crypto/bn/bn_lcl.h - platform/external/openssl - Git at Google

 /* 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 <openssl/bn.h>

 #ifdef  __cplusplus
 extern "C" {
 #endif


 /*
  * 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.
  */
 #if 1
 #define BN_window_bits_for_exponent_size(b) \
 		((b) > 671 ? 6 : \
 		 (b) > 239 ? 5 : \
 		 (b) >  79 ? 4 : \
 		 (b) >  23 ? 3 : 1)
 #else
 /* Old SSLeay/OpenSSL table.
  * Maximum window size was 5, so this table differs for b==1024;
  * but it coincides for other interesting values (b==160, b==512).
  */
 #define BN_window_bits_for_exponent_size(b) \
 		((b) > 255 ? 5 : \
 		 (b) > 127 ? 4 : \
 		 (b) >  17 ? 3 : 1)
 #endif


 /* 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 */

 #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
 #   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		/* 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 */

 #if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS)
 #undef bn_div_words
 #endif

 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);

 #ifdef  __cplusplus
 }
 #endif

 #endif
	/* 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 <openssl/bn.h>

	#ifdef __cplusplus
	extern "C" {
	#endif


	/*
	* 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.
	*/
	#if 1
	#define BN_window_bits_for_exponent_size(b) \
	((b) > 671 ? 6 : \
	(b) > 239 ? 5 : \
	(b) > 79 ? 4 : \
	(b) > 23 ? 3 : 1)
	#else
	/* Old SSLeay/OpenSSL table.
	* Maximum window size was 5, so this table differs for b==1024;
	* but it coincides for other interesting values (b==160, b==512).
	*/
	#define BN_window_bits_for_exponent_size(b) \
	((b) > 255 ? 5 : \
	(b) > 127 ? 4 : \
	(b) > 17 ? 3 : 1)
	#endif



	/* 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 */

	#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 2N integer type, then you have to replace every NN
	* 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
	# 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 /* 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 */

	#if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS)
	#undef bn_div_words
	#endif

	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);

	#ifdef __cplusplus
	}
	#endif

	#endif