Abstract
In a few places in the mathcw library, we need to work with an intermediate precision having at least twice as many digits as storage precision. In almost all historical floating-point architectures, for single-precision computation, the double-precision format satisfies that requirement (see Table H.1 on page 948). However, for double-precision work, higher precision may be unavailable, as is the case in many programming languages, or it may be insufficiently precise, such as the IEEE 754 80-bit format compared to the 64-bit format.
The computation of a*b - c*d in Java will produce the same result everywhere, but it may be the same very wrong result everywhere!
— Fred G. Gustavson, José E. Moreira and Robert F. Enenkel (1999).
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Beebe, N.H.F. (2017). Pair-precision arithmetic. In: The Mathematical-Function Computation Handbook. Springer, Cham. https://doi.org/10.1007/978-3-319-64110-2_13
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DOI: https://doi.org/10.1007/978-3-319-64110-2_13
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