SU537344A1 - Device for calculating trigonometric tangent - Google Patents

Description

one

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

A device for calculating mathematical functions is known, which contains a control unit whose outputs are connected to cumulative and shifting registers and memory block, and cumulative register outputs are connected to the first inputs of single-bit totalizers-subtractors, outputs connected to the accumulative register registers, the pseudo-partial digit determination unit, convergence analysis unit; and a reset unit, the output of which is connected to the control unit.

The purpose of the invention is to expand the class of tasks to be solved by calculating the function of the trigonometric tangent.

For this, a second convergence analysis block, two switching logic circuits and a gate through which the control block is connected to the second accumulator register are entered into the device. The control inputs of the valve, switching logic circuits, and the pseudo-part digit determination unit are connected to the common output of the control unit, the outputs of the second and third cumulative registers are connected to the inputs of the second and third shift registers, respectively, whose outputs are cross-connected to the second inputs of the second and third totalizers of the readers. The output of the memory unit is connected via the first switching logic circuit to the second input of the first totalizer, convergence analysis input blocks to the bit outputs of the first and third cumulative registers, respectively, and to the second switching logic circuit, the output of which is connected to the reset unit. The inputs of the pseudo-part digit determination unit are connected to the outputs of the sign bits of the first and third terminal registers, and the outputs, respectively, to the third input of the first and combined third inputs of the second and third one-bit adders-subtractors. The block diagram of the device is presented in

drawing.

The device includes single-digit combiners-subtractors 1-3 of combinational type, cumulative register 4, switching logic circuit 5, memory block 6, executed in the form of one-sided memory with random sampling of two words simultaneously, cumulative registers 7, 8, shifting registers 9, 10, pseudo-part digit definition block, analysis blocks 12, 13

convergence (comparison circuits), switching logic 14, reset unit 15 (process stop), control unit 16, valve 17.

The device contains three recirculation cells consisting of looped adders and accumulative registers. Memory block 6 stores constants of the form arctg2 (+ i and 2- (J + i), which are selected simultaneously at the same address with each clock pulse from the output

18 of control 16. Signed bits

19 accumulative registers 4 and 8 are connected to the inputs of the pseudo-part digit determination unit 11. From the output 20 of the block 11, either the pseudo-part number or its inversion is output, the 21-number pseudo-part number is output. The value of the next digit of the pseudo-part determines the mode of addition - subtraction of one-digit totalizers-subtractors 1-3.

The valve 17, the switching logic circuit 5, the blocks 11 and 14 are controlled by a control signal for the reorganization of connections in the structure of the device.

The cycle of calculating the trigonometric tangent consists of two stages. At the first stage, the values of trigonometric sine and cosine are calculated. The interval of change of the argument, defined by current practical requirements, is as follows:. The calculation principle is based on the operations of pseudo-division and pseudo-multiplication with parallel solution of difference recurrence relations in an iterative process:

2o in Zy + i in - QJ + I Zj -.arctg2- +)

+ 1 at

qj sign Zj 1 when

J Q ,, ..., n

X, X ,, Xj-qjY, 2-Cf

l

. convened

Y, 0 U; +1 Yf- qjXj2- J Г „- Г„, sinQ

j

(1 + 2-2 (/ - 1) L J 0

In the initial state, the value of the argument E is entered into register 4, the zero value is entered into register 7, and the value of the reciprocal value of the vector elongation coefficient is entered into register 8. Each recurrence relation is calculated sequentially in () cycles, where n is the number of bits of the argument, and m is the number of additional bits to compensate for the round-off error during the shift. At the first stage of the calculation, the control pulse from the output 22 of the control unit 16 opens the valve 17, switches the output of the block 12 to the input of the block 15 and the sign bit 19 of the cumulative register of the first recirculation cell, the contents of which is in this stage a pseudo divider, to the input of the block 11. At the same time, at outputs 20 and 21 of block 11, after each iteration, the next value of the digit (bit) of the pseudo-part for the next iteration appears. The circuit 5 passes to the input 23 of the adder-subtractor the value of the constants arctg). In any iteration from the outputs 18 of the control block 16 in

0 registers and a series of clock pulses arrives at the input of memory block 6. In this case, the value of arctg 2 - + at qj (or summation at qj - 1) is subtracted from the contents of register 4.

5 The contents of the registers 7 and 8 pseudo-multiplier cells are cross-summed — subtracted with the shifted redirected coordinate components of the trigonometric vector, which rotates by

0 is a converging sequence of angular increments (constants).

The result obtained in each iteration successively, starting with the least significant bits, is entered into the liberated ones

5 bits are cumulative registers and shifted to the end of the register.

After performing n + 1 iterations in register 4, the zero value is found, in register 7, the sine value, in register 8, the value

0 cosine. However, for most argument values, the iteration process converges on an iteration whose number is less than n. In register 4, the content is zero and convergence analysis block 12 (digital circuit

5 comparisons with logical zero) issues a signal to reset unit 15, and control unit 16 stops producing clock pulses at the next iteration. After stopping the calculation process the block

16, the control removes the signal from output 22. The second step of calculating the trigonometric tangent — the operation of dividing the resulting sine by cosine — is also based on the principle of pseudo-division and pseudo-multiplication in an iterative process with parallel resolution of difference recurrence ratios. Each ratio is calculated sequentially in () cycles. The division algorithm is written as:

X, Xn, Xj + r Xj - qjYn, 2- (i „- O

.. +1 at.

: rrsign ::: J / n

J

 {-1 When + 2-)

  tg9.

P,

After removing the control pulse, which corresponds to the beginning of the second calculation step, the valve 17 is closed, the circuit 14 connects the output of the convergence analysis block 13 to the input of the block 15, and the circuit 5 - the second output of block 6

memory with constants of the form 2 - at the entrance