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Floating-Point Computations with Very-High-Speed Integrated Circuit Hardware Description Language and Xilinx System Generator (SysGen) Tools
Published in A. Arockia Bazil Raj, FPGA-Based Embedded System Developer's Guide, 2018
The double-precision floating-point number system provides more digits to the right side of the binary point than a single-precision number. The term double-precision is something of a misnomer because the precision is not really double; however, the double-precision number system uses twice as many bits as the single-precision floating-point number system. For example, the single-precision floating-point number system requires 32 bits and its double, that is, 64 bits, is required for the double-precision floating-point number system. The additional 32 bits increase not only the precision but also the range of magnitudes that can be covered. Double-precision floating-point format is a computer number format that occupies 8 bytes, that is, 64 bits, in computer memory and represents a wide and dynamic range of values by using a floating point [127–131].
Nonlinear Equations
Published in Jeffery J. Leader, Numerical Analysis and Scientific Computation, 2022
Note that single precision and double precision are defined by the machine, not the programming language. This means, for example, that the same computation performed on two different machines could give two different answers due to differences in how numbers are represented and in how arithmetic operations are implemented. This issue of portability of software has been a continual source of frustration for those who write and test numerical programs. Fortunately most computers use the same IEEE 754 compliant arithmetic systems. While there can still be slight variations even between implementations of IEEE standard arithmetic as the standard does not cover all possibilities, you are much less likely to encounter such issues nowadays.
Preliminaries
Published in Subrata Ray, Fortran 2018 with Parallel Programming, 2019
Double precision constants are more precise than the corresponding single precision values. Such a constant is expressed in scientific notation. To indicate ten to the power for double precision constants, ‘D’ or ‘d’ is used; π, correct up to 15 decimal places, is written as 3.141592653589793d0.
Accelerated parallel computation of field quantities for the boundary element method applied to stress analysis using multi-core CPUs, GPUs and FPGAs
Published in Cogent Engineering, 2018
Junjie Gu, Attila Michael Zsaki
Accuracy is of importance for numerical computation in engineering and science. Many numerical models and methods, like solution of a system of equations, are sensitive to round-off errors or the number of significant digits in input parameters. Thus, most of these methods generally employ double-precision computation. Even though the accuracy in computation is important, one has to consider the quality of input parameters. For example, in geomechanics, most input parameters, like rock mass properties, are seldom know within 20–30% of their true mean (Starfield & Cundall, 1988), presenting an opportunity for accepting “less-than-accurate” computation. To investigate the potential loss of accuracy and perhaps speed gains, Algorithms 1–4 were modified to use double-precision constants and variables. Also, appropriate arithmetic functions (e.g. going from fabsf() to fabs()) were used to avoid unnecessary casts resulting in speed reduction. All test cases were re-run using double precision for both the serial algorithm and the hardware-accelerated ones, where double-precision computation was possible.