feat(cmp4): modied certain annotations for mpn_cmp and proved correctness of mpn_cmp4.
This commit is contained in:
xiaoh105
@ -102,26 +102,26 @@ mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
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/*@
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With cap1 cap2 val1 val2
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Require
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mpd_store_Z(ap, val1, n, cap1) *
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mpd_store_Z(bp, val2, n, cap2) &&
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0 < n && n <= cap1 && n <= cap2 &&
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mpd_store_Z_compact(ap, val1, n, cap1) *
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mpd_store_Z_compact(bp, val2, n, cap2) &&
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0 <= n && n <= cap1 && n <= cap2 &&
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cap1 <= 100000000 && cap2 <= 100000000
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Ensure
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(val1 > val2 && __return == 1 ||
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val1 == val2 && __return == 0 ||
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val1 < val2 && __return == -1) &&
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mpd_store_Z(ap@pre, val1, n@pre, cap1) *
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mpd_store_Z(bp@pre, val2, n@pre, cap2)
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mpd_store_Z_compact(ap@pre, val1, n@pre, cap1) *
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mpd_store_Z_compact(bp@pre, val2, n@pre, cap2)
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*/
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{
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/*@
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mpd_store_Z(ap@pre, val1, n@pre, cap1) * mpd_store_Z(bp@pre, val2, n@pre, cap2)
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mpd_store_Z_compact(ap@pre, val1, n@pre, cap1) * mpd_store_Z_compact(bp@pre, val2, n@pre, cap2)
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which implies
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exists l1 l2,
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store_uint_array(ap@pre, n@pre, l1) * store_uint_array(bp@pre, n@pre, l2) *
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store_undef_uint_array_rec(ap@pre, n@pre + 1, cap1) *
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store_undef_uint_array_rec(bp@pre, n@pre + 1, cap2) &&
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list_store_Z(l1, val1) && list_store_Z(l2, val2) &&
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list_store_Z_compact(l1, val1) && list_store_Z_compact(l2, val2) &&
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n@pre == Zlength(l1) && n@pre == Zlength(l2)
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*/
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/*@
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@ -133,7 +133,7 @@ mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
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store_uint_array(ap@pre, n@pre, l1) * store_uint_array(bp@pre, n@pre, l2) *
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store_undef_uint_array_rec(ap@pre, n@pre + 1, cap1) *
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store_undef_uint_array_rec(bp@pre, n@pre + 1, cap2) &&
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list_store_Z(l1, val1) && list_store_Z(l2, val2) &&
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list_store_Z_compact(l1, val1) && list_store_Z_compact(l2, val2) &&
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n@pre == Zlength(l1) && n@pre == Zlength(l2) &&
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sublist(n + 1, n@pre, l1) == sublist(n + 1, n@pre, l2)
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*/
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@ -157,24 +157,45 @@ mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
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/*处理位数不同的情况*/
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static int
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mpn_cmp4 (unsigned int *ap, int an, unsigned int *bp, int bn)
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/*@
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With cap1 cap2 val1 val2
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Require
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mpd_store_Z_compact(ap, val1, an, cap1) *
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mpd_store_Z_compact(bp, val2, bn, cap2) &&
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an >= 0 && bn >= 0 && an <= cap1 && bn <= cap2 &&
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cap1 <= 100000000 && cap2 <= 100000000
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Ensure
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(val1 > val2 && __return == 1 ||
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val1 == val2 && __return == 0 ||
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val1 < val2 && __return == -1) &&
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mpd_store_Z_compact(ap@pre, val1, an@pre, cap1) *
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mpd_store_Z_compact(bp@pre, val2, bn@pre, cap2)
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*/
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{
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if (an != bn)
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return an < bn ? -1 : 1;
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else
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else {
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/*@
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an@pre == bn@pre && bn@pre <= cap2
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which implies
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an@pre <= cap2
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*/
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return mpn_cmp (ap, bp, an);
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}
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}
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/*返回非0的位数*/
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static int
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/*static int
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mpn_normalized_size (unsigned int *xp, int n)
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{
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while (n > 0 && xp[n-1] == 0)
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--n;
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return n;
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}
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}*/
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/* 多精度数ap 加上单精度数b，返回最后产生的进位 */
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unsigned int
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/*unsigned int
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mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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{
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int i;
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@ -183,17 +204,17 @@ mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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do
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{
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unsigned int r = ap[i] + b;
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/* Carry out */
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// Carry out
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b = (r < b);
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rp[i] = r;
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}
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while (++i < n);
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return b;
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}
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}*/
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/* 位数相同的多精度数ap 加上多精度数bp，返回最后产生的进位 */
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unsigned int
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/*unsigned int
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mpn_add_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
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{
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int i;
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@ -210,10 +231,10 @@ mpn_add_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
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rp[i] = r;
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}
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return cy;
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}
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}*/
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/*不同位数的多精度数相加，返回最后的进位*/
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unsigned int
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/*unsigned int
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mpn_add (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
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{
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unsigned int cy;
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@ -222,9 +243,9 @@ mpn_add (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
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if (an > bn)
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cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
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return cy;
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}
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}*/
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unsigned int
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/*unsigned int
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mpn_sub_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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{
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int i;
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@ -233,7 +254,7 @@ mpn_sub_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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do
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{
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unsigned int a = ap[i];
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/* Carry out */
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// Carry out
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unsigned int cy = a < b;
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rp[i] = a - b;
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b = cy;
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@ -241,9 +262,9 @@ mpn_sub_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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while (++i < n);
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return b;
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}
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}*/
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unsigned int
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/*unsigned int
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mpn_sub_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
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{
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int i;
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@ -259,9 +280,9 @@ mpn_sub_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
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rp[i] = a - b;
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}
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return cy;
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}
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}*/
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unsigned int
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/*unsigned int
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mpn_sub (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
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{
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unsigned int cy;
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@ -270,18 +291,18 @@ mpn_sub (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
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if (an > bn)
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cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
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return cy;
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}
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}*/
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/* MPZ interface */
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void
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/*void
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mpz_clear (mpz_t r)
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{
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if (r->_mp_alloc)
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gmp_free_limbs (r->_mp_d, r->_mp_alloc);
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}
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}*/
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static unsigned int *
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/*static unsigned int *
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mpz_realloc (mpz_t r, int size)
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{
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size = gmp_max (size, 1);
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@ -296,31 +317,31 @@ mpz_realloc (mpz_t r, int size)
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r->_mp_size = 0;
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return r->_mp_d;
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}
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}*/
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/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
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unsigned int *mrz_realloc_if(mpz_t z,int n) {
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/*unsigned int *mrz_realloc_if(mpz_t z,int n) {
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return n > z->_mp_alloc ? mpz_realloc(z, n) : z->_mp_d;
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}
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}*/
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/* MPZ comparisons and the like. */
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int
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/*int
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mpz_sgn (const mpz_t u)
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{
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return gmp_cmp (u->_mp_size, 0);
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}
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}*/
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void
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/*void
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mpz_swap (mpz_t u, mpz_t v)
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{
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int_swap (u->_mp_alloc, v->_mp_alloc);
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unsigned int *_swap(u->_mp_d, v->_mp_d);
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int_swap (u->_mp_size, v->_mp_size);
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}
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}*/
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/* MPZ addition and subtraction */
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static int
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/*static int
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mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
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{
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int an = gmp_abs (a->_mp_size);
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@ -340,9 +361,9 @@ mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
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rp[an] = cy;
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return an + cy;
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}
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}*/
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static int
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/*static int
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mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
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{
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int an = gmp_abs (a->_mp_size);
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@ -365,9 +386,9 @@ mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
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}
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else
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return 0;
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}
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}*/
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void
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/*void
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mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
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{
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int rn;
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@ -378,9 +399,9 @@ mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
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rn = mpz_abs_sub (r, a, b);
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r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
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}
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}*/
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void
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/*void
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mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
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{
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int rn;
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@ -391,4 +412,4 @@ mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
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rn = mpz_abs_add (r, a, b);
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r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
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}
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}*/
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