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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ #ifndef __BIDECIMAL_H #define __BIDECIMAL_H #include "bid_conf.h" #include "bid_functions.h" #define __BID_INLINE__ static __inline /********************************************************************* * * Logical Shift Macros * *********************************************************************/ #define __shr_128(Q, A, k) \ { \ (Q).w[0] = (A).w[0] >> k; \ (Q).w[0] |= (A).w[1] << (64-k); \ (Q).w[1] = (A).w[1] >> k; \ } #define __shr_128_long(Q, A, k) \ { \ if((k)<64) { \ (Q).w[0] = (A).w[0] >> k; \ (Q).w[0] |= (A).w[1] << (64-k); \ (Q).w[1] = (A).w[1] >> k; \ } \ else { \ (Q).w[0] = (A).w[1]>>((k)-64); \ (Q).w[1] = 0; \ } \ } #define __shl_128_long(Q, A, k) \ { \ if((k)<64) { \ (Q).w[1] = (A).w[1] << k; \ (Q).w[1] |= (A).w[0] >> (64-k); \ (Q).w[0] = (A).w[0] << k; \ } \ else { \ (Q).w[1] = (A).w[0]<<((k)-64); \ (Q).w[0] = 0; \ } \ } #define __low_64(Q) (Q).w[0] /********************************************************************* * * String Macros * *********************************************************************/ #define tolower_macro(x) (((unsigned char)((x)-'A')<=('Z'-'A'))?((x)-'A'+'a'):(x)) /********************************************************************* * * Compare Macros * *********************************************************************/ // greater than // return 0 if A<=B // non-zero if A>B #define __unsigned_compare_gt_128(A, B) \ ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>B.w[0]))) // greater-or-equal #define __unsigned_compare_ge_128(A, B) \ ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>=B.w[0]))) #define __test_equal_128(A, B) (((A).w[1]==(B).w[1]) && ((A).w[0]==(B).w[0])) // tighten exponent range #define __tight_bin_range_128(bp, P, bin_expon) \ { \ UINT64 M; \ M = 1; \ (bp) = (bin_expon); \ if((bp)<63) { \ M <<= ((bp)+1); \ if((P).w[0] >= M) (bp)++; } \ else if((bp)>64) { \ M <<= ((bp)+1-64); \ if(((P).w[1]>M) ||((P).w[1]==M && (P).w[0]))\ (bp)++; } \ else if((P).w[1]) (bp)++; \ } /********************************************************************* * * Add/Subtract Macros * *********************************************************************/ // add 64-bit value to 128-bit #define __add_128_64(R128, A128, B64) \ { \ UINT64 R64H; \ R64H = (A128).w[1]; \ (R128).w[0] = (B64) + (A128).w[0]; \ if((R128).w[0] < (B64)) \ R64H ++; \ (R128).w[1] = R64H; \ } // subtract 64-bit value from 128-bit #define __sub_128_64(R128, A128, B64) \ { \ UINT64 R64H; \ R64H = (A128).w[1]; \ if((A128).w[0] < (B64)) \ R64H --; \ (R128).w[1] = R64H; \ (R128).w[0] = (A128).w[0] - (B64); \ } // add 128-bit value to 128-bit // assume no carry-out #define __add_128_128(R128, A128, B128) \ { \ UINT128 Q128; \ Q128.w[1] = (A128).w[1]+(B128).w[1]; \ Q128.w[0] = (B128).w[0] + (A128).w[0]; \ if(Q128.w[0] < (B128).w[0]) \ Q128.w[1] ++; \ (R128).w[1] = Q128.w[1]; \ (R128).w[0] = Q128.w[0]; \ } #define __sub_128_128(R128, A128, B128) \ { \ UINT128 Q128; \ Q128.w[1] = (A128).w[1]-(B128).w[1]; \ Q128.w[0] = (A128).w[0] - (B128).w[0]; \ if((A128).w[0] < (B128).w[0]) \ Q128.w[1] --; \ (R128).w[1] = Q128.w[1]; \ (R128).w[0] = Q128.w[0]; \ } #define __add_carry_out(S, CY, X, Y) \ { \ UINT64 X1=X; \ S = X + Y; \ CY = (S<X1) ? 1 : 0; \ } #define __add_carry_in_out(S, CY, X, Y, CI) \ { \ UINT64 X1; \ X1 = X + CI; \ S = X1 + Y; \ CY = ((S<X1) || (X1<CI)) ? 1 : 0; \ } #define __sub_borrow_out(S, CY, X, Y) \ { \ UINT64 X1=X; \ S = X - Y; \ CY = (S>X1) ? 1 : 0; \ } #define __sub_borrow_in_out(S, CY, X, Y, CI) \ { \ UINT64 X1, X0=X; \ X1 = X - CI; \ S = X1 - Y; \ CY = ((S>X1) || (X1>X0)) ? 1 : 0; \ } // increment C128 and check for rounding overflow: // if (C_128) = 10^34 then (C_128) = 10^33 and increment the exponent #define INCREMENT(C_128, exp) \ { \ C_128.w[0]++; \ if (C_128.w[0] == 0) C_128.w[1]++; \ if (C_128.w[1] == 0x0001ed09bead87c0ull && \ C_128.w[0] == 0x378d8e6400000000ull) { \ exp++; \ C_128.w[1] = 0x0000314dc6448d93ull; \ C_128.w[0] = 0x38c15b0a00000000ull; \ } \ } // decrement C128 and check for rounding underflow, but only at the // boundary: if C_128 = 10^33 - 1 and exp > 0 then C_128 = 10^34 - 1 // and decrement the exponent #define DECREMENT(C_128, exp) \ { \ C_128.w[0]--; \ if (C_128.w[0] == 0xffffffffffffffffull) C_128.w[1]--; \ if (C_128.w[1] == 0x0000314dc6448d93ull && \ C_128.w[0] == 0x38c15b09ffffffffull && exp > 0) { \ exp--; \ C_128.w[1] = 0x0001ed09bead87c0ull; \ C_128.w[0] = 0x378d8e63ffffffffull; \ } \ } /********************************************************************* * * Multiply Macros * *********************************************************************/ #define __mul_64x64_to_64(P64, CX, CY) (P64) = (CX) * (CY) /*************************************** * Signed, Full 64x64-bit Multiply ***************************************/ #define __imul_64x64_to_128(P, CX, CY) \ { \ UINT64 SX, SY; \ __mul_64x64_to_128(P, CX, CY); \ \ SX = ((SINT64)(CX))>>63; \ SY = ((SINT64)(CY))>>63; \ SX &= CY; SY &= CX; \ \ (P).w[1] = (P).w[1] - SX - SY; \ } /*************************************** * Signed, Full 64x128-bit Multiply ***************************************/ #define __imul_64x128_full(Ph, Ql, A, B) \ { \ UINT128 ALBL, ALBH, QM2, QM; \ \ __imul_64x64_to_128(ALBH, (A), (B).w[1]); \ __imul_64x64_to_128(ALBL, (A), (B).w[0]); \ \ (Ql).w[0] = ALBL.w[0]; \ QM.w[0] = ALBL.w[1]; \ QM.w[1] = ((SINT64)ALBL.w[1])>>63; \ __add_128_128(QM2, ALBH, QM); \ (Ql).w[1] = QM2.w[0]; \ Ph = QM2.w[1]; \ } /***************************************************** * Unsigned Multiply Macros *****************************************************/ // get full 64x64bit product // #define __mul_64x64_to_128(P, CX, CY) \ { \ UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ CXH = (CX) >> 32; \ CXL = (UINT32)(CX); \ CYH = (CY) >> 32; \ CYL = (UINT32)(CY); \ \ PM = CXH*CYL; \ PH = CXH*CYH; \ PL = CXL*CYL; \ PM2 = CXL*CYH; \ PH += (PM>>32); \ PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ \ (P).w[1] = PH + (PM>>32); \ (P).w[0] = (PM<<32)+(UINT32)PL; \ } // get full 64x64bit product // Note: // This macro is used for CX < 2^61, CY < 2^61 // #define __mul_64x64_to_128_fast(P, CX, CY) \ { \ UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ CXH = (CX) >> 32; \ CXL = (UINT32)(CX); \ CYH = (CY) >> 32; \ CYL = (UINT32)(CY); \ \ PM = CXH*CYL; \ PL = CXL*CYL; \ PH = CXH*CYH; \ PM += CXL*CYH; \ PM += (PL>>32); \ \ (P).w[1] = PH + (PM>>32); \ (P).w[0] = (PM<<32)+(UINT32)PL; \ } // used for CX< 2^60 #define __sqr64_fast(P, CX) \ { \ UINT64 CXH, CXL, PL, PH, PM; \ CXH = (CX) >> 32; \ CXL = (UINT32)(CX); \ \ PM = CXH*CXL; \ PL = CXL*CXL; \ PH = CXH*CXH; \ PM += PM; \ PM += (PL>>32); \ \ (P).w[1] = PH + (PM>>32); \ (P).w[0] = (PM<<32)+(UINT32)PL; \ } // get full 64x64bit product // Note: // This implementation is used for CX < 2^61, CY < 2^61 // #define __mul_64x64_to_64_high_fast(P, CX, CY) \ { \ UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ CXH = (CX) >> 32; \ CXL = (UINT32)(CX); \ CYH = (CY) >> 32; \ CYL = (UINT32)(CY); \ \ PM = CXH*CYL; \ PL = CXL*CYL; \ PH = CXH*CYH; \ PM += CXL*CYH; \ PM += (PL>>32); \ \ (P) = PH + (PM>>32); \ } // get full 64x64bit product // #define __mul_64x64_to_128_full(P, CX, CY) \ { \ UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ CXH = (CX) >> 32; \ CXL = (UINT32)(CX); \ CYH = (CY) >> 32; \ CYL = (UINT32)(CY); \ \ PM = CXH*CYL; \ PH = CXH*CYH; \ PL = CXL*CYL; \ PM2 = CXL*CYH; \ PH += (PM>>32); \ PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ \ (P).w[1] = PH + (PM>>32); \ (P).w[0] = (PM<<32)+(UINT32)PL; \ } #define __mul_128x128_high(Q, A, B) \ { \ UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ \ __mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ __mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ __mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ \ __add_128_128(QM, ALBH, AHBL); \ __add_128_64(QM2, QM, ALBL.w[1]); \ __add_128_64((Q), AHBH, QM2.w[1]); \ } #define __mul_128x128_full(Qh, Ql, A, B) \ { \ UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ \ __mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ __mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ __mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ \ __add_128_128(QM, ALBH, AHBL); \ (Ql).w[0] = ALBL.w[0]; \ __add_128_64(QM2, QM, ALBL.w[1]); \ __add_128_64((Qh), AHBH, QM2.w[1]); \ (Ql).w[1] = QM2.w[0]; \ } #define __mul_128x128_low(Ql, A, B) \ { \ UINT128 ALBL; \ UINT64 QM64; \ \ __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ QM64 = (B).w[0]*(A).w[1] + (A).w[0]*(B).w[1]; \ \ (Ql).w[0] = ALBL.w[0]; \ (Ql).w[1] = QM64 + ALBL.w[1]; \ } #define __mul_64x128_low(Ql, A, B) \ { \ UINT128 ALBL, ALBH, QM2; \ __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ (Ql).w[0] = ALBL.w[0]; \ __add_128_64(QM2, ALBH, ALBL.w[1]); \ (Ql).w[1] = QM2.w[0]; \ } #define __mul_64x128_full(Ph, Ql, A, B) \ { \ UINT128 ALBL, ALBH, QM2; \ \ __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ \ (Ql).w[0] = ALBL.w[0]; \ __add_128_64(QM2, ALBH, ALBL.w[1]); \ (Ql).w[1] = QM2.w[0]; \ Ph = QM2.w[1]; \ } #define __mul_64x128_to_192(Q, A, B) \ { \ UINT128 ALBL, ALBH, QM2; \ \ __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ \ (Q).w[0] = ALBL.w[0]; \ __add_128_64(QM2, ALBH, ALBL.w[1]); \ (Q).w[1] = QM2.w[0]; \ (Q).w[2] = QM2.w[1]; \ } #define __mul_64x128_to192(Q, A, B) \ { \ UINT128 ALBL, ALBH, QM2; \ \ __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ \ (Q).w[0] = ALBL.w[0]; \ __add_128_64(QM2, ALBH, ALBL.w[1]); \ (Q).w[1] = QM2.w[0]; \ (Q).w[2] = QM2.w[1]; \ } #define __mul_128x128_to_256(P256, A, B) \ { \ UINT128 Qll, Qlh; \ UINT64 Phl, Phh, CY1, CY2; \ \ __mul_64x128_full(Phl, Qll, A.w[0], B); \ __mul_64x128_full(Phh, Qlh, A.w[1], B); \ (P256).w[0] = Qll.w[0]; \ __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ (P256).w[3] = Phh + CY2; \ } // // For better performance, will check A.w[1] against 0, // but not B.w[1] // Use this macro accordingly #define __mul_128x128_to_256_check_A(P256, A, B) \ { \ UINT128 Qll, Qlh; \ UINT64 Phl, Phh, CY1, CY2; \ \ __mul_64x128_full(Phl, Qll, A.w[0], B); \ (P256).w[0] = Qll.w[0]; \ if(A.w[1]) { \ __mul_64x128_full(Phh, Qlh, A.w[1], B); \ __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ (P256).w[3] = Phh + CY2; } \ else { \ (P256).w[1] = Qll.w[1]; \ (P256).w[2] = Phl; \ (P256).w[3] = 0; } \ } #define __mul_64x192_to_256(lP, lA, lB) \ { \ UINT128 lP0,lP1,lP2; \ UINT64 lC; \ __mul_64x64_to_128(lP0, lA, (lB).w[0]); \ __mul_64x64_to_128(lP1, lA, (lB).w[1]); \ __mul_64x64_to_128(lP2, lA, (lB).w[2]); \ (lP).w[0] = lP0.w[0]; \ __add_carry_out((lP).w[1],lC,lP1.w[0],lP0.w[1]); \ __add_carry_in_out((lP).w[2],lC,lP2.w[0],lP1.w[1],lC); \ (lP).w[3] = lP2.w[1] + lC; \ } #define __mul_64x256_to_320(P, A, B) \ { \ UINT128 lP0,lP1,lP2,lP3; \ UINT64 lC; \ __mul_64x64_to_128(lP0, A, (B).w[0]); \ __mul_64x64_to_128(lP1, A, (B).w[1]); \ __mul_64x64_to_128(lP2, A, (B).w[2]); \ __mul_64x64_to_128(lP3, A, (B).w[3]); \ (P).w[0] = lP0.w[0]; \ __add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ __add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ __add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ (P).w[4] = lP3.w[1] + lC; \ } #define __mul_192x192_to_384(P, A, B) \ { \ UINT256 P0,P1,P2; \ UINT64 CY; \ __mul_64x192_to_256(P0, (A).w[0], B); \ __mul_64x192_to_256(P1, (A).w[1], B); \ __mul_64x192_to_256(P2, (A).w[2], B); \ (P).w[0] = P0.w[0]; \ __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ (P).w[4] = P1.w[3] + CY; \ __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ (P).w[5] = P2.w[3] + CY; \ } #define __mul_64x320_to_384(P, A, B) \ { \ UINT128 lP0,lP1,lP2,lP3,lP4; \ UINT64 lC; \ __mul_64x64_to_128(lP0, A, (B).w[0]); \ __mul_64x64_to_128(lP1, A, (B).w[1]); \ __mul_64x64_to_128(lP2, A, (B).w[2]); \ __mul_64x64_to_128(lP3, A, (B).w[3]); \ __mul_64x64_to_128(lP4, A, (B).w[4]); \ (P).w[0] = lP0.w[0]; \ __add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ __add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ __add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ __add_carry_in_out((P).w[4],lC,lP4.w[0],lP3.w[1],lC); \ (P).w[5] = lP4.w[1] + lC; \ } // A*A // Full 128x128-bit product #define __sqr128_to_256(P256, A) \ { \ UINT128 Qll, Qlh, Qhh; \ UINT64 TMP_C1, TMP_C2; \ \ __mul_64x64_to_128(Qhh, A.w[1], A.w[1]); \ __mul_64x64_to_128(Qlh, A.w[0], A.w[1]); \ Qhh.w[1] += (Qlh.w[1]>>63); \ Qlh.w[1] = (Qlh.w[1]+Qlh.w[1])|(Qlh.w[0]>>63); \ Qlh.w[0] += Qlh.w[0]; \ __mul_64x64_to_128(Qll, A.w[0], A.w[0]); \ \ __add_carry_out((P256).w[1],TMP_C1, Qlh.w[0], Qll.w[1]); \ (P256).w[0] = Qll.w[0]; \ __add_carry_in_out((P256).w[2],TMP_C2, Qlh.w[1], Qhh.w[0], TMP_C1); \ (P256).w[3] = Qhh.w[1]+TMP_C2; \ } #define __mul_128x128_to_256_low_high(PQh, PQl, A, B) \ { \ UINT128 Qll, Qlh; \ UINT64 Phl, Phh, C1, C2; \ \ __mul_64x128_full(Phl, Qll, A.w[0], B); \ __mul_64x128_full(Phh, Qlh, A.w[1], B); \ (PQl).w[0] = Qll.w[0]; \ __add_carry_out((PQl).w[1],C1, Qlh.w[0], Qll.w[1]); \ __add_carry_in_out((PQh).w[0],C2, Qlh.w[1], Phl, C1); \ (PQh).w[1] = Phh + C2; \ } #define __mul_256x256_to_512(P, A, B) \ { \ UINT512 P0,P1,P2,P3; \ UINT64 CY; \ __mul_64x256_to_320(P0, (A).w[0], B); \ __mul_64x256_to_320(P1, (A).w[1], B); \ __mul_64x256_to_320(P2, (A).w[2], B); \ __mul_64x256_to_320(P3, (A).w[3], B); \ (P).w[0] = P0.w[0]; \ __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ (P).w[5] = P1.w[4] + CY; \ __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ __add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ (P).w[6] = P2.w[4] + CY; \ __add_carry_out((P).w[3],CY,P3.w[0],(P).w[3]); \ __add_carry_in_out((P).w[4],CY,P3.w[1],(P).w[4],CY); \ __add_carry_in_out((P).w[5],CY,P3.w[2],(P).w[5],CY); \ __add_carry_in_out((P).w[6],CY,P3.w[3],(P).w[6],CY); \ (P).w[7] = P3.w[4] + CY; \ } #define __mul_192x256_to_448(P, A, B) \ { \ UINT512 P0,P1,P2; \ UINT64 CY; \ __mul_64x256_to_320(P0, (A).w[0], B); \ __mul_64x256_to_320(P1, (A).w[1], B); \ __mul_64x256_to_320(P2, (A).w[2], B); \ (P).w[0] = P0.w[0]; \ __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ (P).w[5] = P1.w[4] + CY; \ __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ __add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ (P).w[6] = P2.w[4] + CY; \ } #define __mul_320x320_to_640(P, A, B) \ { \ UINT512 P0,P1,P2,P3; \ UINT64 CY; \ __mul_256x256_to_512((P), (A), B); \ __mul_64x256_to_320(P1, (A).w[4], B); \ __mul_64x256_to_320(P2, (B).w[4], A); \ __mul_64x64_to_128(P3, (A).w[4], (B).w[4]); \ __add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ __add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ __add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ __add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ __add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ P3.w[1] += CY; \ __add_carry_out((P).w[4],CY,(P).w[4],P0.w[0]); \ __add_carry_in_out((P).w[5],CY,(P).w[5],P0.w[1],CY); \ __add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[2],CY); \ __add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[3],CY); \ __add_carry_in_out((P).w[8],CY,P3.w[0],P0.w[4],CY); \ (P).w[9] = P3.w[1] + CY; \ } #define __mul_384x384_to_768(P, A, B) \ { \ UINT512 P0,P1,P2,P3; \ UINT64 CY; \ __mul_320x320_to_640((P), (A), B); \ __mul_64x320_to_384(P1, (A).w[5], B); \ __mul_64x320_to_384(P2, (B).w[5], A); \ __mul_64x64_to_128(P3, (A).w[5], (B).w[5]); \ __add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ __add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ __add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ __add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ __add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ __add_carry_in_out((P0).w[5],CY,P1.w[5],P2.w[5],CY); \ P3.w[1] += CY; \ __add_carry_out((P).w[5],CY,(P).w[5],P0.w[0]); \ __add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[1],CY); \ __add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[2],CY); \ __add_carry_in_out((P).w[8],CY,(P).w[8],P0.w[3],CY); \ __add_carry_in_out((P).w[9],CY,(P).w[9],P0.w[4],CY); \ __add_carry_in_out((P).w[10],CY,P3.w[0],P0.w[5],CY); \ (P).w[11] = P3.w[1] + CY; \ } #define __mul_64x128_short(Ql, A, B) \ { \ UINT64 ALBH_L; \ \ __mul_64x64_to_64(ALBH_L, (A),(B).w[1]); \ __mul_64x64_to_128((Ql), (A), (B).w[0]); \ \ (Ql).w[1] += ALBH_L; \ } #define __scale128_10(D,_TMP) \ { \ UINT128 _TMP2,_TMP8; \ _TMP2.w[1] = (_TMP.w[1]<<1)|(_TMP.w[0]>>63); \ _TMP2.w[0] = _TMP.w[0]<<1; \ _TMP8.w[1] = (_TMP.w[1]<<3)|(_TMP.w[0]>>61); \ _TMP8.w[0] = _TMP.w[0]<<3; \ __add_128_128(D, _TMP2, _TMP8); \ } // 64x64-bit product #define __mul_64x64_to_128MACH(P128, CX64, CY64) \ { \ UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ CXH = (CX64) >> 32; \ CXL = (UINT32)(CX64); \ CYH = (CY64) >> 32; \ CYL = (UINT32)(CY64); \ PM = CXH*CYL; \ PH = CXH*CYH; \ PL = CXL*CYL; \ PM2 = CXL*CYH; \ PH += (PM>>32); \ PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ (P128).w[1] = PH + (PM>>32); \ (P128).w[0] = (PM<<32)+(UINT32)PL; \ } // 64x64-bit product #define __mul_64x64_to_128HIGH(P64, CX64, CY64) \ { \ UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ CXH = (CX64) >> 32; \ CXL = (UINT32)(CX64); \ CYH = (CY64) >> 32; \ CYL = (UINT32)(CY64); \ PM = CXH*CYL; \ PH = CXH*CYH; \ PL = CXL*CYL; \ PM2 = CXL*CYH; \ PH += (PM>>32); \ PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ P64 = PH + (PM>>32); \ } #define __mul_128x64_to_128(Q128, A64, B128) \ { \ UINT64 ALBH_L; \ ALBH_L = (A64) * (B128).w[1]; \ __mul_64x64_to_128MACH((Q128), (A64), (B128).w[0]); \ (Q128).w[1] += ALBH_L; \ } // might simplify by calculating just QM2.w[0] #define __mul_64x128_to_128(Ql, A, B) \ { \ UINT128 ALBL, ALBH, QM2; \ __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ (Ql).w[0] = ALBL.w[0]; \ __add_128_64(QM2, ALBH, ALBL.w[1]); \ (Ql).w[1] = QM2.w[0]; \ } /********************************************************************* * * BID Pack/Unpack Macros * *********************************************************************/ ///////////////////////////////////////// // BID64 definitions //////////////////////////////////////// #define DECIMAL_MAX_EXPON_64 767 #define DECIMAL_EXPONENT_BIAS 398 #define MAX_FORMAT_DIGITS 16 ///////////////////////////////////////// // BID128 definitions //////////////////////////////////////// #define DECIMAL_MAX_EXPON_128 12287 #define DECIMAL_EXPONENT_BIAS_128 6176 #define MAX_FORMAT_DIGITS_128 34 ///////////////////////////////////////// // BID32 definitions //////////////////////////////////////// #define DECIMAL_MAX_EXPON_32 191 #define DECIMAL_EXPONENT_BIAS_32 101 #define MAX_FORMAT_DIGITS_32 7 //////////////////////////////////////// // Constant Definitions /////////////////////////////////////// #define SPECIAL_ENCODING_MASK64 0x6000000000000000ull #define INFINITY_MASK64 0x7800000000000000ull #define SINFINITY_MASK64 0xf800000000000000ull #define SSNAN_MASK64 0xfc00000000000000ull #define NAN_MASK64 0x7c00000000000000ull #define SNAN_MASK64 0x7e00000000000000ull #define QUIET_MASK64 0xfdffffffffffffffull #define LARGE_COEFF_MASK64 0x0007ffffffffffffull #define LARGE_COEFF_HIGH_BIT64 0x0020000000000000ull #define SMALL_COEFF_MASK64 0x001fffffffffffffull #define EXPONENT_MASK64 0x3ff #define EXPONENT_SHIFT_LARGE64 51 #define EXPONENT_SHIFT_SMALL64 53 #define LARGEST_BID64 0x77fb86f26fc0ffffull #define SMALLEST_BID64 0xf7fb86f26fc0ffffull #define SMALL_COEFF_MASK128 0x0001ffffffffffffull #define LARGE_COEFF_MASK128 0x00007fffffffffffull #define EXPONENT_MASK128 0x3fff #define LARGEST_BID128_HIGH 0x5fffed09bead87c0ull #define LARGEST_BID128_LOW 0x378d8e63ffffffffull #define SPECIAL_ENCODING_MASK32 0x60000000ul #define INFINITY_MASK32 0x78000000ul #define LARGE_COEFF_MASK32 0x007ffffful #define LARGE_COEFF_HIGH_BIT32 0x00800000ul #define SMALL_COEFF_MASK32 0x001ffffful #define EXPONENT_MASK32 0xff #define LARGEST_BID32 0x77f8967f #define NAN_MASK32 0x7c000000 #define SNAN_MASK32 0x7e000000 #define MASK_BINARY_EXPONENT 0x7ff0000000000000ull #define BINARY_EXPONENT_BIAS 0x3ff #define UPPER_EXPON_LIMIT 51 // data needed for BID pack/unpack macros extern UINT64 round_const_table[][19]; extern UINT128 reciprocals10_128[]; extern int recip_scale[]; extern UINT128 power10_table_128[]; extern int estimate_decimal_digits[]; extern int estimate_bin_expon[]; extern UINT64 power10_index_binexp[]; extern int short_recip_scale[]; extern UINT64 reciprocals10_64[]; extern UINT128 power10_index_binexp_128[]; extern UINT128 round_const_table_128[][36]; ////////////////////////////////////////////// // Status Flag Handling ///////////////////////////////////////////// #define __set_status_flags(fpsc, status) *(fpsc) |= status #define is_inexact(fpsc) ((*(fpsc))&INEXACT_EXCEPTION) __BID_INLINE__ UINT64 unpack_BID64 (UINT64 * psign_x, int *pexponent_x, UINT64 * pcoefficient_x, UINT64 x) { UINT64 tmp, coeff; *psign_x = x & 0x8000000000000000ull; if ((x & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) { // special encodings // coefficient coeff = (x & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64; if ((x & INFINITY_MASK64) == INFINITY_MASK64) { *pexponent_x = 0; *pcoefficient_x = x & 0xfe03ffffffffffffull; if ((x & 0x0003ffffffffffffull) >= 1000000000000000ull) *pcoefficient_x = x & 0xfe00000000000000ull; if ((x & NAN_MASK64) == INFINITY_MASK64) *pcoefficient_x = x & SINFINITY_MASK64; return 0; // NaN or Infinity } // check for non-canonical values if (coeff >= 10000000000000000ull) coeff = 0; *pcoefficient_x = coeff; // get exponent tmp = x >> EXPONENT_SHIFT_LARGE64; *pexponent_x = (int) (tmp & EXPONENT_MASK64); return coeff; } // exponent tmp = x >> EXPONENT_SHIFT_SMALL64; *pexponent_x = (int) (tmp & EXPONENT_MASK64); // coefficient *pcoefficient_x = (x & SMALL_COEFF_MASK64); return *pcoefficient_x; } // // BID64 pack macro (general form) // __BID_INLINE__ UINT64 get_BID64 (UINT64 sgn, int expon, UINT64 coeff, int rmode, unsigned *fpsc) { UINT128 Stemp, Q_low; UINT64 QH, r, mask, C64, remainder_h, CY, carry; int extra_digits, amount, amount2; unsigned status; if (coeff > 9999999999999999ull) { expon++; coeff = 1000000000000000ull; } // check for possible underflow/overflow if (((unsigned) expon) >= 3 * 256) { if (expon < 0) { // underflow if (expon + MAX_FORMAT_DIGITS < 0) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == ROUNDING_DOWN && sgn) return 0x8000000000000001ull; if (rmode == ROUNDING_UP && !sgn) return 1ull; #endif #endif // result is 0 return sgn; } #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (sgn && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #endif #endif // get digits to be shifted out extra_digits = -expon; coeff += round_const_table[rmode][extra_digits]; // get coeff*(2^M[extra_digits])/10^extra_digits __mul_64x128_full (QH, Q_low, coeff, reciprocals10_128[extra_digits]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[extra_digits]; C64 = QH >> amount; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == 0) //ROUNDING_TO_NEAREST #endif if (C64 & 1) { // check whether fractional part of initial_P/10^extra_digits is exactly .5 // get remainder amount2 = 64 - amount; remainder_h = 0; remainder_h--; remainder_h >>= amount2; remainder_h = remainder_h & QH; if (!remainder_h && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) { C64--; } } #endif #ifdef SET_STATUS_FLAGS if (is_inexact (fpsc)) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); else { status = INEXACT_EXCEPTION; // get remainder remainder_h = QH << (64 - amount); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if (remainder_h == 0x8000000000000000ull && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if (!remainder_h && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) status = EXACT_STATUS; break; default: // round up __add_carry_out (Stemp.w[0], CY, Q_low.w[0], reciprocals10_128[extra_digits].w[0]); __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], reciprocals10_128[extra_digits].w[1], CY); if ((remainder_h >> (64 - amount)) + carry >= (((UINT64) 1) << amount)) status = EXACT_STATUS; } if (status != EXACT_STATUS) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); } #endif return sgn | C64; } while (coeff < 1000000000000000ull && expon >= 3 * 256) { expon--; coeff = (coeff << 3) + (coeff << 1); } if (expon > DECIMAL_MAX_EXPON_64) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif // overflow r = sgn | INFINITY_MASK64; switch (rmode) { case ROUNDING_DOWN: if (!sgn) r = LARGEST_BID64; break; case ROUNDING_TO_ZERO: r = sgn | LARGEST_BID64; break; case ROUNDING_UP: // round up if (sgn) r = SMALLEST_BID64; } return r; } } mask = 1; mask <<= EXPONENT_SHIFT_SMALL64; // check whether coefficient fits in 10*5+3 bits if (coeff < mask) { r = expon; r <<= EXPONENT_SHIFT_SMALL64; r |= (coeff | sgn); return r; } // special format // eliminate the case coeff==10^16 after rounding if (coeff == 10000000000000000ull) { r = expon + 1; r <<= EXPONENT_SHIFT_SMALL64; r |= (1000000000000000ull | sgn); return r; } r = expon; r <<= EXPONENT_SHIFT_LARGE64; r |= (sgn | SPECIAL_ENCODING_MASK64); // add coeff, without leading bits mask = (mask >> 2) - 1; coeff &= mask; r |= coeff; return r; } // // No overflow/underflow checking // __BID_INLINE__ UINT64 fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { UINT64 r, mask; mask = 1; mask <<= EXPONENT_SHIFT_SMALL64; // check whether coefficient fits in 10*5+3 bits if (coeff < mask) { r = expon; r <<= EXPONENT_SHIFT_SMALL64; r |= (coeff | sgn); return r; } // special format // eliminate the case coeff==10^16 after rounding if (coeff == 10000000000000000ull) { r = expon + 1; r <<= EXPONENT_SHIFT_SMALL64; r |= (1000000000000000ull | sgn); return r; } r = expon; r <<= EXPONENT_SHIFT_LARGE64; r |= (sgn | SPECIAL_ENCODING_MASK64); // add coeff, without leading bits mask = (mask >> 2) - 1; coeff &= mask; r |= coeff; return r; } // // no underflow checking // __BID_INLINE__ UINT64 fast_get_BID64_check_OF (UINT64 sgn, int expon, UINT64 coeff, int rmode, unsigned *fpsc) { UINT64 r, mask; if (((unsigned) expon) >= 3 * 256 - 1) { if ((expon == 3 * 256 - 1) && coeff == 10000000000000000ull) { expon = 3 * 256; coeff = 1000000000000000ull; } if (((unsigned) expon) >= 3 * 256) { while (coeff < 1000000000000000ull && expon >= 3 * 256) { expon--; coeff = (coeff << 3) + (coeff << 1); } if (expon > DECIMAL_MAX_EXPON_64) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif // overflow r = sgn | INFINITY_MASK64; switch (rmode) { case ROUNDING_DOWN: if (!sgn) r = LARGEST_BID64; break; case ROUNDING_TO_ZERO: r = sgn | LARGEST_BID64; break; case ROUNDING_UP: // round up if (sgn) r = SMALLEST_BID64; } return r; } } } mask = 1; mask <<= EXPONENT_SHIFT_SMALL64; // check whether coefficient fits in 10*5+3 bits if (coeff < mask) { r = expon; r <<= EXPONENT_SHIFT_SMALL64; r |= (coeff | sgn); return r; } // special format // eliminate the case coeff==10^16 after rounding if (coeff == 10000000000000000ull) { r = expon + 1; r <<= EXPONENT_SHIFT_SMALL64; r |= (1000000000000000ull | sgn); return r; } r = expon; r <<= EXPONENT_SHIFT_LARGE64; r |= (sgn | SPECIAL_ENCODING_MASK64); // add coeff, without leading bits mask = (mask >> 2) - 1; coeff &= mask; r |= coeff; return r; } // // No overflow/underflow checking // or checking for coefficients equal to 10^16 (after rounding) // __BID_INLINE__ UINT64 very_fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { UINT64 r, mask; mask = 1; mask <<= EXPONENT_SHIFT_SMALL64; // check whether coefficient fits in 10*5+3 bits if (coeff < mask) { r = expon; r <<= EXPONENT_SHIFT_SMALL64; r |= (coeff | sgn); return r; } // special format r = expon; r <<= EXPONENT_SHIFT_LARGE64; r |= (sgn | SPECIAL_ENCODING_MASK64); // add coeff, without leading bits mask = (mask >> 2) - 1; coeff &= mask; r |= coeff; return r; } // // No overflow/underflow checking or checking for coefficients above 2^53 // __BID_INLINE__ UINT64 very_fast_get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff) { // no UF/OF UINT64 r; r = expon; r <<= EXPONENT_SHIFT_SMALL64; r |= (coeff | sgn); return r; } // // This pack macro is used when underflow is known to occur // __BID_INLINE__ UINT64 get_BID64_UF (UINT64 sgn, int expon, UINT64 coeff, UINT64 R, int rmode, unsigned *fpsc) { UINT128 C128, Q_low, Stemp; UINT64 C64, remainder_h, QH, carry, CY; int extra_digits, amount, amount2; unsigned status; // underflow if (expon + MAX_FORMAT_DIGITS < 0) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == ROUNDING_DOWN && sgn) return 0x8000000000000001ull; if (rmode == ROUNDING_UP && !sgn) return 1ull; #endif #endif // result is 0 return sgn; } // 10*coeff coeff = (coeff << 3) + (coeff << 1); #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (sgn && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #endif #endif if (R) coeff |= 1; // get digits to be shifted out extra_digits = 1 - expon; C128.w[0] = coeff + round_const_table[rmode][extra_digits]; // get coeff*(2^M[extra_digits])/10^extra_digits __mul_64x128_full (QH, Q_low, C128.w[0], reciprocals10_128[extra_digits]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[extra_digits]; C64 = QH >> amount; //__shr_128(C128, Q_high, amount); #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == 0) //ROUNDING_TO_NEAREST #endif if (C64 & 1) { // check whether fractional part of initial_P/10^extra_digits is exactly .5 // get remainder amount2 = 64 - amount; remainder_h = 0; remainder_h--; remainder_h >>= amount2; remainder_h = remainder_h & QH; if (!remainder_h && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) { C64--; } } #endif #ifdef SET_STATUS_FLAGS if (is_inexact (fpsc)) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); else { status = INEXACT_EXCEPTION; // get remainder remainder_h = QH << (64 - amount); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if (remainder_h == 0x8000000000000000ull && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if (!remainder_h && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) status = EXACT_STATUS; break; default: // round up __add_carry_out (Stemp.w[0], CY, Q_low.w[0], reciprocals10_128[extra_digits].w[0]); __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], reciprocals10_128[extra_digits].w[1], CY); if ((remainder_h >> (64 - amount)) + carry >= (((UINT64) 1) << amount)) status = EXACT_STATUS; } if (status != EXACT_STATUS) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); } #endif return sgn | C64; } // // This pack macro doesnot check for coefficients above 2^53 // __BID_INLINE__ UINT64 get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff, int rmode, unsigned *fpsc) { UINT128 C128, Q_low, Stemp; UINT64 r, mask, C64, remainder_h, QH, carry, CY; int extra_digits, amount, amount2; unsigned status; // check for possible underflow/overflow if (((unsigned) expon) >= 3 * 256) { if (expon < 0) { // underflow if (expon + MAX_FORMAT_DIGITS < 0) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == ROUNDING_DOWN && sgn) return 0x8000000000000001ull; if (rmode == ROUNDING_UP && !sgn) return 1ull; #endif #endif // result is 0 return sgn; } #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (sgn && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #endif #endif // get digits to be shifted out extra_digits = -expon; C128.w[0] = coeff + round_const_table[rmode][extra_digits]; // get coeff*(2^M[extra_digits])/10^extra_digits __mul_64x128_full (QH, Q_low, C128.w[0], reciprocals10_128[extra_digits]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[extra_digits]; C64 = QH >> amount; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == 0) //ROUNDING_TO_NEAREST #endif if (C64 & 1) { // check whether fractional part of initial_P/10^extra_digits is exactly .5 // get remainder amount2 = 64 - amount; remainder_h = 0; remainder_h--; remainder_h >>= amount2; remainder_h = remainder_h & QH; if (!remainder_h && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) { C64--; } } #endif #ifdef SET_STATUS_FLAGS if (is_inexact (fpsc)) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); else { status = INEXACT_EXCEPTION; // get remainder remainder_h = QH << (64 - amount); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if (remainder_h == 0x8000000000000000ull && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if (!remainder_h && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] && Q_low.w[0] < reciprocals10_128[extra_digits].w[0]))) status = EXACT_STATUS; break; default: // round up __add_carry_out (Stemp.w[0], CY, Q_low.w[0], reciprocals10_128[extra_digits].w[0]); __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], reciprocals10_128[extra_digits].w[1], CY); if ((remainder_h >> (64 - amount)) + carry >= (((UINT64) 1) << amount)) status = EXACT_STATUS; } if (status != EXACT_STATUS) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); } #endif return sgn | C64; } while (coeff < 1000000000000000ull && expon >= 3 * 256) { expon--; coeff = (coeff << 3) + (coeff << 1); } if (expon > DECIMAL_MAX_EXPON_64) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif // overflow r = sgn | INFINITY_MASK64; switch (rmode) { case ROUNDING_DOWN: if (!sgn) r = LARGEST_BID64; break; case ROUNDING_TO_ZERO: r = sgn | LARGEST_BID64; break; case ROUNDING_UP: // round up if (sgn) r = SMALLEST_BID64; } return r; } else { mask = 1; mask <<= EXPONENT_SHIFT_SMALL64; if (coeff >= mask) { r = expon; r <<= EXPONENT_SHIFT_LARGE64; r |= (sgn | SPECIAL_ENCODING_MASK64); // add coeff, without leading bits mask = (mask >> 2) - 1; coeff &= mask; r |= coeff; return r; } } } r = expon; r <<= EXPONENT_SHIFT_SMALL64; r |= (coeff | sgn); return r; } /***************************************************************************** * * BID128 pack/unpack macros * *****************************************************************************/ // // Macro for handling BID128 underflow // sticky bit given as additional argument // __BID_INLINE__ UINT128 * handle_UF_128_rem (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, UINT64 R, unsigned *prounding_mode, unsigned *fpsc) { UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CQ2, CQ8; UINT64 carry, CY; int ed2, amount; unsigned rmode, status; // UF occurs if (expon + MAX_FORMAT_DIGITS_128 < 0) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif pres->w[1] = sgn; pres->w[0] = 0; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if ((sgn && *prounding_mode == ROUNDING_DOWN) || (!sgn && *prounding_mode == ROUNDING_UP)) pres->w[0] = 1ull; #endif #endif return pres; } // CQ *= 10 CQ2.w[1] = (CQ.w[1] << 1) | (CQ.w[0] >> 63); CQ2.w[0] = CQ.w[0] << 1; CQ8.w[1] = (CQ.w[1] << 3) | (CQ.w[0] >> 61); CQ8.w[0] = CQ.w[0] << 3; __add_128_128 (CQ, CQ2, CQ8); // add remainder if (R) CQ.w[0] |= 1; ed2 = 1 - expon; // add rounding constant to CQ #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST rmode = *prounding_mode; if (sgn && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #else rmode = 0; #endif #else rmode = 0; #endif T128 = round_const_table_128[rmode][ed2]; __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); CQ.w[1] = CQ.w[1] + T128.w[1] + carry; TP128 = reciprocals10_128[ed2]; __mul_128x128_full (Qh, Ql, CQ, TP128); amount = recip_scale[ed2]; if (amount >= 64) { CQ.w[0] = Qh.w[1] >> (amount - 64); CQ.w[1] = 0; } else { __shr_128 (CQ, Qh, amount); } expon = 0; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (!(*prounding_mode)) #endif if (CQ.w[0] & 1) { // check whether fractional part of initial_P/10^ed1 is exactly .5 // get remainder __shl_128_long (Qh1, Qh, (128 - amount)); if (!Qh1.w[1] && !Qh1.w[0] && (Ql.w[1] < reciprocals10_128[ed2].w[1] || (Ql.w[1] == reciprocals10_128[ed2].w[1] && Ql.w[0] < reciprocals10_128[ed2].w[0]))) { CQ.w[0]--; } } #endif #ifdef SET_STATUS_FLAGS if (is_inexact (fpsc)) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); else { status = INEXACT_EXCEPTION; // get remainder __shl_128_long (Qh1, Qh, (128 - amount)); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) && (Ql.w[1] < reciprocals10_128[ed2].w[1] || (Ql.w[1] == reciprocals10_128[ed2].w[1] && Ql.w[0] < reciprocals10_128[ed2].w[0]))) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if ((!Qh1.w[1]) && (!Qh1.w[0]) && (Ql.w[1] < reciprocals10_128[ed2].w[1] || (Ql.w[1] == reciprocals10_128[ed2].w[1] && Ql.w[0] < reciprocals10_128[ed2].w[0]))) status = EXACT_STATUS; break; default: // round up __add_carry_out (Stemp.w[0], CY, Ql.w[0], reciprocals10_128[ed2].w[0]); __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], reciprocals10_128[ed2].w[1], CY); __shr_128_long (Qh, Qh1, (128 - amount)); Tmp.w[0] = 1; Tmp.w[1] = 0; __shl_128_long (Tmp1, Tmp, amount); Qh.w[0] += carry; if (Qh.w[0] < carry) Qh.w[1]++; if (__unsigned_compare_ge_128 (Qh, Tmp1)) status = EXACT_STATUS; } if (status != EXACT_STATUS) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); } #endif pres->w[1] = sgn | CQ.w[1]; pres->w[0] = CQ.w[0]; return pres; } // // Macro for handling BID128 underflow // __BID_INLINE__ UINT128 * handle_UF_128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, unsigned *prounding_mode, unsigned *fpsc) { UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1; UINT64 carry, CY; int ed2, amount; unsigned rmode, status; // UF occurs if (expon + MAX_FORMAT_DIGITS_128 < 0) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif pres->w[1] = sgn; pres->w[0] = 0; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if ((sgn && *prounding_mode == ROUNDING_DOWN) || (!sgn && *prounding_mode == ROUNDING_UP)) pres->w[0] = 1ull; #endif #endif return pres; } ed2 = 0 - expon; // add rounding constant to CQ #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST rmode = *prounding_mode; if (sgn && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #else rmode = 0; #endif #else rmode = 0; #endif T128 = round_const_table_128[rmode][ed2]; __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); CQ.w[1] = CQ.w[1] + T128.w[1] + carry; TP128 = reciprocals10_128[ed2]; __mul_128x128_full (Qh, Ql, CQ, TP128); amount = recip_scale[ed2]; if (amount >= 64) { CQ.w[0] = Qh.w[1] >> (amount - 64); CQ.w[1] = 0; } else { __shr_128 (CQ, Qh, amount); } expon = 0; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (!(*prounding_mode)) #endif if (CQ.w[0] & 1) { // check whether fractional part of initial_P/10^ed1 is exactly .5 // get remainder __shl_128_long (Qh1, Qh, (128 - amount)); if (!Qh1.w[1] && !Qh1.w[0] && (Ql.w[1] < reciprocals10_128[ed2].w[1] || (Ql.w[1] == reciprocals10_128[ed2].w[1] && Ql.w[0] < reciprocals10_128[ed2].w[0]))) { CQ.w[0]--; } } #endif #ifdef SET_STATUS_FLAGS if (is_inexact (fpsc)) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); else { status = INEXACT_EXCEPTION; // get remainder __shl_128_long (Qh1, Qh, (128 - amount)); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) && (Ql.w[1] < reciprocals10_128[ed2].w[1] || (Ql.w[1] == reciprocals10_128[ed2].w[1] && Ql.w[0] < reciprocals10_128[ed2].w[0]))) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if ((!Qh1.w[1]) && (!Qh1.w[0]) && (Ql.w[1] < reciprocals10_128[ed2].w[1] || (Ql.w[1] == reciprocals10_128[ed2].w[1] && Ql.w[0] < reciprocals10_128[ed2].w[0]))) status = EXACT_STATUS; break; default: // round up __add_carry_out (Stemp.w[0], CY, Ql.w[0], reciprocals10_128[ed2].w[0]); __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], reciprocals10_128[ed2].w[1], CY); __shr_128_long (Qh, Qh1, (128 - amount)); Tmp.w[0] = 1; Tmp.w[1] = 0; __shl_128_long (Tmp1, Tmp, amount); Qh.w[0] += carry; if (Qh.w[0] < carry) Qh.w[1]++; if (__unsigned_compare_ge_128 (Qh, Tmp1)) status = EXACT_STATUS; } if (status != EXACT_STATUS) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); } #endif pres->w[1] = sgn | CQ.w[1]; pres->w[0] = CQ.w[0]; return pres; } // // BID128 unpack, input passed by value // __BID_INLINE__ UINT64 unpack_BID128_value (UINT64 * psign_x, int *pexponent_x, UINT128 * pcoefficient_x, UINT128 x) { UINT128 coeff, T33, T34; UINT64 ex; *psign_x = (x.w[1]) & 0x8000000000000000ull; // special encodings if ((x.w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { if ((x.w[1] & INFINITY_MASK64) < INFINITY_MASK64) { // non-canonical input pcoefficient_x->w[0] = 0; pcoefficient_x->w[1] = 0; ex = (x.w[1]) >> 47; *pexponent_x = ((int) ex) & EXPONENT_MASK128; return 0; } // 10^33 T33 = power10_table_128[33]; /*coeff.w[0] = x.w[0]; coeff.w[1] = (x.w[1]) & LARGE_COEFF_MASK128; pcoefficient_x->w[0] = x.w[0]; pcoefficient_x->w[1] = x.w[1]; if (__unsigned_compare_ge_128 (coeff, T33)) // non-canonical pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); */ pcoefficient_x->w[0] = x.w[0]; pcoefficient_x->w[1] = (x.w[1]) & 0x00003fffffffffffull; if (__unsigned_compare_ge_128 ((*pcoefficient_x), T33)) // non-canonical { pcoefficient_x->w[1] = (x.w[1]) & 0xfe00000000000000ull; pcoefficient_x->w[0] = 0; } else pcoefficient_x->w[1] = (x.w[1]) & 0xfe003fffffffffffull; if ((x.w[1] & NAN_MASK64) == INFINITY_MASK64) { pcoefficient_x->w[0] = 0; pcoefficient_x->w[1] = x.w[1] & SINFINITY_MASK64; } *pexponent_x = 0; return 0; // NaN or Infinity } coeff.w[0] = x.w[0]; coeff.w[1] = (x.w[1]) & SMALL_COEFF_MASK128; // 10^34 T34 = power10_table_128[34]; // check for non-canonical values if (__unsigned_compare_ge_128 (coeff, T34)) coeff.w[0] = coeff.w[1] = 0; pcoefficient_x->w[0] = coeff.w[0]; pcoefficient_x->w[1] = coeff.w[1]; ex = (x.w[1]) >> 49; *pexponent_x = ((int) ex) & EXPONENT_MASK128; return coeff.w[0] | coeff.w[1]; } // // BID128 unpack, input pased by reference // __BID_INLINE__ UINT64 unpack_BID128 (UINT64 * psign_x, int *pexponent_x, UINT128 * pcoefficient_x, UINT128 * px) { UINT128 coeff, T33, T34; UINT64 ex; *psign_x = (px->w[1]) & 0x8000000000000000ull; // special encodings if ((px->w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { if ((px->w[1] & INFINITY_MASK64) < INFINITY_MASK64) { // non-canonical input pcoefficient_x->w[0] = 0; pcoefficient_x->w[1] = 0; ex = (px->w[1]) >> 47; *pexponent_x = ((int) ex) & EXPONENT_MASK128; return 0; } // 10^33 T33 = power10_table_128[33]; coeff.w[0] = px->w[0]; coeff.w[1] = (px->w[1]) & LARGE_COEFF_MASK128; pcoefficient_x->w[0] = px->w[0]; pcoefficient_x->w[1] = px->w[1]; if (__unsigned_compare_ge_128 (coeff, T33)) { // non-canonical pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); pcoefficient_x->w[0] = 0; } *pexponent_x = 0; return 0; // NaN or Infinity } coeff.w[0] = px->w[0]; coeff.w[1] = (px->w[1]) & SMALL_COEFF_MASK128; // 10^34 T34 = power10_table_128[34]; // check for non-canonical values if (__unsigned_compare_ge_128 (coeff, T34)) coeff.w[0] = coeff.w[1] = 0; pcoefficient_x->w[0] = coeff.w[0]; pcoefficient_x->w[1] = coeff.w[1]; ex = (px->w[1]) >> 49; *pexponent_x = ((int) ex) & EXPONENT_MASK128; return coeff.w[0] | coeff.w[1]; } // // Pack macro checks for overflow, but not underflow // __BID_INLINE__ UINT128 * get_BID128_very_fast_OF (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff, unsigned *prounding_mode, unsigned *fpsc) { UINT128 T; UINT64 tmp, tmp2; if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; while (__unsigned_compare_gt_128 (T, coeff) && expon > DECIMAL_MAX_EXPON_128) { coeff.w[1] = (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + (coeff.w[0] >> 63); tmp2 = coeff.w[0] << 3; coeff.w[0] = (coeff.w[0] << 1) + tmp2; if (coeff.w[0] < tmp2) coeff.w[1]++; expon--; } } if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { // OF #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (*prounding_mode == ROUNDING_TO_ZERO || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn && *prounding_mode == ROUNDING_DOWN)) { pres->w[1] = sgn | LARGEST_BID128_HIGH; pres->w[0] = LARGEST_BID128_LOW; } else #endif #endif { pres->w[1] = sgn | INFINITY_MASK64; pres->w[0] = 0; } return pres; } } pres->w[0] = coeff.w[0]; tmp = expon; tmp <<= 49; pres->w[1] = sgn | tmp | coeff.w[1]; return pres; } // // No overflow/underflow checks // No checking for coefficient == 10^34 (rounding artifact) // __BID_INLINE__ UINT128 * get_BID128_very_fast (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { UINT64 tmp; pres->w[0] = coeff.w[0]; tmp = expon; tmp <<= 49; pres->w[1] = sgn | tmp | coeff.w[1]; return pres; } // // No overflow/underflow checks // __BID_INLINE__ UINT128 * get_BID128_fast (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { UINT64 tmp; // coeff==10^34? if (coeff.w[1] == 0x0001ed09bead87c0ull && coeff.w[0] == 0x378d8e6400000000ull) { expon++; // set coefficient to 10^33 coeff.w[1] = 0x0000314dc6448d93ull; coeff.w[0] = 0x38c15b0a00000000ull; } pres->w[0] = coeff.w[0]; tmp = expon; tmp <<= 49; pres->w[1] = sgn | tmp | coeff.w[1]; return pres; } // // General BID128 pack macro // __BID_INLINE__ UINT128 * get_BID128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff, unsigned *prounding_mode, unsigned *fpsc) { UINT128 T; UINT64 tmp, tmp2; // coeff==10^34? if (coeff.w[1] == 0x0001ed09bead87c0ull && coeff.w[0] == 0x378d8e6400000000ull) { expon++; // set coefficient to 10^33 coeff.w[1] = 0x0000314dc6448d93ull; coeff.w[0] = 0x38c15b0a00000000ull; } // check OF, UF if (expon < 0 || expon > DECIMAL_MAX_EXPON_128) { // check UF if (expon < 0) { return handle_UF_128 (pres, sgn, expon, coeff, prounding_mode, fpsc); } if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; while (__unsigned_compare_gt_128 (T, coeff) && expon > DECIMAL_MAX_EXPON_128) { coeff.w[1] = (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + (coeff.w[0] >> 63); tmp2 = coeff.w[0] << 3; coeff.w[0] = (coeff.w[0] << 1) + tmp2; if (coeff.w[0] < tmp2) coeff.w[1]++; expon--; } } if (expon > DECIMAL_MAX_EXPON_128) { if (!(coeff.w[1] | coeff.w[0])) { pres->w[1] = sgn | (((UINT64) DECIMAL_MAX_EXPON_128) << 49); pres->w[0] = 0; return pres; } // OF #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (*prounding_mode == ROUNDING_TO_ZERO || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn && *prounding_mode == ROUNDING_DOWN)) { pres->w[1] = sgn | LARGEST_BID128_HIGH; pres->w[0] = LARGEST_BID128_LOW; } else #endif #endif { pres->w[1] = sgn | INFINITY_MASK64; pres->w[0] = 0; } return pres; } } pres->w[0] = coeff.w[0]; tmp = expon; tmp <<= 49; pres->w[1] = sgn | tmp | coeff.w[1]; return pres; } // // Macro used for conversions from string // (no additional arguments given for rounding mode, status flags) // __BID_INLINE__ UINT128 * get_BID128_string (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { UINT128 D2, D8; UINT64 tmp; unsigned rmode = 0, status; // coeff==10^34? if (coeff.w[1] == 0x0001ed09bead87c0ull && coeff.w[0] == 0x378d8e6400000000ull) { expon++; // set coefficient to 10^33 coeff.w[1] = 0x0000314dc6448d93ull; coeff.w[0] = 0x38c15b0a00000000ull; } // check OF, UF if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { // check UF if (expon < 0) return handle_UF_128 (pres, sgn, expon, coeff, &rmode, &status); // OF if (expon < DECIMAL_MAX_EXPON_128 + 34) { while (expon > DECIMAL_MAX_EXPON_128 && (coeff.w[1] < power10_table_128[33].w[1] || (coeff.w[1] == power10_table_128[33].w[1] && coeff.w[0] < power10_table_128[33].w[0]))) { D2.w[1] = (coeff.w[1] << 1) | (coeff.w[0] >> 63); D2.w[0] = coeff.w[0] << 1; D8.w[1] = (coeff.w[1] << 3) | (coeff.w[0] >> 61); D8.w[0] = coeff.w[0] << 3; __add_128_128 (coeff, D2, D8); expon--; } } else if (!(coeff.w[0] | coeff.w[1])) expon = DECIMAL_MAX_EXPON_128; if (expon > DECIMAL_MAX_EXPON_128) { pres->w[1] = sgn | INFINITY_MASK64; pres->w[0] = 0; switch (rmode) { case ROUNDING_DOWN: if (!sgn) { pres->w[1] = LARGEST_BID128_HIGH; pres->w[0] = LARGEST_BID128_LOW; } break; case ROUNDING_TO_ZERO: pres->w[1] = sgn | LARGEST_BID128_HIGH; pres->w[0] = LARGEST_BID128_LOW; break; case ROUNDING_UP: // round up if (sgn) { pres->w[1] = sgn | LARGEST_BID128_HIGH; pres->w[0] = LARGEST_BID128_LOW; } break; } return pres; } } pres->w[0] = coeff.w[0]; tmp = expon; tmp <<= 49; pres->w[1] = sgn | tmp | coeff.w[1]; return pres; } /***************************************************************************** * * BID32 pack/unpack macros * *****************************************************************************/ __BID_INLINE__ UINT32 unpack_BID32 (UINT32 * psign_x, int *pexponent_x, UINT32 * pcoefficient_x, UINT32 x) { UINT32 tmp; *psign_x = x & 0x80000000; if ((x & SPECIAL_ENCODING_MASK32) == SPECIAL_ENCODING_MASK32) { // special encodings if ((x & INFINITY_MASK32) == INFINITY_MASK32) { *pcoefficient_x = x & 0xfe0fffff; if ((x & 0x000fffff) >= 1000000) *pcoefficient_x = x & 0xfe000000; if ((x & NAN_MASK32) == INFINITY_MASK32) *pcoefficient_x = x & 0xf8000000; *pexponent_x = 0; return 0; // NaN or Infinity } // coefficient *pcoefficient_x = (x & SMALL_COEFF_MASK32) | LARGE_COEFF_HIGH_BIT32; // check for non-canonical value if (*pcoefficient_x >= 10000000) *pcoefficient_x = 0; // get exponent tmp = x >> 21; *pexponent_x = tmp & EXPONENT_MASK32; return 1; } // exponent tmp = x >> 23; *pexponent_x = tmp & EXPONENT_MASK32; // coefficient *pcoefficient_x = (x & LARGE_COEFF_MASK32); return *pcoefficient_x; } // // General pack macro for BID32 // __BID_INLINE__ UINT32 get_BID32 (UINT32 sgn, int expon, UINT64 coeff, int rmode, unsigned *fpsc) { UINT128 Q; UINT64 C64, remainder_h, carry, Stemp; UINT32 r, mask; int extra_digits, amount, amount2; unsigned status; if (coeff > 9999999ull) { expon++; coeff = 1000000ull; } // check for possible underflow/overflow if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { if (expon < 0) { // underflow if (expon + MAX_FORMAT_DIGITS_32 < 0) { #ifdef SET_STATUS_FLAGS __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == ROUNDING_DOWN && sgn) return 0x80000001; if (rmode == ROUNDING_UP && !sgn) return 1; #endif #endif // result is 0 return sgn; } // get digits to be shifted out #ifdef IEEE_ROUND_NEAREST_TIES_AWAY rmode = 0; #endif #ifdef IEEE_ROUND_NEAREST rmode = 0; #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (sgn && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #endif #endif extra_digits = -expon; coeff += round_const_table[rmode][extra_digits]; // get coeff*(2^M[extra_digits])/10^extra_digits __mul_64x64_to_128 (Q, coeff, reciprocals10_64[extra_digits]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = short_recip_scale[extra_digits]; C64 = Q.w[1] >> amount; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == 0) //ROUNDING_TO_NEAREST #endif if (C64 & 1) { // check whether fractional part of initial_P/10^extra_digits is exactly .5 // get remainder amount2 = 64 - amount; remainder_h = 0; remainder_h--; remainder_h >>= amount2; remainder_h = remainder_h & Q.w[1]; if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) { C64--; } } #endif #ifdef SET_STATUS_FLAGS if (is_inexact (fpsc)) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); else { status = INEXACT_EXCEPTION; // get remainder remainder_h = Q.w[1] << (64 - amount); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if (remainder_h == 0x8000000000000000ull && (Q.w[0] < reciprocals10_64[extra_digits])) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) status = EXACT_STATUS; break; default: // round up __add_carry_out (Stemp, carry, Q.w[0], reciprocals10_64[extra_digits]); if ((remainder_h >> (64 - amount)) + carry >= (((UINT64) 1) << amount)) status = EXACT_STATUS; } if (status != EXACT_STATUS) __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); } #endif return sgn | (UINT32) C64; } while (coeff < 1000000 && expon > DECIMAL_MAX_EXPON_32) { coeff = (coeff << 3) + (coeff << 1); expon--; } if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); // overflow r = sgn | INFINITY_MASK32; switch (rmode) { case ROUNDING_DOWN: if (!sgn) r = LARGEST_BID32; break; case ROUNDING_TO_ZERO: r = sgn | LARGEST_BID32; break; case ROUNDING_UP: // round up if (sgn) r = sgn | LARGEST_BID32; } return r; } } mask = 1 << 23; // check whether coefficient fits in DECIMAL_COEFF_FIT bits if (coeff < mask) { r = expon; r <<= 23; r |= ((UINT32) coeff | sgn); return r; } // special format r = expon; r <<= 21; r |= (sgn | SPECIAL_ENCODING_MASK32); // add coeff, without leading bits mask = (1 << 21) - 1; r |= (((UINT32) coeff) & mask); return r; } // // no overflow/underflow checks // __BID_INLINE__ UINT32 very_fast_get_BID32 (UINT32 sgn, int expon, UINT32 coeff) { UINT32 r, mask; mask = 1 << 23; // check whether coefficient fits in 10*2+3 bits if (coeff < mask) { r = expon; r <<= 23; r |= (coeff | sgn); return r; } // special format r = expon; r <<= 21; r |= (sgn | SPECIAL_ENCODING_MASK32); // add coeff, without leading bits mask = (1 << 21) - 1; coeff &= mask; r |= coeff; return r; } /************************************************************* * *************************************************************/ typedef ALIGN (16) struct { UINT64 w[6]; } UINT384; typedef ALIGN (16) struct { UINT64 w[8]; } UINT512; // #define P 34 #define MASK_STEERING_BITS 0x6000000000000000ull #define MASK_BINARY_EXPONENT1 0x7fe0000000000000ull #define MASK_BINARY_SIG1 0x001fffffffffffffull #define MASK_BINARY_EXPONENT2 0x1ff8000000000000ull //used to take G[2:w+3] (sec 3.3) #define MASK_BINARY_SIG2 0x0007ffffffffffffull //used to mask out G4:T0 (sec 3.3) #define MASK_BINARY_OR2 0x0020000000000000ull //used to prefix 8+G4 to T (sec 3.3) #define UPPER_EXPON_LIMIT 51 #define MASK_EXP 0x7ffe000000000000ull #define MASK_SPECIAL 0x7800000000000000ull #define MASK_NAN 0x7c00000000000000ull #define MASK_SNAN 0x7e00000000000000ull #define MASK_ANY_INF 0x7c00000000000000ull #define MASK_INF 0x7800000000000000ull #define MASK_SIGN 0x8000000000000000ull #define MASK_COEFF 0x0001ffffffffffffull #define BIN_EXP_BIAS (0x1820ull << 49) #define EXP_MIN 0x0000000000000000ull // EXP_MIN = (-6176 + 6176) << 49 #define EXP_MAX 0x5ffe000000000000ull // EXP_MAX = (6111 + 6176) << 49 #define EXP_MAX_P1 0x6000000000000000ull // EXP_MAX + 1 = (6111 + 6176 + 1) << 49 #define EXP_P1 0x0002000000000000ull // EXP_ P1= 1 << 49 #define expmin -6176 // min unbiased exponent #define expmax 6111 // max unbiased exponent #define expmin16 -398 // min unbiased exponent #define expmax16 369 // max unbiased exponent #define SIGNMASK32 0x80000000 #define BID64_SIG_MAX 0x002386F26FC0ffffull #define SIGNMASK64 0x8000000000000000ull // typedef unsigned int FPSC; // floating-point status and control // bit31: // bit30: // bit29: // bit28: // bit27: // bit26: // bit25: // bit24: // bit23: // bit22: // bit21: // bit20: // bit19: // bit18: // bit17: // bit16: // bit15: // bit14: RC:2 // bit13: RC:1 // bit12: RC:0 // bit11: PM // bit10: UM // bit9: OM // bit8: ZM // bit7: DM // bit6: IM // bit5: PE // bit4: UE // bit3: OE // bit2: ZE // bit1: DE // bit0: IE #define ROUNDING_MODE_MASK 0x00007000 typedef struct _DEC_DIGITS { unsigned int digits; UINT64 threshold_hi; UINT64 threshold_lo; unsigned int digits1; } DEC_DIGITS; extern DEC_DIGITS nr_digits[]; extern UINT64 midpoint64[]; extern UINT128 midpoint128[]; extern UINT192 midpoint192[]; extern UINT256 midpoint256[]; extern UINT64 ten2k64[]; extern UINT128 ten2k128[]; extern UINT256 ten2k256[]; extern UINT128 ten2mk128[]; extern UINT64 ten2mk64[]; extern UINT128 ten2mk128trunc[]; extern int shiftright128[]; extern UINT64 maskhigh128[]; extern UINT64 maskhigh128M[]; extern UINT64 maskhigh192M[]; extern UINT64 maskhigh256M[]; extern UINT64 onehalf128[]; extern UINT64 onehalf128M[]; extern UINT64 onehalf192M[]; extern UINT64 onehalf256M[]; extern UINT128 ten2mk128M[]; extern UINT128 ten2mk128truncM[]; extern UINT192 ten2mk192truncM[]; extern UINT256 ten2mk256truncM[]; extern int shiftright128M[]; extern int shiftright192M[]; extern int shiftright256M[]; extern UINT192 ten2mk192M[]; extern UINT256 ten2mk256M[]; extern unsigned char char_table2[]; extern unsigned char char_table3[]; extern UINT64 ten2m3k64[]; extern unsigned int shift_ten2m3k64[]; extern UINT128 ten2m3k128[]; extern unsigned int shift_ten2m3k128[]; /*************************************************************************** *************** TABLES FOR GENERAL ROUNDING FUNCTIONS ********************* ***************************************************************************/ extern UINT64 Kx64[]; extern unsigned int Ex64m64[]; extern UINT64 half64[]; extern UINT64 mask64[]; extern UINT64 ten2mxtrunc64[]; extern UINT128 Kx128[]; extern unsigned int Ex128m128[]; extern UINT64 half128[]; extern UINT64 mask128[]; extern UINT128 ten2mxtrunc128[]; extern UINT192 Kx192[]; extern unsigned int Ex192m192[]; extern UINT64 half192[]; extern UINT64 mask192[]; extern UINT192 ten2mxtrunc192[]; extern UINT256 Kx256[]; extern unsigned int Ex256m256[]; extern UINT64 half256[]; extern UINT64 mask256[]; extern UINT256 ten2mxtrunc256[]; typedef union __bid64_128 { UINT64 b64; UINT128 b128; } BID64_128; BID64_128 bid_fma (unsigned int P0, BID64_128 x1, unsigned int P1, BID64_128 y1, unsigned int P2, BID64_128 z1, unsigned int P3, unsigned int rnd_mode, FPSC * fpsc); #define P16 16 #define P34 34 union __int_double { UINT64 i; double d; }; typedef union __int_double int_double; union __int_float { UINT32 i; float d; }; typedef union __int_float int_float; #define SWAP(A,B,T) {\ T = A; \ A = B; \ B = T; \ } // this macro will find coefficient_x to be in [2^A, 2^(A+1) ) // ie it knows that it is A bits long #define NUMBITS(A, coefficient_x, tempx){\ temp_x.d=(float)coefficient_x;\ A=((tempx.i >>23) & EXPONENT_MASK32) - 0x7f;\ } enum class_types { signalingNaN, quietNaN, negativeInfinity, negativeNormal, negativeSubnormal, negativeZero, positiveZero, positiveSubnormal, positiveNormal, positiveInfinity }; typedef union { UINT64 ui64; double d; } BID_UI64DOUBLE; #endif
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