/* Copyright (C) 2007-2020 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
. */
#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 = (SX1) ? 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);
}
#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);
}
#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