Linear integer programming method for constructing minimum core particle library in integrated chip design

Abstract

The invention provides a linear integer programming method for constructing a minimum core particle library in integrated chip design, which comprises the following steps of: respectively generating an interval matrix A based on interval attribute mapping and generating a category matrix B based on category attribute mapping by judging whether data in the core particle library belongs to an interval type or not, and further constructing and generating a matrix C for representing mixed attributes; based on the matrix C, obtaining a constraint coefficient matrix, a constant vector corresponding to the constraint condition and an optimization coefficient matrix generated through optimization through the constraint condition of the orthogonal characteristic corresponding to each interval type in the core particle; therefore, based on a linear integer programming model, an integer programming solver is called to obtain a minimum core particle library.

Description

Technical Field

[0001] The invention belongs to the technical field of integrated chip design, and in particular relates to a linear integer programming method for constructing a very small core particle library in integrated chip design. Background Art

[0002] For the modern semiconductor industry, chips are the key factor driving the continuous progress of information technology. As electronic devices evolve towards miniaturization, high performance, and low power consumption, traditional monolithic integrated circuit (System on Chip, SoC) design methods face the challenge of Moore's Law. Integrated chip technology provides a new solution.

[0003] Integrated chip technology breaks down complex SoCs into smaller, function-specific modules. Each module is designed and manufactured as an independent small chip, called a core particle. The core particles are then integrated with advanced packaging technology to obtain integrated chips with complex functions required by the application. This modular design not only reduces manufacturing costs and improves production flexibility, but also accelerates the product's time to market. Integrated chip technology overcomes the problem of area limitations with the help of interconnection technology, improves chip integration and performance, and allows core particles of multiple different process nodes to coexist, thereby optimizing performance and cost.

[0004] However, the development of integrated chip technology faces a series of challenges. In particular, the introduction of coreparticle technology has brought modular design ideas, reduced manufacturing costs, and improved production flexibility, but it has also brought new problems. For example, as a design unit, what types and models of coreparticles are needed to meet the needs of complex applications. In other words, the construction of a very small coreparticle library and the evaluation of orthogonality have become urgent issues to be solved.

[0005] Currently, the existing technology lacks an effective method to accurately construct a library of extremely small core particles and conduct a complete orthogonality evaluation on them. This makes it difficult to find the optimal combination of core particles during the design of integrated chips, thus affecting the performance improvement and manufacturing cost of the chip. Summary of the invention

[0006] In view of the problems existing in the above-mentioned prior art, the present invention aims to provide a linear integer programming method for constructing a minimal coreparticle library in integrated chip design, so as to optimize and determine the minimal coreparticle library in the coreparticle library, and accurately evaluate its orthogonality and redundancy, thereby effectively reducing the cycle and cost of integrated chip simulation design and development.

[0007] The technical solution specifically adopted by the present invention to solve the technical problem is:

[0008] A linear integer programming method for constructing a minimal coreparticle library in integrated chip design: by judging whether each data in the coreparticle library belongs to the interval type, an interval matrix A is generated based on the interval attribute mapping, and a category matrix B is generated based on the category attribute mapping, and then a matrix C representing mixed attributes is further constructed; based on the matrix C, a constraint coefficient matrix is ​​obtained through the constraint conditions of the orthogonal characteristics corresponding to each type of interval in the coreparticle. The constant vector b corresponding to the constraint conditions and the optimization coefficient matrix generated by optimization Based on the linear integer programming model, the minimum core particle library is obtained by calling the integer programming solver.

[0009] Furthermore, the objective function of the linear integer programming model is to minimize the number of selected core particles and satisfy the constraints: ensuring that the attributes of the selected core particles can cover the entire interval range; ensuring that the orthogonality of the selected core particles in all categories is greater than the set threshold ∈:

[0010] min x T 1

[0011]

[0012] in It is used to indicate whether the core particle in the core particle library is selected; if the solution result is 1, it means that the core particle needs to be selected; if it is 0, it means that the core particle is redundant; n represents the number of core particles in the original core particle library, 1 m represents the m remaining right-hand side terms of the constraints after preprocessing.

[0013] Furthermore, the generation of the interval matrix A based on interval attribute mapping is specifically:

[0014] The step size is selected according to the interval length, and the entire interval is divided into several sub-intervals. Then, based on the coverage of each core particle on the sub-interval, the interval matrix A is generated through the constructed mapping:

[0015] First, set the step size precision of interval data The numerator represents the interval length, and the step length is set according to the interval length of the core particle interval attribute data;

[0016] Then set the number of sub-intervals and the mapping strategy from interval coverage to interval matrix: use core particle attributes to establish attribute mapping strategy, map the core particle's physical data into a numerical matrix, and set the position of the sub-interval that can be covered by the core particle interval to 1, and the position of the sub-interval that cannot be covered to 0;

[0017] The generation of the category matrix B based on the category attribute mapping is specifically as follows:

[0018] The mapping strategy for categorical attribute data is: map the same type of core particles to the same column and assign a value of 1, and assign a value of 0 to non-same type core particles, thereby generating a category matrix B.

[0019] Furthermore, the construction generates the matrix C representing the mixed attributes by mapping the interval matrix A and the category matrix B into a binary matrix C representing the mixed attributes through Kronecker product and vector multiplication, so as to serve as the coefficient matrix required by the linear integer programming model.

[0020] Furthermore, the constraint coefficient matrix is ​​obtained by the constraint conditions of the orthogonal characteristics corresponding to each type of interval in the core particle Specifically:

[0021] Based on the category matrix B and the coefficient matrix C, extract the sub-matrices of each category from the matrix C; for each category of the sub-matrix, calculate the number of all non-zero columns Col nnz , and the total number of non-zero values ​​Num under this category nnz , specifically expressed as:

[0022]

[0023] Among them, ∈∈(0, 1) is an indicator for evaluating the orthogonality of the core particle library under a specific category attribute. The larger the value, the stronger the orthogonality. Then, the orthogonality constraint coefficients of all category attributes are sorted into column vector form to form a coefficient matrix

[0024] Furthermore, the optimization coefficient matrix is ​​generated by optimization The specific process is as follows: based on matrix C, the rref simplification method is used to eliminate duplicate columns, all-0 columns, and all-1 columns in matrix C; then the matrix CUR decomposition is used to further eliminate redundant rows of matrix C to obtain the optimized coefficient matrix

[0025] Furthermore, based on the coreparticle data of the original coreparticle library P and the minimal coreparticle library M, an accurate quantitative evaluation of the completeness Comp and redundancy Redu of the minimal coreparticle library M is achieved:

[0026] First, using the core particle data of the original core particle library P, calculate the total length L of the interval union in a certain interval attribute of all core particles P ; Based on the core particle data of the minimal core particle library M, calculate the interval length L covered by the minimal core particle library M ; The calculation formulas for quantitatively evaluating the completeness Comp and redundancy Redu of the minimal core library performance are:

[0027]

[0028] A linear integer programming system for constructing a very small core library in integrated chip design, comprising:

[0029] A data processing module, used for generating an interval matrix A based on interval attribute mapping by judging whether each data in the core particle library belongs to the interval type;

[0030] A coefficient matrix generation module is used to generate a category matrix B based on category attribute mapping, and construct a matrix C representing mixed attributes;

[0031] The orthogonality constraint characterization module obtains the constraint coefficient matrix based on the matrix C through the orthogonal characteristic constraint conditions corresponding to each type of interval in the core particle. The constant vector b corresponding to the constraint conditions;

[0032] The optimization module generates an optimization coefficient matrix based on the matrix C by optimization

[0033] And, the linear integer programming model, according to the output results of the characterization module and the optimization module under the orthogonality constraint condition, obtains the minimal core particle library by calling the integer programming solver.

[0034] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the linear integer programming method for constructing a minimal core library in integrated chip design as described above are implemented.

[0035] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the linear integer programming method for constructing a minimal core library in integrated chip design as described above.

[0036] Achieving global optimal design of integrated chips in complex coreparticle systems faces major challenges, requiring comprehensive consideration of the collaborative optimization of functional modules under multiple constraints such as performance, power consumption, interference, cost, and performance loss and functional redundancy compared to customized designs. Current coreparticle designs are mostly modified based on existing chips. These coreparticles cannot optimally meet the needs of multi-coreparticle systems through combination. There is currently a lack of standards for the construction of coreparticle libraries, and there is a lack of complete and concise mathematical descriptions of coreparticles with different functions in the coreparticle library and application models that can be used for the construction of extremely small coreparticle libraries. Compared with the prior art, the present invention and its preferred embodiment overcome the above defects and deficiencies, achieve the optimization and determination of the extremely small coreparticle library in the coreparticle library, and further achieve accurate evaluation of its orthogonality and redundancy, thereby effectively reducing the cycle and cost of integrated chip simulation design and development. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0038] Figure 1 The figure is a flow chart of an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to make the features and advantages of this patent more obvious and easy to understand, the following embodiments are specifically described in detail as follows:

[0040] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0041] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0042] The overall flow diagram of the embodiment of the present invention is as follows Figure 1 shown.

[0043] First, import the core particle library P and determine whether each data in the library is interval type. If yes, generate the interval matrix A based on the interval attribute mapping for the interval data. If no, generate the category matrix B based on the category attribute mapping.

[0044] Based on the generated interval matrix A and category matrix B, a matrix C representing mixed attributes is further constructed;

[0045] For the matrix C, the constraint coefficients are stored in the coefficient matrix in the form of column vectors through the orthogonal constraint conditions corresponding to each type of interval in the core particle. In the above example, the constant vector of the constraint condition is recorded as vector b; and by optimizing the matrix C, the optimization coefficient matrix is ​​generated and recorded as

[0046] The coefficient matrix The vector b is input into the linear integer programming model, and the integer programming solver is called to obtain the minimal core particle library M:

[0047] Finally, based on the coreparticle data of the original coreparticle library P and the minimal coreparticle library M, an accurate quantitative evaluation of the completeness Comp and redundancy Redu of the minimal coreparticle library M is achieved.

[0048] It specifically includes the following steps:

[0049] Step 1: Establish an attribute mapping strategy to process the interval attribute data of core particles. Select an appropriate step size based on the interval length, divide the entire interval into several sub-intervals, and then generate the interval matrix A through the constructed mapping based on the coverage of each core particle on these sub-intervals. For category attribute data, the mapping strategy maps the same type of core particles to the same column and assigns a value of 1, and assigns a value of 0 to different types, thereby generating a category matrix B. Specifically, it includes the following contents:

[0050] (1) Setting the step size precision of interval data

[0051] Set an appropriate step length according to the interval length of the core particle interval attribute data. For example, for a temperature sensor core particle, the default temperature measurement interval step length is α 1 =10, working voltage interval step α 2 =0.2.

[0052] (2) Setting the number of subintervals and the mapping strategy from interval coverage to interval matrix;

[0053] Using core particle attributes to establish attribute mapping strategies, mapping the core particle's physical data into a numerical matrix is ​​more conducive to the establishment of mathematical models and the application of mathematical methods. This setting sets the position of the sub-interval that the core particle interval can cover to 1, and the position that cannot be covered to 0.

[0054] (3) Set the mapping strategy from categorical data to categorical matrix.

[0055] Integrated chips are composed of core particles with different functions. Core particles with different functions belong to different categories. Core particles with the same function are also divided into different categories due to different manufacturing processes. This setting maps the category attributes of core particles into a numerical matrix. The values ​​of the columns of the same type are 1, and the values ​​of the rest are 0.

[0056] Step 2: Based on the characteristics of core particle data, a new matrix operation method is defined with the help of the mathematical principles of Kronecker product and vector multiplication. The defined operation maps the interval matrix A and the category matrix B obtained in step 1 into a binary matrix C as the coefficient matrix required by the linear integer programming model:

[0057] Since most core particle attributes are a mixture of interval and category attributes, this embodiment first clarifies the mapping strategy of these two attributes through step 1. For the more common mixed attribute situation, an innovative matrix operation is introduced with the help of the mathematical principle of Kronecker product and vector multiplication. This operation cleverly combines the interval matrix A and the category matrix B to construct a matrix C representing the mixed attributes:

[0058]

[0059] This operation aims to accurately record the interval attribute value of each core particle within its category.

[0060] In one example, the matrix is ​​of the form:

[0061]

[0062] Step 3: Based on the coefficient matrix C obtained in step 2, construct constraints that can accurately describe the orthogonal characteristics corresponding to each type of interval in the core particle, and store the constraint coefficients in the form of column vectors in the coefficient matrix In the example, let the constant vector on the right side of the constraint be vector b:

[0063] This paper further explores the orthogonality of core particles under different category attributes, aiming to integrate the orthogonality constraints for each category of core particles into the linear integer programming model. Based on the category matrix B and the coefficient matrix C, sub-matrices of each category are extracted from the matrix C. For each category of sub-matrices, the number of all non-zero columns Col is calculated. nnz , and the total number of non-zero values ​​Num under this category nnz , specifically expressed as:

[0064]

[0065] Among them, ∈∈(0, 1) is an indicator for evaluating the orthogonality of the core particle library under a specific category attribute. The larger its value, the stronger the orthogonality. Then, the orthogonality constraint coefficients of all category attributes are sorted into column vector form to form a coefficient matrix Let the constant on the right side of the constraint be vector b.

[0066] Step 4: Based on the coefficient matrix C obtained in step 2, the row minimum (rref) method is used to eliminate duplicate columns, all-0 columns, and all-1 columns in matrix C. Specifically, the duplicate columns of matrix C represent duplicate constraints, and all-0 columns and all-1 columns correspond to invalid constraints. This method can effectively remove unnecessary constraints in the linear integer programming model. Subsequently, the matrix CUR decomposition technique is used to further eliminate redundant rows of matrix C, and the optimized coefficient matrix is ​​recorded as

[0067] The coefficient matrix C contains a lot of redundant information, such as some attribute mapping columns that are all 0 or all 1. These columns are unnecessary constraints when building a linear integer programming model. At the same time, there are many repeated column attributes that represent the same constraints. To eliminate this redundancy, the row simplest transformation method can be used to effectively remove these useless column information.

[0068] After the redundant information is removed, the new matrix may still contain linearly related rows, which is also unnecessary when constructing a linear integer programming model. Therefore, the matrix CUR decomposition technique is further used to remove these linearly related rows to obtain a simplified coefficient matrix This can significantly reduce the time complexity and storage requirements of subsequent calculations.

[0069] Step 5: Substitute the coefficient matrix obtained in steps 3 and 4 The vector b is input into the linear integer programming model, and the integer programming solver is called to obtain the minimal core particle library M:

[0070] min x T 1

[0071]

[0072] The objective function of the model aims to minimize the number of selected coreparticles while satisfying the following two major constraints: ensuring that the properties of the selected coreparticles can cover the entire interval range; the second constraint is to ensure that the orthogonality of the selected coreparticles in all categories is greater than the set threshold ∈.

[0073] Step six, based on the coreparticle data of the original coreparticle library P and the minimal coreparticle library M obtained in step five, accurately quantify and evaluate the completeness Comp and redundancy Redu of the minimal coreparticle library M.

[0074] This step first uses the core particle data of the original core particle library P to calculate the total length L of the interval union in a certain interval attribute of all core particles P Based on the core particle data of the minimal core particle library M, calculate the interval length L covered by the minimal core particle library M Finally, a calculation formula for quantitatively evaluating the completeness and redundancy of the performance of the minimal core library is given:

[0075]

[0076] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0077] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0078] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0079] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0080] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0081] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0082] This patent is not limited to the above-mentioned optimal implementation mode. Anyone can derive various other forms of linear integer programming methods for constructing a very small core particle library in integrated chip design under the inspiration of this patent. All equal changes and modifications made according to the scope of the patent application of the present invention should be covered by this patent.

Claims

1. A linear integer programming method for constructing a minimal core library in integrated chip design, characterized in that: By judging whether each data in the core particle library belongs to the interval type, an interval matrix A is generated based on the interval attribute mapping, and a category matrix B is generated based on the category attribute mapping, and then a matrix C representing the mixed attributes is further constructed; based on the matrix C, the constraint coefficient matrix is ​​obtained through the constraint conditions of the orthogonal characteristics corresponding to each type of interval in the core particle. The constant vector b corresponding to the constraint conditions and the optimization coefficient matrix generated by optimization Based on the linear integer programming model, the minimum core particle library is obtained by calling the integer programming solver.

2. The linear integer programming method for constructing a minimal core library in integrated chip design according to claim 1, characterized in that: The objective function of the linear integer programming model is to minimize the number of selected core particles and meet the constraints: ensure that the properties of the selected core particles can cover the entire interval range; ensure that the orthogonality of the selected core particles in all categories is greater than the set threshold ∈: my x T 1 in It is used to indicate whether the coreparticle in the coreparticle library is selected; if the solution result is 1, it means that the coreparticle needs to be selected; if it is 0, it indicates that the coreparticle is redundant; n represents the number of coreparticles in the original coreparticle library, and 1m represents the remaining m right-hand side terms of the constraint after preprocessing.

3. The linear integer programming method for constructing a minimal core library in integrated chip design according to claim 1, characterized in that: The generation of interval matrix A based on interval attribute mapping is specifically as follows: The step size is selected according to the interval length, and the entire interval is divided into several sub-intervals. Then, based on the coverage of each core particle on the sub-interval, the interval matrix A is generated through the constructed mapping: First, set the step size precision of interval data The numerator represents the interval length, and the step length is set according to the interval length of the core particle interval attribute data; Then set the number of sub-intervals and the mapping strategy from interval coverage to interval matrix: use core particle attributes to establish attribute mapping strategy, map the core particle's physical data into a numerical matrix, and set the position of the sub-interval that can be covered by the core particle interval to 1, and the position of the sub-interval that cannot be covered to 0; The generation of the category matrix B based on the category attribute mapping is specifically as follows: The mapping strategy for categorical attribute data is: map the same type of core particles to the same column and assign a value of 1, and assign a value of 0 to non-same type core particles, thereby generating a category matrix B.

4. The linear integer programming method for constructing a minimal core library in integrated chip design according to claim 1, characterized in that: The construction and generation of the matrix C representing the mixed attributes is specifically to map the interval matrix A and the category matrix B into a binary matrix C representing the mixed attributes through Kronecker product and vector multiplication, so as to serve as the coefficient matrix required by the linear integer programming model.

5. The linear integer programming method for constructing a minimal core library in integrated chip design according to claim 1, characterized in that: The constraint coefficient matrix is ​​obtained by the constraint conditions of the orthogonal characteristics corresponding to each type of interval in the core particle Specifically: Based on the category matrix B and the coefficient matrix C, extract the sub-matrices of each category from the matrix C; for each category of the sub-matrix, calculate the number of all non-zero columns Col nnz , and the total number of non-zero values ​​Num under this category nnz , specifically expressed as: Among them, ∈∈(0, 1) is an indicator for evaluating the orthogonality of the core particle library under a specific category attribute. The larger the value, the stronger the orthogonality. Then, the orthogonality constraint coefficients of all category attributes are sorted into column vector form to form a coefficient matrix 6. The linear integer programming method for constructing a minimal core library in integrated chip design according to claim 1, characterized in that: Generate the optimization coefficient matrix through optimization The specific process is as follows: based on matrix C, the rref simplification method is used to eliminate duplicate columns, all-0 columns, and all-1 columns in matrix C; then the matrix CUR decomposition is used to further eliminate redundant rows of matrix C to obtain the optimized coefficient matrix 7. The linear integer programming method for constructing a minimal core library in integrated chip design according to claim 1, characterized in that: Based on the coreparticle data of the original coreparticle library P and the minimal coreparticle library M, the completeness Comp and redundancy Redu of the minimal coreparticle library M are accurately and quantitatively evaluated: First, using the core particle data of the original core particle library P, calculate the total length L of the interval union in a certain interval attribute of all core particles P ; Based on the core particle data of the minimal core particle library M, calculate the interval length L covered by the minimal core particle library M ; The calculation formulas for quantitatively evaluating the completeness Comp and redundancy Redu of the minimal core library performance are:

8. A linear integer programming system for constructing a minimal core library in integrated chip design, characterized in that: include: A data processing module, used for generating an interval matrix A based on interval attribute mapping by judging whether each data in the core particle library belongs to the interval type; A coefficient matrix generation module is used to generate a category matrix B based on category attribute mapping, and construct a matrix C representing mixed attributes; The orthogonality constraint characterization module obtains the constraint coefficient matrix based on the matrix C through the orthogonal characteristic constraint conditions corresponding to each type of interval in the core particle. The constant vector b corresponding to the constraint conditions; The optimization module generates an optimization coefficient matrix based on the matrix C by optimization And, the linear integer programming model, according to the output results of the characterization module and the optimization module under the orthogonality constraint condition, obtains the minimal core particle library by calling the integer programming solver.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the linear integer programming method for constructing a minimal core particle library in integrated chip design as described in any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the linear integer programming method for constructing a minimal core particle library in integrated chip design as described in any one of claims 1 to 7 are implemented.

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