text: /* $OpenBSD: bn.h,v 1.38 2018/02/20 17:13:14 jsing Exp $ */
  /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
   * All rights reserved.
   *
   * This package is an SSL implementation written
   * by Eric Young (eay@cryptsoft.com).
   * The implementation was written so as to conform with Netscapes SSL.
   *
   * This library is free for commercial and non-commercial use as long as
   * the following conditions are aheared to.  The following conditions
   * apply to all code found in this distribution, be it the RC4, RSA,
   * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
   * included with this distribution is covered by the same copyright terms
   * except that the holder is Tim Hudson (tjh@cryptsoft.com).
   *
   * Copyright remains Eric Young's, and as such any Copyright notices in
   * the code are not to be removed.
   * If this package is used in a product, Eric Young should be given attribution
   * as the author of the parts of the library used.
   * This can be in the form of a textual message at program startup or
   * in documentation (online or textual) provided with the package.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   * 1. Redistributions of source code must retain the copyright
   *    notice, this list of conditions and the following disclaimer.
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in the
   *    documentation and/or other materials provided with the distribution.
   * 3. All advertising materials mentioning features or use of this software
   *    must display the following acknowledgement:
   *    "This product includes cryptographic software written by
   *     Eric Young (eay@cryptsoft.com)"
   *    The word 'cryptographic' can be left out if the rouines from the library
   *    being used are not cryptographic related :-).
   * 4. If you include any Windows specific code (or a derivative thereof) from
   *    the apps directory (application code) you must include an acknowledgement:
   *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
   *
   * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
   * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
   * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
   * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   *
   * The licence and distribution terms for any publically available version or
   * derivative of this code cannot be changed.  i.e. this code cannot simply be
   * copied and put under another distribution licence
   * [including the GNU Public Licence.]
   */
  /* ====================================================================
   * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. All advertising materials mentioning features or use of this
   *    software must display the following acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
   *
   * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
   *    endorse or promote products derived from this software without
   *    prior written permission. For written permission, please contact
   *    openssl-core@openssl.org.
   *
   * 5. Products derived from this software may not be called "OpenSSL"
   *    nor may "OpenSSL" appear in their names without prior written
   *    permission of the OpenSSL Project.
   *
   * 6. Redistributions of any form whatsoever must retain the following
   *    acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
   *
   * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
   * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
   * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
   * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
   * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
   * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
   * OF THE POSSIBILITY OF SUCH DAMAGE.
   * ====================================================================
   *
   * This product includes cryptographic software written by Eric Young
   * (eay@cryptsoft.com).  This product includes software written by Tim
   * Hudson (tjh@cryptsoft.com).
   *
   */
  /* ====================================================================
   * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
   *
   * Portions of the attached software ("Contribution") are developed by
   * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
   *
   * The Contribution is licensed pursuant to the Eric Young open source
   * license provided above.
   *
   * The binary polynomial arithmetic software is originally written by
   * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
   *
   */
  
  #ifndef HEADER_BN_H
  #define HEADER_BN_H
  
  #include <stdio.h>
  #include <stdlib.h>
  
  #include <openssl/opensslconf.h>
  
  #include <openssl/ossl_typ.h>
  #include <openssl/crypto.h>
  #include <openssl/bio.h>
  
  #ifdef  __cplusplus
  extern "C" {
  #endif
  
  /* These preprocessor symbols control various aspects of the bignum headers and
   * library code. They're not defined by any "normal" configuration, as they are
   * intended for development and testing purposes. NB: defining all three can be
   * useful for debugging application code as well as openssl itself.
   *
   * BN_DEBUG - turn on various debugging alterations to the bignum code
   * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
   * mismanagement of bignum internals. You must also define BN_DEBUG.
   */
  /* #define BN_DEBUG */
  /* #define BN_DEBUG_RAND */
  
  #ifndef OPENSSL_SMALL_FOOTPRINT
  #define BN_MUL_COMBA
  #define BN_SQR_COMBA
  #define BN_RECURSION
  #endif
  
  /* This next option uses the C libraries (2 word)/(1 word) function.
   * If it is not defined, I use my C version (which is slower).
   * The reason for this flag is that when the particular C compiler
   * library routine is used, and the library is linked with a different
   * compiler, the library is missing.  This mostly happens when the
   * library is built with gcc and then linked using normal cc.  This would
   * be a common occurrence because gcc normally produces code that is
   * 2 times faster than system compilers for the big number stuff.
   * For machines with only one compiler (or shared libraries), this should
   * be on.  Again this in only really a problem on machines
   * using "long long's", are 32bit, and are not using my assembler code. */
  /* #define BN_DIV2W */
  
  #ifdef _LP64
  #undef	BN_LLONG
  #define BN_ULONG	unsigned long
  #define BN_LONG		long
  #define BN_BITS		128
  #define BN_BYTES	8
  #define BN_BITS2	64
  #define BN_BITS4	32
  #define BN_MASK2	(0xffffffffffffffffL)
  #define BN_MASK2l	(0xffffffffL)
  #define BN_MASK2h	(0xffffffff00000000L)
  #define BN_MASK2h1	(0xffffffff80000000L)
  #define BN_TBIT		(0x8000000000000000L)
  #define BN_DEC_CONV	(10000000000000000000UL)
  #define BN_DEC_FMT1	"%lu"
  #define BN_DEC_FMT2	"%019lu"
  #define BN_DEC_NUM	19
  #define BN_HEX_FMT1	"%lX"
  #define BN_HEX_FMT2	"%016lX"
  #else
  #define BN_ULLONG	unsigned long long
  #define	BN_LLONG
  #define BN_ULONG	unsigned int
  #define BN_LONG		int
  #define BN_BITS		64
  #define BN_BYTES	4
  #define BN_BITS2	32
  #define BN_BITS4	16
  #define BN_MASK		(0xffffffffffffffffLL)
  #define BN_MASK2	(0xffffffffL)
  #define BN_MASK2l	(0xffff)
  #define BN_MASK2h1	(0xffff8000L)
  #define BN_MASK2h	(0xffff0000L)
  #define BN_TBIT		(0x80000000L)
  #define BN_DEC_CONV	(1000000000L)
  #define BN_DEC_FMT1	"%u"
  #define BN_DEC_FMT2	"%09u"
  #define BN_DEC_NUM	9
  #define BN_HEX_FMT1	"%X"
  #define BN_HEX_FMT2	"%08X"
  #endif
  
  #define BN_FLG_MALLOCED		0x01
  #define BN_FLG_STATIC_DATA	0x02
  #define BN_FLG_CONSTTIME	0x04 /* avoid leaking exponent information through timing,
                                        * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
                                        * BN_div() will call BN_div_no_branch,
                                        * BN_mod_inverse() will call BN_mod_inverse_no_branch.
                                        */
  
  #ifndef OPENSSL_NO_DEPRECATED
  #define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME /* deprecated name for the flag */
                                        /* avoid leaking exponent information through timings
                                        * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
  #endif
  
  #ifndef OPENSSL_NO_DEPRECATED
  #define BN_FLG_FREE		0x8000	/* used for debuging */
  #endif
  #define BN_set_flags(b,n)	((b)->flags|=(n))
  #define BN_get_flags(b,n)	((b)->flags&(n))
  
  /* get a clone of a BIGNUM with changed flags, for *temporary* use only
   * (the two BIGNUMs cannot not be used in parallel!) */
  #define BN_with_flags(dest,b,n)  ((dest)->d=(b)->d, \
                                    (dest)->top=(b)->top, \
                                    (dest)->dmax=(b)->dmax, \
                                    (dest)->neg=(b)->neg, \
                                    (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
                                                   |  ((b)->flags & ~BN_FLG_MALLOCED) \
                                                   |  BN_FLG_STATIC_DATA \
                                                   |  (n)))
  
  struct bignum_st {
  	BN_ULONG *d;	/* Pointer to an array of 'BN_BITS2' bit chunks. */
  	int top;	/* Index of last used d +1. */
  	/* The next are internal book keeping for bn_expand. */
  	int dmax;	/* Size of the d array. */
  	int neg;	/* one if the number is negative */
  	int flags;
  };
  
  /* Used for montgomery multiplication */
  struct bn_mont_ctx_st {
  	int ri;        /* number of bits in R */
  	BIGNUM RR;     /* used to convert to montgomery form */
  	BIGNUM N;      /* The modulus */
  	BIGNUM Ni;     /* R*(1/R mod N) - N*Ni = 1
  	                * (Ni is only stored for bignum algorithm) */
  	BN_ULONG n0[2];/* least significant word(s) of Ni;
  	                  (type changed with 0.9.9, was "BN_ULONG n0;" before) */
  	int flags;
  };
  
  /* Used for reciprocal division/mod functions
   * It cannot be shared between threads
   */
  struct bn_recp_ctx_st {
  	BIGNUM N;	/* the divisor */
  	BIGNUM Nr;	/* the reciprocal */
  	int num_bits;
  	int shift;
  	int flags;
  };
  
  /* Used for slow "generation" functions. */
  struct bn_gencb_st {
  	unsigned int ver;	/* To handle binary (in)compatibility */
  	void *arg;		/* callback-specific data */
  	union {
  		/* if(ver==1) - handles old style callbacks */
  		void (*cb_1)(int, int, void *);
  		/* if(ver==2) - new callback style */
  		int (*cb_2)(int, int, BN_GENCB *);
  	} cb;
  };
  
  BN_GENCB *BN_GENCB_new(void);
  void BN_GENCB_free(BN_GENCB *cb);
  void *BN_GENCB_get_arg(BN_GENCB *cb);
  
  /* Wrapper function to make using BN_GENCB easier,  */
  int BN_GENCB_call(BN_GENCB *cb, int a, int b);
  /* Macro to populate a BN_GENCB structure with an "old"-style callback */
  #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
  		BN_GENCB *tmp_gencb = (gencb); \
  		tmp_gencb->ver = 1; \
  		tmp_gencb->arg = (cb_arg); \
  		tmp_gencb->cb.cb_1 = (callback); }
  /* Macro to populate a BN_GENCB structure with a "new"-style callback */
  #define BN_GENCB_set(gencb, callback, cb_arg) { \
  		BN_GENCB *tmp_gencb = (gencb); \
  		tmp_gencb->ver = 2; \
  		tmp_gencb->arg = (cb_arg); \
  		tmp_gencb->cb.cb_2 = (callback); }
  
  #define BN_prime_checks 0 /* default: select number of iterations
  			     based on the size of the number */
  
  /* number of Miller-Rabin iterations for an error rate  of less than 2^-80
   * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
   * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
   * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
   * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
  #define BN_prime_checks_for_size(b) ((b) >= 1300 ?  2 : \
                                  (b) >=  850 ?  3 : \
                                  (b) >=  650 ?  4 : \
                                  (b) >=  550 ?  5 : \
                                  (b) >=  450 ?  6 : \
                                  (b) >=  400 ?  7 : \
                                  (b) >=  350 ?  8 : \
                                  (b) >=  300 ?  9 : \
                                  (b) >=  250 ? 12 : \
                                  (b) >=  200 ? 15 : \
                                  (b) >=  150 ? 18 : \
                                  /* b >= 100 */ 27)
  
  #define BN_num_bytes(a)	((BN_num_bits(a)+7)/8)
  
  /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
  #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
  				(((w) == 0) && ((a)->top == 0)))
  #define BN_is_zero(a)       ((a)->top == 0)
  #define BN_is_one(a)        (BN_abs_is_word((a),1) && !(a)->neg)
  #define BN_is_word(a,w)     (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
  #define BN_is_odd(a)	    (((a)->top > 0) && ((a)->d[0] & 1))
  
  #define BN_one(a)	(BN_set_word((a),1))
  #define BN_zero_ex(a) \
  	do { \
  		BIGNUM *_tmp_bn = (a); \
  		_tmp_bn->top = 0; \
  		_tmp_bn->neg = 0; \
  	} while(0)
  
  #ifdef OPENSSL_NO_DEPRECATED
  #define BN_zero(a)	BN_zero_ex(a)
  #else
  #define BN_zero(a)	(BN_set_word((a),0))
  #endif
  
  const BIGNUM *BN_value_one(void);
  char *	BN_options(void);
  BN_CTX *BN_CTX_new(void);
  #ifndef OPENSSL_NO_DEPRECATED
  void	BN_CTX_init(BN_CTX *c);
  #endif
  void	BN_CTX_free(BN_CTX *c);
  void	BN_CTX_start(BN_CTX *ctx);
  BIGNUM *BN_CTX_get(BN_CTX *ctx);
  void	BN_CTX_end(BN_CTX *ctx);
  int     BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
  int     BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
  int	BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
  int	BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
  int	BN_num_bits(const BIGNUM *a);
  int	BN_num_bits_word(BN_ULONG);
  BIGNUM *BN_new(void);
  void	BN_init(BIGNUM *);
  void	BN_clear_free(BIGNUM *a);
  BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
  void	BN_swap(BIGNUM *a, BIGNUM *b);
  BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
  int	BN_bn2bin(const BIGNUM *a, unsigned char *to);
  BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
  int	BN_bn2mpi(const BIGNUM *a, unsigned char *to);
  int	BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
  int	BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
  int	BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
  int	BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
  int	BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
  int	BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
  /** BN_set_negative sets sign of a BIGNUM
   * \param  b  pointer to the BIGNUM object
   * \param  n  0 if the BIGNUM b should be positive and a value != 0 otherwise
   */
  void	BN_set_negative(BIGNUM *b, int n);
  /** BN_is_negative returns 1 if the BIGNUM is negative
   * \param  a  pointer to the BIGNUM object
   * \return 1 if a < 0 and 0 otherwise
   */
  #define BN_is_negative(a) ((a)->neg != 0)
  
  #ifndef LIBRESSL_INTERNAL
  int	BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
      BN_CTX *ctx);
  #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
  #endif
  int	BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
  int	BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
  int	BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
  int	BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
      const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
  int	BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
  
  BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
  BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
  int	BN_mul_word(BIGNUM *a, BN_ULONG w);
  int	BN_add_word(BIGNUM *a, BN_ULONG w);
  int	BN_sub_word(BIGNUM *a, BN_ULONG w);
  int	BN_set_word(BIGNUM *a, BN_ULONG w);
  BN_ULONG BN_get_word(const BIGNUM *a);
  
  int	BN_cmp(const BIGNUM *a, const BIGNUM *b);
  void	BN_free(BIGNUM *a);
  int	BN_is_bit_set(const BIGNUM *a, int n);
  int	BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
  int	BN_lshift1(BIGNUM *r, const BIGNUM *a);
  int	BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
  
  #ifndef LIBRESSL_INTERNAL
  int	BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx);
  int	BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
  #endif
  int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);
  int	BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
  int	BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
      const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
      BN_CTX *ctx, BN_MONT_CTX *m_ctx);
  int	BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx);
  
  int	BN_mask_bits(BIGNUM *a, int n);
  int	BN_print_fp(FILE *fp, const BIGNUM *a);
  int	BN_print(BIO *fp, const BIGNUM *a);
  int	BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
  int	BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
  int	BN_rshift1(BIGNUM *r, const BIGNUM *a);
  void	BN_clear(BIGNUM *a);
  BIGNUM *BN_dup(const BIGNUM *a);
  int	BN_ucmp(const BIGNUM *a, const BIGNUM *b);
  int	BN_set_bit(BIGNUM *a, int n);
  int	BN_clear_bit(BIGNUM *a, int n);
  char *	BN_bn2hex(const BIGNUM *a);
  char *	BN_bn2dec(const BIGNUM *a);
  int 	BN_hex2bn(BIGNUM **a, const char *str);
  int 	BN_dec2bn(BIGNUM **a, const char *str);
  int	BN_asc2bn(BIGNUM **a, const char *str);
  #ifndef LIBRESSL_INTERNAL
  int	BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
  #endif
  int	BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
  #ifndef LIBRESSL_INTERNAL
  BIGNUM *BN_mod_inverse(BIGNUM *ret,
      const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
  #endif
  BIGNUM *BN_mod_sqrt(BIGNUM *ret,
      const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
  
  void	BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
  
  /* Deprecated versions */
  #ifndef OPENSSL_NO_DEPRECATED
  BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
      const BIGNUM *add, const BIGNUM *rem,
      void (*callback)(int, int, void *), void *cb_arg);
  int	BN_is_prime(const BIGNUM *p, int nchecks,
      void (*callback)(int, int, void *),
      BN_CTX *ctx, void *cb_arg);
  int	BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
      void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
      int do_trial_division);
  #endif /* !defined(OPENSSL_NO_DEPRECATED) */
  
  /* Newer versions */
  int	BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
      const BIGNUM *rem, BN_GENCB *cb);
  int	BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
  int	BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
      int do_trial_division, BN_GENCB *cb);
  
  int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
  
  int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
      const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
      const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb);
  int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
      BIGNUM *Xp1, BIGNUM *Xp2,
      const BIGNUM *Xp,
      const BIGNUM *e, BN_CTX *ctx,
      BN_GENCB *cb);
  
  BN_MONT_CTX *BN_MONT_CTX_new(void );
  void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
  int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
      BN_MONT_CTX *mont, BN_CTX *ctx);
  #define BN_to_montgomery(r,a,mont,ctx)	BN_mod_mul_montgomery(\
  	(r),(a),&((mont)->RR),(mont),(ctx))
  int BN_from_montgomery(BIGNUM *r, const BIGNUM *a,
      BN_MONT_CTX *mont, BN_CTX *ctx);
  void BN_MONT_CTX_free(BN_MONT_CTX *mont);
  int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
  BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
  BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
      const BIGNUM *mod, BN_CTX *ctx);
  
  /* BN_BLINDING flags */
  #define	BN_BLINDING_NO_UPDATE	0x00000001
  #define	BN_BLINDING_NO_RECREATE	0x00000002
  
  BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
  void BN_BLINDING_free(BN_BLINDING *b);
  int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
  int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
  int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
  int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
  int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
  #ifndef OPENSSL_NO_DEPRECATED
  unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
  void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
  #endif
  CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
  unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
  void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
  BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
      const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
      int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
      BN_MONT_CTX *m_ctx);
  
  #ifndef OPENSSL_NO_DEPRECATED
  void BN_set_params(int mul, int high, int low, int mont);
  int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
  #endif
  
  void	BN_RECP_CTX_init(BN_RECP_CTX *recp);
  BN_RECP_CTX *BN_RECP_CTX_new(void);
  void	BN_RECP_CTX_free(BN_RECP_CTX *recp);
  int	BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
  int	BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
      BN_RECP_CTX *recp, BN_CTX *ctx);
  int	BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
      const BIGNUM *m, BN_CTX *ctx);
  int	BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
      BN_RECP_CTX *recp, BN_CTX *ctx);
  
  #ifndef OPENSSL_NO_EC2M
  
  /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
   *
   * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
   * ignored.
   *
   * Note that input arguments are not const so that their bit arrays can
   * be expanded to the appropriate size if needed.
   */
  
  int	BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
  #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
  int	BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
  int
  BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  	const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
  int
  BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
  	BN_CTX *ctx); /* r = (a * a) mod p */
  int
  BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
  	BN_CTX *ctx); /* r = (1 / b) mod p */
  int
  BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  	const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
  int
  BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  	const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
  int
  BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
  	BN_CTX *ctx); /* r = sqrt(a) mod p */
  int	BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
  	BN_CTX *ctx); /* r^2 + r = a mod p */
  #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
  /* Some functions allow for representation of the irreducible polynomials
   * as an unsigned int[], say p.  The irreducible f(t) is then of the form:
   *     t^p[0] + t^p[1] + ... + t^p[k]
   * where m = p[0] > p[1] > ... > p[k] = 0.
   */
  int	BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
  /* r = a mod p */
  int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  	const int p[], BN_CTX *ctx); /* r = (a * b) mod p */
  int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
  	BN_CTX *ctx); /* r = (a * a) mod p */
  int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
  	BN_CTX *ctx); /* r = (1 / b) mod p */
  int	BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  	const int p[], BN_CTX *ctx); /* r = (a / b) mod p */
  int	BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  	const int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
  int	BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
  	const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
  int	BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
  	const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
  int	BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
  int	BN_GF2m_arr2poly(const int p[], BIGNUM *a);
  
  #endif
  
  /* faster mod functions for the 'NIST primes'
   * 0 <= a < p^2 */
  int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
  int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
  int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
  int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
  int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
  
  const BIGNUM *BN_get0_nist_prime_192(void);
  const BIGNUM *BN_get0_nist_prime_224(void);
  const BIGNUM *BN_get0_nist_prime_256(void);
  const BIGNUM *BN_get0_nist_prime_384(void);
  const BIGNUM *BN_get0_nist_prime_521(void);
  
  /* Primes from RFC 2409 */
  BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
  BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
  BIGNUM *BN_get_rfc2409_prime_768(BIGNUM *bn);
  BIGNUM *BN_get_rfc2409_prime_1024(BIGNUM *bn);
  
  /* Primes from RFC 3526 */
  BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
  BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
  BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
  BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
  BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
  BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
  BIGNUM *BN_get_rfc3526_prime_1536(BIGNUM *bn);
  BIGNUM *BN_get_rfc3526_prime_2048(BIGNUM *bn);
  BIGNUM *BN_get_rfc3526_prime_3072(BIGNUM *bn);
  BIGNUM *BN_get_rfc3526_prime_4096(BIGNUM *bn);
  BIGNUM *BN_get_rfc3526_prime_6144(BIGNUM *bn);
  BIGNUM *BN_get_rfc3526_prime_8192(BIGNUM *bn);
  
  /* BEGIN ERROR CODES */
  /* The following lines are auto generated by the script mkerr.pl. Any changes
   * made after this point may be overwritten when the script is next run.
   */
  void ERR_load_BN_strings(void);
  
  /* Error codes for the BN functions. */
  
  /* Function codes. */
  #define BN_F_BNRAND					 127
  #define BN_F_BN_BLINDING_CONVERT_EX			 100
  #define BN_F_BN_BLINDING_CREATE_PARAM			 128
  #define BN_F_BN_BLINDING_INVERT_EX			 101
  #define BN_F_BN_BLINDING_NEW				 102
  #define BN_F_BN_BLINDING_UPDATE				 103
  #define BN_F_BN_BN2DEC					 104
  #define BN_F_BN_BN2HEX					 105
  #define BN_F_BN_CTX_GET					 116
  #define BN_F_BN_CTX_NEW					 106
  #define BN_F_BN_CTX_START				 129
  #define BN_F_BN_DIV					 107
  #define BN_F_BN_DIV_NO_BRANCH				 138
  #define BN_F_BN_DIV_RECP				 130
  #define BN_F_BN_EXP					 123
  #define BN_F_BN_EXPAND2					 108
  #define BN_F_BN_GENERATE_PRIME_EX			 140
  #define BN_F_BN_EXPAND_INTERNAL				 120
  #define BN_F_BN_GF2M_MOD				 131
  #define BN_F_BN_GF2M_MOD_EXP				 132
  #define BN_F_BN_GF2M_MOD_MUL				 133
  #define BN_F_BN_GF2M_MOD_SOLVE_QUAD			 134
  #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR			 135
  #define BN_F_BN_GF2M_MOD_SQR				 136
  #define BN_F_BN_GF2M_MOD_SQRT				 137
  #define BN_F_BN_MOD_EXP2_MONT				 118
  #define BN_F_BN_MOD_EXP_MONT				 109
  #define BN_F_BN_MOD_EXP_MONT_CONSTTIME			 124
  #define BN_F_BN_MOD_EXP_MONT_WORD			 117
  #define BN_F_BN_MOD_EXP_RECP				 125
  #define BN_F_BN_MOD_EXP_SIMPLE				 126
  #define BN_F_BN_MOD_INVERSE				 110
  #define BN_F_BN_MOD_INVERSE_NO_BRANCH			 139
  #define BN_F_BN_MOD_LSHIFT_QUICK			 119
  #define BN_F_BN_MOD_MUL_RECIPROCAL			 111
  #define BN_F_BN_MOD_SQRT				 121
  #define BN_F_BN_MPI2BN					 112
  #define BN_F_BN_NEW					 113
  #define BN_F_BN_RAND					 114
  #define BN_F_BN_RAND_RANGE				 122
  #define BN_F_BN_USUB					 115
  
  /* Reason codes. */
  #define BN_R_ARG2_LT_ARG3				 100
  #define BN_R_BAD_RECIPROCAL				 101
  #define BN_R_BIGNUM_TOO_LONG				 114
  #define BN_R_BITS_TOO_SMALL				 117
  #define BN_R_CALLED_WITH_EVEN_MODULUS			 102
  #define BN_R_DIV_BY_ZERO				 103
  #define BN_R_ENCODING_ERROR				 104
  #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA		 105
  #define BN_R_INPUT_NOT_REDUCED				 110
  #define BN_R_INVALID_LENGTH				 106
  #define BN_R_INVALID_RANGE				 115
  #define BN_R_NOT_A_SQUARE				 111
  #define BN_R_NOT_INITIALIZED				 107
  #define BN_R_NO_INVERSE					 108
  #define BN_R_NO_SOLUTION				 116
  #define BN_R_P_IS_NOT_PRIME				 112
  #define BN_R_TOO_MANY_ITERATIONS			 113
  #define BN_R_TOO_MANY_TEMPORARY_VARIABLES		 109
  
  #ifdef  __cplusplus
  }
  #endif
  #endif
  