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#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include <float.h>
#include <stdbool.h>
#define EPS 2*DBL_EPSILON
typedef struct {double v; double e;} double_error;
double_error int_to_valuetype(int i){
double_error de;
de.v = (double) i;
de.e = EPS*abs(i);
return de;
}
double_error int_to_exptype(double d){
double_error de;
de.v = d;
de.e = EPS*fabs(d) + DBL_MIN;
return de;
}
bool to_string(char* s, double_error de){
sprintf(s,"%f… +/- %6.1e",de.v,de.e);
return true;
}
double_error sum(double_error de1, double_error de2){
double_error de;
de.v = de1.v + de2.v;
de.e = de1.e + de2.e + ( fabs(de1.v) + fabs(de2.v) + de1.e + de2.e )*EPS + DBL_MIN;
return de;
}
double_error difference(double_error de1, double_error de2){
double_error de2m;
de2m.v = -de2.v;
de2m.e = de2.e;
return sum(de1,de2m);
}
bool is_greater_certainly(double_error de1, double_error de2){
return de1.v-de1.e > de2.v+de2.e + EPS*(fabs(de1.v)+fabs(de1.e)+fabs(de2.v)+fabs(de2.e)) + DBL_MIN;
}
bool is_greater_possibly(double_error de1, double_error de2){
return de1.v+de1.e + EPS*(fabs(de1.v)+fabs(de1.e)+fabs(de2.v)+fabs(de2.e)) + DBL_MIN > de2.v-de2.e;
}
double_error maximum(double_error de1, double_error de2){
if(is_greater_certainly(de1,de2)) return de1;
else if(is_greater_certainly(de2,de1)) return de2;
else{
double_error de;
if( de1.v >= de2.v ) de.v = de1.v;
else de.v = de2.v;
if( de1.e >= de2.e ) de.e = de1.e;
else de.e = de2.e;
return de;
}
}
double_error product(double_error de1, double_error de2){
double_error de;
de.v = de1.v * de2.v;
double p12 = fabs(de1.v)*de2.e*(1+EPS) + DBL_MIN;
double p21 = fabs(de2.v)*de1.e*(1+EPS) + DBL_MIN;
double p22 = de1.e*de2.e*(1+EPS) + DBL_MIN;
double s = (p12 + p21 + p22)*(1+2*EPS);
de.e = s + ( fabs(de.v) + s )*EPS + DBL_MIN;
return de;
}
double_error ratio(double_error de1, double_error de2){
double_error de2i;
de2i.v = 1/de2.v;
if(de2.e > fabs(de2.v)/2) de2i.e = INFINITY;
else de2i.e = 2*de2.e/(de2.v*de2.v) + fabs(de2i.v)*EPS + DBL_MIN; //2* is extra margin in case de2.e is near de2.v/2
return product(de1,de2i);
}
double_error absolute(double_error de){
double_error dea;
dea.v = fabs(de.v);
dea.e = de.e;
return dea;
}
double_error power(double_error de, double_error p) {
double_error dep;
dep.v = pow(de.v,p.v);
double dmin = (de.v - de.e)*(1-EPS);
double dmax = (de.v + de.e)*(1+EPS);
double pmin = (p.v - p.e)*(1-EPS);
double pmax = (p.v + p.e)*(1+EPS);
double rmin,rmax;
if(dmin >= 1){
rmin = pow(dmin,pmin);
rmax = pow(dmax,pmax);
} else if(dmax >= 1) {
rmin = pow(dmin,pmax);
rmax = pow(dmax,pmax);
} else {
rmin = pow(dmin,pmax);
rmax = pow(dmax,pmin);
}
if(dmin >= 0) dep.e = rmax-rmin + 2*EPS*rmax;
else dep.e = (1+2*EPS)*rmax;
return dep;
}
double to_double(double_error de){ return de.v; }
bool root_to_string(char* s, double_error de, double_error p){
double_error de1p = power(de,ratio(int_to_valuetype(1),p));
to_string(s,de1p);
return true;
}
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