CN116186471A - Index function-based table lookup method and device, electronic equipment and storage medium - Google Patents

Index function-based table lookup method and device, electronic equipment and storage medium Download PDF

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CN116186471A
CN116186471A CN202310317485.6A CN202310317485A CN116186471A CN 116186471 A CN116186471 A CN 116186471A CN 202310317485 A CN202310317485 A CN 202310317485A CN 116186471 A CN116186471 A CN 116186471A
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function
target
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唐璇
郭振江
郭璟
于莉莉
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Shanghai Silang Technology Co ltd
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Abstract

The application discloses a lookup method, a lookup device, electronic equipment and a storage medium based on an exponential function. The method comprises the following steps: obtaining a table look-up calculation request, wherein the table look-up calculation request comprises: looking up an index function required by table lookup and a preset value interval of the index function; responding to the table look-up calculation request, and acquiring a pre-established target index function table; acquiring address information of an independent variable of the exponential function in the preset value interval from the target exponential function table; and calculating an objective function value corresponding to the argument of the exponential function by using the address information. According to the method and the device, the address information of the independent variable of the index function in the preset value interval is obtained from the target index function table, and the address information is utilized to calculate the target function value corresponding to the independent variable of the index function, so that the operation result with high precision can be obtained efficiently when the independent variable of the index function is in any value range.

Description

Index function-based table lookup method and device, electronic equipment and storage medium
Technical Field
The present disclosure relates to the field of lookup methods, apparatuses, electronic devices, and storage media based on exponential functions.
Background
Exponential functions are a common basic elementary function in engineering calculations and are generally widely used in scientific research and industrial production. The method is nonlinear mathematical operation and is usually realized by a table look-up method when in hardware calculation. The general method for looking up the table is: firstly, a lookup table is manufactured, and aiming at an exponential function, in a certain independent variable interval, the most intuitive method is to utilize power series expansion of the exponential function:
Figure BDA0004150515880000011
taking the coefficients of the first n items according to the expansion items and storing the coefficients into a lookup table; when the value of the independent variable is calculated, the address of the corresponding coefficient can be found, and then the function value is calculated. The accuracy and duration of the calculation of the method are related to the Taylor expansion coefficient. For e x Function, when |x| < 1, the function calculation can quickly obtain accurate result under the condition of less expansion terms, but if |x| is expected to be increased, e x With the same precision of the function values, more expansion terms are needed, and as expansion terms of different stages are realized corresponding to different hardware structures, the more expansion terms, the slower the calculation speed becomes, and the required calculation time length is increased.
Disclosure of Invention
In order to solve the technical problems or at least partially solve the technical problems, the application provides a lookup method, a lookup device, an electronic device and a storage medium based on an exponential function.
According to an aspect of the embodiments of the present application, there is provided a lookup table method based on an exponential function, including:
obtaining a table look-up calculation request, wherein the table look-up calculation request comprises: looking up an index function required by table lookup and a preset value interval of the index function;
responding to the table look-up calculation request, and acquiring a pre-established target index function table;
acquiring address information of an independent variable of the exponential function in the preset value interval from the target exponential function table;
and calculating an objective function value corresponding to the argument of the exponential function by using the address information.
Further, the obtaining a pre-established target index function table includes:
acquiring a Taylor expansion coefficient of the exponential function in the preset value interval;
and creating a target index function table by using the Taylor expansion coefficient and the preset value interval.
Further, the creating the target exponent function table by using the taylor expansion coefficient and the preset value interval includes:
obtaining a segmentation parameter corresponding to the preset value interval;
dividing the preset value interval according to the dividing parameters to obtain a plurality of sub value intervals, and determining a Taylor expansion coefficient corresponding to each sub value interval;
and creating a target index function table based on the Taylor expansion coefficients corresponding to each subvalue interval.
Further, before obtaining address information of the argument of the exponent function in the preset value interval from the target exponent function table, the method further includes:
determining a logarithmic function value of the argument of the exponential function based on 2;
and adjusting the independent variable of the exponential function to the preset value interval by utilizing the logarithmic function value.
Further, the obtaining, from the target exponent function table, address information of an argument of the exponent function in the preset value interval includes:
acquiring a target column corresponding to the independent variable of the exponential function in the preset value interval from the target exponential function table;
and taking the target column as the address information.
Further, the calculating the objective function value corresponding to the argument of the exponential function using the address information includes:
acquiring a target Taylor expansion coefficient associated with the target column;
calculating an initial exponential function value corresponding to an independent variable of the exponential function based on a Taylor expansion formula and the target Taylor expansion coefficient;
and calculating the objective function value by using the initial function value and a preset conversion factor.
According to another aspect of the embodiments of the present application, there is also provided a lookup table device based on an exponential function, including:
the acquisition module is used for acquiring a table look-up calculation request, wherein the table look-up calculation request comprises: looking up an index function required by table lookup and a preset value interval of the index function;
the response module is used for responding to the table look-up calculation request and acquiring a pre-established target index function table;
the query module is used for acquiring address information of the independent variable of the exponential function in the preset value interval from the target exponential function table;
and the calculating module is used for calculating the objective function value corresponding to the independent variable of the exponential function by utilizing the address information.
According to another aspect of the embodiments of the present application, there is also provided a storage medium including a stored program that performs the steps described above when running.
According to another aspect of the embodiments of the present application, there is provided an electronic device including a processor, a communication interface, a memory, and a communication bus, where the processor, the communication interface, and the memory complete communication with each other through the communication bus; wherein: a memory for storing a computer program; and a processor for executing the steps of the method by running a program stored on the memory.
Embodiments of the present application also provide a computer program product comprising instructions which, when run on a computer, cause the computer to perform the steps of the above method.
Compared with the prior art, the technical scheme provided by the embodiment of the application has the following advantages: according to the method provided by the embodiment of the application, the address information of the independent variable of the index function in the preset value interval is obtained from the target index function table, and the address information is utilized to calculate the target function value corresponding to the independent variable of the index function, so that the high-precision operation result can be obtained efficiently when the independent variable of the index function is in any value range.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the description of the embodiments or the prior art will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a flowchart of a lookup method based on an exponential function according to an embodiment of the present application;
FIG. 2 is a block diagram of a lookup table device based on an exponential function according to an embodiment of the present application;
fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments, the exemplary embodiments of the present application and the descriptions thereof are used to explain the present application and do not constitute undue limitations of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present application based on the embodiments herein.
It should be noted that in this document, relational terms such as "first" and "second" and the like are used solely to distinguish one entity or action from another similar entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The embodiment of the application provides a lookup method, a lookup device, electronic equipment and a storage medium based on an exponential function. The method provided by the embodiment of the invention can be applied to any needed electronic equipment, for example, the electronic equipment can be a server, a terminal and the like, is not particularly limited, and is convenient to describe and is called as the electronic equipment for short hereinafter.
According to an aspect of the embodiments of the present application, there is provided a method embodiment of a lookup table method based on an exponential function, and fig. 1 is a flowchart of a lookup table method based on an exponential function, as shown in fig. 1, where the method includes:
step S11, obtaining a table look-up calculation request, wherein the table look-up calculation request comprises: and looking up an index function required by the table, and presetting a value interval of the index function.
The method provided by the embodiment of the application is applied to the processor, and the processor can receive the table lookup calculation request issued by the terminal equipment and then perform table lookup operation by using the table lookup calculation request. Specifically, when the terminal device currently has a table look-up requirement, the user may preset a preset value interval of the exponential function, generate a table look-up calculation request from the exponential function and the preset value interval of the exponential function, and then issue the table look-up calculation request to the processor.
Step S12, a pre-established target index function table is obtained in response to the table lookup calculation request.
In the embodiment of the present application, obtaining a pre-established target exponent function table includes: acquiring a Taylor expansion coefficient of the exponential function in a preset value interval; and creating a target index function table by using the Taylor expansion coefficient and a preset value interval.
In the embodiment of the present application, creating a target exponent function table using a taylor expansion coefficient and a preset value interval includes: obtaining a segmentation parameter corresponding to a preset value interval; dividing a preset value interval according to the dividing parameters to obtain a plurality of sub value intervals, and determining a Taylor expansion coefficient corresponding to each sub value interval; and creating a target index function table based on the Taylor expansion coefficients corresponding to each subvalue interval.
In the embodiment of the application, the exponential function e is based on Taylor expansion x Expanding and making a function table in the interval [0.5, 1). The exponential function table size is set to a×b, where a rows correspond to uniformly dividing x into a parts in the [0.5,1 ] interval and b columns correspond to taylor expansion coefficients. Calculation when x=x i Results of taylor expansion at time, x i For the ith value of x in the interval [0.5, 1), x will be i The Taylor expansion coefficients k1, k2, k3 and … of each stage corresponding to the values are stored in the ith row of the index function table, so that the index function table which is completed is used as a target index function table.
Step S13, obtaining the address information of the independent variable of the exponential function in the preset value interval from the target exponential function table.
In this embodiment of the present application, before obtaining address information of an argument of an exponent function in a preset value interval from a target exponent function table, the method further includes: determining the logarithmic function value of the independent variable of the exponential function with 2 as a base; and adjusting the independent variable of the exponential function to a preset value interval by utilizing the logarithmic function value.
In the present embodiment, the x value lying within the (- ≡infinity) interval is defined as the [0.5,1 ] interval. Specifically, according to the IEEE 754 floating point standard, a single-precision floating point number in a computer occupies 4 bytes and 32 bits, and a double-precision floating point number occupies 8 bytes and 64 bits. The single and double precision binary memory structures are sign bits, exponent bits and mantissa bits. The highest bit (31 bit or 63 bit) of the two is a sign bit, 30-23 bits of single precision and 62-52 bits of double precision are exponential parts, and the rest 23 bits (22-0) and 52 bits (51-0) are tail digits respectively.
Any one real Y can be converted by binary through IEEE 754 floating point standard, expressed as
Figure BDA0004150515880000081
Where s is 0 (positive number) or 1 (negative number), i represents the i-th bit from left to right of the mantissa digit, m i Representing the value at bit i on the mantissa (equal to 0 or 1), m=23 in single precision floating point numbers, x=e-127, and 52 in double precision floating point numbers, x=e-1023.
It should be noted that any one of the real numbers y= (-1) S ×y×2 X Where y.epsilon.1, 2). From this, log 2 |Y|＝X+log 2 y, log of 2 The Y is rounded down to X, where X can be directly obtained by subtracting 127 (single precision floating point number) or 1023 (double precision floating point number) from the exponent bit E of the binary representation of Y, without additional computation.
Specifically, the logarithmic function value based on 2 of the argument x of the numerical function is calculated, and as can be seen from the above formula, log can be directly obtained by the exponent bits of the binary representation of |x| 2 The result of the downward rounding of |x| is given by s=log 2 And (3) rounding X downwards to obtain S'. The argument x is then adjusted to the interval [0.5, 1): from the foregoing mathematical expressions, log 2 |x|＝S’+log 2 y, where y e [1, 2), in order to be able to adjust the interval, let the conversion factor a=2 -(S'+1) The range of x 'can be limited to the [0.5, 1) interval by x' = |x|x|a.
In this embodiment of the present application, obtaining address information of an argument of an exponential function in a preset value interval from a target exponential function table includes: acquiring a target column corresponding to an independent variable of an index function in a preset value interval from a target index function table; the target column is taken as address information.
Step S14, calculating the objective function value corresponding to the argument of the exponential function by using the address information.
In the embodiment of the present application, calculating the objective function value corresponding to the argument of the exponential function using the address information includes: acquiring a target Taylor expansion coefficient associated with a target column; calculating an initial exponential function value corresponding to an independent variable of the exponential function based on the Taylor expansion formula and the target Taylor expansion coefficient; and calculating an objective function value by using the initial function value and a preset conversion factor.
Calculating the address of the function table in the first step according to the value of x ', obtaining the corresponding Taylor expansion coefficient, and obtaining the index function value e corresponding to x' according to the Taylor expansion formula x '。
According to the known e x' And x' = |x|x a, can be obtained
Figure BDA0004150515880000091
Thus e |x| The value of (2) passes->
Figure BDA0004150515880000092
E x' The continuous multiplication is available, and the final exponential function e x The values are:
Figure BDA0004150515880000093
according to the method provided by the embodiment of the application, the address information of the independent variable of the index function in the preset value interval is obtained from the target index function table, and the address information is utilized to calculate the target function value corresponding to the independent variable of the index function, so that the high-precision operation result can be obtained efficiently when the independent variable of the index function is in any value range.
Fig. 2 is a block diagram of a lookup table device based on an exponential function according to an embodiment of the present application, where the device may be implemented as part or all of an electronic device by software, hardware, or a combination of both. As shown in fig. 2, the apparatus includes:
the obtaining module 21 is configured to obtain a lookup calculation request, where the lookup calculation request includes: looking up an index function required by table lookup and a preset value interval of the index function;
the response module 22 is configured to obtain a pre-established target index function table in response to the lookup calculation request;
the query module 23 is configured to obtain, from the target exponent function table, address information of an argument of the exponent function within a preset value interval;
a calculating module 24, configured to calculate an objective function value corresponding to the argument of the exponential function using the address information.
In the embodiment of the present application, the obtaining module 21 is configured to obtain a taylor expansion coefficient of the exponential function in a preset value interval; and creating a target index function table by using the Taylor expansion coefficient and a preset value interval.
In the embodiment of the present application, the obtaining module 21 is configured to obtain a segmentation parameter corresponding to a preset value interval; dividing a preset value interval according to the dividing parameters to obtain a plurality of sub value intervals, and determining a Taylor expansion coefficient corresponding to each sub value interval; and creating a target index function table based on the Taylor expansion coefficients corresponding to each subvalue interval.
In an embodiment of the present application, the lookup table device based on the exponential function further includes: the adjusting module is used for determining a logarithmic function value with an independent variable of the exponential function as a base number of 2; and adjusting the independent variable of the exponential function to a preset value interval by utilizing the logarithmic function value.
In this embodiment of the present application, the query module 23 is configured to obtain, from a target exponential function table, a target column corresponding to an argument of an exponential function within a preset value interval; the target column is taken as address information.
In the embodiment of the present application, the calculating module 24 is configured to obtain a target taylor expansion coefficient associated with the target column; calculating an initial exponential function value corresponding to an independent variable of the exponential function based on the Taylor expansion formula and the target Taylor expansion coefficient; and calculating an objective function value by using the initial function value and a preset conversion factor.
The embodiment of the application further provides an electronic device, as shown in fig. 3, the electronic device may include: the device comprises a processor 1501, a communication interface 1502, a memory 1503 and a communication bus 1504, wherein the processor 1501, the communication interface 1502 and the memory 1503 are in communication with each other through the communication bus 1504.
A memory 1503 for storing a computer program;
the processor 1501, when executing the computer program stored in the memory 1503, implements the steps of the above embodiments.
The communication bus mentioned by the above terminal may be a peripheral component interconnect standard (Peripheral Component Interconnect, abbreviated as PCI) bus or an extended industry standard architecture (Extended Industry Standard Architecture, abbreviated as EISA) bus, etc. The communication bus may be classified as an address bus, a data bus, a control bus, or the like. For ease of illustration, the figures are shown with only one bold line, but not with only one bus or one type of bus.
The communication interface is used for communication between the terminal and other devices.
The memory may include random access memory (Random Access Memory, RAM) or non-volatile memory (non-volatile memory), such as at least one disk memory. Optionally, the memory may also be at least one memory device located remotely from the aforementioned processor.
The processor may be a general-purpose processor, including a central processing unit (Central Processing Unit, CPU for short), a network processor (Network Processor, NP for short), etc.; but also digital signal processors (Digital Signal Processing, DSP for short), application specific integrated circuits (Application Specific Integrated Circuit, ASIC for short), field-programmable gate arrays (Field-Programmable Gate Array, FPGA for short) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.
In yet another embodiment provided herein, a computer readable storage medium having instructions stored therein that when executed on a computer cause the computer to perform the exponential function based look-up table method of any of the above embodiments is also provided.
In yet another embodiment provided herein, there is also provided a computer program product containing instructions that, when run on a computer, cause the computer to perform the exponential function based look-up table method of any of the above embodiments.
In the above embodiments, it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, produces a flow or function in accordance with embodiments of the present application, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by a wired (e.g., coaxial cable, fiber optic, digital subscriber line), or wireless (e.g., infrared, wireless, microwave, etc.). The computer readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that contains an integration of one or more available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid State Disk), etc.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the scope of the present application. Any modifications, equivalent substitutions, improvements, etc. that are within the spirit and principles of the present application are intended to be included within the scope of the present application.
The foregoing is merely a specific embodiment of the application to enable one skilled in the art to understand or practice the application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. A lookup method based on an exponential function, comprising:
obtaining a table look-up calculation request, wherein the table look-up calculation request comprises: looking up an index function required by table lookup and a preset value interval of the index function;
responding to the table look-up calculation request, and acquiring a pre-established target index function table;
acquiring address information of an independent variable of the exponential function in the preset value interval from the target exponential function table;
and calculating an objective function value corresponding to the argument of the exponential function by using the address information.
2. The method of claim 1, wherein the obtaining a pre-established target exponent function table comprises:
acquiring a Taylor expansion coefficient of the exponential function in the preset value interval;
and creating a target index function table by using the Taylor expansion coefficient and the preset value interval.
3. The method of claim 2, wherein creating a target exponent function table using the taylor expansion coefficient and the preset value interval comprises:
obtaining a segmentation parameter corresponding to the preset value interval;
dividing the preset value interval according to the dividing parameters to obtain a plurality of sub value intervals, and determining a Taylor expansion coefficient corresponding to each sub value interval;
and taking the subvalue intervals as rows, and taking Taylor expansion coefficients corresponding to each subvalue interval as columns to generate a target index function table.
4. The method according to claim 1, wherein before obtaining address information of an argument of the exponent function within the preset value interval from the target exponent function table, the method further comprises:
determining a logarithmic function value of the argument of the exponential function based on 2;
and adjusting the independent variable of the exponential function to the preset value interval by utilizing the logarithmic function value.
5. The method according to claim 1, wherein the obtaining, from the target exponent function table, address information of an argument of the exponent function within the preset value interval includes:
acquiring a target column corresponding to the independent variable of the exponential function in the preset value interval from the target exponential function table;
and taking the target column as the address information.
6. The method of claim 5, wherein calculating the objective function value corresponding to the argument of the exponential function using the address information, comprises:
acquiring a target Taylor expansion coefficient associated with the target column;
calculating an initial exponential function value corresponding to an independent variable of the exponential function based on a Taylor expansion formula and the target Taylor expansion coefficient;
and calculating the objective function value by using the initial function value and a preset conversion factor.
7. A lookup table device based on an exponential function, comprising:
the acquisition module is used for acquiring a table look-up calculation request, wherein the table look-up calculation request comprises: looking up an index function required by table lookup and a preset value interval of the index function;
the response module is used for responding to the table look-up calculation request and acquiring a pre-established target index function table;
the query module is used for acquiring address information of the independent variable of the exponential function in the preset value interval from the target exponential function table;
and the calculating module is used for calculating the objective function value corresponding to the independent variable of the exponential function by utilizing the address information.
8. A storage medium comprising a stored program, wherein the program when run performs the method steps of any of the preceding claims 1 to 6.
9. The electronic equipment is characterized by comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are communicated with each other through the communication bus; wherein:
a memory for storing a computer program;
a processor for executing the method steps of any one of claims 1 to 6 by running a program stored on a memory.
CN202310317485.6A 2023-03-28 2023-03-28 Index function-based table lookup method and device, electronic equipment and storage medium Pending CN116186471A (en)

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