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>

 #include <inttypes.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, unsigned bits);

 #if defined(OPENSSL_64_BIT)

 #define BN_ULLONG	unsigned long long
 #define BN_BITS		128
 #define BN_BYTES	8
 #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	"%" PRIu64
 #define BN_DEC_FMT2	"%019" PRIu64
 #define BN_DEC_NUM	19
 #define BN_HEX_FMT1	"%" PRIx64

 #elif defined(OPENSSL_32_BIT)

 #define BN_ULLONG	unsigned long long
 #define BN_MASK	(0xffffffffffffffffLL)
 #define BN_BITS		64
 #define BN_BYTES	4
 #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	"%" PRIu32
 #define BN_DEC_FMT2	"%09" PRIu32
 #define BN_DEC_NUM	9
 #define BN_HEX_FMT1	"%" PRIx32

 #else
 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
 #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 */

 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);

 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);

 #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;                     \
   }

 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64)
 # 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
 # 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(OPENSSL_NO_ASM) && defined(OPENSSL_AARCH64)
 # 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


 #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>

	#include <inttypes.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, unsigned bits);

	#if defined(OPENSSL_64_BIT)

	#define BN_ULLONG unsigned long long
	#define BN_BITS 128
	#define BN_BYTES 8
	#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 "%" PRIu64
	#define BN_DEC_FMT2 "%019" PRIu64
	#define BN_DEC_NUM 19
	#define BN_HEX_FMT1 "%" PRIx64

	#elif defined(OPENSSL_32_BIT)

	#define BN_ULLONG unsigned long long
	#define BN_MASK (0xffffffffffffffffLL)
	#define BN_BITS 64
	#define BN_BYTES 4
	#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 "%" PRIu32
	#define BN_DEC_FMT2 "%09" PRIu32
	#define BN_DEC_NUM 9
	#define BN_HEX_FMT1 "%" PRIx32

	#else
	#error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
	#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 */

	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);

	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);

	#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; \
	}

	#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64)
	# 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
	# 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(OPENSSL_NO_ASM) && defined(OPENSSL_AARCH64)
	# 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


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

	#endif /* OPENSSL_HEADER_BN_INTERNAL_H */