Why is there a different answer in the face and in the reverse?

Why when the sums are in the straight (value in variable)
s1
and reverse order (s2
Is the answer different?#include <stdlib.h> #include <stdio.h>
int main() {
float s1, s2;
long long int n;s1 = 0.; for (n = 1; n <= 100000000; n++) s1 += 1. / (n * n); s2 = 0.; for (n = 100000000; n >= 1; n) s2 += 1. / (n * n); printf("%.17lf\n", s1); printf("%.17lf\n\n", s2); system("pause"); return 0;
}

situation next (all as @avp) float is limited to the precision of a certain ring in the sign after the comma, so
1 + 10000000000000000000 = 10000000000000000000 (1e19)
Location of float in area 7 after comma, so the same number
10000000000000000000
float includes only the first 7 digits1000000*************
and the rest do not affect any number, that is.999999999999 + 10000000000000000000 = 10000000000000000000 (1e19)
Now what do you two cycles of yours:
The first cycle starts to fold from a larger number to a smaller one, at some point it doesn't matter what you're shaking, it won't affect the result.
for float in your code after
n = 4096
All other deductions are so small as to the amount that does not affect the amountThe second cycle begins to fold from smaller numbers to large, so the nonrecognized in the first case, after n = 4096, all adds a value that affects the total
so, you see the difference.
s1 1.64472532 float s2 1.64493406 float
In the first case, smaller in the second largest in the amount
n = 4096
beforen = 100000000
♪ And actually somewhere ♪n = 370728
By the way,
double
Mantissus is much larger (the whole type is 8 bytes instead of 4 for float), so the results will be different for the reasons described above, but they will be smaller.s1 1.6449340578345750 double s2 1.6449340568482265 double
and in the first cycle the rechargings shall not be counted except c
n = 94906266