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/* Copyright (C) 2007-2015 Free Software Foundation, Inc. |
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This file is part of GCC. |
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GCC is free software; you can redistribute it and/or modify it under |
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the terms of the GNU General Public License as published by the Free |
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Software Foundation; either version 3, or (at your option) any later |
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version. |
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY |
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WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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for more details. |
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Under Section 7 of GPL version 3, you are granted additional |
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permissions described in the GCC Runtime Library Exception, version |
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3.1, as published by the Free Software Foundation. |
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You should have received a copy of the GNU General Public License and |
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a copy of the GCC Runtime Library Exception along with this program; |
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
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. */ |
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#ifndef __BIDECIMAL_H |
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#define __BIDECIMAL_H |
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#include "bid_conf.h" |
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#include "bid_functions.h" |
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#define __BID_INLINE__ static __inline |
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/********************************************************************* |
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* |
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* Logical Shift Macros |
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* |
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*********************************************************************/ |
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#define __shr_128(Q, A, k) \ |
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{ \ |
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(Q).w[0] = (A).w[0] >> k; \ |
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(Q).w[0] |= (A).w[1] << (64-k); \ |
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(Q).w[1] = (A).w[1] >> k; \ |
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} |
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#define __shr_128_long(Q, A, k) \ |
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{ \ |
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if((k)<64) { \ |
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(Q).w[0] = (A).w[0] >> k; \ |
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(Q).w[0] |= (A).w[1] << (64-k); \ |
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(Q).w[1] = (A).w[1] >> k; \ |
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} \ |
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else { \ |
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(Q).w[0] = (A).w[1]>>((k)-64); \ |
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(Q).w[1] = 0; \ |
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} \ |
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} |
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#define __shl_128_long(Q, A, k) \ |
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{ \ |
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if((k)<64) { \ |
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(Q).w[1] = (A).w[1] << k; \ |
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(Q).w[1] |= (A).w[0] >> (64-k); \ |
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(Q).w[0] = (A).w[0] << k; \ |
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} \ |
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else { \ |
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(Q).w[1] = (A).w[0]<<((k)-64); \ |
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(Q).w[0] = 0; \ |
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} \ |
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} |
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#define __low_64(Q) (Q).w[0] |
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/********************************************************************* |
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* |
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* String Macros |
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* |
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*********************************************************************/ |
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#define tolower_macro(x) (((unsigned char)((x)-'A')<=('Z'-'A'))?((x)-'A'+'a'):(x)) |
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/********************************************************************* |
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* |
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* Compare Macros |
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* |
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*********************************************************************/ |
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// greater than |
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// return 0 if A<=B |
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// non-zero if A>B |
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#define __unsigned_compare_gt_128(A, B) \ |
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((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>B.w[0]))) |
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// greater-or-equal |
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#define __unsigned_compare_ge_128(A, B) \ |
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((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>=B.w[0]))) |
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#define __test_equal_128(A, B) (((A).w[1]==(B).w[1]) && ((A).w[0]==(B).w[0])) |
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// tighten exponent range |
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#define __tight_bin_range_128(bp, P, bin_expon) \ |
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{ \ |
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UINT64 M; \ |
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M = 1; \ |
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(bp) = (bin_expon); \ |
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if((bp)<63) { \ |
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M <<= ((bp)+1); \ |
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if((P).w[0] >= M) (bp)++; } \ |
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else if((bp)>64) { \ |
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M <<= ((bp)+1-64); \ |
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if(((P).w[1]>M) ||((P).w[1]==M && (P).w[0]))\ |
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(bp)++; } \ |
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else if((P).w[1]) (bp)++; \ |
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} |
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/********************************************************************* |
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* |
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* Add/Subtract Macros |
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* |
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*********************************************************************/ |
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// add 64-bit value to 128-bit |
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#define __add_128_64(R128, A128, B64) \ |
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{ \ |
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UINT64 R64H; \ |
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R64H = (A128).w[1]; \ |
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(R128).w[0] = (B64) + (A128).w[0]; \ |
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if((R128).w[0] < (B64)) \ |
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R64H ++; \ |
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(R128).w[1] = R64H; \ |
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} |
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// subtract 64-bit value from 128-bit |
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#define __sub_128_64(R128, A128, B64) \ |
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{ \ |
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UINT64 R64H; \ |
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R64H = (A128).w[1]; \ |
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if((A128).w[0] < (B64)) \ |
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R64H --; \ |
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(R128).w[1] = R64H; \ |
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(R128).w[0] = (A128).w[0] - (B64); \ |
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} |
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// add 128-bit value to 128-bit |
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// assume no carry-out |
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#define __add_128_128(R128, A128, B128) \ |
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{ \ |
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UINT128 Q128; \ |
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Q128.w[1] = (A128).w[1]+(B128).w[1]; \ |
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Q128.w[0] = (B128).w[0] + (A128).w[0]; \ |
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if(Q128.w[0] < (B128).w[0]) \ |
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Q128.w[1] ++; \ |
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(R128).w[1] = Q128.w[1]; \ |
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(R128).w[0] = Q128.w[0]; \ |
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} |
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#define __sub_128_128(R128, A128, B128) \ |
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{ \ |
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UINT128 Q128; \ |
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Q128.w[1] = (A128).w[1]-(B128).w[1]; \ |
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Q128.w[0] = (A128).w[0] - (B128).w[0]; \ |
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if((A128).w[0] < (B128).w[0]) \ |
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Q128.w[1] --; \ |
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(R128).w[1] = Q128.w[1]; \ |
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(R128).w[0] = Q128.w[0]; \ |
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} |
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#define __add_carry_out(S, CY, X, Y) \ |
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{ \ |
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UINT64 X1=X; \ |
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S = X + Y; \ |
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CY = (S |
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} |
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#define __add_carry_in_out(S, CY, X, Y, CI) \ |
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{ \ |
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UINT64 X1; \ |
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X1 = X + CI; \ |
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S = X1 + Y; \ |
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CY = ((S |
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} |
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#define __sub_borrow_out(S, CY, X, Y) \ |
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{ \ |
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UINT64 X1=X; \ |
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S = X - Y; \ |
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CY = (S>X1) ? 1 : 0; \ |
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} |
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#define __sub_borrow_in_out(S, CY, X, Y, CI) \ |
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{ \ |
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UINT64 X1, X0=X; \ |
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X1 = X - CI; \ |
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S = X1 - Y; \ |
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CY = ((S>X1) || (X1>X0)) ? 1 : 0; \ |
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} |
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// increment C128 and check for rounding overflow: |
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// if (C_128) = 10^34 then (C_128) = 10^33 and increment the exponent |
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#define INCREMENT(C_128, exp) \ |
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{ \ |
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C_128.w[0]++; \ |
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if (C_128.w[0] == 0) C_128.w[1]++; \ |
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if (C_128.w[1] == 0x0001ed09bead87c0ull && \ |
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C_128.w[0] == 0x378d8e6400000000ull) { \ |
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exp++; \ |
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C_128.w[1] = 0x0000314dc6448d93ull; \ |
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C_128.w[0] = 0x38c15b0a00000000ull; \ |
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} \ |
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} |
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// decrement C128 and check for rounding underflow, but only at the |
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// boundary: if C_128 = 10^33 - 1 and exp > 0 then C_128 = 10^34 - 1 |
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// and decrement the exponent |
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#define DECREMENT(C_128, exp) \ |
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{ \ |
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C_128.w[0]--; \ |
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if (C_128.w[0] == 0xffffffffffffffffull) C_128.w[1]--; \ |
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if (C_128.w[1] == 0x0000314dc6448d93ull && \ |
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C_128.w[0] == 0x38c15b09ffffffffull && exp > 0) { \ |
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exp--; \ |
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C_128.w[1] = 0x0001ed09bead87c0ull; \ |
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C_128.w[0] = 0x378d8e63ffffffffull; \ |
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} \ |
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} |
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/********************************************************************* |
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* |
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* Multiply Macros |
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* |
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*********************************************************************/ |
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#define __mul_64x64_to_64(P64, CX, CY) (P64) = (CX) * (CY) |
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/*************************************** |
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* Signed, Full 64x64-bit Multiply |
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***************************************/ |
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#define __imul_64x64_to_128(P, CX, CY) \ |
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{ \ |
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UINT64 SX, SY; \ |
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__mul_64x64_to_128(P, CX, CY); \ |
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\ |
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SX = ((SINT64)(CX))>>63; \ |
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SY = ((SINT64)(CY))>>63; \ |
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SX &= CY; SY &= CX; \ |
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\ |
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(P).w[1] = (P).w[1] - SX - SY; \ |
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} |
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/*************************************** |
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* Signed, Full 64x128-bit Multiply |
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***************************************/ |
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#define __imul_64x128_full(Ph, Ql, A, B) \ |
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{ \ |
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UINT128 ALBL, ALBH, QM2, QM; \ |
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\ |
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__imul_64x64_to_128(ALBH, (A), (B).w[1]); \ |
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__imul_64x64_to_128(ALBL, (A), (B).w[0]); \ |
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\ |
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(Ql).w[0] = ALBL.w[0]; \ |
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QM.w[0] = ALBL.w[1]; \ |
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QM.w[1] = ((SINT64)ALBL.w[1])>>63; \ |
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__add_128_128(QM2, ALBH, QM); \ |
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(Ql).w[1] = QM2.w[0]; \ |
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Ph = QM2.w[1]; \ |
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} |
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/***************************************************** |
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* Unsigned Multiply Macros |
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*****************************************************/ |
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// get full 64x64bit product |
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// |
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#define __mul_64x64_to_128(P, CX, CY) \ |
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{ \ |
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UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ |
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CXH = (CX) >> 32; \ |
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CXL = (UINT32)(CX); \ |
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CYH = (CY) >> 32; \ |
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CYL = (UINT32)(CY); \ |
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\ |
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PM = CXH*CYL; \ |
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PH = CXH*CYH; \ |
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PL = CXL*CYL; \ |
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PM2 = CXL*CYH; \ |
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PH += (PM>>32); \ |
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PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ |
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\ |
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(P).w[1] = PH + (PM>>32); \ |
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(P).w[0] = (PM<<32)+(UINT32)PL; \ |
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} |
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// get full 64x64bit product |
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// Note: |
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// This macro is used for CX < 2^61, CY < 2^61 |
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// |
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#define __mul_64x64_to_128_fast(P, CX, CY) \ |
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{ \ |
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UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ |
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CXH = (CX) >> 32; \ |
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CXL = (UINT32)(CX); \ |
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CYH = (CY) >> 32; \ |
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CYL = (UINT32)(CY); \ |
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\ |
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PM = CXH*CYL; \ |
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PL = CXL*CYL; \ |
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PH = CXH*CYH; \ |
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PM += CXL*CYH; \ |
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PM += (PL>>32); \ |
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\ |
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(P).w[1] = PH + (PM>>32); \ |
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(P).w[0] = (PM<<32)+(UINT32)PL; \ |
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} |
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// used for CX< 2^60 |
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#define __sqr64_fast(P, CX) \ |
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{ \ |
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UINT64 CXH, CXL, PL, PH, PM; \ |
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CXH = (CX) >> 32; \ |
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CXL = (UINT32)(CX); \ |
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\ |
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PM = CXH*CXL; \ |
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PL = CXL*CXL; \ |
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PH = CXH*CXH; \ |
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PM += PM; \ |
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PM += (PL>>32); \ |
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\ |
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(P).w[1] = PH + (PM>>32); \ |
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(P).w[0] = (PM<<32)+(UINT32)PL; \ |
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} |
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// get full 64x64bit product |
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// Note: |
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// This implementation is used for CX < 2^61, CY < 2^61 |
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// |
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#define __mul_64x64_to_64_high_fast(P, CX, CY) \ |
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{ \ |
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UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ |
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CXH = (CX) >> 32; \ |
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CXL = (UINT32)(CX); \ |
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CYH = (CY) >> 32; \ |
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CYL = (UINT32)(CY); \ |
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\ |
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PM = CXH*CYL; \ |
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PL = CXL*CYL; \ |
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PH = CXH*CYH; \ |
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PM += CXL*CYH; \ |
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PM += (PL>>32); \ |
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\ |
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(P) = PH + (PM>>32); \ |
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} |
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// get full 64x64bit product |
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// |
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#define __mul_64x64_to_128_full(P, CX, CY) \ |
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{ \ |
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UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ |
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CXH = (CX) >> 32; \ |
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CXL = (UINT32)(CX); \ |
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CYH = (CY) >> 32; \ |
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CYL = (UINT32)(CY); \ |
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\ |
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PM = CXH*CYL; \ |
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PH = CXH*CYH; \ |
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PL = CXL*CYL; \ |
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PM2 = CXL*CYH; \ |
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PH += (PM>>32); \ |
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PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ |
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\ |
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(P).w[1] = PH + (PM>>32); \ |
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(P).w[0] = (PM<<32)+(UINT32)PL; \ |
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} |
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#define __mul_128x128_high(Q, A, B) \ |
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{ \ |
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UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ |
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\ |
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__mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ |
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__mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ |
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__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ |
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__mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ |
|
|
353 |
\ |
|
|
354 |
__add_128_128(QM, ALBH, AHBL); \ |
|
|
355 |
__add_128_64(QM2, QM, ALBL.w[1]); \ |
|
|
356 |
__add_128_64((Q), AHBH, QM2.w[1]); \ |
|
|
357 |
} |
|
|
358 |
#define __mul_128x128_full(Qh, Ql, A, B) \ |
|
|
359 |
{ \ |
|
|
360 |
UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ |
|
|
361 |
\ |
|
|
362 |
__mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ |
|
|
363 |
__mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ |
|
|
364 |
__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ |
|
|
365 |
__mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ |
|
|
366 |
\ |
|
|
367 |
__add_128_128(QM, ALBH, AHBL); \ |
|
|
368 |
(Ql).w[0] = ALBL.w[0]; \ |
|
|
369 |
__add_128_64(QM2, QM, ALBL.w[1]); \ |
|
|
370 |
__add_128_64((Qh), AHBH, QM2.w[1]); \ |
|
|
371 |
(Ql).w[1] = QM2.w[0]; \ |
|
|
372 |
} |
|
|
373 |
#define __mul_128x128_low(Ql, A, B) \ |
|
|
374 |
{ \ |
|
|
375 |
UINT128 ALBL; \ |
|
|
376 |
UINT64 QM64; \ |
|
|
377 |
\ |
|
|
378 |
__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ |
|
|
379 |
QM64 = (B).w[0]*(A).w[1] + (A).w[0]*(B).w[1]; \ |
|
|
380 |
\ |
|
|
381 |
(Ql).w[0] = ALBL.w[0]; \ |
|
|
382 |
(Ql).w[1] = QM64 + ALBL.w[1]; \ |
|
|
383 |
} |
|
|
384 |
#define __mul_64x128_low(Ql, A, B) \ |
|
|
385 |
{ \ |
|
|
386 |
UINT128 ALBL, ALBH, QM2; \ |
|
|
387 |
__mul_64x64_to_128(ALBH, (A), (B).w[1]); \ |
|
|
388 |
__mul_64x64_to_128(ALBL, (A), (B).w[0]); \ |
|
|
389 |
(Ql).w[0] = ALBL.w[0]; \ |
|
|
390 |
__add_128_64(QM2, ALBH, ALBL.w[1]); \ |
|
|
391 |
(Ql).w[1] = QM2.w[0]; \ |
|
|
392 |
} |
|
|
393 |
#define __mul_64x128_full(Ph, Ql, A, B) \ |
|
|
394 |
{ \ |
|
|
395 |
UINT128 ALBL, ALBH, QM2; \ |
|
|
396 |
\ |
|
|
397 |
__mul_64x64_to_128(ALBH, (A), (B).w[1]); \ |
|
|
398 |
__mul_64x64_to_128(ALBL, (A), (B).w[0]); \ |
|
|
399 |
\ |
|
|
400 |
(Ql).w[0] = ALBL.w[0]; \ |
|
|
401 |
__add_128_64(QM2, ALBH, ALBL.w[1]); \ |
|
|
402 |
(Ql).w[1] = QM2.w[0]; \ |
|
|
403 |
Ph = QM2.w[1]; \ |
|
|
404 |
} |
|
|
405 |
#define __mul_64x128_to_192(Q, A, B) \ |
|
|
406 |
{ \ |
|
|
407 |
UINT128 ALBL, ALBH, QM2; \ |
|
|
408 |
\ |
|
|
409 |
__mul_64x64_to_128(ALBH, (A), (B).w[1]); \ |
|
|
410 |
__mul_64x64_to_128(ALBL, (A), (B).w[0]); \ |
|
|
411 |
\ |
|
|
412 |
(Q).w[0] = ALBL.w[0]; \ |
|
|
413 |
__add_128_64(QM2, ALBH, ALBL.w[1]); \ |
|
|
414 |
(Q).w[1] = QM2.w[0]; \ |
|
|
415 |
(Q).w[2] = QM2.w[1]; \ |
|
|
416 |
} |
|
|
417 |
#define __mul_64x128_to192(Q, A, B) \ |
|
|
418 |
{ \ |
|
|
419 |
UINT128 ALBL, ALBH, QM2; \ |
|
|
420 |
\ |
|
|
421 |
__mul_64x64_to_128(ALBH, (A), (B).w[1]); \ |
|
|
422 |
__mul_64x64_to_128(ALBL, (A), (B).w[0]); \ |
|
|
423 |
\ |
|
|
424 |
(Q).w[0] = ALBL.w[0]; \ |
|
|
425 |
__add_128_64(QM2, ALBH, ALBL.w[1]); \ |
|
|
426 |
(Q).w[1] = QM2.w[0]; \ |
|
|
427 |
(Q).w[2] = QM2.w[1]; \ |
|
|
428 |
} |
|
|
429 |
#define __mul_128x128_to_256(P256, A, B) \ |
|
|
430 |
{ \ |
|
|
431 |
UINT128 Qll, Qlh; \ |
|
|
432 |
UINT64 Phl, Phh, CY1, CY2; \ |
|
|
433 |
\ |
|
|
434 |
__mul_64x128_full(Phl, Qll, A.w[0], B); \ |
|
|
435 |
__mul_64x128_full(Phh, Qlh, A.w[1], B); \ |
|
|
436 |
(P256).w[0] = Qll.w[0]; \ |
|
|
437 |
__add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ |
|
|
438 |
__add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ |
|
|
439 |
(P256).w[3] = Phh + CY2; \ |
|
|
440 |
} |
|
|
441 |
// |
|
|
442 |
// For better performance, will check A.w[1] against 0, |
|
|
443 |
// but not B.w[1] |
|
|
444 |
// Use this macro accordingly |
|
|
445 |
#define __mul_128x128_to_256_check_A(P256, A, B) \ |
|
|
446 |
{ \ |
|
|
447 |
UINT128 Qll, Qlh; \ |
|
|
448 |
UINT64 Phl, Phh, CY1, CY2; \ |
|
|
449 |
\ |
|
|
450 |
__mul_64x128_full(Phl, Qll, A.w[0], B); \ |
|
|
451 |
(P256).w[0] = Qll.w[0]; \ |
|
|
452 |
if(A.w[1]) { \ |
|
|
453 |
__mul_64x128_full(Phh, Qlh, A.w[1], B); \ |
|
|
454 |
__add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ |
|
|
455 |
__add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ |
|
|
456 |
(P256).w[3] = Phh + CY2; } \ |
|
|
457 |
else { \ |
|
|
458 |
(P256).w[1] = Qll.w[1]; \ |
|
|
459 |
(P256).w[2] = Phl; \ |
|
|
460 |
(P256).w[3] = 0; } \ |
|
|
461 |
} |
|
|
462 |
#define __mul_64x192_to_256(lP, lA, lB) \ |
|
|
463 |
{ \ |
|
|
464 |
UINT128 lP0,lP1,lP2; \ |
|
|
465 |
UINT64 lC; \ |
|
|
466 |
__mul_64x64_to_128(lP0, lA, (lB).w[0]); \ |
|
|
467 |
__mul_64x64_to_128(lP1, lA, (lB).w[1]); \ |
|
|
468 |
__mul_64x64_to_128(lP2, lA, (lB).w[2]); \ |
|
|
469 |
(lP).w[0] = lP0.w[0]; \ |
|
|
470 |
__add_carry_out((lP).w[1],lC,lP1.w[0],lP0.w[1]); \ |
|
|
471 |
__add_carry_in_out((lP).w[2],lC,lP2.w[0],lP1.w[1],lC); \ |
|
|
472 |
(lP).w[3] = lP2.w[1] + lC; \ |
|
|
473 |
} |
|
|
474 |
#define __mul_64x256_to_320(P, A, B) \ |
|
|
475 |
{ \ |
|
|
476 |
UINT128 lP0,lP1,lP2,lP3; \ |
|
|
477 |
UINT64 lC; \ |
|
|
478 |
__mul_64x64_to_128(lP0, A, (B).w[0]); \ |
|
|
479 |
__mul_64x64_to_128(lP1, A, (B).w[1]); \ |
|
|
480 |
__mul_64x64_to_128(lP2, A, (B).w[2]); \ |
|
|
481 |
__mul_64x64_to_128(lP3, A, (B).w[3]); \ |
|
|
482 |
(P).w[0] = lP0.w[0]; \ |
|
|
483 |
__add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ |
|
|
484 |
__add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ |
|
|
485 |
__add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ |
|
|
486 |
(P).w[4] = lP3.w[1] + lC; \ |
|
|
487 |
} |
|
|
488 |
#define __mul_192x192_to_384(P, A, B) \ |
|
|
489 |
{ \ |
|
|
490 |
UINT256 P0,P1,P2; \ |
|
|
491 |
UINT64 CY; \ |
|
|
492 |
__mul_64x192_to_256(P0, (A).w[0], B); \ |
|
|
493 |
__mul_64x192_to_256(P1, (A).w[1], B); \ |
|
|
494 |
__mul_64x192_to_256(P2, (A).w[2], B); \ |
|
|
495 |
(P).w[0] = P0.w[0]; \ |
|
|
496 |
__add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ |
|
|
497 |
__add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ |
|
|
498 |
__add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ |
|
|
499 |
(P).w[4] = P1.w[3] + CY; \ |
|
|
500 |
__add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ |
|
|
501 |
__add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ |
|
|
502 |
__add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ |
|
|
503 |
(P).w[5] = P2.w[3] + CY; \ |
|
|
504 |
} |
|
|
505 |
#define __mul_64x320_to_384(P, A, B) \ |
|
|
506 |
{ \ |
|
|
507 |
UINT128 lP0,lP1,lP2,lP3,lP4; \ |
|
|
508 |
UINT64 lC; \ |
|
|
509 |
__mul_64x64_to_128(lP0, A, (B).w[0]); \ |
|
|
510 |
__mul_64x64_to_128(lP1, A, (B).w[1]); \ |
|
|
511 |
__mul_64x64_to_128(lP2, A, (B).w[2]); \ |
|
|
512 |
__mul_64x64_to_128(lP3, A, (B).w[3]); \ |
|
|
513 |
__mul_64x64_to_128(lP4, A, (B).w[4]); \ |
|
|
514 |
(P).w[0] = lP0.w[0]; \ |
|
|
515 |
__add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ |
|
|
516 |
__add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ |
|
|
517 |
__add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ |
|
|
518 |
__add_carry_in_out((P).w[4],lC,lP4.w[0],lP3.w[1],lC); \ |
|
|
519 |
(P).w[5] = lP4.w[1] + lC; \ |
|
|
520 |
} |
|
|
521 |
// A*A |
|
|
522 |
// Full 128x128-bit product |
|
|
523 |
#define __sqr128_to_256(P256, A) \ |
|
|
524 |
{ \ |
|
|
525 |
UINT128 Qll, Qlh, Qhh; \ |
|
|
526 |
UINT64 TMP_C1, TMP_C2; \ |
|
|
527 |
\ |
|
|
528 |
__mul_64x64_to_128(Qhh, A.w[1], A.w[1]); \ |
|
|
529 |
__mul_64x64_to_128(Qlh, A.w[0], A.w[1]); \ |
|
|
530 |
Qhh.w[1] += (Qlh.w[1]>>63); \ |
|
|
531 |
Qlh.w[1] = (Qlh.w[1]+Qlh.w[1])|(Qlh.w[0]>>63); \ |
|
|
532 |
Qlh.w[0] += Qlh.w[0]; \ |
|
|
533 |
__mul_64x64_to_128(Qll, A.w[0], A.w[0]); \ |
|
|
534 |
\ |
|
|
535 |
__add_carry_out((P256).w[1],TMP_C1, Qlh.w[0], Qll.w[1]); \ |
|
|
536 |
(P256).w[0] = Qll.w[0]; \ |
|
|
537 |
__add_carry_in_out((P256).w[2],TMP_C2, Qlh.w[1], Qhh.w[0], TMP_C1); \ |
|
|
538 |
(P256).w[3] = Qhh.w[1]+TMP_C2; \ |
|
|
539 |
} |
|
|
540 |
#define __mul_128x128_to_256_low_high(PQh, PQl, A, B) \ |
|
|
541 |
{ \ |
|
|
542 |
UINT128 Qll, Qlh; \ |
|
|
543 |
UINT64 Phl, Phh, C1, C2; \ |
|
|
544 |
\ |
|
|
545 |
__mul_64x128_full(Phl, Qll, A.w[0], B); \ |
|
|
546 |
__mul_64x128_full(Phh, Qlh, A.w[1], B); \ |
|
|
547 |
(PQl).w[0] = Qll.w[0]; \ |
|
|
548 |
__add_carry_out((PQl).w[1],C1, Qlh.w[0], Qll.w[1]); \ |
|
|
549 |
__add_carry_in_out((PQh).w[0],C2, Qlh.w[1], Phl, C1); \ |
|
|
550 |
(PQh).w[1] = Phh + C2; \ |
|
|
551 |
} |
|
|
552 |
#define __mul_256x256_to_512(P, A, B) \ |
|
|
553 |
{ \ |
|
|
554 |
UINT512 P0,P1,P2,P3; \ |
|
|
555 |
UINT64 CY; \ |
|
|
556 |
__mul_64x256_to_320(P0, (A).w[0], B); \ |
|
|
557 |
__mul_64x256_to_320(P1, (A).w[1], B); \ |
|
|
558 |
__mul_64x256_to_320(P2, (A).w[2], B); \ |
|
|
559 |
__mul_64x256_to_320(P3, (A).w[3], B); \ |
|
|
560 |
(P).w[0] = P0.w[0]; \ |
|
|
561 |
__add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ |
|
|
562 |
__add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ |
|
|
563 |
__add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ |
|
|
564 |
__add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ |
|
|
565 |
(P).w[5] = P1.w[4] + CY; \ |
|
|
566 |
__add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ |
|
|
567 |
__add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ |
|
|
568 |
__add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ |
|
|
569 |
__add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ |
|
|
570 |
(P).w[6] = P2.w[4] + CY; \ |
|
|
571 |
__add_carry_out((P).w[3],CY,P3.w[0],(P).w[3]); \ |
|
|
572 |
__add_carry_in_out((P).w[4],CY,P3.w[1],(P).w[4],CY); \ |
|
|
573 |
__add_carry_in_out((P).w[5],CY,P3.w[2],(P).w[5],CY); \ |
|
|
574 |
__add_carry_in_out((P).w[6],CY,P3.w[3],(P).w[6],CY); \ |
|
|
575 |
(P).w[7] = P3.w[4] + CY; \ |
|
|
576 |
} |
|
|
577 |
#define __mul_192x256_to_448(P, A, B) \ |
|
|
578 |
{ \ |
|
|
579 |
UINT512 P0,P1,P2; \ |
|
|
580 |
UINT64 CY; \ |
|
|
581 |
__mul_64x256_to_320(P0, (A).w[0], B); \ |
|
|
582 |
__mul_64x256_to_320(P1, (A).w[1], B); \ |
|
|
583 |
__mul_64x256_to_320(P2, (A).w[2], B); \ |
|
|
584 |
(P).w[0] = P0.w[0]; \ |
|
|
585 |
__add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ |
|
|
586 |
__add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ |
|
|
587 |
__add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ |
|
|
588 |
__add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ |
|
|
589 |
(P).w[5] = P1.w[4] + CY; \ |
|
|
590 |
__add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ |
|
|
591 |
__add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ |
|
|
592 |
__add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ |
|
|
593 |
__add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ |
|
|
594 |
(P).w[6] = P2.w[4] + CY; \ |
|
|
595 |
} |
|
|
596 |
#define __mul_320x320_to_640(P, A, B) \ |
|
|
597 |
{ \ |
|
|
598 |
UINT512 P0,P1,P2,P3; \ |
|
|
599 |
UINT64 CY; \ |
|
|
600 |
__mul_256x256_to_512((P), (A), B); \ |
|
|
601 |
__mul_64x256_to_320(P1, (A).w[4], B); \ |
|
|
602 |
__mul_64x256_to_320(P2, (B).w[4], A); \ |
|
|
603 |
__mul_64x64_to_128(P3, (A).w[4], (B).w[4]); \ |
|
|
604 |
__add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ |
|
|
605 |
__add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ |
|
|
606 |
__add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ |
|
|
607 |
__add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ |
|
|
608 |
__add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ |
|
|
609 |
P3.w[1] += CY; \ |
|
|
610 |
__add_carry_out((P).w[4],CY,(P).w[4],P0.w[0]); \ |
|
|
611 |
__add_carry_in_out((P).w[5],CY,(P).w[5],P0.w[1],CY); \ |
|
|
612 |
__add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[2],CY); \ |
|
|
613 |
__add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[3],CY); \ |
|
|
614 |
__add_carry_in_out((P).w[8],CY,P3.w[0],P0.w[4],CY); \ |
|
|
615 |
(P).w[9] = P3.w[1] + CY; \ |
|
|
616 |
} |
|
|
617 |
#define __mul_384x384_to_768(P, A, B) \ |
|
|
618 |
{ \ |
|
|
619 |
UINT512 P0,P1,P2,P3; \ |
|
|
620 |
UINT64 CY; \ |
|
|
621 |
__mul_320x320_to_640((P), (A), B); \ |
|
|
622 |
__mul_64x320_to_384(P1, (A).w[5], B); \ |
|
|
623 |
__mul_64x320_to_384(P2, (B).w[5], A); \ |
|
|
624 |
__mul_64x64_to_128(P3, (A).w[5], (B).w[5]); \ |
|
|
625 |
__add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ |
|
|
626 |
__add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ |
|
|
627 |
__add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ |
|
|
628 |
__add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ |
|
|
629 |
__add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ |
|
|
630 |
__add_carry_in_out((P0).w[5],CY,P1.w[5],P2.w[5],CY); \ |
|
|
631 |
P3.w[1] += CY; \ |
|
|
632 |
__add_carry_out((P).w[5],CY,(P).w[5],P0.w[0]); \ |
|
|
633 |
__add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[1],CY); \ |
|
|
634 |
__add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[2],CY); \ |
|
|
635 |
__add_carry_in_out((P).w[8],CY,(P).w[8],P0.w[3],CY); \ |
|
|
636 |
__add_carry_in_out((P).w[9],CY,(P).w[9],P0.w[4],CY); \ |
|
|
637 |
__add_carry_in_out((P).w[10],CY,P3.w[0],P0.w[5],CY); \ |
|
|
638 |
(P).w[11] = P3.w[1] + CY; \ |
|
|
639 |
} |
|
|
640 |
#define __mul_64x128_short(Ql, A, B) \ |
|
|
641 |
{ \ |
|
|
642 |
UINT64 ALBH_L; \ |
|
|
643 |
\ |
|
|
644 |
__mul_64x64_to_64(ALBH_L, (A),(B).w[1]); \ |
|
|
645 |
__mul_64x64_to_128((Ql), (A), (B).w[0]); \ |
|
|
646 |
\ |
|
|
647 |
(Ql).w[1] += ALBH_L; \ |
|
|
648 |
} |
|
|
649 |
#define __scale128_10(D,_TMP) \ |
|
|
650 |
{ \ |
|
|
651 |
UINT128 _TMP2,_TMP8; \ |
|
|
652 |
_TMP2.w[1] = (_TMP.w[1]<<1)|(_TMP.w[0]>>63); \ |
|
|
653 |
_TMP2.w[0] = _TMP.w[0]<<1; \ |
|
|
654 |
_TMP8.w[1] = (_TMP.w[1]<<3)|(_TMP.w[0]>>61); \ |
|
|
655 |
_TMP8.w[0] = _TMP.w[0]<<3; \ |
|
|
656 |
__add_128_128(D, _TMP2, _TMP8); \ |
|
|
657 |
} |
|
|
658 |
// 64x64-bit product |
|
|
659 |
#define __mul_64x64_to_128MACH(P128, CX64, CY64) \ |
|
|
660 |
{ \ |
|
|
661 |
UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ |
|
|
662 |
CXH = (CX64) >> 32; \ |
|
|
663 |
CXL = (UINT32)(CX64); \ |
|
|
664 |
CYH = (CY64) >> 32; \ |
|
|
665 |
CYL = (UINT32)(CY64); \ |
|
|
666 |
PM = CXH*CYL; \ |
|
|
667 |
PH = CXH*CYH; \ |
|
|
668 |
PL = CXL*CYL; \ |
|
|
669 |
PM2 = CXL*CYH; \ |
|
|
670 |
PH += (PM>>32); \ |
|
|
671 |
PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ |
|
|
672 |
(P128).w[1] = PH + (PM>>32); \ |
|
|
673 |
(P128).w[0] = (PM<<32)+(UINT32)PL; \ |
|
|
674 |
} |
|
|
675 |
// 64x64-bit product |
|
|
676 |
#define __mul_64x64_to_128HIGH(P64, CX64, CY64) \ |
|
|
677 |
{ \ |
|
|
678 |
UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ |
|
|
679 |
CXH = (CX64) >> 32; \ |
|
|
680 |
CXL = (UINT32)(CX64); \ |
|
|
681 |
CYH = (CY64) >> 32; \ |
|
|
682 |
CYL = (UINT32)(CY64); \ |
|
|
683 |
PM = CXH*CYL; \ |
|
|
684 |
PH = CXH*CYH; \ |
|
|
685 |
PL = CXL*CYL; \ |
|
|
686 |
PM2 = CXL*CYH; \ |
|
|
687 |
PH += (PM>>32); \ |
|
|
688 |
PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ |
|
|
689 |
P64 = PH + (PM>>32); \ |
|
|
690 |
} |
|
|
691 |
#define __mul_128x64_to_128(Q128, A64, B128) \ |
|
|
692 |
{ \ |
|
|
693 |
UINT64 ALBH_L; \ |
|
|
694 |
ALBH_L = (A64) * (B128).w[1]; \ |
|
|
695 |
__mul_64x64_to_128MACH((Q128), (A64), (B128).w[0]); \ |
|
|
696 |
(Q128).w[1] += ALBH_L; \ |
|
|
697 |
} |
|
|
698 |
// might simplify by calculating just QM2.w[0] |
|
|
699 |
#define __mul_64x128_to_128(Ql, A, B) \ |
|
|
700 |
{ \ |
|
|
701 |
UINT128 ALBL, ALBH, QM2; \ |
|
|
702 |
__mul_64x64_to_128(ALBH, (A), (B).w[1]); \ |
|
|
703 |
__mul_64x64_to_128(ALBL, (A), (B).w[0]); \ |
|
|
704 |
(Ql).w[0] = ALBL.w[0]; \ |
|
|
705 |
__add_128_64(QM2, ALBH, ALBL.w[1]); \ |
|
|
706 |
(Ql).w[1] = QM2.w[0]; \ |
|
|
707 |
} |
|
|
708 |
/********************************************************************* |
|
|
709 |
* |
|
|
710 |
* BID Pack/Unpack Macros |
|
|
711 |
* |
|
|
712 |
*********************************************************************/ |
|
|
713 |
///////////////////////////////////////// |
|
|
714 |
// BID64 definitions |
|
|
715 |
//////////////////////////////////////// |
|
|
716 |
#define DECIMAL_MAX_EXPON_64 767 |
|
|
717 |
#define DECIMAL_EXPONENT_BIAS 398 |
|
|
718 |
#define MAX_FORMAT_DIGITS 16 |
|
|
719 |
///////////////////////////////////////// |
|
|
720 |
// BID128 definitions |
|
|
721 |
//////////////////////////////////////// |
|
|
722 |
#define DECIMAL_MAX_EXPON_128 12287 |
|
|
723 |
#define DECIMAL_EXPONENT_BIAS_128 6176 |
|
|
724 |
#define MAX_FORMAT_DIGITS_128 34 |
|
|
725 |
///////////////////////////////////////// |
|
|
726 |
// BID32 definitions |
|
|
727 |
//////////////////////////////////////// |
|
|
728 |
#define DECIMAL_MAX_EXPON_32 191 |
|
|
729 |
#define DECIMAL_EXPONENT_BIAS_32 101 |
|
|
730 |
#define MAX_FORMAT_DIGITS_32 7 |
|
|
731 |
//////////////////////////////////////// |
|
|
732 |
// Constant Definitions |
|
|
733 |
/////////////////////////////////////// |
|
|
734 |
#define SPECIAL_ENCODING_MASK64 0x6000000000000000ull |
|
|
735 |
#define INFINITY_MASK64 0x7800000000000000ull |
|
|
736 |
#define SINFINITY_MASK64 0xf800000000000000ull |
|
|
737 |
#define SSNAN_MASK64 0xfc00000000000000ull |
|
|
738 |
#define NAN_MASK64 0x7c00000000000000ull |
|
|
739 |
#define SNAN_MASK64 0x7e00000000000000ull |
|
|
740 |
#define QUIET_MASK64 0xfdffffffffffffffull |
|
|
741 |
#define LARGE_COEFF_MASK64 0x0007ffffffffffffull |
|
|
742 |
#define LARGE_COEFF_HIGH_BIT64 0x0020000000000000ull |
|
|
743 |
#define SMALL_COEFF_MASK64 0x001fffffffffffffull |
|
|
744 |
#define EXPONENT_MASK64 0x3ff |
|
|
745 |
#define EXPONENT_SHIFT_LARGE64 51 |
|
|
746 |
#define EXPONENT_SHIFT_SMALL64 53 |
|
|
747 |
#define LARGEST_BID64 0x77fb86f26fc0ffffull |
|
|
748 |
#define SMALLEST_BID64 0xf7fb86f26fc0ffffull |
|
|
749 |
#define SMALL_COEFF_MASK128 0x0001ffffffffffffull |
|
|
750 |
#define LARGE_COEFF_MASK128 0x00007fffffffffffull |
|
|
751 |
#define EXPONENT_MASK128 0x3fff |
|
|
752 |
#define LARGEST_BID128_HIGH 0x5fffed09bead87c0ull |
|
|
753 |
#define LARGEST_BID128_LOW 0x378d8e63ffffffffull |
|
|
754 |
#define SPECIAL_ENCODING_MASK32 0x60000000ul |
|
|
755 |
#define INFINITY_MASK32 0x78000000ul |
|
|
756 |
#define LARGE_COEFF_MASK32 0x007ffffful |
|
|
757 |
#define LARGE_COEFF_HIGH_BIT32 0x00800000ul |
|
|
758 |
#define SMALL_COEFF_MASK32 0x001ffffful |
|
|
759 |
#define EXPONENT_MASK32 0xff |
|
|
760 |
#define LARGEST_BID32 0x77f8967f |
|
|
761 |
#define NAN_MASK32 0x7c000000 |
|
|
762 |
#define SNAN_MASK32 0x7e000000 |
|
|
763 |
#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull |
|
|
764 |
#define BINARY_EXPONENT_BIAS 0x3ff |
|
|
765 |
#define UPPER_EXPON_LIMIT 51 |
|
|
766 |
// data needed for BID pack/unpack macros |
|
|
767 |
extern UINT64 round_const_table[][19]; |
|
|
768 |
extern UINT128 reciprocals10_128[]; |
|
|
769 |
extern int recip_scale[]; |
|
|
770 |
extern UINT128 power10_table_128[]; |
|
|
771 |
extern int estimate_decimal_digits[]; |
|
|
772 |
extern int estimate_bin_expon[]; |
|
|
773 |
extern UINT64 power10_index_binexp[]; |
|
|
774 |
extern int short_recip_scale[]; |
|
|
775 |
extern UINT64 reciprocals10_64[]; |
|
|
776 |
extern UINT128 power10_index_binexp_128[]; |
|
|
777 |
extern UINT128 round_const_table_128[][36]; |
|
|
778 |
|
|
|
779 |
|
|
|
780 |
////////////////////////////////////////////// |
|
|
781 |
// Status Flag Handling |
|
|
782 |
///////////////////////////////////////////// |
|
|
783 |
#define __set_status_flags(fpsc, status) *(fpsc) |= status |
|
|
784 |
#define is_inexact(fpsc) ((*(fpsc))&INEXACT_EXCEPTION) |
|
|
785 |
|
|
|
786 |
__BID_INLINE__ UINT64 |
|
|
787 |
unpack_BID64 (UINT64 * psign_x, int *pexponent_x, |
|
|
788 |
UINT64 * pcoefficient_x, UINT64 x) { |
|
|
789 |
UINT64 tmp, coeff; |
|
|
790 |
|
|
|
791 |
*psign_x = x & 0x8000000000000000ull; |
|
|
792 |
|
|
|
793 |
if ((x & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) { |
|
|
794 |
// special encodings |
|
|
795 |
// coefficient |
|
|
796 |
coeff = (x & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64; |
|
|
797 |
|
|
|
798 |
if ((x & INFINITY_MASK64) == INFINITY_MASK64) { |
|
|
799 |
*pexponent_x = 0; |
|
|
800 |
*pcoefficient_x = x & 0xfe03ffffffffffffull; |
|
|
801 |
if ((x & 0x0003ffffffffffffull) >= 1000000000000000ull) |
|
|
802 |
*pcoefficient_x = x & 0xfe00000000000000ull; |
|
|
803 |
if ((x & NAN_MASK64) == INFINITY_MASK64) |
|
|
804 |
*pcoefficient_x = x & SINFINITY_MASK64; |
|
|
805 |
return 0; // NaN or Infinity |
|
|
806 |
} |
|
|
807 |
// check for non-canonical values |
|
|
808 |
if (coeff >= 10000000000000000ull) |
|
|
809 |
coeff = 0; |
|
|
810 |
*pcoefficient_x = coeff; |
|
|
811 |
// get exponent |
|
|
812 |
tmp = x >> EXPONENT_SHIFT_LARGE64; |
|
|
813 |
*pexponent_x = (int) (tmp & EXPONENT_MASK64); |
|
|
814 |
return coeff; |
|
|
815 |
} |
|
|
816 |
// exponent |
|
|
817 |
tmp = x >> EXPONENT_SHIFT_SMALL64; |
|
|
818 |
*pexponent_x = (int) (tmp & EXPONENT_MASK64); |
|
|
819 |
// coefficient |
|
|
820 |
*pcoefficient_x = (x & SMALL_COEFF_MASK64); |
|
|
821 |
|
|
|
822 |
return *pcoefficient_x; |
|
|
823 |
} |
|
|
824 |
|
|
|
825 |
// |
|
|
826 |
// BID64 pack macro (general form) |
|
|
827 |
// |
|
|
828 |
__BID_INLINE__ UINT64 |
|
|
829 |
get_BID64 (UINT64 sgn, int expon, UINT64 coeff, int rmode, |
|
|
830 |
unsigned *fpsc) { |
|
|
831 |
UINT128 Stemp, Q_low; |
|
|
832 |
UINT64 QH, r, mask, C64, remainder_h, CY, carry; |
|
|
833 |
int extra_digits, amount, amount2; |
|
|
834 |
unsigned status; |
|
|
835 |
|
|
|
836 |
if (coeff > 9999999999999999ull) { |
|
|
837 |
expon++; |
|
|
838 |
coeff = 1000000000000000ull; |
|
|
839 |
} |
|
|
840 |
// check for possible underflow/overflow |
|
|
841 |
if (((unsigned) expon) >= 3 * 256) { |
|
|
842 |
if (expon < 0) { |
|
|
843 |
// underflow |
|
|
844 |
if (expon + MAX_FORMAT_DIGITS < 0) { |
|
|
845 |
#ifdef SET_STATUS_FLAGS |
|
|
846 |
__set_status_flags (fpsc, |
|
|
847 |
UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
848 |
#endif |
|
|
849 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
850 |
#ifndef IEEE_ROUND_NEAREST |
|
|
851 |
if (rmode == ROUNDING_DOWN && sgn) |
|
|
852 |
return 0x8000000000000001ull; |
|
|
853 |
if (rmode == ROUNDING_UP && !sgn) |
|
|
854 |
return 1ull; |
|
|
855 |
#endif |
|
|
856 |
#endif |
|
|
857 |
// result is 0 |
|
|
858 |
return sgn; |
|
|
859 |
} |
|
|
860 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
861 |
#ifndef IEEE_ROUND_NEAREST |
|
|
862 |
if (sgn && (unsigned) (rmode - 1) < 2) |
|
|
863 |
rmode = 3 - rmode; |
|
|
864 |
#endif |
|
|
865 |
#endif |
|
|
866 |
// get digits to be shifted out |
|
|
867 |
extra_digits = -expon; |
|
|
868 |
coeff += round_const_table[rmode][extra_digits]; |
|
|
869 |
|
|
|
870 |
// get coeff*(2^M[extra_digits])/10^extra_digits |
|
|
871 |
__mul_64x128_full (QH, Q_low, coeff, |
|
|
872 |
reciprocals10_128[extra_digits]); |
|
|
873 |
|
|
|
874 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
875 |
amount = recip_scale[extra_digits]; |
|
|
876 |
|
|
|
877 |
C64 = QH >> amount; |
|
|
878 |
|
|
|
879 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
880 |
#ifndef IEEE_ROUND_NEAREST |
|
|
881 |
if (rmode == 0) //ROUNDING_TO_NEAREST |
|
|
882 |
#endif |
|
|
883 |
if (C64 & 1) { |
|
|
884 |
// check whether fractional part of initial_P/10^extra_digits is exactly .5 |
|
|
885 |
|
|
|
886 |
// get remainder |
|
|
887 |
amount2 = 64 - amount; |
|
|
888 |
remainder_h = 0; |
|
|
889 |
remainder_h--; |
|
|
890 |
remainder_h >>= amount2; |
|
|
891 |
remainder_h = remainder_h & QH; |
|
|
892 |
|
|
|
893 |
if (!remainder_h |
|
|
894 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
895 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
896 |
&& Q_low.w[0] < |
|
|
897 |
reciprocals10_128[extra_digits].w[0]))) { |
|
|
898 |
C64--; |
|
|
899 |
} |
|
|
900 |
} |
|
|
901 |
#endif |
|
|
902 |
|
|
|
903 |
#ifdef SET_STATUS_FLAGS |
|
|
904 |
|
|
|
905 |
if (is_inexact (fpsc)) |
|
|
906 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION); |
|
|
907 |
else { |
|
|
908 |
status = INEXACT_EXCEPTION; |
|
|
909 |
// get remainder |
|
|
910 |
remainder_h = QH << (64 - amount); |
|
|
911 |
|
|
|
912 |
switch (rmode) { |
|
|
913 |
case ROUNDING_TO_NEAREST: |
|
|
914 |
case ROUNDING_TIES_AWAY: |
|
|
915 |
// test whether fractional part is 0 |
|
|
916 |
if (remainder_h == 0x8000000000000000ull |
|
|
917 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
918 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
919 |
&& Q_low.w[0] < |
|
|
920 |
reciprocals10_128[extra_digits].w[0]))) |
|
|
921 |
status = EXACT_STATUS; |
|
|
922 |
break; |
|
|
923 |
case ROUNDING_DOWN: |
|
|
924 |
case ROUNDING_TO_ZERO: |
|
|
925 |
if (!remainder_h |
|
|
926 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
927 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
928 |
&& Q_low.w[0] < |
|
|
929 |
reciprocals10_128[extra_digits].w[0]))) |
|
|
930 |
status = EXACT_STATUS; |
|
|
931 |
break; |
|
|
932 |
default: |
|
|
933 |
// round up |
|
|
934 |
__add_carry_out (Stemp.w[0], CY, Q_low.w[0], |
|
|
935 |
reciprocals10_128[extra_digits].w[0]); |
|
|
936 |
__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], |
|
|
937 |
reciprocals10_128[extra_digits].w[1], CY); |
|
|
938 |
if ((remainder_h >> (64 - amount)) + carry >= |
|
|
939 |
(((UINT64) 1) << amount)) |
|
|
940 |
status = EXACT_STATUS; |
|
|
941 |
} |
|
|
942 |
|
|
|
943 |
if (status != EXACT_STATUS) |
|
|
944 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); |
|
|
945 |
} |
|
|
946 |
|
|
|
947 |
#endif |
|
|
948 |
|
|
|
949 |
return sgn | C64; |
|
|
950 |
} |
|
|
951 |
while (coeff < 1000000000000000ull && expon >= 3 * 256) { |
|
|
952 |
expon--; |
|
|
953 |
coeff = (coeff << 3) + (coeff << 1); |
|
|
954 |
} |
|
|
955 |
if (expon > DECIMAL_MAX_EXPON_64) { |
|
|
956 |
#ifdef SET_STATUS_FLAGS |
|
|
957 |
__set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
958 |
#endif |
|
|
959 |
// overflow |
|
|
960 |
r = sgn | INFINITY_MASK64; |
|
|
961 |
switch (rmode) { |
|
|
962 |
case ROUNDING_DOWN: |
|
|
963 |
if (!sgn) |
|
|
964 |
r = LARGEST_BID64; |
|
|
965 |
break; |
|
|
966 |
case ROUNDING_TO_ZERO: |
|
|
967 |
r = sgn | LARGEST_BID64; |
|
|
968 |
break; |
|
|
969 |
case ROUNDING_UP: |
|
|
970 |
// round up |
|
|
971 |
if (sgn) |
|
|
972 |
r = SMALLEST_BID64; |
|
|
973 |
} |
|
|
974 |
return r; |
|
|
975 |
} |
|
|
976 |
} |
|
|
977 |
|
|
|
978 |
mask = 1; |
|
|
979 |
mask <<= EXPONENT_SHIFT_SMALL64; |
|
|
980 |
|
|
|
981 |
// check whether coefficient fits in 10*5+3 bits |
|
|
982 |
if (coeff < mask) { |
|
|
983 |
r = expon; |
|
|
984 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
985 |
r |= (coeff | sgn); |
|
|
986 |
return r; |
|
|
987 |
} |
|
|
988 |
// special format |
|
|
989 |
|
|
|
990 |
// eliminate the case coeff==10^16 after rounding |
|
|
991 |
if (coeff == 10000000000000000ull) { |
|
|
992 |
r = expon + 1; |
|
|
993 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
994 |
r |= (1000000000000000ull | sgn); |
|
|
995 |
return r; |
|
|
996 |
} |
|
|
997 |
|
|
|
998 |
r = expon; |
|
|
999 |
r <<= EXPONENT_SHIFT_LARGE64; |
|
|
1000 |
r |= (sgn | SPECIAL_ENCODING_MASK64); |
|
|
1001 |
// add coeff, without leading bits |
|
|
1002 |
mask = (mask >> 2) - 1; |
|
|
1003 |
coeff &= mask; |
|
|
1004 |
r |= coeff; |
|
|
1005 |
|
|
|
1006 |
return r; |
|
|
1007 |
} |
|
|
1008 |
|
|
|
1009 |
|
|
|
1010 |
|
|
|
1011 |
|
|
|
1012 |
// |
|
|
1013 |
// No overflow/underflow checking |
|
|
1014 |
// |
|
|
1015 |
__BID_INLINE__ UINT64 |
|
|
1016 |
fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { |
|
|
1017 |
UINT64 r, mask; |
|
|
1018 |
|
|
|
1019 |
mask = 1; |
|
|
1020 |
mask <<= EXPONENT_SHIFT_SMALL64; |
|
|
1021 |
|
|
|
1022 |
// check whether coefficient fits in 10*5+3 bits |
|
|
1023 |
if (coeff < mask) { |
|
|
1024 |
r = expon; |
|
|
1025 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1026 |
r |= (coeff | sgn); |
|
|
1027 |
return r; |
|
|
1028 |
} |
|
|
1029 |
// special format |
|
|
1030 |
|
|
|
1031 |
// eliminate the case coeff==10^16 after rounding |
|
|
1032 |
if (coeff == 10000000000000000ull) { |
|
|
1033 |
r = expon + 1; |
|
|
1034 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1035 |
r |= (1000000000000000ull | sgn); |
|
|
1036 |
return r; |
|
|
1037 |
} |
|
|
1038 |
|
|
|
1039 |
r = expon; |
|
|
1040 |
r <<= EXPONENT_SHIFT_LARGE64; |
|
|
1041 |
r |= (sgn | SPECIAL_ENCODING_MASK64); |
|
|
1042 |
// add coeff, without leading bits |
|
|
1043 |
mask = (mask >> 2) - 1; |
|
|
1044 |
coeff &= mask; |
|
|
1045 |
r |= coeff; |
|
|
1046 |
|
|
|
1047 |
return r; |
|
|
1048 |
} |
|
|
1049 |
|
|
|
1050 |
|
|
|
1051 |
// |
|
|
1052 |
// no underflow checking |
|
|
1053 |
// |
|
|
1054 |
__BID_INLINE__ UINT64 |
|
|
1055 |
fast_get_BID64_check_OF (UINT64 sgn, int expon, UINT64 coeff, int rmode, |
|
|
1056 |
unsigned *fpsc) { |
|
|
1057 |
UINT64 r, mask; |
|
|
1058 |
|
|
|
1059 |
if (((unsigned) expon) >= 3 * 256 - 1) { |
|
|
1060 |
if ((expon == 3 * 256 - 1) && coeff == 10000000000000000ull) { |
|
|
1061 |
expon = 3 * 256; |
|
|
1062 |
coeff = 1000000000000000ull; |
|
|
1063 |
} |
|
|
1064 |
|
|
|
1065 |
if (((unsigned) expon) >= 3 * 256) { |
|
|
1066 |
while (coeff < 1000000000000000ull && expon >= 3 * 256) { |
|
|
1067 |
expon--; |
|
|
1068 |
coeff = (coeff << 3) + (coeff << 1); |
|
|
1069 |
} |
|
|
1070 |
if (expon > DECIMAL_MAX_EXPON_64) { |
|
|
1071 |
#ifdef SET_STATUS_FLAGS |
|
|
1072 |
__set_status_flags (fpsc, |
|
|
1073 |
OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1074 |
#endif |
|
|
1075 |
// overflow |
|
|
1076 |
r = sgn | INFINITY_MASK64; |
|
|
1077 |
switch (rmode) { |
|
|
1078 |
case ROUNDING_DOWN: |
|
|
1079 |
if (!sgn) |
|
|
1080 |
r = LARGEST_BID64; |
|
|
1081 |
break; |
|
|
1082 |
case ROUNDING_TO_ZERO: |
|
|
1083 |
r = sgn | LARGEST_BID64; |
|
|
1084 |
break; |
|
|
1085 |
case ROUNDING_UP: |
|
|
1086 |
// round up |
|
|
1087 |
if (sgn) |
|
|
1088 |
r = SMALLEST_BID64; |
|
|
1089 |
} |
|
|
1090 |
return r; |
|
|
1091 |
} |
|
|
1092 |
} |
|
|
1093 |
} |
|
|
1094 |
|
|
|
1095 |
mask = 1; |
|
|
1096 |
mask <<= EXPONENT_SHIFT_SMALL64; |
|
|
1097 |
|
|
|
1098 |
// check whether coefficient fits in 10*5+3 bits |
|
|
1099 |
if (coeff < mask) { |
|
|
1100 |
r = expon; |
|
|
1101 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1102 |
r |= (coeff | sgn); |
|
|
1103 |
return r; |
|
|
1104 |
} |
|
|
1105 |
// special format |
|
|
1106 |
|
|
|
1107 |
// eliminate the case coeff==10^16 after rounding |
|
|
1108 |
if (coeff == 10000000000000000ull) { |
|
|
1109 |
r = expon + 1; |
|
|
1110 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1111 |
r |= (1000000000000000ull | sgn); |
|
|
1112 |
return r; |
|
|
1113 |
} |
|
|
1114 |
|
|
|
1115 |
r = expon; |
|
|
1116 |
r <<= EXPONENT_SHIFT_LARGE64; |
|
|
1117 |
r |= (sgn | SPECIAL_ENCODING_MASK64); |
|
|
1118 |
// add coeff, without leading bits |
|
|
1119 |
mask = (mask >> 2) - 1; |
|
|
1120 |
coeff &= mask; |
|
|
1121 |
r |= coeff; |
|
|
1122 |
|
|
|
1123 |
return r; |
|
|
1124 |
} |
|
|
1125 |
|
|
|
1126 |
|
|
|
1127 |
// |
|
|
1128 |
// No overflow/underflow checking |
|
|
1129 |
// or checking for coefficients equal to 10^16 (after rounding) |
|
|
1130 |
// |
|
|
1131 |
__BID_INLINE__ UINT64 |
|
|
1132 |
very_fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { |
|
|
1133 |
UINT64 r, mask; |
|
|
1134 |
|
|
|
1135 |
mask = 1; |
|
|
1136 |
mask <<= EXPONENT_SHIFT_SMALL64; |
|
|
1137 |
|
|
|
1138 |
// check whether coefficient fits in 10*5+3 bits |
|
|
1139 |
if (coeff < mask) { |
|
|
1140 |
r = expon; |
|
|
1141 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1142 |
r |= (coeff | sgn); |
|
|
1143 |
return r; |
|
|
1144 |
} |
|
|
1145 |
// special format |
|
|
1146 |
r = expon; |
|
|
1147 |
r <<= EXPONENT_SHIFT_LARGE64; |
|
|
1148 |
r |= (sgn | SPECIAL_ENCODING_MASK64); |
|
|
1149 |
// add coeff, without leading bits |
|
|
1150 |
mask = (mask >> 2) - 1; |
|
|
1151 |
coeff &= mask; |
|
|
1152 |
r |= coeff; |
|
|
1153 |
|
|
|
1154 |
return r; |
|
|
1155 |
} |
|
|
1156 |
|
|
|
1157 |
// |
|
|
1158 |
// No overflow/underflow checking or checking for coefficients above 2^53 |
|
|
1159 |
// |
|
|
1160 |
__BID_INLINE__ UINT64 |
|
|
1161 |
very_fast_get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff) { |
|
|
1162 |
// no UF/OF |
|
|
1163 |
UINT64 r; |
|
|
1164 |
|
|
|
1165 |
r = expon; |
|
|
1166 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1167 |
r |= (coeff | sgn); |
|
|
1168 |
return r; |
|
|
1169 |
} |
|
|
1170 |
|
|
|
1171 |
|
|
|
1172 |
// |
|
|
1173 |
// This pack macro is used when underflow is known to occur |
|
|
1174 |
// |
|
|
1175 |
__BID_INLINE__ UINT64 |
|
|
1176 |
get_BID64_UF (UINT64 sgn, int expon, UINT64 coeff, UINT64 R, int rmode, |
|
|
1177 |
unsigned *fpsc) { |
|
|
1178 |
UINT128 C128, Q_low, Stemp; |
|
|
1179 |
UINT64 C64, remainder_h, QH, carry, CY; |
|
|
1180 |
int extra_digits, amount, amount2; |
|
|
1181 |
unsigned status; |
|
|
1182 |
|
|
|
1183 |
// underflow |
|
|
1184 |
if (expon + MAX_FORMAT_DIGITS < 0) { |
|
|
1185 |
#ifdef SET_STATUS_FLAGS |
|
|
1186 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1187 |
#endif |
|
|
1188 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1189 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1190 |
if (rmode == ROUNDING_DOWN && sgn) |
|
|
1191 |
return 0x8000000000000001ull; |
|
|
1192 |
if (rmode == ROUNDING_UP && !sgn) |
|
|
1193 |
return 1ull; |
|
|
1194 |
#endif |
|
|
1195 |
#endif |
|
|
1196 |
// result is 0 |
|
|
1197 |
return sgn; |
|
|
1198 |
} |
|
|
1199 |
// 10*coeff |
|
|
1200 |
coeff = (coeff << 3) + (coeff << 1); |
|
|
1201 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1202 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1203 |
if (sgn && (unsigned) (rmode - 1) < 2) |
|
|
1204 |
rmode = 3 - rmode; |
|
|
1205 |
#endif |
|
|
1206 |
#endif |
|
|
1207 |
if (R) |
|
|
1208 |
coeff |= 1; |
|
|
1209 |
// get digits to be shifted out |
|
|
1210 |
extra_digits = 1 - expon; |
|
|
1211 |
C128.w[0] = coeff + round_const_table[rmode][extra_digits]; |
|
|
1212 |
|
|
|
1213 |
// get coeff*(2^M[extra_digits])/10^extra_digits |
|
|
1214 |
__mul_64x128_full (QH, Q_low, C128.w[0], |
|
|
1215 |
reciprocals10_128[extra_digits]); |
|
|
1216 |
|
|
|
1217 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
1218 |
amount = recip_scale[extra_digits]; |
|
|
1219 |
|
|
|
1220 |
C64 = QH >> amount; |
|
|
1221 |
//__shr_128(C128, Q_high, amount); |
|
|
1222 |
|
|
|
1223 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1224 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1225 |
if (rmode == 0) //ROUNDING_TO_NEAREST |
|
|
1226 |
#endif |
|
|
1227 |
if (C64 & 1) { |
|
|
1228 |
// check whether fractional part of initial_P/10^extra_digits is exactly .5 |
|
|
1229 |
|
|
|
1230 |
// get remainder |
|
|
1231 |
amount2 = 64 - amount; |
|
|
1232 |
remainder_h = 0; |
|
|
1233 |
remainder_h--; |
|
|
1234 |
remainder_h >>= amount2; |
|
|
1235 |
remainder_h = remainder_h & QH; |
|
|
1236 |
|
|
|
1237 |
if (!remainder_h |
|
|
1238 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
1239 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
1240 |
&& Q_low.w[0] < |
|
|
1241 |
reciprocals10_128[extra_digits].w[0]))) { |
|
|
1242 |
C64--; |
|
|
1243 |
} |
|
|
1244 |
} |
|
|
1245 |
#endif |
|
|
1246 |
|
|
|
1247 |
#ifdef SET_STATUS_FLAGS |
|
|
1248 |
|
|
|
1249 |
if (is_inexact (fpsc)) |
|
|
1250 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION); |
|
|
1251 |
else { |
|
|
1252 |
status = INEXACT_EXCEPTION; |
|
|
1253 |
// get remainder |
|
|
1254 |
remainder_h = QH << (64 - amount); |
|
|
1255 |
|
|
|
1256 |
switch (rmode) { |
|
|
1257 |
case ROUNDING_TO_NEAREST: |
|
|
1258 |
case ROUNDING_TIES_AWAY: |
|
|
1259 |
// test whether fractional part is 0 |
|
|
1260 |
if (remainder_h == 0x8000000000000000ull |
|
|
1261 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
1262 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
1263 |
&& Q_low.w[0] < |
|
|
1264 |
reciprocals10_128[extra_digits].w[0]))) |
|
|
1265 |
status = EXACT_STATUS; |
|
|
1266 |
break; |
|
|
1267 |
case ROUNDING_DOWN: |
|
|
1268 |
case ROUNDING_TO_ZERO: |
|
|
1269 |
if (!remainder_h |
|
|
1270 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
1271 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
1272 |
&& Q_low.w[0] < |
|
|
1273 |
reciprocals10_128[extra_digits].w[0]))) |
|
|
1274 |
status = EXACT_STATUS; |
|
|
1275 |
break; |
|
|
1276 |
default: |
|
|
1277 |
// round up |
|
|
1278 |
__add_carry_out (Stemp.w[0], CY, Q_low.w[0], |
|
|
1279 |
reciprocals10_128[extra_digits].w[0]); |
|
|
1280 |
__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], |
|
|
1281 |
reciprocals10_128[extra_digits].w[1], CY); |
|
|
1282 |
if ((remainder_h >> (64 - amount)) + carry >= |
|
|
1283 |
(((UINT64) 1) << amount)) |
|
|
1284 |
status = EXACT_STATUS; |
|
|
1285 |
} |
|
|
1286 |
|
|
|
1287 |
if (status != EXACT_STATUS) |
|
|
1288 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); |
|
|
1289 |
} |
|
|
1290 |
|
|
|
1291 |
#endif |
|
|
1292 |
|
|
|
1293 |
return sgn | C64; |
|
|
1294 |
|
|
|
1295 |
} |
|
|
1296 |
|
|
|
1297 |
|
|
|
1298 |
|
|
|
1299 |
// |
|
|
1300 |
// This pack macro doesnot check for coefficients above 2^53 |
|
|
1301 |
// |
|
|
1302 |
__BID_INLINE__ UINT64 |
|
|
1303 |
get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff, |
|
|
1304 |
int rmode, unsigned *fpsc) { |
|
|
1305 |
UINT128 C128, Q_low, Stemp; |
|
|
1306 |
UINT64 r, mask, C64, remainder_h, QH, carry, CY; |
|
|
1307 |
int extra_digits, amount, amount2; |
|
|
1308 |
unsigned status; |
|
|
1309 |
|
|
|
1310 |
// check for possible underflow/overflow |
|
|
1311 |
if (((unsigned) expon) >= 3 * 256) { |
|
|
1312 |
if (expon < 0) { |
|
|
1313 |
// underflow |
|
|
1314 |
if (expon + MAX_FORMAT_DIGITS < 0) { |
|
|
1315 |
#ifdef SET_STATUS_FLAGS |
|
|
1316 |
__set_status_flags (fpsc, |
|
|
1317 |
UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1318 |
#endif |
|
|
1319 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1320 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1321 |
if (rmode == ROUNDING_DOWN && sgn) |
|
|
1322 |
return 0x8000000000000001ull; |
|
|
1323 |
if (rmode == ROUNDING_UP && !sgn) |
|
|
1324 |
return 1ull; |
|
|
1325 |
#endif |
|
|
1326 |
#endif |
|
|
1327 |
// result is 0 |
|
|
1328 |
return sgn; |
|
|
1329 |
} |
|
|
1330 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1331 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1332 |
if (sgn && (unsigned) (rmode - 1) < 2) |
|
|
1333 |
rmode = 3 - rmode; |
|
|
1334 |
#endif |
|
|
1335 |
#endif |
|
|
1336 |
// get digits to be shifted out |
|
|
1337 |
extra_digits = -expon; |
|
|
1338 |
C128.w[0] = coeff + round_const_table[rmode][extra_digits]; |
|
|
1339 |
|
|
|
1340 |
// get coeff*(2^M[extra_digits])/10^extra_digits |
|
|
1341 |
__mul_64x128_full (QH, Q_low, C128.w[0], |
|
|
1342 |
reciprocals10_128[extra_digits]); |
|
|
1343 |
|
|
|
1344 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
1345 |
amount = recip_scale[extra_digits]; |
|
|
1346 |
|
|
|
1347 |
C64 = QH >> amount; |
|
|
1348 |
|
|
|
1349 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1350 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1351 |
if (rmode == 0) //ROUNDING_TO_NEAREST |
|
|
1352 |
#endif |
|
|
1353 |
if (C64 & 1) { |
|
|
1354 |
// check whether fractional part of initial_P/10^extra_digits is exactly .5 |
|
|
1355 |
|
|
|
1356 |
// get remainder |
|
|
1357 |
amount2 = 64 - amount; |
|
|
1358 |
remainder_h = 0; |
|
|
1359 |
remainder_h--; |
|
|
1360 |
remainder_h >>= amount2; |
|
|
1361 |
remainder_h = remainder_h & QH; |
|
|
1362 |
|
|
|
1363 |
if (!remainder_h |
|
|
1364 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
1365 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
1366 |
&& Q_low.w[0] < |
|
|
1367 |
reciprocals10_128[extra_digits].w[0]))) { |
|
|
1368 |
C64--; |
|
|
1369 |
} |
|
|
1370 |
} |
|
|
1371 |
#endif |
|
|
1372 |
|
|
|
1373 |
#ifdef SET_STATUS_FLAGS |
|
|
1374 |
|
|
|
1375 |
if (is_inexact (fpsc)) |
|
|
1376 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION); |
|
|
1377 |
else { |
|
|
1378 |
status = INEXACT_EXCEPTION; |
|
|
1379 |
// get remainder |
|
|
1380 |
remainder_h = QH << (64 - amount); |
|
|
1381 |
|
|
|
1382 |
switch (rmode) { |
|
|
1383 |
case ROUNDING_TO_NEAREST: |
|
|
1384 |
case ROUNDING_TIES_AWAY: |
|
|
1385 |
// test whether fractional part is 0 |
|
|
1386 |
if (remainder_h == 0x8000000000000000ull |
|
|
1387 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
1388 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
1389 |
&& Q_low.w[0] < |
|
|
1390 |
reciprocals10_128[extra_digits].w[0]))) |
|
|
1391 |
status = EXACT_STATUS; |
|
|
1392 |
break; |
|
|
1393 |
case ROUNDING_DOWN: |
|
|
1394 |
case ROUNDING_TO_ZERO: |
|
|
1395 |
if (!remainder_h |
|
|
1396 |
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
|
|
1397 |
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] |
|
|
1398 |
&& Q_low.w[0] < |
|
|
1399 |
reciprocals10_128[extra_digits].w[0]))) |
|
|
1400 |
status = EXACT_STATUS; |
|
|
1401 |
break; |
|
|
1402 |
default: |
|
|
1403 |
// round up |
|
|
1404 |
__add_carry_out (Stemp.w[0], CY, Q_low.w[0], |
|
|
1405 |
reciprocals10_128[extra_digits].w[0]); |
|
|
1406 |
__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], |
|
|
1407 |
reciprocals10_128[extra_digits].w[1], CY); |
|
|
1408 |
if ((remainder_h >> (64 - amount)) + carry >= |
|
|
1409 |
(((UINT64) 1) << amount)) |
|
|
1410 |
status = EXACT_STATUS; |
|
|
1411 |
} |
|
|
1412 |
|
|
|
1413 |
if (status != EXACT_STATUS) |
|
|
1414 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); |
|
|
1415 |
} |
|
|
1416 |
|
|
|
1417 |
#endif |
|
|
1418 |
|
|
|
1419 |
return sgn | C64; |
|
|
1420 |
} |
|
|
1421 |
|
|
|
1422 |
while (coeff < 1000000000000000ull && expon >= 3 * 256) { |
|
|
1423 |
expon--; |
|
|
1424 |
coeff = (coeff << 3) + (coeff << 1); |
|
|
1425 |
} |
|
|
1426 |
if (expon > DECIMAL_MAX_EXPON_64) { |
|
|
1427 |
#ifdef SET_STATUS_FLAGS |
|
|
1428 |
__set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1429 |
#endif |
|
|
1430 |
// overflow |
|
|
1431 |
r = sgn | INFINITY_MASK64; |
|
|
1432 |
switch (rmode) { |
|
|
1433 |
case ROUNDING_DOWN: |
|
|
1434 |
if (!sgn) |
|
|
1435 |
r = LARGEST_BID64; |
|
|
1436 |
break; |
|
|
1437 |
case ROUNDING_TO_ZERO: |
|
|
1438 |
r = sgn | LARGEST_BID64; |
|
|
1439 |
break; |
|
|
1440 |
case ROUNDING_UP: |
|
|
1441 |
// round up |
|
|
1442 |
if (sgn) |
|
|
1443 |
r = SMALLEST_BID64; |
|
|
1444 |
} |
|
|
1445 |
return r; |
|
|
1446 |
} else { |
|
|
1447 |
mask = 1; |
|
|
1448 |
mask <<= EXPONENT_SHIFT_SMALL64; |
|
|
1449 |
if (coeff >= mask) { |
|
|
1450 |
r = expon; |
|
|
1451 |
r <<= EXPONENT_SHIFT_LARGE64; |
|
|
1452 |
r |= (sgn | SPECIAL_ENCODING_MASK64); |
|
|
1453 |
// add coeff, without leading bits |
|
|
1454 |
mask = (mask >> 2) - 1; |
|
|
1455 |
coeff &= mask; |
|
|
1456 |
r |= coeff; |
|
|
1457 |
return r; |
|
|
1458 |
} |
|
|
1459 |
} |
|
|
1460 |
} |
|
|
1461 |
|
|
|
1462 |
r = expon; |
|
|
1463 |
r <<= EXPONENT_SHIFT_SMALL64; |
|
|
1464 |
r |= (coeff | sgn); |
|
|
1465 |
|
|
|
1466 |
return r; |
|
|
1467 |
} |
|
|
1468 |
|
|
|
1469 |
|
|
|
1470 |
/***************************************************************************** |
|
|
1471 |
* |
|
|
1472 |
* BID128 pack/unpack macros |
|
|
1473 |
* |
|
|
1474 |
*****************************************************************************/ |
|
|
1475 |
|
|
|
1476 |
// |
|
|
1477 |
// Macro for handling BID128 underflow |
|
|
1478 |
// sticky bit given as additional argument |
|
|
1479 |
// |
|
|
1480 |
__BID_INLINE__ UINT128 * |
|
|
1481 |
handle_UF_128_rem (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, |
|
|
1482 |
UINT64 R, unsigned *prounding_mode, unsigned *fpsc) { |
|
|
1483 |
UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CQ2, CQ8; |
|
|
1484 |
UINT64 carry, CY; |
|
|
1485 |
int ed2, amount; |
|
|
1486 |
unsigned rmode, status; |
|
|
1487 |
|
|
|
1488 |
// UF occurs |
|
|
1489 |
if (expon + MAX_FORMAT_DIGITS_128 < 0) { |
|
|
1490 |
#ifdef SET_STATUS_FLAGS |
|
|
1491 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1492 |
#endif |
|
|
1493 |
pres->w[1] = sgn; |
|
|
1494 |
pres->w[0] = 0; |
|
|
1495 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1496 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1497 |
if ((sgn && *prounding_mode == ROUNDING_DOWN) |
|
|
1498 |
|| (!sgn && *prounding_mode == ROUNDING_UP)) |
|
|
1499 |
pres->w[0] = 1ull; |
|
|
1500 |
#endif |
|
|
1501 |
#endif |
|
|
1502 |
return pres; |
|
|
1503 |
} |
|
|
1504 |
// CQ *= 10 |
|
|
1505 |
CQ2.w[1] = (CQ.w[1] << 1) | (CQ.w[0] >> 63); |
|
|
1506 |
CQ2.w[0] = CQ.w[0] << 1; |
|
|
1507 |
CQ8.w[1] = (CQ.w[1] << 3) | (CQ.w[0] >> 61); |
|
|
1508 |
CQ8.w[0] = CQ.w[0] << 3; |
|
|
1509 |
__add_128_128 (CQ, CQ2, CQ8); |
|
|
1510 |
|
|
|
1511 |
// add remainder |
|
|
1512 |
if (R) |
|
|
1513 |
CQ.w[0] |= 1; |
|
|
1514 |
|
|
|
1515 |
ed2 = 1 - expon; |
|
|
1516 |
// add rounding constant to CQ |
|
|
1517 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1518 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1519 |
rmode = *prounding_mode; |
|
|
1520 |
if (sgn && (unsigned) (rmode - 1) < 2) |
|
|
1521 |
rmode = 3 - rmode; |
|
|
1522 |
#else |
|
|
1523 |
rmode = 0; |
|
|
1524 |
#endif |
|
|
1525 |
#else |
|
|
1526 |
rmode = 0; |
|
|
1527 |
#endif |
|
|
1528 |
T128 = round_const_table_128[rmode][ed2]; |
|
|
1529 |
__add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); |
|
|
1530 |
CQ.w[1] = CQ.w[1] + T128.w[1] + carry; |
|
|
1531 |
|
|
|
1532 |
TP128 = reciprocals10_128[ed2]; |
|
|
1533 |
__mul_128x128_full (Qh, Ql, CQ, TP128); |
|
|
1534 |
amount = recip_scale[ed2]; |
|
|
1535 |
|
|
|
1536 |
if (amount >= 64) { |
|
|
1537 |
CQ.w[0] = Qh.w[1] >> (amount - 64); |
|
|
1538 |
CQ.w[1] = 0; |
|
|
1539 |
} else { |
|
|
1540 |
__shr_128 (CQ, Qh, amount); |
|
|
1541 |
} |
|
|
1542 |
|
|
|
1543 |
expon = 0; |
|
|
1544 |
|
|
|
1545 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1546 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1547 |
if (!(*prounding_mode)) |
|
|
1548 |
#endif |
|
|
1549 |
if (CQ.w[0] & 1) { |
|
|
1550 |
// check whether fractional part of initial_P/10^ed1 is exactly .5 |
|
|
1551 |
|
|
|
1552 |
// get remainder |
|
|
1553 |
__shl_128_long (Qh1, Qh, (128 - amount)); |
|
|
1554 |
|
|
|
1555 |
if (!Qh1.w[1] && !Qh1.w[0] |
|
|
1556 |
&& (Ql.w[1] < reciprocals10_128[ed2].w[1] |
|
|
1557 |
|| (Ql.w[1] == reciprocals10_128[ed2].w[1] |
|
|
1558 |
&& Ql.w[0] < reciprocals10_128[ed2].w[0]))) { |
|
|
1559 |
CQ.w[0]--; |
|
|
1560 |
} |
|
|
1561 |
} |
|
|
1562 |
#endif |
|
|
1563 |
|
|
|
1564 |
#ifdef SET_STATUS_FLAGS |
|
|
1565 |
|
|
|
1566 |
if (is_inexact (fpsc)) |
|
|
1567 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION); |
|
|
1568 |
else { |
|
|
1569 |
status = INEXACT_EXCEPTION; |
|
|
1570 |
// get remainder |
|
|
1571 |
__shl_128_long (Qh1, Qh, (128 - amount)); |
|
|
1572 |
|
|
|
1573 |
switch (rmode) { |
|
|
1574 |
case ROUNDING_TO_NEAREST: |
|
|
1575 |
case ROUNDING_TIES_AWAY: |
|
|
1576 |
// test whether fractional part is 0 |
|
|
1577 |
if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) |
|
|
1578 |
&& (Ql.w[1] < reciprocals10_128[ed2].w[1] |
|
|
1579 |
|| (Ql.w[1] == reciprocals10_128[ed2].w[1] |
|
|
1580 |
&& Ql.w[0] < reciprocals10_128[ed2].w[0]))) |
|
|
1581 |
status = EXACT_STATUS; |
|
|
1582 |
break; |
|
|
1583 |
case ROUNDING_DOWN: |
|
|
1584 |
case ROUNDING_TO_ZERO: |
|
|
1585 |
if ((!Qh1.w[1]) && (!Qh1.w[0]) |
|
|
1586 |
&& (Ql.w[1] < reciprocals10_128[ed2].w[1] |
|
|
1587 |
|| (Ql.w[1] == reciprocals10_128[ed2].w[1] |
|
|
1588 |
&& Ql.w[0] < reciprocals10_128[ed2].w[0]))) |
|
|
1589 |
status = EXACT_STATUS; |
|
|
1590 |
break; |
|
|
1591 |
default: |
|
|
1592 |
// round up |
|
|
1593 |
__add_carry_out (Stemp.w[0], CY, Ql.w[0], |
|
|
1594 |
reciprocals10_128[ed2].w[0]); |
|
|
1595 |
__add_carry_in_out (Stemp.w[1], carry, Ql.w[1], |
|
|
1596 |
reciprocals10_128[ed2].w[1], CY); |
|
|
1597 |
__shr_128_long (Qh, Qh1, (128 - amount)); |
|
|
1598 |
Tmp.w[0] = 1; |
|
|
1599 |
Tmp.w[1] = 0; |
|
|
1600 |
__shl_128_long (Tmp1, Tmp, amount); |
|
|
1601 |
Qh.w[0] += carry; |
|
|
1602 |
if (Qh.w[0] < carry) |
|
|
1603 |
Qh.w[1]++; |
|
|
1604 |
if (__unsigned_compare_ge_128 (Qh, Tmp1)) |
|
|
1605 |
status = EXACT_STATUS; |
|
|
1606 |
} |
|
|
1607 |
|
|
|
1608 |
if (status != EXACT_STATUS) |
|
|
1609 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); |
|
|
1610 |
} |
|
|
1611 |
|
|
|
1612 |
#endif |
|
|
1613 |
|
|
|
1614 |
pres->w[1] = sgn | CQ.w[1]; |
|
|
1615 |
pres->w[0] = CQ.w[0]; |
|
|
1616 |
|
|
|
1617 |
return pres; |
|
|
1618 |
|
|
|
1619 |
} |
|
|
1620 |
|
|
|
1621 |
|
|
|
1622 |
// |
|
|
1623 |
// Macro for handling BID128 underflow |
|
|
1624 |
// |
|
|
1625 |
__BID_INLINE__ UINT128 * |
|
|
1626 |
handle_UF_128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, |
|
|
1627 |
unsigned *prounding_mode, unsigned *fpsc) { |
|
|
1628 |
UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1; |
|
|
1629 |
UINT64 carry, CY; |
|
|
1630 |
int ed2, amount; |
|
|
1631 |
unsigned rmode, status; |
|
|
1632 |
|
|
|
1633 |
// UF occurs |
|
|
1634 |
if (expon + MAX_FORMAT_DIGITS_128 < 0) { |
|
|
1635 |
#ifdef SET_STATUS_FLAGS |
|
|
1636 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1637 |
#endif |
|
|
1638 |
pres->w[1] = sgn; |
|
|
1639 |
pres->w[0] = 0; |
|
|
1640 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1641 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1642 |
if ((sgn && *prounding_mode == ROUNDING_DOWN) |
|
|
1643 |
|| (!sgn && *prounding_mode == ROUNDING_UP)) |
|
|
1644 |
pres->w[0] = 1ull; |
|
|
1645 |
#endif |
|
|
1646 |
#endif |
|
|
1647 |
return pres; |
|
|
1648 |
} |
|
|
1649 |
|
|
|
1650 |
ed2 = 0 - expon; |
|
|
1651 |
// add rounding constant to CQ |
|
|
1652 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1653 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1654 |
rmode = *prounding_mode; |
|
|
1655 |
if (sgn && (unsigned) (rmode - 1) < 2) |
|
|
1656 |
rmode = 3 - rmode; |
|
|
1657 |
#else |
|
|
1658 |
rmode = 0; |
|
|
1659 |
#endif |
|
|
1660 |
#else |
|
|
1661 |
rmode = 0; |
|
|
1662 |
#endif |
|
|
1663 |
|
|
|
1664 |
T128 = round_const_table_128[rmode][ed2]; |
|
|
1665 |
__add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); |
|
|
1666 |
CQ.w[1] = CQ.w[1] + T128.w[1] + carry; |
|
|
1667 |
|
|
|
1668 |
TP128 = reciprocals10_128[ed2]; |
|
|
1669 |
__mul_128x128_full (Qh, Ql, CQ, TP128); |
|
|
1670 |
amount = recip_scale[ed2]; |
|
|
1671 |
|
|
|
1672 |
if (amount >= 64) { |
|
|
1673 |
CQ.w[0] = Qh.w[1] >> (amount - 64); |
|
|
1674 |
CQ.w[1] = 0; |
|
|
1675 |
} else { |
|
|
1676 |
__shr_128 (CQ, Qh, amount); |
|
|
1677 |
} |
|
|
1678 |
|
|
|
1679 |
expon = 0; |
|
|
1680 |
|
|
|
1681 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1682 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1683 |
if (!(*prounding_mode)) |
|
|
1684 |
#endif |
|
|
1685 |
if (CQ.w[0] & 1) { |
|
|
1686 |
// check whether fractional part of initial_P/10^ed1 is exactly .5 |
|
|
1687 |
|
|
|
1688 |
// get remainder |
|
|
1689 |
__shl_128_long (Qh1, Qh, (128 - amount)); |
|
|
1690 |
|
|
|
1691 |
if (!Qh1.w[1] && !Qh1.w[0] |
|
|
1692 |
&& (Ql.w[1] < reciprocals10_128[ed2].w[1] |
|
|
1693 |
|| (Ql.w[1] == reciprocals10_128[ed2].w[1] |
|
|
1694 |
&& Ql.w[0] < reciprocals10_128[ed2].w[0]))) { |
|
|
1695 |
CQ.w[0]--; |
|
|
1696 |
} |
|
|
1697 |
} |
|
|
1698 |
#endif |
|
|
1699 |
|
|
|
1700 |
#ifdef SET_STATUS_FLAGS |
|
|
1701 |
|
|
|
1702 |
if (is_inexact (fpsc)) |
|
|
1703 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION); |
|
|
1704 |
else { |
|
|
1705 |
status = INEXACT_EXCEPTION; |
|
|
1706 |
// get remainder |
|
|
1707 |
__shl_128_long (Qh1, Qh, (128 - amount)); |
|
|
1708 |
|
|
|
1709 |
switch (rmode) { |
|
|
1710 |
case ROUNDING_TO_NEAREST: |
|
|
1711 |
case ROUNDING_TIES_AWAY: |
|
|
1712 |
// test whether fractional part is 0 |
|
|
1713 |
if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) |
|
|
1714 |
&& (Ql.w[1] < reciprocals10_128[ed2].w[1] |
|
|
1715 |
|| (Ql.w[1] == reciprocals10_128[ed2].w[1] |
|
|
1716 |
&& Ql.w[0] < reciprocals10_128[ed2].w[0]))) |
|
|
1717 |
status = EXACT_STATUS; |
|
|
1718 |
break; |
|
|
1719 |
case ROUNDING_DOWN: |
|
|
1720 |
case ROUNDING_TO_ZERO: |
|
|
1721 |
if ((!Qh1.w[1]) && (!Qh1.w[0]) |
|
|
1722 |
&& (Ql.w[1] < reciprocals10_128[ed2].w[1] |
|
|
1723 |
|| (Ql.w[1] == reciprocals10_128[ed2].w[1] |
|
|
1724 |
&& Ql.w[0] < reciprocals10_128[ed2].w[0]))) |
|
|
1725 |
status = EXACT_STATUS; |
|
|
1726 |
break; |
|
|
1727 |
default: |
|
|
1728 |
// round up |
|
|
1729 |
__add_carry_out (Stemp.w[0], CY, Ql.w[0], |
|
|
1730 |
reciprocals10_128[ed2].w[0]); |
|
|
1731 |
__add_carry_in_out (Stemp.w[1], carry, Ql.w[1], |
|
|
1732 |
reciprocals10_128[ed2].w[1], CY); |
|
|
1733 |
__shr_128_long (Qh, Qh1, (128 - amount)); |
|
|
1734 |
Tmp.w[0] = 1; |
|
|
1735 |
Tmp.w[1] = 0; |
|
|
1736 |
__shl_128_long (Tmp1, Tmp, amount); |
|
|
1737 |
Qh.w[0] += carry; |
|
|
1738 |
if (Qh.w[0] < carry) |
|
|
1739 |
Qh.w[1]++; |
|
|
1740 |
if (__unsigned_compare_ge_128 (Qh, Tmp1)) |
|
|
1741 |
status = EXACT_STATUS; |
|
|
1742 |
} |
|
|
1743 |
|
|
|
1744 |
if (status != EXACT_STATUS) |
|
|
1745 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); |
|
|
1746 |
} |
|
|
1747 |
|
|
|
1748 |
#endif |
|
|
1749 |
|
|
|
1750 |
pres->w[1] = sgn | CQ.w[1]; |
|
|
1751 |
pres->w[0] = CQ.w[0]; |
|
|
1752 |
|
|
|
1753 |
return pres; |
|
|
1754 |
|
|
|
1755 |
} |
|
|
1756 |
|
|
|
1757 |
|
|
|
1758 |
|
|
|
1759 |
// |
|
|
1760 |
// BID128 unpack, input passed by value |
|
|
1761 |
// |
|
|
1762 |
__BID_INLINE__ UINT64 |
|
|
1763 |
unpack_BID128_value (UINT64 * psign_x, int *pexponent_x, |
|
|
1764 |
UINT128 * pcoefficient_x, UINT128 x) { |
|
|
1765 |
UINT128 coeff, T33, T34; |
|
|
1766 |
UINT64 ex; |
|
|
1767 |
|
|
|
1768 |
*psign_x = (x.w[1]) & 0x8000000000000000ull; |
|
|
1769 |
|
|
|
1770 |
// special encodings |
|
|
1771 |
if ((x.w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { |
|
|
1772 |
if ((x.w[1] & INFINITY_MASK64) < INFINITY_MASK64) { |
|
|
1773 |
// non-canonical input |
|
|
1774 |
pcoefficient_x->w[0] = 0; |
|
|
1775 |
pcoefficient_x->w[1] = 0; |
|
|
1776 |
ex = (x.w[1]) >> 47; |
|
|
1777 |
*pexponent_x = ((int) ex) & EXPONENT_MASK128; |
|
|
1778 |
return 0; |
|
|
1779 |
} |
|
|
1780 |
// 10^33 |
|
|
1781 |
T33 = power10_table_128[33]; |
|
|
1782 |
/*coeff.w[0] = x.w[0]; |
|
|
1783 |
coeff.w[1] = (x.w[1]) & LARGE_COEFF_MASK128; |
|
|
1784 |
pcoefficient_x->w[0] = x.w[0]; |
|
|
1785 |
pcoefficient_x->w[1] = x.w[1]; |
|
|
1786 |
if (__unsigned_compare_ge_128 (coeff, T33)) // non-canonical |
|
|
1787 |
pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); */ |
|
|
1788 |
|
|
|
1789 |
pcoefficient_x->w[0] = x.w[0]; |
|
|
1790 |
pcoefficient_x->w[1] = (x.w[1]) & 0x00003fffffffffffull; |
|
|
1791 |
if (__unsigned_compare_ge_128 ((*pcoefficient_x), T33)) // non-canonical |
|
|
1792 |
{ |
|
|
1793 |
pcoefficient_x->w[1] = (x.w[1]) & 0xfe00000000000000ull; |
|
|
1794 |
pcoefficient_x->w[0] = 0; |
|
|
1795 |
} else |
|
|
1796 |
pcoefficient_x->w[1] = (x.w[1]) & 0xfe003fffffffffffull; |
|
|
1797 |
if ((x.w[1] & NAN_MASK64) == INFINITY_MASK64) { |
|
|
1798 |
pcoefficient_x->w[0] = 0; |
|
|
1799 |
pcoefficient_x->w[1] = x.w[1] & SINFINITY_MASK64; |
|
|
1800 |
} |
|
|
1801 |
*pexponent_x = 0; |
|
|
1802 |
return 0; // NaN or Infinity |
|
|
1803 |
} |
|
|
1804 |
|
|
|
1805 |
coeff.w[0] = x.w[0]; |
|
|
1806 |
coeff.w[1] = (x.w[1]) & SMALL_COEFF_MASK128; |
|
|
1807 |
|
|
|
1808 |
// 10^34 |
|
|
1809 |
T34 = power10_table_128[34]; |
|
|
1810 |
// check for non-canonical values |
|
|
1811 |
if (__unsigned_compare_ge_128 (coeff, T34)) |
|
|
1812 |
coeff.w[0] = coeff.w[1] = 0; |
|
|
1813 |
|
|
|
1814 |
pcoefficient_x->w[0] = coeff.w[0]; |
|
|
1815 |
pcoefficient_x->w[1] = coeff.w[1]; |
|
|
1816 |
|
|
|
1817 |
ex = (x.w[1]) >> 49; |
|
|
1818 |
*pexponent_x = ((int) ex) & EXPONENT_MASK128; |
|
|
1819 |
|
|
|
1820 |
return coeff.w[0] | coeff.w[1]; |
|
|
1821 |
} |
|
|
1822 |
|
|
|
1823 |
|
|
|
1824 |
// |
|
|
1825 |
// BID128 unpack, input pased by reference |
|
|
1826 |
// |
|
|
1827 |
__BID_INLINE__ UINT64 |
|
|
1828 |
unpack_BID128 (UINT64 * psign_x, int *pexponent_x, |
|
|
1829 |
UINT128 * pcoefficient_x, UINT128 * px) { |
|
|
1830 |
UINT128 coeff, T33, T34; |
|
|
1831 |
UINT64 ex; |
|
|
1832 |
|
|
|
1833 |
*psign_x = (px->w[1]) & 0x8000000000000000ull; |
|
|
1834 |
|
|
|
1835 |
// special encodings |
|
|
1836 |
if ((px->w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { |
|
|
1837 |
if ((px->w[1] & INFINITY_MASK64) < INFINITY_MASK64) { |
|
|
1838 |
// non-canonical input |
|
|
1839 |
pcoefficient_x->w[0] = 0; |
|
|
1840 |
pcoefficient_x->w[1] = 0; |
|
|
1841 |
ex = (px->w[1]) >> 47; |
|
|
1842 |
*pexponent_x = ((int) ex) & EXPONENT_MASK128; |
|
|
1843 |
return 0; |
|
|
1844 |
} |
|
|
1845 |
// 10^33 |
|
|
1846 |
T33 = power10_table_128[33]; |
|
|
1847 |
coeff.w[0] = px->w[0]; |
|
|
1848 |
coeff.w[1] = (px->w[1]) & LARGE_COEFF_MASK128; |
|
|
1849 |
pcoefficient_x->w[0] = px->w[0]; |
|
|
1850 |
pcoefficient_x->w[1] = px->w[1]; |
|
|
1851 |
if (__unsigned_compare_ge_128 (coeff, T33)) { // non-canonical |
|
|
1852 |
pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); |
|
|
1853 |
pcoefficient_x->w[0] = 0; |
|
|
1854 |
} |
|
|
1855 |
*pexponent_x = 0; |
|
|
1856 |
return 0; // NaN or Infinity |
|
|
1857 |
} |
|
|
1858 |
|
|
|
1859 |
coeff.w[0] = px->w[0]; |
|
|
1860 |
coeff.w[1] = (px->w[1]) & SMALL_COEFF_MASK128; |
|
|
1861 |
|
|
|
1862 |
// 10^34 |
|
|
1863 |
T34 = power10_table_128[34]; |
|
|
1864 |
// check for non-canonical values |
|
|
1865 |
if (__unsigned_compare_ge_128 (coeff, T34)) |
|
|
1866 |
coeff.w[0] = coeff.w[1] = 0; |
|
|
1867 |
|
|
|
1868 |
pcoefficient_x->w[0] = coeff.w[0]; |
|
|
1869 |
pcoefficient_x->w[1] = coeff.w[1]; |
|
|
1870 |
|
|
|
1871 |
ex = (px->w[1]) >> 49; |
|
|
1872 |
*pexponent_x = ((int) ex) & EXPONENT_MASK128; |
|
|
1873 |
|
|
|
1874 |
return coeff.w[0] | coeff.w[1]; |
|
|
1875 |
} |
|
|
1876 |
|
|
|
1877 |
// |
|
|
1878 |
// Pack macro checks for overflow, but not underflow |
|
|
1879 |
// |
|
|
1880 |
__BID_INLINE__ UINT128 * |
|
|
1881 |
get_BID128_very_fast_OF (UINT128 * pres, UINT64 sgn, int expon, |
|
|
1882 |
UINT128 coeff, unsigned *prounding_mode, |
|
|
1883 |
unsigned *fpsc) { |
|
|
1884 |
UINT128 T; |
|
|
1885 |
UINT64 tmp, tmp2; |
|
|
1886 |
|
|
|
1887 |
if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { |
|
|
1888 |
|
|
|
1889 |
if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { |
|
|
1890 |
T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; |
|
|
1891 |
while (__unsigned_compare_gt_128 (T, coeff) |
|
|
1892 |
&& expon > DECIMAL_MAX_EXPON_128) { |
|
|
1893 |
coeff.w[1] = |
|
|
1894 |
(coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + |
|
|
1895 |
(coeff.w[0] >> 63); |
|
|
1896 |
tmp2 = coeff.w[0] << 3; |
|
|
1897 |
coeff.w[0] = (coeff.w[0] << 1) + tmp2; |
|
|
1898 |
if (coeff.w[0] < tmp2) |
|
|
1899 |
coeff.w[1]++; |
|
|
1900 |
|
|
|
1901 |
expon--; |
|
|
1902 |
} |
|
|
1903 |
} |
|
|
1904 |
if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { |
|
|
1905 |
// OF |
|
|
1906 |
#ifdef SET_STATUS_FLAGS |
|
|
1907 |
__set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
1908 |
#endif |
|
|
1909 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1910 |
#ifndef IEEE_ROUND_NEAREST |
|
|
1911 |
if (*prounding_mode == ROUNDING_TO_ZERO |
|
|
1912 |
|| (sgn && *prounding_mode == ROUNDING_UP) || (!sgn |
|
|
1913 |
&& |
|
|
1914 |
*prounding_mode |
|
|
1915 |
== |
|
|
1916 |
ROUNDING_DOWN)) |
|
|
1917 |
{ |
|
|
1918 |
pres->w[1] = sgn | LARGEST_BID128_HIGH; |
|
|
1919 |
pres->w[0] = LARGEST_BID128_LOW; |
|
|
1920 |
} else |
|
|
1921 |
#endif |
|
|
1922 |
#endif |
|
|
1923 |
{ |
|
|
1924 |
pres->w[1] = sgn | INFINITY_MASK64; |
|
|
1925 |
pres->w[0] = 0; |
|
|
1926 |
} |
|
|
1927 |
return pres; |
|
|
1928 |
} |
|
|
1929 |
} |
|
|
1930 |
|
|
|
1931 |
pres->w[0] = coeff.w[0]; |
|
|
1932 |
tmp = expon; |
|
|
1933 |
tmp <<= 49; |
|
|
1934 |
pres->w[1] = sgn | tmp | coeff.w[1]; |
|
|
1935 |
|
|
|
1936 |
return pres; |
|
|
1937 |
} |
|
|
1938 |
|
|
|
1939 |
|
|
|
1940 |
// |
|
|
1941 |
// No overflow/underflow checks |
|
|
1942 |
// No checking for coefficient == 10^34 (rounding artifact) |
|
|
1943 |
// |
|
|
1944 |
__BID_INLINE__ UINT128 * |
|
|
1945 |
get_BID128_very_fast (UINT128 * pres, UINT64 sgn, int expon, |
|
|
1946 |
UINT128 coeff) { |
|
|
1947 |
UINT64 tmp; |
|
|
1948 |
|
|
|
1949 |
pres->w[0] = coeff.w[0]; |
|
|
1950 |
tmp = expon; |
|
|
1951 |
tmp <<= 49; |
|
|
1952 |
pres->w[1] = sgn | tmp | coeff.w[1]; |
|
|
1953 |
|
|
|
1954 |
return pres; |
|
|
1955 |
} |
|
|
1956 |
|
|
|
1957 |
// |
|
|
1958 |
// No overflow/underflow checks |
|
|
1959 |
// |
|
|
1960 |
__BID_INLINE__ UINT128 * |
|
|
1961 |
get_BID128_fast (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { |
|
|
1962 |
UINT64 tmp; |
|
|
1963 |
|
|
|
1964 |
// coeff==10^34? |
|
|
1965 |
if (coeff.w[1] == 0x0001ed09bead87c0ull |
|
|
1966 |
&& coeff.w[0] == 0x378d8e6400000000ull) { |
|
|
1967 |
expon++; |
|
|
1968 |
// set coefficient to 10^33 |
|
|
1969 |
coeff.w[1] = 0x0000314dc6448d93ull; |
|
|
1970 |
coeff.w[0] = 0x38c15b0a00000000ull; |
|
|
1971 |
} |
|
|
1972 |
|
|
|
1973 |
pres->w[0] = coeff.w[0]; |
|
|
1974 |
tmp = expon; |
|
|
1975 |
tmp <<= 49; |
|
|
1976 |
pres->w[1] = sgn | tmp | coeff.w[1]; |
|
|
1977 |
|
|
|
1978 |
return pres; |
|
|
1979 |
} |
|
|
1980 |
|
|
|
1981 |
// |
|
|
1982 |
// General BID128 pack macro |
|
|
1983 |
// |
|
|
1984 |
__BID_INLINE__ UINT128 * |
|
|
1985 |
get_BID128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff, |
|
|
1986 |
unsigned *prounding_mode, unsigned *fpsc) { |
|
|
1987 |
UINT128 T; |
|
|
1988 |
UINT64 tmp, tmp2; |
|
|
1989 |
|
|
|
1990 |
// coeff==10^34? |
|
|
1991 |
if (coeff.w[1] == 0x0001ed09bead87c0ull |
|
|
1992 |
&& coeff.w[0] == 0x378d8e6400000000ull) { |
|
|
1993 |
expon++; |
|
|
1994 |
// set coefficient to 10^33 |
|
|
1995 |
coeff.w[1] = 0x0000314dc6448d93ull; |
|
|
1996 |
coeff.w[0] = 0x38c15b0a00000000ull; |
|
|
1997 |
} |
|
|
1998 |
// check OF, UF |
|
|
1999 |
if (expon < 0 || expon > DECIMAL_MAX_EXPON_128) { |
|
|
2000 |
// check UF |
|
|
2001 |
if (expon < 0) { |
|
|
2002 |
return handle_UF_128 (pres, sgn, expon, coeff, prounding_mode, |
|
|
2003 |
fpsc); |
|
|
2004 |
} |
|
|
2005 |
|
|
|
2006 |
if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { |
|
|
2007 |
T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; |
|
|
2008 |
while (__unsigned_compare_gt_128 (T, coeff) |
|
|
2009 |
&& expon > DECIMAL_MAX_EXPON_128) { |
|
|
2010 |
coeff.w[1] = |
|
|
2011 |
(coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + |
|
|
2012 |
(coeff.w[0] >> 63); |
|
|
2013 |
tmp2 = coeff.w[0] << 3; |
|
|
2014 |
coeff.w[0] = (coeff.w[0] << 1) + tmp2; |
|
|
2015 |
if (coeff.w[0] < tmp2) |
|
|
2016 |
coeff.w[1]++; |
|
|
2017 |
|
|
|
2018 |
expon--; |
|
|
2019 |
} |
|
|
2020 |
} |
|
|
2021 |
if (expon > DECIMAL_MAX_EXPON_128) { |
|
|
2022 |
if (!(coeff.w[1] | coeff.w[0])) { |
|
|
2023 |
pres->w[1] = sgn | (((UINT64) DECIMAL_MAX_EXPON_128) << 49); |
|
|
2024 |
pres->w[0] = 0; |
|
|
2025 |
return pres; |
|
|
2026 |
} |
|
|
2027 |
// OF |
|
|
2028 |
#ifdef SET_STATUS_FLAGS |
|
|
2029 |
__set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
2030 |
#endif |
|
|
2031 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
2032 |
#ifndef IEEE_ROUND_NEAREST |
|
|
2033 |
if (*prounding_mode == ROUNDING_TO_ZERO |
|
|
2034 |
|| (sgn && *prounding_mode == ROUNDING_UP) || (!sgn |
|
|
2035 |
&& |
|
|
2036 |
*prounding_mode |
|
|
2037 |
== |
|
|
2038 |
ROUNDING_DOWN)) |
|
|
2039 |
{ |
|
|
2040 |
pres->w[1] = sgn | LARGEST_BID128_HIGH; |
|
|
2041 |
pres->w[0] = LARGEST_BID128_LOW; |
|
|
2042 |
} else |
|
|
2043 |
#endif |
|
|
2044 |
#endif |
|
|
2045 |
{ |
|
|
2046 |
pres->w[1] = sgn | INFINITY_MASK64; |
|
|
2047 |
pres->w[0] = 0; |
|
|
2048 |
} |
|
|
2049 |
return pres; |
|
|
2050 |
} |
|
|
2051 |
} |
|
|
2052 |
|
|
|
2053 |
pres->w[0] = coeff.w[0]; |
|
|
2054 |
tmp = expon; |
|
|
2055 |
tmp <<= 49; |
|
|
2056 |
pres->w[1] = sgn | tmp | coeff.w[1]; |
|
|
2057 |
|
|
|
2058 |
return pres; |
|
|
2059 |
} |
|
|
2060 |
|
|
|
2061 |
|
|
|
2062 |
// |
|
|
2063 |
// Macro used for conversions from string |
|
|
2064 |
// (no additional arguments given for rounding mode, status flags) |
|
|
2065 |
// |
|
|
2066 |
__BID_INLINE__ UINT128 * |
|
|
2067 |
get_BID128_string (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { |
|
|
2068 |
UINT128 D2, D8; |
|
|
2069 |
UINT64 tmp; |
|
|
2070 |
unsigned rmode = 0, status; |
|
|
2071 |
|
|
|
2072 |
// coeff==10^34? |
|
|
2073 |
if (coeff.w[1] == 0x0001ed09bead87c0ull |
|
|
2074 |
&& coeff.w[0] == 0x378d8e6400000000ull) { |
|
|
2075 |
expon++; |
|
|
2076 |
// set coefficient to 10^33 |
|
|
2077 |
coeff.w[1] = 0x0000314dc6448d93ull; |
|
|
2078 |
coeff.w[0] = 0x38c15b0a00000000ull; |
|
|
2079 |
} |
|
|
2080 |
// check OF, UF |
|
|
2081 |
if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { |
|
|
2082 |
// check UF |
|
|
2083 |
if (expon < 0) |
|
|
2084 |
return handle_UF_128 (pres, sgn, expon, coeff, &rmode, &status); |
|
|
2085 |
|
|
|
2086 |
// OF |
|
|
2087 |
|
|
|
2088 |
if (expon < DECIMAL_MAX_EXPON_128 + 34) { |
|
|
2089 |
while (expon > DECIMAL_MAX_EXPON_128 && |
|
|
2090 |
(coeff.w[1] < power10_table_128[33].w[1] || |
|
|
2091 |
(coeff.w[1] == power10_table_128[33].w[1] |
|
|
2092 |
&& coeff.w[0] < power10_table_128[33].w[0]))) { |
|
|
2093 |
D2.w[1] = (coeff.w[1] << 1) | (coeff.w[0] >> 63); |
|
|
2094 |
D2.w[0] = coeff.w[0] << 1; |
|
|
2095 |
D8.w[1] = (coeff.w[1] << 3) | (coeff.w[0] >> 61); |
|
|
2096 |
D8.w[0] = coeff.w[0] << 3; |
|
|
2097 |
|
|
|
2098 |
__add_128_128 (coeff, D2, D8); |
|
|
2099 |
expon--; |
|
|
2100 |
} |
|
|
2101 |
} else if (!(coeff.w[0] | coeff.w[1])) |
|
|
2102 |
expon = DECIMAL_MAX_EXPON_128; |
|
|
2103 |
|
|
|
2104 |
if (expon > DECIMAL_MAX_EXPON_128) { |
|
|
2105 |
pres->w[1] = sgn | INFINITY_MASK64; |
|
|
2106 |
pres->w[0] = 0; |
|
|
2107 |
switch (rmode) { |
|
|
2108 |
case ROUNDING_DOWN: |
|
|
2109 |
if (!sgn) { |
|
|
2110 |
pres->w[1] = LARGEST_BID128_HIGH; |
|
|
2111 |
pres->w[0] = LARGEST_BID128_LOW; |
|
|
2112 |
} |
|
|
2113 |
break; |
|
|
2114 |
case ROUNDING_TO_ZERO: |
|
|
2115 |
pres->w[1] = sgn | LARGEST_BID128_HIGH; |
|
|
2116 |
pres->w[0] = LARGEST_BID128_LOW; |
|
|
2117 |
break; |
|
|
2118 |
case ROUNDING_UP: |
|
|
2119 |
// round up |
|
|
2120 |
if (sgn) { |
|
|
2121 |
pres->w[1] = sgn | LARGEST_BID128_HIGH; |
|
|
2122 |
pres->w[0] = LARGEST_BID128_LOW; |
|
|
2123 |
} |
|
|
2124 |
break; |
|
|
2125 |
} |
|
|
2126 |
|
|
|
2127 |
return pres; |
|
|
2128 |
} |
|
|
2129 |
} |
|
|
2130 |
|
|
|
2131 |
pres->w[0] = coeff.w[0]; |
|
|
2132 |
tmp = expon; |
|
|
2133 |
tmp <<= 49; |
|
|
2134 |
pres->w[1] = sgn | tmp | coeff.w[1]; |
|
|
2135 |
|
|
|
2136 |
return pres; |
|
|
2137 |
} |
|
|
2138 |
|
|
|
2139 |
|
|
|
2140 |
|
|
|
2141 |
/***************************************************************************** |
|
|
2142 |
* |
|
|
2143 |
* BID32 pack/unpack macros |
|
|
2144 |
* |
|
|
2145 |
*****************************************************************************/ |
|
|
2146 |
|
|
|
2147 |
|
|
|
2148 |
__BID_INLINE__ UINT32 |
|
|
2149 |
unpack_BID32 (UINT32 * psign_x, int *pexponent_x, |
|
|
2150 |
UINT32 * pcoefficient_x, UINT32 x) { |
|
|
2151 |
UINT32 tmp; |
|
|
2152 |
|
|
|
2153 |
*psign_x = x & 0x80000000; |
|
|
2154 |
|
|
|
2155 |
if ((x & SPECIAL_ENCODING_MASK32) == SPECIAL_ENCODING_MASK32) { |
|
|
2156 |
// special encodings |
|
|
2157 |
if ((x & INFINITY_MASK32) == INFINITY_MASK32) { |
|
|
2158 |
*pcoefficient_x = x & 0xfe0fffff; |
|
|
2159 |
if ((x & 0x000fffff) >= 1000000) |
|
|
2160 |
*pcoefficient_x = x & 0xfe000000; |
|
|
2161 |
if ((x & NAN_MASK32) == INFINITY_MASK32) |
|
|
2162 |
*pcoefficient_x = x & 0xf8000000; |
|
|
2163 |
*pexponent_x = 0; |
|
|
2164 |
return 0; // NaN or Infinity |
|
|
2165 |
} |
|
|
2166 |
// coefficient |
|
|
2167 |
*pcoefficient_x = (x & SMALL_COEFF_MASK32) | LARGE_COEFF_HIGH_BIT32; |
|
|
2168 |
// check for non-canonical value |
|
|
2169 |
if (*pcoefficient_x >= 10000000) |
|
|
2170 |
*pcoefficient_x = 0; |
|
|
2171 |
// get exponent |
|
|
2172 |
tmp = x >> 21; |
|
|
2173 |
*pexponent_x = tmp & EXPONENT_MASK32; |
|
|
2174 |
return 1; |
|
|
2175 |
} |
|
|
2176 |
// exponent |
|
|
2177 |
tmp = x >> 23; |
|
|
2178 |
*pexponent_x = tmp & EXPONENT_MASK32; |
|
|
2179 |
// coefficient |
|
|
2180 |
*pcoefficient_x = (x & LARGE_COEFF_MASK32); |
|
|
2181 |
|
|
|
2182 |
return *pcoefficient_x; |
|
|
2183 |
} |
|
|
2184 |
|
|
|
2185 |
// |
|
|
2186 |
// General pack macro for BID32 |
|
|
2187 |
// |
|
|
2188 |
__BID_INLINE__ UINT32 |
|
|
2189 |
get_BID32 (UINT32 sgn, int expon, UINT64 coeff, int rmode, |
|
|
2190 |
unsigned *fpsc) { |
|
|
2191 |
UINT128 Q; |
|
|
2192 |
UINT64 C64, remainder_h, carry, Stemp; |
|
|
2193 |
UINT32 r, mask; |
|
|
2194 |
int extra_digits, amount, amount2; |
|
|
2195 |
unsigned status; |
|
|
2196 |
|
|
|
2197 |
if (coeff > 9999999ull) { |
|
|
2198 |
expon++; |
|
|
2199 |
coeff = 1000000ull; |
|
|
2200 |
} |
|
|
2201 |
// check for possible underflow/overflow |
|
|
2202 |
if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { |
|
|
2203 |
if (expon < 0) { |
|
|
2204 |
// underflow |
|
|
2205 |
if (expon + MAX_FORMAT_DIGITS_32 < 0) { |
|
|
2206 |
#ifdef SET_STATUS_FLAGS |
|
|
2207 |
__set_status_flags (fpsc, |
|
|
2208 |
UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
2209 |
#endif |
|
|
2210 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
2211 |
#ifndef IEEE_ROUND_NEAREST |
|
|
2212 |
if (rmode == ROUNDING_DOWN && sgn) |
|
|
2213 |
return 0x80000001; |
|
|
2214 |
if (rmode == ROUNDING_UP && !sgn) |
|
|
2215 |
return 1; |
|
|
2216 |
#endif |
|
|
2217 |
#endif |
|
|
2218 |
// result is 0 |
|
|
2219 |
return sgn; |
|
|
2220 |
} |
|
|
2221 |
// get digits to be shifted out |
|
|
2222 |
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
2223 |
rmode = 0; |
|
|
2224 |
#endif |
|
|
2225 |
#ifdef IEEE_ROUND_NEAREST |
|
|
2226 |
rmode = 0; |
|
|
2227 |
#endif |
|
|
2228 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
2229 |
#ifndef IEEE_ROUND_NEAREST |
|
|
2230 |
if (sgn && (unsigned) (rmode - 1) < 2) |
|
|
2231 |
rmode = 3 - rmode; |
|
|
2232 |
#endif |
|
|
2233 |
#endif |
|
|
2234 |
|
|
|
2235 |
extra_digits = -expon; |
|
|
2236 |
coeff += round_const_table[rmode][extra_digits]; |
|
|
2237 |
|
|
|
2238 |
// get coeff*(2^M[extra_digits])/10^extra_digits |
|
|
2239 |
__mul_64x64_to_128 (Q, coeff, reciprocals10_64[extra_digits]); |
|
|
2240 |
|
|
|
2241 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
2242 |
amount = short_recip_scale[extra_digits]; |
|
|
2243 |
|
|
|
2244 |
C64 = Q.w[1] >> amount; |
|
|
2245 |
|
|
|
2246 |
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
2247 |
#ifndef IEEE_ROUND_NEAREST |
|
|
2248 |
if (rmode == 0) //ROUNDING_TO_NEAREST |
|
|
2249 |
#endif |
|
|
2250 |
if (C64 & 1) { |
|
|
2251 |
// check whether fractional part of initial_P/10^extra_digits is exactly .5 |
|
|
2252 |
|
|
|
2253 |
// get remainder |
|
|
2254 |
amount2 = 64 - amount; |
|
|
2255 |
remainder_h = 0; |
|
|
2256 |
remainder_h--; |
|
|
2257 |
remainder_h >>= amount2; |
|
|
2258 |
remainder_h = remainder_h & Q.w[1]; |
|
|
2259 |
|
|
|
2260 |
if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) { |
|
|
2261 |
C64--; |
|
|
2262 |
} |
|
|
2263 |
} |
|
|
2264 |
#endif |
|
|
2265 |
|
|
|
2266 |
#ifdef SET_STATUS_FLAGS |
|
|
2267 |
|
|
|
2268 |
if (is_inexact (fpsc)) |
|
|
2269 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION); |
|
|
2270 |
else { |
|
|
2271 |
status = INEXACT_EXCEPTION; |
|
|
2272 |
// get remainder |
|
|
2273 |
remainder_h = Q.w[1] << (64 - amount); |
|
|
2274 |
|
|
|
2275 |
switch (rmode) { |
|
|
2276 |
case ROUNDING_TO_NEAREST: |
|
|
2277 |
case ROUNDING_TIES_AWAY: |
|
|
2278 |
// test whether fractional part is 0 |
|
|
2279 |
if (remainder_h == 0x8000000000000000ull |
|
|
2280 |
&& (Q.w[0] < reciprocals10_64[extra_digits])) |
|
|
2281 |
status = EXACT_STATUS; |
|
|
2282 |
break; |
|
|
2283 |
case ROUNDING_DOWN: |
|
|
2284 |
case ROUNDING_TO_ZERO: |
|
|
2285 |
if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) |
|
|
2286 |
status = EXACT_STATUS; |
|
|
2287 |
break; |
|
|
2288 |
default: |
|
|
2289 |
// round up |
|
|
2290 |
__add_carry_out (Stemp, carry, Q.w[0], |
|
|
2291 |
reciprocals10_64[extra_digits]); |
|
|
2292 |
if ((remainder_h >> (64 - amount)) + carry >= |
|
|
2293 |
(((UINT64) 1) << amount)) |
|
|
2294 |
status = EXACT_STATUS; |
|
|
2295 |
} |
|
|
2296 |
|
|
|
2297 |
if (status != EXACT_STATUS) |
|
|
2298 |
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); |
|
|
2299 |
} |
|
|
2300 |
|
|
|
2301 |
#endif |
|
|
2302 |
|
|
|
2303 |
return sgn | (UINT32) C64; |
|
|
2304 |
} |
|
|
2305 |
|
|
|
2306 |
while (coeff < 1000000 && expon > DECIMAL_MAX_EXPON_32) { |
|
|
2307 |
coeff = (coeff << 3) + (coeff << 1); |
|
|
2308 |
expon--; |
|
|
2309 |
} |
|
|
2310 |
if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { |
|
|
2311 |
__set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); |
|
|
2312 |
// overflow |
|
|
2313 |
r = sgn | INFINITY_MASK32; |
|
|
2314 |
switch (rmode) { |
|
|
2315 |
case ROUNDING_DOWN: |
|
|
2316 |
if (!sgn) |
|
|
2317 |
r = LARGEST_BID32; |
|
|
2318 |
break; |
|
|
2319 |
case ROUNDING_TO_ZERO: |
|
|
2320 |
r = sgn | LARGEST_BID32; |
|
|
2321 |
break; |
|
|
2322 |
case ROUNDING_UP: |
|
|
2323 |
// round up |
|
|
2324 |
if (sgn) |
|
|
2325 |
r = sgn | LARGEST_BID32; |
|
|
2326 |
} |
|
|
2327 |
return r; |
|
|
2328 |
} |
|
|
2329 |
} |
|
|
2330 |
|
|
|
2331 |
mask = 1 << 23; |
|
|
2332 |
|
|
|
2333 |
// check whether coefficient fits in DECIMAL_COEFF_FIT bits |
|
|
2334 |
if (coeff < mask) { |
|
|
2335 |
r = expon; |
|
|
2336 |
r <<= 23; |
|
|
2337 |
r |= ((UINT32) coeff | sgn); |
|
|
2338 |
return r; |
|
|
2339 |
} |
|
|
2340 |
// special format |
|
|
2341 |
|
|
|
2342 |
r = expon; |
|
|
2343 |
r <<= 21; |
|
|
2344 |
r |= (sgn | SPECIAL_ENCODING_MASK32); |
|
|
2345 |
// add coeff, without leading bits |
|
|
2346 |
mask = (1 << 21) - 1; |
|
|
2347 |
r |= (((UINT32) coeff) & mask); |
|
|
2348 |
|
|
|
2349 |
return r; |
|
|
2350 |
} |
|
|
2351 |
|
|
|
2352 |
|
|
|
2353 |
|
|
|
2354 |
// |
|
|
2355 |
// no overflow/underflow checks |
|
|
2356 |
// |
|
|
2357 |
__BID_INLINE__ UINT32 |
|
|
2358 |
very_fast_get_BID32 (UINT32 sgn, int expon, UINT32 coeff) { |
|
|
2359 |
UINT32 r, mask; |
|
|
2360 |
|
|
|
2361 |
mask = 1 << 23; |
|
|
2362 |
|
|
|
2363 |
// check whether coefficient fits in 10*2+3 bits |
|
|
2364 |
if (coeff < mask) { |
|
|
2365 |
r = expon; |
|
|
2366 |
r <<= 23; |
|
|
2367 |
r |= (coeff | sgn); |
|
|
2368 |
return r; |
|
|
2369 |
} |
|
|
2370 |
// special format |
|
|
2371 |
r = expon; |
|
|
2372 |
r <<= 21; |
|
|
2373 |
r |= (sgn | SPECIAL_ENCODING_MASK32); |
|
|
2374 |
// add coeff, without leading bits |
|
|
2375 |
mask = (1 << 21) - 1; |
|
|
2376 |
coeff &= mask; |
|
|
2377 |
r |= coeff; |
|
|
2378 |
|
|
|
2379 |
return r; |
|
|
2380 |
} |
|
|
2381 |
|
|
|
2382 |
|
|
|
2383 |
|
|
|
2384 |
/************************************************************* |
|
|
2385 |
* |
|
|
2386 |
*************************************************************/ |
|
|
2387 |
typedef |
|
|
2388 |
ALIGN (16) |
|
|
2389 |
struct { |
|
|
2390 |
UINT64 w[6]; |
|
|
2391 |
} UINT384; |
|
|
2392 |
typedef ALIGN (16) |
|
|
2393 |
struct { |
|
|
2394 |
UINT64 w[8]; |
|
|
2395 |
} UINT512; |
|
|
2396 |
|
|
|
2397 |
// #define P 34 |
|
|
2398 |
#define MASK_STEERING_BITS 0x6000000000000000ull |
|
|
2399 |
#define MASK_BINARY_EXPONENT1 0x7fe0000000000000ull |
|
|
2400 |
#define MASK_BINARY_SIG1 0x001fffffffffffffull |
|
|
2401 |
#define MASK_BINARY_EXPONENT2 0x1ff8000000000000ull |
|
|
2402 |
//used to take G[2:w+3] (sec 3.3) |
|
|
2403 |
#define MASK_BINARY_SIG2 0x0007ffffffffffffull |
|
|
2404 |
//used to mask out G4:T0 (sec 3.3) |
|
|
2405 |
#define MASK_BINARY_OR2 0x0020000000000000ull |
|
|
2406 |
//used to prefix 8+G4 to T (sec 3.3) |
|
|
2407 |
#define UPPER_EXPON_LIMIT 51 |
|
|
2408 |
#define MASK_EXP 0x7ffe000000000000ull |
|
|
2409 |
#define MASK_SPECIAL 0x7800000000000000ull |
|
|
2410 |
#define MASK_NAN 0x7c00000000000000ull |
|
|
2411 |
#define MASK_SNAN 0x7e00000000000000ull |
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|
2412 |
#define MASK_ANY_INF 0x7c00000000000000ull |
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|
2413 |
#define MASK_INF 0x7800000000000000ull |
|
|
2414 |
#define MASK_SIGN 0x8000000000000000ull |
|
|
2415 |
#define MASK_COEFF 0x0001ffffffffffffull |
|
|
2416 |
#define BIN_EXP_BIAS (0x1820ull << 49) |
|
|
2417 |
|
|
|
2418 |
#define EXP_MIN 0x0000000000000000ull |
|
|
2419 |
// EXP_MIN = (-6176 + 6176) << 49 |
|
|
2420 |
#define EXP_MAX 0x5ffe000000000000ull |
|
|
2421 |
// EXP_MAX = (6111 + 6176) << 49 |
|
|
2422 |
#define EXP_MAX_P1 0x6000000000000000ull |
|
|
2423 |
// EXP_MAX + 1 = (6111 + 6176 + 1) << 49 |
|
|
2424 |
#define EXP_P1 0x0002000000000000ull |
|
|
2425 |
// EXP_ P1= 1 << 49 |
|
|
2426 |
#define expmin -6176 |
|
|
2427 |
// min unbiased exponent |
|
|
2428 |
#define expmax 6111 |
|
|
2429 |
// max unbiased exponent |
|
|
2430 |
#define expmin16 -398 |
|
|
2431 |
// min unbiased exponent |
|
|
2432 |
#define expmax16 369 |
|
|
2433 |
// max unbiased exponent |
|
|
2434 |
|
|
|
2435 |
#define SIGNMASK32 0x80000000 |
|
|
2436 |
#define BID64_SIG_MAX 0x002386F26FC0ffffull |
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|
2437 |
#define SIGNMASK64 0x8000000000000000ull |
|
|
2438 |
|
|
|
2439 |
// typedef unsigned int FPSC; // floating-point status and control |
|
|
2440 |
// bit31: |
|
|
2441 |
// bit30: |
|
|
2442 |
// bit29: |
|
|
2443 |
// bit28: |
|
|
2444 |
// bit27: |
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|
2445 |
// bit26: |
|
|
2446 |
// bit25: |
|
|
2447 |
// bit24: |
|
|
2448 |
// bit23: |
|
|
2449 |
// bit22: |
|
|
2450 |
// bit21: |
|
|
2451 |
// bit20: |
|
|
2452 |
// bit19: |
|
|
2453 |
// bit18: |
|
|
2454 |
// bit17: |
|
|
2455 |
// bit16: |
|
|
2456 |
// bit15: |
|
|
2457 |
// bit14: RC:2 |
|
|
2458 |
// bit13: RC:1 |
|
|
2459 |
// bit12: RC:0 |
|
|
2460 |
// bit11: PM |
|
|
2461 |
// bit10: UM |
|
|
2462 |
// bit9: OM |
|
|
2463 |
// bit8: ZM |
|
|
2464 |
// bit7: DM |
|
|
2465 |
// bit6: IM |
|
|
2466 |
// bit5: PE |
|
|
2467 |
// bit4: UE |
|
|
2468 |
// bit3: OE |
|
|
2469 |
// bit2: ZE |
|
|
2470 |
// bit1: DE |
|
|
2471 |
// bit0: IE |
|
|
2472 |
|
|
|
2473 |
#define ROUNDING_MODE_MASK 0x00007000 |
|
|
2474 |
|
|
|
2475 |
typedef struct _DEC_DIGITS { |
|
|
2476 |
unsigned int digits; |
|
|
2477 |
UINT64 threshold_hi; |
|
|
2478 |
UINT64 threshold_lo; |
|
|
2479 |
unsigned int digits1; |
|
|
2480 |
} DEC_DIGITS; |
|
|
2481 |
|
|
|
2482 |
extern DEC_DIGITS nr_digits[]; |
|
|
2483 |
extern UINT64 midpoint64[]; |
|
|
2484 |
extern UINT128 midpoint128[]; |
|
|
2485 |
extern UINT192 midpoint192[]; |
|
|
2486 |
extern UINT256 midpoint256[]; |
|
|
2487 |
extern UINT64 ten2k64[]; |
|
|
2488 |
extern UINT128 ten2k128[]; |
|
|
2489 |
extern UINT256 ten2k256[]; |
|
|
2490 |
extern UINT128 ten2mk128[]; |
|
|
2491 |
extern UINT64 ten2mk64[]; |
|
|
2492 |
extern UINT128 ten2mk128trunc[]; |
|
|
2493 |
extern int shiftright128[]; |
|
|
2494 |
extern UINT64 maskhigh128[]; |
|
|
2495 |
extern UINT64 maskhigh128M[]; |
|
|
2496 |
extern UINT64 maskhigh192M[]; |
|
|
2497 |
extern UINT64 maskhigh256M[]; |
|
|
2498 |
extern UINT64 onehalf128[]; |
|
|
2499 |
extern UINT64 onehalf128M[]; |
|
|
2500 |
extern UINT64 onehalf192M[]; |
|
|
2501 |
extern UINT64 onehalf256M[]; |
|
|
2502 |
extern UINT128 ten2mk128M[]; |
|
|
2503 |
extern UINT128 ten2mk128truncM[]; |
|
|
2504 |
extern UINT192 ten2mk192truncM[]; |
|
|
2505 |
extern UINT256 ten2mk256truncM[]; |
|
|
2506 |
extern int shiftright128M[]; |
|
|
2507 |
extern int shiftright192M[]; |
|
|
2508 |
extern int shiftright256M[]; |
|
|
2509 |
extern UINT192 ten2mk192M[]; |
|
|
2510 |
extern UINT256 ten2mk256M[]; |
|
|
2511 |
extern unsigned char char_table2[]; |
|
|
2512 |
extern unsigned char char_table3[]; |
|
|
2513 |
|
|
|
2514 |
extern UINT64 ten2m3k64[]; |
|
|
2515 |
extern unsigned int shift_ten2m3k64[]; |
|
|
2516 |
extern UINT128 ten2m3k128[]; |
|
|
2517 |
extern unsigned int shift_ten2m3k128[]; |
|
|
2518 |
|
|
|
2519 |
|
|
|
2520 |
|
|
|
2521 |
/*************************************************************************** |
|
|
2522 |
*************** TABLES FOR GENERAL ROUNDING FUNCTIONS ********************* |
|
|
2523 |
***************************************************************************/ |
|
|
2524 |
|
|
|
2525 |
extern UINT64 Kx64[]; |
|
|
2526 |
extern unsigned int Ex64m64[]; |
|
|
2527 |
extern UINT64 half64[]; |
|
|
2528 |
extern UINT64 mask64[]; |
|
|
2529 |
extern UINT64 ten2mxtrunc64[]; |
|
|
2530 |
|
|
|
2531 |
extern UINT128 Kx128[]; |
|
|
2532 |
extern unsigned int Ex128m128[]; |
|
|
2533 |
extern UINT64 half128[]; |
|
|
2534 |
extern UINT64 mask128[]; |
|
|
2535 |
extern UINT128 ten2mxtrunc128[]; |
|
|
2536 |
|
|
|
2537 |
extern UINT192 Kx192[]; |
|
|
2538 |
extern unsigned int Ex192m192[]; |
|
|
2539 |
extern UINT64 half192[]; |
|
|
2540 |
extern UINT64 mask192[]; |
|
|
2541 |
extern UINT192 ten2mxtrunc192[]; |
|
|
2542 |
|
|
|
2543 |
extern UINT256 Kx256[]; |
|
|
2544 |
extern unsigned int Ex256m256[]; |
|
|
2545 |
extern UINT64 half256[]; |
|
|
2546 |
extern UINT64 mask256[]; |
|
|
2547 |
extern UINT256 ten2mxtrunc256[]; |
|
|
2548 |
|
|
|
2549 |
typedef union __bid64_128 { |
|
|
2550 |
UINT64 b64; |
|
|
2551 |
UINT128 b128; |
|
|
2552 |
} BID64_128; |
|
|
2553 |
|
|
|
2554 |
BID64_128 bid_fma (unsigned int P0, |
|
|
2555 |
BID64_128 x1, unsigned int P1, |
|
|
2556 |
BID64_128 y1, unsigned int P2, |
|
|
2557 |
BID64_128 z1, unsigned int P3, |
|
|
2558 |
unsigned int rnd_mode, FPSC * fpsc); |
|
|
2559 |
|
|
|
2560 |
#define P16 16 |
|
|
2561 |
#define P34 34 |
|
|
2562 |
|
|
|
2563 |
union __int_double { |
|
|
2564 |
UINT64 i; |
|
|
2565 |
double d; |
|
|
2566 |
}; |
|
|
2567 |
typedef union __int_double int_double; |
|
|
2568 |
|
|
|
2569 |
|
|
|
2570 |
union __int_float { |
|
|
2571 |
UINT32 i; |
|
|
2572 |
float d; |
|
|
2573 |
}; |
|
|
2574 |
typedef union __int_float int_float; |
|
|
2575 |
|
|
|
2576 |
#define SWAP(A,B,T) {\ |
|
|
2577 |
T = A; \ |
|
|
2578 |
A = B; \ |
|
|
2579 |
B = T; \ |
|
|
2580 |
} |
|
|
2581 |
|
|
|
2582 |
// this macro will find coefficient_x to be in [2^A, 2^(A+1) ) |
|
|
2583 |
// ie it knows that it is A bits long |
|
|
2584 |
#define NUMBITS(A, coefficient_x, tempx){\ |
|
|
2585 |
temp_x.d=(float)coefficient_x;\ |
|
|
2586 |
A=((tempx.i >>23) & EXPONENT_MASK32) - 0x7f;\ |
|
|
2587 |
} |
|
|
2588 |
|
|
|
2589 |
enum class_types { |
|
|
2590 |
signalingNaN, |
|
|
2591 |
quietNaN, |
|
|
2592 |
negativeInfinity, |
|
|
2593 |
negativeNormal, |
|
|
2594 |
negativeSubnormal, |
|
|
2595 |
negativeZero, |
|
|
2596 |
positiveZero, |
|
|
2597 |
positiveSubnormal, |
|
|
2598 |
positiveNormal, |
|
|
2599 |
positiveInfinity |
|
|
2600 |
}; |
|
|
2601 |
|
|
|
2602 |
typedef union { |
|
|
2603 |
UINT64 ui64; |
|
|
2604 |
double d; |
|
|
2605 |
} BID_UI64DOUBLE; |
|
|
2606 |
|
|
|
2607 |
#endif |