| Mathematical constants, some convenient functions wrappers and type traits to support arbitrary-precision arithmetic. |
| Bit manipulations for testing whether an integer is a power of two, for computing the exponent of an integer that is a power of two, for determining the leading and trailing 1-valued bits of an integer, and for rounding an integer up or down to a power of two. |
| A template class IEEEBinary encapsules some information about floating-point numbers in the IEEE 754-2008 Standard for Floating-Point Arithmetic. IEEEBinary32 and IEEEBinary64 are explicitly instantiated. IEEEBinary16 is an implementation of 16-bit floating-point arithmetic. |
| In the acronyms for the files and classes, BS stands for "binary scientific". The template type UIntegerType is either UIntegerAP32 for arbitrary precision arithmetic using std::vector storage or UIntegerFP32<N> for user-selected fixed-precision arithmetic using std::array storage. BSNumber (Binary Scientific Number) is an implementation of arbitrary precision floating-point arithmetic that supports addition, subtraction, and multiplication. If you have an algorithm that requires division, use BSRational. The QFNumber class encapsulates quadratic-field arithmetic. The APConversion class encapsulates several estimation functions for quadratic-field numbers and conversions from arbitrary-precision numbers to floating-point numbers. Much of this code is expanded in the Geometric Tools Library that will ship in the first half of 2020. It is based on my forthcoming book Robust and Error-Free Geometric Computing. |
| Support for interval arithmetic. The FPInterval file uses std::fesetround and std::fegetround (found in <cfenv>) to change the rounding mode of the floating-point hardware. Unfortunately, GCC does not support this via C++ (you can do it with assembly instructions). Microsoft Visual Studio support this, but with a pragma that is not part of the C++ specifications. Moreover, the pragmas must occur at file scope (not function-block scope). These issues are problematic when trying to provide template classes with template parameters float or double in stand-alone header files. Instead, consider using the SWInterval file that relies on std::nextafter and produces slightly larger intervals. The APInterval file provides interval arithmetic for arbitrary-precision numbers. |
| Jonathan Richard Shewchuk's web page with a link to his paper on adaptive precision floating-point arithmetic and fast robust geometric predicates. Links are also provided to source code and related resources. |