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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
       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);

	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).

       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 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 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)

3rd Berkeley Distribution	    0.9.6m			bn_internal(3)
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