bn_internal(3)              OpenSSL              bn_internal(3)





NAME
       bn_mul_words, bn_mul_add_words, bn_sqr_words,
       bn_div_words, bn_add_words, bn_sub_words, bn_mul_comba4,
       bn_mul_comba8, bn_sqr_comba4, bn_sqr_comba8,
       bn_cmp_words, bn_mul_normal, bn_mul_low_normal,
       bn_mul_recursive, bn_mul_part_recursive,
       bn_mul_low_recursive, bn_mul_high, bn_sqr_normal,
       bn_sqr_recursive, bn_expand, bn_wexpand, bn_expand2,
       bn_fix_top, bn_check_top, bn_print, bn_dump, bn_set_max,
       bn_set_high, bn_set_low - BIGNUM library internal func-
       tions

SYNOPSIS
        BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
        BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
          BN_ULONG w);
        void     bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
        BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
        BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
          int num);
        BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
          int num);

        void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
        void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
        void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
        void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);

        int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);

        void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
          int nb);
        void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
        void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
          int dna,int dnb,BN_ULONG *tmp);
        void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
          int n, int tna,int tnb, BN_ULONG *tmp);
        void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
          int n2, BN_ULONG *tmp);
        void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
          int n2, BN_ULONG *tmp);

        void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
        void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);

        void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
        void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
        void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);

        BIGNUM *bn_expand(BIGNUM *a, int bits);
        BIGNUM *bn_wexpand(BIGNUM *a, int n);
        BIGNUM *bn_expand2(BIGNUM *a, int n);
        void bn_fix_top(BIGNUM *a);

        void bn_check_top(BIGNUM *a);
        void bn_print(BIGNUM *a);
        void bn_dump(BN_ULONG *d, int n);
        void bn_set_max(BIGNUM *a);
        void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
        void bn_set_low(BIGNUM *r, BIGNUM *a, int n);

DESCRIPTION
       This page documents the internal functions used by the
       OpenSSL BIGNUM implementation. They are described here
       to facilitate debugging and extending the library. They
       are not to be used by applications.

       The BIGNUM structure

        typedef struct bignum_st
               {
               int top;      /* index of last used d (most significant word) */
               BN_ULONG *d;  /* pointer to an array of 'BITS2' bit chunks */
               int max;      /* size of the d array */
               int neg;      /* sign */
               } BIGNUM;

       The big number is stored in d, a malloc()ed array of
       BN_ULONGs, least significant first. A BN_ULONG can be
       either 16, 32 or 64 bits in size (BITS2), depending on
       the 'number of bits' specified in "openssl/bn.h".

       max is the size of the d array that has been allocated.
       top is the 'last' entry being used, so for a value of 4,
       bn.d[0]=4 and bn.top=1.  neg is 1 if the number is nega-
       tive.  When a BIGNUM is 0, the d field can be NULL and
       top == 0.

       Various routines in this library require the use of tem-
       porary BIGNUM variables during their execution.  Since
       dynamic memory allocation to create BIGNUMs is rather
       expensive when used in conjunction with repeated subrou-
       tine calls, the BN_CTX structure is used.  This struc-
       ture contains BN_CTX_NUM BIGNUMs, see BN_CTX_start(3).

       Low-level arithmetic operations

       These functions are implemented in C and for several
       platforms in assembly language:

       bn_mul_words(rp, ap, num, w) operates on the num word
       arrays rp and ap.  It computes ap * w, places the result
       in rp, and returns the high word (carry).

       bn_mul_add_words(rp, ap, num, w) operates on the num
       word arrays rp and ap.  It computes ap * w + rp, places
       the result in rp, and returns the high word (carry).

       bn_sqr_words(rp, ap, n) operates on the num word array
       ap and the 2*num word array ap.  It computes ap * ap
       word-wise, and places the low and high bytes of the
       result in rp.

       bn_div_words(h, l, d) divides the two word number (h,l)
       by d and returns the result.

       bn_add_words(rp, ap, bp, num) operates on the num word
       arrays ap, bp and rp.  It computes ap + bp, places the
       result in rp, and returns the high word (carry).

       bn_sub_words(rp, ap, bp, num) operates on the num word
       arrays ap, bp and rp.  It computes ap - bp, places the
       result in rp, and returns the carry (1 if bp > ap, 0
       otherwise).

       bn_mul_comba4(r, a, b) operates on the 4 word arrays a
       and b and the 8 word array r.  It computes a*b and
       places the result in r.

       bn_mul_comba8(r, a, b) operates on the 8 word arrays a
       and b and the 16 word array r.  It computes a*b and
       places the result in r.

       bn_sqr_comba4(r, a, b) operates on the 4 word arrays a
       and b and the 8 word array r.

       bn_sqr_comba8(r, a, b) operates on the 8 word arrays a
       and b and the 16 word array r.

       The following functions are implemented in C:

       bn_cmp_words(a, b, n) operates on the n word arrays a
       and b.  It returns 1, 0 and -1 if a is greater than,
       equal and less than b.

       bn_mul_normal(r, a, na, b, nb) operates on the na word
       array a, the nb word array b and the na+nb word array r.
       It computes a*b and places the result in r.

       bn_mul_low_normal(r, a, b, n) operates on the n word
       arrays r, a and b.  It computes the n low words of a*b
       and places the result in r.

       bn_mul_recursive(r, a, b, n2, dna, dnb, t) operates on
       the word arrays a and b of length n2+dna and n2+dnb (dna
       and dnb are currently allowed to be 0 or negative) and
       the 2*n2 word arrays r and t.  n2 must be a power of 2.
       It computes a*b and places the result in r.

       bn_mul_part_recursive(r, a, b, n, tna, tnb, tmp) oper-
       ates on the word arrays a and b of length n+tna and
       n+tnb and the 4*n word arrays r and tmp.

       bn_mul_low_recursive(r, a, b, n2, tmp) operates on the
       n2 word arrays r and tmp and the n2/2 word arrays a and
       b.

       bn_mul_high(r, a, b, l, n2, tmp) operates on the n2 word
       arrays r, a, b and l (?) and the 3*n2 word array tmp.

       BN_mul() calls bn_mul_normal(), or an optimized imple-
       mentation if the factors have the same size:
       bn_mul_comba8() is used if they are 8 words long,
       bn_mul_recursive() if they are larger than
       BN_MULL_SIZE_NORMAL and the size is an exact multiple of
       the word size, and bn_mul_part_recursive() for others
       that are larger than BN_MULL_SIZE_NORMAL.

       bn_sqr_normal(r, a, n, tmp) operates on the n word array
       a and the 2*n word arrays tmp and r.

       The implementations use the following macros which,
       depending on the architecture, may use "long long" C
       operations or inline assembler.  They are defined in
       "bn_lcl.h".

       mul(r, a, w, c) computes w*a+c and places the low word
       of the result in r and the high word in c.

       mul_add(r, a, w, c) computes w*a+r+c and places the low
       word of the result in r and the high word in c.

       sqr(r0, r1, a) computes a*a and places the low word of
       the result in r0 and the high word in r1.

       Size changes

       bn_expand() ensures that b has enough space for a bits
       bit number.  bn_wexpand() ensures that b has enough
       space for an n word number.  If the number has to be
       expanded, both macros call bn_expand2(), which allocates
       a new d array and copies the data.  They return NULL on
       error, b otherwise.

       The bn_fix_top() macro reduces a->top to point to the
       most significant non-zero word when a has shrunk.

       Debugging

       bn_check_top() verifies that "((a)->top >= 0 && (a)->top
       <= (a)->max)".  A violation will cause the program to
       abort.

       bn_print() prints a to stderr. bn_dump() prints n words
       at d (in reverse order, i.e. most significant word
       first) to stderr.

       bn_set_max() makes a a static number with a max of its
       current size.  This is used by bn_set_low() and
       bn_set_high() to make r a read-only BIGNUM that contains
       the n low or high words of a.

       If BN_DEBUG is not defined, bn_check_top(), bn_print(),
       bn_dump() and bn_set_max() are defined as empty macros.

SEE ALSO
       bn(3)



0.9.7c                     2002-05-30            bn_internal(3)
