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734 |
jeremybenn |
/* Copyright (C) 2007, 2009 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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<http://www.gnu.org/licenses/>. */
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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<X1) ? 1 : 0; \
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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<X1) || (X1<CI)) ? 1 : 0; \
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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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| 272 |
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#define __mul_64x64_to_128_fast(P, CX, CY) \
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| 273 |
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{ \
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| 274 |
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UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \
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| 275 |
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CXH = (CX) >> 32; \
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| 276 |
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CXL = (UINT32)(CX); \
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| 277 |
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CYH = (CY) >> 32; \
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| 278 |
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CYL = (UINT32)(CY); \
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| 279 |
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\
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| 280 |
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PM = CXH*CYL; \
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| 281 |
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PL = CXL*CYL; \
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| 282 |
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PH = CXH*CYH; \
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| 283 |
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PM += CXL*CYH; \
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| 284 |
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PM += (PL>>32); \
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| 285 |
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\
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| 286 |
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(P).w[1] = PH + (PM>>32); \
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| 287 |
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(P).w[0] = (PM<<32)+(UINT32)PL; \
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| 288 |
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}
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| 289 |
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// used for CX< 2^60
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#define __sqr64_fast(P, CX) \
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| 291 |
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{ \
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| 292 |
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UINT64 CXH, CXL, PL, PH, PM; \
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| 293 |
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CXH = (CX) >> 32; \
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| 294 |
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CXL = (UINT32)(CX); \
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| 295 |
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\
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| 296 |
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PM = CXH*CXL; \
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PL = CXL*CXL; \
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| 298 |
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PH = CXH*CXH; \
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PM += PM; \
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| 300 |
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PM += (PL>>32); \
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\
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| 302 |
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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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| 305 |
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// get full 64x64bit product
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| 306 |
|
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// Note:
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| 307 |
|
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// This implementation is used for CX < 2^61, CY < 2^61
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| 308 |
|
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//
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| 309 |
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|
#define __mul_64x64_to_64_high_fast(P, CX, CY) \
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| 310 |
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{ \
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| 311 |
|
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UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \
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| 312 |
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CXH = (CX) >> 32; \
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CXL = (UINT32)(CX); \
|
| 314 |
|
|
CYH = (CY) >> 32; \
|
| 315 |
|
|
CYL = (UINT32)(CY); \
|
| 316 |
|
|
\
|
| 317 |
|
|
PM = CXH*CYL; \
|
| 318 |
|
|
PL = CXL*CYL; \
|
| 319 |
|
|
PH = CXH*CYH; \
|
| 320 |
|
|
PM += CXL*CYH; \
|
| 321 |
|
|
PM += (PL>>32); \
|
| 322 |
|
|
\
|
| 323 |
|
|
(P) = PH + (PM>>32); \
|
| 324 |
|
|
}
|
| 325 |
|
|
// get full 64x64bit product
|
| 326 |
|
|
//
|
| 327 |
|
|
#define __mul_64x64_to_128_full(P, CX, CY) \
|
| 328 |
|
|
{ \
|
| 329 |
|
|
UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\
|
| 330 |
|
|
CXH = (CX) >> 32; \
|
| 331 |
|
|
CXL = (UINT32)(CX); \
|
| 332 |
|
|
CYH = (CY) >> 32; \
|
| 333 |
|
|
CYL = (UINT32)(CY); \
|
| 334 |
|
|
\
|
| 335 |
|
|
PM = CXH*CYL; \
|
| 336 |
|
|
PH = CXH*CYH; \
|
| 337 |
|
|
PL = CXL*CYL; \
|
| 338 |
|
|
PM2 = CXL*CYH; \
|
| 339 |
|
|
PH += (PM>>32); \
|
| 340 |
|
|
PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \
|
| 341 |
|
|
\
|
| 342 |
|
|
(P).w[1] = PH + (PM>>32); \
|
| 343 |
|
|
(P).w[0] = (PM<<32)+(UINT32)PL; \
|
| 344 |
|
|
}
|
| 345 |
|
|
#define __mul_128x128_high(Q, A, B) \
|
| 346 |
|
|
{ \
|
| 347 |
|
|
UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \
|
| 348 |
|
|
\
|
| 349 |
|
|
__mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \
|
| 350 |
|
|
__mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \
|
| 351 |
|
|
__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \
|
| 352 |
|
|
__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
|
| 2412 |
|
|
#define MASK_ANY_INF 0x7c00000000000000ull
|
| 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
|
| 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:
|
| 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
|
