Mercurial > hg > CbC > CbC_gcc
diff libgcc/config/libbid/bid_internal.h @ 0:a06113de4d67
first commit
| author | kent <kent@cr.ie.u-ryukyu.ac.jp> |
|---|---|
| date | Fri, 17 Jul 2009 14:47:48 +0900 |
| parents | |
| children | 04ced10e8804 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libgcc/config/libbid/bid_internal.h Fri Jul 17 14:47:48 2009 +0900 @@ -0,0 +1,2607 @@ +/* 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