Add annotations to gmp.c

projects/mini-gmp.c

@@ -1,14 +1,35 @@
 #include "mini-gmp.h"
+#include "verification_stdlib.h"
+#include "verification_list.h"
+#include "int_array_def.h"
 
-mp_size_t gmp_abs(mp_size_t x) {
+int gmp_abs(int x)
+/*@
+  Require emp
+  Ensure __return == Zabs(x)
+*/
+{
   return x >= 0 ? x : -x;
 }
 
-mp_size_t gmp_max(mp_size_t a, mp_size_t b) {
+int gmp_max(int a, int b)
+/*@
+  Require emp
+  Ensure __return == Zmax(a, b)
+*/
+{
   return a > b ? a : b;
 }
 
-int gmp_cmp(mp_size_t a, mp_size_t b) {
+int gmp_cmp(int a, int b)
+/*@
+  Require emp
+  Ensure 
+    a > b && __return == 1 || 
+    a == b && __return == 0 ||
+    a < b && __return == -1
+*/
+{
   return (a > b) - (a < b);
 }
 
@@ -16,16 +37,42 @@ int gmp_cmp(mp_size_t a, mp_size_t b) {
 
 /* 从 低地址向高地址 顺序复制 */
 void
-mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
+mpn_copyi (unsigned int *d, unsigned int *s, int n)
+/*@
+  With val data cap1 cap2
+  Require
+    mpd_store_Z(s, val, n, cap1) *
+    store_uint_array(d, cap2, data)
+  Ensure 
+    mpd_store_Z(s, val, n, cap1) *
+    mpd_store_Z(d, val, n, cap2)
+*/
 {
-  mp_size_t i;
+  /*
+    mpd_store_Z(s, val, n, cap1)
+    which implies
+    exists l,
+      store_uint_array(s, n, l) **
+      store_undef
+  */
+  int i;
   for (i = 0; i < n; i++)
     d[i] = s[i];
 }
 
 /* 大于返回1，小于返回-1，等于返回0 */
 int
-mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
+/*@
+  With cap1 cap2 val1 val2
+  Require
+    mpd_store_Z(ap, val1, n, cap1) **
+    mpd_store_Z(bp, val2, n, cap2)
+  Ensure
+    val1 > val2 && __return == 1 ||
+    val1 == val2 && __return == 0 ||
+    val1 < val2 && __return == -1
+*/
 {
   while (--n >= 0)
     {
@@ -37,7 +84,7 @@ mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
 
 /*处理位数不同的情况*/
 static int
-mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
+mpn_cmp4 (unsigned int *ap, int an, unsigned int *bp, int bn)
 {
   if (an != bn)
     return an < bn ? -1 : 1;
@@ -46,8 +93,8 @@ mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
 }
 
 /*返回非0的位数*/
-static mp_size_t
-mpn_normalized_size (mp_srcptr xp, mp_size_t n)
+static int
+mpn_normalized_size (unsigned int *xp, int n)
 {
   while (n > 0 && xp[n-1] == 0)
     --n;
@@ -55,15 +102,15 @@ mpn_normalized_size (mp_srcptr xp, mp_size_t n)
 }
 
 /* 多精度数ap 加上单精度数b，返回最后产生的进位 */
-mp_limb_t
-mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
+unsigned int
+mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
 {
-  mp_size_t i;
+  int i;
   //assert (n > 0);
   i = 0;
   do
     {
-      mp_limb_t r = ap[i] + b;
+      unsigned int r = ap[i] + b;
       /* Carry out */
       b = (r < b);
       rp[i] = r;
@@ -74,15 +121,15 @@ mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
 }
 
 /* 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 */
-mp_limb_t
-mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+unsigned int
+mpn_add_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
 {
-  mp_size_t i;
-  mp_limb_t cy;
+  int i;
+  unsigned int cy;
 
   for (i = 0, cy = 0; i < n; i++)
     {
-      mp_limb_t a, b, r;
+      unsigned int a, b, r;
       a = ap[i]; b = bp[i];
       r = a + cy;
       cy = (r < cy);
@@ -94,10 +141,10 @@ mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
 }
 
 /*不同位数的多精度数相加，返回最后的进位*/
-mp_limb_t
-mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
+unsigned int
+mpn_add (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
 {
-  mp_limb_t cy;
+  unsigned int cy;
   //assert (an >= bn);
   cy = mpn_add_n (rp, ap, bp, bn);
   if (an > bn)
@@ -105,17 +152,17 @@ mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
   return cy;
 }
 
-mp_limb_t
-mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
+unsigned int
+mpn_sub_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
 {
-  mp_size_t i;
+  int i;
   //assert (n > 0);
   i = 0;
   do
     {
-      mp_limb_t a = ap[i];
+      unsigned int a = ap[i];
       /* Carry out */
-      mp_limb_t cy = a < b;
+      unsigned int cy = a < b;
       rp[i] = a - b;
       b = cy;
     }
@@ -124,15 +171,15 @@ mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
   return b;
 }
 
-mp_limb_t
-mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+unsigned int
+mpn_sub_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
 {
-  mp_size_t i;
-  mp_limb_t cy;
+  int i;
+  unsigned int cy;
 
   for (i = 0, cy = 0; i < n; i++)
     {
-      mp_limb_t a, b;
+      unsigned int a, b;
       a = ap[i]; b = bp[i];
       b += cy;
       cy = (b < cy);
@@ -142,10 +189,10 @@ mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
   return cy;
 }
 
-mp_limb_t
-mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
+unsigned int
+mpn_sub (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
 {
-  mp_limb_t cy;
+  unsigned int cy;
   //assert (an >= bn);
   cy = mpn_sub_n (rp, ap, bp, bn);
   if (an > bn)
@@ -162,8 +209,8 @@ mpz_clear (mpz_t r)
     gmp_free_limbs (r->_mp_d, r->_mp_alloc);
 }
 
-static mp_ptr
-mpz_realloc (mpz_t r, mp_size_t size)
+static unsigned int *
+mpz_realloc (mpz_t r, int size)
 {
   size = gmp_max (size, 1);
 
@@ -180,7 +227,7 @@ mpz_realloc (mpz_t r, mp_size_t size)
 }
 
 /* Realloc for an mpz_t WHAT if it has less than NEEDED limbs.  */
-mp_ptr mrz_realloc_if(mpz_t z,mp_size_t n) {
+unsigned int *mrz_realloc_if(mpz_t z,int n) {
   return n > z->_mp_alloc ? mpz_realloc(z, n) : z->_mp_d;
 }
 
@@ -194,25 +241,25 @@ mpz_sgn (const mpz_t u)
 void
 mpz_swap (mpz_t u, mpz_t v)
 {
-  mp_size_t_swap (u->_mp_alloc, v->_mp_alloc);
-  mp_ptr_swap(u->_mp_d, v->_mp_d);
-  mp_size_t_swap (u->_mp_size, v->_mp_size);
+  int_swap (u->_mp_alloc, v->_mp_alloc);
+  unsigned int *_swap(u->_mp_d, v->_mp_d);
+  int_swap (u->_mp_size, v->_mp_size);
 }
 
 /* MPZ addition and subtraction */
 
-static mp_size_t
+static int
 mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
 {
-  mp_size_t an = gmp_abs (a->_mp_size);
-  mp_size_t bn = gmp_abs (b->_mp_size);
-  mp_ptr rp;
-  mp_limb_t cy;
+  int an = gmp_abs (a->_mp_size);
+  int bn = gmp_abs (b->_mp_size);
+  unsigned int *rp;
+  unsigned int cy;
 
   if (an < bn)
     {
       mpz_srcptr_swap (a, b);
-      mp_size_t_swap (an, bn);
+      int_swap (an, bn);
     }
 
   rp = mrz_realloc_if (r, an + 1);
@@ -223,13 +270,13 @@ mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
   return an + cy;
 }
 
-static mp_size_t
+static int
 mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
 {
-  mp_size_t an = gmp_abs (a->_mp_size);
-  mp_size_t bn = gmp_abs (b->_mp_size);
+  int an = gmp_abs (a->_mp_size);
+  int bn = gmp_abs (b->_mp_size);
   int cmp;
-  mp_ptr rp;
+  unsigned int *rp;
 
   cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
   if (cmp > 0)
@@ -251,7 +298,7 @@ mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
 void
 mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
 {
-  mp_size_t rn;
+  int rn;
 
   if ( (a->_mp_size ^ b->_mp_size) >= 0)
     rn = mpz_abs_add (r, a, b);
@@ -264,7 +311,7 @@ mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
 void
 mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
 {
-  mp_size_t rn;
+  int rn;
 
   if ( (a->_mp_size ^ b->_mp_size) >= 0)
     rn = mpz_abs_sub (r, a, b);