bn_internal(3)

     bn_internal(3)         0.9.6h (2000-09-19)         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 functions

     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,
             BN_ULONG *tmp);
           void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
             int tn, int n, 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);

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           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 negative.
          When a BIGNUM is 0, the d field can be NULL and top == 0.

          Various routines in this library require the use of
          temporary BIGNUM variables during their execution.  Since
          dynamic memory allocation to create BIGNUMs is rather
          expensive when used in conjunction with repeated subroutine
          calls, the BN_CTX structure is used.  This structure
          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).

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          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, t) operates on the n2 word
          arrays a and b 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, tn, n, tmp) operates on the
          n+tn word arrays a and b and the 4*n word arrays r and tmp.

          bn_mul_low_recursive(r, a, b, n2, tmp) operates on the n2

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          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
          implementation 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

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          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)

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