bn_local.h

/*
 * Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the Apache License 2.0 (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

#ifndef OSSL_CRYPTO_BN_LOCAL_H
#define OSSL_CRYPTO_BN_LOCAL_H

/*
 * The EDK2 build doesn't use bn_conf.h; it sets THIRTY_TWO_BIT or
 * SIXTY_FOUR_BIT in its own environment since it doesn't re-run our
 * Configure script and needs to support both 32-bit and 64-bit.
 */
#include <openssl/opensslconf.h>

#if !defined(OPENSSL_SYS_UEFI)
#include "crypto/bn_conf.h"
#endif

#include "crypto/bn.h"
#include "internal/cryptlib.h"
#include "internal/numbers.h"

/*
 * 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
 * them can be useful for debugging application code as well as openssl
 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
 * code BN_RAND_DEBUG - uses random poisoning of unused words to trip up
 * mismanagement of bignum internals. Enable BN_RAND_DEBUG is known to
 * break some of the OpenSSL tests.
 */
#if defined(BN_RAND_DEBUG) && !defined(BN_DEBUG)
#define BN_DEBUG
#endif
#if defined(BN_RAND_DEBUG)
#include <openssl/rand.h>
#endif

/*
 * This should limit the stack usage due to alloca to about 4K.
 * BN_SOFT_LIMIT is a soft limit equivalent to 2*OPENSSL_RSA_MAX_MODULUS_BITS.
 * Beyond that size bn_mul_mont is no longer used, and the constant time
 * assembler code is disabled, due to the blatant alloca and bn_mul_mont usage.
 * Note that bn_mul_mont does an alloca that is hidden away in assembly.
 * It is not recommended to do computations with numbers exceeding this limit,
 * since the result will be highly version dependent:
 * While the current OpenSSL version will use non-optimized, but safe code,
 * previous versions will use optimized code, that may crash due to unexpected
 * stack overflow, and future versions may very well turn this into a hard
 * limit.
 * Note however, that it is possible to override the size limit using
 * "./config -DBN_SOFT_LIMIT=<limit>" if necessary, and the O/S specific
 * stack limit is known and taken into consideration.
 */
#ifndef BN_SOFT_LIMIT
#define BN_SOFT_LIMIT (4096 / BN_BYTES)
#endif

#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_RAND_DEBUG 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
/*
 * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
 * bn_correct_top, in other words such vectors are permitted to have zeros
 * in most significant limbs. Such vectors are used internally to achieve
 * execution time invariance for critical operations with private keys.
 * It's BN_DEBUG-only flag, because user application is not supposed to
 * observe it anyway. Moreover, optimizing compiler would actually remove
 * all operations manipulating the bit in question in non-BN_DEBUG build.
 */
#define BN_FLG_FIXED_TOP 0x10000
#ifdef BN_RAND_DEBUG
#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));                            \
            (void)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)
#else
#define bn_pollute(a)
#endif
#define bn_check_top(a)                                                                                                                   \
    do {                                                                                                                                  \
        const BIGNUM *_bnum2 = (a);                                                                                                       \
        if (_bnum2 != NULL) {                                                                                                             \
            int _top = _bnum2->top;                                                                                                       \
            (void)ossl_assert((_top == 0 && !_bnum2->neg) || (_top && ((_bnum2->flags & BN_FLG_FIXED_TOP) || _bnum2->d[_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_FLG_FIXED_TOP 0
#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. These chunks are organised in
                  * a least significant chunk first order.
                  */
    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,
                  possibly zero-padded */
    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_consttime 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 */

#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
/*
 * BN_UMULT_HIGH section.
 * 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 (e.g.,
 * PowerPC, Alpha, and IA-64) 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:-) Note that more recent compilers do
 * support 2*64 integer type, which is also used here.
 */
#if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16 && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
#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; })
#elif 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_PPC64) && 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
#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
#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 */

#ifdef BN_RAND_DEBUG
#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
/*******************************************************************
 * Using the long long type, has to be twice as wide as BN_ULONG...
 */
#define Lw(t) (((BN_ULONG)(t)) & BN_MASK2)
#define Hw(t) (((BN_ULONG)((t) >> BN_BITS2)) & BN_MASK2)

#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));                  \
        (c) += high;                        \
        ret += low;                         \
        (c) += (ret < low);                 \
        (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);                \
        (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));                  \
        (c) += high;                        \
        ret += low;                         \
        (c) += (ret < low);                 \
        (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);                \
        (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;           \
        ht += L2HBITS((BN_ULONG)(m < m1)); \
        ht += HBITS(m);                    \
        m1 = L2HBITS(m);                   \
        lt = (lt + m1) & BN_MASK2;         \
        ht += (lt < m1);                   \
        (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;                  \
        h += (l < m);                            \
        (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; \
        h += (l < (c));           \
        (c) = (r);                \
        l = (l + (c)) & BN_MASK2; \
        h += (l < (c));           \
        (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);                    \
        h += ((l & BN_MASK2) < (c)); \
        (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);
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);
void bn_correct_top_consttime(BIGNUM *a);
BIGNUM *int_bn_mod_inverse(BIGNUM *in,
    const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
    int *noinv);

static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
{
    if (bits > (INT_MAX - BN_BITS2 + 1))
        return NULL;

    if (((bits + BN_BITS2 - 1) / BN_BITS2) <= (a)->dmax)
        return a;

    return bn_expand2((a), (bits + BN_BITS2 - 1) / BN_BITS2);
}

int ossl_bn_check_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
    int do_trial_division, BN_GENCB *cb);

#endif