decimal.h File Reference

Decimal literal -> T, without a detour through double when T is exact. More...

#include <cctype>
#include <cstdlib>
#include <string>
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for decimal.h:

Go to the source code of this file.

Namespaces
namespace	line

Functions
Rational	line::rational_from_decimal (const std::string &s)
	The literal as an exact rational, num/10^k with no rounding.
template<class T>
T	line::num_from_decimal (const std::string &s)
	Parse a decimal literal into T.
template<>
Rational	line::num_from_decimal< Rational > (const std::string &s)
double	line::dbl_from_decimal (const std::string &s, double fallback)
	Parse a decimal literal as a plain double (multiplicities, populations, tolerances).

Detailed Description

Decimal literal -> T, without a detour through double when T is exact.

This is the boundary at which a model file becomes numbers, and it is the one place where "exact arithmetic" has to decide what it is exact ABOUT. A host demand written 0.01 in an .lqnx file denotes the rational 1/100. The double nearest to it is 0.01000000000000000020816681711721685...; routing that literal through num_traits<Rational>::from_double would make the exact backend compute, with no rounding at all, the answer to a model that is not the one on disk. So the exact backend parses the decimal digits directly into num/10^k, and the inexact backends keep strtod, which is what MATLAB's str2double and Java's Double.parseDouble also do.

The consequence to keep in mind when comparing the two runs: they are not two evaluations of one arithmetic problem, they are the exact solution of the declared model versus the floating-point solution of its double rounding. Their difference is bounded below by the input rounding, of order 1e-17 relative here, and any larger gap is accumulated error in the solver.

Definition in file decimal.h.