CN102073472B - Trigonometric function CORDIC iteration operation coprocessor and operation processing method thereof - Google Patents
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Abstract
The invention relates to a trigonometric function coordinate rotation digital computer (CORDIC) iteration operation coprocessor. The coprocessor comprises a CORDIC iteration operation unit, an operation result output unit and an angle range conversion unit, wherein the CORDIC iteration operation unit performs CORDIC iteration operation according to an input angle and outputs an operation result to the operation result output unit; the angle range conversion unit divides the input angle by pi/2 in the CORDIC iteration operation unit to obtain a quotient and decomposes the quotient into an m part, an n part and a p part; the quotient is 4*m+n+p, m and n are integers, n is more than or equal to 0 and less than or equal to 3, and p is a floating-point number of less than 1; and the CORDIC iteration operation unit performs CORDIC trigonometric function iteration operation on the value of p*pi/2. Through the technical scheme, the trigonometric function CORDIC iteration operation coprocessor supports full-angle trigonometric function operation and has higher operation efficiency.
Description
Technical field
The present invention relates to a kind of trigonometric function CORDIC interative computation coprocessor and arithmetic processing method, particularly comprise the wireless communication signals floating-point coprocessor of trigonometric function operation.
Background technology
Widely used floating-point coprocessor generally all can be supported trigonometric function operations such as sine, cosine, tangent in wireless communication signals is handled at present, generally uses the Cordic algorithm to carry out the coprocessor design.The Cordic algorithm is by J.E Volder exploitation and called after Coordinate Rotation Digital Computer, and come the computing of multiplication and division, logarithm and index perfect through expanded to right angle and hyperbolic coordinates by the circumference rotation.The Cordic algorithm provides a kind of uniform way to realize various basic functions, has therefore obtained in fields such as computing machine and communications using widely.
The Cordic algorithm comprises three kinds of coordinate systems, if the vector (X under rectangular coordinate system
0, Y
0) obtain vector (X according to following direction anglec of rotation θ shown in Figure 1
1, Y
1), the relation of two coordinates can be expressed as so:
X
1?=?X
0*cosθ?–?Y
0*sinθ
Y
1?=?Y
0*cosθ?+?X
0*sinθ
Also can be expressed as through conversion:
X
1?=?cosθ*?(X
0?–?Y
0*tanθ)
Y
1?=?cosθ*?(Y
0?+?X
0*tanθ)
And, if we remove the influence of cos θ, can obtain pseudo-rotation equation:
X
1?=?X
0?–?Y
0*tanθ
Y
1?=?Y
0?+?X
0*tanθ
In order to be beneficial to the realization of scale-of-two hardware circuit, we let tan θ=2
-iAnd we define d
iThe direction of expression rotation, angle accumulator Z is used for following the trail of the angle stack of iteration rotation.Computing in the so above-mentioned formula just can realize with the mode of displacement, and is as follows:
X
1?=?cosθ*?(X
0?–?d
i*Y
0*2
-i)
Y
1?=?cosθ*?(Y
0?+?d
i*X
0*2
-i)
Z
1?=?Z
0?–?d
i*θ
i
Cordic can also use other coordinate system to carry out the angle rotation, and general the application is linear coordinate system and hyperbolic coordinate system more widely.The Cordic algorithm is for hard-wired convenience, and is the computing in three coordinate systems is all unified in a standardized system of equations, as follows:
X
n+1?=?X
n?–?u*d
n*Y
n*2
-n
Y
n+1?=?Y
n?+?d
n*X
n*2
-n
Z
n+1?=?Z
n?–?d
n*e
i
Wherein u is following with the difference of e under three kinds of coordinate systems:
Circumferential coordinates: u=1; e
i=tan
-12
-i
Linear coordinate: u=0; e
i=2
-i
Hyperbolic coordinate: u=-1; e
i=tanh
-12
-i
For above-mentioned trigonometric function operation, sinusoidal computing adopts the rotary mode of circumferential coordinates to realize, rotates to 0 through making angle accumulator, draws the result of sin functional operation; The same computing of cosine adopts the rotary mode of circumferential coordinates to realize, rotates to 0 through making angle accumulator, draws the result of cos functional operation; The tangent computing need be carried out the computing of secondary Cordic engine, is respectively sine, the computing of cosine and the computing of division.At first carry out the computing of sin and cos function through the rotary mode of circumferential coordinates, the result's through sin and cos division arithmetic draws the value of tan functional operation then.Wherein division arithmetic can adopt the arrow pattern of rectangular coordinate to carry out computing, moves closer in 0 through making the Y path components, finally draws the result of division arithmetic at the Z path direction.
Use shown in Cordic engine such as the following table 1:
Table 1
Computing for above-mentioned trigonometric function; The input data of computing can receive the restriction of Cordic algorithm input angle; According to analysis to the Cordic algorithm, be the angular range between-99.7-99.7 in the input angle, the interative computation under the circumferential coordinates all can be restrained; Therefore general design all can limit the input angle within this scope, and is very big for the operational limits of trigonometric function.
Summary of the invention
The purpose of this invention is to provide a kind of trigonometric function CORDIC interative computation coprocessor and arithmetic processing method
,Input translation circuit through trigonometric function transforms within the input range of Cordic algorithm permission input parameter, thereby reaches the trigonometric function operation of supporting full angle, and does not have the restriction of input range.
The present invention is achieved in that a kind of trigonometric function CORDIC interative computation coprocessor, and said coprocessor comprises, CORDIC interative computation unit and operation result output unit; Said CORDIC interative computation unit is carried out the CORDIC interative computation and operation result is outputed to said operation result output unit according to the input angle, and said coprocessor also comprises, the angular range converting unit; Said angular range converting unit is carried out said input angle divided by the pi/2 computing in CORDIC interative computation unit, obtains and its merchant is decomposed into m, n; P three parts, said merchant equals 4*m+n+p, wherein m; N is an integer; And 0 ≤n ≤3, p is the floating number less than 1, and CORDIC trigonometric function interative computation is carried out to the value of p* pi/2 in said CORDIC interative computation unit.
Further; Said coprocessor also comprises the input pretreatment unit; The value and 1023 that said input pretreatment unit will be imported 11 exponent bits of data compares; If the value of input data exponent bits is greater than 1023, then said input data are carried out angle through said angular range converting unit earlier and are transformed; If the value of input data exponent bits is less than 1023, then said input data are directly carried out said CORDIC trigonometric function interative computation.
Further, said coprocessor also comprises displacement matching treatment unit, is used for the mantissa of input data is carried out shifting processing.
Further; Said coprocessor also comprises trigonometric function converting unit as a result, said trigonometric function as a result converting unit select sin (p* pi/2) and cos (p* pi/2) according to the value of sign bit and the n of input data value as a result of and the sign bit that draws operation result.
Further, said CORDIC interative computation unit carries out the directions X path of computing and the bit wide in Y direction path is 108, and the bit wide in Z direction path is 56.
Further, after the accomplishing divided by the pi/2 computing of said angular range converting unit, operation result is exported from Z direction path.
Further, said coprocessor also comprises the standardization and the processing unit that rounds off, and makes the output result meet the IEEE-754 standard through standard with rounding off to handle.
The present invention also provides a kind of trigonometric function operation disposal route of CORDIC interative computation coprocessor, and said method comprises,
The first step, said coprocessor are carried out exponent arithmetic and pre-service and displacement matching treatment in the same clock period, accomplish Cordic interative computation operand and prepare;
In second step, said coprocessor carries out the Cordic division iterations computing divided by pi/2 of said operand;
In the 3rd step, the next cycle after said division iterations computing is accomplished carries out pi/2 shift operation and angular transition;
In the 4th step, use Cordic interative computation unit to carry out trigonometric function operation;
In the 5th step, in a clock period, carry out the trigonometric function operation conversion after trigonometric function operation is accomplished and round off and format processing.
After adopting technical scheme of the present invention, the trigonometric function operation of full angle is supported in the support of trigonometric function CORDIC interative computation coprocessor, and operation efficiency is higher.
Description of drawings
Fig. 1 is a Cordic circumference rotation synoptic diagram;
Fig. 2 is arbitrarily angled conversion synoptic diagram;
Fig. 3 is a floating-point trigonometric function operation structural drawing;
Fig. 4 is a Cordic interative computation input data layout synoptic diagram;
Fig. 5 is mantissa's displacement matching treatment synoptic diagram;
Fig. 6 is that the shift operation of pi/2 multiple is handled;
Fig. 7 is trigonometric function operation and selection figure as a result;
Fig. 8 is a floating-point triangulo operation sequential chart of the present invention.
Embodiment
In order to make the object of the invention, technical scheme and advantage clearer,, the present invention is further elaborated below in conjunction with accompanying drawing and embodiment.Should be appreciated that specific embodiment described herein only in order to explanation the present invention, and be not used in qualification the present invention.
For trigonometric function operation, be periodic function, therefore, can carry out computing through the triangular equation conversion so if the Cordic algorithm can carry out the trigonometric function operation of angle between 0 ~ pi/2.Above-mentioned trigonometric function all is to be 2 π in the cycle; And pi/2 ~ 2 π all can obtain through the triangular equation conversion through the angle of 0 ~ pi/2; In like manner, the angle between pi/2 ~ 2 π can be the angle of 0 ~ pi/2 through angular transformation also, and is as shown in Figure 2.
If 0 ~ 2 π is divided into 0 ~ pi/2, pi/2 ~ π, π ~ 3 pi/2s, 3 pi/2s ~ four intervals of 2 π, carry out the angle θ of trigonometric function operation for needs so and the angle a of 0 ~ pi/2 has:
If θ belongs to 0 ~ pi/2, so: θ=a;
If θ belongs to pi/2 ~ π, so: θ=pi/2+a;
If θ belongs to π ~ 3 pi/2s, so: θ=π+a;
If θ belongs to 3 pi/2s ~ 2 π, so: θ=3 pi/2s+a;
If the value of θ is greater than 2 π, so according to the periodicity of trigonometric function, can with θ convert into 2n π and above-mentioned four intervals angle with.Wherein n is the integer quotient of θ divided by 2 π.The synoptic diagram of arbitrarily angled conversion is as shown in Figure 2.
According to foregoing description,, just can draw the trigonometric function operation result of θ through the functional operation result conversion of a if draw the trigonometric function operation of the angle a between 0 ~ pi/2 through the computing of Cordic algorithm.Concrete conversion is as shown in table 2.
Table 2
| Trigonometric function | θ = 2nπ+a | θ = 2nπ+π/2+a | θ = 2nπ+π+a | θ = 2nπ+3π/2+a |
| Sinusoidal sin | sin(θ) = sin(a) | sin(θ) = cos(a) | sin(θ) = -sin(a) | sin(θ) = -cos(a) |
| Cosine cos | cos(θ) = cos(a) | cos(θ) = -sin(a) | cos(θ) = -cos(a) | cos(θ) = sin(a) |
| Tangent tan | tan(θ) = tan(a) | tan(θ) = -1/ tan(a) | tan(θ) = tan(a) | tan(θ) = -1/ tan(a) |
According to the characteristic of above-mentioned Cordic algorithm and trigonometric function operation, operation that the trigonometric function operation of supporting the full angle floating-point to import need carry out and computing comprise exponent arithmetic and processing, Cordic input data processing, division and trigonometric function operation, angle and operation result conversion and floating number standardization processing.The present invention has designed a kind of trigonometric function operation of floating-point efficiently device, and structural drawing is as shown in Figure 3, in floating-point trigonometric function operation device 101; Comprise exponent arithmetic and pretreatment unit 102; Be used to prepare the displacement matching treatment unit 103 of Cordic computing input data, Cordic interative computation unit 104, pi/2 shift operation treatment circuit 105; Angular transition arithmetic element 106, trigonometric function operation be translation operation 107 and the standardization and the processing unit 108 that rounds off as a result.
In design of the present invention, do not carry out of the computing of trigonometric function operation input data, but carry out computing divided by pi/2 divided by 2 π.Before carrying out division arithmetic, need to import data and carry out the processing of exponential sum mantissa so that the floating number of the double precision of input converts the form that can carry out the Cordic interative computation to.Among the present invention for more effective completion functional operation; Definition is input to that Cordic iteration unit 107 is carried out the directions X path of computing and the bit wide in Y direction path is 108; Wherein high 4 is the signed integer position; Low 104 is decimal place, that is to say between high 4 and low 104 to have hidden radix point.The bit wide in definition Z direction path is 56, and wherein high 4 is the signed integer position, and low 52 is decimal place.Data layout as shown in Figure 4.
In exponent arithmetic and pretreatment unit 102, with the value and 1023 (2 of 11 exponent bits importing data
10-1) compare, and draw the input data index be littler or bigger than 1023 than 1023.Can know that by double-precision floating points index decoding definition 1023 expression indexes are+0.If the exponent e xpn of input data is less than 1023, the value that calculates 1023-expn so is as difference; If expn is greater than 1023, the value that calculates expn-1023 so is as difference.
That need handle simultaneously also has the exponent arithmetic result, is certain to less than pi/2 if expn, that is to say the data of input less than 1023, therefore need not carry out division arithmetic and can directly carry out trigonometric function operation.If expn is greater than 1023, and because pi/2=1.570796326794896619231 use double-precision floating point to represent that the index frameshit is 1023, therefore the exponent arithmetic result for the division arithmetic of importing data and pi/2 is the difference of expn and 1023.
In displacement matching treatment unit 103, the mantissa that imports data is carried out shifting processing then.For index less than 1023 input data, 104 of the lowest orders of integer-bit in the 1 corresponding Cordic input data layout of hiding in the mantissa, mantissa from left to right is 52 since 103.Therefore 1 and the mantissa that needs the to hide expn-1023 position that moves to right is carried out trigonometric function operation then, and the displacement synoptic diagram is as shown in Figure 5., need not be shifted greater than 1023 input data for index.
After displacement was accomplished, data layout had met the requirement of Cordic interative computation, therefore began the Cordic function iteration; According to the judgement in exponent arithmetic and the pretreatment unit 102; If the exponent e xpn of input data so at first need import the computing of data divided by pi/2, in Cordic interative computation unit 104 greater than 1023; After division arithmetic was accomplished, operation result was exported from Z direction path.Corresponding index is the value of expn-1023 in exponent arithmetic and the pretreatment unit 102.
Pi/2 shift operation treatment circuit 105 carries out the conversion of angle through the multiple relation.In order to represent to import the multiple relation of data and pi/2 more intuitively; The result that the computing of Z direction is drawn according to exponent arithmetic as a result the value of expn-1023 be shifted; Because the input data of the directions X of above-mentioned division and Y direction are all between 1 ~ 2, so the result of Z direction is also inevitable between 1 ~ 2, in shifting process; The operation result of Z direction is carried out shifting left of expn-1023 size; 56 results after the displacement are exactly the merchant's of input data and pi/2 partial results, wherein high 4 be integral part hang down 4, hanging down 52 is fraction part.Value in the invention after the definition displacement is quotient [55:0].
Because quotient [55:0] is the merchant of input data divided by pi/2, if definition:
m?=?quotient[55:54]
n?=?quotient?[53:52]
p?=?quotient?[51:0]
Have input data datain to be expressed as so:
datain?=?quotient*π/2?=?m*4*π/2?+?n*π/2?+?p*π/2?=?m*2π+?n*π/2?+?p*π/2。
M wherein, n is an integer, and wherein n is 0,1,2,3, and p is the floating number less than 1.
According to the trigonometric function characteristic in aforesaid Cordic computing input range and the table 2, the trigonometric function operation of input data datain can be drawn through conversion by the trigonometric function operation result of p* pi/2.With sinusoidal computing is example:
sin(datain)?=?sin(m*2π+?n*π/2?+?p*π/2)
=?sin(n*π/2?+?p*π/2)
According to the sinuso sine protractor in the table 2, above-mentioned computing can draw through the result of sin (p* pi/2) or cos (p* pi/2).In order to carry out the computing of sin (p* pi/2) or cos (p* pi/2), in angular transition unit 106, carry out the multiplying of p* pi/2, circuit structure is one 54 a multiplier.In addition, the value that in angular transition unit 106, also need preserve n is to select the result of sinusoidal or cosine after the Cordic trigonometric function operation is accomplished.
After angular transition is accomplished, in Cordic interative computation unit 107, carry out trigonometric function operation, through the rotary mode computing under the circumferential coordinates, can be through drawing the value of sin (p* pi/2) and cos (p* pi/2).After computing was accomplished, at trigonometric function as a result in the converting unit 108, the value of selecting sin (p* pi/2) and cos (p* pi/2) according to the value of the sign bit of input data and n as a result of and the sign bit that draws operation result.
Table 3
The result need round off and standardization processing to the result after selecting to accomplish, with the operation result of output double-precision floating point number format.In the standardization and the processing unit 109 that rounds off; The result of computing is carried out leading 0 counting,, therefore leading 0 calculate 0 the number that occurs first front of 1 among the result because mantissa's integer-bit of the floating number of formative double precision is 1; Be shifted according to count results then; First 1 is displaced to the lowest order of integer-bit and aligns, and according to the figure place of displacement index is adjusted, final output meets the operation result of IEEE-754 standard.Whole trigonometric function operation and result treatment synoptic diagram are as shown in Figure 7.
The circuit sequence aspect, for the path delay and the computing of each unit of balance, exponent arithmetic and pretreatment unit and displacement matching treatment unit carried out in the same clock period.Accomplish Cordic interative computation operand and prepare to carry out afterwards the computing of Cordic division iterations, the next cycle after interative computation is accomplished carries out pi/2 shift operation and angular transition.Use Cordic interative computation unit to carry out trigonometric function operation then, in a clock period, carry out the trigonometric function operation conversion after computing is accomplished and round off and format processing.As shown in Figure 8, begin to start and carry out exponential sum displacement matching treatment in the computing next cycle 201 afterwards, carry out division arithmetic at Cordic iteration cycle 202 then, the division arithmetic iteration needs 18 clock period.Accomplish after the division, the result according to the merchant who obtains in the next clock period 203 draws the value of m, n and p, and carries out angular transition to carry out trigonometric function operation.Value pppid2 according to the p* pi/2 after converting carries out trigonometric function operation in second interative computation cycle 204.In the clock period 205, carry out result's conversion with the symbol of importing data after iteration is accomplished, and round off and standardization processing according to n, at next cycle output operation result dataout, and the computing of set simultaneously complement mark done.
The above is merely preferred embodiment of the present invention, not in order to restriction the present invention, all any modifications of within spirit of the present invention and principle, being done, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.
Claims (5)
1. trigonometric function CORDIC interative computation coprocessor; Said coprocessor comprises; CORDIC interative computation unit and operation result output unit; Said CORDIC interative computation unit is carried out the CORDIC interative computation and operation result is outputed to said operation result output unit according to the input angle, it is characterized in that said input angle is a double-precision floating points; Said coprocessor also comprises input pretreatment unit, angular range converting unit and trigonometric function converting unit and the standardization as a result and the processing unit that rounds off; The value and 1023 that said input pretreatment unit will be imported 11 exponent bits of angle compares, if the value of input angle exponent bits less than 1023, then said input angle is directly carried out CORDIC trigonometric function interative computation; If the value of input angle exponent bits is greater than 1023, then said input angle is carried out angle through said angular range converting unit earlier and is transformed; Said angular range converting unit carries out said input angle divided by the pi/2 computing, obtains and its merchant is decomposed into m, n; P three parts; Said merchant equals 4*m+n+p, m wherein, and n is an integer; And 0 ≤n ≤3; P is the floating number less than 1, carries out the multiplying of p* pi/2 in said CORDIC interative computation unit then, and CORDIC trigonometric function sin (p* pi/2) and cos (p* pi/2) interative computation are carried out to the value of p* pi/2 in said CORDIC interative computation unit; Said trigonometric function as a result converting unit select sin (p* pi/2) or cos (p* pi/2) according to the value of n value as a result of; And draw the sign bit of operation result according to the sign bit of input angle, and the said trigonometric function operation result of converting unit as a result rounds off and standardization processing through the said standardization and the processing unit that rounds off again, and net result is exported by said operation result output unit.
2. coprocessor as claimed in claim 1 is characterized in that, said coprocessor also comprises displacement matching treatment unit, is used for the mantissa of input angle is carried out shifting processing.
3. coprocessor as claimed in claim 1 is characterized in that, after the accomplishing of said angular range converting unit divided by the pi/2 computing, and the output operation result.
4. like the described coprocessor of claim 1 to 3, it is characterized in that the said standardization and the processing unit that rounds off make the output result of said angular range converting unit meet the IEEE-754 standard.
5. the trigonometric function operation disposal route of a CORDIC interative computation coprocessor is characterized in that, the input angle that said method is handled is a double-precision floating points, and said method comprises,
The first step; Said coprocessor carries out exponent arithmetic and pre-service and displacement matching treatment with the angle of input, accomplishes CORDIC interative computation operand and prepares, when importing angle less than pi/2; Directly carry out CORDIC trigonometric function interative computation, otherwise changed for second step over to;
In second step, said coprocessor carries out the CORDIC division iterations computing divided by pi/2 of said operand, the output operation result;
The 3rd step was shifted to the output result in second step, and decompose the merchant and be m, n, p three parts, said merchant equals 4*m+n+p, m wherein, n is an integer, and 0 ≤n ≤3, p is the floating number less than 1;
In the 4th step, use the computing of CORDIC multiplying carrying out p* pi/2;
The 5th step; The 4th step operation result is carried out CORDIC trigonometric function sin (p* pi/2) and cos (p* pi/2) interative computation; The value of selecting sin (p* pi/2) or cos (p* pi/2) according to the value of n as a result of, and the sign bit that draws operation result according to the sign bit of input angle;
The 6th the step, to the result round off with standardization processing make output the result meet the IEEE-754 standard.
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| CN108196822B (en) * | 2017-12-24 | 2021-12-17 | 北京卫星信息工程研究所 | Double-precision floating point evolution operation method and system |
| CN108733349B (en) * | 2018-07-27 | 2023-05-05 | 珠海一微半导体股份有限公司 | Trigonometric function operation circuit based on fixed point number |
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