crypto/bn/internal.h - boringssl.git - Git at Google


            
            /* 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 OPENSSL_HEADER_BN_INTERNAL_H

            
            #define OPENSSL_HEADER_BN_INTERNAL_H


            #include <openssl/base.h>


            #if defined(OPENSSL_X86_64) && defined(_MSC_VER)

            
            OPENSSL_MSVC_PRAGMA(warning(push, 3))

            
            #include <intrin.h>

            
            OPENSSL_MSVC_PRAGMA(warning(pop))

            
            #pragma intrinsic(__umulh, _umul128)

            
            #endif


            #include "../internal.h"


            #if defined(__cplusplus)

            
            extern "C" {

            
            #endif


            /* bn_expand acts the same as |bn_wexpand|, but takes a number of bits rather

            
             * than a number of words. */

            
            BIGNUM *bn_expand(BIGNUM *bn, size_t bits);


            #if defined(OPENSSL_64_BIT)


            #if !defined(_MSC_VER)

            
            /* MSVC doesn't support two-word integers on 64-bit. */

            
            #define BN_ULLONG	uint128_t

            
            #endif


            #define BN_BITS2	64

            
            #define BN_BYTES	8

            
            #define BN_BITS4	32

            
            #define BN_MASK2	(0xffffffffffffffffUL)

            
            #define BN_MASK2l	(0xffffffffUL)

            
            #define BN_MASK2h	(0xffffffff00000000UL)

            
            #define BN_MASK2h1	(0xffffffff80000000UL)

            
            #define BN_MONT_CTX_N0_LIMBS 1

            
            #define BN_TBIT		(0x8000000000000000UL)

            
            #define BN_DEC_CONV	(10000000000000000000UL)

            
            #define BN_DEC_NUM	19

            
            #define TOBN(hi, lo) ((BN_ULONG)hi << 32 | lo)


            #elif defined(OPENSSL_32_BIT)


            #define BN_ULLONG	uint64_t

            
            #define BN_BITS2	32

            
            #define BN_BYTES	4

            
            #define BN_BITS4	16

            
            #define BN_MASK2	(0xffffffffUL)

            
            #define BN_MASK2l	(0xffffUL)

            
            #define BN_MASK2h1	(0xffff8000UL)

            
            #define BN_MASK2h	(0xffff0000UL)

            
            /* On some 32-bit platforms, Montgomery multiplication is done using 64-bit

            
             * arithmetic with SIMD instructions. On such platforms, |BN_MONT_CTX::n0|

            
             * needs to be two words long. Only certain 32-bit platforms actually make use

            
             * of n0[1] and shorter R value would suffice for the others. However,

            
             * currently only the assembly files know which is which. */

            
            #define BN_MONT_CTX_N0_LIMBS 2

            
            #define BN_TBIT		(0x80000000UL)

            
            #define BN_DEC_CONV	(1000000000UL)

            
            #define BN_DEC_NUM	9

            
            #define TOBN(hi, lo) lo, hi


            #else

            
            #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"

            
            #endif


            #define STATIC_BIGNUM(x)                                \

            
              {                                                     \

            
                (BN_ULONG *)x, sizeof(x) / sizeof(BN_ULONG),        \

            
                sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \

            
              }


            #if defined(BN_ULLONG)

            
            #define Lw(t) (((BN_ULONG)(t))&BN_MASK2)

            
            #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)

            
            #endif


            /* bn_set_words sets |bn| to the value encoded in the |num| words in |words|,

            
             * least significant word first. */

            
            int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num);


            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_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);


            void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);

            
            void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);

            
            void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);

            
            void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);


            /* bn_cmp_words returns a value less than, equal to or greater than zero if

            
             * the, length |n|, array |a| is less than, equal to or greater than |b|. */

            
            int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);


            /* bn_cmp_words returns a value less than, equal to or greater than zero if the

            
             * array |a| is less than, equal to or greater than |b|. The arrays can be of

            
             * different lengths: |cl| gives the minimum of the two lengths and |dl| gives

            
             * the length of |a| minus the length of |b|. */

            
            int bn_cmp_part_words(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);


            uint64_t bn_mont_n0(const BIGNUM *n);


            #if defined(OPENSSL_X86_64) && defined(_MSC_VER)

            
            #define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high)))

            
            #endif


            #if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI)

            
            #error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform."

            
            #endif


            #if defined(__cplusplus)

            
            }  /* extern C */

            
            #endif


            #endif  /* OPENSSL_HEADER_BN_INTERNAL_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 OPENSSL_HEADER_BN_INTERNAL_H
	#define OPENSSL_HEADER_BN_INTERNAL_H

	#include <openssl/base.h>

	#if defined(OPENSSL_X86_64) && defined(_MSC_VER)
	OPENSSL_MSVC_PRAGMA(warning(push, 3))
	#include <intrin.h>
	OPENSSL_MSVC_PRAGMA(warning(pop))
	#pragma intrinsic(__umulh, _umul128)
	#endif

	#include "../internal.h"

	#if defined(__cplusplus)
	extern "C" {
	#endif

	/* bn_expand acts the same as \|bn_wexpand\|, but takes a number of bits rather
	* than a number of words. */
	BIGNUM bn_expand(BIGNUM bn, size_t bits);

	#if defined(OPENSSL_64_BIT)

	#if !defined(_MSC_VER)
	/* MSVC doesn't support two-word integers on 64-bit. */
	#define BN_ULLONG uint128_t
	#endif

	#define BN_BITS2 64
	#define BN_BYTES 8
	#define BN_BITS4 32
	#define BN_MASK2 (0xffffffffffffffffUL)
	#define BN_MASK2l (0xffffffffUL)
	#define BN_MASK2h (0xffffffff00000000UL)
	#define BN_MASK2h1 (0xffffffff80000000UL)
	#define BN_MONT_CTX_N0_LIMBS 1
	#define BN_TBIT (0x8000000000000000UL)
	#define BN_DEC_CONV (10000000000000000000UL)
	#define BN_DEC_NUM 19
	#define TOBN(hi, lo) ((BN_ULONG)hi << 32 \| lo)

	#elif defined(OPENSSL_32_BIT)

	#define BN_ULLONG uint64_t
	#define BN_BITS2 32
	#define BN_BYTES 4
	#define BN_BITS4 16
	#define BN_MASK2 (0xffffffffUL)
	#define BN_MASK2l (0xffffUL)
	#define BN_MASK2h1 (0xffff8000UL)
	#define BN_MASK2h (0xffff0000UL)
	/* On some 32-bit platforms, Montgomery multiplication is done using 64-bit
	* arithmetic with SIMD instructions. On such platforms, \|BN_MONT_CTX::n0\|
	* needs to be two words long. Only certain 32-bit platforms actually make use
	* of n0[1] and shorter R value would suffice for the others. However,
	* currently only the assembly files know which is which. */
	#define BN_MONT_CTX_N0_LIMBS 2
	#define BN_TBIT (0x80000000UL)
	#define BN_DEC_CONV (1000000000UL)
	#define BN_DEC_NUM 9
	#define TOBN(hi, lo) lo, hi

	#else
	#error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
	#endif


	#define STATIC_BIGNUM(x) \
	{ \
	(BN_ULONG *)x, sizeof(x) / sizeof(BN_ULONG), \
	sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \
	}

	#if defined(BN_ULLONG)
	#define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
	#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
	#endif

	/* bn_set_words sets \|bn\| to the value encoded in the \|num\| words in \|words\|,
	* least significant word first. */
	int bn_set_words(BIGNUM bn, const BN_ULONG words, size_t num);

	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_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);

	void bn_mul_comba4(BN_ULONG r, BN_ULONG a, BN_ULONG *b);
	void bn_mul_comba8(BN_ULONG r, BN_ULONG a, BN_ULONG *b);
	void bn_sqr_comba8(BN_ULONG r, const BN_ULONG a);
	void bn_sqr_comba4(BN_ULONG r, const BN_ULONG a);

	/* bn_cmp_words returns a value less than, equal to or greater than zero if
	* the, length \|n\|, array \|a\| is less than, equal to or greater than \|b\|. */
	int bn_cmp_words(const BN_ULONG a, const BN_ULONG b, int n);

	/* bn_cmp_words returns a value less than, equal to or greater than zero if the
	* array \|a\| is less than, equal to or greater than \|b\|. The arrays can be of
	* different lengths: \|cl\| gives the minimum of the two lengths and \|dl\| gives
	* the length of \|a\| minus the length of \|b\|. */
	int bn_cmp_part_words(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);

	uint64_t bn_mont_n0(const BIGNUM *n);

	#if defined(OPENSSL_X86_64) && defined(_MSC_VER)
	#define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high)))
	#endif

	#if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI)
	#error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform."
	#endif


	#if defined(__cplusplus)
	} /* extern C */
	#endif

	#endif /* OPENSSL_HEADER_BN_INTERNAL_H */