TWI420325B - Sine/cosine value generation apparatus - Google Patents

Description

Sine/cosine value generating device

The present invention relates to a sine/cosine value generating apparatus, and more particularly to a sine/cosine value generating apparatus using less memory space.

In many engineering fields, mathematical functions are often used. However, in all mathematical calculations, Trigonometric Functions are relatively simple, but they are very important. In the calculation of trigonometric functions, sine/cosine (Sine/Cosine) is the most commonly used mathematical function calculation, because the related applications in the engineering field are often based on sine/cosine functions, and then deduced to derive more cumbersome mathematical calculations. In the field of communications engineering, sine/cosine waveforms are often the most basic form of signal used in signal processing mechanisms.

According to the mathematical definition, a circle is divided into four quadrants, each having an angular value of 90 degrees. In the traditional sine/cosine value generation mechanism, the sine/cosine values of all angles in the first quadrant (0 to 90 degrees) are usually calculated and stored, and then these values are used to find any angle between 0 and 360. Sine/cosine values, but sometimes you need to add a negative sign. For example, referring to Figure 1, it shows a basic characteristic diagram of a sine/cosine function. Wherein, for a sinusoidal function, all values of the first and second quadrants are positive, and for the cosine function, all values of the first and fourth quadrants are positive. If, for example, a value of any angle of the sine function is required, assuming 210 degrees, the angle must be mapped to the corresponding angle in the first quadrant before the sine/cosine value can be further calculated. More specifically, by the formula: sin(π + θ) = sinπcos θ + cosπsin θ, the angle of 210 degrees can be converted to a corresponding angle of 30 degrees in the first quadrant, but the final result value must be added with a minus sign. Therefore, the sine of 210 degrees is equal to the sine of 30 degrees plus a minus sign. In the above conventional method, the values of all the sine/cosine functions in the first quadrant must be calculated in advance to further obtain the sine/cosine values of any angle.

Based on the above considerations, it is an object of the present invention to provide a low cost sine/cosine value generating device. Compared with the conventional method of calculating the characteristics of all sine/cosine values in the first quadrant (90 degrees) in advance, the present invention only needs to calculate all the sine/cosine values in the first octant (Octant, 45 degrees) in advance. You can then calculate the sine/cosine values at any angle, thus saving half the memory footprint.

In view of the above, the present invention discloses a sine/cosine value generating device for generating an input phase sine/cosine value, including a phase projector, a look-up table/arithmetic unit, a temporary sine/cosine value generator, and a Sine/cosine generator. The phase projector is used to map the input phase to an octant phase within an octant and is determined to determine whether the input phase is pi/4, 3*pi/4, 5*pi/4 or 7* A flag of pi/4. The look-up table/arithmetic unit is used to receive the octant phase and output a sine/cosine value corresponding to the octant phase. A temporary sine/cosine generator is used to receive a sine/cosine value corresponding to the octant phase to produce a temporary sine/cosine value based on the flag. The sine/cosine generator selectively selects the temporary sine/cosine value as a sine/cosine function value or changes the sign according to an octant index for displaying the octant position of the input phase, as the above Enter the sine/cosine value of the phase.

The above described objects, features, and advantages of the present invention will become more apparent from the aspects of the preferred embodiments illustrated herein A block diagram of the sine/cosine value generating device 100. The sine/cosine value generating apparatus 100 includes a phase projector 120, a look-up table/arithmetic unit 140, a temporary sine/cosine value generator 160, and a sine/cosine value generator 180. In FIG. 2, the phase projector 120 receives an input phase value Phase_Value for generating an octant phase Phase_Octant, an octant index Octant_Idx, and a flag Ph_on_pi/4. The look-up table/arithmetic unit 140 is configured to receive the octant phase Phase_Octant and output a corresponding sine function value Sin_Dout and a cosine function value Cos_Dout. The temporary sine/cosine value generator 160 is configured to receive the sine function value Sin_Dout, the cosine function value Cos_Dout, the flag Ph_on_pi/4, and the octant index Octant_Idx, and output a pair of index indexes Invert_Swap, a temporary sine value Sin_Oct, and a temporary cosine value. Cos_Oct. The sine/cosine value generator 180 is operative to receive the offset index Invert_Swap, the temporary sine value Sin_Oct, and the temporary cosine value Cos_Oct, and to generate the final sine value Sin_Val and the cosine value Cos_Val. Hereinafter, the present invention will explain the detailed operational flow of the sine/cosine value generating apparatus 100.

Figure 3 shows a block diagram of a phase projector 120 in accordance with an embodiment of the present invention. The input phase value Phase_Value received by the phase projector 120 is represented by N bits and is divided into two parts. The first part is the first three high bits of the N-bit, denoted as Phase_MSB. The second part is the lower N-3 lower bit of the N-bit, which is represented as Phase_LSB. In addition, the octant index Octant_Idx is used to display which octant of the input phase value Phase_Value is located in a circle, so that the phase position of the input phase value Phase_Value can be defined by the octant index Octant_Idx. For example, for an input phase value Phase_Value at the 0th octant, its octant index Octant_Idx is expressed as 000. Similarly, for an input phase value Phase_Value at the 7th octant, its octant index Octant_Idx is represented as 111. The flag Ph_on_pi/4 is used to display whether the input phase value Phase_Value is exactly an angle value of π/4, 3π/4, 5π/4 or 7π/4. For the case where the input phase value Phase_Value is exactly the angle value π/4, 3π/4, 5π/4 or 7π/4, the wrong sine/cosine value may be read, so additional measures must be taken. It must be understood that the present invention only needs to calculate and store all sine/cosine values from 0 to 45 degrees in the first octant in advance, and thereby obtain the sine/cosine values of any angle.

As shown in FIG. 3, the phase projector 120 includes capture units 301 and 303, a complement digital generator 305 of a 2, a selector 307, and a logic circuit 309. The capturing unit 301 is configured to obtain the first three high bits (Phase_MSB) of the input phase value Phase_Value, and output an octant index Octant_Idx. The capturing unit 303 is configured to obtain the last N-3 lower bits (Phase_LSB) of the input phase value Phase_Value. The complement generator 305 of 2 is used to determine the complement value of 2 of the output value of the capture unit 303. The selector 307 is used to select the output value of the capture unit 303 or the output value of the complement generator 305 as an octant phase Phase_Octant. The mechanism of its selection is based on a control signal Phase_MSB[0], that is, the lowest bit of the first three high bits Phase_MSB of the phase value Phase_Value. In other words, when the control signal Phase_MSB[0] is 1 (that is, when the input phase value Phase_Value is within the first, third, fifth or seventh octant), the complement value of the output value of the capture unit 303 is 2 The output is the octant phase Phase_Octant. On the other hand, when the control signal Phase_MSB[0] is 0 (that is, when the input phase value Phase_Value is within 0, 2, 4 or 6 octants), the output value of the capturing unit 303 is directly taken as eight points. Round phase Phase_Octant. The input phase value Phase_Value can be mapped to a corresponding angle within the 0th octant by the complement digital generator 305 and the selector 307 of the capture units 303, 2.

As shown in FIG. 3, the logic circuit 309 receives the octant phase Phase_Octant and the control signal Phase_MSB[0] for generating the flag Ph_on_pi/4. In this embodiment, the logic circuit 309 further includes a comparator 311 and a gate 313. The comparator 311 is configured to determine whether all the bits of the octant phase Phase_Octant are 0. The gate 313 pulls the flag Ph_on_pi/4 to a high level only when the control signal Phase_MSB[0] and the output of the comparator 311 are both logic 1. That is, the gate 313 pulls the flag Ph_on_pi/4 to a high level only when the output of the control signal Phase_MSB[0] is logic 1 and all bits of the octant phase Phase_Octant are 0. In other words, when the input phase value Phase_Value is exactly π/4, 3π/4, 5π/4 or 7π/4, the flag Ph_on_pi/4 will be in a high potential state.

Figures 4A, 4B and 4C show block diagrams of three embodiments of the look-up table/arithmetic unit 140 in accordance with the present invention. The look-up table/arithmetic unit 140 is configured to receive the octant phase Phase_Octant and output a corresponding sine function value Sin_Dout and a cosine function value Cos_Dout. Figure 4A shows an embodiment of a look-up table/arithmetic unit 140 in accordance with the present invention implemented in a full-Look Up Table (full-LUT) approach. In Figure 4A, all sine/cosine values in the 0th octant are calculated in advance and stored in a Read-Only Memory. Based on the octant phase Phase_Octant received from the phase projector 120, the look-up table/arithmetic unit 140 reads the corresponding sine/cosine value from the read-only memory in a look-up manner and reads the sine/ The cosine value is output as a sine function value Sin_Dout and a cosine function value Cos_Dout. Figure 4B shows another embodiment of the look-up table/arithmetic unit 140 in accordance with the present invention, which is implemented in a full-arithmetic manner. In Figure 4B, all sine/cosine values in the 0th octant are calculated in advance by a processor that implements the Coordinate Rotation Digital Computer (CORDIC) iteration algorithm. And a normalized octant phase Phase_Normalized obtained by multiplying the octant phase Phase_Octan by a constant π/4 and then truncating the resulting value into K bits, the processor can be used to calculate the corresponding sine The /cosine value is taken as the sine function value Sin_Dout and the cosine function value Cos_Dout of the output. Figure 4C still shows another embodiment of the look-up table/arithmetic unit 140 in accordance with the present invention, which is implemented in a LUT-arithmetic hybrid approach. In Figure 4C, all sine/cosine values in the 0th octant are stored in a read-only memory, and the result can be multiplied by a constant π/4 by multiplying the octant phase Phase_Octan. A normalized octant phase Phase_Normalized is obtained by truncating the value into K bits. The normalized octant phase Phase_Normalized consists of two parts: the first part is the first L high order elements of the normalized octant phase Phase_Normalized, and the second part is the normal (KL) low order of the normalized octant phase Phase_Normalized. yuan. The sine/cosine values of the first part can be read by the read-only memory in a look-up manner, and the sine/cosine values of the second part can be calculated by a processor implementing the CORDIC iterative algorithm. The output values read by the read-only memory and the values output by the processor implementing the CORDIC iterative algorithm can be combined into a sine function value Sin_Dout and a cosine function value Cos_Dout. In more detail, it is assumed that the normalized octant phase Phase_Normalized is represented as A+B, A is the first part, and B is the second part. Since sin( A + B )=sin A *cos B +cos A *sin B and cos( A + B )=cos A *cos B -sin A *sin B , it can be obtained by looking up the table. The values of sin A and sin B , and by using a processor that implements the CORDIC iterative algorithm, the values of cos A and cos B can be calculated, and finally the output values read from the read-only memory are processed by the processor. The output values are combined to find sin( A + B ) and cos( A + B ). FIG. 4D is a diagram showing a data storage format in a read-only memory according to an embodiment of the invention. In the embodiment of Fig. 4D, the cosine value is stored in the left portion of the read only memory, and the sine value is stored in the right portion of the read only memory.

Referring back to FIG. 2, the temporary sine/cosine value generator 160 further includes selectors 501 and 502, and a look-up table 503 as shown in FIGS. 5A and 5B. Based on the received sine function value Sin_Dout, the cosine function value Cos_Dout, the flag Ph_on_pi/4, and the octant index Octant_Idx, the temporary sine/cosine value generator 160 outputs a reverse index Invert_Swap, a temporary sine value Sin_Oct, and a temporary cosine value Cos_Oct. Referring to FIG. 5A, the selector 501 selects the constant π/4 or the cosine function value Cos_Dout as the temporary cosine value Cos_Oct, and the selector 502 selects the constant π/4 or the sine function value Sin_Dout as the temporary sine value Sin_Oct. This selection is based on the flag Ph_on_pi/4. In more detail, when the input phase value Phase_Value is exactly π/4, 3π/4, 5π/4 or 7π/4, the flag Ph_on_pi/4 will be in a high potential state, and the selectors 501 and 502 will have a constant π. The /4 simultaneous output is used as the temporary sine value Sin_Oct and the temporary cosine value Cos_Oct. On the contrary, the flag Ph_on_pi/4 will be in a low potential state, and the selectors 501 and 502 respectively output the sine function value Sin_Dout and the cosine function value Cos_Dout as the temporary sine value Sin_Oct and the temporary cosine value Cos_Oct.

Referring to FIG. 5B, there is a one-to-one mapping relationship between the index index Invert_Swap and the octant index Octant_Idx in the lookup table 503. In this embodiment, the index index Invert_Swap and the octant index Octant_Idx are all three bits. It must be understood that although the lookup table 503 is integrated into the temporary sine/cosine generator 160 in this embodiment, it may be integrated into other components, such as the phase projector 120, table lookup/arithmetic. Unit 140 or sine/cosine value generator 180. The detailed usage of the index index Invert_Swap will be explained later.

Referring back to FIG. 2, the sine/cosine value generator 180 generates a final sine value Sin_Val and a cosine value Cos_Val according to the received index of the index Invert_Swap, the temporary sine value Sin_Oct, and the temporary cosine value Cos_Oct. Referring to Fig. 6, the first selectors 601 and 603 are used to add a sign (positive sign) to the temporary sine value Sin_Oct and the temporary cosine value Cos_Oct, and the temporary sine value Sin_Oct and the temporary cosine value Cos_Oct with positive and negative signs are further output. To the second selectors 605 and 607. The first selectors 601 and 603 individually select the temporary sine value Sin_Oct and the temporary cosine value Cos_Oct (positive value) according to the control signals Invert_Swap[1] and Invert_Swap[2] output by the temporary sine/cosine value generator 160, or It is its complement value (negative value) of 2 as its output. On the other hand, the second selectors 605 and 607 also select (1) the output value of the selector 603 as the final cosine value Cos_Val according to the control signal Invert_Swap[0] outputted by the temporary sine/cosine value generator 160, selecting The output of the 601 is the final sine value Sin_Val, or (2) the output of the selector 601 is the final cosine value Cos_Val, and the output of the selector 603 is the final sine value Sin_Val.

The sine/cosine value generating device 100 of the present invention has been described in the above. However, although the present invention has been disclosed in the above preferred embodiments, it is not intended to limit the scope of the present invention. In the spirit and scope of the invention, the scope of the invention is defined by the scope of the appended claims.

100. . . Sine/cosine value generating device

120. . . Phase projector

140. . . Table lookup/arithmetic unit

160. . . Temporary sine/cosine generator

180. . . Sine/cosine generator

301, 303. . . Capture unit

305. . . 2 complement digital generator

307, 501, 502, 601, 603, 605, 607. . . Selector

309. . . Logic circuit

311. . . Comparators

313. . . Gate

Figure 1 shows the basic characteristic diagram of the sine/cosine function;

2 is a block diagram showing a sine/cosine value generating apparatus according to an embodiment of the present invention;

3 is a block diagram showing a phase projector according to an embodiment of the invention;

4A is a diagram showing an embodiment of a look-up table/arithmetic unit according to the present invention, which is implemented in a full look-up table method;

Figure 4B shows another embodiment of a look-up table/arithmetic unit in accordance with the present invention, which is implemented in a fully arithmetic manner;

Figure 4C still shows another embodiment of the look-up table/arithmetic unit according to the present invention, which is implemented in a table-arithmetic mixing method;

4D is a diagram showing a data storage format in a read-only memory according to an embodiment of the invention;

FIG. 5A is a diagram showing a process of generating a temporary sine/cosine value according to an embodiment of the invention;

FIG. 5B is a diagram showing a lookup table between a index of an index and an index of an octant according to an embodiment of the invention;

Figure 6 shows the generation of the final sine/cosine value in accordance with an embodiment of the present invention.

100. . . Sine/cosine value generating device

120. . . Phase projector

140. . . Table lookup/arithmetic unit

160. . . Temporary sine/cosine generator

180. . . Sine/cosine generator

Claims (9)

A sine/cosine value generating device for generating an input phase sine/cosine value, wherein the input phase is between 0 and 2*pi, and is represented by N bits, including: a phase projector that inputs the input The phase is mapped to an octant phase within an octant and is determined to determine whether the input phase is pi/4, 3*pi/4, 5*pi/4 or 7*pi/4 a flag, wherein the phase projector further determines the octant index, wherein the phase projector further comprises: a first capturing unit, obtaining the first three high bits of the input phase as the octant index; a second capture unit obtains the last N-3 lower bits of the input phase; a complement generator of one 2 obtains a complement of N-3 low bits obtained by the second capture unit; a selector And selecting, according to the lower bit of the octant index, the N-3 lower bits obtained by the second capturing unit, or the complement of the N-3 low bits obtained by the complementary digital generator of the 2, As the above octant phase, and a logic circuit, according to the above octant phase and the above The lower bit of the circular index is used to generate the above flag; a lookup table/arithmetic unit receives the octant phase and outputs a sine/cosine value corresponding to the octant phase; a temporary sine/cosine value generator, Receiving a sine/cosine value corresponding to the above octant phase to generate a temporary sine/cosine according to the above flag And a sine/cosine value generator selectively aligning the temporary sine/cosine value to a sine/cosine function value according to an octant index for displaying an octant position of the input phase Change the sign to be the sine/cosine value of the above input phase. The sine/cosine value generating device of claim 1, wherein the logic circuit further comprises: a comparator for determining whether all of the bits of the octant phase are all logic 0; and The lower bit of the octant index is logic 1, and when the comparator determines that all the bits of the octant phase are logic 0, the flag is raised to a logic 1 level. The sine/cosine value generating apparatus according to claim 1, wherein the look-up table/arithmetic unit further comprises: a read-only memory storing a sine/cosine value of the 0th octant, and the output corresponds to The sine/cosine value of the above octant phase. The sine/cosine value generating apparatus according to claim 1, wherein the look-up table/arithmetic unit further comprises: a processor, according to a normalized phase, using a CORDIC iterative algorithm to output the corresponding eight The sine/cosine value of the rounded phase, wherein the normalized phase is obtained by first obtaining the result value obtained by multiplying the octant phase by pi/4, and then cutting the result value into K bits. The sine/cosine value generating apparatus according to claim 1, wherein the look-up table/arithmetic unit further comprises: a read-only memory storing a sine/cosine value of the 0th octant, and And outputting a sine/cosine value of the first part of the normalized phase, wherein the normalized phase is obtained by first obtaining the result value of the octant phase multiplied by pi/4, and then cutting the result value into K bits. And a processor that uses a CORDIC iterative algorithm to generate a sine/cosine value of the second portion of the normalized phase, and by combining the sine/cosine of the first and second portions of the normalized phase The value is to output a sine/cosine value corresponding to the above octant phase. The sine/cosine value generating device of claim 1, wherein the temporary sine/cosine value generator further comprises: a first selector for selecting a constant value or the octant phase according to the flag The cosine value is used as the temporary sine value; and a second selector selects the constant value or the sine value of the octant phase as the temporary cosine value according to the flag. The sine/cosine value generating apparatus according to claim 6, wherein the temporary sine/cosine value generator further comprises: a look-up table, and outputting a pair of index according to the octant index to display corresponding to Whether the sine/cosine value of the above octant phase is required to be the sine/cosine function value in the sine/cosine value generator of the next stage, or the action of changing the sign. The sine/cosine value generating apparatus of claim 1, wherein the sine/cosine value generator further comprises: a first selector, selecting the temporary sine/cosine value according to the octant index, or the above a complement of 2 of the temporary sine/cosine value as the output of the first selector; and a second selector for selecting the first selection according to the octant index The output of the selector is taken as the sine/cosine value of the above input phase. The sine/cosine value generating device of claim 7, wherein the sine/cosine value generator further comprises: a first selector, and selecting the temporary sine value or the temporary sine value according to the index of the above-mentioned index a complement of 2, and according to the above-mentioned index of reversal, selecting a comma of the temporary cosine value or 2 of the temporary cosine value as the output of the first selector; and a second selector, selecting according to the index of the above-mentioned index The output of the first selector described above is used as the sine or cosine of the input phase.