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C++ Arbitrary Precision Floating Point Library
Závada, Vladislav ; Šnobl, Pavel (referee) ; Hruška, Tomáš (advisor)
This thesis deals with the design of a floating point module, which allows to perform operations with floating point operands that have any bit width. For this purpose, the module is implemented as a template class in C ++. The module is designed to allow it to be used when designing an application-specific processor. First, the floating point number and template functions in c ++ are described. In the practical part the algorithms of the individual operations and the design of the module itself are described as template libraries.
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Specialized Computer System Automatic Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of calculations of specialized system. The reader is acquainted with the numerical solution of differential equations by Taylor series method and numerical integrators. The practical aim of this work is to analyze parallel characteristics of Taylor series method, specification of parallel math operations and design of control of this operations.
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Enhanced mathematical library for C++
Temel, Aleš ; Macho, Tomáš (referee) ; Petyovský, Petr (advisor)
I create a library for storing matrices and working with matrices in this bachelor’s thesis. In this case, the issues concern mainly so-called sparse matrices. C++ do not provide among the standard libraries tools for easy working with sparse matrices. The most frequent alternative is the application of two-dimensional array (2D array). 2D array may be realized as a double pointer representing the rows and the columns of the matrix. The basic problem is that behavior of 2D array is identical both to the sparse, and to the full non-zero matrix. 2D array ignores the possibility to store matrices more favorable. The library for storing matrices designed by me takes into account the storing of sparse matrices by several different ways. It offers the sparse format CSR (Compressed sparse rows), as well as alternatives to save the specially structured matrices. In the course of creating library the main emphasis first of all I put on the amount of memory that is necessary for storing matrices. Because it is a mathematical library, it contains different functions suitable for working with matrices, such as determinant calculation, inverse matrix calculation and so. When calculate these functions it is necessary to take into account used memory size as well. Intermediate results are stored also in sparse format, and removed as soon as possible after their use. I created also the second library that deals with the floating point numbers stored with greater precision than standard data types like float and double. The size of occupied memory increases according to precision of floating point number.
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Hardware Realization of Higher Order Numerical Integrator
Matečný, František ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.
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Automatic Computation Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of numerical calculations. The reader is acquainted with the numerical solution of differential equations and the parallel, serial, and series-parallel numerical integrator. The practical aim of this work is to design control circuits for the three mentioned variants of integrators. The design includes the development of a software simulator of the control circuit for the series-parallel integrator in a fixed point.
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Audio equalizer implementation based on FPGA structure
Otisk, Libor ; Valach, Soběslav (referee) ; Kváš, Marek (advisor)
The bachelor thesis introduces the basic types of audio equalizers. It describes the design of digital filters for graphic equalizer, the correct choice of structure, placement and shape of digital filters. It also describes the implementation of graphic equalizer in the fixed-point arithmetic. It further describes an implementation of the algorithm graphic equalizer on PC and the implementation in gate array of FPGA.
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Simulation tool for fixed-point arithmetic
Grézl, Vojtěch ; Kunz, Jan (referee) ; Čala, Martin (advisor)
This bachelor's thesis is focused on creating tool for simulating calculations with fixed point. This tool simplifies and increases the efficiency of performing operations with values of different data types. By calculating and graphically displaying absolute errors, which creates a conversion of values between data types and conversion through maximum absolute errors, the user can evaluate whether this conversion is optimal or not. After getting acquainted with this issue in the theoretical introduction part, the design of the practical part follows, which summarizes the implementation and procedure of program design in the LabVIEW 2021. Process of draft of the practical part is based on attributes of LabVIEW and it’s part FPGA module and aim on creating of transparent and user-friendly user interface. The output of the practical part is a tool that works with the created VI, containing a sequence of different operations with different input and output data types. The program is used to convert numbers of different data types to another type, mainly for a conversion to a fixed point data type. The user gives the main direction by creating a sample VI, the operations of which will then be performed. Other parameters that the user can set and affect the program are listed on the user interface.
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Simulation tool for fixed-point arithmetic
Grézl, Vojtěch ; Kunz, Jan (referee) ; Čala, Martin (advisor)
This bachelor's thesis is focused on creating tool for simulating calculations with fixed point. This tool simplifies and increases the efficiency of performing operations with values of different data types. By calculating and graphically displaying absolute errors, which creates a conversion of values between data types and conversion through maximum absolute errors, the user can evaluate whether this conversion is optimal or not. After getting acquainted with this issue in the theoretical introduction part, the design of the practical part follows, which summarizes the implementation and procedure of program design in the LabVIEW 2021. Process of draft of the practical part is based on attributes of LabVIEW and it’s part FPGA module and aim on creating of transparent and user-friendly user interface. The output of the practical part is a tool that works with the created VI, containing a sequence of different operations with different input and output data types. The program is used to convert numbers of different data types to another type, mainly for a conversion to a fixed point data type. The user gives the main direction by creating a sample VI, the operations of which will then be performed. Other parameters that the user can set and affect the program are listed on the user interface.
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C++ Arbitrary Precision Floating Point Library
Závada, Vladislav ; Šnobl, Pavel (referee) ; Hruška, Tomáš (advisor)
This thesis deals with the design of a floating point module, which allows to perform operations with floating point operands that have any bit width. For this purpose, the module is implemented as a template class in C ++. The module is designed to allow it to be used when designing an application-specific processor. First, the floating point number and template functions in c ++ are described. In the practical part the algorithms of the individual operations and the design of the module itself are described as template libraries.
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Hardware Realization of Higher Order Numerical Integrator
Matečný, František ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.
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