Glauco Masotti - Academia.edu (original) (raw)

Papers by Glauco Masotti

Research paper thumbnail of Floating-point numbers with error estimates

Computer Aided Design, Sep 1, 1993

The study addresses the problem of precision in floating-point computations. A method for estimat... more The study addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill conditioned problems to be detected. A hardware implementation of the method by means of a special floatingpoint processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.

Research paper thumbnail of A multi-strategy optimizer for arbitrary generic functions in multidimensional space

arXiv (Cornell University), Feb 27, 2017

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points... more An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior, irregular and noisy, with steep variations and exhibiting a lot of local sub-optimal points. The complications of having to deal with a finite domain, as this is usually the case, are taken into account. The method is composed of a number of cascaded stages, each employing a different strategy to improve over the results of the previous stage. Many ideas and concepts employed in known methods are re-elaborated in a coherent scheme, plus several new ideas are introduced. Line minimization plays an important role in most stages, for this purpose a new and powerful algorithm for line minimization is used as well.

Research paper thumbnail of An algorithm for minimization of arbitrary generic functions in one dimension over a finite domain

arXiv (Cornell University), Feb 27, 2017

A new algorithm for one-dimensional minimization is described in detail and the results of some t... more A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be applied in "difficult" cases, that is when the function is highly irregular and has multiple sub-optimal local minima. The algorithm uses quadratic or cubic interpolation and subdivision of intervals in golden ratio as a last resort. It improves over Brent's method and similar ones in several aspects. It manages multiple local minima, takes into account the complications of having to deal with a finite domain, rather than an unlimited one, and has a slightly faster convergence in most cases.

Research paper thumbnail of Floating-Point Numbers with Error Estimates (revised)

arXiv (Cornell University), Jan 28, 2012

The original work [25] is here reconsidered, so many years after. The old text has been revised, ... more The original work [25] is here reconsidered, so many years after. The old text has been revised, plus several considerations have been added, in order to clarify some controversial aspects of the work, and to envision possible developments. A section has been added, to review the effects of the original paper. The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic idea consists of representing FP numbers by means of a data structure collecting value and estimated error information. Under certain constraints, the estimate of the absolute error is accurate and has a compact statistical distribution. By monitoring the estimated relative error during a computation (an ad-hoc definition of relative error has been used), the validity of results can be ensured. The error estimate enables the implementation of robust algorithms, and the detection of ill-conditioned problems. A dynamic extension of number precision, under the control of error estimates, is advocated, in order to compute results within given error bounds. A reduced time penalty could be achieved by a specialized FP processor. The realization of a hardwired processor incorporating the method, with current technology, should not be anymore a problem and would make the practical adoption of the method feasible for most applications. Index terms-floating-point computations, floating-point processor, floating-point errors, error estimation, numerical accuracy, ill-conditioned problems, computer arithmetic, dynamic precision extension. Preamble What has brought me to revise my old paper [25], more than 18 years after, and publish this document? A part some casual circumstances, the main reasons are perhaps the conviction that this is still a good idea, and also my sufferance in seeing my past work so much neglected or misunderstood in all these years. This document is thus also a prayer to experts in the field and to hardware architects to reconsider this work for practical implementation.

Research paper thumbnail of A multi-strategy optimizer for arbitrary generic functions in multidimensional space

Cornell University - arXiv, Feb 27, 2017

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points... more An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior, irregular and noisy, with steep variations and exhibiting a lot of local sub-optimal points. The complications of having to deal with a finite domain, as this is usually the case, are taken into account. The method is composed of a number of cascaded stages, each employing a different strategy to improve over the results of the previous stage. Many ideas and concepts employed in known methods are re-elaborated in a coherent scheme, plus several new ideas are introduced. Line minimization plays an important role in most stages, for this purpose a new and powerful algorithm for line minimization is used as well.

Research paper thumbnail of An algorithm for minimization of arbitrary generic functions in one dimension over a finite domain

arXiv: Optimization and Control, 2017

A new algorithm for one-dimensional minimization is described in detail and the results of some t... more A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be applied in "difficult" cases, that is when the function is highly irregular and has multiple sub-optimal local minima. The algorithm uses quadratic or cubic interpolation and subdivision of intervals in golden ratio as a last resort. It improves over Brent's method and similar ones in several aspects. It manages multiple local minima, takes into account the complications of having to deal with a finite domain, rather than an unlimited one, and has a slightly faster convergence in most cases.

Research paper thumbnail of Floating-Point Numbers with Error Estimates (revised)

ArXiv, 2012

The study addresses the problem of precision in floating-point (FP) computations. A method for es... more The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic idea consists of representing FP numbers by means of a data structure collecting value and estimated error information. Under certain constraints, the estimate of the absolute error is accurate and has a compact statistical distribution. By monitoring the estimated relative error during a computation (an ad-hoc definition of relative error has been used), the validity of results can be ensured. The error estimate enables the implementation of robust algorithms, and the detection of ill-conditioned problems. A dynamic extension of number precision, under the control of error estimates, is advocated, in order to compute results within given error bounds. A reduced time penalty could be achieved by a specialized FP processor. The realization of a har...

Research paper thumbnail of Automatic production of NC code for machining form features in generic parts

Computing & Control Engineering Journal, 1992

ABSTRACT A prototype system for CAPP (computer-aided process planning) and the automatic generati... more ABSTRACT A prototype system for CAPP (computer-aided process planning) and the automatic generation of NC code for machining form features in generic parts is described. By means of this system, it is possible to program and simulate all the operations involved in the production of a part. The planning of the production process starts with the solid model of the final part, the solid model of the blank, as well as models of the available machine tools. It is assumed that the part has been modelled using a design-by-feature approach. This has two advantages: it makes the design easier, and features are automatically tagged for recognition at the process planning stage. Features are available in an archive and are stored in parametric form. After having specified the setup of the raw or semi-machined part, the machinable features are selected. A number of possible machining processes are associated with each feature. Machining processes are stored in a knowledge base organised as a network. The most suitable process is selected, on the basis of available knowledge, or directly by the user. The system then determines the list of required tools, their optimal sequencing, and the transfer and working paths for each tool. Machining commands for tool operations are then generated

Research paper thumbnail of Floating-point numbers with error estimates

Computer-Aided Design, 1993

The study addresses the problem of precision in floating-point computations. A method for estimat... more The study addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill conditioned problems to be detected. A hardware implementation of the method by means of a special floatingpoint processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.

Research paper thumbnail of Floating-point numbers with error estimates

Computer Aided Design, Sep 1, 1993

The study addresses the problem of precision in floating-point computations. A method for estimat... more The study addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill conditioned problems to be detected. A hardware implementation of the method by means of a special floatingpoint processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.

Research paper thumbnail of A multi-strategy optimizer for arbitrary generic functions in multidimensional space

arXiv (Cornell University), Feb 27, 2017

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points... more An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior, irregular and noisy, with steep variations and exhibiting a lot of local sub-optimal points. The complications of having to deal with a finite domain, as this is usually the case, are taken into account. The method is composed of a number of cascaded stages, each employing a different strategy to improve over the results of the previous stage. Many ideas and concepts employed in known methods are re-elaborated in a coherent scheme, plus several new ideas are introduced. Line minimization plays an important role in most stages, for this purpose a new and powerful algorithm for line minimization is used as well.

Research paper thumbnail of An algorithm for minimization of arbitrary generic functions in one dimension over a finite domain

arXiv (Cornell University), Feb 27, 2017

A new algorithm for one-dimensional minimization is described in detail and the results of some t... more A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be applied in "difficult" cases, that is when the function is highly irregular and has multiple sub-optimal local minima. The algorithm uses quadratic or cubic interpolation and subdivision of intervals in golden ratio as a last resort. It improves over Brent's method and similar ones in several aspects. It manages multiple local minima, takes into account the complications of having to deal with a finite domain, rather than an unlimited one, and has a slightly faster convergence in most cases.

Research paper thumbnail of Floating-Point Numbers with Error Estimates (revised)

arXiv (Cornell University), Jan 28, 2012

The original work [25] is here reconsidered, so many years after. The old text has been revised, ... more The original work [25] is here reconsidered, so many years after. The old text has been revised, plus several considerations have been added, in order to clarify some controversial aspects of the work, and to envision possible developments. A section has been added, to review the effects of the original paper. The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic idea consists of representing FP numbers by means of a data structure collecting value and estimated error information. Under certain constraints, the estimate of the absolute error is accurate and has a compact statistical distribution. By monitoring the estimated relative error during a computation (an ad-hoc definition of relative error has been used), the validity of results can be ensured. The error estimate enables the implementation of robust algorithms, and the detection of ill-conditioned problems. A dynamic extension of number precision, under the control of error estimates, is advocated, in order to compute results within given error bounds. A reduced time penalty could be achieved by a specialized FP processor. The realization of a hardwired processor incorporating the method, with current technology, should not be anymore a problem and would make the practical adoption of the method feasible for most applications. Index terms-floating-point computations, floating-point processor, floating-point errors, error estimation, numerical accuracy, ill-conditioned problems, computer arithmetic, dynamic precision extension. Preamble What has brought me to revise my old paper [25], more than 18 years after, and publish this document? A part some casual circumstances, the main reasons are perhaps the conviction that this is still a good idea, and also my sufferance in seeing my past work so much neglected or misunderstood in all these years. This document is thus also a prayer to experts in the field and to hardware architects to reconsider this work for practical implementation.

Research paper thumbnail of A multi-strategy optimizer for arbitrary generic functions in multidimensional space

Cornell University - arXiv, Feb 27, 2017

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points... more An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior, irregular and noisy, with steep variations and exhibiting a lot of local sub-optimal points. The complications of having to deal with a finite domain, as this is usually the case, are taken into account. The method is composed of a number of cascaded stages, each employing a different strategy to improve over the results of the previous stage. Many ideas and concepts employed in known methods are re-elaborated in a coherent scheme, plus several new ideas are introduced. Line minimization plays an important role in most stages, for this purpose a new and powerful algorithm for line minimization is used as well.

Research paper thumbnail of An algorithm for minimization of arbitrary generic functions in one dimension over a finite domain

arXiv: Optimization and Control, 2017

A new algorithm for one-dimensional minimization is described in detail and the results of some t... more A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be applied in "difficult" cases, that is when the function is highly irregular and has multiple sub-optimal local minima. The algorithm uses quadratic or cubic interpolation and subdivision of intervals in golden ratio as a last resort. It improves over Brent's method and similar ones in several aspects. It manages multiple local minima, takes into account the complications of having to deal with a finite domain, rather than an unlimited one, and has a slightly faster convergence in most cases.

Research paper thumbnail of Floating-Point Numbers with Error Estimates (revised)

ArXiv, 2012

The study addresses the problem of precision in floating-point (FP) computations. A method for es... more The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic idea consists of representing FP numbers by means of a data structure collecting value and estimated error information. Under certain constraints, the estimate of the absolute error is accurate and has a compact statistical distribution. By monitoring the estimated relative error during a computation (an ad-hoc definition of relative error has been used), the validity of results can be ensured. The error estimate enables the implementation of robust algorithms, and the detection of ill-conditioned problems. A dynamic extension of number precision, under the control of error estimates, is advocated, in order to compute results within given error bounds. A reduced time penalty could be achieved by a specialized FP processor. The realization of a har...

Research paper thumbnail of Automatic production of NC code for machining form features in generic parts

Computing & Control Engineering Journal, 1992

ABSTRACT A prototype system for CAPP (computer-aided process planning) and the automatic generati... more ABSTRACT A prototype system for CAPP (computer-aided process planning) and the automatic generation of NC code for machining form features in generic parts is described. By means of this system, it is possible to program and simulate all the operations involved in the production of a part. The planning of the production process starts with the solid model of the final part, the solid model of the blank, as well as models of the available machine tools. It is assumed that the part has been modelled using a design-by-feature approach. This has two advantages: it makes the design easier, and features are automatically tagged for recognition at the process planning stage. Features are available in an archive and are stored in parametric form. After having specified the setup of the raw or semi-machined part, the machinable features are selected. A number of possible machining processes are associated with each feature. Machining processes are stored in a knowledge base organised as a network. The most suitable process is selected, on the basis of available knowledge, or directly by the user. The system then determines the list of required tools, their optimal sequencing, and the transfer and working paths for each tool. Machining commands for tool operations are then generated

Research paper thumbnail of Floating-point numbers with error estimates

Computer-Aided Design, 1993

The study addresses the problem of precision in floating-point computations. A method for estimat... more The study addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill conditioned problems to be detected. A hardware implementation of the method by means of a special floatingpoint processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.