Author: [email protected]
Date: 29-Jan-2016
A template number class for estimating the floating point rounding errors introduced in operations
Replace all variables with
float -> Floatdouble -> Double
The code will double all operations once in the type used (float/double) and once in "long double" precision. At any moment you can inspect the error of the operation
e.g.
#include <iostream>
#include <fperror.h>
int main(int, char**)
{
Float a = 100.00001f;
Float b = 100.0f;
// The following two are equivalent
Float c = a*a - b*b; // - introduces a catastrophic cancellation
Float d = (a+b)*(a-b); // +/- introduces a benign cancellation
c.dump(std::cout,"c=") << std::endl;
d.dump(std::cout,"d=") << std::endl;
return 0;
}
Compile and run:
$ make test
g++ -o test test.cc -Wall -I.. -O3
$ ./test
c=f:0.001953125 r:0.0015258789644576609134674072265625 e:0.000427246036
d=f:0.00152587890625 r:0.0015258789644576609134674072265625 e:-5.82076609e-11
It is visible that the error introduced by the first operation is dramatic compared to the second.