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feat(cmp): Proved correctness of mpn_cmp.

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xiaoh105
2025-06-11 16:54:36 +08:00
parent 4c0b0e98fa
commit 36204b8877
7 changed files with 824 additions and 18 deletions
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32
projects/mini-gmp.c
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@ -104,44 +104,46 @@ mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
Require
mpd_store_Z(ap, val1, n, cap1) *
mpd_store_Z(bp, val2, n, cap2) &&
n <= cap1 && n <= cap2
0 < n && n <= cap1 && n <= cap2 &&
cap1 <= 100000000 && cap2 <= 100000000
Ensure
val1 > val2 && __return == 1 ||
(val1 > val2 && __return == 1 ||
val1 == val2 && __return == 0 ||
val1 < val2 && __return == -1
val1 < val2 && __return == -1) &&
mpd_store_Z(ap@pre, val1, n@pre, cap1) *
mpd_store_Z(bp@pre, val2, n@pre, cap2)
*/
{
/*@
mpd_store_Z(ap, val1, n, cap1) * mpd_store_Z(bp, val2, n, cap2)
mpd_store_Z(ap@pre, val1, n@pre, cap1) * mpd_store_Z(bp@pre, val2, n@pre, cap2)
which implies
exists l1 l2,
mpd_store_list(ap, l1, cap1) * mpd_store_list(bp, l2, cap2) &&
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) &&
list_store_Z(l1, val1) && list_store_Z(l2, val2) &&
n == Zlength(l1) && n == Zlength(l2)
n@pre == Zlength(l1) && n@pre == Zlength(l2)
*/
/*@
Given l1 l2
*/
--n;
/*@Inv
mpd_store_list(ap, l1, cap1) * mpd_store_list(bp, l2, cap2) &&
-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) &&
list_store_Z(l1, val1) && list_store_Z(l2, val2) &&
n@pre == Zlength(l1) && n@pre == Zlength(l2) &&
sublist(n, n@pre, l1) == sublist(n, n@pre, l2)
sublist(n + 1, n@pre, l1) == sublist(n + 1, n@pre, l2)
*/
while (n >= 0)
{
/*@
mpd_store_list(ap, l1, cap1) * mpd_store_list(bp, l2, cap2)
which implies
store_uint_array(ap, n, l1) * store_uint_array(bp, n, l2) *
store_undef_uint_array(ap, n + 1, cap1) * store_uint_array(bp, n + 1, cap2) &&
*/
if (ap[n] != bp[n])
return ap[n] > bp[n] ? 1 : -1;
--n;
}
// Note: The parser cannot parse "--n" in loop so we paraphrased it.
// Note: The parser cannot parse "--n" in loop condition so we paraphrased it.
/*
while (--n >= 0)
{