Merge remote-tracking branch 'origin/main' into mpz_sgn
This commit is contained in:
xiaoh105
@ -228,7 +228,7 @@ mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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/*@
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With val l2 cap1 cap2
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Require
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mpd_store_Z_compact(ap, val, n, cap1) *
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mpd_store_Z(ap, val, n, cap1) *
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store_uint_array(rp, cap2, l2) &&
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Zlength(l2) == cap2 &&
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cap2 >= n &&
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@ -237,13 +237,13 @@ mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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n > 0 && n <= cap1
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Ensure
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exists val',
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mpd_store_Z_compact(ap@pre, val, n@pre, cap1) *
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mpd_store_Z(ap@pre, val, n@pre, cap1) *
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mpd_store_Z(rp@pre, val', n@pre, cap2) &&
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(val' + __return * Z::pow(UINT_MOD, n@pre) == val + b@pre)
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*/
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{
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/*@
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mpd_store_Z_compact(ap@pre, val, n@pre, cap1)
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mpd_store_Z(ap@pre, val, n@pre, cap1)
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which implies
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exists l,
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n@pre <= cap1 &&
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@ -251,7 +251,7 @@ mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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cap1 <= 100000000 &&
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store_uint_array(ap@pre, n@pre, l) *
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store_undef_uint_array_rec(ap@pre, n@pre, cap1) &&
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list_store_Z_compact(l, val)
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list_store_Z(l, val)
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*/
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int i;
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//assert (n > 0);
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@ -278,7 +278,7 @@ mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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/*@Inv
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exists l l' l'' val1 val2,
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0 <= i && i <= n@pre &&
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list_store_Z_compact(l, val) && n@pre <= cap1 &&
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list_store_Z(l, val) && n@pre <= cap1 &&
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store_uint_array(ap@pre, n@pre, l) *
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store_undef_uint_array_rec(ap@pre, n@pre, cap1) &&
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list_store_Z(sublist(0, i, l), val1) &&
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@ -313,24 +313,104 @@ mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
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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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With cap_a cap_b cap_r val_a val_b l_r
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Require
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mpd_store_Z(ap, val_a, n, cap_a) *
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mpd_store_Z(bp, val_b, n, cap_b) *
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store_uint_array(rp, cap_r, l_r) &&
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Zlength(l_r) == cap_r &&
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cap_a <= 100000000 &&
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cap_b <= 100000000 &&
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cap_r <= 100000000 &&
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n > 0 && n <= cap_a && n <= cap_b && n <= cap_r
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Ensure
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exists val_r_out,
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mpd_store_Z(ap@pre, val_a, n@pre, cap_a) *
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mpd_store_Z(bp@pre, val_b, n@pre, cap_b) *
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mpd_store_Z(rp@pre, val_r_out, n@pre, cap_r) &&
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(val_r_out + __return * Z::pow(UINT_MOD, n@pre) == val_a + val_b)
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*/
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{
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/*@
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mpd_store_Z(ap@pre, val_a, n@pre, cap_a)
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which implies
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exists l_a,
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n@pre <= cap_a &&
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Zlength(l_a) == n@pre &&
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cap_a <= 100000000 &&
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store_uint_array(ap@pre, n@pre, l_a) *
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store_undef_uint_array_rec(ap@pre, n@pre, cap_a) &&
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list_store_Z(l_a, val_a)
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*/
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/*@
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mpd_store_Z(bp@pre, val_b, n@pre, cap_b)
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which implies
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exists l_b,
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n@pre <= cap_b &&
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Zlength(l_b) == n@pre &&
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cap_b <= 100000000 &&
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store_uint_array(bp@pre, n@pre, l_b) *
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store_undef_uint_array_rec(bp@pre, n@pre, cap_b) &&
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list_store_Z(l_b, val_b)
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*/
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int i;
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unsigned int cy;
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for (i = 0, cy = 0; i < n; i++)
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/*@
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store_uint_array(rp@pre, cap_r, l_r) && Zlength(l_r) == cap_r
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which implies
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store_uint_array_rec(rp@pre, 0, cap_r, l_r) * store_uint_array(rp@pre, 0, nil) &&
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Zlength(l_r) == cap_r
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*/
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i = 0;
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cy = 0;
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/*@Inv
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exists l_a l_b l_r_prefix l_r_suffix val_a_prefix val_b_prefix val_r_prefix,
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0 <= i && i <= n@pre && n@pre <= cap_a && n@pre <= cap_b && n@pre <= cap_r &&
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list_store_Z(l_a, val_a) &&
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list_store_Z(l_b, val_b) &&
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list_store_Z(sublist(0, i, l_a), val_a_prefix) &&
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list_store_Z(sublist(0, i, l_b), val_b_prefix) &&
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list_store_Z(l_r_prefix, val_r_prefix) &&
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Zlength(l_r_prefix) == i &&
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(val_r_prefix + cy * Z::pow(UINT_MOD, i) == val_a_prefix + val_b_prefix) &&
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store_uint_array(ap@pre, n@pre, l_a) *
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store_undef_uint_array_rec(ap@pre, n@pre, cap_a) *
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store_uint_array(bp@pre, n@pre, l_b) *
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store_undef_uint_array_rec(bp@pre, n@pre, cap_b) *
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store_uint_array(rp@pre, i, l_r_prefix) *
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store_uint_array_rec(rp@pre, i, cap_r, l_r_suffix)
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*/
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while (i < n)
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{
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/*@
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Given l_a l_b l_r_prefix l_r_suffix val_a_prefix val_b_prefix val_r_prefix
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*/
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/*@ 0 <= cy && cy <= UINT_MAX by local */
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unsigned int a, b, r;
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a = ap[i]; b = bp[i];
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r = a + cy;
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cy = (r < cy);
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r += b;
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cy += (r < b);
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/*@
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0 <= i && i < n@pre && n@pre <= cap_r &&
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store_uint_array(rp@pre, i, l_r_prefix) *
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store_uint_array_rec(rp@pre, i, cap_r, l_r_suffix)
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which implies
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exists a l_r_suffix',
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l_r_suffix == cons(a, l_r_suffix') && 0 <= i && i < n@pre && n@pre <= cap_r &&
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store_uint_array_rec(rp@pre, i+1, cap_r, l_r_suffix') *
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store_uint_array(rp@pre, i+1, app(l_r_prefix, cons(a, nil)))
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*/
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rp[i] = r;
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++i;
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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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