/* crypto/bn/bn.h */
/* 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 <openssl/e_os2.h>
# ifndef OPENSSL_NO_FP_API
#  include <stdio.h>            /* FILE */
# endif
# include <openssl/ossl_typ.h>
# include <openssl/crypto.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.
 */
# if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
    defined(OPENSSL_SYS_WIN32) || defined(linux)
#  ifndef BN_DIV2W
#   define BN_DIV2W
#  endif
# endif

/*
 * assuming long is 64bit - this is the DEC Alpha unsigned long long is only
 * 64 bits :-(, don't define BN_LLONG for the DEC Alpha
 */
# ifdef SIXTY_FOUR_BIT_LONG
#  define BN_ULLONG       unsigned long long
#  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_MASK         (0xffffffffffffffffffffffffffffffffLL)
#  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"
# endif

/*
 * This is where the long long data type is 64 bits, but long is 32. For
 * machines where there are 64bit registers, this is the mode to use. IRIX,
 * on R4000 and above should use this mode, along with the relevant assembler
 * code :-).  Do NOT define BN_LLONG.
 */
# ifdef SIXTY_FOUR_BIT
#  undef BN_LLONG
#  undef BN_ULLONG
#  define BN_ULONG        unsigned long long
#  define BN_LONG         long long
#  define BN_BITS         128
#  define BN_BYTES        8
#  define BN_BITS2        64
#  define BN_BITS4        32
#  define BN_MASK2        (0xffffffffffffffffLL)
#  define BN_MASK2l       (0xffffffffL)
#  define BN_MASK2h       (0xffffffff00000000LL)
#  define BN_MASK2h1      (0xffffffff80000000LL)
#  define BN_TBIT         (0x8000000000000000LL)
#  define BN_DEC_CONV     (10000000000000000000ULL)
#  define BN_DEC_FMT1     "%llu"
#  define BN_DEC_FMT2     "%019llu"
#  define BN_DEC_NUM      19
#  define BN_HEX_FMT1     "%llX"
#  define BN_HEX_FMT2     "%016llX"
# endif

# ifdef THIRTY_TWO_BIT
#  ifdef BN_LLONG
#   if defined(_WIN32) && !defined(__GNUC__)
#    define BN_ULLONG     unsigned __int64
#    define BN_MASK       (0xffffffffffffffffI64)
#   else
#    define BN_ULLONG     unsigned long long
#    define BN_MASK       (0xffffffffffffffffLL)
#   endif
#  endif
#  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_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

/*
 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
 * size_t was used to perform integer-only operations on pointers.  This
 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
 * is still only 32 bits.  What's needed in these cases is an integer type
 * with the same size as a pointer, which size_t is not certain to be. The
 * only fix here is VMS-specific.
 */
# if defined(OPENSSL_SYS_VMS)
#  if __INITIAL_POINTER_SIZE == 64
#   define PTR_SIZE_INT long long
#  else                         /* __INITIAL_POINTER_SIZE == 64 */
#   define PTR_SIZE_INT int
#  endif                        /* __INITIAL_POINTER_SIZE == 64 [else] */
# else                          /* defined(OPENSSL_SYS_VMS) */
#  define PTR_SIZE_INT size_t
# endif                         /* defined(OPENSSL_SYS_VMS) [else] */

OPENSSL_compile_assert(BN_BITS2 == sizeof(BN_ULONG) * 8, BN_BITS_SET_CORRECTLY);

# define BN_DEFAULT_BITS 1280

# define BN_FLG_MALLOCED         0x01
# define BN_FLG_STATIC_DATA      0x02

/*
 * 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.
 */
# define BN_FLG_CONSTTIME        0x04

# ifdef OPENSSL_NO_DEPRECATED
/* deprecated name for the flag */
#  define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
/*
 * 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)))

/* Already declared in ossl_typ.h */
# if 0
typedef struct bignum_st BIGNUM;
/* Used for temp variables (declaration hidden in bn_lcl.h) */
typedef struct bignum_ctx BN_CTX;
typedef struct bn_blinding_st BN_BLINDING;
typedef struct bn_mont_ctx_st BN_MONT_CTX;
typedef struct bn_recp_ctx_st BN_RECP_CTX;
typedef struct bn_gencb_st BN_GENCB;
# endif

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;
};
/* 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)

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))
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);

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);
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);
# ifndef OPENSSL_NO_FP_API
int BN_print_fp(FILE *fp, const BIGNUM *a);
# endif
# ifdef HEADER_BIO_H
int BN_print(BIO *fp, const BIGNUM *a);
# else
int BN_print(void *fp, const BIGNUM *a);
# endif
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);
int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
                                                                  * -2 for
                                                                  * error */
BIGNUM *BN_mod_inverse(BIGNUM *ret,
                       const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
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.
 */

/*
 * r = a + b
 */
int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
#  define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
/*
 * r=a mod p
 */
int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
/* r = (a * b) mod p */
int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                    const BIGNUM *p, BN_CTX *ctx);
/* r = (a * a) mod p */
int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
/* r = (1 / b) mod p */
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
/* r = (a / 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 = sqrt(a) mod p */
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                     BN_CTX *ctx);
/* r^2 + r = a mod p */
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                           BN_CTX *ctx);
#  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.
 */
/* r = a mod p */
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
/* r = (a * b) mod p */
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                        const int p[], BN_CTX *ctx);
/* r = (a * a) mod p */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
                        BN_CTX *ctx);
/* r = (1 / b) mod p */
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
                        BN_CTX *ctx);
/* r = (a / 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 = sqrt(a) mod p */
int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
                         const int p[], BN_CTX *ctx);
/* r^2 + r = a mod p */
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
                               const int p[], BN_CTX *ctx);
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);

/* library internal functions */

# define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
        (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
# define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
BIGNUM *bn_expand2(BIGNUM *a, int words);
# ifndef OPENSSL_NO_DEPRECATED
BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
# endif

/*-
 * Bignum consistency macros
 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
 * bignum data after direct manipulations on the data. There is also an
 * "internal" macro, bn_check_top(), for verifying that there are no leading
 * zeroes. Unfortunately, some auditing is required due to the fact that
 * bn_fix_top() has become an overabused duct-tape because bignum data is
 * occasionally passed around in an inconsistent state. So the following
 * changes have been made to sort this out;
 * - bn_fix_top()s implementation has been moved to bn_correct_top()
 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
 *   bn_check_top() is as before.
 * - if BN_DEBUG *is* defined;
 *   - bn_check_top() tries to pollute unused words even if the bignum 'top' is
 *     consistent. (ed: only if BN_DEBUG_RAND is defined)
 *   - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
 * The idea is to have debug builds flag up inconsistent bignums when they
 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
 * was not appropriate, we convert it permanently to bn_check_top() and track
 * down the cause of the bug. Eventually, no internal code should be using the
 * bn_fix_top() macro. External applications and libraries should try this with
 * their own code too, both in terms of building against the openssl headers
 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
 * defined. This not only improves external code, it provides more test
 * coverage for openssl's own code.
 */

# ifdef BN_DEBUG

/* We only need OPENSSL_port_assert() when debugging */
#  include <assert.h>

#  ifdef BN_DEBUG_RAND
/* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
#   ifndef RAND_pseudo_bytes
int RAND_pseudo_bytes(unsigned char *buf, int num);
#    define BN_DEBUG_TRIX
#   endif
#   define bn_pollute(a) \
        do { \
                const BIGNUM *_bnum1 = (a); \
                if(_bnum1->top < _bnum1->dmax) { \
                        unsigned char _tmp_char; \
                        /* We cast away const without the compiler knowing, any \
                         * *genuinely* constant variables that aren't mutable \
                         * wouldn't be constructed with top!=dmax. */ \
                        BN_ULONG *_not_const; \
                        OPENSSL_port_memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
                        /* Debug only - safe to ignore error return */ \
                        RAND_pseudo_bytes(&_tmp_char, 1); \
                        OPENSSL_port_memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
                                (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
                } \
        } while(0)
#   ifdef BN_DEBUG_TRIX
#    undef RAND_pseudo_bytes
#   endif
#  else
#   define bn_pollute(a)
#  endif
#  define bn_check_top(a) \
        do { \
                const BIGNUM *_bnum2 = (a); \
                if (_bnum2 != NULL) { \
                        OPENSSL_port_assert((_bnum2->top == 0) || \
                                (_bnum2->d[_bnum2->top - 1] != 0)); \
                        bn_pollute(_bnum2); \
                } \
        } while(0)

#  define bn_fix_top(a)           bn_check_top(a)

#  define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
#  define bn_wcheck_size(bn, words) \
        do { \
                const BIGNUM *_bnum2 = (bn); \
                OPENSSL_port_assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
                /* avoid unused variable warning with NDEBUG */ \
                (void)(_bnum2); \
        } while(0)

# else                          /* !BN_DEBUG */

#  define bn_pollute(a)
#  define bn_check_top(a)
#  define bn_fix_top(a)           bn_correct_top(a)
#  define bn_check_size(bn, bits)
#  define bn_wcheck_size(bn, words)

# endif

# define bn_correct_top(a) \
        { \
        BN_ULONG *ftl; \
        int tmp_top = (a)->top; \
        if (tmp_top > 0) \
                { \
                for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
                        if (*(ftl--)) break; \
                (a)->top = tmp_top; \
                } \
        bn_pollute(a); \
        }

BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
                          BN_ULONG w);
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
void bn_sqr_words(BN_ULONG *rp, const 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, const BN_ULONG *ap, const BN_ULONG *bp,
                      int num);
BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
                      int num);

/* Primes from RFC 2409 */
BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
BIGNUM *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);

int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);

/* 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_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_LSHIFT                                   145
# 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_RSHIFT                                   146
# 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                              118
# 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_INVALID_SHIFT                               119
# 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