Put the first stage of my bignum debugging adventures into CVS. This code
[openssl.git] / crypto / bn / bn_lib.c
index e7349099680a28a845c02a6fb2b427974b35bd3d..85b72e0eebf568951d1cdb7fbeb6d217aa762753 100644 (file)
  * [including the GNU Public Licence.]
  */
 
+#ifndef BN_DEBUG
+# undef NDEBUG /* avoid conflicting definitions */
+# define NDEBUG
+#endif
+
+#include <assert.h>
+#include <limits.h>
 #include <stdio.h>
 #include "cryptlib.h"
 #include "bn_lcl.h"
@@ -71,41 +78,41 @@ const char *BN_version="Big Number" OPENSSL_VERSION_PTEXT;
  * 7 - 128 == 4096
  * 8 - 256 == 8192
  */
-OPENSSL_GLOBAL int bn_limit_bits=0;
-OPENSSL_GLOBAL int bn_limit_num=8;        /* (1<<bn_limit_bits) */
-OPENSSL_GLOBAL int bn_limit_bits_low=0;
-OPENSSL_GLOBAL int bn_limit_num_low=8;    /* (1<<bn_limit_bits_low) */
-OPENSSL_GLOBAL int bn_limit_bits_high=0;
-OPENSSL_GLOBAL int bn_limit_num_high=8;   /* (1<<bn_limit_bits_high) */
-OPENSSL_GLOBAL int bn_limit_bits_mont=0;
-OPENSSL_GLOBAL int bn_limit_num_mont=8;   /* (1<<bn_limit_bits_mont) */
+static int bn_limit_bits=0;
+static int bn_limit_num=8;        /* (1<<bn_limit_bits) */
+static int bn_limit_bits_low=0;
+static int bn_limit_num_low=8;    /* (1<<bn_limit_bits_low) */
+static int bn_limit_bits_high=0;
+static int bn_limit_num_high=8;   /* (1<<bn_limit_bits_high) */
+static int bn_limit_bits_mont=0;
+static int bn_limit_num_mont=8;   /* (1<<bn_limit_bits_mont) */
 
 void BN_set_params(int mult, int high, int low, int mont)
        {
        if (mult >= 0)
                {
-               if (mult > (sizeof(int)*8)-1)
+               if (mult > (int)(sizeof(int)*8)-1)
                        mult=sizeof(int)*8-1;
                bn_limit_bits=mult;
                bn_limit_num=1<<mult;
                }
        if (high >= 0)
                {
-               if (high > (sizeof(int)*8)-1)
+               if (high > (int)(sizeof(int)*8)-1)
                        high=sizeof(int)*8-1;
                bn_limit_bits_high=high;
                bn_limit_num_high=1<<high;
                }
        if (low >= 0)
                {
-               if (low > (sizeof(int)*8)-1)
+               if (low > (int)(sizeof(int)*8)-1)
                        low=sizeof(int)*8-1;
                bn_limit_bits_low=low;
                bn_limit_num_low=1<<low;
                }
        if (mont >= 0)
                {
-               if (mont > (sizeof(int)*8)-1)
+               if (mont > (int)(sizeof(int)*8)-1)
                        mont=sizeof(int)*8-1;
                bn_limit_bits_mont=mont;
                bn_limit_num_mont=1<<mont;
@@ -121,7 +128,7 @@ int BN_get_params(int which)
        else return(0);
        }
 
-BIGNUM *BN_value_one(void)
+const BIGNUM *BN_value_one(void)
        {
        static BN_ULONG data_one=1L;
        static BIGNUM const_one={&data_one,1,1,0};
@@ -244,14 +251,8 @@ int BN_num_bits(const BIGNUM *a)
 
        if (a->top == 0) return(0);
        l=a->d[a->top-1];
+       assert(l != 0);
        i=(a->top-1)*BN_BITS2;
-       if (l == 0)
-               {
-#if !defined(NO_STDIO) && !defined(WIN16)
-               fprintf(stderr,"BAD TOP VALUE\n");
-#endif
-               abort();
-               }
        return(i+BN_num_bits_word(l));
        }
 
@@ -262,36 +263,37 @@ void BN_clear_free(BIGNUM *a)
        if (a == NULL) return;
        if (a->d != NULL)
                {
-               memset(a->d,0,a->max*sizeof(a->d[0]));
+               OPENSSL_cleanse(a->d,a->dmax*sizeof(a->d[0]));
                if (!(BN_get_flags(a,BN_FLG_STATIC_DATA)))
-                       Free(a->d);
+                       OPENSSL_free(a->d);
                }
        i=BN_get_flags(a,BN_FLG_MALLOCED);
-       memset(a,0,sizeof(BIGNUM));
+       OPENSSL_cleanse(a,sizeof(BIGNUM));
        if (i)
-               Free(a);
+               OPENSSL_free(a);
        }
 
 void BN_free(BIGNUM *a)
        {
        if (a == NULL) return;
        if ((a->d != NULL) && !(BN_get_flags(a,BN_FLG_STATIC_DATA)))
-               Free(a->d);
+               OPENSSL_free(a->d);
        a->flags|=BN_FLG_FREE; /* REMOVE? */
        if (a->flags & BN_FLG_MALLOCED)
-               Free(a);
+               OPENSSL_free(a);
        }
 
 void BN_init(BIGNUM *a)
        {
        memset(a,0,sizeof(BIGNUM));
+       bn_check_top(a);
        }
 
 BIGNUM *BN_new(void)
        {
        BIGNUM *ret;
 
-       if ((ret=(BIGNUM *)Malloc(sizeof(BIGNUM))) == NULL)
+       if ((ret=(BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL)
                {
                BNerr(BN_F_BN_NEW,ERR_R_MALLOC_FAILURE);
                return(NULL);
@@ -299,208 +301,190 @@ BIGNUM *BN_new(void)
        ret->flags=BN_FLG_MALLOCED;
        ret->top=0;
        ret->neg=0;
-       ret->max=0;
+       ret->dmax=0;
        ret->d=NULL;
+       bn_check_top(ret);
        return(ret);
        }
 
-
-BN_CTX *BN_CTX_new(void)
+/* This is used both by bn_expand2() and bn_dup_expand() */
+/* The caller MUST check that words > b->dmax before calling this */
+static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
        {
-       BN_CTX *ret;
+       BN_ULONG *A,*a = NULL;
+       const BN_ULONG *B;
+       int i;
 
-       ret=(BN_CTX *)Malloc(sizeof(BN_CTX));
-       if (ret == NULL)
+       if (words > (INT_MAX/(4*BN_BITS2)))
                {
-               BNerr(BN_F_BN_CTX_NEW,ERR_R_MALLOC_FAILURE);
+               BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_BIGNUM_TOO_LONG);
+               return NULL;
+               }
+
+       bn_check_top(b);        
+       if (BN_get_flags(b,BN_FLG_STATIC_DATA))
+               {
+               BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
                return(NULL);
                }
+       a=A=(BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG)*(words+1));
+       if (A == NULL)
+               {
+               BNerr(BN_F_BN_EXPAND_INTERNAL,ERR_R_MALLOC_FAILURE);
+               return(NULL);
+               }
+#if 1
+       B=b->d;
+       /* Check if the previous number needs to be copied */
+       if (B != NULL)
+               {
+               for (i=b->top>>2; i>0; i--,A+=4,B+=4)
+                       {
+                       /*
+                        * The fact that the loop is unrolled
+                        * 4-wise is a tribute to Intel. It's
+                        * the one that doesn't have enough
+                        * registers to accomodate more data.
+                        * I'd unroll it 8-wise otherwise:-)
+                        *
+                        *              <appro@fy.chalmers.se>
+                        */
+                       BN_ULONG a0,a1,a2,a3;
+                       a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
+                       A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
+                       }
+               switch (b->top&3)
+                       {
+               case 3: A[2]=B[2];
+               case 2: A[1]=B[1];
+               case 1: A[0]=B[0];
+               case 0: /* workaround for ultrix cc: without 'case 0', the optimizer does
+                        * the switch table by doing a=top&3; a--; goto jump_table[a];
+                        * which fails for top== 0 */
+                       ;
+                       }
+               }
 
-       BN_CTX_init(ret);
-       ret->flags=BN_FLG_MALLOCED;
-       return(ret);
+#else
+       memset(A,0,sizeof(BN_ULONG)*(words+1));
+       memcpy(A,b->d,sizeof(b->d[0])*b->top);
+#endif
+               
+       return(a);
        }
 
-void BN_CTX_init(BN_CTX *ctx)
-       {
-       memset(ctx,0,sizeof(BN_CTX));
-       ctx->tos=0;
-       ctx->flags=0;
-       }
+/* This is an internal function that can be used instead of bn_expand2()
+ * when there is a need to copy BIGNUMs instead of only expanding the
+ * data part, while still expanding them.
+ * Especially useful when needing to expand BIGNUMs that are declared
+ * 'const' and should therefore not be changed.
+ * The reason to use this instead of a BN_dup() followed by a bn_expand2()
+ * is memory allocation overhead.  A BN_dup() followed by a bn_expand2()
+ * will allocate new memory for the BIGNUM data twice, and free it once,
+ * while bn_dup_expand() makes sure allocation is made only once.
+ */
 
-void BN_CTX_free(BN_CTX *c)
+BIGNUM *bn_dup_expand(const BIGNUM *b, int words)
        {
-       int i;
+       BIGNUM *r = NULL;
+
+       /* This function does not work if
+        *      words <= b->dmax && top < words
+        * because BN_dup() does not preserve 'dmax'!
+        * (But bn_dup_expand() is not used anywhere yet.)
+        */
+       
+       if (words > b->dmax)
+               {
+               BN_ULONG *a = bn_expand_internal(b, words);
 
-       if(c == NULL)
-           return;
+               if (a)
+                       {
+                       r = BN_new();
+                       if (r)
+                               {
+                               r->top = b->top;
+                               r->dmax = words;
+                               r->neg = b->neg;
+                               r->d = a;
+                               }
+                       else
+                               {
+                               /* r == NULL, BN_new failure */
+                               OPENSSL_free(a);
+                               }
+                       }
+               /* If a == NULL, there was an error in allocation in
+                  bn_expand_internal(), and NULL should be returned */
+               }
+       else
+               {
+               r = BN_dup(b);
+               }
 
-       for (i=0; i<BN_CTX_NUM; i++)
-               BN_clear_free(&(c->bn[i]));
-       if (c->flags & BN_FLG_MALLOCED)
-               Free(c);
+       bn_check_top(r);
+       return r;
        }
 
 /* This is an internal function that should not be used in applications.
- * It ensures that 'b' has enough room for a 'bits' bit number.  It is
- * mostly used by the various BIGNUM routines.  If there is an error,
- * NULL is returned. if not, 'b' is returned.
- */
+ * It ensures that 'b' has enough room for a 'words' word number
+ * and initialises any unused part of b->d with leading zeros.
+ * It is mostly used by the various BIGNUM routines. If there is an error,
+ * NULL is returned. If not, 'b' is returned. */
+
 BIGNUM *bn_expand2(BIGNUM *b, int words)
        {
-       BN_ULONG *A,*a;
-       const BN_ULONG *B;
+       BN_ULONG *A;
        int i;
 
-       bn_check_top(b);
-
-       if (words > b->max)
+       if (words > b->dmax)
                {
-               bn_check_top(b);        
-               if (BN_get_flags(b,BN_FLG_STATIC_DATA))
-                       {
-                       BNerr(BN_F_BN_EXPAND2,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
-                       return(NULL);
-                       }
-               a=A=(BN_ULONG *)Malloc(sizeof(BN_ULONG)*(words+1));
-               if (A == NULL)
-                       {
-                       BNerr(BN_F_BN_EXPAND2,ERR_R_MALLOC_FAILURE);
-                       return(NULL);
-                       }
-#if 1
-               B=b->d;
-               /* Check if the previous number needs to be copied */
-               if (B != NULL)
+               BN_ULONG *a = bn_expand_internal(b, words);
+
+               if (a)
                        {
-#if 0
-                       /* This lot is an unrolled loop to copy b->top 
-                        * BN_ULONGs from B to A
-                        */
-/*
- * I have nothing against unrolling but it's usually done for
- * several reasons, namely:
- * - minimize percentage of decision making code, i.e. branches;
- * - avoid cache trashing;
- * - make it possible to schedule loads earlier;
- * Now let's examine the code below. The cornerstone of C is
- * "programmer is always right" and that's what we love it for:-)
- * For this very reason C compilers have to be paranoid when it
- * comes to data aliasing and assume the worst. Yeah, but what
- * does it mean in real life? This means that loop body below will
- * be compiled to sequence of loads immediately followed by stores
- * as compiler assumes the worst, something in A==B+1 style. As a
- * result CPU pipeline is going to starve for incoming data. Secondly
- * if A and B happen to share same cache line such code is going to
- * cause severe cache trashing. Both factors have severe impact on
- * performance of modern CPUs and this is the reason why this
- * particular piece of code is #ifdefed away and replaced by more
- * "friendly" version found in #else section below. This comment
- * also applies to BN_copy function.
- *
- *                                     <appro@fy.chalmers.se>
- */
-                       for (i=b->top&(~7); i>0; i-=8)
-                               {
-                               A[0]=B[0]; A[1]=B[1]; A[2]=B[2]; A[3]=B[3];
-                               A[4]=B[4]; A[5]=B[5]; A[6]=B[6]; A[7]=B[7];
-                               A+=8;
-                               B+=8;
-                               }
-                       switch (b->top&7)
-                               {
-                       case 7:
-                               A[6]=B[6];
-                       case 6:
-                               A[5]=B[5];
-                       case 5:
-                               A[4]=B[4];
-                       case 4:
-                               A[3]=B[3];
-                       case 3:
-                               A[2]=B[2];
-                       case 2:
-                               A[1]=B[1];
-                       case 1:
-                               A[0]=B[0];
-                       case 0:
-                               /* I need the 'case 0' entry for utrix cc.
-                                * If the optimizer is turned on, it does the
-                                * switch table by doing
-                                * a=top&7
-                                * a--;
-                                * goto jump_table[a];
-                                * If top is 0, this makes us jump to 0xffffffc 
-                                * which is rather bad :-(.
-                                * eric 23-Apr-1998
-                                */
-                               ;
-                               }
-#else
-                       for (i=b->top>>2; i>0; i--,A+=4,B+=4)
-                               {
-                               /*
-                                * The fact that the loop is unrolled
-                                * 4-wise is a tribute to Intel. It's
-                                * the one that doesn't have enough
-                                * registers to accomodate more data.
-                                * I'd unroll it 8-wise otherwise:-)
-                                *
-                                *              <appro@fy.chalmers.se>
-                                */
-                               BN_ULONG a0,a1,a2,a3;
-                               a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
-                               A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
-                               }
-                       switch (b->top&3)
-                               {
-                               case 3: A[2]=B[2];
-                               case 2: A[1]=B[1];
-                               case 1: A[0]=B[0];
-                               case 0: ; /* ultrix cc workaround, see above */
-                               }
-#endif
-                       Free(b->d);
+                       if (b->d)
+                               OPENSSL_free(b->d);
+                       b->d=a;
+                       b->dmax=words;
                        }
-
-               b->d=a;
-               b->max=words;
-
-               /* Now need to zero any data between b->top and b->max */
-
-               A= &(b->d[b->top]);
-               for (i=(b->max - b->top)>>3; i>0; i--,A+=8)
+               else
+                       b = NULL;
+               }
+       
+       /* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */
+       if ((b != NULL) && (b->top < b->dmax))
+               {
+               A = &(b->d[b->top]);
+               for (i=(b->dmax - b->top)>>3; i>0; i--,A+=8)
                        {
                        A[0]=0; A[1]=0; A[2]=0; A[3]=0;
                        A[4]=0; A[5]=0; A[6]=0; A[7]=0;
                        }
-               for (i=(b->max - b->top)&7; i>0; i--,A++)
+               for (i=(b->dmax - b->top)&7; i>0; i--,A++)
                        A[0]=0;
-#else
-                       memset(A,0,sizeof(BN_ULONG)*(words+1));
-                       memcpy(A,b->d,sizeof(b->d[0])*b->top);
-                       b->d=a;
-                       b->max=words;
-#endif
-               
-/*             memset(&(p[b->max]),0,((words+1)-b->max)*sizeof(BN_ULONG)); */
-/*     { int i; for (i=b->max; i<words+1; i++) p[i]=i;} */
-
+               assert(A == &(b->d[b->dmax]));
                }
-       return(b);
+       else if(b) bn_check_top(b);
+       return b;
        }
 
 BIGNUM *BN_dup(const BIGNUM *a)
        {
-       BIGNUM *r;
+       BIGNUM *r, *t;
 
        if (a == NULL) return NULL;
 
        bn_check_top(a);
 
-       r=BN_new();
-       if (r == NULL) return(NULL);
-       return((BIGNUM *)BN_copy(r,a));
+       t = BN_new();
+       if (t == NULL) return(NULL);
+       r = BN_copy(t, a);
+       /* now  r == t || r == NULL */
+       if (r == NULL)
+               BN_free(t);
+       bn_check_top(r);
+       return r;
        }
 
 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
@@ -528,7 +512,7 @@ BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
                case 3: A[2]=B[2];
                case 2: A[1]=B[1];
                case 1: A[0]=B[0];
-               case 0: ; /* ultrix cc workaround, see comments in bn_expand2 */
+               case 0: ; /* ultrix cc workaround, see comments in bn_expand_internal */
                }
 #else
        memcpy(a->d,b->d,sizeof(b->d[0])*b->top);
@@ -539,24 +523,103 @@ BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
        if ((a->top == 0) && (a->d != NULL))
                a->d[0]=0;
        a->neg=b->neg;
+       bn_check_top(a);
        return(a);
        }
 
+BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n)
+       {
+       int i, min;
+       BN_ULONG *A;
+       const BN_ULONG *B;
+
+       bn_check_top(b);
+
+       if (a == b)
+               return a;
+
+       min = (b->top < (int)n)? b->top: (int)n;
+
+       if (!min)
+               {
+               BN_zero(a);
+               return a;
+               }
+
+       if (bn_wexpand(a, min) == NULL)
+               return NULL;
+
+       A=a->d;
+       B=b->d;
+       for (i=min>>2; i>0; i--, A+=4, B+=4)
+               {
+               BN_ULONG a0,a1,a2,a3;
+               a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
+               A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
+               }
+       switch (min&3)
+               {
+               case 3: A[2]=B[2];
+               case 2: A[1]=B[1];
+               case 1: A[0]=B[0];
+               case 0: ;
+               }
+       a->top = min;
+
+       a->neg = b->neg;
+       bn_correct_top(a);
+
+       bn_check_top(a);
+       return(a);
+       }
+
+void BN_swap(BIGNUM *a, BIGNUM *b)
+       {
+       int flags_old_a, flags_old_b;
+       BN_ULONG *tmp_d;
+       int tmp_top, tmp_dmax, tmp_neg;
+       
+       flags_old_a = a->flags;
+       flags_old_b = b->flags;
+
+       tmp_d = a->d;
+       tmp_top = a->top;
+       tmp_dmax = a->dmax;
+       tmp_neg = a->neg;
+       
+       a->d = b->d;
+       a->top = b->top;
+       a->dmax = b->dmax;
+       a->neg = b->neg;
+       
+       b->d = tmp_d;
+       b->top = tmp_top;
+       b->dmax = tmp_dmax;
+       b->neg = tmp_neg;
+       
+       a->flags = (flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA);
+       b->flags = (flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA);
+       bn_check_top(a);
+       bn_check_top(b);
+       }
+
+
 void BN_clear(BIGNUM *a)
        {
        if (a->d != NULL)
-               memset(a->d,0,a->max*sizeof(a->d[0]));
+               memset(a->d,0,a->dmax*sizeof(a->d[0]));
        a->top=0;
        a->neg=0;
+       bn_check_top(a);
        }
 
-BN_ULONG BN_get_word(BIGNUM *a)
+BN_ULONG BN_get_word(const BIGNUM *a)
        {
        int i,n;
        BN_ULONG ret=0;
 
        n=BN_num_bytes(a);
-       if (n > sizeof(BN_ULONG))
+       if (n > (int)sizeof(BN_ULONG))
                return(BN_MASK2);
        for (i=a->top-1; i>=0; i--)
                {
@@ -574,7 +637,7 @@ BN_ULONG BN_get_word(BIGNUM *a)
 int BN_set_word(BIGNUM *a, BN_ULONG w)
        {
        int i,n;
-       if (bn_expand(a,sizeof(BN_ULONG)*8) == NULL) return(0);
+       if (bn_expand(a,(int)sizeof(BN_ULONG)*8) == NULL) return(0);
 
        n=sizeof(BN_ULONG)/BN_BYTES;
        a->neg=0;
@@ -595,10 +658,10 @@ int BN_set_word(BIGNUM *a, BN_ULONG w)
                a->d[i]=(BN_ULONG)w&BN_MASK2;
                if (a->d[i] != 0) a->top=i+1;
                }
+       bn_check_top(a);
        return(1);
        }
 
-/* ignore negative */
 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
        {
        unsigned int i,m;
@@ -619,6 +682,7 @@ BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
        i=((n-1)/BN_BYTES)+1;
        m=((n-1)%(BN_BYTES));
        ret->top=i;
+       ret->neg=0;
        while (n-- > 0)
                {
                l=(l<<8L)| *(s++);
@@ -631,7 +695,7 @@ BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
                }
        /* need to call this due to clear byte at top if avoiding
         * having the top bit set (-ve number) */
-       bn_fix_top(ret);
+       bn_correct_top(ret);
        return(ret);
        }
 
@@ -647,6 +711,7 @@ int BN_bn2bin(const BIGNUM *a, unsigned char *to)
                l=a->d[i/BN_BYTES];
                *(to++)=(unsigned char)(l>>(8*(i%BN_BYTES)))&0xff;
                }
+       bn_check_top(a);
        return(n);
        }
 
@@ -728,6 +793,7 @@ int BN_set_bit(BIGNUM *a, int n)
                }
 
        a->d[i]|=(((BN_ULONG)1)<<j);
+       bn_check_top(a);
        return(1);
        }
 
@@ -740,7 +806,7 @@ int BN_clear_bit(BIGNUM *a, int n)
        if (a->top <= i) return(0);
 
        a->d[i]&=(~(((BN_ULONG)1)<<j));
-       bn_fix_top(a);
+       bn_correct_top(a);
        return(1);
        }
 
@@ -769,11 +835,11 @@ int BN_mask_bits(BIGNUM *a, int n)
                a->top=w+1;
                a->d[w]&= ~(BN_MASK2<<b);
                }
-       bn_fix_top(a);
+       bn_correct_top(a);
        return(1);
        }
 
-int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n)
+int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
        {
        int i;
        BN_ULONG aa,bb;
@@ -790,3 +856,42 @@ int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n)
        return(0);
        }
 
+/* Here follows a specialised variants of bn_cmp_words().  It has the
+   property of performing the operation on arrays of different sizes.
+   The sizes of those arrays is expressed through cl, which is the
+   common length ( basicall, min(len(a),len(b)) ), and dl, which is the
+   delta between the two lengths, calculated as len(a)-len(b).
+   All lengths are the number of BN_ULONGs...  */
+
+int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
+       int cl, int dl)
+       {
+       int n,i;
+       n = cl-1;
+
+       if (dl < 0)
+               {
+               for (i=dl; i<0; i++)
+                       {
+                       if (b[n-i] != 0)
+                               return -1; /* a < b */
+                       }
+               }
+       if (dl > 0)
+               {
+               for (i=dl; i>0; i--)
+                       {
+                       if (a[n+i] != 0)
+                               return 1; /* a > b */
+                       }
+               }
+       return bn_cmp_words(a,b,cl);
+       }
+
+/* See the comments surrounding BIGNUM_C in bn.h */
+#ifdef BN_DEBUG
+const BIGNUM *BIGNUM_CONST(const BIGNUM_C *bn)
+       {
+       return (const BIGNUM *)bn;
+       }
+#endif