ZYM/MiniGmp-Verification
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feat(normalized_size): Proved correctness of mpd_normalized_size. Fix minor bugs in previous proves.

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xiaoh105
2025-06-12 22:11:54 +08:00
parent f7432dca84
commit 257241df90
6 changed files with 643 additions and 81 deletions
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44
projects/mini-gmp.c
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@ -59,7 +59,7 @@ mpn_copyi (unsigned int *d, unsigned int *s, int n)
Zlength(l) == n &&
cap1 <= 100000000 &&
store_uint_array(s, n, l) *
store_undef_uint_array_rec(s, n + 1, cap1) &&
store_undef_uint_array_rec(s, n, cap1) &&
list_store_Z(l, val)
*/
/*@
@ -74,7 +74,7 @@ mpn_copyi (unsigned int *d, unsigned int *s, int n)
0 <= i && i <= n && Zlength(l) == n &&
list_store_Z(l, val) && n <= cap1 &&
store_uint_array(s, n, l) *
store_undef_uint_array_rec(s, n + 1, cap1) *
store_undef_uint_array_rec(s, n, cap1) *
store_uint_array(d, i, sublist(0, i, l)) *
store_uint_array_rec(d, i, cap2, l')
*/
@ -119,8 +119,8 @@ mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
which implies
exists l1 l2,
store_uint_array(ap@pre, n@pre, l1) * store_uint_array(bp@pre, n@pre, l2) *
store_undef_uint_array_rec(ap@pre, n@pre + 1, cap1) *
store_undef_uint_array_rec(bp@pre, n@pre + 1, cap2) &&
store_undef_uint_array_rec(ap@pre, n@pre, cap1) *
store_undef_uint_array_rec(bp@pre, n@pre, cap2) &&
list_store_Z_compact(l1, val1) && list_store_Z_compact(l2, val2) &&
n@pre == Zlength(l1) && n@pre == Zlength(l2)
*/
@ -131,8 +131,8 @@ mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
/*@Inv
-1 <= n && n < n@pre &&
store_uint_array(ap@pre, n@pre, l1) * store_uint_array(bp@pre, n@pre, l2) *
store_undef_uint_array_rec(ap@pre, n@pre + 1, cap1) *
store_undef_uint_array_rec(bp@pre, n@pre + 1, cap2) &&
store_undef_uint_array_rec(ap@pre, n@pre, cap1) *
store_undef_uint_array_rec(bp@pre, n@pre, cap2) &&
list_store_Z_compact(l1, val1) && list_store_Z_compact(l2, val2) &&
n@pre == Zlength(l1) && n@pre == Zlength(l2) &&
sublist(n + 1, n@pre, l1) == sublist(n + 1, n@pre, l2)
@ -186,13 +186,41 @@ mpn_cmp4 (unsigned int *ap, int an, unsigned int *bp, int bn)
/*返回非0的位数*/
/*static int
static int
mpn_normalized_size (unsigned int *xp, int n)
/*@
With cap val
Require
mpd_store_Z(xp, val, n, cap) &&
0 <= n && n <= cap && cap <= 100000000
Ensure
0 <= __return && __return <= cap &&
mpd_store_Z_compact(xp@pre, val, __return, cap)
*/
{
/*@
mpd_store_Z(xp@pre, val, n, cap)
which implies
exists l,
list_store_Z(sublist(0, n, l), val) &&
Zlength(l) == n &&
store_uint_array(xp@pre, n, sublist(0, n, l)) *
store_undef_uint_array_rec(xp@pre, n, cap)
*/
/*@
Given l
*/
/*@Inv
n >= 0 && n <= n@pre &&
n@pre >= 0 && n@pre <= cap && cap <= 100000000 &&
list_store_Z(sublist(0, n, l), val) &&
store_uint_array(xp@pre, n, sublist(0, n, l)) *
store_undef_uint_array_rec(xp@pre, n, cap)
*/
while (n > 0 && xp[n-1] == 0)
--n;
return n;
}*/
}
/* 多精度数ap 加上单精度数b，返回最后产生的进位 */
/*unsigned int