File size: 1,847 Bytes
bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | /*@ Extern Coq
(PrimeFactorization : Z -> list Z -> Prop)
(FactorizationProgress : Z -> list Z -> Z -> Z -> Prop)
*/
/*@ Import Coq Require Import PVbench.Algorithms.integer_divide.rocq.spec_lib */
/*@ Import Coq Require Import PVbench.Algorithms.integer_divide.rocq.helper_lib */
void divide(int n, int *p)
/*@ With (original : Z)
Require
n == original &&
1 <= original && original <= INT_MAX &&
IntArray::undef_full(p, original)
Ensure
exists factors,
PrimeFactorization(original, factors) &&
IntArray::undef_seg(p, 0, 1) *
IntArray::seg(p, 1, 1 + Zlength(factors), factors) *
IntArray::undef_seg(p, 1 + Zlength(factors), original)
*/
{
int cnt = 0;
/*@ Inv Assert
exists factors,
p == p@pre &&
1 <= original && original <= INT_MAX &&
1 <= n && n <= original &&
2 <= i && i <= INT_MAX && i <= original + 1 &&
0 <= cnt && cnt < original &&
Zlength(factors) == cnt &&
FactorizationProgress(original, factors, n, i) &&
IntArray::undef_seg(p@pre, 0, 1) *
IntArray::seg(p@pre, 1, 1 + cnt, factors) *
IntArray::undef_seg(p@pre, 1 + cnt, original)
*/
for (int i = 2; i <= n; i++) {
/*@ Inv Assert
exists factors,
p == p@pre &&
1 <= original && original <= INT_MAX &&
1 <= n && n <= original &&
2 <= i && i <= original &&
(n == 1 || i <= n) &&
0 <= cnt && cnt < original &&
Zlength(factors) == cnt &&
FactorizationProgress(original, factors, n, i) &&
IntArray::undef_seg(p@pre, 0, 1) *
IntArray::seg(p@pre, 1, 1 + cnt, factors) *
IntArray::undef_seg(p@pre, 1 + cnt, original)
*/
while (n % i == 0) {
/*@ cnt + 1 < original by local */
cnt++;
p[cnt] = i;
n /= i;
}
if (n == 1) {
break;
}
/*@ i < INT_MAX by local */
}
}
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