CN102073472A - 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 by 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 allow 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 as follows 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 by 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 by 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 by the rotary mode of circumferential coordinates, the division arithmetic of the result by sin and cos 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 by making the Y path components, finally draws the result of division arithmetic at the Z path direction.
Use the Cordic engine as shown in following table 1:
Table 1
Computing for above-mentioned trigonometric function, the input data of computing can be subjected to the restriction of Cordic algorithm input angle, according to analysis to the Cordic algorithm, in the input angle is angular range between-99.7-99.7, 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 by 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, described coprocessor comprises, CORDIC interative computation unit and operation result output unit, described CORDIC interative computation unit is carried out the CORDIC interative computation and operation result is outputed to described operation result output unit according to the input angle, described coprocessor also comprises, the angular range converting unit, described angular range converting unit is carried out described input angle divided by the pi/2 computing in CORDIC interative computation unit, obtain and its merchant is decomposed into m, n, p three parts, described merchant equals 4*m+n+p, wherein m, n is an integer, and 0＜=n＜=3, p is the floating number less than 1, CORDIC trigonometric function interative computation is carried out to the value of p* pi/2 in described CORDIC interative computation unit.
Further, described coprocessor also comprises the input pretreatment unit, the value and 1023 that described 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 described input data are carried out angle by described angular range converting unit earlier and are transformed; If the value of input data exponent bits is less than 1023, then described input data are directly carried out described CORDIC trigonometric function interative computation.
Further, described coprocessor also comprises displacement matching treatment unit, is used for the mantissa of input data is carried out shifting processing.
Further, described coprocessor also comprises trigonometric function converting unit as a result, described trigonometric function as a result converting unit select sin (p* pi/2) and cos (p* pi/2) according to the value of input sign bit of data and n value as a result of and the sign bit that draws operation result.
Further, described 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 finishing divided by the pi/2 computing of described angular range converting unit, operation result is exported from Z direction path.
Further, described coprocessor also comprises the standardization and the processing unit that rounds off, and makes the output result meet the IEEE-754 standard through the standard and the processing of rounding off.
The present invention also provides a kind of trigonometric function operation disposal route of CORDIC interative computation coprocessor, and described method comprises,
The first step, described coprocessor are carried out exponent arithmetic and pre-service and displacement matching treatment in the same clock period, finish Cordic interative computation operand and prepare;
In second step, described coprocessor carries out the Cordic division iterations computing divided by pi/2 of described operand;
In the 3rd step, the next cycle after described division iterations computing is finished 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, trigonometric function operation carries out the trigonometric function operation conversion after finishing and rounds off and format processing in a clock period.
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 purpose of the present invention, technical scheme and advantage clearer,, the present invention is further elaborated below in conjunction with drawings and Examples.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 by 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 by the triangular equation conversion by the angle of 0 ~ pi/2, in like manner, the angle between pi/2 ~ 2 π can be the angle of 0 ~ pi/2 by angular transformation also, 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, θ can be converted to 2n π and above-mentioned four intervals angle and.Wherein n is the integer quotient of θ divided by 2 π.The synoptic diagram of arbitrarily angled conversion as shown in Figure 2.
According to foregoing description,, just can draw the trigonometric function operation result of θ by the functional operation result conversion of a if draw the trigonometric function operation of the angle a between 0 ~ pi/2 by 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 feature 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, structural drawing 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, the input data need be carried 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.Finish functional operation for more effective among the present invention, 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, the value and 1023 (2 of 11 exponent bits of data will be imported
10-1) compare, and draw the input data index be littler or bigger than 1023 than 1023.By double-precision floating points index decoding definition as can be known, 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.
What need simultaneously to handle 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, does not therefore need to carry out division arithmetic and can directly carry out trigonometric function operation.If expn is greater than 1023, and because pi/2=1.570796326794896619231 represent that with double-precision floating point 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 as shown in Figure 5., do not need to be shifted greater than 1023 input data for index.
After displacement is finished, data layout has met the requirement of Cordic interative computation, therefore begin 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 needs to import the computing of data divided by pi/2, in Cordic interative computation unit 104 greater than 1023, after division arithmetic was finished, 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 by 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, therefore 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 is the low 4 of integral part, and low 52 is fraction part.Value in the invention after the definition displacement is quotient[55:0].
Because quotient[55:0] be 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 by 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, in angular transition unit 106, also need to preserve the value of n after the Cordic trigonometric function operation is finished, to select the result of sine or cosine.
After angular transition is finished, in Cordic interative computation unit 107, carry out trigonometric function operation, by the rotary mode computing under the circumferential coordinates, can be by drawing the value of sin (p* pi/2) and cos (p* pi/2).After computing was finished, 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 finish, with the operation result of output double-precision floating point number format.In the standardization and the processing unit 109 that rounds off, result to computing carries out leading 0 counting, because mantissa's integer-bit of the floating number of formative double precision is 1, therefore leading 0 calculate 0 the number that occurs first front of 1 among the result, 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.Finish Cordic interative computation operand and prepare to carry out afterwards the computing of Cordic division iterations, the next cycle after interative computation is finished carries out pi/2 shift operation and angular transition.Use Cordic interative computation unit to carry out trigonometric function operation then, computing is carried out the trigonometric function operation conversion after finishing and is rounded off and format processing in a clock period.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.Finish 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 finished, 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 only is preferred embodiment of the present invention, not in order to restriction the present invention, all any modifications of being done within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.
Claims (8)
1. trigonometric function CORDIC interative computation coprocessor, described coprocessor comprises, CORDIC interative computation unit and operation result output unit, described CORDIC interative computation unit is carried out the CORDIC interative computation and operation result is outputed to described operation result output unit according to the input angle, it is characterized in that, described coprocessor also comprises, the angular range converting unit, described angular range converting unit is carried out described input angle divided by the pi/2 computing in CORDIC interative computation unit, obtain and its merchant is decomposed into m, n, p three parts, described merchant equals 4*m+n+p, m wherein, 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 described CORDIC interative computation unit.
2. coprocessor as claimed in claim 1, it is characterized in that, described coprocessor also comprises the input pretreatment unit, the value and 1023 that described 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 described input data are carried out angle by described angular range converting unit earlier and are transformed; If the value of input data exponent bits is less than 1023, then described input data are directly carried out described CORDIC trigonometric function interative computation.
3. coprocessor as claimed in claim 2 is characterized in that, described coprocessor also comprises displacement matching treatment unit, is used for the mantissa of input data is carried out shifting processing.
4. coprocessor as claimed in claim 2, it is characterized in that, described coprocessor also comprises trigonometric function converting unit as a result, described trigonometric function as a result converting unit select sin (p* pi/2) and cos (p* pi/2) according to the value of input sign bit of data and n value as a result of and the sign bit that draws operation result.
5. as any described coprocessor in the claim 1 to 4, it is characterized in that described CORDIC interative computation unit carries out the directions X path of computing and the bit wide in Y direction path is 108, the bit wide in Z direction path is 56.
6. coprocessor as claimed in claim 5 is characterized in that, after the finishing divided by the pi/2 computing of described angular range converting unit, operation result is exported from Z direction path.
7. coprocessor as claimed in claim 6 is characterized in that, described coprocessor also comprises the standardization and the processing unit that rounds off, and makes the output result meet the IEEE-754 standard through the standard and the processing of rounding off.
8. the trigonometric function operation disposal route of a CORDIC interative computation coprocessor is characterized in that, described method comprises,
The first step, described coprocessor are carried out exponent arithmetic and pre-service and displacement matching treatment in the same clock period, finish Cordic interative computation operand and prepare;
In second step, described coprocessor carries out the Cordic division iterations computing divided by pi/2 of described operand;
In the 3rd step, the next cycle after described division iterations computing is finished 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, trigonometric function operation carries out the trigonometric function operation conversion after finishing and rounds off and format processing in a clock period.
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| CN107329732A (en) * | 2016-04-29 | 2017-11-07 | 北京中科寒武纪科技有限公司 | It is a kind of to be used to perform a variety of apparatus and method for surmounting function computing |
| CN107329732B (en) * | 2016-04-29 | 2021-07-16 | 中科寒武纪科技股份有限公司 | Device and method for executing multiple transcendental function operations |
| CN110998514A (en) * | 2017-08-08 | 2020-04-10 | 德克萨斯仪器股份有限公司 | Interruptible trigonometric operation |
| CN110998514B (en) * | 2017-08-08 | 2024-01-09 | 德克萨斯仪器股份有限公司 | Interruptible trigonometric operations |
| CN108196822A (en) * | 2017-12-24 | 2018-06-22 | 北京卫星信息工程研究所 | A kind of method and system of double-precision floating point extracting operation |
| 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 |
| CN108733349A (en) * | 2018-07-27 | 2018-11-02 | 珠海市微半导体有限公司 | A kind of trigonometric computing circuit based on fixed-point number |
| 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 |
| CN113711157A (en) * | 2019-02-20 | 2021-11-26 | 优创半导体科技有限公司 | Apparatus and method for hardware efficient adaptive computation of floating point trigonometric functions using coordinate rotation digital computer (CORDIC) |
| CN110147218A (en) * | 2019-04-09 | 2019-08-20 | 珠海市杰理科技股份有限公司 | Computing circuit and method based on Cordic algorithm |
| CN110147218B (en) * | 2019-04-09 | 2021-05-11 | 珠海市杰理科技股份有限公司 | Operation circuit and method based on Cordic algorithm |
| CN110187866A (en) * | 2019-06-03 | 2019-08-30 | 南京宁麒智能计算芯片研究院有限公司 | A kind of logarithmic multiplication computing system and method based on hyperbolic CORDIC |
| CN111752532A (en) * | 2020-06-24 | 2020-10-09 | 上海擎昆信息科技有限公司 | Method, system and device for realizing 32-bit integer division with high precision |
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