, and the output of the last one - with the control inputs of all adders-subtractors. The first three outputs of the control unit are connected to the shift inputs of the corresponding storage shift registers.

The purpose of the invention is to increase the speed and simplify the device.

This is achieved by inserting two shift registers into the device, the memory block

and a comparison unit. In this case, the information inputs of the comparison unit are connected with the corresponding outputs of the first storage shift register, and its output - with the input of the control unit. The fourth and fifth outputs of the control unit are connected respectively to the shift inputs of the nerve and second shift registers, the information inputs of these registers are connected to the same

information outputs, respectively, of the first and second cumulative shift registers, and the outputs of the lower triggers to the second inputs of the second and first adders, respectively. 6th exit

the control unit is connected to the input of the unit, the output of which is connected to the second input of the third adder-subtractor.

The drawing shows a block diagram of a device for calculating the inverse hyperbolic tangent, where 1, 2, and 3 are summators and readers; 4 - cumulative shift register; 5 and 6 - shift registers; 7 - cumulative shift register; 8- memory block; 9 - cumulative shift register; 10 is a non-shared block; 11 — block compared; 12 - control unit.

The device consists of three recirculation cells. Each of them is based on a cumulative shift register connected to the input of a one-bit sum3

Torah subtractor, the output of which is associated with the input of this register. The outputs of the cumulative shift register are connected to the information inputs of the shift register, and the output of the shift register is connected to the controllable input of the adder-subtractor of another cell. The output of the shift register of the second cell is connected to the controllable input of the adder-subtractor of the first cell. The output of the memory unit is fed to the control input of the third cell adder. The memory that is inserted into the device is one-way. The output of the high-order trigger of the cumulative shift register 4 of the pseudo-divider is connected to the pseudo-partial unit 10, the remaining bits of this register are fed to the comparison unit 11. The output of block 11 is connected to control block 12.

The outputs of the control unit 12, which receive a series of shifting clock pulses, are connected to the shift inputs of the registers and a memory sample, the output of the unit 10 is connected to the control inputs of the summators and readings.

In the initial state in register 4 is the argument Y, in register 7 is the unit that is represented by all significant bits to the right of the binary comma, in the cumulative shift register 9 is zero.

The production of the inverse hyperbolic tangent is based on the following ratios:

UO Y, U J- qjKj- 2 -LU "O,

. , r-j-1 at. s, gny, |, priU ,,

ho 1, Xj Xj-qjtjj к „-

AV

chti

0 1, b / y + f / y.arth 2 -, „- atrhr /,

/ g „p (-1-2-2 /). y-1

/ - 1, 2, 3, 4, 4, ..., 3ft + 1, 3 / g - f,. .., P.

These differential recurrence relations are implemented in a parallel-serial device structure. All ratios are resolved in parallel. Each ratio is solved sequentially per / g clock cycles in each iteration.

Since the system of basic functions, converging with a sequence of angular increments of arth does not satisfy the conditions

arlh 2. 2 arlh 2

-ft

then, in order to eliminate divergence zones, the necessary repetition in two times is only 4, 13th, and so on, of iterations determined by the formula

/ 3m + 1, s 1, 2, 3, .... This makes it possible to significantly reduce the computation time.

At any iteration from the control unit, a series of shift pulses is output. From the contents of register 4 in adder-subtractor 1 the redirected value of register 7 is shifted to the lower bits. By the sign of the difference, the next digit of the pseudoparticle in block 10 (turn operator) is determined / 7 /. which is used in the next iteration. In adder-subtractor 2, the shifted redirected value of register 4 is subtracted from the contents of register 7, i.e., cross-subtraction or addition. In the cy.Mmanxipe-reader 3, the constants coming from the memory are summed with the previous value of register 9. At the next digit 9 / - 1, the operations in the totalizers subtracts.

After completing n iterations in register 4, its content becomes zero. In register 7, the content is equal to the hyperbolic seance, the value of which is increased by „times. Register 9 contains the value of the inverse hyperbolic tangent.

For the overwhelming majority of the argument values, the process converges on iteration, the number of which is /. In this case, in register 9, the exact value of the inverse hyperbolic tangent is found, and in register 4, the content is zero. The comparator generates a reset signal when all bits of the register 4, except for the sign bit, are insignificant. The control unit for this signal stops the supply of the shifting clock pulses at the next iteration. This provides asynchronous mode. In addition, the control unit when moving to 5 ,. The 14th, and so on iterations, does not change the number of the next iteration, therefore, the process involved the former redirected components shifted by the same number of digits, and the previous one: a constant. The values of the ns-partial qj can be different at two iterations.

For almost necessary accuracy in solving problems, controlling the cycle time, calculating the inverse hyperbolic tangent in cycles is equal to Г п + 5 / г -} - 4, which is two times less than that of protin. In addition, the value of the hyperbolic secant is obtained simultaneously.

PREED MET OF INVENTION:

A device for calculating the inverse hyperbolic tangent, containing three cumulative shift registers, three adders-subtractor, pseudo-part unit and control unit, with the outputs of the lower, triggers of the first, second and third cumulative shift registers connected to the first inputs of the first, second and third adders subtractors, the outputs of which are connected to the counting inputs of the senior triggers of the corresponding cumulative shift registers; the output of the high trigger of the first cumulative shift register is connected to the input of the pseudo-partial block, the output of which is connected to the control inputs of the adders-subtractors; The first three outputs of the control unit are connected to the shift inputs of the corresponding storage shift registers, characterized in that, in order to increase speed and simplify the device, it contains two shift registers, a memory unit and a comparison unit, the information inputs of the comparison unit are connected to the corresponding outputs of the first cumulative shift register, and its output is connected to the input of the control unit; the fourth and fifth outputs of the control unit are connected respectively to the shift inputs of the first and second shift registers, the information inputs of which are connected to the information outputs of the same name of the first and second accumulative shift registers, respectively, and the outputs of the lower triggers, respectively, of the second and first summers of the recipients; the sixth output of the control unit is connected to the input of the memory unit, the output of which is connected to the second input of the third adder-subtractor.