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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <float.h>
#include <stdbool.h>
typedef unsigned long long num;
typedef struct {bool s; num n; num d;} rational;
num safe_sum(num n1, num n2){
if(n2 > ULLONG_MAX-n1){
printf("Sum overflow: Adding %llu and %llu\n",n1,n2);
exit(1);
}
else {
return n1+n2;
}
}
num safe_product(num n1, num n2){
if(n1 != 0 && n2 > ULLONG_MAX/n1){
printf("Product overflow: Multiplying %llu by %llu\n",n1,n2);
exit(1);
}
else {
return n1*n2;
}
}
rational int_to_valuetype(int i){
rational r;
r.d = 1;
r.n = abs(i);
if(i >= 0) { r.s=false; } else { r.s=true; }
return r;
}
unsigned int infinity_to_exptype(){ return UINT_MAX; }
bool exptype_is_infinite(num p){ return p == UINT_MAX; }
unsigned int int_to_exptype(unsigned int i){ return i; }
num gcd(num a, num b){
num c;
while (b) {
c = a % b;
a = b;
b = c;
}
return a;
}
rational cancel(rational r){
num a = gcd(r.n,r.d);
rational res = {r.s,r.n/a,r.d/a};
return res;
}
rational sum(rational r1, rational r2){
num a = gcd(r1.d,r2.d);
num r1da = r1.d/a;
num r2da = r2.d/a;
rational r;
r.d = safe_product(r1da,r2.d);
num n1 = safe_product(r1.n,r2da);
num n2 = safe_product(r2.n,r1da);
if(r1.s == r2.s){
r.n = safe_sum(n1,n2);
r.s = r1.s;
}
else {
if(n1 >= n2) {
r.n = n1 - n2;
r.s = r1.s;
}
else {
r.n = n2 - n1;
r.s = r2.s;
}
}
return cancel(r);
}
rational difference(rational r1, rational r2){
r2.s = !r2.s;
return sum(r1,r2);
}
bool is_greater_certainly(rational r1, rational r2){
rational diff = difference(r1,r2);
return !diff.s && diff.n > 0;
}
bool is_greater_possibly(rational r1, rational r2){
return is_greater_certainly(r1,r2);
}
rational maximum(rational r1, rational r2){
if(is_greater_certainly(r1,r2)) return r1;
else return r2;
}
rational product(rational r1, rational r2){
rational r;
rational s1 = {r1.s, r1.n, r2.d};
rational s2 = {r2.s, r2.n, r1.d};
rational t1 = cancel(s1);
rational t2 = cancel(s2);
r.s = t1.s^t2.s;
r.n = safe_product(t1.n,t2.n);
r.d = safe_product(t1.d,t2.d);
return cancel(r);
}
rational ratio(rational r1, rational r2){
rational r2i = {r2.s,r2.d,r2.n};
return product(r1,r2i);
}
rational absolute(rational r){
rational s = {false,r.n,r.d};
return s;
}
rational power(rational r, unsigned int p){
rational s = {0,1,1};
for(int i = 1; i<= p; i++){
s = product(r,s);
}
return s;
}
int exptype_to_string(char *s, unsigned int p){
if(exptype_is_infinite(p)) sprintf(s,"inf",p);
else sprintf(s,"%d",p);
return 0;
}
int exptype_to_latex(char *s, unsigned int p){
if(exptype_is_infinite(p)) sprintf(s,"\\infty",p);
else sprintf(s,"%d",p);
return 0;
}
double valuetype_to_double(rational r){
double i;
if(r.s) { i=-1.0; } else { i=1.0; }
return i*((double)r.n)/((double)r.d);
}
int valuetype_to_string(char* s, rational r){
if(r.d == 1) {
if(r.n == 0) sprintf(s,"0");
else if(r.s) sprintf(s,"-%lld",r.n);
else if(!r.s) sprintf(s,"%lld",r.n);
}
else{
double f = valuetype_to_double(r);
sprintf(s,"%llu / %llu = %f…",r.n,r.d,f);
}
return 0;
}
int valuetype_to_latex(char* s, rational r){
if(r.d == 1) {
if(r.n == 0) sprintf(s,"0");
else if(r.s) sprintf(s,"-%lld",r.n);
else if(!r.s) sprintf(s,"%lld",r.n);
}
else{
double f = valuetype_to_double(r);
sprintf(s,"\\frac{%llu}{%llu} = %4.3f\\ldots",r.n,r.d,f);
//sprintf(s,"\\frac{%llu}{%llu} = %3.2f\\ldots \\pm %1.0e",r.n,r.d,f,f*DBL_EPSILON);
}
return 0;
}
int root_to_string(char* s, rational r, unsigned int p){
if(exptype_is_infinite(p) || p == 1) valuetype_to_string(s,r);
else{
double f = pow(valuetype_to_double(r),1.0/p);
sprintf(s,"(%llu / %llu)^1/%i = %f…",r.n,r.d,p,f);
}
return 0;
}
int root_to_latex(char* s, rational r, unsigned int p){
if(exptype_is_infinite(p) || p == 1) valuetype_to_latex(s,r);
else{
double f = pow(valuetype_to_double(r),1.0/p);
sprintf(s,"\\bigl(\\frac{%llu}{%llu}\\bigr)^{\\frac1{%i}} = %4.3f\\ldots",r.n,r.d,p,f);
//sprintf(s,"\\bigl(\\frac{%llu}{%llu}\\bigr)^{\\frac1{%i}} = %3.2f\\ldots \\pm %1.0e",r.n,r.d,p,f,2*DBL_EPSILON*f);
}
return 0;
}
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