view libgcc/config/libbid/bid_internal.h @ 0:a06113de4d67

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author kent <kent@cr.ie.u-ryukyu.ac.jp>
date Fri, 17 Jul 2009 14:47:48 +0900
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/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

#ifndef __BIDECIMAL_H
#define __BIDECIMAL_H

#include "bid_conf.h"
#include "bid_functions.h"

#define __BID_INLINE__ static __inline

/*********************************************************************
 *
 *      Logical Shift Macros
 *
 *********************************************************************/

#define __shr_128(Q, A, k)                        \
{                                                 \
     (Q).w[0] = (A).w[0] >> k;                      \
	 (Q).w[0] |= (A).w[1] << (64-k);               \
	 (Q).w[1] = (A).w[1] >> k;                    \
}

#define __shr_128_long(Q, A, k)                   \
{                                                 \
	if((k)<64) {                                  \
     (Q).w[0] = (A).w[0] >> k;                    \
	 (Q).w[0] |= (A).w[1] << (64-k);              \
	 (Q).w[1] = (A).w[1] >> k;                    \
	}                                             \
	else {                                        \
	 (Q).w[0] = (A).w[1]>>((k)-64);               \
	 (Q).w[1] = 0;                                \
	}                                             \
}

#define __shl_128_long(Q, A, k)                   \
{                                                 \
	if((k)<64) {                                  \
     (Q).w[1] = (A).w[1] << k;                    \
	 (Q).w[1] |= (A).w[0] >> (64-k);              \
	 (Q).w[0] = (A).w[0] << k;                    \
	}                                             \
	else {                                        \
	 (Q).w[1] = (A).w[0]<<((k)-64);               \
	 (Q).w[0] = 0;                                \
	}                                             \
}

#define __low_64(Q)  (Q).w[0]
/*********************************************************************
 *
 *      String Macros
 *
 *********************************************************************/
#define tolower_macro(x) (((unsigned char)((x)-'A')<=('Z'-'A'))?((x)-'A'+'a'):(x))
/*********************************************************************
 *
 *      Compare Macros
 *
 *********************************************************************/
// greater than
//  return 0 if A<=B
//  non-zero if A>B
#define __unsigned_compare_gt_128(A, B)  \
    ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>B.w[0])))
// greater-or-equal
#define __unsigned_compare_ge_128(A, B)  \
    ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>=B.w[0])))
#define __test_equal_128(A, B)  (((A).w[1]==(B).w[1]) && ((A).w[0]==(B).w[0]))
// tighten exponent range
#define __tight_bin_range_128(bp, P, bin_expon)  \
{                                                \
UINT64 M;                                        \
	M = 1;                                       \
	(bp) = (bin_expon);                          \
	if((bp)<63) {                                \
	  M <<= ((bp)+1);                            \
	  if((P).w[0] >= M) (bp)++; }                 \
	else if((bp)>64) {                           \
	  M <<= ((bp)+1-64);                         \
	  if(((P).w[1]>M) ||((P).w[1]==M && (P).w[0]))\
	      (bp)++; }                              \
	else if((P).w[1]) (bp)++;                    \
}
/*********************************************************************
 *
 *      Add/Subtract Macros
 *
 *********************************************************************/
// add 64-bit value to 128-bit 
#define __add_128_64(R128, A128, B64)    \
{                                        \
UINT64 R64H;                             \
	R64H = (A128).w[1];                 \
	(R128).w[0] = (B64) + (A128).w[0];     \
	if((R128).w[0] < (B64))               \
	  R64H ++;                           \
    (R128).w[1] = R64H;                  \
}
// subtract 64-bit value from 128-bit 
#define __sub_128_64(R128, A128, B64)    \
{                                        \
UINT64 R64H;                             \
	R64H = (A128).w[1];                  \
	if((A128).w[0] < (B64))               \
	  R64H --;                           \
    (R128).w[1] = R64H;                  \
	(R128).w[0] = (A128).w[0] - (B64);     \
}
// add 128-bit value to 128-bit 
// assume no carry-out
#define __add_128_128(R128, A128, B128)  \
{                                        \
UINT128 Q128;                            \
	Q128.w[1] = (A128).w[1]+(B128).w[1]; \
	Q128.w[0] = (B128).w[0] + (A128).w[0];  \
	if(Q128.w[0] < (B128).w[0])            \
	  Q128.w[1] ++;                      \
    (R128).w[1] = Q128.w[1];             \
    (R128).w[0] = Q128.w[0];               \
}
#define __sub_128_128(R128, A128, B128)  \
{                                        \
UINT128 Q128;                            \
	Q128.w[1] = (A128).w[1]-(B128).w[1]; \
	Q128.w[0] = (A128).w[0] - (B128).w[0];  \
	if((A128).w[0] < (B128).w[0])          \
	  Q128.w[1] --;                      \
    (R128).w[1] = Q128.w[1];             \
    (R128).w[0] = Q128.w[0];               \
}
#define __add_carry_out(S, CY, X, Y)    \
{                                      \
UINT64 X1=X;                           \
	S = X + Y;                         \
	CY = (S<X1) ? 1 : 0;                \
}
#define __add_carry_in_out(S, CY, X, Y, CI)    \
{                                             \
UINT64 X1;                                    \
	X1 = X + CI;                              \
	S = X1 + Y;                               \
	CY = ((S<X1) || (X1<CI)) ? 1 : 0;          \
}
#define __sub_borrow_out(S, CY, X, Y)    \
{                                      \
UINT64 X1=X;                           \
	S = X - Y;                         \
	CY = (S>X1) ? 1 : 0;                \
}
#define __sub_borrow_in_out(S, CY, X, Y, CI)    \
{                                             \
UINT64 X1, X0=X;                              \
	X1 = X - CI;                              \
	S = X1 - Y;                               \
	CY = ((S>X1) || (X1>X0)) ? 1 : 0;          \
}
// increment C128 and check for rounding overflow: 
// if (C_128) = 10^34 then (C_128) = 10^33 and increment the exponent
#define INCREMENT(C_128, exp)                                           \
{                                                                       \
  C_128.w[0]++;                                                         \
  if (C_128.w[0] == 0) C_128.w[1]++;                                    \
  if (C_128.w[1] == 0x0001ed09bead87c0ull &&                            \
      C_128.w[0] == 0x378d8e6400000000ull) {                            \
    exp++;                                                              \
    C_128.w[1] = 0x0000314dc6448d93ull;                                 \
    C_128.w[0] = 0x38c15b0a00000000ull;                                 \
  }                                                                     \
}
// decrement C128 and check for rounding underflow, but only at the
// boundary: if C_128 = 10^33 - 1 and exp > 0 then C_128 = 10^34 - 1 
// and decrement the exponent 
#define DECREMENT(C_128, exp)                                           \
{                                                                       \
  C_128.w[0]--;                                                         \
  if (C_128.w[0] == 0xffffffffffffffffull) C_128.w[1]--;                \
  if (C_128.w[1] == 0x0000314dc6448d93ull &&                            \
      C_128.w[0] == 0x38c15b09ffffffffull && exp > 0) {                 \
    exp--;                                                              \
    C_128.w[1] = 0x0001ed09bead87c0ull;                                 \
    C_128.w[0] = 0x378d8e63ffffffffull;                                 \
  }                                                                     \
}

 /*********************************************************************
 *
 *      Multiply Macros
 *
 *********************************************************************/
#define __mul_64x64_to_64(P64, CX, CY)  (P64) = (CX) * (CY)
/***************************************
 *  Signed, Full 64x64-bit Multiply
 ***************************************/
#define __imul_64x64_to_128(P, CX, CY)  \
{                                       \
UINT64 SX, SY;                          \
   __mul_64x64_to_128(P, CX, CY);       \
                                        \
   SX = ((SINT64)(CX))>>63;             \
   SY = ((SINT64)(CY))>>63;             \
   SX &= CY;   SY &= CX;                \
                                        \
   (P).w[1] = (P).w[1] - SX - SY;       \
}
/***************************************
 *  Signed, Full 64x128-bit Multiply
 ***************************************/
#define __imul_64x128_full(Ph, Ql, A, B)          \
{                                                 \
UINT128 ALBL, ALBH, QM2, QM;                      \
                                                  \
	__imul_64x64_to_128(ALBH, (A), (B).w[1]);     \
	__imul_64x64_to_128(ALBL, (A), (B).w[0]);      \
                                                  \
	(Ql).w[0] = ALBL.w[0];                          \
	QM.w[0] = ALBL.w[1];                           \
	QM.w[1] = ((SINT64)ALBL.w[1])>>63;            \
    __add_128_128(QM2, ALBH, QM);                 \
	(Ql).w[1] = QM2.w[0];                          \
    Ph = QM2.w[1];                                \
}
/*****************************************************
 *      Unsigned Multiply Macros
 *****************************************************/
// get full 64x64bit product
//
#define __mul_64x64_to_128(P, CX, CY)   \
{                                       \
UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\
	CXH = (CX) >> 32;                     \
	CXL = (UINT32)(CX);                   \
	CYH = (CY) >> 32;                     \
	CYL = (UINT32)(CY);                   \
	                                      \
    PM = CXH*CYL;                         \
	PH = CXH*CYH;                         \
	PL = CXL*CYL;                         \
	PM2 = CXL*CYH;                        \
	PH += (PM>>32);                       \
	PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \
                                          \
	(P).w[1] = PH + (PM>>32);             \
	(P).w[0] = (PM<<32)+(UINT32)PL;       \
}
// get full 64x64bit product
// Note:
// This macro is used for CX < 2^61, CY < 2^61
//
#define __mul_64x64_to_128_fast(P, CX, CY)   \
{                                       \
UINT64 CXH, CXL, CYH, CYL, PL, PH, PM;  \
	CXH = (CX) >> 32;                   \
	CXL = (UINT32)(CX);                 \
	CYH = (CY) >> 32;                   \
	CYL = (UINT32)(CY);                 \
	                                    \
    PM = CXH*CYL;                       \
	PL = CXL*CYL;                       \
	PH = CXH*CYH;                       \
	PM += CXL*CYH;                      \
	PM += (PL>>32);                     \
                                        \
	(P).w[1] = PH + (PM>>32);           \
	(P).w[0] = (PM<<32)+(UINT32)PL;      \
}
// used for CX< 2^60
#define __sqr64_fast(P, CX)   \
{                                       \
UINT64 CXH, CXL, PL, PH, PM;            \
	CXH = (CX) >> 32;                   \
	CXL = (UINT32)(CX);                 \
	                                    \
    PM = CXH*CXL;                       \
	PL = CXL*CXL;                       \
	PH = CXH*CXH;                       \
	PM += PM;                           \
	PM += (PL>>32);                     \
                                        \
	(P).w[1] = PH + (PM>>32);           \
	(P).w[0] = (PM<<32)+(UINT32)PL;     \
}
// get full 64x64bit product
// Note:
// This implementation is used for CX < 2^61, CY < 2^61
//
#define __mul_64x64_to_64_high_fast(P, CX, CY)   \
{                                       \
UINT64 CXH, CXL, CYH, CYL, PL, PH, PM;  \
	CXH = (CX) >> 32;                   \
	CXL = (UINT32)(CX);                 \
	CYH = (CY) >> 32;                   \
	CYL = (UINT32)(CY);                 \
	                                    \
    PM = CXH*CYL;                       \
	PL = CXL*CYL;                       \
	PH = CXH*CYH;                       \
	PM += CXL*CYH;                      \
	PM += (PL>>32);                     \
                                        \
	(P) = PH + (PM>>32);                \
}
// get full 64x64bit product 
//
#define __mul_64x64_to_128_full(P, CX, CY)     \
{                                         \
UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\
	CXH = (CX) >> 32;                     \
	CXL = (UINT32)(CX);                   \
	CYH = (CY) >> 32;                     \
	CYL = (UINT32)(CY);                   \
	                                      \
    PM = CXH*CYL;                         \
	PH = CXH*CYH;                         \
	PL = CXL*CYL;                         \
	PM2 = CXL*CYH;                        \
	PH += (PM>>32);                       \
	PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \
                                          \
	(P).w[1] = PH + (PM>>32);             \
	(P).w[0] = (PM<<32)+(UINT32)PL;        \
}
#define __mul_128x128_high(Q, A, B)               \
{                                                 \
UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2;          \
                                                  \
	__mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]);  \
	__mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]);  \
	__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]);   \
	__mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]);  \
                                                  \
    __add_128_128(QM, ALBH, AHBL);                \
    __add_128_64(QM2, QM, ALBL.w[1]);             \
    __add_128_64((Q), AHBH, QM2.w[1]);            \
}
#define __mul_128x128_full(Qh, Ql, A, B)          \
{                                                 \
UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2;          \
                                                  \
	__mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]);  \
	__mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]);  \
	__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]);   \
	__mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]);  \
                                                  \
    __add_128_128(QM, ALBH, AHBL);                \
	(Ql).w[0] = ALBL.w[0];                          \
    __add_128_64(QM2, QM, ALBL.w[1]);             \
    __add_128_64((Qh), AHBH, QM2.w[1]);           \
	(Ql).w[1] = QM2.w[0];                          \
}
#define __mul_128x128_low(Ql, A, B)               \
{                                                 \
UINT128 ALBL;                                     \
UINT64 QM64;                                      \
                                                  \
	__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]);   \
	QM64 = (B).w[0]*(A).w[1] + (A).w[0]*(B).w[1];   \
                                                  \
	(Ql).w[0] = ALBL.w[0];                          \
	(Ql).w[1] = QM64 + ALBL.w[1];                 \
}
#define __mul_64x128_low(Ql, A, B)                \
{                                                 \
  UINT128 ALBL, ALBH, QM2;                        \
  __mul_64x64_to_128(ALBH, (A), (B).w[1]);        \
  __mul_64x64_to_128(ALBL, (A), (B).w[0]);        \
  (Ql).w[0] = ALBL.w[0];                          \
  __add_128_64(QM2, ALBH, ALBL.w[1]);             \
  (Ql).w[1] = QM2.w[0];                           \
}
#define __mul_64x128_full(Ph, Ql, A, B)           \
{                                                 \
UINT128 ALBL, ALBH, QM2;                          \
                                                  \
	__mul_64x64_to_128(ALBH, (A), (B).w[1]);      \
	__mul_64x64_to_128(ALBL, (A), (B).w[0]);       \
                                                  \
	(Ql).w[0] = ALBL.w[0];                          \
    __add_128_64(QM2, ALBH, ALBL.w[1]);           \
	(Ql).w[1] = QM2.w[0];                          \
    Ph = QM2.w[1];                                \
}
#define __mul_64x128_to_192(Q, A, B)              \
{                                                 \
UINT128 ALBL, ALBH, QM2;                          \
                                                  \
	__mul_64x64_to_128(ALBH, (A), (B).w[1]);      \
	__mul_64x64_to_128(ALBL, (A), (B).w[0]);      \
                                                  \
	(Q).w[0] = ALBL.w[0];                         \
    __add_128_64(QM2, ALBH, ALBL.w[1]);           \
	(Q).w[1] = QM2.w[0];                          \
    (Q).w[2] = QM2.w[1];                          \
}
#define __mul_64x128_to192(Q, A, B)          \
{                                             \
UINT128 ALBL, ALBH, QM2;                      \
                                              \
    __mul_64x64_to_128(ALBH, (A), (B).w[1]);  \
    __mul_64x64_to_128(ALBL, (A), (B).w[0]);  \
                                              \
    (Q).w[0] = ALBL.w[0];                    \
    __add_128_64(QM2, ALBH, ALBL.w[1]);       \
    (Q).w[1] = QM2.w[0];                     \
    (Q).w[2] = QM2.w[1];                     \
}
#define __mul_128x128_to_256(P256, A, B)                         \
{                                                                \
UINT128 Qll, Qlh;                                                \
UINT64 Phl, Phh, CY1, CY2;                                         \
                                                                 \
   __mul_64x128_full(Phl, Qll, A.w[0], B);                       \
   __mul_64x128_full(Phh, Qlh, A.w[1], B);                       \
  (P256).w[0] = Qll.w[0];                                        \
	   __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]);      \
	   __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1);    \
	   (P256).w[3] = Phh + CY2;                                   \
}
//
// For better performance, will check A.w[1] against 0,
//                         but not B.w[1]
// Use this macro accordingly
#define __mul_128x128_to_256_check_A(P256, A, B)                   \
{                                                                  \
UINT128 Qll, Qlh;                                                  \
UINT64 Phl, Phh, CY1, CY2;                                           \
                                                                   \
   __mul_64x128_full(Phl, Qll, A.w[0], B);                          \
  (P256).w[0] = Qll.w[0];                                        \
   if(A.w[1])  {                                                   \
	   __mul_64x128_full(Phh, Qlh, A.w[1], B);                     \
	   __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]);      \
	   __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1);   \
	   (P256).w[3] = Phh + CY2;   }                              \
   else  {                                                         \
	   (P256).w[1] = Qll.w[1];                                  \
	   (P256).w[2] = Phl;                                       \
	   (P256).w[3] = 0;  }                                      \
}
#define __mul_64x192_to_256(lP, lA, lB)                      \
{                                                         \
UINT128 lP0,lP1,lP2;                                      \
UINT64 lC;                                                 \
	__mul_64x64_to_128(lP0, lA, (lB).w[0]);              \
	__mul_64x64_to_128(lP1, lA, (lB).w[1]);              \
	__mul_64x64_to_128(lP2, lA, (lB).w[2]);              \
	(lP).w[0] = lP0.w[0];                                \
	__add_carry_out((lP).w[1],lC,lP1.w[0],lP0.w[1]);      \
	__add_carry_in_out((lP).w[2],lC,lP2.w[0],lP1.w[1],lC); \
	(lP).w[3] = lP2.w[1] + lC;                           \
}
#define __mul_64x256_to_320(P, A, B)                    \
{                                                       \
UINT128 lP0,lP1,lP2,lP3;                                \
UINT64 lC;                                               \
	__mul_64x64_to_128(lP0, A, (B).w[0]);             \
	__mul_64x64_to_128(lP1, A, (B).w[1]);             \
	__mul_64x64_to_128(lP2, A, (B).w[2]);             \
	__mul_64x64_to_128(lP3, A, (B).w[3]);             \
	(P).w[0] = lP0.w[0];                               \
	__add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]);      \
	__add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \
	__add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \
	(P).w[4] = lP3.w[1] + lC;                          \
}
#define __mul_192x192_to_384(P, A, B)                          \
{                                                              \
UINT256 P0,P1,P2;                                              \
UINT64 CY;                                                      \
	__mul_64x192_to_256(P0, (A).w[0], B);                   \
	__mul_64x192_to_256(P1, (A).w[1], B);                   \
	__mul_64x192_to_256(P2, (A).w[2], B);                   \
	(P).w[0] = P0.w[0];                                  \
	__add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]);      \
	__add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \
	__add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \
	(P).w[4] = P1.w[3] + CY;                              \
	__add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]);     \
	__add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY);   \
	__add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY);   \
	(P).w[5] = P2.w[3] + CY;                              \
}
#define __mul_64x320_to_384(P, A, B)                    \
{                                                       \
UINT128 lP0,lP1,lP2,lP3,lP4;                            \
UINT64 lC;                                               \
	__mul_64x64_to_128(lP0, A, (B).w[0]);             \
	__mul_64x64_to_128(lP1, A, (B).w[1]);             \
	__mul_64x64_to_128(lP2, A, (B).w[2]);             \
	__mul_64x64_to_128(lP3, A, (B).w[3]);             \
	__mul_64x64_to_128(lP4, A, (B).w[4]);             \
	(P).w[0] = lP0.w[0];                               \
	__add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]);      \
	__add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \
	__add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \
	__add_carry_in_out((P).w[4],lC,lP4.w[0],lP3.w[1],lC); \
	(P).w[5] = lP4.w[1] + lC;                          \
}
// A*A
// Full 128x128-bit product
#define __sqr128_to_256(P256, A)                                 \
{                                                                \
UINT128 Qll, Qlh, Qhh;                                           \
UINT64 TMP_C1, TMP_C2;                                 \
                                                                 \
   __mul_64x64_to_128(Qhh, A.w[1], A.w[1]);                      \
   __mul_64x64_to_128(Qlh, A.w[0], A.w[1]);                      \
   Qhh.w[1] += (Qlh.w[1]>>63);                                   \
   Qlh.w[1] = (Qlh.w[1]+Qlh.w[1])|(Qlh.w[0]>>63);                \
   Qlh.w[0] += Qlh.w[0];                                         \
   __mul_64x64_to_128(Qll, A.w[0], A.w[0]);                      \
                                                                 \
   __add_carry_out((P256).w[1],TMP_C1, Qlh.w[0], Qll.w[1]);      \
   (P256).w[0] = Qll.w[0];                                       \
   __add_carry_in_out((P256).w[2],TMP_C2, Qlh.w[1], Qhh.w[0], TMP_C1);    \
   (P256).w[3] = Qhh.w[1]+TMP_C2;                                         \
}
#define __mul_128x128_to_256_low_high(PQh, PQl, A, B)            \
{                                                                \
UINT128 Qll, Qlh;                                                \
UINT64 Phl, Phh, C1, C2;                                         \
                                                                 \
   __mul_64x128_full(Phl, Qll, A.w[0], B);                       \
   __mul_64x128_full(Phh, Qlh, A.w[1], B);                       \
  (PQl).w[0] = Qll.w[0];                                        \
	   __add_carry_out((PQl).w[1],C1, Qlh.w[0], Qll.w[1]);      \
	   __add_carry_in_out((PQh).w[0],C2, Qlh.w[1], Phl, C1);    \
	   (PQh).w[1] = Phh + C2;                                   \
}
#define __mul_256x256_to_512(P, A, B)                          \
{                                                              \
UINT512 P0,P1,P2,P3;                                           \
UINT64 CY;                                                      \
	__mul_64x256_to_320(P0, (A).w[0], B);                   \
	__mul_64x256_to_320(P1, (A).w[1], B);                   \
	__mul_64x256_to_320(P2, (A).w[2], B);                   \
	__mul_64x256_to_320(P3, (A).w[3], B);                   \
	(P).w[0] = P0.w[0];                                  \
	__add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]);      \
	__add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \
	__add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \
	__add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \
	(P).w[5] = P1.w[4] + CY;                              \
	__add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]);     \
	__add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY);   \
	__add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY);   \
	__add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY);   \
	(P).w[6] = P2.w[4] + CY;                              \
	__add_carry_out((P).w[3],CY,P3.w[0],(P).w[3]);     \
	__add_carry_in_out((P).w[4],CY,P3.w[1],(P).w[4],CY);   \
	__add_carry_in_out((P).w[5],CY,P3.w[2],(P).w[5],CY);   \
	__add_carry_in_out((P).w[6],CY,P3.w[3],(P).w[6],CY);   \
	(P).w[7] = P3.w[4] + CY;                              \
}
#define __mul_192x256_to_448(P, A, B)                          \
{                                                              \
UINT512 P0,P1,P2;                                           \
UINT64 CY;                                                      \
	__mul_64x256_to_320(P0, (A).w[0], B);                   \
	__mul_64x256_to_320(P1, (A).w[1], B);                   \
	__mul_64x256_to_320(P2, (A).w[2], B);                   \
	(P).w[0] = P0.w[0];                                  \
	__add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]);      \
	__add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \
	__add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \
	__add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \
	(P).w[5] = P1.w[4] + CY;                              \
	__add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]);     \
	__add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY);   \
	__add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY);   \
	__add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY);   \
	(P).w[6] = P2.w[4] + CY;                              \
}
#define __mul_320x320_to_640(P, A, B)                          \
{                                                              \
UINT512 P0,P1,P2,P3;                                           \
UINT64 CY;                                                     \
	__mul_256x256_to_512((P), (A), B);                   \
	__mul_64x256_to_320(P1, (A).w[4], B);                   \
	__mul_64x256_to_320(P2, (B).w[4], A);                   \
	__mul_64x64_to_128(P3, (A).w[4], (B).w[4]);               \
	__add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]);      \
	__add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \
	__add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \
	__add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \
	__add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \
	P3.w[1] += CY;                                       \
	__add_carry_out((P).w[4],CY,(P).w[4],P0.w[0]);      \
	__add_carry_in_out((P).w[5],CY,(P).w[5],P0.w[1],CY); \
	__add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[2],CY); \
	__add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[3],CY); \
	__add_carry_in_out((P).w[8],CY,P3.w[0],P0.w[4],CY); \
	(P).w[9] = P3.w[1] + CY;                             \
}
#define __mul_384x384_to_768(P, A, B)                          \
{                                                              \
UINT512 P0,P1,P2,P3;                                           \
UINT64 CY;                                                     \
	__mul_320x320_to_640((P), (A), B);                         \
	__mul_64x320_to_384(P1, (A).w[5], B);                   \
	__mul_64x320_to_384(P2, (B).w[5], A);                   \
	__mul_64x64_to_128(P3, (A).w[5], (B).w[5]);               \
	__add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]);      \
	__add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \
	__add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \
	__add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \
	__add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \
	__add_carry_in_out((P0).w[5],CY,P1.w[5],P2.w[5],CY); \
	P3.w[1] += CY;                                       \
	__add_carry_out((P).w[5],CY,(P).w[5],P0.w[0]);      \
	__add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[1],CY); \
	__add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[2],CY); \
	__add_carry_in_out((P).w[8],CY,(P).w[8],P0.w[3],CY); \
	__add_carry_in_out((P).w[9],CY,(P).w[9],P0.w[4],CY); \
	__add_carry_in_out((P).w[10],CY,P3.w[0],P0.w[5],CY); \
	(P).w[11] = P3.w[1] + CY;                             \
}
#define __mul_64x128_short(Ql, A, B)              \
{                                                 \
UINT64 ALBH_L;                                    \
                                                  \
	__mul_64x64_to_64(ALBH_L, (A),(B).w[1]);      \
	__mul_64x64_to_128((Ql), (A), (B).w[0]);       \
                                                  \
	(Ql).w[1] += ALBH_L;                          \
}
#define __scale128_10(D,_TMP)                            \
{                                                        \
UINT128 _TMP2,_TMP8;                                     \
	  _TMP2.w[1] = (_TMP.w[1]<<1)|(_TMP.w[0]>>63);       \
	  _TMP2.w[0] = _TMP.w[0]<<1;                         \
	  _TMP8.w[1] = (_TMP.w[1]<<3)|(_TMP.w[0]>>61);       \
	  _TMP8.w[0] = _TMP.w[0]<<3;                         \
	  __add_128_128(D, _TMP2, _TMP8);                    \
}
// 64x64-bit product
#define __mul_64x64_to_128MACH(P128, CX64, CY64)  \
{                                                  \
  UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2;     \
  CXH = (CX64) >> 32;                              \
  CXL = (UINT32)(CX64);                            \
  CYH = (CY64) >> 32;                              \
  CYL = (UINT32)(CY64);                            \
  PM = CXH*CYL;                                    \
  PH = CXH*CYH;                                    \
  PL = CXL*CYL;                                    \
  PM2 = CXL*CYH;                                   \
  PH += (PM>>32);                                  \
  PM = (UINT64)((UINT32)PM)+PM2+(PL>>32);          \
  (P128).w[1] = PH + (PM>>32);                     \
  (P128).w[0] = (PM<<32)+(UINT32)PL;                \
}
// 64x64-bit product
#define __mul_64x64_to_128HIGH(P64, CX64, CY64)  \
{                                                  \
  UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2;     \
  CXH = (CX64) >> 32;                              \
  CXL = (UINT32)(CX64);                            \
  CYH = (CY64) >> 32;                              \
  CYL = (UINT32)(CY64);                            \
  PM = CXH*CYL;                                    \
  PH = CXH*CYH;                                    \
  PL = CXL*CYL;                                    \
  PM2 = CXL*CYH;                                   \
  PH += (PM>>32);                                  \
  PM = (UINT64)((UINT32)PM)+PM2+(PL>>32);          \
  P64 = PH + (PM>>32);                     \
}
#define __mul_128x64_to_128(Q128, A64, B128)        \
{                                                  \
  UINT64 ALBH_L;                                   \
  ALBH_L = (A64) * (B128).w[1];                    \
  __mul_64x64_to_128MACH((Q128), (A64), (B128).w[0]);   \
  (Q128).w[1] += ALBH_L;                           \
}
// might simplify by calculating just QM2.w[0]
#define __mul_64x128_to_128(Ql, A, B)           \
{                                                 \
  UINT128 ALBL, ALBH, QM2;                        \
  __mul_64x64_to_128(ALBH, (A), (B).w[1]);        \
  __mul_64x64_to_128(ALBL, (A), (B).w[0]);        \
  (Ql).w[0] = ALBL.w[0];                          \
  __add_128_64(QM2, ALBH, ALBL.w[1]);             \
  (Ql).w[1] = QM2.w[0];                           \
}
/*********************************************************************
 *
 *      BID Pack/Unpack Macros
 *
 *********************************************************************/
/////////////////////////////////////////
// BID64 definitions
////////////////////////////////////////
#define DECIMAL_MAX_EXPON_64  767
#define DECIMAL_EXPONENT_BIAS 398
#define MAX_FORMAT_DIGITS     16
/////////////////////////////////////////
// BID128 definitions
////////////////////////////////////////
#define DECIMAL_MAX_EXPON_128  12287
#define DECIMAL_EXPONENT_BIAS_128  6176
#define MAX_FORMAT_DIGITS_128      34
/////////////////////////////////////////
// BID32 definitions
////////////////////////////////////////
#define DECIMAL_MAX_EXPON_32  191
#define DECIMAL_EXPONENT_BIAS_32  101
#define MAX_FORMAT_DIGITS_32      7
////////////////////////////////////////
// Constant Definitions
///////////////////////////////////////
#define SPECIAL_ENCODING_MASK64 0x6000000000000000ull
#define INFINITY_MASK64         0x7800000000000000ull
#define SINFINITY_MASK64        0xf800000000000000ull
#define SSNAN_MASK64            0xfc00000000000000ull
#define NAN_MASK64              0x7c00000000000000ull
#define SNAN_MASK64             0x7e00000000000000ull
#define QUIET_MASK64            0xfdffffffffffffffull
#define LARGE_COEFF_MASK64      0x0007ffffffffffffull
#define LARGE_COEFF_HIGH_BIT64  0x0020000000000000ull
#define SMALL_COEFF_MASK64      0x001fffffffffffffull
#define EXPONENT_MASK64         0x3ff
#define EXPONENT_SHIFT_LARGE64  51
#define EXPONENT_SHIFT_SMALL64  53
#define LARGEST_BID64           0x77fb86f26fc0ffffull
#define SMALLEST_BID64          0xf7fb86f26fc0ffffull
#define SMALL_COEFF_MASK128     0x0001ffffffffffffull
#define LARGE_COEFF_MASK128     0x00007fffffffffffull
#define EXPONENT_MASK128        0x3fff
#define LARGEST_BID128_HIGH     0x5fffed09bead87c0ull
#define LARGEST_BID128_LOW      0x378d8e63ffffffffull
#define SPECIAL_ENCODING_MASK32 0x60000000ul
#define INFINITY_MASK32         0x78000000ul
#define LARGE_COEFF_MASK32      0x007ffffful
#define LARGE_COEFF_HIGH_BIT32  0x00800000ul
#define SMALL_COEFF_MASK32      0x001ffffful
#define EXPONENT_MASK32         0xff
#define LARGEST_BID32           0x77f8967f
#define NAN_MASK32              0x7c000000
#define SNAN_MASK32             0x7e000000
#define MASK_BINARY_EXPONENT  0x7ff0000000000000ull
#define BINARY_EXPONENT_BIAS  0x3ff
#define UPPER_EXPON_LIMIT     51
// data needed for BID pack/unpack macros
extern UINT64 round_const_table[][19];
extern UINT128 reciprocals10_128[];
extern int recip_scale[];
extern UINT128 power10_table_128[];
extern int estimate_decimal_digits[];
extern int estimate_bin_expon[];
extern UINT64 power10_index_binexp[];
extern int short_recip_scale[];
extern UINT64 reciprocals10_64[];
extern UINT128 power10_index_binexp_128[];
extern UINT128 round_const_table_128[][36];


//////////////////////////////////////////////
//  Status Flag Handling
/////////////////////////////////////////////
#define __set_status_flags(fpsc, status)  *(fpsc) |= status
#define is_inexact(fpsc)  ((*(fpsc))&INEXACT_EXCEPTION)

__BID_INLINE__ UINT64
unpack_BID64 (UINT64 * psign_x, int *pexponent_x,
	      UINT64 * pcoefficient_x, UINT64 x) {
  UINT64 tmp, coeff;

  *psign_x = x & 0x8000000000000000ull;

  if ((x & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) {
    // special encodings
    // coefficient
    coeff = (x & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64;

    if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
      *pexponent_x = 0;
      *pcoefficient_x = x & 0xfe03ffffffffffffull;
      if ((x & 0x0003ffffffffffffull) >= 1000000000000000ull)
	*pcoefficient_x = x & 0xfe00000000000000ull;
      if ((x & NAN_MASK64) == INFINITY_MASK64)
	*pcoefficient_x = x & SINFINITY_MASK64;
      return 0;	// NaN or Infinity
    }
    // check for non-canonical values
    if (coeff >= 10000000000000000ull)
      coeff = 0;
    *pcoefficient_x = coeff;
    // get exponent
    tmp = x >> EXPONENT_SHIFT_LARGE64;
    *pexponent_x = (int) (tmp & EXPONENT_MASK64);
    return coeff;
  }
  // exponent
  tmp = x >> EXPONENT_SHIFT_SMALL64;
  *pexponent_x = (int) (tmp & EXPONENT_MASK64);
  // coefficient
  *pcoefficient_x = (x & SMALL_COEFF_MASK64);

  return *pcoefficient_x;
}

//
//   BID64 pack macro (general form)
//
__BID_INLINE__ UINT64
get_BID64 (UINT64 sgn, int expon, UINT64 coeff, int rmode,
	   unsigned *fpsc) {
  UINT128 Stemp, Q_low;
  UINT64 QH, r, mask, C64, remainder_h, CY, carry;
  int extra_digits, amount, amount2;
  unsigned status;

  if (coeff > 9999999999999999ull) {
    expon++;
    coeff = 1000000000000000ull;
  }
  // check for possible underflow/overflow
  if (((unsigned) expon) >= 3 * 256) {
    if (expon < 0) {
      // underflow
      if (expon + MAX_FORMAT_DIGITS < 0) {
#ifdef SET_STATUS_FLAGS
	__set_status_flags (fpsc,
			    UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
	if (rmode == ROUNDING_DOWN && sgn)
	  return 0x8000000000000001ull;
	if (rmode == ROUNDING_UP && !sgn)
	  return 1ull;
#endif
#endif
	// result is 0
	return sgn;
      }
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (sgn && (unsigned) (rmode - 1) < 2)
	rmode = 3 - rmode;
#endif
#endif
      // get digits to be shifted out
      extra_digits = -expon;
      coeff += round_const_table[rmode][extra_digits];

      // get coeff*(2^M[extra_digits])/10^extra_digits
      __mul_64x128_full (QH, Q_low, coeff,
			 reciprocals10_128[extra_digits]);

      // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
      amount = recip_scale[extra_digits];

      C64 = QH >> amount;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (rmode == 0)	//ROUNDING_TO_NEAREST
#endif
	if (C64 & 1) {
	  // check whether fractional part of initial_P/10^extra_digits is exactly .5

	  // get remainder
	  amount2 = 64 - amount;
	  remainder_h = 0;
	  remainder_h--;
	  remainder_h >>= amount2;
	  remainder_h = remainder_h & QH;

	  if (!remainder_h
	      && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
		  || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		      && Q_low.w[0] <
		      reciprocals10_128[extra_digits].w[0]))) {
	    C64--;
	  }
	}
#endif

#ifdef SET_STATUS_FLAGS

      if (is_inexact (fpsc))
	__set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
      else {
	status = INEXACT_EXCEPTION;
	// get remainder
	remainder_h = QH << (64 - amount);

	switch (rmode) {
	case ROUNDING_TO_NEAREST:
	case ROUNDING_TIES_AWAY:
	  // test whether fractional part is 0
	  if (remainder_h == 0x8000000000000000ull
	      && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
		  || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		      && Q_low.w[0] <
		      reciprocals10_128[extra_digits].w[0])))
	    status = EXACT_STATUS;
	  break;
	case ROUNDING_DOWN:
	case ROUNDING_TO_ZERO:
	  if (!remainder_h
	      && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
		  || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		      && Q_low.w[0] <
		      reciprocals10_128[extra_digits].w[0])))
	    status = EXACT_STATUS;
	  break;
	default:
	  // round up
	  __add_carry_out (Stemp.w[0], CY, Q_low.w[0],
			   reciprocals10_128[extra_digits].w[0]);
	  __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
			      reciprocals10_128[extra_digits].w[1], CY);
	  if ((remainder_h >> (64 - amount)) + carry >=
	      (((UINT64) 1) << amount))
	    status = EXACT_STATUS;
	}

	if (status != EXACT_STATUS)
	  __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status);
      }

#endif

      return sgn | C64;
    }
    while (coeff < 1000000000000000ull && expon >= 3 * 256) {
      expon--;
      coeff = (coeff << 3) + (coeff << 1);
    }
    if (expon > DECIMAL_MAX_EXPON_64) {
#ifdef SET_STATUS_FLAGS
      __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
      // overflow
      r = sgn | INFINITY_MASK64;
      switch (rmode) {
      case ROUNDING_DOWN:
	if (!sgn)
	  r = LARGEST_BID64;
	break;
      case ROUNDING_TO_ZERO:
	r = sgn | LARGEST_BID64;
	break;
      case ROUNDING_UP:
	// round up
	if (sgn)
	  r = SMALLEST_BID64;
      }
      return r;
    }
  }

  mask = 1;
  mask <<= EXPONENT_SHIFT_SMALL64;

  // check whether coefficient fits in 10*5+3 bits
  if (coeff < mask) {
    r = expon;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (coeff | sgn);
    return r;
  }
  // special format

  // eliminate the case coeff==10^16 after rounding
  if (coeff == 10000000000000000ull) {
    r = expon + 1;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (1000000000000000ull | sgn);
    return r;
  }

  r = expon;
  r <<= EXPONENT_SHIFT_LARGE64;
  r |= (sgn | SPECIAL_ENCODING_MASK64);
  // add coeff, without leading bits
  mask = (mask >> 2) - 1;
  coeff &= mask;
  r |= coeff;

  return r;
}




//
//   No overflow/underflow checking 
//
__BID_INLINE__ UINT64
fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) {
  UINT64 r, mask;

  mask = 1;
  mask <<= EXPONENT_SHIFT_SMALL64;

  // check whether coefficient fits in 10*5+3 bits
  if (coeff < mask) {
    r = expon;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (coeff | sgn);
    return r;
  }
  // special format

  // eliminate the case coeff==10^16 after rounding
  if (coeff == 10000000000000000ull) {
    r = expon + 1;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (1000000000000000ull | sgn);
    return r;
  }

  r = expon;
  r <<= EXPONENT_SHIFT_LARGE64;
  r |= (sgn | SPECIAL_ENCODING_MASK64);
  // add coeff, without leading bits
  mask = (mask >> 2) - 1;
  coeff &= mask;
  r |= coeff;

  return r;
}


//
//   no underflow checking
//
__BID_INLINE__ UINT64
fast_get_BID64_check_OF (UINT64 sgn, int expon, UINT64 coeff, int rmode,
			 unsigned *fpsc) {
  UINT64 r, mask;

  if (((unsigned) expon) >= 3 * 256 - 1) {
    if ((expon == 3 * 256 - 1) && coeff == 10000000000000000ull) {
      expon = 3 * 256;
      coeff = 1000000000000000ull;
    }

    if (((unsigned) expon) >= 3 * 256) {
      while (coeff < 1000000000000000ull && expon >= 3 * 256) {
	expon--;
	coeff = (coeff << 3) + (coeff << 1);
      }
      if (expon > DECIMAL_MAX_EXPON_64) {
#ifdef SET_STATUS_FLAGS
	__set_status_flags (fpsc,
			    OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
	// overflow
	r = sgn | INFINITY_MASK64;
	switch (rmode) {
	case ROUNDING_DOWN:
	  if (!sgn)
	    r = LARGEST_BID64;
	  break;
	case ROUNDING_TO_ZERO:
	  r = sgn | LARGEST_BID64;
	  break;
	case ROUNDING_UP:
	  // round up
	  if (sgn)
	    r = SMALLEST_BID64;
	}
	return r;
      }
    }
  }

  mask = 1;
  mask <<= EXPONENT_SHIFT_SMALL64;

  // check whether coefficient fits in 10*5+3 bits
  if (coeff < mask) {
    r = expon;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (coeff | sgn);
    return r;
  }
  // special format

  // eliminate the case coeff==10^16 after rounding
  if (coeff == 10000000000000000ull) {
    r = expon + 1;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (1000000000000000ull | sgn);
    return r;
  }

  r = expon;
  r <<= EXPONENT_SHIFT_LARGE64;
  r |= (sgn | SPECIAL_ENCODING_MASK64);
  // add coeff, without leading bits
  mask = (mask >> 2) - 1;
  coeff &= mask;
  r |= coeff;

  return r;
}


//
//   No overflow/underflow checking 
//   or checking for coefficients equal to 10^16 (after rounding)
//
__BID_INLINE__ UINT64
very_fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) {
  UINT64 r, mask;

  mask = 1;
  mask <<= EXPONENT_SHIFT_SMALL64;

  // check whether coefficient fits in 10*5+3 bits
  if (coeff < mask) {
    r = expon;
    r <<= EXPONENT_SHIFT_SMALL64;
    r |= (coeff | sgn);
    return r;
  }
  // special format
  r = expon;
  r <<= EXPONENT_SHIFT_LARGE64;
  r |= (sgn | SPECIAL_ENCODING_MASK64);
  // add coeff, without leading bits
  mask = (mask >> 2) - 1;
  coeff &= mask;
  r |= coeff;

  return r;
}

//
//   No overflow/underflow checking or checking for coefficients above 2^53
//
__BID_INLINE__ UINT64
very_fast_get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff) {
  // no UF/OF
  UINT64 r;

  r = expon;
  r <<= EXPONENT_SHIFT_SMALL64;
  r |= (coeff | sgn);
  return r;
}


//
// This pack macro is used when underflow is known to occur
//
__BID_INLINE__ UINT64
get_BID64_UF (UINT64 sgn, int expon, UINT64 coeff, UINT64 R, int rmode,
	      unsigned *fpsc) {
  UINT128 C128, Q_low, Stemp;
  UINT64 C64, remainder_h, QH, carry, CY;
  int extra_digits, amount, amount2;
  unsigned status;

  // underflow
  if (expon + MAX_FORMAT_DIGITS < 0) {
#ifdef SET_STATUS_FLAGS
    __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
    if (rmode == ROUNDING_DOWN && sgn)
      return 0x8000000000000001ull;
    if (rmode == ROUNDING_UP && !sgn)
      return 1ull;
#endif
#endif
    // result is 0
    return sgn;
  }
  // 10*coeff
  coeff = (coeff << 3) + (coeff << 1);
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  if (sgn && (unsigned) (rmode - 1) < 2)
    rmode = 3 - rmode;
#endif
#endif
  if (R)
    coeff |= 1;
  // get digits to be shifted out
  extra_digits = 1 - expon;
  C128.w[0] = coeff + round_const_table[rmode][extra_digits];

  // get coeff*(2^M[extra_digits])/10^extra_digits
  __mul_64x128_full (QH, Q_low, C128.w[0],
		     reciprocals10_128[extra_digits]);

  // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
  amount = recip_scale[extra_digits];

  C64 = QH >> amount;
  //__shr_128(C128, Q_high, amount); 

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  if (rmode == 0)	//ROUNDING_TO_NEAREST
#endif
    if (C64 & 1) {
      // check whether fractional part of initial_P/10^extra_digits is exactly .5

      // get remainder
      amount2 = 64 - amount;
      remainder_h = 0;
      remainder_h--;
      remainder_h >>= amount2;
      remainder_h = remainder_h & QH;

      if (!remainder_h
	  && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
	      || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		  && Q_low.w[0] <
		  reciprocals10_128[extra_digits].w[0]))) {
	C64--;
      }
    }
#endif

#ifdef SET_STATUS_FLAGS

  if (is_inexact (fpsc))
    __set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
  else {
    status = INEXACT_EXCEPTION;
    // get remainder
    remainder_h = QH << (64 - amount);

    switch (rmode) {
    case ROUNDING_TO_NEAREST:
    case ROUNDING_TIES_AWAY:
      // test whether fractional part is 0
      if (remainder_h == 0x8000000000000000ull
	  && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
	      || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		  && Q_low.w[0] <
		  reciprocals10_128[extra_digits].w[0])))
	status = EXACT_STATUS;
      break;
    case ROUNDING_DOWN:
    case ROUNDING_TO_ZERO:
      if (!remainder_h
	  && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
	      || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		  && Q_low.w[0] <
		  reciprocals10_128[extra_digits].w[0])))
	status = EXACT_STATUS;
      break;
    default:
      // round up
      __add_carry_out (Stemp.w[0], CY, Q_low.w[0],
		       reciprocals10_128[extra_digits].w[0]);
      __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
			  reciprocals10_128[extra_digits].w[1], CY);
      if ((remainder_h >> (64 - amount)) + carry >=
	  (((UINT64) 1) << amount))
	status = EXACT_STATUS;
    }

    if (status != EXACT_STATUS)
      __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status);
  }

#endif

  return sgn | C64;

}



//
//   This pack macro doesnot check for coefficients above 2^53 
//
__BID_INLINE__ UINT64
get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff,
			  int rmode, unsigned *fpsc) {
  UINT128 C128, Q_low, Stemp;
  UINT64 r, mask, C64, remainder_h, QH, carry, CY;
  int extra_digits, amount, amount2;
  unsigned status;

  // check for possible underflow/overflow
  if (((unsigned) expon) >= 3 * 256) {
    if (expon < 0) {
      // underflow
      if (expon + MAX_FORMAT_DIGITS < 0) {
#ifdef SET_STATUS_FLAGS
	__set_status_flags (fpsc,
			    UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
	if (rmode == ROUNDING_DOWN && sgn)
	  return 0x8000000000000001ull;
	if (rmode == ROUNDING_UP && !sgn)
	  return 1ull;
#endif
#endif
	// result is 0
	return sgn;
      }
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (sgn && (unsigned) (rmode - 1) < 2)
	rmode = 3 - rmode;
#endif
#endif
      // get digits to be shifted out
      extra_digits = -expon;
      C128.w[0] = coeff + round_const_table[rmode][extra_digits];

      // get coeff*(2^M[extra_digits])/10^extra_digits
      __mul_64x128_full (QH, Q_low, C128.w[0],
			 reciprocals10_128[extra_digits]);

      // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
      amount = recip_scale[extra_digits];

      C64 = QH >> amount;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (rmode == 0)	//ROUNDING_TO_NEAREST
#endif
	if (C64 & 1) {
	  // check whether fractional part of initial_P/10^extra_digits is exactly .5

	  // get remainder
	  amount2 = 64 - amount;
	  remainder_h = 0;
	  remainder_h--;
	  remainder_h >>= amount2;
	  remainder_h = remainder_h & QH;

	  if (!remainder_h
	      && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
		  || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		      && Q_low.w[0] <
		      reciprocals10_128[extra_digits].w[0]))) {
	    C64--;
	  }
	}
#endif

#ifdef SET_STATUS_FLAGS

      if (is_inexact (fpsc))
	__set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
      else {
	status = INEXACT_EXCEPTION;
	// get remainder
	remainder_h = QH << (64 - amount);

	switch (rmode) {
	case ROUNDING_TO_NEAREST:
	case ROUNDING_TIES_AWAY:
	  // test whether fractional part is 0
	  if (remainder_h == 0x8000000000000000ull
	      && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
		  || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		      && Q_low.w[0] <
		      reciprocals10_128[extra_digits].w[0])))
	    status = EXACT_STATUS;
	  break;
	case ROUNDING_DOWN:
	case ROUNDING_TO_ZERO:
	  if (!remainder_h
	      && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
		  || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
		      && Q_low.w[0] <
		      reciprocals10_128[extra_digits].w[0])))
	    status = EXACT_STATUS;
	  break;
	default:
	  // round up
	  __add_carry_out (Stemp.w[0], CY, Q_low.w[0],
			   reciprocals10_128[extra_digits].w[0]);
	  __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
			      reciprocals10_128[extra_digits].w[1], CY);
	  if ((remainder_h >> (64 - amount)) + carry >=
	      (((UINT64) 1) << amount))
	    status = EXACT_STATUS;
	}

	if (status != EXACT_STATUS)
	  __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status);
      }

#endif

      return sgn | C64;
    }

    while (coeff < 1000000000000000ull && expon >= 3 * 256) {
      expon--;
      coeff = (coeff << 3) + (coeff << 1);
    }
    if (expon > DECIMAL_MAX_EXPON_64) {
#ifdef SET_STATUS_FLAGS
      __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
      // overflow
      r = sgn | INFINITY_MASK64;
      switch (rmode) {
      case ROUNDING_DOWN:
	if (!sgn)
	  r = LARGEST_BID64;
	break;
      case ROUNDING_TO_ZERO:
	r = sgn | LARGEST_BID64;
	break;
      case ROUNDING_UP:
	// round up
	if (sgn)
	  r = SMALLEST_BID64;
      }
      return r;
    } else {
      mask = 1;
      mask <<= EXPONENT_SHIFT_SMALL64;
      if (coeff >= mask) {
	r = expon;
	r <<= EXPONENT_SHIFT_LARGE64;
	r |= (sgn | SPECIAL_ENCODING_MASK64);
	// add coeff, without leading bits
	mask = (mask >> 2) - 1;
	coeff &= mask;
	r |= coeff;
	return r;
      }
    }
  }

  r = expon;
  r <<= EXPONENT_SHIFT_SMALL64;
  r |= (coeff | sgn);

  return r;
}


/*****************************************************************************
*
*    BID128 pack/unpack macros
*
*****************************************************************************/

//
//   Macro for handling BID128 underflow
//         sticky bit given as additional argument
//
__BID_INLINE__ UINT128 *
handle_UF_128_rem (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ,
		   UINT64 R, unsigned *prounding_mode, unsigned *fpsc) {
  UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CQ2, CQ8;
  UINT64 carry, CY;
  int ed2, amount;
  unsigned rmode, status;

  // UF occurs
  if (expon + MAX_FORMAT_DIGITS_128 < 0) {
#ifdef SET_STATUS_FLAGS
    __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
    pres->w[1] = sgn;
    pres->w[0] = 0;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
    if ((sgn && *prounding_mode == ROUNDING_DOWN)
	|| (!sgn && *prounding_mode == ROUNDING_UP))
      pres->w[0] = 1ull;
#endif
#endif
    return pres;
  }
  // CQ *= 10
  CQ2.w[1] = (CQ.w[1] << 1) | (CQ.w[0] >> 63);
  CQ2.w[0] = CQ.w[0] << 1;
  CQ8.w[1] = (CQ.w[1] << 3) | (CQ.w[0] >> 61);
  CQ8.w[0] = CQ.w[0] << 3;
  __add_128_128 (CQ, CQ2, CQ8);

  // add remainder
  if (R)
    CQ.w[0] |= 1;

  ed2 = 1 - expon;
  // add rounding constant to CQ
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  rmode = *prounding_mode;
  if (sgn && (unsigned) (rmode - 1) < 2)
    rmode = 3 - rmode;
#else
  rmode = 0;
#endif
#else
  rmode = 0;
#endif
  T128 = round_const_table_128[rmode][ed2];
  __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]);
  CQ.w[1] = CQ.w[1] + T128.w[1] + carry;

  TP128 = reciprocals10_128[ed2];
  __mul_128x128_full (Qh, Ql, CQ, TP128);
  amount = recip_scale[ed2];

  if (amount >= 64) {
    CQ.w[0] = Qh.w[1] >> (amount - 64);
    CQ.w[1] = 0;
  } else {
    __shr_128 (CQ, Qh, amount);
  }

  expon = 0;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  if (!(*prounding_mode))
#endif
    if (CQ.w[0] & 1) {
      // check whether fractional part of initial_P/10^ed1 is exactly .5

      // get remainder
      __shl_128_long (Qh1, Qh, (128 - amount));

      if (!Qh1.w[1] && !Qh1.w[0]
	  && (Ql.w[1] < reciprocals10_128[ed2].w[1]
	      || (Ql.w[1] == reciprocals10_128[ed2].w[1]
		  && Ql.w[0] < reciprocals10_128[ed2].w[0]))) {
	CQ.w[0]--;
      }
    }
#endif

#ifdef SET_STATUS_FLAGS

  if (is_inexact (fpsc))
    __set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
  else {
    status = INEXACT_EXCEPTION;
    // get remainder
    __shl_128_long (Qh1, Qh, (128 - amount));

    switch (rmode) {
    case ROUNDING_TO_NEAREST:
    case ROUNDING_TIES_AWAY:
      // test whether fractional part is 0
      if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0])
	  && (Ql.w[1] < reciprocals10_128[ed2].w[1]
	      || (Ql.w[1] == reciprocals10_128[ed2].w[1]
		  && Ql.w[0] < reciprocals10_128[ed2].w[0])))
	status = EXACT_STATUS;
      break;
    case ROUNDING_DOWN:
    case ROUNDING_TO_ZERO:
      if ((!Qh1.w[1]) && (!Qh1.w[0])
	  && (Ql.w[1] < reciprocals10_128[ed2].w[1]
	      || (Ql.w[1] == reciprocals10_128[ed2].w[1]
		  && Ql.w[0] < reciprocals10_128[ed2].w[0])))
	status = EXACT_STATUS;
      break;
    default:
      // round up
      __add_carry_out (Stemp.w[0], CY, Ql.w[0],
		       reciprocals10_128[ed2].w[0]);
      __add_carry_in_out (Stemp.w[1], carry, Ql.w[1],
			  reciprocals10_128[ed2].w[1], CY);
      __shr_128_long (Qh, Qh1, (128 - amount));
      Tmp.w[0] = 1;
      Tmp.w[1] = 0;
      __shl_128_long (Tmp1, Tmp, amount);
      Qh.w[0] += carry;
      if (Qh.w[0] < carry)
	Qh.w[1]++;
      if (__unsigned_compare_ge_128 (Qh, Tmp1))
	status = EXACT_STATUS;
    }

    if (status != EXACT_STATUS)
      __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status);
  }

#endif

  pres->w[1] = sgn | CQ.w[1];
  pres->w[0] = CQ.w[0];

  return pres;

}


//
//   Macro for handling BID128 underflow
//
__BID_INLINE__ UINT128 *
handle_UF_128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ,
	       unsigned *prounding_mode, unsigned *fpsc) {
  UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1;
  UINT64 carry, CY;
  int ed2, amount;
  unsigned rmode, status;

  // UF occurs
  if (expon + MAX_FORMAT_DIGITS_128 < 0) {
#ifdef SET_STATUS_FLAGS
    __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
    pres->w[1] = sgn;
    pres->w[0] = 0;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
    if ((sgn && *prounding_mode == ROUNDING_DOWN)
	|| (!sgn && *prounding_mode == ROUNDING_UP))
      pres->w[0] = 1ull;
#endif
#endif
    return pres;
  }

  ed2 = 0 - expon;
  // add rounding constant to CQ
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  rmode = *prounding_mode;
  if (sgn && (unsigned) (rmode - 1) < 2)
    rmode = 3 - rmode;
#else
  rmode = 0;
#endif
#else
  rmode = 0;
#endif

  T128 = round_const_table_128[rmode][ed2];
  __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]);
  CQ.w[1] = CQ.w[1] + T128.w[1] + carry;

  TP128 = reciprocals10_128[ed2];
  __mul_128x128_full (Qh, Ql, CQ, TP128);
  amount = recip_scale[ed2];

  if (amount >= 64) {
    CQ.w[0] = Qh.w[1] >> (amount - 64);
    CQ.w[1] = 0;
  } else {
    __shr_128 (CQ, Qh, amount);
  }

  expon = 0;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  if (!(*prounding_mode))
#endif
    if (CQ.w[0] & 1) {
      // check whether fractional part of initial_P/10^ed1 is exactly .5

      // get remainder
      __shl_128_long (Qh1, Qh, (128 - amount));

      if (!Qh1.w[1] && !Qh1.w[0]
	  && (Ql.w[1] < reciprocals10_128[ed2].w[1]
	      || (Ql.w[1] == reciprocals10_128[ed2].w[1]
		  && Ql.w[0] < reciprocals10_128[ed2].w[0]))) {
	CQ.w[0]--;
      }
    }
#endif

#ifdef SET_STATUS_FLAGS

  if (is_inexact (fpsc))
    __set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
  else {
    status = INEXACT_EXCEPTION;
    // get remainder
    __shl_128_long (Qh1, Qh, (128 - amount));

    switch (rmode) {
    case ROUNDING_TO_NEAREST:
    case ROUNDING_TIES_AWAY:
      // test whether fractional part is 0
      if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0])
	  && (Ql.w[1] < reciprocals10_128[ed2].w[1]
	      || (Ql.w[1] == reciprocals10_128[ed2].w[1]
		  && Ql.w[0] < reciprocals10_128[ed2].w[0])))
	status = EXACT_STATUS;
      break;
    case ROUNDING_DOWN:
    case ROUNDING_TO_ZERO:
      if ((!Qh1.w[1]) && (!Qh1.w[0])
	  && (Ql.w[1] < reciprocals10_128[ed2].w[1]
	      || (Ql.w[1] == reciprocals10_128[ed2].w[1]
		  && Ql.w[0] < reciprocals10_128[ed2].w[0])))
	status = EXACT_STATUS;
      break;
    default:
      // round up
      __add_carry_out (Stemp.w[0], CY, Ql.w[0],
		       reciprocals10_128[ed2].w[0]);
      __add_carry_in_out (Stemp.w[1], carry, Ql.w[1],
			  reciprocals10_128[ed2].w[1], CY);
      __shr_128_long (Qh, Qh1, (128 - amount));
      Tmp.w[0] = 1;
      Tmp.w[1] = 0;
      __shl_128_long (Tmp1, Tmp, amount);
      Qh.w[0] += carry;
      if (Qh.w[0] < carry)
	Qh.w[1]++;
      if (__unsigned_compare_ge_128 (Qh, Tmp1))
	status = EXACT_STATUS;
    }

    if (status != EXACT_STATUS)
      __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status);
  }

#endif

  pres->w[1] = sgn | CQ.w[1];
  pres->w[0] = CQ.w[0];

  return pres;

}



//
//  BID128 unpack, input passed by value
//
__BID_INLINE__ UINT64
unpack_BID128_value (UINT64 * psign_x, int *pexponent_x,
		     UINT128 * pcoefficient_x, UINT128 x) {
  UINT128 coeff, T33, T34;
  UINT64 ex;

  *psign_x = (x.w[1]) & 0x8000000000000000ull;

  // special encodings
  if ((x.w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) {
    if ((x.w[1] & INFINITY_MASK64) < INFINITY_MASK64) {
      // non-canonical input
      pcoefficient_x->w[0] = 0;
      pcoefficient_x->w[1] = 0;
      ex = (x.w[1]) >> 47;
      *pexponent_x = ((int) ex) & EXPONENT_MASK128;
      return 0;
    }
    // 10^33
    T33 = power10_table_128[33];
    /*coeff.w[0] = x.w[0];
       coeff.w[1] = (x.w[1]) & LARGE_COEFF_MASK128;
       pcoefficient_x->w[0] = x.w[0];
       pcoefficient_x->w[1] = x.w[1];
       if (__unsigned_compare_ge_128 (coeff, T33)) // non-canonical
       pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); */

    pcoefficient_x->w[0] = x.w[0];
    pcoefficient_x->w[1] = (x.w[1]) & 0x00003fffffffffffull;
    if (__unsigned_compare_ge_128 ((*pcoefficient_x), T33))	// non-canonical
    {
      pcoefficient_x->w[1] = (x.w[1]) & 0xfe00000000000000ull;
      pcoefficient_x->w[0] = 0;
    } else
      pcoefficient_x->w[1] = (x.w[1]) & 0xfe003fffffffffffull;
    if ((x.w[1] & NAN_MASK64) == INFINITY_MASK64) {
      pcoefficient_x->w[0] = 0;
      pcoefficient_x->w[1] = x.w[1] & SINFINITY_MASK64;
    }
    *pexponent_x = 0;
    return 0;	// NaN or Infinity 
  }

  coeff.w[0] = x.w[0];
  coeff.w[1] = (x.w[1]) & SMALL_COEFF_MASK128;

  // 10^34
  T34 = power10_table_128[34];
  // check for non-canonical values
  if (__unsigned_compare_ge_128 (coeff, T34))
    coeff.w[0] = coeff.w[1] = 0;

  pcoefficient_x->w[0] = coeff.w[0];
  pcoefficient_x->w[1] = coeff.w[1];

  ex = (x.w[1]) >> 49;
  *pexponent_x = ((int) ex) & EXPONENT_MASK128;

  return coeff.w[0] | coeff.w[1];
}


//
//  BID128 unpack, input pased by reference
//
__BID_INLINE__ UINT64
unpack_BID128 (UINT64 * psign_x, int *pexponent_x,
	       UINT128 * pcoefficient_x, UINT128 * px) {
  UINT128 coeff, T33, T34;
  UINT64 ex;

  *psign_x = (px->w[1]) & 0x8000000000000000ull;

  // special encodings
  if ((px->w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) {
    if ((px->w[1] & INFINITY_MASK64) < INFINITY_MASK64) {
      // non-canonical input
      pcoefficient_x->w[0] = 0;
      pcoefficient_x->w[1] = 0;
      ex = (px->w[1]) >> 47;
      *pexponent_x = ((int) ex) & EXPONENT_MASK128;
      return 0;
    }
    // 10^33
    T33 = power10_table_128[33];
    coeff.w[0] = px->w[0];
    coeff.w[1] = (px->w[1]) & LARGE_COEFF_MASK128;
    pcoefficient_x->w[0] = px->w[0];
    pcoefficient_x->w[1] = px->w[1];
    if (__unsigned_compare_ge_128 (coeff, T33)) {	// non-canonical
      pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128);
      pcoefficient_x->w[0] = 0;
    }
    *pexponent_x = 0;
    return 0;	// NaN or Infinity 
  }

  coeff.w[0] = px->w[0];
  coeff.w[1] = (px->w[1]) & SMALL_COEFF_MASK128;

  // 10^34
  T34 = power10_table_128[34];
  // check for non-canonical values
  if (__unsigned_compare_ge_128 (coeff, T34))
    coeff.w[0] = coeff.w[1] = 0;

  pcoefficient_x->w[0] = coeff.w[0];
  pcoefficient_x->w[1] = coeff.w[1];

  ex = (px->w[1]) >> 49;
  *pexponent_x = ((int) ex) & EXPONENT_MASK128;

  return coeff.w[0] | coeff.w[1];
}

//
//   Pack macro checks for overflow, but not underflow
//
__BID_INLINE__ UINT128 *
get_BID128_very_fast_OF (UINT128 * pres, UINT64 sgn, int expon,
			 UINT128 coeff, unsigned *prounding_mode,
			 unsigned *fpsc) {
  UINT128 T;
  UINT64 tmp, tmp2;

  if ((unsigned) expon > DECIMAL_MAX_EXPON_128) {

    if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) {
      T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1];
      while (__unsigned_compare_gt_128 (T, coeff)
	     && expon > DECIMAL_MAX_EXPON_128) {
	coeff.w[1] =
	  (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) +
	  (coeff.w[0] >> 63);
	tmp2 = coeff.w[0] << 3;
	coeff.w[0] = (coeff.w[0] << 1) + tmp2;
	if (coeff.w[0] < tmp2)
	  coeff.w[1]++;

	expon--;
      }
    }
    if ((unsigned) expon > DECIMAL_MAX_EXPON_128) {
      // OF
#ifdef SET_STATUS_FLAGS
      __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (*prounding_mode == ROUNDING_TO_ZERO
	  || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn
							 &&
							 *prounding_mode
							 ==
							 ROUNDING_DOWN))
      {
	pres->w[1] = sgn | LARGEST_BID128_HIGH;
	pres->w[0] = LARGEST_BID128_LOW;
      } else
#endif
#endif
      {
	pres->w[1] = sgn | INFINITY_MASK64;
	pres->w[0] = 0;
      }
      return pres;
    }
  }

  pres->w[0] = coeff.w[0];
  tmp = expon;
  tmp <<= 49;
  pres->w[1] = sgn | tmp | coeff.w[1];

  return pres;
}


//
//   No overflow/underflow checks
//   No checking for coefficient == 10^34 (rounding artifact)
//
__BID_INLINE__ UINT128 *
get_BID128_very_fast (UINT128 * pres, UINT64 sgn, int expon,
		      UINT128 coeff) {
  UINT64 tmp;

  pres->w[0] = coeff.w[0];
  tmp = expon;
  tmp <<= 49;
  pres->w[1] = sgn | tmp | coeff.w[1];

  return pres;
}

//
//   No overflow/underflow checks
//
__BID_INLINE__ UINT128 *
get_BID128_fast (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) {
  UINT64 tmp;

  // coeff==10^34?
  if (coeff.w[1] == 0x0001ed09bead87c0ull
      && coeff.w[0] == 0x378d8e6400000000ull) {
    expon++;
    // set coefficient to 10^33
    coeff.w[1] = 0x0000314dc6448d93ull;
    coeff.w[0] = 0x38c15b0a00000000ull;
  }

  pres->w[0] = coeff.w[0];
  tmp = expon;
  tmp <<= 49;
  pres->w[1] = sgn | tmp | coeff.w[1];

  return pres;
}

//
//   General BID128 pack macro
//
__BID_INLINE__ UINT128 *
get_BID128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff,
	    unsigned *prounding_mode, unsigned *fpsc) {
  UINT128 T;
  UINT64 tmp, tmp2;

  // coeff==10^34?
  if (coeff.w[1] == 0x0001ed09bead87c0ull
      && coeff.w[0] == 0x378d8e6400000000ull) {
    expon++;
    // set coefficient to 10^33
    coeff.w[1] = 0x0000314dc6448d93ull;
    coeff.w[0] = 0x38c15b0a00000000ull;
  }
  // check OF, UF
  if (expon < 0 || expon > DECIMAL_MAX_EXPON_128) {
    // check UF
    if (expon < 0) {
      return handle_UF_128 (pres, sgn, expon, coeff, prounding_mode,
			    fpsc);
    }

    if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) {
      T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1];
      while (__unsigned_compare_gt_128 (T, coeff)
	     && expon > DECIMAL_MAX_EXPON_128) {
	coeff.w[1] =
	  (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) +
	  (coeff.w[0] >> 63);
	tmp2 = coeff.w[0] << 3;
	coeff.w[0] = (coeff.w[0] << 1) + tmp2;
	if (coeff.w[0] < tmp2)
	  coeff.w[1]++;

	expon--;
      }
    }
    if (expon > DECIMAL_MAX_EXPON_128) {
      if (!(coeff.w[1] | coeff.w[0])) {
	pres->w[1] = sgn | (((UINT64) DECIMAL_MAX_EXPON_128) << 49);
	pres->w[0] = 0;
	return pres;
      }
      // OF
#ifdef SET_STATUS_FLAGS
      __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (*prounding_mode == ROUNDING_TO_ZERO
	  || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn
							 &&
							 *prounding_mode
							 ==
							 ROUNDING_DOWN))
      {
	pres->w[1] = sgn | LARGEST_BID128_HIGH;
	pres->w[0] = LARGEST_BID128_LOW;
      } else
#endif
#endif
      {
	pres->w[1] = sgn | INFINITY_MASK64;
	pres->w[0] = 0;
      }
      return pres;
    }
  }

  pres->w[0] = coeff.w[0];
  tmp = expon;
  tmp <<= 49;
  pres->w[1] = sgn | tmp | coeff.w[1];

  return pres;
}


//
//  Macro used for conversions from string 
//        (no additional arguments given for rounding mode, status flags) 
//
__BID_INLINE__ UINT128 *
get_BID128_string (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) {
  UINT128 D2, D8;
  UINT64 tmp;
  unsigned rmode = 0, status;

  // coeff==10^34?
  if (coeff.w[1] == 0x0001ed09bead87c0ull
      && coeff.w[0] == 0x378d8e6400000000ull) {
    expon++;
    // set coefficient to 10^33
    coeff.w[1] = 0x0000314dc6448d93ull;
    coeff.w[0] = 0x38c15b0a00000000ull;
  }
  // check OF, UF
  if ((unsigned) expon > DECIMAL_MAX_EXPON_128) {
    // check UF
    if (expon < 0)
      return handle_UF_128 (pres, sgn, expon, coeff, &rmode, &status);

    // OF

    if (expon < DECIMAL_MAX_EXPON_128 + 34) {
      while (expon > DECIMAL_MAX_EXPON_128 &&
	     (coeff.w[1] < power10_table_128[33].w[1] ||
	      (coeff.w[1] == power10_table_128[33].w[1]
	       && coeff.w[0] < power10_table_128[33].w[0]))) {
	D2.w[1] = (coeff.w[1] << 1) | (coeff.w[0] >> 63);
	D2.w[0] = coeff.w[0] << 1;
	D8.w[1] = (coeff.w[1] << 3) | (coeff.w[0] >> 61);
	D8.w[0] = coeff.w[0] << 3;

	__add_128_128 (coeff, D2, D8);
	expon--;
      }
    } else if (!(coeff.w[0] | coeff.w[1]))
      expon = DECIMAL_MAX_EXPON_128;

    if (expon > DECIMAL_MAX_EXPON_128) {
      pres->w[1] = sgn | INFINITY_MASK64;
      pres->w[0] = 0;
      switch (rmode) {
      case ROUNDING_DOWN:
	if (!sgn) {
	  pres->w[1] = LARGEST_BID128_HIGH;
	  pres->w[0] = LARGEST_BID128_LOW;
	}
	break;
      case ROUNDING_TO_ZERO:
	pres->w[1] = sgn | LARGEST_BID128_HIGH;
	pres->w[0] = LARGEST_BID128_LOW;
	break;
      case ROUNDING_UP:
	// round up
	if (sgn) {
	  pres->w[1] = sgn | LARGEST_BID128_HIGH;
	  pres->w[0] = LARGEST_BID128_LOW;
	}
	break;
      }

      return pres;
    }
  }

  pres->w[0] = coeff.w[0];
  tmp = expon;
  tmp <<= 49;
  pres->w[1] = sgn | tmp | coeff.w[1];

  return pres;
}



/*****************************************************************************
*
*    BID32 pack/unpack macros
*
*****************************************************************************/


__BID_INLINE__ UINT32
unpack_BID32 (UINT32 * psign_x, int *pexponent_x,
	      UINT32 * pcoefficient_x, UINT32 x) {
  UINT32 tmp;

  *psign_x = x & 0x80000000;

  if ((x & SPECIAL_ENCODING_MASK32) == SPECIAL_ENCODING_MASK32) {
    // special encodings
    if ((x & INFINITY_MASK32) == INFINITY_MASK32) {
      *pcoefficient_x = x & 0xfe0fffff;
      if ((x & 0x000fffff) >= 1000000)
	*pcoefficient_x = x & 0xfe000000;
      if ((x & NAN_MASK32) == INFINITY_MASK32)
	*pcoefficient_x = x & 0xf8000000;
      *pexponent_x = 0;
      return 0;	// NaN or Infinity
    }
    // coefficient
    *pcoefficient_x = (x & SMALL_COEFF_MASK32) | LARGE_COEFF_HIGH_BIT32;
    // check for non-canonical value
    if (*pcoefficient_x >= 10000000)
      *pcoefficient_x = 0;
    // get exponent
    tmp = x >> 21;
    *pexponent_x = tmp & EXPONENT_MASK32;
    return 1;
  }
  // exponent
  tmp = x >> 23;
  *pexponent_x = tmp & EXPONENT_MASK32;
  // coefficient
  *pcoefficient_x = (x & LARGE_COEFF_MASK32);

  return *pcoefficient_x;
}

//
//   General pack macro for BID32 
//
__BID_INLINE__ UINT32
get_BID32 (UINT32 sgn, int expon, UINT64 coeff, int rmode,
	   unsigned *fpsc) {
  UINT128 Q;
  UINT64 C64, remainder_h, carry, Stemp;
  UINT32 r, mask;
  int extra_digits, amount, amount2;
  unsigned status;

  if (coeff > 9999999ull) {
    expon++;
    coeff = 1000000ull;
  }
  // check for possible underflow/overflow
  if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) {
    if (expon < 0) {
      // underflow
      if (expon + MAX_FORMAT_DIGITS_32 < 0) {
#ifdef SET_STATUS_FLAGS
	__set_status_flags (fpsc,
			    UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
	if (rmode == ROUNDING_DOWN && sgn)
	  return 0x80000001;
	if (rmode == ROUNDING_UP && !sgn)
	  return 1;
#endif
#endif
	// result is 0
	return sgn;
      }
      // get digits to be shifted out
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
      rmode = 0;
#endif
#ifdef IEEE_ROUND_NEAREST
      rmode = 0;
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (sgn && (unsigned) (rmode - 1) < 2)
	rmode = 3 - rmode;
#endif
#endif

      extra_digits = -expon;
      coeff += round_const_table[rmode][extra_digits];

      // get coeff*(2^M[extra_digits])/10^extra_digits
      __mul_64x64_to_128 (Q, coeff, reciprocals10_64[extra_digits]);

      // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
      amount = short_recip_scale[extra_digits];

      C64 = Q.w[1] >> amount;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (rmode == 0)	//ROUNDING_TO_NEAREST
#endif
	if (C64 & 1) {
	  // check whether fractional part of initial_P/10^extra_digits is exactly .5

	  // get remainder
	  amount2 = 64 - amount;
	  remainder_h = 0;
	  remainder_h--;
	  remainder_h >>= amount2;
	  remainder_h = remainder_h & Q.w[1];

	  if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) {
	    C64--;
	  }
	}
#endif

#ifdef SET_STATUS_FLAGS

      if (is_inexact (fpsc))
	__set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
      else {
	status = INEXACT_EXCEPTION;
	// get remainder
	remainder_h = Q.w[1] << (64 - amount);

	switch (rmode) {
	case ROUNDING_TO_NEAREST:
	case ROUNDING_TIES_AWAY:
	  // test whether fractional part is 0
	  if (remainder_h == 0x8000000000000000ull
	      && (Q.w[0] < reciprocals10_64[extra_digits]))
	    status = EXACT_STATUS;
	  break;
	case ROUNDING_DOWN:
	case ROUNDING_TO_ZERO:
	  if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits]))
	    status = EXACT_STATUS;
	  break;
	default:
	  // round up
	  __add_carry_out (Stemp, carry, Q.w[0],
			   reciprocals10_64[extra_digits]);
	  if ((remainder_h >> (64 - amount)) + carry >=
	      (((UINT64) 1) << amount))
	    status = EXACT_STATUS;
	}

	if (status != EXACT_STATUS)
	  __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status);
      }

#endif

      return sgn | (UINT32) C64;
    }

    while (coeff < 1000000 && expon > DECIMAL_MAX_EXPON_32) {
      coeff = (coeff << 3) + (coeff << 1);
      expon--;
    }
    if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) {
      __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
      // overflow
      r = sgn | INFINITY_MASK32;
      switch (rmode) {
      case ROUNDING_DOWN:
	if (!sgn)
	  r = LARGEST_BID32;
	break;
      case ROUNDING_TO_ZERO:
	r = sgn | LARGEST_BID32;
	break;
      case ROUNDING_UP:
	// round up
	if (sgn)
	  r = sgn | LARGEST_BID32;
      }
      return r;
    }
  }

  mask = 1 << 23;

  // check whether coefficient fits in DECIMAL_COEFF_FIT bits
  if (coeff < mask) {
    r = expon;
    r <<= 23;
    r |= ((UINT32) coeff | sgn);
    return r;
  }
  // special format

  r = expon;
  r <<= 21;
  r |= (sgn | SPECIAL_ENCODING_MASK32);
  // add coeff, without leading bits
  mask = (1 << 21) - 1;
  r |= (((UINT32) coeff) & mask);

  return r;
}



//
//   no overflow/underflow checks
//
__BID_INLINE__ UINT32
very_fast_get_BID32 (UINT32 sgn, int expon, UINT32 coeff) {
  UINT32 r, mask;

  mask = 1 << 23;

  // check whether coefficient fits in 10*2+3 bits
  if (coeff < mask) {
    r = expon;
    r <<= 23;
    r |= (coeff | sgn);
    return r;
  }
  // special format
  r = expon;
  r <<= 21;
  r |= (sgn | SPECIAL_ENCODING_MASK32);
  // add coeff, without leading bits
  mask = (1 << 21) - 1;
  coeff &= mask;
  r |= coeff;

  return r;
}



/*************************************************************
 *
 *************************************************************/
typedef
ALIGN (16)
     struct {
       UINT64 w[6];
     } UINT384;
     typedef ALIGN (16)
     struct {
       UINT64 w[8];
     } UINT512;

// #define P                               34
#define MASK_STEERING_BITS              0x6000000000000000ull
#define MASK_BINARY_EXPONENT1           0x7fe0000000000000ull
#define MASK_BINARY_SIG1                0x001fffffffffffffull
#define MASK_BINARY_EXPONENT2           0x1ff8000000000000ull
    //used to take G[2:w+3] (sec 3.3)
#define MASK_BINARY_SIG2                0x0007ffffffffffffull
    //used to mask out G4:T0 (sec 3.3)
#define MASK_BINARY_OR2                 0x0020000000000000ull
    //used to prefix 8+G4 to T (sec 3.3)
#define UPPER_EXPON_LIMIT               51
#define MASK_EXP                        0x7ffe000000000000ull
#define MASK_SPECIAL                    0x7800000000000000ull
#define MASK_NAN                        0x7c00000000000000ull
#define MASK_SNAN                       0x7e00000000000000ull
#define MASK_ANY_INF                    0x7c00000000000000ull
#define MASK_INF                        0x7800000000000000ull
#define MASK_SIGN                       0x8000000000000000ull
#define MASK_COEFF                      0x0001ffffffffffffull
#define BIN_EXP_BIAS                    (0x1820ull << 49)

#define EXP_MIN                         0x0000000000000000ull
   // EXP_MIN = (-6176 + 6176) << 49
#define EXP_MAX                         0x5ffe000000000000ull
  // EXP_MAX = (6111 + 6176) << 49
#define EXP_MAX_P1                      0x6000000000000000ull
  // EXP_MAX + 1 = (6111 + 6176 + 1) << 49
#define EXP_P1                          0x0002000000000000ull
  // EXP_ P1= 1 << 49
#define expmin                            -6176
  // min unbiased exponent
#define expmax                            6111
  // max unbiased exponent
#define expmin16                          -398
  // min unbiased exponent
#define expmax16                          369
  // max unbiased exponent

#define SIGNMASK32 0x80000000
#define BID64_SIG_MAX 0x002386F26FC0ffffull
#define SIGNMASK64    0x8000000000000000ull

// typedef unsigned int FPSC; // floating-point status and control
	// bit31:
	// bit30:
	// bit29:
	// bit28:
	// bit27:
	// bit26:
	// bit25:
	// bit24:
	// bit23:
	// bit22:
	// bit21:
	// bit20:
	// bit19:
	// bit18:
	// bit17:
	// bit16:
	// bit15:
	// bit14: RC:2
	// bit13: RC:1
	// bit12: RC:0
	// bit11: PM
	// bit10: UM
	// bit9:  OM
	// bit8:  ZM
	// bit7:  DM
	// bit6:  IM
	// bit5:  PE
	// bit4:  UE
	// bit3:  OE
	// bit2:  ZE
	// bit1:  DE
	// bit0:  IE

#define ROUNDING_MODE_MASK	0x00007000

     typedef struct _DEC_DIGITS {
       unsigned int digits;
       UINT64 threshold_hi;
       UINT64 threshold_lo;
       unsigned int digits1;
     } DEC_DIGITS;

     extern DEC_DIGITS nr_digits[];
     extern UINT64 midpoint64[];
     extern UINT128 midpoint128[];
     extern UINT192 midpoint192[];
     extern UINT256 midpoint256[];
     extern UINT64 ten2k64[];
     extern UINT128 ten2k128[];
     extern UINT256 ten2k256[];
     extern UINT128 ten2mk128[];
     extern UINT64 ten2mk64[];
     extern UINT128 ten2mk128trunc[];
     extern int shiftright128[];
     extern UINT64 maskhigh128[];
     extern UINT64 maskhigh128M[];
     extern UINT64 maskhigh192M[];
     extern UINT64 maskhigh256M[];
     extern UINT64 onehalf128[];
     extern UINT64 onehalf128M[];
     extern UINT64 onehalf192M[];
     extern UINT64 onehalf256M[];
     extern UINT128 ten2mk128M[];
     extern UINT128 ten2mk128truncM[];
     extern UINT192 ten2mk192truncM[];
     extern UINT256 ten2mk256truncM[];
     extern int shiftright128M[];
     extern int shiftright192M[];
     extern int shiftright256M[];
     extern UINT192 ten2mk192M[];
     extern UINT256 ten2mk256M[];
     extern unsigned char char_table2[];
     extern unsigned char char_table3[];

     extern UINT64 ten2m3k64[];
     extern unsigned int shift_ten2m3k64[];
     extern UINT128 ten2m3k128[];
     extern unsigned int shift_ten2m3k128[];



/***************************************************************************
 *************** TABLES FOR GENERAL ROUNDING FUNCTIONS *********************
 ***************************************************************************/

     extern UINT64 Kx64[];
     extern unsigned int Ex64m64[];
     extern UINT64 half64[];
     extern UINT64 mask64[];
     extern UINT64 ten2mxtrunc64[];

     extern UINT128 Kx128[];
     extern unsigned int Ex128m128[];
     extern UINT64 half128[];
     extern UINT64 mask128[];
     extern UINT128 ten2mxtrunc128[];

     extern UINT192 Kx192[];
     extern unsigned int Ex192m192[];
     extern UINT64 half192[];
     extern UINT64 mask192[];
     extern UINT192 ten2mxtrunc192[];

     extern UINT256 Kx256[];
     extern unsigned int Ex256m256[];
     extern UINT64 half256[];
     extern UINT64 mask256[];
     extern UINT256 ten2mxtrunc256[];

     typedef union __bid64_128 {
       UINT64 b64;
       UINT128 b128;
     } BID64_128;

     BID64_128 bid_fma (unsigned int P0,
			BID64_128 x1, unsigned int P1,
			BID64_128 y1, unsigned int P2,
			BID64_128 z1, unsigned int P3,
			unsigned int rnd_mode, FPSC * fpsc);

#define         P16     16
#define         P34     34

     union __int_double {
       UINT64 i;
       double d;
     };
     typedef union __int_double int_double;


     union __int_float {
       UINT32 i;
       float d;
     };
     typedef union __int_float int_float;

#define SWAP(A,B,T) {\
        T = A; \
        A = B; \
        B = T; \
}

// this macro will find coefficient_x to be in [2^A, 2^(A+1) )
// ie it knows that it is A bits long
#define NUMBITS(A, coefficient_x, tempx){\
      temp_x.d=(float)coefficient_x;\
      A=((tempx.i >>23) & EXPONENT_MASK32) - 0x7f;\
}

     enum class_types {
       signalingNaN,
       quietNaN,
       negativeInfinity,
       negativeNormal,
       negativeSubnormal,
       negativeZero,
       positiveZero,
       positiveSubnormal,
       positiveNormal,
       positiveInfinity
     };

     typedef union {
       UINT64 ui64;
       double d;
     } BID_UI64DOUBLE;

#endif