The Experts below are selected from a list of 11667 Experts worldwide ranked by ideXlab platform
Tsuneo Kato - One of the best experts on this subject based on the ideXlab platform.
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ACCURATE PARAMETER GENERATION USING FIXED-Point ARITHMETIC FOR EMBEDDED HMM-BASED SPEECH SYNTHESIZERS
2016Co-Authors: Nobuyuki Nishizawa, Tsuneo KatoAbstract:Parameter trajectory generation for HMM-based speech synthesis is practically achieved using only fixed-Point arithmetic with 32-bit integers. Since processors for embedded devices often provide no hardware-based Floating-Point Number processor, a speech synthe-sizer using only fixed-Point arithmetic is necessary for such devices. In this study, a new method to reduce rounding errors is introduced, as well as optimizing value scaling, and the generation of F0 trajec-tory is discussed. The experimental results indicated that RMSE in a logarithmic scale of F0 can be reduced down to approximately 0.04 semitones (1 semitone = 1/12 octaves) by the proposed method even where a 2-bit margin was arranged to avoid calculation overflow. An extension for trajectories considering the global variance (GV) us-ing the basic program for trajectories without consideration of GV is also introduced. The extension method reduces required iteration counts to 5 for 0.05-semitone RMSE comparable to the converged results of the conventional method. Index Terms — HMM-based speech synthesis, fixed-Point arith-metic, embedded devices, global variance 1
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accurate parameter generation using fixed Point arithmetic for embedded hmm based speech synthesizers
International Conference on Acoustics Speech and Signal Processing, 2011Co-Authors: Nobuyuki Nishizawa, Tsuneo KatoAbstract:Parameter trajectory generation for HMM-based speech synthesis is practically achieved using only fixed-Point arithmetic with 32-bit integers. Since processors for embedded devices often provide no hardware-based Floating-Point Number processor, a speech synthesizer using only fixed-Point arithmetic is necessary for such devices. In this study, a new method to reduce rounding errors is introduced, as well as optimizing value scaling, and the generation of F 0 trajectory is discussed. The experimental results indicated that RMSE in a logarithmic scale of F 0 can be reduced down to approximately 0.04 semitones (1 semitone = 1/12 octaves) by the proposed method even where a 2-bit margin was arranged to avoid calculation overflow. An extension for trajectories considering the global variance (GV) using the basic program for trajectories without consideration of GV is also introduced. The extension method reduces required iteration counts to 5 for 0.05-semitone RMSE comparable to the converged results of the conventional method.
Yungko Chen - One of the best experts on this subject based on the ideXlab platform.
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arithmetic operations beyond Floating Point Number precision
Computational Science and Engineering, 2011Co-Authors: Chihyueh Wang, Chenyang Yin, Hongyu Chen, Yungko ChenAbstract:In basic computational physics classes, students often raise the question of how to compute a Number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilised in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the approach of calculating the exact value of a large Number beyond the Floating Point Number precision, using the basic scientific programming language Fortran. The basic concept is to utilise arrays to decompose the Number and allocate finite memory. Examples of the successive multiplication of even Number and the multiplication and division of two overflowing floats are presented. The multiple precision schemes have been applied to hardware and firmware design for digital signal processing (DSP) systems, and is gaining importance to scientific computing. Such basic arithmetic operations can be integrated to solve advanced mathematical problems to almost arbitrarily-high precision that is limited by the memory of the host machine.
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arithmetic operations beyond Floating Point Number precision
arXiv: Computational Physics, 2010Co-Authors: Chihyueh Wang, Chenyang Yin, Hongyu Chen, Yungko ChenAbstract:In basic computational physics classes, students often raise the question of how to compute a Number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the approach of calculating the exact value of a large Number beyond the Floating Point Number precision, using the basic scientific programming language Fortran. The basic concept is to utilize arrays to decompose the Number and allocate finite memory. Examples of the successive multiplication of even Number and the multiplication and division of two overflowing floats are presented. The multiple precision scheme has been applied to hardware and firmware design for digital signal processing (DSP) systems, and is gaining importance to scientific computing. Such basic arithmetic operations can be integrated to solve advanced mathematical problems to almost arbitrarily-high precision that is limited by the memory of the host machine.
Nobuyuki Nishizawa - One of the best experts on this subject based on the ideXlab platform.
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ACCURATE PARAMETER GENERATION USING FIXED-Point ARITHMETIC FOR EMBEDDED HMM-BASED SPEECH SYNTHESIZERS
2016Co-Authors: Nobuyuki Nishizawa, Tsuneo KatoAbstract:Parameter trajectory generation for HMM-based speech synthesis is practically achieved using only fixed-Point arithmetic with 32-bit integers. Since processors for embedded devices often provide no hardware-based Floating-Point Number processor, a speech synthe-sizer using only fixed-Point arithmetic is necessary for such devices. In this study, a new method to reduce rounding errors is introduced, as well as optimizing value scaling, and the generation of F0 trajec-tory is discussed. The experimental results indicated that RMSE in a logarithmic scale of F0 can be reduced down to approximately 0.04 semitones (1 semitone = 1/12 octaves) by the proposed method even where a 2-bit margin was arranged to avoid calculation overflow. An extension for trajectories considering the global variance (GV) us-ing the basic program for trajectories without consideration of GV is also introduced. The extension method reduces required iteration counts to 5 for 0.05-semitone RMSE comparable to the converged results of the conventional method. Index Terms — HMM-based speech synthesis, fixed-Point arith-metic, embedded devices, global variance 1
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accurate parameter generation using fixed Point arithmetic for embedded hmm based speech synthesizers
International Conference on Acoustics Speech and Signal Processing, 2011Co-Authors: Nobuyuki Nishizawa, Tsuneo KatoAbstract:Parameter trajectory generation for HMM-based speech synthesis is practically achieved using only fixed-Point arithmetic with 32-bit integers. Since processors for embedded devices often provide no hardware-based Floating-Point Number processor, a speech synthesizer using only fixed-Point arithmetic is necessary for such devices. In this study, a new method to reduce rounding errors is introduced, as well as optimizing value scaling, and the generation of F 0 trajectory is discussed. The experimental results indicated that RMSE in a logarithmic scale of F 0 can be reduced down to approximately 0.04 semitones (1 semitone = 1/12 octaves) by the proposed method even where a 2-bit margin was arranged to avoid calculation overflow. An extension for trajectories considering the global variance (GV) using the basic program for trajectories without consideration of GV is also introduced. The extension method reduces required iteration counts to 5 for 0.05-semitone RMSE comparable to the converged results of the conventional method.
Higham, Nicholas J. - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Rounding and its Probabilistic Backward Error Analysis
2020Co-Authors: Connolly, Michael P., Higham, Nicholas J., Mary TheoAbstract:Stochastic rounding rounds a real Number to the next larger or smaller Floating-Point Number with probabilities $1$ minus the relative distances to those Numbers. It is gaining attention in deep learning because it can increase the success of low precision computations. We compare basic properties of stochastic rounding with those for round to nearest, finding properties in common as well as significant differences. We prove that for stochastic rounding the rounding errors are mean independent random variables with zero mean. We derive a new version of our probabilistic error analysis theorem from [{\em SIAM J. Sci. Comput.}, 41 (2019), pp.\ A2815--A2835], weakening the assumption of independence of the random variables to mean independence. These results imply that for a wide range of linear algebra computations the backward error for stochastic rounding is unconditionally bounded by a multiple of $\sqrt{n}\mkern1muu$ to first order, with a certain probability, where $n$ is the problem size and $u$ is the unit roundoff. This is the first scenario where the rule of thumb that one can replace $nu$ by $\sqrt{n}\mkern1muu$ in a rounding error bound has been shown to hold without any additional assumptions on the rounding errors. We also explain how stochastic rounding avoids the phenomenon of stagnation in sums, whereby small addends are obliterated by round to nearest when they are too small relative to the sum
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Stochastic Rounding and its Probabilistic Backward Error Analysis
2020Co-Authors: Connolly, Michael P., Higham, Nicholas J., Mary TheoAbstract:Stochastic rounding rounds a real Number to the next larger or smaller Floating-Point Number with probabilities $1$ minus the relative distances to those Numbers. % It has a larger worst-case error than round to nearest % but has useful statistical properties. It is gaining attention in deep learning because it can improve the accuracy of the computations. We compare basic properties of stochastic rounding with those for round to nearest, finding properties in common as well as significant differences. We prove that for stochastic rounding the rounding errors are mean independent random variables with zero mean. We derive a new version of our probabilistic error analysis theorem from [{\em SIAM J. Sci. Comput.}, 41 (2019), pp.\ A2815--A2835], weakening the assumption of independence of the random variables to mean independence. These results imply that for a wide range of linear algebra computations the backward error for stochastic rounding is unconditionally bounded by a multiple of $\sqrt{n}u$ to first order, with a certain probability, where $n$ is the problem size and $u$ is the unit roundoff. This is the first scenario where the rule of thumb that one can replace $nu$ by $\sqrt{n}u$ in a rounding error bound has been shown to hold without any additional assumptions on the rounding errors. We also explain how stochastic rounding avoids the phenomenon of stagnation in sums, whereby small addends are obliterated by round to nearest when they are too small relative to the sum
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Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers
Wiley, 2019Co-Authors: Anzt Hartwig, Dongarra Jack, Flegar Goran, Higham, Nicholas J., Quintana-orti, Enrique S.Abstract:This is the pre-peer reviewed version of the following article: Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers, which has been published in final form at https://doi.org/10.1002/cpe.4460. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block‐Jacobi preconditioner in different precision formats (half, single, or double). This specialized preconditioner can then be combined with any Krylov subspace method for the solution of sparse linear systems to perform all arithmetic in double precision. We assess the effects of the adaptive precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver. A preconditioned conjugate gradient method is, in general, a memory bandwidth‐bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's data in memory. Given this observation, we propose a model that quantifies the time and energy savings of our approach based on the assumption that these two costs depend linearly on the bit length of a Floating Point Number. Furthermore, we use a Number of test problems from the SuiteSparse matrix collection to estimate the potential benefits of the adaptive block‐Jacobi preconditioning scheme
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Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers
'Wiley', 2019Co-Authors: Anzt Hartwig, Dongarra Jack, Flegar Goran, Higham, Nicholas J., Quintana Ortí, Enrique SalvadorAbstract:This is the peer reviewed version of the following article: Anzt, H, Dongarra, J, Flegar, G, Higham, NJ, Quintana-Ortí, ES. Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers. Concurrency Computat Pract Exper. 2019; 31:e4460, which has been published in final form at https://doi.org/10.1002/cpe.4460. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block-Jacobi preconditioner in different precision formats (half, single, or double). This specialized preconditioner can then be combined with any Krylov subspace method for the solution of sparse linear systems to perform all arithmetic in double precision. We assess the effects of the adaptive precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver. A preconditioned conjugate gradient method is, in general, a memory bandwidth-bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's data in memory. Given this observation, we propose a model that quantifies the time and energy savings of our approach based on the assumption that these two costs depend linearly on the bit length of a Floating Point Number. Furthermore, we use a Number of test problems from the SuiteSparse matrix collection to estimate the potential benefits of the adaptive block-Jacobi preconditioning scheme.Impuls und Vernetzungsfond of the Helmholtz Association, Grant/Award Number: VH-NG-1241; MINECO and FEDER, Grant/Award Number: TIN2014-53495-R; H2020 EU FETHPC Project, Grant/Award Number: 732631; MathWorks; Engineering and Physical Sciences Research Council, Grant/Award Number: EP/P020720/1; Exascale Computing Project, Grant/Award Number: 17-SC-20-SCAnzt, H.; Dongarra, J.; Flegar, G.; Higham, NJ.; Quintana Ortí, ES. (2019). Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers. Concurrency and Computation Practice and Experience. 31(6):1-12. https://doi.org/10.1002/cpe.4460S11231
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Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers
2017Co-Authors: Anzt Hartwig, Dongarra Jack, Flegar Goran, Higham, Nicholas J., Quintana-orti, Enrique S.Abstract:We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block Jacobi preconditioner in different precision formats (half, single, or double). This specialized preconditioner can then be combined with any Krylov subspace method for the solution of sparse linear systems to perform all arithmetic in double precision. We assess the effects of the adaptive-precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver. A preconditioned conjugate gradient method is, in general, a memory-bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's data in memory. Given this observation, we propose a model that quantifies the time and energy savings of our approach based on the assumption that these two costs depend linearly on the bit length of a Floating Point Number. Furthermore, we use a Number of test problems from the SuiteSparse matrix collection to estimate the potential benefits of the adaptive block-Jacobi preconditioning scheme
Chihyueh Wang - One of the best experts on this subject based on the ideXlab platform.
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arithmetic operations beyond Floating Point Number precision
Computational Science and Engineering, 2011Co-Authors: Chihyueh Wang, Chenyang Yin, Hongyu Chen, Yungko ChenAbstract:In basic computational physics classes, students often raise the question of how to compute a Number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilised in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the approach of calculating the exact value of a large Number beyond the Floating Point Number precision, using the basic scientific programming language Fortran. The basic concept is to utilise arrays to decompose the Number and allocate finite memory. Examples of the successive multiplication of even Number and the multiplication and division of two overflowing floats are presented. The multiple precision schemes have been applied to hardware and firmware design for digital signal processing (DSP) systems, and is gaining importance to scientific computing. Such basic arithmetic operations can be integrated to solve advanced mathematical problems to almost arbitrarily-high precision that is limited by the memory of the host machine.
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arithmetic operations beyond Floating Point Number precision
arXiv: Computational Physics, 2010Co-Authors: Chihyueh Wang, Chenyang Yin, Hongyu Chen, Yungko ChenAbstract:In basic computational physics classes, students often raise the question of how to compute a Number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the approach of calculating the exact value of a large Number beyond the Floating Point Number precision, using the basic scientific programming language Fortran. The basic concept is to utilize arrays to decompose the Number and allocate finite memory. Examples of the successive multiplication of even Number and the multiplication and division of two overflowing floats are presented. The multiple precision scheme has been applied to hardware and firmware design for digital signal processing (DSP) systems, and is gaining importance to scientific computing. Such basic arithmetic operations can be integrated to solve advanced mathematical problems to almost arbitrarily-high precision that is limited by the memory of the host machine.