229 lines
8.6 KiB
Text
229 lines
8.6 KiB
Text
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=pod
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=head1 NAME
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bn_internal - BIGNUM library internal functions
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=head1 SYNOPSIS
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BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
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BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
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BN_ULONG w);
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void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
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BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
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BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
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int num);
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BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
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int num);
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void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
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void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
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void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
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void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
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int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
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void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
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int nb);
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void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
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void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
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BN_ULONG *tmp);
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void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
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int tn, int n, BN_ULONG *tmp);
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void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
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int n2, BN_ULONG *tmp);
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void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
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int n2, BN_ULONG *tmp);
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void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
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void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
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void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
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void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
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void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
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BIGNUM *bn_expand(BIGNUM *a, int bits);
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BIGNUM *bn_wexpand(BIGNUM *a, int n);
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BIGNUM *bn_expand2(BIGNUM *a, int n);
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void bn_fix_top(BIGNUM *a);
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void bn_check_top(BIGNUM *a);
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void bn_print(BIGNUM *a);
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void bn_dump(BN_ULONG *d, int n);
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void bn_set_max(BIGNUM *a);
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void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
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void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
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=head1 DESCRIPTION
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This page documents the internal functions used by the OpenSSL
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B<BIGNUM> implementation. They are described here to facilitate
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debugging and extending the library. They are I<not> to be used by
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applications.
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=head2 The BIGNUM structure
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typedef struct bignum_st
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{
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int top; /* index of last used d (most significant word) */
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BN_ULONG *d; /* pointer to an array of 'BITS2' bit chunks */
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int max; /* size of the d array */
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int neg; /* sign */
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} BIGNUM;
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The big number is stored in B<d>, a malloc()ed array of B<BN_ULONG>s,
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least significant first. A B<BN_ULONG> can be either 16, 32 or 64 bits
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in size (B<BITS2>), depending on the 'number of bits' specified in
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C<openssl/bn.h>.
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B<max> is the size of the B<d> array that has been allocated. B<top>
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is the 'last' entry being used, so for a value of 4, bn.d[0]=4 and
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bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is
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B<0>, the B<d> field can be B<NULL> and B<top> == B<0>.
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Various routines in this library require the use of temporary
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B<BIGNUM> variables during their execution. Since dynamic memory
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allocation to create B<BIGNUM>s is rather expensive when used in
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conjunction with repeated subroutine calls, the B<BN_CTX> structure is
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used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s.
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B<BN_CTX_NUM> is the maximum number of temporary B<BIGNUM>s any
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publicly exported function will use.
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#define BN_CTX_NUM 12
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typedef struct bignum_ctx
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{
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int tos; /* top of stack */
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BIGNUM *bn[BN_CTX_NUM]; /* The variables */
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} BN_CTX;
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B<tos> is the index of the first unused B<BIGNUM> in the B<bn> array.
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=head2 Low-level arithmetic operations
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These functions are implemented in C and for several platforms in
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assembly language:
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bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word
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arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result
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in B<rp>, and returns the high word (carry).
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bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num>
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word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places
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the result in B<rp>, and returns the high word (carry).
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bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array
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B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap>
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word-wise, and places the low and high bytes of the result in B<rp>.
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bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>,B<l>)
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by B<d> and returns the result.
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bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
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arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the
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result in B<rp>, and returns the high word (carry).
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bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
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arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the
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result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0
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otherwise).
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bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
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B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the
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result in B<r>.
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bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
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B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the
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result in B<r>.
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bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
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B<b> and the 8 word array B<r>.
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bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
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B<b> and the 16 word array B<r>.
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The following functions are implemented in C:
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bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a>
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and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and
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less than B<b>.
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bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na>
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word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word
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array B<r>. It computes B<a>*B<b> and places the result in B<r>.
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bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word
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arrays B<r>, B<a> und B<b>. It computes the B<n> low words of
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B<a>*B<b> and places the result in B<r>.
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bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<t>) operates on the B<n2>
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word arrays B<a> and B<b> and the 2*B<n2> word arrays B<r> and B<t>.
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B<n2> must be a power of 2. It computes B<a>*B<b> and places the
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result in B<r>.
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bn_mul_part_recursive(B<r>, B<a>, B<b>, B<tn>, B<n>, B<tmp>) operates
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on the B<n>+B<tn> word arrays B<a> and B<b> and the 4*B<n> word arrays
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B<r> and B<tmp>.
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bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the
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B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a>
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and B<b>.
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bn_mul_high(B<r>, B<a>, B<b>, B<l>, B<n2>, B<tmp>) operates on the
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B<n2> word arrays B<r>, B<a>, B<b> and B<l> (?) and the 3*B<n2> word
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array B<tmp>.
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BN_mul() calls bn_mul_normal(), or an optimized implementation if the
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factors have the same size: bn_mul_comba8() is used if they are 8
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words long, bn_mul_recursive() if they are larger than
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B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word
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size, and bn_mul_part_recursive() for others that are larger than
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B<BN_MULL_SIZE_NORMAL>.
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bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array
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B<a> and the 2*B<n> word arrays B<tmp> and B<r>.
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The implementations use the following macros which, depending on the
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architecture, may use "long long" C operations or inline assembler.
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They are defined in C<bn_lcl.h>.
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mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the
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low word of the result in B<r> and the high word in B<c>.
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mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and
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places the low word of the result in B<r> and the high word in B<c>.
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sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word
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of the result in B<r0> and the high word in B<r1>.
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=head2 Size changes
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bn_expand() ensures that B<b> has enough space for a B<bits> bit
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number. bn_wexpand() ensures that B<b> has enough space for an
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B<n> word number. If the number has to be expanded, both macros
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call bn_expand2(), which allocates a new B<d> array and copies the
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data. They return B<NULL> on error, B<b> otherwise.
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The bn_fix_top() macro reduces B<a-E<gt>top> to most significant
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non-zero word when B<a> has shrunk.
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=head2 Debugging
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bn_check_top() verifies that C<((a)->top E<gt>= 0 && (a)-E<gt>top
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E<lt>= (a)-E<gt>max)>. A violation will cause the program to abort.
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bn_print() prints B<a> to stderr. bn_dump() prints B<n> words at B<d>
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(in reverse order, i.e. most significant word first) to stderr.
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bn_set_max() makes B<a> a static number with a B<max> of its current size.
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This is used by bn_set_low() and bn_set_high() to make B<r> a read-only
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B<BIGNUM> that contains the B<n> lower or higher words of B<a>.
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If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump()
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and bn_set_max() are defined as empty macros.
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=head1 SEE ALSO
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L<bn(3)|bn(3)>
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=cut
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