A very simple, header-only, implementation of pair arithmetic (see Faithfully Rounded Floating-point Computations). Destined to be used when a C++ program needs a local boost in accuracy but cannot easily be refactored to be more numerically stable.
To use this library, you just need to drop the PairArithmetic folder in your program.
We provide compensated numbers that can be cast from and to IEEE-754 types (such as float and double) in PairArithmetic/numbers.h and compensated complex numbers (to reduce casting needs) in PairArithmetic/complex.h.
#include "PairArithmetic/numbers.h"
using Pdouble = CompensatedNumber<double>;
const double x = 1e100;
const Pdouble y = 1.0;
// you can mix double and Pdouble in your computations
// the error will be compensated as long as one argument of the operations is a Pdouble
Pdouble z = x + y;
// and use in-place operators
z -= 1e100;
// cast back to double in order to get the compensated, improved-precision, result
const double z_corrected = static_cast<double>(z); // 1.0We do not implement the following operations:
- some constructors,
- boolean operations,
- the square root of a real number,
- some complex operations.
Feel free to request them (or submit a PR adding them), they should be fairly easy to implement.