| /* Copyright (C) 2007-2021 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); |
| } |
| |
| #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 |
