CN107329732A - It is a kind of to be used to perform a variety of apparatus and method for surmounting function computing - Google Patents
It is a kind of to be used to perform a variety of apparatus and method for surmounting function computing Download PDFInfo
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- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
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Abstract
It is used to perform a variety of apparatus and method for surmounting function computing the invention discloses a kind of, the device includes pretreatment unit group, core cell and post-processing unit group, pretreatment unit group, for the independent variable a of outside input to be transformed into coordinate x, y, angle z, remaining information k, and determine the operator scheme mode that core cell is taken；Core cell, for coordinate x, y, angle z to carry out triangle or hyperbolic transformation, the coordinate x ', y ', angle z ' after being converted simultaneously are exported and are given post-processing unit group；Post-processing unit group, enters line translation and obtains output result c for remaining information k and function f inputted according to pretreatment unit group, the coordinate x ', y ' inputted to core cell, angle z '.Using the present invention, the problem of excessive and purely linear approximate way precision of general processor mode expense is not enough is solved, is effectively increased to the various supports for surmounting function computing.
Description
Technical field
The present invention relates to computing field is surmounted function, it is used to perform a variety of apparatus and method for surmounting function computing more particularly to a kind of, in particular for performing triangle, hyperbolic, index or the apparatus and method of logarithmic function computing.
Background technology
Triangle, hyperbolic, index, logarithm etc., which surmount function, is not only usually used in all kinds of scientific algorithms, is also commonly used for the activation primitive in multi-layer artificial neural network.Multi-layer artificial neural network is widely used in the fields such as pattern-recognition, image procossing, function approximation and optimization calculating, multi-layer artificial neural network in recent years due to its higher recognition accuracy and preferably can concurrency, more and more widely paid close attention to by academia and industrial quarters.
It is a kind of to support that the above-mentioned various known methods for surmounting function calculating are to use general processor.This method performs universal command by using general-purpose register and general utility functions part and comes that approximate calculation is various to be surmounted function.One of shortcoming of this method is can not to be integrated with the special purpose device of multi-layer artificial neural network, causes other steps can not enjoy the performance boost of such device.In addition, general processor needs to be decoded into a queue of computing and access instruction sequence calculating is surmounted function, the decoding of processor front end brings larger power dissipation overhead.
Another method surmounted function that calculated in multi-layer artificial neural network is linear approximation.This method (is wherein much surmounted function) by the way that domain of definition to be segmented and store the coefficient of each section of linear approximation come approximate calculation activation primitive.The shortcoming of this method is that the hop count that piece wire approximation can be split is limited, the need for precision can not meet the development of artificial neural network, is more not used to scientific algorithm, and image procossing equally accurate requires higher purposes.
The content of the invention
(1) technical problem to be solved
In view of this, it is a kind of for performing a variety of apparatus and method for surmounting function computing it is a primary object of the present invention to provide, to solve the problem of excessive and purely linear approximate way precision of general processor mode expense is not enough, improve to the various supports for surmounting function computing.
(2) technical scheme
To reach above-mentioned purpose, it is used to perform a variety of devices for surmounting function computing the invention provides a kind of, the device includes pretreatment unit group, core cell and post-processing unit group, wherein：
Pretreatment unit group, for the independent variable a of outside input to be transformed into coordinate x, y, angle z, remaining information k, and determines the operator scheme mode that core cell is taken；
Core cell, for coordinate x, y, angle z to carry out triangle or hyperbolic transformation, the coordinate x ', y ', angle z ' after being converted simultaneously are exported and are given post-processing unit group；
Post-processing unit group, enters line translation and obtains output result c for remaining information k and function f inputted according to pretreatment unit group, the coordinate x ', y ' inputted to core cell, angle z '.
In such scheme, the pretreatment unit group includes selector 1 and processor 2, post-processing unit group includes the first post-processing unit 4, the second post-processing unit 5 and the 3rd post-processing unit 6, wherein selector 1 receives the independent variable a and function f of outside input, judge the four kinds of different operatings that should be taken, it is specific as follows：
If I, when independent variable a under inputting or exporting the specification used is linear or each personal floating number of result and true value of second approximation is represented error no more than last position of mantissa, cause independent variable a too small, then independent variable a and function f are directly output to the first post-processing unit 4 in post-processing unit group by selector 1, first post-processing unit 4 draws independent variable a linear approximation formula according to function f, and obtains output result c to independent variable a progress additions and multiplication；
II, if independent variable a is without departing from core cell convergence domain, ordinate y=0 under default mode lower angle z=0 or vector pattern can be reached in fintie number of steps, independent variable a directly can be received by the corresponding modes of core cell 3, then selector 1 draws independent variable a coordinate x according to function f, y, the mode m ode that angle z and core cell are taken, by x, y, z, mode is exported to core cell 3, core cell 3 is based on mode m ode to x, y, z carries out triangle or hyperbolic transformation, coordinate x ' after being converted, y ', angle z ' is simultaneously exported to the second post-processing unit 5 in post-processing unit group, the coordinate x ' that second post-processing unit 5 is exported according to core cell, y ', angle z ' and function f obtain output result c；
III, if independent variable a directly can not be received by the corresponding modes of core cell 3, then independent variable a and function f are given processor 2 and carry out pre-treatment by selector 1, processor 2 carries out decomposed information processing according to function f to independent variable a, obtain coordinate x, y, angle z, mode m ode and remaining information k that core cell 3 is taken, wherein coordinate x, y, angle z, the mode m ode that core cell 3 is taken is identical with II, coordinate x, y, angle z, the mode m ode that core cell 3 is taken is exported to core cell, and remaining information k and function f are directly output to the 3rd post-processing unit 6 in post-processing unit group；Core cell 3 is based on mode m ode and x, y, z is carried out triangle or hyperbolic transformation, obtain x ', y ', z ' is exported to the 3rd post-processing unit 6 in post-processing unit group；The k and function f that the x ' that 3rd post-processing unit 6 is exported according to core cell 3, y ', z ' and processor 2 are provided obtain output result c；
If IV, the maximum magnitude that independent variable a true value is represented beyond floating number in the case where inputting or exporting the specification used, selector 1 directly export independent variable a and function f.
In such scheme, in the case where inputting or exporting the specification used, independent variable a true value exceeds the maximum magnitude that represents of floating number in the IV, is that maximum absolute value is (1024+1023) or 1024 × 2 under the accuracy floating-point numbers of IEEE754 half30-15=65504.
To reach above-mentioned purpose, it is used to perform a variety of methods for surmounting function computing present invention also offers a kind of, this method includes：
Step 1：Selector receives the independent variable a and function f of input, judges the I kinds, ii kind, four kinds of different operatings of ii I kinds or iv kind that should be taken；
Step 2：Processor can be received independent variable a and function f the progress multiplication or shift transformation of input when taking ii I kinds to operate by core cell, and record coversion information k, sign is for used in the 3rd post-processing unit, wherein sign is only effective under partial function；
Step 3：Processor is when taking ii kind or ii I kinds to operate, and core cell realizes following four triangle or hyperbolic transformation in abscissa x, ordinate y and angle z this 3 number by plus-minus and shifting function：
Triangle is given tacit consent to：(x, y, z) → (A (xcosz-ysinz), A (ycosz+xsinz), 0)
Hyperbolic is given tacit consent to：(x, y, z) → (B (xcoshz+ysinhz), B (ycoshz+xsinhz), 0)
A and B are the constants relevant with taken iterations in above-mentioned formula, shifting function be multiply 2 power；
Step 4a：Processor is when taking I kinds to operate, and the first post-processing unit calculates linear or second approximation according to input function f and exported；
Step 4b：Processor is when taking ii kind or ii I kinds are operated, output of the information that second post-processing unit is provided according to input function f and pretreatment unit group processor to core cell is added and subtracted, multiply constant, division, shifting function, output result c is obtained, the information that wherein pretreatment unit group processor is provided is only effective in the operation of ii I kinds.
(3) beneficial effect
It is this for performing a variety of apparatus and method for surmounting function computing that the present invention is provided, the result that triangle or hyperbolic type system are converted is sought by the value surmounted function will be asked to be converted to, ensure that the angle absolute value of each step rotation is fixed by the way of iteration, reverse rotation is taken during ovdersteering, take and rotated forward so that only need to store a series of coefficient of fixations when not enough, predetermined angular sequence ziSo that tanzi(it is tanhz in the case of hyperbolici) be 2 power, make they and transverse and longitudinal coordinate x, y multiplication can be realized by simpler displacement, and then reduce time or power wastage that phase cross multiplication between variable is brought, it in turn ensure that and reach permissible accuracy, the calculating of all kinds of trigonometric functions, hyperbolic functions, exponential function and logarithmic function can be realized, the problem of excessive and purely linear approximate way precision of general processor mode expense is not enough is solved, effectively increases to the various supports for surmounting function computing.
Brief description of the drawings
For a more complete understanding of the present invention and its advantage, referring now to the following description with reference to accompanying drawing, wherein：
Fig. 1 shows the structural representation for being used to perform a variety of devices for surmounting function computing according to embodiments of the present invention.
Fig. 2 shows the schematic diagram of core cell trigonometric function relation required by iterative approach under triangle model in Fig. 1.
Fig. 3 shows the schematic diagram of core cell hyperbolic functions relation required by iterative approach under hyperbolic pattern in Fig. 1.
Fig. 4, which is shown, according to embodiments of the present invention to be used to perform a variety of method flow diagrams for surmounting function computing.
Table 1 shows concrete operations of each unit under each input function f and independent variable a (under 16 floating numbers) according to embodiments of the present invention.The multiplication of constant and displacement (powers of multiplication and division 2) realization, only a small amount of division and (during second approximation) low required precision can mainly be added and subtracted, multiplied to these computings.If input and output permissible accuracy is different, the part range in table 1 should be adjusted accordingly.
Embodiment
According to reference to accompanying drawing, to the described in detail below of exemplary embodiment of the present, other side, advantage and prominent features of the invention will become obvious for those skilled in the art.
In the present invention, term " comprising " and " containing " and its derivative mean including and it is unrestricted；Term "or" is inclusive, mean and/or.
In this manual, following various embodiments for being used to describe the principle of the invention are explanation, should not be construed in any way the scope for limitation invention.Referring to the drawings described below is used to help the exemplary embodiment of the invention that comprehensive understanding is limited by claim and its equivalent.It is described below to help to understand including a variety of details, but these details are considered as what is be merely exemplary.Therefore, it will be appreciated by those of ordinary skill in the art that in the case of without departing substantially from scope and spirit of the present invention, can be made various changes and modifications to embodiment described herein.In addition, for clarity and brevity, eliminating the description of known function and structure.In addition, through accompanying drawing, same reference numbers are used for identity function and operation.
Fig. 1 shows the structural representation for being used to perform a variety of devices for surmounting function computing according to embodiments of the present invention.As shown in figure 1, the device includes pretreatment unit group (1,2), core cell 3 and post-processing unit group (4,5,6), wherein：
Pretreatment unit group, for the independent variable a of outside input to be transformed into coordinate x, y, angle z, remaining information k, and determines the operator scheme mode that core cell is taken；
Core cell 3, for coordinate x, y, angle z to carry out triangle or hyperbolic transformation, the coordinate x ', y ', angle z ' after being converted simultaneously are exported and are given post-processing unit group；
Post-processing unit group, enters line translation and obtains output result c for remaining information k and function f inputted according to pretreatment unit group, the coordinate x ', y ' inputted to core cell, angle z '.
Wherein pretreatment unit group includes selector 1 and processor 2, post-processing unit group includes the first post-processing unit 4, the second post-processing unit 5 and the 3rd post-processing unit 6, can be realized by hardware integration circuit (such as application-specific integrated circuit ASIC).Selector 1 receives the independent variable a and function f of outside input, judges the four kinds of different operatings that should be taken, specific as follows：
If I, when independent variable a under inputting or exporting the specification used is linear or each personal floating number of result and true value of second approximation is represented error no more than last position of mantissa, cause independent variable a too small, then independent variable a and function f are directly output to the first post-processing unit 4 in post-processing unit group by selector 1, first post-processing unit 4 draws independent variable a linear approximation formula according to function f, and obtains output result c to independent variable a progress additions and multiplication；For details see attached table 1；
II, if independent variable a is without departing from core cell convergence domain, ordinate y=0 under default mode lower angle z=0 or vector pattern can be reached in fintie number of steps, independent variable a directly can be received by the corresponding modes of core cell, then selector 1 draws independent variable a coordinate x according to function f, y, the mode m ode that angle z and core cell 3 are taken, by x, y, z, mode is exported to core cell 3, core cell 3 is based on mode m ode to x, y, z carries out triangle or hyperbolic transformation, coordinate x ' after being converted, y ', angle z ' is simultaneously exported to the second post-processing unit 5 in post-processing unit group, the coordinate x ' that second post-processing unit 5 is exported according to core cell, y ', angle z ' and function f obtain output result c；
III, if independent variable a directly can not be received by the corresponding modes of core cell, then independent variable a and function f are given processor 2 and carry out pre-treatment by selector 1, processor 2 carries out decomposed information processing according to function f to independent variable a, obtain coordinate x, y, angle z, mode m ode and remaining information k that core cell 3 is taken, wherein coordinate x, y, angle z, the mode m ode that core cell 3 is taken is identical with II, coordinate x, y, angle z, the mode m ode that core cell 3 is taken is exported to core cell 3, and remaining information k and function f are directly output to the 3rd post-processing unit 6 in post-processing unit group；Core cell 3 is based on mode m ode and x, y, z is carried out triangle or hyperbolic transformation, obtain x ', y ', z ' is exported to the 3rd post-processing unit 6 in post-processing unit group；The k and function f that the x ' that 3rd post-processing unit 6 is exported according to core cell 3, y ', z ' and processor 2 are provided obtain output result c；
If maximum absolute value is (1024+1023) or 1024 × 2 under IV, the maximum magnitude that independent variable a true value is represented beyond floating number in the case where inputting or exporting the specification used, such as the accuracy floating-point numbers of IEEE754 half30-15=65504, then selector 1 is directly by independent variable a and function f outputs (NaN).Operation of each input function in the case of situation I, II, III and IV specific determination range and four kinds is shown in Table 1 under the precision of IEEE754 half (binary16) floating number.
The embodiment of the present invention is additionally provided for performing a variety of methods for surmounting function computing, it is specific as shown in figure 4, Fig. 4 show it is according to embodiments of the present invention be used to perform a variety of method flow diagrams for surmounting function computing, comprise the following steps：
Step 1：Selector receives the independent variable a and function f of input, judges the I kinds, ii kind, four kinds of different operatings of ii I kinds or iv kind that should be taken；
If I, when independent variable a under inputting or exporting the specification used is linear or each personal floating number of result and true value of second approximation is represented error no more than last position of mantissa, cause independent variable a too small, then independent variable a and function f are directly output to the first post-processing unit in post-processing unit group by selector, first post-processing unit draws independent variable a linear approximation formula according to function f, and obtains output result c to independent variable a progress additions and multiplication；Refer to table 1；
II, if independent variable a is without departing from core cell convergence domain, ordinate y=0 under default mode lower angle z=0 or vector pattern can be reached in fintie number of steps, independent variable a directly can be received by the corresponding modes of core cell, then selector draws independent variable a coordinate x according to function f, y, the mode m ode that angle z and core cell are taken, by x, y, z, mode is exported to core cell, core cell is based on mode m ode to x, y, z carries out triangle or hyperbolic transformation, coordinate x ' after being converted, y ', angle z ' is simultaneously exported to the second post-processing unit in post-processing unit group, the coordinate x ' that second post-processing unit is exported according to core cell, y ', angle z ' and function f obtain output result c；
III, if independent variable a directly can not be received by the corresponding modes of core cell, then independent variable a and function f are given processor and carry out pre-treatment by selector, processor carries out decomposed information processing according to function f to independent variable a, obtain coordinate x, y, angle z, mode m ode and remaining information k that core cell is taken, wherein coordinate x, y, angle z, the mode m ode that core cell is taken is identical with II, coordinate x, y, angle z, the mode m ode that core cell is taken is exported to core cell, and remaining information k and function f are directly output to the 3rd post-processing unit in post-processing unit group；Core cell is based on mode m ode and x, y, z is carried out triangle or hyperbolic transformation, obtain x ', y ', z ' is exported to the 3rd post-processing unit in post-processing unit group；The k and function f that the x ' that 3rd post-processing unit is exported according to core cell, y ', z ' and processor are provided obtain output result c；
If maximum absolute value is (1024+1023) or 1024 × 2 under IV, the maximum magnitude that independent variable a true value is represented beyond floating number in the case where inputting or exporting the specification used, such as the accuracy floating-point numbers of IEEE754 half30-15=65504, then selector is directly by independent variable a and function f outputs (NaN).Operation of each input function in the case of situation I, II, III and IV specific determination range and four kinds is shown in Table 1 under the precision of IEEE754 half (binary16) floating number.
Step 2：Processor can be received independent variable a and function f the progress multiplication or shift transformation of input when taking ii I kinds to operate by core cell, and record coversion information k, sign is for used in the 3rd post-processing unit, wherein sign is only effective under partial function；The concrete operations example of processor is shown in Table 1 under each input function.
Step 3：Processor is when taking ii kind or ii I kinds to operate, and core cell realizes following four triangle or hyperbolic transformation in abscissa x, ordinate y and angle z this 3 number by plus-minus and shifting function：
Triangle is given tacit consent to：(x, y, z) → (A (xcosz-ysinz), A (ycosz+xsinz), 0)
Hyperbolic is given tacit consent to：(x, y, z) → (B (xcoshz+ysinhz), B (ycoshz+xsinhz), 0)
A and B are the constants relevant with taken iterations in above-mentioned formula, shifting function be multiply 2 power；The angle that the conversion should be rotated by iterative approach is completed：
I-th step anglec of rotation zi, forward or backwards according to following judgement：Rotate forward, reversely rotated during z ＜ 0 when target z=0 under default mode, z ＞ 0；Reversely rotate, rotated forward during y ＜ 0 when target y=0 under vector pattern, y ＞ 0；
Fig. 2 intuitively shows that the principle that required triangular transformation is approached with a series of triangular transformation of fixed angles (for the sake of convenient, often walks amplification transverse and longitudinal coordinate 1/cos ziDo not represent again).Fig. 3 intuitively shows that the principle that required hyperbolic transformation is approached with a series of hyperbolic transformation of fixed angles (for the sake of convenient, often walks amplification transverse and longitudinal coordinate 1/cosh ziDo not represent again).
Per single-step iteration equivalent to rotating z forward or backwardsiAnd transverse and longitudinal coordinate is amplified into 1/cos ziTimes, wherein being amplification 1/cosh z under hyperbolic patterniTimes：
Triangle is positive：(x, y, z) → ((x-ytanzi), (y+xtanzi), z-zi)
Triangle is reverse：(x, y, z) → ((x+ytanzi), (y-xtanzi), z+zi)
Hyperbolic is positive：(x, y, z) → ((x+ytanhzi), (y+xtanhzi), z-zi)
Hyperbolic is reverse：(x, y, z) → ((x-ytanhzi), (y-xtanhzi), z+zi)
Only realized per single-step iteration and restrained, z with plus-minus and displacement in order to realizeiFollowing sequence should be taken：
Triangle：zi=arctan2-i, i=0,1,2 ...
Hyperbolic：zi=arctanh2-j, j=i-k, when (3k+1-1)/2+k≤i≤(3k+2- 1)/2+k+1, i=1,2,3 ...
Specific iterations, i.e. i maximums, are flexibly selected according to handled floating number precision, and foregoing constant can be calculated after selected maximum iterationThe selection of above-mentioned four kinds of patterns is shown in Table 1 under each input function.
Step 4a：Processor is when taking I kinds to operate, and the first post-processing unit calculates linear or second approximation according to input function f and exported；The concrete operations of the first post-processing unit are shown in Table 1 under each input function.
Step 4b：Processor is when taking ii kind or ii I kinds are operated, output of the information that second post-processing unit is provided according to input function f and pretreatment unit group processor to core cell is added and subtracted, multiply constant, division, shifting function, output result c is obtained, the information that wherein pretreatment unit group processor is provided is only effective in the operation of ii I kinds.The concrete operations of the second post-processing unit are shown in Table 1 under each input function.
Pass through foregoing description, it is this for performing a variety of apparatus and method for surmounting function computing that the present invention is provided, the result that triangle or hyperbolic type system are converted is sought by the value surmounted function will be asked to be converted to, ensure that the angle absolute value of each step rotation is fixed by the way of iteration, reverse rotation is taken during ovdersteering, take and rotated forward so that only need to store a series of coefficient of fixations when not enough, predetermined angular sequence ziSo that tanzi(it is tanhz in the case of hyperbolici) be 2 power, make they and transverse and longitudinal coordinate x, y multiplication can be realized by simpler displacement, and then reduce time or power wastage that phase cross multiplication between variable is brought, it in turn ensure that and reach permissible accuracy, the calculating of all kinds of trigonometric functions, hyperbolic functions, exponential function and logarithmic function can be realized, the problem of excessive and purely linear approximate way precision of general processor mode expense is not enough is solved, effectively increases to the various supports for surmounting function computing.
The process or method described in accompanying drawing above can by including hardware (for example, circuit, special logic etc.), firmware, software (for example, be embodied in the software in non-transient computer-readable media), or both the processing logic of combination perform.Although process or method are described according to the operation of some orders above, however, it is to be understood that described some operations can be performed with different order.In addition, concurrently rather than some operations can be sequentially performed.
In foregoing specification, various embodiments of the present invention are described with reference to its certain exemplary embodiments.Obviously, various modifications can be made to each embodiment, without departing from the wider spirit and scope of the invention described in appended claims.Correspondingly, specification and drawings should be considered as illustrative and not restrictive.
Claims (9)
1. a kind of be used to perform a variety of devices for surmounting function computing, it is characterised in that the device bag
Pretreatment unit group, core cell and post-processing unit group are included, wherein：
Pretreatment unit group, for by the independent variable a of outside input be transformed to coordinate x, y, angle z,
Remaining information k, and determine the operator scheme mode that core cell is taken；
Core cell, for coordinate x, y, angle z to be carried out triangle or hyperbolic transformation, converted
Coordinate x ', y ' afterwards, angle z ' are simultaneously exported and are given post-processing unit group；
Post-processing unit group, for remaining information k and function f inputted according to pretreatment unit group,
Coordinate x ', y ', the angle z ' inputted to core cell enters line translation and obtains output result c.
2. according to claim 1 be used to perform a variety of devices for surmounting function computing, it is special
Levy and be, the pretreatment unit group includes selector (1) and processor (2), post-processing unit
Group includes the first post-processing unit (4), the second post-processing unit (5) and the 3rd post-processing unit (6),
Wherein selector (1) receives the independent variable a and function f of outside input, judges should take four kinds not
Biconditional operation, it is specific as follows：
If I, in the case where inputting or exporting the specification used, independent variable a is linear or result of second approximation
Error is no more than last position of mantissa when being represented with each personal floating number of true value, causes independent variable a too small,
Then selector (1) by independent variable a and function f be directly output in post-processing unit group first after locate
Unit (4) is managed, the first post-processing unit (4) draws independent variable a linear approximation formula according to function f,
And output result c is obtained to independent variable a progress additions and multiplication；
If II, independent variable a are without departing from core cell convergence domain, acquiescence can be reached in fintie number of steps
Ordinate y=0 under pattern lower angle z=0 or vector pattern, independent variable a can be directly by core cell
Corresponding modes receive, then selector (1) draws independent variable a coordinate x, y, angle according to function f
The mode m ode that z and core cell are taken, by x, y, z, mode is exported to core cell, core cell
(3) based on mode m ode to x, y, z progress triangles or hyperbolic transformation, coordinate x ', y ' after being converted,
Angle z ' is simultaneously exported to the second post-processing unit (5) in post-processing unit group, the second post-processing unit
(5) coordinate x ', y ', angle z ' and the function f exported according to core cell obtains output result c；
If III, independent variable a directly can not be received by the corresponding modes of core cell (3), select
Select device (1) and give processor (2) progress pre-treatment, processor (2) by independent variable a and function f
Decomposed information processing is carried out to independent variable a according to function f, coordinate x, y, angle z, core list is obtained
Mode m ode and remaining information k that first (3) take, wherein coordinate x, y, angle z, core list
The mode m ode that first (3) take is identical with II, and coordinate x, y, angle z, core cell (3) are adopted
The mode m ode taken is exported to core cell (3), and remaining information k and function f is directly defeated
Go out to the 3rd post-processing unit (6) in post-processing unit group；Core cell (3) is based on mode m ode
To x, y, z carries out triangle or hyperbolic transformation, obtains x ', y ', z ' is exported to after the 3rd in post-processing unit group
Processing unit (6)；The x ' that 3rd post-processing unit (6) is exported according to core cell, y ', z ' and place
The k and function f that reason device (2) is provided obtain output result c；
If IV, in the case where inputting or exporting the specification used, independent variable a true value is represented beyond floating number
Maximum magnitude, then selector (1) directly independent variable a and function f are exported.
3. according to claim 2 be used to perform a variety of devices for surmounting function computing, it is special
Levy and be, independent variable a true value exceeds floating number in the case where inputting or exporting the specification used in the IV
The maximum magnitude of expression, is that maximum absolute value is (1024+1023) under the accuracy floating-point numbers of IEEE754 half
Or 1024 × 230-15=65504.
4. a kind of be used to perform a variety of methods for surmounting function computing, applied to claims 1 to 3
Any one of device, it is characterised in that this method includes：
Step 1：Selector receive input independent variable a and function f, judge should take I kinds,
Ii kind, four kinds of different operatings of ii I kinds or iv kind；
Step 2：Processor enters when taking ii I kinds to operate to the independent variable a and function f of input
Row multiplication or shift transformation can be received by core cell, and record coversion information k, sign supplies
Used in three post-processing units, wherein sign is only effective under partial function；
Step 3：Processor when taking ii kind or ii I kinds to operate, core cell abscissa x,
Following four triangle or double is realized by plus-minus and shifting function in this 3 number of ordinate y and angle z
Qu Bianhuan：
Triangle is given tacit consent to：(x, y, z) → (A (xcosz-ysinz), A (ycosz+xsinz), 0)
Triangle vector：
Hyperbolic is given tacit consent to：(x, y, z) → (B (xcoshz+ysinhz), B (ycoshz+xsinhz), 0)
Hyperbolic vector：
A and B are the constants relevant with taken iterations in above-mentioned formula, and shifting function is to multiply 2
Power；
Step 4a：Processor is when taking I kinds to operate, and the first post-processing unit is according to input function
F calculates linear or second approximation and exported；
Step 4b：Processor when taking ii kind or ii I kinds to operate, the second post-processing unit according to
Output of the information that input function f and pretreatment unit group processor are provided to core cell is added
Subtract, multiply constant, division, shifting function obtains output result c, and wherein pretreatment unit group is handled
The information that device is provided is only effective in the operation of ii I kinds.
5. according to claim 4 be used to perform a variety of methods for surmounting function computing, it is special
Levy and be, the operation of I kinds described in step 1 is：
If I, in the case where inputting or exporting the specification used, independent variable a is linear or result of second approximation
Error is no more than last position of mantissa when being represented with each personal floating number of true value, causes independent variable a too small,
The first post processing that then independent variable a and function f are directly output in post-processing unit group by selector is single
Member, the first post-processing unit draws independent variable a linear approximation formula according to function f, and to independent variable
A carries out addition and multiplication obtains output result c.
6. according to claim 4 be used to perform a variety of methods for surmounting function computing, it is special
Levy and be, the operation of ii kind described in step 1 is：
If II, independent variable a are without departing from core cell convergence domain, acquiescence can be reached in fintie number of steps
Ordinate y=0 under pattern lower angle z=0 or vector pattern, independent variable a can be directly by core cell
Corresponding modes receive, then selector draws independent variable a coordinate x, y, angle z and core according to function f
The mode m ode that heart unit is taken, by x, y, z, mode is exported to core cell, and core cell is based on mould
Formula mode carries out triangle or hyperbolic transformation to x, y, z, and the coordinate x ', y ', angle z ' after being converted are simultaneously defeated
Go out to the second post-processing unit in post-processing unit group, the second post-processing unit is defeated according to core cell
Coordinate x ', y ', angle z ' and the function f gone out obtains output result c.
7. according to claim 4 be used to perform a variety of methods for surmounting function computing, it is special
Levy and be, the operation of the kind of ii I described in step 1 is：
If III, independent variable a directly can not be received by the corresponding modes of core cell, selector will
Independent variable a and function f give processor and carry out pre-treatment, and processor is according to function f to independent variable a
Carry out decomposed information processing, obtain coordinate x, y, mode m ode that angle z, core cell are taken with
And remaining information k, wherein coordinate x, the mode m ode and II phases that y, angle z, core cell are taken
Together, the mode m ode that coordinate x, y, angle z, core cell are taken is exported to core cell, and
Remaining information k and function f are directly output to the 3rd post-processing unit in post-processing unit group；Core
Heart unit is based on mode m ode and x, y, z is carried out triangle or hyperbolic transformation, obtain x ', y ', z ' is exported to after
The 3rd post-processing unit in processing unit group；What the 3rd post-processing unit was exported according to core cell
The k and function f that x ', y ', z ' and processor are provided obtain output result c.
8. according to claim 4 be used to perform a variety of methods for surmounting function computing, it is special
Levy and be, the operation of iv kind described in step 1 is：
If IV, in the case where inputting or exporting the specification used, independent variable a true value is represented beyond floating number
Maximum magnitude, then selector directly independent variable a and function f are exported.
9. according to claim 4 be used to perform a variety of methods for surmounting function computing, it is special
Levy and be, core cell described in step 3 is in this 3 number of abscissa x, ordinate y and angle z
Upper to realize following four triangle or hyperbolic transformation by plus-minus and shifting function, the conversion is forced by iteration
The angle that should closely rotate is completed：
I-th step anglec of rotation zi, forward or backwards according to following judgement：Target z=0 under default mode,
Rotate forward, reversely rotated during z ＜ 0 during z ＞ 0；When target y=0 under vector pattern, y ＞ 0
Reversely rotate, rotated forward during y ＜ 0；
Per single-step iteration equivalent to rotating z forward or backwardsiAnd transverse and longitudinal coordinate is amplified into 1/cos zi, wherein
It is 1/cosh z under hyperbolic patterniTimes：
Triangle is positive：(x, y, z) → ((x-ytanzi), (y+xtanzi), z-zi)
Triangle is reverse：(x, y, z) → ((x+ytanzi), (y-xtanzi), z+zi)
Hyperbolic is positive：(x, y, z) → ((x+ytanhzi), (y+xtanhzi), z-zi)
Hyperbolic is reverse：(x, y, z) → ((x-ytanhzi), (y-xtanhzi), z+zi)
Only realized per single-step iteration and restrained, z with plus-minus and displacement in order to realizeiIt should take as follows
Sequence：
Triangle：zi=arctan2-i, i=0,1,2 ...
Hyperbolic：zi=arctanh2-j, j=i-k, when (3k+1-1)/2+k≤i≤(3k+2-
1)/2+k+1, i=1,2,3 ...
Specific iterations, i.e. i maximums, are flexibly selected according to handled floating number precision, are selected
Foregoing constant can be calculated after maximum iteration
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