openssl/crypto/bn/bn_lcl.h

/* Copyright (C) 1995-1998 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) 1998-2000 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).
 *
 */

#ifndef HEADER_BN_LCL_H
# define HEADER_BN_LCL_H

# include "internal/bn_conf.h"
# include "internal/bn_int.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)
#  define BN_DIV2W
# endif

/*
 * 64-bit processor with LP64 ABI
 */
# ifdef SIXTY_FOUR_BIT_LONG
#  define BN_ULLONG       unsigned long long
#  define BN_BITS4        32
#  define BN_MASK2        (0xffffffffffffffffL)
#  define BN_MASK2l       (0xffffffffL)
#  define BN_MASK2h       (0xffffffff00000000L)
#  define BN_MASK2h1      (0xffffffff80000000L)
#  define BN_DEC_CONV     (10000000000000000000UL)
#  define BN_DEC_NUM      19
#  define BN_DEC_FMT1     "%lu"
#  define BN_DEC_FMT2     "%019lu"
# endif

/*
 * 64-bit processor other than LP64 ABI
 */
# ifdef SIXTY_FOUR_BIT
#  undef BN_LLONG
#  undef BN_ULLONG
#  define BN_BITS4        32
#  define BN_MASK2        (0xffffffffffffffffLL)
#  define BN_MASK2l       (0xffffffffL)
#  define BN_MASK2h       (0xffffffff00000000LL)
#  define BN_MASK2h1      (0xffffffff80000000LL)
#  define BN_DEC_CONV     (10000000000000000000ULL)
#  define BN_DEC_NUM      19
#  define BN_DEC_FMT1     "%llu"
#  define BN_DEC_FMT2     "%019llu"
# endif

# ifdef THIRTY_TWO_BIT
#  ifdef BN_LLONG
#   if defined(_WIN32) && !defined(__GNUC__)
#    define BN_ULLONG     unsigned __int64
#   else
#    define BN_ULLONG     unsigned long long
#   endif
#  endif
#  define BN_BITS4        16
#  define BN_MASK2        (0xffffffffL)
#  define BN_MASK2l       (0xffff)
#  define BN_MASK2h1      (0xffff8000L)
#  define BN_MASK2h       (0xffff0000L)
#  define BN_DEC_CONV     (1000000000L)
#  define BN_DEC_NUM      9
#  define BN_DEC_FMT1     "%u"
#  define BN_DEC_FMT2     "%09u"
# 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 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; \
                        memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
                        RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
                        memset(_not_const + _bnum1->top, _tmp_char, \
                                sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
                } \
        } 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) { \
                        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); \
                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

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);

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_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
 *
 *
 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
 * the number of multiplications is a constant plus on average
 *
 *    2^(w-1) + (b-w)/(w+1);
 *
 * here  2^(w-1)  is for precomputing the table (we actually need
 * entries only for windows that have the lowest bit set), and
 * (b-w)/(w+1)  is an approximation for the expected number of
 * w-bit windows, not counting the first one.
 *
 * Thus we should use
 *
 *    w >= 6  if        b > 671
 *     w = 5  if  671 > b > 239
 *     w = 4  if  239 > b >  79
 *     w = 3  if   79 > b >  23
 *    w <= 2  if   23 > b
 *
 * (with draws in between).  Very small exponents are often selected
 * with low Hamming weight, so we use  w = 1  for b <= 23.
 */
# define BN_window_bits_for_exponent_size(b) \
                ((b) > 671 ? 6 : \
                 (b) > 239 ? 5 : \
                 (b) >  79 ? 4 : \
                 (b) >  23 ? 3 : 1)

/*
 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
 * line width of the target processor is at least the following value.
 */
# define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH      ( 64 )
# define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK       (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)

/*
 * Window sizes optimized for fixed window size modular exponentiation
 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
 * defined for cache line sizes of 32 and 64, cache line sizes where
 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
 * used on processors that have a 128 byte or greater cache line size.
 */
# if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64

#  define BN_window_bits_for_ctime_exponent_size(b) \
                ((b) > 937 ? 6 : \
                 (b) > 306 ? 5 : \
                 (b) >  89 ? 4 : \
                 (b) >  22 ? 3 : 1)
#  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (6)

# elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32

#  define BN_window_bits_for_ctime_exponent_size(b) \
                ((b) > 306 ? 5 : \
                 (b) >  89 ? 4 : \
                 (b) >  22 ? 3 : 1)
#  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (5)

# endif

/* Pentium pro 16,16,16,32,64 */
/* Alpha       16,16,16,16.64 */
# define BN_MULL_SIZE_NORMAL                     (16)/* 32 */
# define BN_MUL_RECURSIVE_SIZE_NORMAL            (16)/* 32 less than */
# define BN_SQR_RECURSIVE_SIZE_NORMAL            (16)/* 32 */
# define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL        (32)/* 32 */
# define BN_MONT_CTX_SET_SIZE_WORD               (64)/* 32 */

/*
 * 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] */
# elif !defined(PTR_SIZE_INT)   /* defined(OPENSSL_SYS_VMS) */
#  define PTR_SIZE_INT size_t
# endif                         /* defined(OPENSSL_SYS_VMS) [else] */

# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
/*
 * BN_UMULT_HIGH section.
 *
 * No, I'm not trying to overwhelm you when stating that the
 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
 * you to be impressed when I say that if the compiler doesn't
 * support 2*N integer type, then you have to replace every N*N
 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
 * and additions which unavoidably results in severe performance
 * penalties. Of course provided that the hardware is capable of
 * producing 2*N result... That's when you normally start
 * considering assembler implementation. However! It should be
 * pointed out that some CPUs (most notably Alpha, PowerPC and
 * upcoming IA-64 family:-) provide *separate* instruction
 * calculating the upper half of the product placing the result
 * into a general purpose register. Now *if* the compiler supports
 * inline assembler, then it's not impossible to implement the
 * "bignum" routines (and have the compiler optimize 'em)
 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
 * macro is about:-)
 *
 *                                      <appro@fy.chalmers.se>
 */
#  if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
#   if defined(__DECC)
#    include <c_asm.h>
#    define BN_UMULT_HIGH(a,b)   (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
#   elif defined(__GNUC__) && __GNUC__>=2
#    define BN_UMULT_HIGH(a,b)   ({      \
        register BN_ULONG ret;          \
        asm ("umulh     %1,%2,%0"       \
             : "=r"(ret)                \
             : "r"(a), "r"(b));         \
        ret;                    })
#   endif                       /* compiler */
#  elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
#   if defined(__GNUC__) && __GNUC__>=2
#    define BN_UMULT_HIGH(a,b)   ({      \
        register BN_ULONG ret;          \
        asm ("mulhdu    %0,%1,%2"       \
             : "=r"(ret)                \
             : "r"(a), "r"(b));         \
        ret;                    })
#   endif                       /* compiler */
#  elif (defined(__x86_64) || defined(__x86_64__)) && \
       (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
#   if defined(__GNUC__) && __GNUC__>=2
#    define BN_UMULT_HIGH(a,b)   ({      \
        register BN_ULONG ret,discard;  \
        asm ("mulq      %3"             \
             : "=a"(discard),"=d"(ret)  \
             : "a"(a), "g"(b)           \
             : "cc");                   \
        ret;                    })
#    define BN_UMULT_LOHI(low,high,a,b)  \
        asm ("mulq      %3"             \
                : "=a"(low),"=d"(high)  \
                : "a"(a),"g"(b)         \
                : "cc");
#   endif
#  elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
#   if defined(_MSC_VER) && _MSC_VER>=1400
unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
                          unsigned __int64 *h);
#    pragma intrinsic(__umulh,_umul128)
#    define BN_UMULT_HIGH(a,b)           __umulh((a),(b))
#    define BN_UMULT_LOHI(low,high,a,b)  ((low)=_umul128((a),(b),&(high)))
#   endif
#  elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
#   if defined(__GNUC__) && __GNUC__>=2
#    if __GNUC__>4 || (__GNUC__>=4 && __GNUC_MINOR__>=4)
                                     /* "h" constraint is no more since 4.4 */
#     define BN_UMULT_HIGH(a,b)          (((__uint128_t)(a)*(b))>>64)
#     define BN_UMULT_LOHI(low,high,a,b) ({     \
        __uint128_t ret=(__uint128_t)(a)*(b);   \
        (high)=ret>>64; (low)=ret;       })
#    else
#     define BN_UMULT_HIGH(a,b) ({      \
        register BN_ULONG ret;          \
        asm ("dmultu    %1,%2"          \
             : "=h"(ret)                \
             : "r"(a), "r"(b) : "l");   \
        ret;                    })
#     define BN_UMULT_LOHI(low,high,a,b)\
        asm ("dmultu    %2,%3"          \
             : "=l"(low),"=h"(high)     \
             : "r"(a), "r"(b));
#    endif
#   endif
#  elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
#   if defined(__GNUC__) && __GNUC__>=2
#    define BN_UMULT_HIGH(a,b)   ({      \
        register BN_ULONG ret;          \
        asm ("umulh     %0,%1,%2"       \
             : "=r"(ret)                \
             : "r"(a), "r"(b));         \
        ret;                    })
#   endif
#  endif                        /* cpu */
# endif                         /* OPENSSL_NO_ASM */

/*************************************************************
 * Using the long long type
 */
# define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
# define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)

# ifdef BN_DEBUG_RAND
#  define bn_clear_top2max(a) \
        { \
        int      ind = (a)->dmax - (a)->top; \
        BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
        for (; ind != 0; ind--) \
                *(++ftl) = 0x0; \
        }
# else
#  define bn_clear_top2max(a)
# endif

# ifdef BN_LLONG
#  define mul_add(r,a,w,c) { \
        BN_ULLONG t; \
        t=(BN_ULLONG)w * (a) + (r) + (c); \
        (r)= Lw(t); \
        (c)= Hw(t); \
        }

#  define mul(r,a,w,c) { \
        BN_ULLONG t; \
        t=(BN_ULLONG)w * (a) + (c); \
        (r)= Lw(t); \
        (c)= Hw(t); \
        }

#  define sqr(r0,r1,a) { \
        BN_ULLONG t; \
        t=(BN_ULLONG)(a)*(a); \
        (r0)=Lw(t); \
        (r1)=Hw(t); \
        }

# elif defined(BN_UMULT_LOHI)
#  define mul_add(r,a,w,c) {              \
        BN_ULONG high,low,ret,tmp=(a);  \
        ret =  (r);                     \
        BN_UMULT_LOHI(low,high,w,tmp);  \
        ret += (c);                     \
        (c) =  (ret<(c))?1:0;           \
        (c) += high;                    \
        ret += low;                     \
        (c) += (ret<low)?1:0;           \
        (r) =  ret;                     \
        }

#  define mul(r,a,w,c)    {               \
        BN_ULONG high,low,ret,ta=(a);   \
        BN_UMULT_LOHI(low,high,w,ta);   \
        ret =  low + (c);               \
        (c) =  high;                    \
        (c) += (ret<low)?1:0;           \
        (r) =  ret;                     \
        }

#  define sqr(r0,r1,a)    {               \
        BN_ULONG tmp=(a);               \
        BN_UMULT_LOHI(r0,r1,tmp,tmp);   \
        }

# elif defined(BN_UMULT_HIGH)
#  define mul_add(r,a,w,c) {              \
        BN_ULONG high,low,ret,tmp=(a);  \
        ret =  (r);                     \
        high=  BN_UMULT_HIGH(w,tmp);    \
        ret += (c);                     \
        low =  (w) * tmp;               \
        (c) =  (ret<(c))?1:0;           \
        (c) += high;                    \
        ret += low;                     \
        (c) += (ret<low)?1:0;           \
        (r) =  ret;                     \
        }

#  define mul(r,a,w,c)    {               \
        BN_ULONG high,low,ret,ta=(a);   \
        low =  (w) * ta;                \
        high=  BN_UMULT_HIGH(w,ta);     \
        ret =  low + (c);               \
        (c) =  high;                    \
        (c) += (ret<low)?1:0;           \
        (r) =  ret;                     \
        }

#  define sqr(r0,r1,a)    {               \
        BN_ULONG tmp=(a);               \
        (r0) = tmp * tmp;               \
        (r1) = BN_UMULT_HIGH(tmp,tmp);  \
        }

# else
/*************************************************************
 * No long long type
 */

#  define LBITS(a)        ((a)&BN_MASK2l)
#  define HBITS(a)        (((a)>>BN_BITS4)&BN_MASK2l)
#  define L2HBITS(a)      (((a)<<BN_BITS4)&BN_MASK2)

#  define LLBITS(a)       ((a)&BN_MASKl)
#  define LHBITS(a)       (((a)>>BN_BITS2)&BN_MASKl)
#  define LL2HBITS(a)     ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)

#  define mul64(l,h,bl,bh) \
        { \
        BN_ULONG m,m1,lt,ht; \
 \
        lt=l; \
        ht=h; \
        m =(bh)*(lt); \
        lt=(bl)*(lt); \
        m1=(bl)*(ht); \
        ht =(bh)*(ht); \
        m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
        ht+=HBITS(m); \
        m1=L2HBITS(m); \
        lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
        (l)=lt; \
        (h)=ht; \
        }

#  define sqr64(lo,ho,in) \
        { \
        BN_ULONG l,h,m; \
 \
        h=(in); \
        l=LBITS(h); \
        h=HBITS(h); \
        m =(l)*(h); \
        l*=l; \
        h*=h; \
        h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
        m =(m&BN_MASK2l)<<(BN_BITS4+1); \
        l=(l+m)&BN_MASK2; if (l < m) h++; \
        (lo)=l; \
        (ho)=h; \
        }

#  define mul_add(r,a,bl,bh,c) { \
        BN_ULONG l,h; \
 \
        h= (a); \
        l=LBITS(h); \
        h=HBITS(h); \
        mul64(l,h,(bl),(bh)); \
 \
        /* non-multiply part */ \
        l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
        (c)=(r); \
        l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
        (c)=h&BN_MASK2; \
        (r)=l; \
        }

#  define mul(r,a,bl,bh,c) { \
        BN_ULONG l,h; \
 \
        h= (a); \
        l=LBITS(h); \
        h=HBITS(h); \
        mul64(l,h,(bl),(bh)); \
 \
        /* non-multiply part */ \
        l+=(c); if ((l&BN_MASK2) < (c)) h++; \
        (c)=h&BN_MASK2; \
        (r)=l&BN_MASK2; \
        }
# endif                         /* !BN_LLONG */

void BN_RECP_CTX_init(BN_RECP_CTX *recp);
void BN_MONT_CTX_init(BN_MONT_CTX *ctx);

void bn_init(BIGNUM *a);
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
                      int dna, int dnb, BN_ULONG *t);
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
                           int n, int tna, int tnb, BN_ULONG *t);
void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
                          BN_ULONG *t);
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
                 BN_ULONG *t);
BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                           int cl, int dl);
BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                           int cl, int dl);
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
                const BN_ULONG *np, const BN_ULONG *n0, int num);

BIGNUM *int_bn_mod_inverse(BIGNUM *in,
                           const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
                           int *noinv);

int bn_probable_prime_dh(BIGNUM *rnd, int bits,
                         const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);

#ifdef  __cplusplus
}
#endif

#endif