Abstract
The previous chapters have given an overview of interesting properties and algorithms that can be built on an IEEE 754-compliant floating-point arithmetic. In this chapter, we discuss the practical issues encountered when trying to implement such algorithms in actual computers using actual programming languages. In particular, we discuss the relationship between standard compliance, portability, accuracy, and performance. This chapter is useful to programmers wishing to obtain a standard-compliant behavior from their programs, but it is also useful for understanding how performance may be improved by relaxing standard compliance and also what traps one may fall into.
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Notes
- 1.
This requirement was introduced in C89 and kept in the subsequent C99 and C11 standards. The original Kernighan and Ritchie C [333] allowed regrouping, even with explicit parentheses in expressions.
- 2.
The International Standard Organization and the International Electrotechnical Commission are two sister international organizations whose members are, respectively, 163 national standard bodies and 83 national committees.
- 3.
- 4.
VFP stands for “Vector Floating-Point” but the vector mode was removed shortly after its introduction.
- 5.
See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=61399 for instance.
- 6.
The SPARC architecture has instructions for quadruple precision, but in practice, current processors generate traps to compute the results in software.
- 7.
Details on https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37845, fixed for GCC 4.9.
- 8.
The C11 standard still does not specify a power function with an integer type as the second argument.
- 9.
Note, however, that this formalization just comes from an interpretation of the ISO C standard, which is written in plain English. Before version 2.5, CompCert behaved differently from other compilers by not rejecting a lexically invalid program.
- 10.
When is_iec559 is true, the C++ standard mandates that infinities and NaNs are available.
- 11.
round_style is a constant member. Therefore, it may well be set to the default round_to_nearest style, even if the architecture allows us to change the rounding direction on the fly.
- 12.
For Python3: https://docs.python.org/3/reference/datamodel.html; For Python2: https://docs.python.org/2/reference/datamodel.html.
- 13.
- 14.
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Muller, JM. et al. (2018). Languages and Compilers. In: Handbook of Floating-Point Arithmetic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-76526-6_6
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