RU2614931C1 - Device for calculating trigonometric functions - Google Patents

Abstract

FIELD: physics, computer engineering.

SUBSTANCE: invention relates to computer engineering, specifically special-purpose computers. The technical result is achieved by a device for calculating trigonometric functions, which comprises sine and cosine registers, increment registers of the same values, two converters for converting direct code into complementary code, connected, besides by connections between said units, with a clock pulse generator, a memory unit and an argument counter.

EFFECT: method of removing limitations on an argument of calculated functions in the range from 0 to + when calculating trigonometric functions.

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Description

The invention relates to the field of computer technology, in particular to specialized computers, and can be used in digital automatic control devices, in devices of digital sweeps of azimuthal orientation, in devices for displaying graphic information, etc.

A device for calculating trigonometric functions [A. S. No. 419896 of the USSR, 1974], containing a sine register, a cosine register and a clock, the output of which is connected to the input of the argument counter. The disadvantage of this device is the increased amount of equipment.

Closest to the claimed invention, a known device [AS USSR 645164, 1979] contains a clock generator, an argument counter, a register of sine increments, a sine register, a register of cosine increments, a cosine register, a direct code to additional converter and a memory block whose input is connected to the output of the argument counter, and the output to the first inputs sine and cosine registers, the second inputs of which are connected to the first output of the clock generator, the second output of which is connected to the first inputs of the sine and cosine increment registers, the outputs of which are connected to the third input m register of the sine and cosine of the register respectively, the cosine register output is connected to the second input register increments of sine and sine output register via the direct converter in additional code coupled to the second input register increments cosine.

) тригонометрических функций.The main disadvantage of this device is the limited range of possible values of the argument (within

) trigonometric functions.

The objective of the present invention is to expand the range of possible values of the argument of trigonometric functions.

The technical result of the invention is the removal of restrictions on the argument of the calculated functions in the range from 0 to + ∞.

The technical result is achieved by the fact that it additionally contains a second converter of direct code to an additional one, included between the output of the cosine register and the second input of the register of sine increments.

до

), а также при любых значениях аргумента тригонометрических функций.The introduction of the second direct code converter into the additional one and its connections with the output of the cosine register and with the second input of the register of sine increments allowed the device to function with negative cosine values (for example, with argument values ranging from

before

), as well as for any values of the argument of trigonometric functions.

The proposed device has an inventive step, since it does not explicitly follow from published scientific data and existing technical solutions that the claimed combination of a block (direct code to additional converter) and its connections with other prototype blocks allows us to expand the range of possible values of the argument of trigonometric functions.

The proposed device for calculating trigonometric functions is industrially applicable, since its technical implementation is possible using typical elements of microelectronic technology (integrated logic circuits).

The drawing shows a block diagram of a device. A device for calculating trigonometric functions includes a clock 1, an argument counter 2, a memory block 3, a register of cosine increments 4, a register of cosine 5, a register of increments of sine 6, a register of sine 7, first 8 and second 9 direct code converters to additional code.

The device operates as follows. The pulse generator 1 produces two sequences of pulses, phase shifted by 180 °.

The nth pulse of the pulse train from the second output of the clock generator t records the numbers a _N ⋅Δ and b _N ⋅Δ through the second 9 and first 8 direct code converters into an additional register of sine increments 6 and into the register of cosine increments 4, respectively, here Δ is the discretization step of the argument, chosen so that the multiplication operation is replaced by a shift a _Ν and b _N - the contents of the register of cosine 5 and the register of sine 7, respectively.

The (N + 1) th pulse of the pulse train from the first output of the generator 1 feeds the contents of the register of increments of cosine 4 and the register of increments of sine 6 to the register of cosine 5 and to the register of sine 7, respectively, which are made in the form of accumulating adders. As a result, in the register of cosine 5 and in the register of sine 7, the numbers will be written:

a _{N + 1} = a _N -b _N ⋅Δ, b _{N + 1} = b _N + a _N ⋅Δ.

There are relations

a _Ν = R _e (a ₀ + i⋅b ₀ ) (1 + i⋅Δ) ^N ], b _N = I _m [(a ₀ + i⋅b ₀ ) (1 + i⋅Δ) ^N ),

where i is the imaginary unit, a ₀ and b ₀ are the originally recorded numbers, respectively, in register 5 and in sine register 7.

Indeed, for a ₀ = 1 and b ₀ = 0, the validity of the indicated equalities is obvious. Suppose that these relations hold for N = K, i.e. (a _k + i⋅b _k ) = (a ₀ + i⋅b ₀ ) (1 + i⋅Δ) ^K.

Then, in accordance with the above relations, for N = K + 1 we obtain

a _{K + 1} + i⋅b _{K + 1} = a _K -b _K ⋅Δ + i⋅ (b _K + a _K ⋅Δ) = a _K + i⋅b _K + i⋅Δ⋅ (a _K + i⋅ b _K ) = (a ₀ + i⋅b ₀ ) ⋅ (1 + i⋅Δ) ^{K + 1} .

The sequence of pulses from the first output of the clock generator 1 also goes to the input of the argument counter 2, the outputs of which are connected to the input of the memory block 3. In the memory block 3 the sines and cosines of some values ϕ _{j of the} argument are stored, and at the time when the current counter code K of argument 2 satisfies the condition K⋅Δ = ϕ _j , the numbers a ₀ = cos ϕ _j and b ₀ = sin ϕ _j are recorded in the cosine register 5 and the sine register 7, respectively.

Suppose that after a specified point in time, N pulses arrived from clock generator 1, then we have:

и arctgΔ≈Δ, получимGiven that for small values

and arctgΔ≈Δ, we obtain

The proposed device does not have restrictions on the range of variation of the function argument, unlike the prototype, where the argument is valid in the range

Claims (1)

A device for calculating trigonometric functions, containing a register of cosine increments, a register of sine increments, a sine register, a cosine register, an argument counter, a clock generator, a direct code converter into an additional one and a memory block whose input is connected to the output of the argument counter, and the output to the first the inputs of the sine and cosine registers, the second inputs of which are connected to the first output of the clock generator, the second output of which is connected to the first inputs of the sine and cosine registers ca, the outputs of which are connected to the third inputs of the sine register and the cosine register, respectively, the output of the cosine register is connected to the second input of the sine increment register, the output of the sine register through the direct code converter is additionally connected to the second input of the cosine increment register, characterized in that it further comprises a second a direct code converter to an additional one, included between the output of the cosine register and the second input of the register of sine increments.

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