In numerical computation,the inherent rounding errors of floating-point operations often affect the precision of mathematical functions.The use of high-precision achieved through software-dependent simulation for prec...In numerical computation,the inherent rounding errors of floating-point operations often affect the precision of mathematical functions.The use of high-precision achieved through software-dependent simulation for precision compensation may result in significant performance overhead.Error-free transformations(EFT)technology,based on hardware-supported precision to approximate high-precision implementation,can effectively balance accuracy and performance.However,enhancing the precision of mathematical functions is a very complex and challenging issue.There is a lack of relevant research on when EFT technology can be used to improve the precision of mathematical functions,what effects can be achieved,and what impact it may have on program performance.In this work,we present an empirical study on the applicability and effectiveness of using error-free transformations(EFT)in floating-point computation to assess their potential and limitations in improving precision over mathematical functions.We select 42 mathematical functions from the GNU Scientific Library(GSL),known for significant rounding errors.We evaluate the EFT techniques from three aspects:the applicability of EFT for different mathematical functions(especially at the maximum error point and its vicinity),the precision improvement of EFT in input domains near the error-triggering input,and the performance of EFT compared with the high-precision versions.Experimental results show that EFT has advantages in reducing floating-point errors across 27 functions.Furthermore,while improving the accuracy of mathematical functions within specific input ranges near the maximum error input,EFT achieves a 10.92×speedup compared to long double precision and a 2426.3×speedup compared to mpmath.These findings suggest that EFT achieves computational accuracy to the real results with much lower overhead than conventional high-precision calculations,which makes EFT a promising technology for balancing accuracy and performance in high performance computing.展开更多
From the process of sedimentation the mathematical relationships among deposition Volume and powder properties as well as sedimentation parameters were deduced. Based on the formula a mathematical model was set up and...From the process of sedimentation the mathematical relationships among deposition Volume and powder properties as well as sedimentation parameters were deduced. Based on the formula a mathematical model was set up and simulated through the computer. At last the validity of mathematical model was supported by the representative experiment on Ti-Mo system FGM prepared by co-sedimentation.展开更多
In this note, we estimate the maximum amplitude for the Solar Cycle 25. We use the curvature technique presented for earlier cycles by Verdes and coworkers. We further extrapolate the location of the solar maximum num...In this note, we estimate the maximum amplitude for the Solar Cycle 25. We use the curvature technique presented for earlier cycles by Verdes and coworkers. We further extrapolate the location of the solar maximum number of Sunspots, of which the prediction made is about 115 in the year 2025 and identify the arrival to the minimum in the year 2031, forecasting the main characteristics for the current Solar Cycle 25 and list a short comparison with a few other predictions.展开更多
The flow past a circular cylinder and airfoil with varying mathematical roughness function are numerically simulated. A new model about blowing and suction is constructed by using the concept of mathematical roughness...The flow past a circular cylinder and airfoil with varying mathematical roughness function are numerically simulated. A new model about blowing and suction is constructed by using the concept of mathematical roughness function. The flow field and the drag are investigated through this new model. By the numerical study about bluff body, some conclusions are drawn to reduce the drag.展开更多
基金supported by the National Key Research and Development Program of China under Grant No.2023YFB3001601.
文摘In numerical computation,the inherent rounding errors of floating-point operations often affect the precision of mathematical functions.The use of high-precision achieved through software-dependent simulation for precision compensation may result in significant performance overhead.Error-free transformations(EFT)technology,based on hardware-supported precision to approximate high-precision implementation,can effectively balance accuracy and performance.However,enhancing the precision of mathematical functions is a very complex and challenging issue.There is a lack of relevant research on when EFT technology can be used to improve the precision of mathematical functions,what effects can be achieved,and what impact it may have on program performance.In this work,we present an empirical study on the applicability and effectiveness of using error-free transformations(EFT)in floating-point computation to assess their potential and limitations in improving precision over mathematical functions.We select 42 mathematical functions from the GNU Scientific Library(GSL),known for significant rounding errors.We evaluate the EFT techniques from three aspects:the applicability of EFT for different mathematical functions(especially at the maximum error point and its vicinity),the precision improvement of EFT in input domains near the error-triggering input,and the performance of EFT compared with the high-precision versions.Experimental results show that EFT has advantages in reducing floating-point errors across 27 functions.Furthermore,while improving the accuracy of mathematical functions within specific input ranges near the maximum error input,EFT achieves a 10.92×speedup compared to long double precision and a 2426.3×speedup compared to mpmath.These findings suggest that EFT achieves computational accuracy to the real results with much lower overhead than conventional high-precision calculations,which makes EFT a promising technology for balancing accuracy and performance in high performance computing.
文摘From the process of sedimentation the mathematical relationships among deposition Volume and powder properties as well as sedimentation parameters were deduced. Based on the formula a mathematical model was set up and simulated through the computer. At last the validity of mathematical model was supported by the representative experiment on Ti-Mo system FGM prepared by co-sedimentation.
文摘In this note, we estimate the maximum amplitude for the Solar Cycle 25. We use the curvature technique presented for earlier cycles by Verdes and coworkers. We further extrapolate the location of the solar maximum number of Sunspots, of which the prediction made is about 115 in the year 2025 and identify the arrival to the minimum in the year 2031, forecasting the main characteristics for the current Solar Cycle 25 and list a short comparison with a few other predictions.
文摘The flow past a circular cylinder and airfoil with varying mathematical roughness function are numerically simulated. A new model about blowing and suction is constructed by using the concept of mathematical roughness function. The flow field and the drag are investigated through this new model. By the numerical study about bluff body, some conclusions are drawn to reduce the drag.
