/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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This file is part of GCC.
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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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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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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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Software Foundation; either version 3, or (at your option) any later
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version.
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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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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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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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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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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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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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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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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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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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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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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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<http://www.gnu.org/licenses/>. */
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/*****************************************************************************
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/*****************************************************************************
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* BID64 divide
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* BID64 divide
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*****************************************************************************
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*****************************************************************************
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*
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*
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* Algorithm description:
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* Algorithm description:
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*
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*
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* if(coefficient_x<coefficient_y)
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* if(coefficient_x<coefficient_y)
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* p = number_digits(coefficient_y) - number_digits(coefficient_x)
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* p = number_digits(coefficient_y) - number_digits(coefficient_x)
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* A = coefficient_x*10^p
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* A = coefficient_x*10^p
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* B = coefficient_y
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* B = coefficient_y
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* CA= A*10^(15+j), j=0 for A>=B, 1 otherwise
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* CA= A*10^(15+j), j=0 for A>=B, 1 otherwise
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* Q = 0
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* Q = 0
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* else
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* else
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* get Q=(int)(coefficient_x/coefficient_y)
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* get Q=(int)(coefficient_x/coefficient_y)
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* (based on double precision divide)
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* (based on double precision divide)
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* check for exact divide case
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* check for exact divide case
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* Let R = coefficient_x - Q*coefficient_y
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* Let R = coefficient_x - Q*coefficient_y
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* Let m=16-number_digits(Q)
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* Let m=16-number_digits(Q)
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* CA=R*10^m, Q=Q*10^m
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* CA=R*10^m, Q=Q*10^m
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* B = coefficient_y
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* B = coefficient_y
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* endif
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* endif
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* if (CA<2^64)
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* if (CA<2^64)
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* Q += CA/B (64-bit unsigned divide)
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* Q += CA/B (64-bit unsigned divide)
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* else
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* else
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* get final Q using double precision divide, followed by 3 integer
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* get final Q using double precision divide, followed by 3 integer
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* iterations
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* iterations
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* if exact result, eliminate trailing zeros
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* if exact result, eliminate trailing zeros
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* check for underflow
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* check for underflow
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* round coefficient to nearest
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* round coefficient to nearest
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*
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*
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****************************************************************************/
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****************************************************************************/
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#include "bid_internal.h"
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#include "bid_internal.h"
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#include "bid_div_macros.h"
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#include "bid_div_macros.h"
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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#include <fenv.h>
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#include <fenv.h>
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#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT
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#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT
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#endif
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#endif
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extern UINT32 convert_table[5][128][2];
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extern UINT32 convert_table[5][128][2];
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extern SINT8 factors[][2];
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extern SINT8 factors[][2];
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extern UINT8 packed_10000_zeros[];
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extern UINT8 packed_10000_zeros[];
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#if DECIMAL_CALL_BY_REFERENCE
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#if DECIMAL_CALL_BY_REFERENCE
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void
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void
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bid64_div (UINT64 * pres, UINT64 * px,
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bid64_div (UINT64 * pres, UINT64 * px,
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UINT64 *
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UINT64 *
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py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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_EXC_INFO_PARAM) {
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UINT64 x, y;
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UINT64 x, y;
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#else
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#else
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UINT64
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UINT64
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bid64_div (UINT64 x,
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bid64_div (UINT64 x,
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UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
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UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
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_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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#endif
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UINT128 CA, CT;
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UINT128 CA, CT;
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y, A, B, QX, PD;
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y, A, B, QX, PD;
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UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res;
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UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res;
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UINT64 valid_x, valid_y;
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UINT64 valid_x, valid_y;
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SINT64 D;
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SINT64 D;
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int_double t_scale, tempq, temp_b;
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int_double t_scale, tempq, temp_b;
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int_float tempx, tempy;
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int_float tempx, tempy;
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double da, db, dq, da_h, da_l;
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double da, db, dq, da_h, da_l;
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int exponent_x, exponent_y, bin_expon_cx;
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int exponent_x, exponent_y, bin_expon_cx;
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int diff_expon, ed1, ed2, bin_index;
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int diff_expon, ed1, ed2, bin_index;
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int rmode, amount;
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int rmode, amount;
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int nzeros, i, j, k, d5;
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int nzeros, i, j, k, d5;
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UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
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UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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fexcept_t binaryflags = 0;
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fexcept_t binaryflags = 0;
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#endif
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#endif
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#if DECIMAL_CALL_BY_REFERENCE
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#if DECIMAL_CALL_BY_REFERENCE
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#if !DECIMAL_GLOBAL_ROUNDING
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#if !DECIMAL_GLOBAL_ROUNDING
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_IDEC_round rnd_mode = *prnd_mode;
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_IDEC_round rnd_mode = *prnd_mode;
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#endif
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#endif
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x = *px;
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x = *px;
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y = *py;
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y = *py;
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#endif
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#endif
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valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
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valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
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valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
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valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
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// unpack arguments, check for NaN or Infinity
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// unpack arguments, check for NaN or Infinity
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if (!valid_x) {
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if (!valid_x) {
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// x is Inf. or NaN
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// x is Inf. or NaN
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#ifdef SET_STATUS_FLAGS
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#ifdef SET_STATUS_FLAGS
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if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN
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if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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#endif
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// test if x is NaN
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// test if x is NaN
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if ((x & NAN_MASK64) == NAN_MASK64) {
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if ((x & NAN_MASK64) == NAN_MASK64) {
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#ifdef SET_STATUS_FLAGS
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#ifdef SET_STATUS_FLAGS
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if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
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if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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#endif
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BID_RETURN (coefficient_x & QUIET_MASK64);
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BID_RETURN (coefficient_x & QUIET_MASK64);
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}
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}
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// x is Infinity?
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// x is Infinity?
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if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
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if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
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// check if y is Inf or NaN
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// check if y is Inf or NaN
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
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// y==Inf, return NaN
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// y==Inf, return NaN
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if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf
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if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf
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#ifdef SET_STATUS_FLAGS
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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#endif
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BID_RETURN (NAN_MASK64);
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BID_RETURN (NAN_MASK64);
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}
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}
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} else {
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} else {
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// otherwise return +/-Inf
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// otherwise return +/-Inf
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
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INFINITY_MASK64);
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INFINITY_MASK64);
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}
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}
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}
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}
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// x==0
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// x==0
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if (((y & INFINITY_MASK64) != INFINITY_MASK64)
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if (((y & INFINITY_MASK64) != INFINITY_MASK64)
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&& !(coefficient_y)) {
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&& !(coefficient_y)) {
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// y==0 , return NaN
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// y==0 , return NaN
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#ifdef SET_STATUS_FLAGS
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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#endif
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BID_RETURN (NAN_MASK64);
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BID_RETURN (NAN_MASK64);
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}
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}
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if (((y & INFINITY_MASK64) != INFINITY_MASK64)) {
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if (((y & INFINITY_MASK64) != INFINITY_MASK64)) {
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if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64)
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if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64)
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exponent_y = ((UINT32) (y >> 51)) & 0x3ff;
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exponent_y = ((UINT32) (y >> 51)) & 0x3ff;
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else
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else
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exponent_y = ((UINT32) (y >> 53)) & 0x3ff;
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exponent_y = ((UINT32) (y >> 53)) & 0x3ff;
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sign_y = y & 0x8000000000000000ull;
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sign_y = y & 0x8000000000000000ull;
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exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
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exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
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if (exponent_x > DECIMAL_MAX_EXPON_64)
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if (exponent_x > DECIMAL_MAX_EXPON_64)
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exponent_x = DECIMAL_MAX_EXPON_64;
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exponent_x = DECIMAL_MAX_EXPON_64;
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else if (exponent_x < 0)
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else if (exponent_x < 0)
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exponent_x = 0;
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exponent_x = 0;
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BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53));
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BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53));
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}
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}
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}
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}
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if (!valid_y) {
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if (!valid_y) {
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// y is Inf. or NaN
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// y is Inf. or NaN
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// test if y is NaN
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// test if y is NaN
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if ((y & NAN_MASK64) == NAN_MASK64) {
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if ((y & NAN_MASK64) == NAN_MASK64) {
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#ifdef SET_STATUS_FLAGS
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#ifdef SET_STATUS_FLAGS
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if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
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if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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#endif
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BID_RETURN (coefficient_y & QUIET_MASK64);
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BID_RETURN (coefficient_y & QUIET_MASK64);
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}
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}
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// y is Infinity?
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// y is Infinity?
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
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// return +/-0
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// return +/-0
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BID_RETURN (((x ^ y) & 0x8000000000000000ull));
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BID_RETURN (((x ^ y) & 0x8000000000000000ull));
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}
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}
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// y is 0
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// y is 0
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#ifdef SET_STATUS_FLAGS
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
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__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
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#endif
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#endif
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BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64);
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BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64);
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}
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}
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
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(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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#endif
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diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
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diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
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if (coefficient_x < coefficient_y) {
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if (coefficient_x < coefficient_y) {
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// get number of decimal digits for c_x, c_y
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// get number of decimal digits for c_x, c_y
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//--- get number of bits in the coefficients of x and y ---
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//--- get number of bits in the coefficients of x and y ---
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tempx.d = (float) coefficient_x;
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tempx.d = (float) coefficient_x;
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tempy.d = (float) coefficient_y;
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tempy.d = (float) coefficient_y;
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bin_index = (tempy.i - tempx.i) >> 23;
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bin_index = (tempy.i - tempx.i) >> 23;
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A = coefficient_x * power10_index_binexp[bin_index];
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A = coefficient_x * power10_index_binexp[bin_index];
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B = coefficient_y;
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B = coefficient_y;
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temp_b.d = (double) B;
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temp_b.d = (double) B;
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// compare A, B
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// compare A, B
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DU = (A - B) >> 63;
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DU = (A - B) >> 63;
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ed1 = 15 + (int) DU;
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ed1 = 15 + (int) DU;
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ed2 = estimate_decimal_digits[bin_index] + ed1;
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ed2 = estimate_decimal_digits[bin_index] + ed1;
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T = power10_table_128[ed1].w[0];
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T = power10_table_128[ed1].w[0];
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__mul_64x64_to_128 (CA, A, T);
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__mul_64x64_to_128 (CA, A, T);
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Q = 0;
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Q = 0;
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diff_expon = diff_expon - ed2;
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diff_expon = diff_expon - ed2;
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// adjust double precision db, to ensure that later A/B - (int)(da/db) > -1
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// adjust double precision db, to ensure that later A/B - (int)(da/db) > -1
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if (coefficient_y < 0x0020000000000000ull) {
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if (coefficient_y < 0x0020000000000000ull) {
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temp_b.i += 1;
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temp_b.i += 1;
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db = temp_b.d;
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db = temp_b.d;
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} else
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} else
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db = (double) (B + 2 + (B & 1));
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db = (double) (B + 2 + (B & 1));
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|
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} else {
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} else {
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// get c_x/c_y
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// get c_x/c_y
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// set last bit before conversion to DP
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// set last bit before conversion to DP
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A2 = coefficient_x | 1;
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A2 = coefficient_x | 1;
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da = (double) A2;
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da = (double) A2;
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db = (double) coefficient_y;
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db = (double) coefficient_y;
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|
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tempq.d = da / db;
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tempq.d = da / db;
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Q = (UINT64) tempq.d;
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Q = (UINT64) tempq.d;
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|
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R = coefficient_x - coefficient_y * Q;
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R = coefficient_x - coefficient_y * Q;
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|
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// will use to get number of dec. digits of Q
|
// will use to get number of dec. digits of Q
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bin_expon_cx = (tempq.i >> 52) - 0x3ff;
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bin_expon_cx = (tempq.i >> 52) - 0x3ff;
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|
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// R<0 ?
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// R<0 ?
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D = ((SINT64) R) >> 63;
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D = ((SINT64) R) >> 63;
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Q += D;
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Q += D;
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R += (coefficient_y & D);
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R += (coefficient_y & D);
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// exact result ?
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// exact result ?
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if (((SINT64) R) <= 0) {
|
if (((SINT64) R) <= 0) {
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// can have R==-1 for coeff_y==1
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// can have R==-1 for coeff_y==1
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res =
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res =
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get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode,
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get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode,
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pfpsf);
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pfpsf);
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
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(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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#endif
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
|
// get decimal digits of Q
|
// get decimal digits of Q
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DU = power10_index_binexp[bin_expon_cx] - Q - 1;
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DU = power10_index_binexp[bin_expon_cx] - Q - 1;
|
DU >>= 63;
|
DU >>= 63;
|
|
|
ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU;
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ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU;
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|
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T = power10_table_128[ed2].w[0];
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T = power10_table_128[ed2].w[0];
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__mul_64x64_to_128 (CA, R, T);
|
__mul_64x64_to_128 (CA, R, T);
|
B = coefficient_y;
|
B = coefficient_y;
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|
|
Q *= power10_table_128[ed2].w[0];
|
Q *= power10_table_128[ed2].w[0];
|
diff_expon -= ed2;
|
diff_expon -= ed2;
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|
|
}
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}
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|
|
if (!CA.w[1]) {
|
if (!CA.w[1]) {
|
Q2 = CA.w[0] / B;
|
Q2 = CA.w[0] / B;
|
B2 = B + B;
|
B2 = B + B;
|
B4 = B2 + B2;
|
B4 = B2 + B2;
|
R = CA.w[0] - Q2 * B;
|
R = CA.w[0] - Q2 * B;
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Q += Q2;
|
Q += Q2;
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} else {
|
} else {
|
|
|
// 2^64
|
// 2^64
|
t_scale.i = 0x43f0000000000000ull;
|
t_scale.i = 0x43f0000000000000ull;
|
// convert CA to DP
|
// convert CA to DP
|
da_h = CA.w[1];
|
da_h = CA.w[1];
|
da_l = CA.w[0];
|
da_l = CA.w[0];
|
da = da_h * t_scale.d + da_l;
|
da = da_h * t_scale.d + da_l;
|
|
|
// quotient
|
// quotient
|
dq = da / db;
|
dq = da / db;
|
Q2 = (UINT64) dq;
|
Q2 = (UINT64) dq;
|
|
|
// get w[0] remainder
|
// get w[0] remainder
|
R = CA.w[0] - Q2 * B;
|
R = CA.w[0] - Q2 * B;
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|
|
// R<0 ?
|
// R<0 ?
|
D = ((SINT64) R) >> 63;
|
D = ((SINT64) R) >> 63;
|
Q2 += D;
|
Q2 += D;
|
R += (B & D);
|
R += (B & D);
|
|
|
// now R<6*B
|
// now R<6*B
|
|
|
// quick divide
|
// quick divide
|
|
|
// 4*B
|
// 4*B
|
B2 = B + B;
|
B2 = B + B;
|
B4 = B2 + B2;
|
B4 = B2 + B2;
|
|
|
R = R - B4;
|
R = R - B4;
|
// R<0 ?
|
// R<0 ?
|
D = ((SINT64) R) >> 63;
|
D = ((SINT64) R) >> 63;
|
// restore R if negative
|
// restore R if negative
|
R += (B4 & D);
|
R += (B4 & D);
|
Q2 += ((~D) & 4);
|
Q2 += ((~D) & 4);
|
|
|
R = R - B2;
|
R = R - B2;
|
// R<0 ?
|
// R<0 ?
|
D = ((SINT64) R) >> 63;
|
D = ((SINT64) R) >> 63;
|
// restore R if negative
|
// restore R if negative
|
R += (B2 & D);
|
R += (B2 & D);
|
Q2 += ((~D) & 2);
|
Q2 += ((~D) & 2);
|
|
|
R = R - B;
|
R = R - B;
|
// R<0 ?
|
// R<0 ?
|
D = ((SINT64) R) >> 63;
|
D = ((SINT64) R) >> 63;
|
// restore R if negative
|
// restore R if negative
|
R += (B & D);
|
R += (B & D);
|
Q2 += ((~D) & 1);
|
Q2 += ((~D) & 1);
|
|
|
Q += Q2;
|
Q += Q2;
|
}
|
}
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if (R) {
|
if (R) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
else
|
else
|
#endif
|
#endif
|
#else
|
#else
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
if (!R)
|
if (!R)
|
#endif
|
#endif
|
#endif
|
#endif
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
{
|
{
|
// eliminate trailing zeros
|
// eliminate trailing zeros
|
|
|
// check whether CX, CY are short
|
// check whether CX, CY are short
|
if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) {
|
if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) {
|
i = (int) coefficient_y - 1;
|
i = (int) coefficient_y - 1;
|
j = (int) coefficient_x - 1;
|
j = (int) coefficient_x - 1;
|
// difference in powers of 2 factors for Y and X
|
// difference in powers of 2 factors for Y and X
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
// difference in powers of 5 factors
|
// difference in powers of 5 factors
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
if (d5 < nzeros)
|
if (d5 < nzeros)
|
nzeros = d5;
|
nzeros = d5;
|
|
|
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]);
|
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]);
|
|
|
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
|
amount = short_recip_scale[nzeros];
|
amount = short_recip_scale[nzeros];
|
Q = CT.w[1] >> amount;
|
Q = CT.w[1] >> amount;
|
|
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
} else {
|
} else {
|
tdigit[0] = Q & 0x3ffffff;
|
tdigit[0] = Q & 0x3ffffff;
|
tdigit[1] = 0;
|
tdigit[1] = 0;
|
QX = Q >> 26;
|
QX = Q >> 26;
|
QX32 = QX;
|
QX32 = QX;
|
nzeros = 0;
|
nzeros = 0;
|
|
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
k = (QX32 & 127);
|
k = (QX32 & 127);
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[1] += convert_table[j][k][1];
|
tdigit[1] += convert_table[j][k][1];
|
if (tdigit[0] >= 100000000) {
|
if (tdigit[0] >= 100000000) {
|
tdigit[0] -= 100000000;
|
tdigit[0] -= 100000000;
|
tdigit[1]++;
|
tdigit[1]++;
|
}
|
}
|
}
|
}
|
|
|
digit = tdigit[0];
|
digit = tdigit[0];
|
if (!digit && !tdigit[1])
|
if (!digit && !tdigit[1])
|
nzeros += 16;
|
nzeros += 16;
|
else {
|
else {
|
if (!digit) {
|
if (!digit) {
|
nzeros += 8;
|
nzeros += 8;
|
digit = tdigit[1];
|
digit = tdigit[1];
|
}
|
}
|
// decompose digit
|
// decompose digit
|
PD = (UINT64) digit *0x068DB8BBull;
|
PD = (UINT64) digit *0x068DB8BBull;
|
digit_h = (UINT32) (PD >> 40);
|
digit_h = (UINT32) (PD >> 40);
|
digit_low = digit - digit_h * 10000;
|
digit_low = digit - digit_h * 10000;
|
|
|
if (!digit_low)
|
if (!digit_low)
|
nzeros += 4;
|
nzeros += 4;
|
else
|
else
|
digit_h = digit_low;
|
digit_h = digit_low;
|
|
|
if (!(digit_h & 1))
|
if (!(digit_h & 1))
|
nzeros +=
|
nzeros +=
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
(digit_h & 7));
|
(digit_h & 7));
|
}
|
}
|
|
|
if (nzeros) {
|
if (nzeros) {
|
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]);
|
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]);
|
|
|
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
|
amount = short_recip_scale[nzeros];
|
amount = short_recip_scale[nzeros];
|
Q = CT.w[1] >> amount;
|
Q = CT.w[1] >> amount;
|
}
|
}
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
|
|
}
|
}
|
if (diff_expon >= 0) {
|
if (diff_expon >= 0) {
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q,
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q,
|
rnd_mode, pfpsf);
|
rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
#endif
|
#endif
|
|
|
if (diff_expon >= 0) {
|
if (diff_expon >= 0) {
|
#ifdef IEEE_ROUND_NEAREST
|
#ifdef IEEE_ROUND_NEAREST
|
// round to nearest code
|
// round to nearest code
|
// R*10
|
// R*10
|
R += R;
|
R += R;
|
R = (R << 2) + R;
|
R = (R << 2) + R;
|
B5 = B4 + B;
|
B5 = B4 + B;
|
|
|
// compare 10*R to 5*B
|
// compare 10*R to 5*B
|
R = B5 - R;
|
R = B5 - R;
|
// correction for (R==0 && (Q&1))
|
// correction for (R==0 && (Q&1))
|
R -= (Q & 1);
|
R -= (Q & 1);
|
// R<0 ?
|
// R<0 ?
|
D = ((UINT64) R) >> 63;
|
D = ((UINT64) R) >> 63;
|
Q += D;
|
Q += D;
|
#else
|
#else
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
// round to nearest code
|
// round to nearest code
|
// R*10
|
// R*10
|
R += R;
|
R += R;
|
R = (R << 2) + R;
|
R = (R << 2) + R;
|
B5 = B4 + B;
|
B5 = B4 + B;
|
|
|
// compare 10*R to 5*B
|
// compare 10*R to 5*B
|
R = B5 - R;
|
R = B5 - R;
|
// correction for (R==0 && (Q&1))
|
// correction for (R==0 && (Q&1))
|
R -= (Q & 1);
|
R -= (Q & 1);
|
// R<0 ?
|
// R<0 ?
|
D = ((UINT64) R) >> 63;
|
D = ((UINT64) R) >> 63;
|
Q += D;
|
Q += D;
|
#else
|
#else
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
rmode = 3 - rmode;
|
rmode = 3 - rmode;
|
switch (rmode) {
|
switch (rmode) {
|
case 0: // round to nearest code
|
case 0: // round to nearest code
|
case ROUNDING_TIES_AWAY:
|
case ROUNDING_TIES_AWAY:
|
// R*10
|
// R*10
|
R += R;
|
R += R;
|
R = (R << 2) + R;
|
R = (R << 2) + R;
|
B5 = B4 + B;
|
B5 = B4 + B;
|
// compare 10*R to 5*B
|
// compare 10*R to 5*B
|
R = B5 - R;
|
R = B5 - R;
|
// correction for (R==0 && (Q&1))
|
// correction for (R==0 && (Q&1))
|
R -= ((Q | (rmode >> 2)) & 1);
|
R -= ((Q | (rmode >> 2)) & 1);
|
// R<0 ?
|
// R<0 ?
|
D = ((UINT64) R) >> 63;
|
D = ((UINT64) R) >> 63;
|
Q += D;
|
Q += D;
|
break;
|
break;
|
case ROUNDING_DOWN:
|
case ROUNDING_DOWN:
|
case ROUNDING_TO_ZERO:
|
case ROUNDING_TO_ZERO:
|
break;
|
break;
|
default: // rounding up
|
default: // rounding up
|
Q++;
|
Q++;
|
break;
|
break;
|
}
|
}
|
#endif
|
#endif
|
#endif
|
#endif
|
|
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode,
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode,
|
pfpsf);
|
pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else {
|
} else {
|
// UF occurs
|
// UF occurs
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((diff_expon + 16 < 0)) {
|
if ((diff_expon + 16 < 0)) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#endif
|
#endif
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
res =
|
res =
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf);
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
|
|
}
|
}
|
}
|
}
|
|
|
|
|
|
|
TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y)
|
TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y)
|
UINT256 CA4 =
|
UINT256 CA4 =
|
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
|
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
|
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
|
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
|
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res;
|
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res;
|
int_float fx, fy, f64;
|
int_float fx, fy, f64;
|
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
|
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
|
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
|
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
|
digits_q, amount;
|
digits_q, amount;
|
int nzeros, i, j, k, d5, done = 0;
|
int nzeros, i, j, k, d5, done = 0;
|
unsigned rmode;
|
unsigned rmode;
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
fexcept_t binaryflags = 0;
|
fexcept_t binaryflags = 0;
|
#endif
|
#endif
|
|
|
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y);
|
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y);
|
|
|
// unpack arguments, check for NaN or Infinity
|
// unpack arguments, check for NaN or Infinity
|
CX.w[1] = 0;
|
CX.w[1] = 0;
|
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) {
|
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN
|
if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN
|
((x & SNAN_MASK64) == SNAN_MASK64))
|
((x & SNAN_MASK64) == SNAN_MASK64))
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
// test if x is NaN
|
// test if x is NaN
|
if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
res = CX.w[0];
|
res = CX.w[0];
|
BID_RETURN (res & QUIET_MASK64);
|
BID_RETURN (res & QUIET_MASK64);
|
}
|
}
|
// x is Infinity?
|
// x is Infinity?
|
if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
// check if y is Inf.
|
// check if y is Inf.
|
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
|
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
|
// return NaN
|
// return NaN
|
{
|
{
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
|
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
|
// otherwise return +/-Inf
|
// otherwise return +/-Inf
|
res =
|
res =
|
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
// x is 0
|
// x is 0
|
if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) {
|
if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) {
|
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) {
|
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
// x=y=0, return NaN
|
// x=y=0, return NaN
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// return 0
|
// return 0
|
res = ((x) ^ y.w[1]) & 0x8000000000000000ull;
|
res = ((x) ^ y.w[1]) & 0x8000000000000000ull;
|
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128;
|
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128;
|
if (exponent_x > DECIMAL_MAX_EXPON_64)
|
if (exponent_x > DECIMAL_MAX_EXPON_64)
|
exponent_x = DECIMAL_MAX_EXPON_64;
|
exponent_x = DECIMAL_MAX_EXPON_64;
|
else if (exponent_x < 0)
|
else if (exponent_x < 0)
|
exponent_x = 0;
|
exponent_x = 0;
|
res |= (((UINT64) exponent_x) << 53);
|
res |= (((UINT64) exponent_x) << 53);
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS);
|
exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS);
|
if (!valid_y) {
|
if (!valid_y) {
|
// y is Inf. or NaN
|
// y is Inf. or NaN
|
|
|
// test if y is NaN
|
// test if y is NaN
|
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
|
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull);
|
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull);
|
Tmp.w[0] = CY.w[0];
|
Tmp.w[0] = CY.w[0];
|
TP128 = reciprocals10_128[18];
|
TP128 = reciprocals10_128[18];
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
amount = recip_scale[18];
|
amount = recip_scale[18];
|
__shr_128 (Tmp, Qh, amount);
|
__shr_128 (Tmp, Qh, amount);
|
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// y is Infinity?
|
// y is Infinity?
|
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
// return +/-0
|
// return +/-0
|
res = sign_x ^ sign_y;
|
res = sign_x ^ sign_y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// y is 0, return +/-Inf
|
// y is 0, return +/-Inf
|
res =
|
res =
|
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
|
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
|
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
|
|
|
if (__unsigned_compare_gt_128 (CY, CX)) {
|
if (__unsigned_compare_gt_128 (CY, CX)) {
|
// CX < CY
|
// CX < CY
|
|
|
// 2^64
|
// 2^64
|
f64.i = 0x5f800000;
|
f64.i = 0x5f800000;
|
|
|
// fx ~ CX, fy ~ CY
|
// fx ~ CX, fy ~ CY
|
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
|
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
|
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
|
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
|
// expon_cy - expon_cx
|
// expon_cy - expon_cx
|
bin_index = (fy.i - fx.i) >> 23;
|
bin_index = (fy.i - fx.i) >> 23;
|
|
|
if (CX.w[1]) {
|
if (CX.w[1]) {
|
T = power10_index_binexp_128[bin_index].w[0];
|
T = power10_index_binexp_128[bin_index].w[0];
|
__mul_64x128_short (CA, T, CX);
|
__mul_64x128_short (CA, T, CX);
|
} else {
|
} else {
|
T128 = power10_index_binexp_128[bin_index];
|
T128 = power10_index_binexp_128[bin_index];
|
__mul_64x128_short (CA, CX.w[0], T128);
|
__mul_64x128_short (CA, CX.w[0], T128);
|
}
|
}
|
|
|
ed2 = 15;
|
ed2 = 15;
|
if (__unsigned_compare_gt_128 (CY, CA))
|
if (__unsigned_compare_gt_128 (CY, CA))
|
ed2++;
|
ed2++;
|
|
|
T128 = power10_table_128[ed2];
|
T128 = power10_table_128[ed2];
|
__mul_128x128_to_256 (CA4, CA, T128);
|
__mul_128x128_to_256 (CA4, CA, T128);
|
|
|
ed2 += estimate_decimal_digits[bin_index];
|
ed2 += estimate_decimal_digits[bin_index];
|
CQ.w[0] = CQ.w[1] = 0;
|
CQ.w[0] = CQ.w[1] = 0;
|
diff_expon = diff_expon - ed2;
|
diff_expon = diff_expon - ed2;
|
|
|
} else {
|
} else {
|
// get CQ = CX/CY
|
// get CQ = CX/CY
|
__div_128_by_128 (&CQ, &CR, CX, CY);
|
__div_128_by_128 (&CQ, &CR, CX, CY);
|
|
|
// get number of decimal digits in CQ
|
// get number of decimal digits in CQ
|
// 2^64
|
// 2^64
|
f64.i = 0x5f800000;
|
f64.i = 0x5f800000;
|
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
|
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
|
// binary expon. of CQ
|
// binary expon. of CQ
|
bin_expon = (fx.i - 0x3f800000) >> 23;
|
bin_expon = (fx.i - 0x3f800000) >> 23;
|
|
|
digits_q = estimate_decimal_digits[bin_expon];
|
digits_q = estimate_decimal_digits[bin_expon];
|
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
|
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
|
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
|
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
|
if (__unsigned_compare_ge_128 (CQ, TP128))
|
if (__unsigned_compare_ge_128 (CQ, TP128))
|
digits_q++;
|
digits_q++;
|
|
|
if (digits_q <= 16) {
|
if (digits_q <= 16) {
|
if (!CR.w[1] && !CR.w[0]) {
|
if (!CR.w[1] && !CR.w[0]) {
|
res = get_BID64 (sign_x ^ sign_y, diff_expon,
|
res = get_BID64 (sign_x ^ sign_y, diff_expon,
|
CQ.w[0], rnd_mode, pfpsf);
|
CQ.w[0], rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
ed2 = 16 - digits_q;
|
ed2 = 16 - digits_q;
|
T128.w[0] = power10_table_128[ed2].w[0];
|
T128.w[0] = power10_table_128[ed2].w[0];
|
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
|
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
|
diff_expon = diff_expon - ed2;
|
diff_expon = diff_expon - ed2;
|
CQ.w[0] *= T128.w[0];
|
CQ.w[0] *= T128.w[0];
|
} else {
|
} else {
|
ed2 = digits_q - 16;
|
ed2 = digits_q - 16;
|
diff_expon += ed2;
|
diff_expon += ed2;
|
T128 = reciprocals10_128[ed2];
|
T128 = reciprocals10_128[ed2];
|
__mul_128x128_to_256 (P256, CQ, T128);
|
__mul_128x128_to_256 (P256, CQ, T128);
|
amount = recip_scale[ed2];
|
amount = recip_scale[ed2];
|
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
|
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
|
CQ.w[1] = 0;
|
CQ.w[1] = 0;
|
|
|
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
|
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
|
|
|
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
|
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
|
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
|
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
|
|
|
CA4.w[1] = CX.w[1] - QB256.w[1];
|
CA4.w[1] = CX.w[1] - QB256.w[1];
|
CA4.w[0] = CX.w[0] - QB256.w[0];
|
CA4.w[0] = CX.w[0] - QB256.w[0];
|
if (CX.w[0] < QB256.w[0])
|
if (CX.w[0] < QB256.w[0])
|
CA4.w[1]--;
|
CA4.w[1]--;
|
if (CR.w[0] || CR.w[1])
|
if (CR.w[0] || CR.w[1])
|
CA4.w[0] |= 1;
|
CA4.w[0] |= 1;
|
done = 1;
|
done = 1;
|
|
|
}
|
}
|
|
|
}
|
}
|
if (!done) {
|
if (!done) {
|
__div_256_by_128 (&CQ, &CA4, CY);
|
__div_256_by_128 (&CQ, &CA4, CY);
|
}
|
}
|
|
|
|
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if (CA4.w[0] || CA4.w[1]) {
|
if (CA4.w[0] || CA4.w[1]) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
else
|
else
|
#endif
|
#endif
|
#else
|
#else
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
if (!CA4.w[0] && !CA4.w[1])
|
if (!CA4.w[0] && !CA4.w[1])
|
#endif
|
#endif
|
#endif
|
#endif
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
// check whether result is exact
|
// check whether result is exact
|
{
|
{
|
// check whether CX, CY are short
|
// check whether CX, CY are short
|
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
|
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
|
i = (int) CY.w[0] - 1;
|
i = (int) CY.w[0] - 1;
|
j = (int) CX.w[0] - 1;
|
j = (int) CX.w[0] - 1;
|
// difference in powers of 2 factors for Y and X
|
// difference in powers of 2 factors for Y and X
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
// difference in powers of 5 factors
|
// difference in powers of 5 factors
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
if (d5 < nzeros)
|
if (d5 < nzeros)
|
nzeros = d5;
|
nzeros = d5;
|
// get P*(2^M[extra_digits])/10^extra_digits
|
// get P*(2^M[extra_digits])/10^extra_digits
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
amount = recip_scale[nzeros];
|
amount = recip_scale[nzeros];
|
__shr_128_long (CQ, Qh, amount);
|
__shr_128_long (CQ, Qh, amount);
|
|
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
} else {
|
} else {
|
// decompose Q as Qh*10^17 + Ql
|
// decompose Q as Qh*10^17 + Ql
|
Q_low = CQ.w[0];
|
Q_low = CQ.w[0];
|
|
|
{
|
{
|
tdigit[0] = Q_low & 0x3ffffff;
|
tdigit[0] = Q_low & 0x3ffffff;
|
tdigit[1] = 0;
|
tdigit[1] = 0;
|
QX = Q_low >> 26;
|
QX = Q_low >> 26;
|
QX32 = QX;
|
QX32 = QX;
|
nzeros = 0;
|
nzeros = 0;
|
|
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
k = (QX32 & 127);
|
k = (QX32 & 127);
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[1] += convert_table[j][k][1];
|
tdigit[1] += convert_table[j][k][1];
|
if (tdigit[0] >= 100000000) {
|
if (tdigit[0] >= 100000000) {
|
tdigit[0] -= 100000000;
|
tdigit[0] -= 100000000;
|
tdigit[1]++;
|
tdigit[1]++;
|
}
|
}
|
}
|
}
|
|
|
if (tdigit[1] >= 100000000) {
|
if (tdigit[1] >= 100000000) {
|
tdigit[1] -= 100000000;
|
tdigit[1] -= 100000000;
|
if (tdigit[1] >= 100000000)
|
if (tdigit[1] >= 100000000)
|
tdigit[1] -= 100000000;
|
tdigit[1] -= 100000000;
|
}
|
}
|
|
|
digit = tdigit[0];
|
digit = tdigit[0];
|
if (!digit && !tdigit[1])
|
if (!digit && !tdigit[1])
|
nzeros += 16;
|
nzeros += 16;
|
else {
|
else {
|
if (!digit) {
|
if (!digit) {
|
nzeros += 8;
|
nzeros += 8;
|
digit = tdigit[1];
|
digit = tdigit[1];
|
}
|
}
|
// decompose digit
|
// decompose digit
|
PD = (UINT64) digit *0x068DB8BBull;
|
PD = (UINT64) digit *0x068DB8BBull;
|
digit_h = (UINT32) (PD >> 40);
|
digit_h = (UINT32) (PD >> 40);
|
digit_low = digit - digit_h * 10000;
|
digit_low = digit - digit_h * 10000;
|
|
|
if (!digit_low)
|
if (!digit_low)
|
nzeros += 4;
|
nzeros += 4;
|
else
|
else
|
digit_h = digit_low;
|
digit_h = digit_low;
|
|
|
if (!(digit_h & 1))
|
if (!(digit_h & 1))
|
nzeros +=
|
nzeros +=
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
(digit_h & 7));
|
(digit_h & 7));
|
}
|
}
|
|
|
if (nzeros) {
|
if (nzeros) {
|
// get P*(2^M[extra_digits])/10^extra_digits
|
// get P*(2^M[extra_digits])/10^extra_digits
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
amount = recip_scale[nzeros];
|
amount = recip_scale[nzeros];
|
__shr_128 (CQ, Qh, amount);
|
__shr_128 (CQ, Qh, amount);
|
}
|
}
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
|
|
}
|
}
|
}
|
}
|
if(diff_expon>=0){
|
if(diff_expon>=0){
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
|
rnd_mode, pfpsf);
|
rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
#endif
|
#endif
|
|
|
if (diff_expon >= 0) {
|
if (diff_expon >= 0) {
|
#ifdef IEEE_ROUND_NEAREST
|
#ifdef IEEE_ROUND_NEAREST
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
|
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
|
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
#else
|
#else
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
|
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
|
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
#else
|
#else
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
rmode = 3 - rmode;
|
rmode = 3 - rmode;
|
switch (rmode) {
|
switch (rmode) {
|
case ROUNDING_TO_NEAREST: // round to nearest code
|
case ROUNDING_TO_NEAREST: // round to nearest code
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
case ROUNDING_TIES_AWAY:
|
case ROUNDING_TIES_AWAY:
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
case ROUNDING_DOWN:
|
case ROUNDING_DOWN:
|
case ROUNDING_TO_ZERO:
|
case ROUNDING_TO_ZERO:
|
break;
|
break;
|
default: // rounding up
|
default: // rounding up
|
CQ.w[0]++;
|
CQ.w[0]++;
|
if (!CQ.w[0])
|
if (!CQ.w[0])
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
}
|
}
|
#endif
|
#endif
|
#endif
|
#endif
|
|
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
|
pfpsf);
|
pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else {
|
} else {
|
// UF occurs
|
// UF occurs
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((diff_expon + 16 < 0)) {
|
if ((diff_expon + 16 < 0)) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#endif
|
#endif
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
res =
|
res =
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
|
|
}
|
}
|
|
|
}
|
}
|
|
|
|
|
//#define LEAVE_TRAILING_ZEROS
|
//#define LEAVE_TRAILING_ZEROS
|
|
|
TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y)
|
TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y)
|
|
|
UINT256 CA4 =
|
UINT256 CA4 =
|
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
|
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
|
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
|
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
|
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y;
|
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y;
|
int_float fx, fy, f64;
|
int_float fx, fy, f64;
|
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
|
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
|
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
|
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
|
digits_q, amount;
|
digits_q, amount;
|
int nzeros, i, j, k, d5, done = 0;
|
int nzeros, i, j, k, d5, done = 0;
|
unsigned rmode;
|
unsigned rmode;
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
fexcept_t binaryflags = 0;
|
fexcept_t binaryflags = 0;
|
#endif
|
#endif
|
|
|
valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y));
|
valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y));
|
|
|
// unpack arguments, check for NaN or Infinity
|
// unpack arguments, check for NaN or Infinity
|
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
|
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
|
// test if x is NaN
|
// test if x is NaN
|
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
|
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
|
(y & 0x7e00000000000000ull) == 0x7e00000000000000ull)
|
(y & 0x7e00000000000000ull) == 0x7e00000000000000ull)
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
|
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
|
Tmp.w[0] = CX.w[0];
|
Tmp.w[0] = CX.w[0];
|
TP128 = reciprocals10_128[18];
|
TP128 = reciprocals10_128[18];
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
amount = recip_scale[18];
|
amount = recip_scale[18];
|
__shr_128 (Tmp, Qh, amount);
|
__shr_128 (Tmp, Qh, amount);
|
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// x is Infinity?
|
// x is Infinity?
|
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
// check if y is Inf.
|
// check if y is Inf.
|
if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull))
|
if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull))
|
// return NaN
|
// return NaN
|
{
|
{
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
|
if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
|
// otherwise return +/-Inf
|
// otherwise return +/-Inf
|
res =
|
res =
|
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
// x is 0
|
// x is 0
|
if (((y & INFINITY_MASK64) != INFINITY_MASK64) &&
|
if (((y & INFINITY_MASK64) != INFINITY_MASK64) &&
|
!(CY.w[0])) {
|
!(CY.w[0])) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
// x=y=0, return NaN
|
// x=y=0, return NaN
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// return 0
|
// return 0
|
if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) {
|
if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) {
|
if (!CY.w[0]) {
|
if (!CY.w[0]) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
exponent_x =
|
exponent_x =
|
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 +
|
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 +
|
(DECIMAL_EXPONENT_BIAS << 1);
|
(DECIMAL_EXPONENT_BIAS << 1);
|
if (exponent_x > DECIMAL_MAX_EXPON_64)
|
if (exponent_x > DECIMAL_MAX_EXPON_64)
|
exponent_x = DECIMAL_MAX_EXPON_64;
|
exponent_x = DECIMAL_MAX_EXPON_64;
|
else if (exponent_x < 0)
|
else if (exponent_x < 0)
|
exponent_x = 0;
|
exponent_x = 0;
|
res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53);
|
res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53);
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
CY.w[1] = 0;
|
CY.w[1] = 0;
|
if (!valid_y) {
|
if (!valid_y) {
|
// y is Inf. or NaN
|
// y is Inf. or NaN
|
|
|
// test if y is NaN
|
// test if y is NaN
|
if ((y & NAN_MASK64) == NAN_MASK64) {
|
if ((y & NAN_MASK64) == NAN_MASK64) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
|
if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
BID_RETURN (CY.w[0] & QUIET_MASK64);
|
BID_RETURN (CY.w[0] & QUIET_MASK64);
|
}
|
}
|
// y is Infinity?
|
// y is Infinity?
|
if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
// return +/-0
|
// return +/-0
|
res = sign_x ^ sign_y;
|
res = sign_x ^ sign_y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// y is 0, return +/-Inf
|
// y is 0, return +/-Inf
|
res =
|
res =
|
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
|
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
diff_expon =
|
diff_expon =
|
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 +
|
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 +
|
(DECIMAL_EXPONENT_BIAS << 1);
|
(DECIMAL_EXPONENT_BIAS << 1);
|
|
|
if (__unsigned_compare_gt_128 (CY, CX)) {
|
if (__unsigned_compare_gt_128 (CY, CX)) {
|
// CX < CY
|
// CX < CY
|
|
|
// 2^64
|
// 2^64
|
f64.i = 0x5f800000;
|
f64.i = 0x5f800000;
|
|
|
// fx ~ CX, fy ~ CY
|
// fx ~ CX, fy ~ CY
|
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
|
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
|
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
|
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
|
// expon_cy - expon_cx
|
// expon_cy - expon_cx
|
bin_index = (fy.i - fx.i) >> 23;
|
bin_index = (fy.i - fx.i) >> 23;
|
|
|
if (CX.w[1]) {
|
if (CX.w[1]) {
|
T = power10_index_binexp_128[bin_index].w[0];
|
T = power10_index_binexp_128[bin_index].w[0];
|
__mul_64x128_short (CA, T, CX);
|
__mul_64x128_short (CA, T, CX);
|
} else {
|
} else {
|
T128 = power10_index_binexp_128[bin_index];
|
T128 = power10_index_binexp_128[bin_index];
|
__mul_64x128_short (CA, CX.w[0], T128);
|
__mul_64x128_short (CA, CX.w[0], T128);
|
}
|
}
|
|
|
ed2 = 15;
|
ed2 = 15;
|
if (__unsigned_compare_gt_128 (CY, CA))
|
if (__unsigned_compare_gt_128 (CY, CA))
|
ed2++;
|
ed2++;
|
|
|
T128 = power10_table_128[ed2];
|
T128 = power10_table_128[ed2];
|
__mul_128x128_to_256 (CA4, CA, T128);
|
__mul_128x128_to_256 (CA4, CA, T128);
|
|
|
ed2 += estimate_decimal_digits[bin_index];
|
ed2 += estimate_decimal_digits[bin_index];
|
CQ.w[0] = CQ.w[1] = 0;
|
CQ.w[0] = CQ.w[1] = 0;
|
diff_expon = diff_expon - ed2;
|
diff_expon = diff_expon - ed2;
|
|
|
} else {
|
} else {
|
// get CQ = CX/CY
|
// get CQ = CX/CY
|
__div_128_by_128 (&CQ, &CR, CX, CY);
|
__div_128_by_128 (&CQ, &CR, CX, CY);
|
|
|
// get number of decimal digits in CQ
|
// get number of decimal digits in CQ
|
// 2^64
|
// 2^64
|
f64.i = 0x5f800000;
|
f64.i = 0x5f800000;
|
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
|
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
|
// binary expon. of CQ
|
// binary expon. of CQ
|
bin_expon = (fx.i - 0x3f800000) >> 23;
|
bin_expon = (fx.i - 0x3f800000) >> 23;
|
|
|
digits_q = estimate_decimal_digits[bin_expon];
|
digits_q = estimate_decimal_digits[bin_expon];
|
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
|
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
|
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
|
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
|
if (__unsigned_compare_ge_128 (CQ, TP128))
|
if (__unsigned_compare_ge_128 (CQ, TP128))
|
digits_q++;
|
digits_q++;
|
|
|
if (digits_q <= 16) {
|
if (digits_q <= 16) {
|
if (!CR.w[1] && !CR.w[0]) {
|
if (!CR.w[1] && !CR.w[0]) {
|
res = get_BID64 (sign_x ^ sign_y, diff_expon,
|
res = get_BID64 (sign_x ^ sign_y, diff_expon,
|
CQ.w[0], rnd_mode, pfpsf);
|
CQ.w[0], rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
ed2 = 16 - digits_q;
|
ed2 = 16 - digits_q;
|
T128.w[0] = power10_table_128[ed2].w[0];
|
T128.w[0] = power10_table_128[ed2].w[0];
|
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
|
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
|
diff_expon = diff_expon - ed2;
|
diff_expon = diff_expon - ed2;
|
CQ.w[0] *= T128.w[0];
|
CQ.w[0] *= T128.w[0];
|
} else {
|
} else {
|
ed2 = digits_q - 16;
|
ed2 = digits_q - 16;
|
diff_expon += ed2;
|
diff_expon += ed2;
|
T128 = reciprocals10_128[ed2];
|
T128 = reciprocals10_128[ed2];
|
__mul_128x128_to_256 (P256, CQ, T128);
|
__mul_128x128_to_256 (P256, CQ, T128);
|
amount = recip_scale[ed2];
|
amount = recip_scale[ed2];
|
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
|
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
|
CQ.w[1] = 0;
|
CQ.w[1] = 0;
|
|
|
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
|
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
|
|
|
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
|
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
|
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
|
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
|
|
|
CA4.w[1] = CX.w[1] - QB256.w[1];
|
CA4.w[1] = CX.w[1] - QB256.w[1];
|
CA4.w[0] = CX.w[0] - QB256.w[0];
|
CA4.w[0] = CX.w[0] - QB256.w[0];
|
if (CX.w[0] < QB256.w[0])
|
if (CX.w[0] < QB256.w[0])
|
CA4.w[1]--;
|
CA4.w[1]--;
|
if (CR.w[0] || CR.w[1])
|
if (CR.w[0] || CR.w[1])
|
CA4.w[0] |= 1;
|
CA4.w[0] |= 1;
|
done = 1;
|
done = 1;
|
if(CA4.w[1]|CA4.w[0]) {
|
if(CA4.w[1]|CA4.w[0]) {
|
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY);
|
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY);
|
}
|
}
|
|
|
}
|
}
|
|
|
}
|
}
|
|
|
if (!done) {
|
if (!done) {
|
__div_256_by_128 (&CQ, &CA4, CY);
|
__div_256_by_128 (&CQ, &CA4, CY);
|
}
|
}
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if (CA4.w[0] || CA4.w[1]) {
|
if (CA4.w[0] || CA4.w[1]) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
else
|
else
|
#endif
|
#endif
|
#else
|
#else
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
if (!CA4.w[0] && !CA4.w[1])
|
if (!CA4.w[0] && !CA4.w[1])
|
#endif
|
#endif
|
#endif
|
#endif
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
// check whether result is exact
|
// check whether result is exact
|
{
|
{
|
if(!done) {
|
if(!done) {
|
// check whether CX, CY are short
|
// check whether CX, CY are short
|
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
|
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
|
i = (int) CY.w[0] - 1;
|
i = (int) CY.w[0] - 1;
|
j = (int) CX.w[0] - 1;
|
j = (int) CX.w[0] - 1;
|
// difference in powers of 2 factors for Y and X
|
// difference in powers of 2 factors for Y and X
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
// difference in powers of 5 factors
|
// difference in powers of 5 factors
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
if (d5 < nzeros)
|
if (d5 < nzeros)
|
nzeros = d5;
|
nzeros = d5;
|
// get P*(2^M[extra_digits])/10^extra_digits
|
// get P*(2^M[extra_digits])/10^extra_digits
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2];
|
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2];
|
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
amount = recip_scale[nzeros];
|
amount = recip_scale[nzeros];
|
__shr_128_long (CQ, Qh, amount);
|
__shr_128_long (CQ, Qh, amount);
|
|
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
} else {
|
} else {
|
// decompose Q as Qh*10^17 + Ql
|
// decompose Q as Qh*10^17 + Ql
|
//T128 = reciprocals10_128[17];
|
//T128 = reciprocals10_128[17];
|
Q_low = CQ.w[0];
|
Q_low = CQ.w[0];
|
|
|
{
|
{
|
tdigit[0] = Q_low & 0x3ffffff;
|
tdigit[0] = Q_low & 0x3ffffff;
|
tdigit[1] = 0;
|
tdigit[1] = 0;
|
QX = Q_low >> 26;
|
QX = Q_low >> 26;
|
QX32 = QX;
|
QX32 = QX;
|
nzeros = 0;
|
nzeros = 0;
|
|
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
k = (QX32 & 127);
|
k = (QX32 & 127);
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[1] += convert_table[j][k][1];
|
tdigit[1] += convert_table[j][k][1];
|
if (tdigit[0] >= 100000000) {
|
if (tdigit[0] >= 100000000) {
|
tdigit[0] -= 100000000;
|
tdigit[0] -= 100000000;
|
tdigit[1]++;
|
tdigit[1]++;
|
}
|
}
|
}
|
}
|
|
|
if (tdigit[1] >= 100000000) {
|
if (tdigit[1] >= 100000000) {
|
tdigit[1] -= 100000000;
|
tdigit[1] -= 100000000;
|
if (tdigit[1] >= 100000000)
|
if (tdigit[1] >= 100000000)
|
tdigit[1] -= 100000000;
|
tdigit[1] -= 100000000;
|
}
|
}
|
|
|
digit = tdigit[0];
|
digit = tdigit[0];
|
if (!digit && !tdigit[1])
|
if (!digit && !tdigit[1])
|
nzeros += 16;
|
nzeros += 16;
|
else {
|
else {
|
if (!digit) {
|
if (!digit) {
|
nzeros += 8;
|
nzeros += 8;
|
digit = tdigit[1];
|
digit = tdigit[1];
|
}
|
}
|
// decompose digit
|
// decompose digit
|
PD = (UINT64) digit *0x068DB8BBull;
|
PD = (UINT64) digit *0x068DB8BBull;
|
digit_h = (UINT32) (PD >> 40);
|
digit_h = (UINT32) (PD >> 40);
|
digit_low = digit - digit_h * 10000;
|
digit_low = digit - digit_h * 10000;
|
|
|
if (!digit_low)
|
if (!digit_low)
|
nzeros += 4;
|
nzeros += 4;
|
else
|
else
|
digit_h = digit_low;
|
digit_h = digit_low;
|
|
|
if (!(digit_h & 1))
|
if (!(digit_h & 1))
|
nzeros +=
|
nzeros +=
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
(digit_h & 7));
|
(digit_h & 7));
|
}
|
}
|
|
|
if (nzeros) {
|
if (nzeros) {
|
// get P*(2^M[extra_digits])/10^extra_digits
|
// get P*(2^M[extra_digits])/10^extra_digits
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
amount = recip_scale[nzeros];
|
amount = recip_scale[nzeros];
|
__shr_128 (CQ, Qh, amount);
|
__shr_128 (CQ, Qh, amount);
|
}
|
}
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
|
|
}
|
}
|
}
|
}
|
}
|
}
|
if(diff_expon>=0){
|
if(diff_expon>=0){
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
|
rnd_mode, pfpsf);
|
rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
#endif
|
#endif
|
|
|
if (diff_expon >= 0) {
|
if (diff_expon >= 0) {
|
#ifdef IEEE_ROUND_NEAREST
|
#ifdef IEEE_ROUND_NEAREST
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
|
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
|
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
//if(CQ.w[0]<carry64)
|
//if(CQ.w[0]<carry64)
|
//CQ.w[1] ++;
|
//CQ.w[1] ++;
|
#else
|
#else
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
|
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
|
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
#else
|
#else
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
rmode = 3 - rmode;
|
rmode = 3 - rmode;
|
switch (rmode) {
|
switch (rmode) {
|
case ROUNDING_TO_NEAREST: // round to nearest code
|
case ROUNDING_TO_NEAREST: // round to nearest code
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
case ROUNDING_TIES_AWAY:
|
case ROUNDING_TIES_AWAY:
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
case ROUNDING_DOWN:
|
case ROUNDING_DOWN:
|
case ROUNDING_TO_ZERO:
|
case ROUNDING_TO_ZERO:
|
break;
|
break;
|
default: // rounding up
|
default: // rounding up
|
CQ.w[0]++;
|
CQ.w[0]++;
|
if (!CQ.w[0])
|
if (!CQ.w[0])
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
}
|
}
|
#endif
|
#endif
|
#endif
|
#endif
|
|
|
|
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
|
pfpsf);
|
pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else {
|
} else {
|
// UF occurs
|
// UF occurs
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((diff_expon + 16 < 0)) {
|
if ((diff_expon + 16 < 0)) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#endif
|
#endif
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
res =
|
res =
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
|
|
}
|
}
|
|
|
}
|
}
|
|
|
//#define LEAVE_TRAILING_ZEROS
|
//#define LEAVE_TRAILING_ZEROS
|
|
|
extern UINT32 convert_table[5][128][2];
|
extern UINT32 convert_table[5][128][2];
|
extern SINT8 factors[][2];
|
extern SINT8 factors[][2];
|
extern UINT8 packed_10000_zeros[];
|
extern UINT8 packed_10000_zeros[];
|
|
|
|
|
//UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf)
|
//UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf)
|
|
|
TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y)
|
TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y)
|
UINT256 CA4 =
|
UINT256 CA4 =
|
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
|
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
|
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
|
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
|
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res;
|
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res;
|
int_float fx, fy, f64;
|
int_float fx, fy, f64;
|
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
|
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
|
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
|
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
|
digits_q, amount;
|
digits_q, amount;
|
int nzeros, i, j, k, d5, done = 0;
|
int nzeros, i, j, k, d5, done = 0;
|
unsigned rmode;
|
unsigned rmode;
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
fexcept_t binaryflags = 0;
|
fexcept_t binaryflags = 0;
|
#endif
|
#endif
|
|
|
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y);
|
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y);
|
|
|
// unpack arguments, check for NaN or Infinity
|
// unpack arguments, check for NaN or Infinity
|
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
|
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
|
// test if x is NaN
|
// test if x is NaN
|
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
|
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
|
(y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull)
|
(y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull)
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
|
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
|
Tmp.w[0] = CX.w[0];
|
Tmp.w[0] = CX.w[0];
|
TP128 = reciprocals10_128[18];
|
TP128 = reciprocals10_128[18];
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
amount = recip_scale[18];
|
amount = recip_scale[18];
|
__shr_128 (Tmp, Qh, amount);
|
__shr_128 (Tmp, Qh, amount);
|
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// x is Infinity?
|
// x is Infinity?
|
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
// check if y is Inf.
|
// check if y is Inf.
|
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
|
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
|
// return NaN
|
// return NaN
|
{
|
{
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
|
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
|
// otherwise return +/-Inf
|
// otherwise return +/-Inf
|
res =
|
res =
|
((x.w[1] ^ y.
|
((x.w[1] ^ y.
|
w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
// x is 0
|
// x is 0
|
if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) {
|
if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) {
|
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) {
|
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
// x=y=0, return NaN
|
// x=y=0, return NaN
|
res = 0x7c00000000000000ull;
|
res = 0x7c00000000000000ull;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// return 0
|
// return 0
|
res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull;
|
res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull;
|
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
|
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
|
if (exponent_x > DECIMAL_MAX_EXPON_64)
|
if (exponent_x > DECIMAL_MAX_EXPON_64)
|
exponent_x = DECIMAL_MAX_EXPON_64;
|
exponent_x = DECIMAL_MAX_EXPON_64;
|
else if (exponent_x < 0)
|
else if (exponent_x < 0)
|
exponent_x = 0;
|
exponent_x = 0;
|
res |= (((UINT64) exponent_x) << 53);
|
res |= (((UINT64) exponent_x) << 53);
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
if (!valid_y) {
|
if (!valid_y) {
|
// y is Inf. or NaN
|
// y is Inf. or NaN
|
|
|
// test if y is NaN
|
// test if y is NaN
|
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
|
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
__set_status_flags (pfpsf, INVALID_EXCEPTION);
|
#endif
|
#endif
|
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull);
|
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull);
|
Tmp.w[0] = CY.w[0];
|
Tmp.w[0] = CY.w[0];
|
TP128 = reciprocals10_128[18];
|
TP128 = reciprocals10_128[18];
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
__mul_128x128_full (Qh, Ql, Tmp, TP128);
|
amount = recip_scale[18];
|
amount = recip_scale[18];
|
__shr_128 (Tmp, Qh, amount);
|
__shr_128 (Tmp, Qh, amount);
|
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// y is Infinity?
|
// y is Infinity?
|
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
|
// return +/-0
|
// return +/-0
|
res = sign_x ^ sign_y;
|
res = sign_x ^ sign_y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// y is 0, return +/-Inf
|
// y is 0, return +/-Inf
|
res =
|
res =
|
((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
|
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
|
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
|
|
|
if (__unsigned_compare_gt_128 (CY, CX)) {
|
if (__unsigned_compare_gt_128 (CY, CX)) {
|
// CX < CY
|
// CX < CY
|
|
|
// 2^64
|
// 2^64
|
f64.i = 0x5f800000;
|
f64.i = 0x5f800000;
|
|
|
// fx ~ CX, fy ~ CY
|
// fx ~ CX, fy ~ CY
|
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
|
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
|
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
|
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
|
// expon_cy - expon_cx
|
// expon_cy - expon_cx
|
bin_index = (fy.i - fx.i) >> 23;
|
bin_index = (fy.i - fx.i) >> 23;
|
|
|
if (CX.w[1]) {
|
if (CX.w[1]) {
|
T = power10_index_binexp_128[bin_index].w[0];
|
T = power10_index_binexp_128[bin_index].w[0];
|
__mul_64x128_short (CA, T, CX);
|
__mul_64x128_short (CA, T, CX);
|
} else {
|
} else {
|
T128 = power10_index_binexp_128[bin_index];
|
T128 = power10_index_binexp_128[bin_index];
|
__mul_64x128_short (CA, CX.w[0], T128);
|
__mul_64x128_short (CA, CX.w[0], T128);
|
}
|
}
|
|
|
ed2 = 15;
|
ed2 = 15;
|
if (__unsigned_compare_gt_128 (CY, CA))
|
if (__unsigned_compare_gt_128 (CY, CA))
|
ed2++;
|
ed2++;
|
|
|
T128 = power10_table_128[ed2];
|
T128 = power10_table_128[ed2];
|
__mul_128x128_to_256 (CA4, CA, T128);
|
__mul_128x128_to_256 (CA4, CA, T128);
|
|
|
ed2 += estimate_decimal_digits[bin_index];
|
ed2 += estimate_decimal_digits[bin_index];
|
CQ.w[0] = CQ.w[1] = 0;
|
CQ.w[0] = CQ.w[1] = 0;
|
diff_expon = diff_expon - ed2;
|
diff_expon = diff_expon - ed2;
|
|
|
} else {
|
} else {
|
// get CQ = CX/CY
|
// get CQ = CX/CY
|
__div_128_by_128 (&CQ, &CR, CX, CY);
|
__div_128_by_128 (&CQ, &CR, CX, CY);
|
|
|
// get number of decimal digits in CQ
|
// get number of decimal digits in CQ
|
// 2^64
|
// 2^64
|
f64.i = 0x5f800000;
|
f64.i = 0x5f800000;
|
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
|
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
|
// binary expon. of CQ
|
// binary expon. of CQ
|
bin_expon = (fx.i - 0x3f800000) >> 23;
|
bin_expon = (fx.i - 0x3f800000) >> 23;
|
|
|
digits_q = estimate_decimal_digits[bin_expon];
|
digits_q = estimate_decimal_digits[bin_expon];
|
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
|
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
|
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
|
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
|
if (__unsigned_compare_ge_128 (CQ, TP128))
|
if (__unsigned_compare_ge_128 (CQ, TP128))
|
digits_q++;
|
digits_q++;
|
|
|
if (digits_q <= 16) {
|
if (digits_q <= 16) {
|
if (!CR.w[1] && !CR.w[0]) {
|
if (!CR.w[1] && !CR.w[0]) {
|
res = get_BID64 (sign_x ^ sign_y, diff_expon,
|
res = get_BID64 (sign_x ^ sign_y, diff_expon,
|
CQ.w[0], rnd_mode, pfpsf);
|
CQ.w[0], rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
ed2 = 16 - digits_q;
|
ed2 = 16 - digits_q;
|
T128.w[0] = power10_table_128[ed2].w[0];
|
T128.w[0] = power10_table_128[ed2].w[0];
|
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
|
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
|
diff_expon = diff_expon - ed2;
|
diff_expon = diff_expon - ed2;
|
CQ.w[0] *= T128.w[0];
|
CQ.w[0] *= T128.w[0];
|
} else {
|
} else {
|
ed2 = digits_q - 16;
|
ed2 = digits_q - 16;
|
diff_expon += ed2;
|
diff_expon += ed2;
|
T128 = reciprocals10_128[ed2];
|
T128 = reciprocals10_128[ed2];
|
__mul_128x128_to_256 (P256, CQ, T128);
|
__mul_128x128_to_256 (P256, CQ, T128);
|
amount = recip_scale[ed2];
|
amount = recip_scale[ed2];
|
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
|
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
|
CQ.w[1] = 0;
|
CQ.w[1] = 0;
|
|
|
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
|
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
|
|
|
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
|
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
|
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
|
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
|
|
|
CA4.w[1] = CX.w[1] - QB256.w[1];
|
CA4.w[1] = CX.w[1] - QB256.w[1];
|
CA4.w[0] = CX.w[0] - QB256.w[0];
|
CA4.w[0] = CX.w[0] - QB256.w[0];
|
if (CX.w[0] < QB256.w[0])
|
if (CX.w[0] < QB256.w[0])
|
CA4.w[1]--;
|
CA4.w[1]--;
|
if (CR.w[0] || CR.w[1])
|
if (CR.w[0] || CR.w[1])
|
CA4.w[0] |= 1;
|
CA4.w[0] |= 1;
|
done = 1;
|
done = 1;
|
if(CA4.w[1]|CA4.w[0]) {
|
if(CA4.w[1]|CA4.w[0]) {
|
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY);
|
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY);
|
}
|
}
|
}
|
}
|
|
|
}
|
}
|
|
|
if (!done) {
|
if (!done) {
|
__div_256_by_128 (&CQ, &CA4, CY);
|
__div_256_by_128 (&CQ, &CA4, CY);
|
}
|
}
|
|
|
|
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if (CA4.w[0] || CA4.w[1]) {
|
if (CA4.w[0] || CA4.w[1]) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
else
|
else
|
#endif
|
#endif
|
#else
|
#else
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
if (!CA4.w[0] && !CA4.w[1])
|
if (!CA4.w[0] && !CA4.w[1])
|
#endif
|
#endif
|
#endif
|
#endif
|
#ifndef LEAVE_TRAILING_ZEROS
|
#ifndef LEAVE_TRAILING_ZEROS
|
// check whether result is exact
|
// check whether result is exact
|
{
|
{
|
if(!done) {
|
if(!done) {
|
// check whether CX, CY are short
|
// check whether CX, CY are short
|
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
|
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
|
i = (int) CY.w[0] - 1;
|
i = (int) CY.w[0] - 1;
|
j = (int) CX.w[0] - 1;
|
j = (int) CX.w[0] - 1;
|
// difference in powers of 2 factors for Y and X
|
// difference in powers of 2 factors for Y and X
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
nzeros = ed2 - factors[i][0] + factors[j][0];
|
// difference in powers of 5 factors
|
// difference in powers of 5 factors
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
d5 = ed2 - factors[i][1] + factors[j][1];
|
if (d5 < nzeros)
|
if (d5 < nzeros)
|
nzeros = d5;
|
nzeros = d5;
|
// get P*(2^M[extra_digits])/10^extra_digits
|
// get P*(2^M[extra_digits])/10^extra_digits
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2];
|
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2];
|
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
amount = recip_scale[nzeros];
|
amount = recip_scale[nzeros];
|
__shr_128_long (CQ, Qh, amount);
|
__shr_128_long (CQ, Qh, amount);
|
|
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
} else {
|
} else {
|
// decompose Q as Qh*10^17 + Ql
|
// decompose Q as Qh*10^17 + Ql
|
//T128 = reciprocals10_128[17];
|
//T128 = reciprocals10_128[17];
|
Q_low = CQ.w[0];
|
Q_low = CQ.w[0];
|
|
|
{
|
{
|
tdigit[0] = Q_low & 0x3ffffff;
|
tdigit[0] = Q_low & 0x3ffffff;
|
tdigit[1] = 0;
|
tdigit[1] = 0;
|
QX = Q_low >> 26;
|
QX = Q_low >> 26;
|
QX32 = QX;
|
QX32 = QX;
|
nzeros = 0;
|
nzeros = 0;
|
|
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
for (j = 0; QX32; j++, QX32 >>= 7) {
|
k = (QX32 & 127);
|
k = (QX32 & 127);
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[0] += convert_table[j][k][0];
|
tdigit[1] += convert_table[j][k][1];
|
tdigit[1] += convert_table[j][k][1];
|
if (tdigit[0] >= 100000000) {
|
if (tdigit[0] >= 100000000) {
|
tdigit[0] -= 100000000;
|
tdigit[0] -= 100000000;
|
tdigit[1]++;
|
tdigit[1]++;
|
}
|
}
|
}
|
}
|
|
|
if (tdigit[1] >= 100000000) {
|
if (tdigit[1] >= 100000000) {
|
tdigit[1] -= 100000000;
|
tdigit[1] -= 100000000;
|
if (tdigit[1] >= 100000000)
|
if (tdigit[1] >= 100000000)
|
tdigit[1] -= 100000000;
|
tdigit[1] -= 100000000;
|
}
|
}
|
|
|
digit = tdigit[0];
|
digit = tdigit[0];
|
if (!digit && !tdigit[1])
|
if (!digit && !tdigit[1])
|
nzeros += 16;
|
nzeros += 16;
|
else {
|
else {
|
if (!digit) {
|
if (!digit) {
|
nzeros += 8;
|
nzeros += 8;
|
digit = tdigit[1];
|
digit = tdigit[1];
|
}
|
}
|
// decompose digit
|
// decompose digit
|
PD = (UINT64) digit *0x068DB8BBull;
|
PD = (UINT64) digit *0x068DB8BBull;
|
digit_h = (UINT32) (PD >> 40);
|
digit_h = (UINT32) (PD >> 40);
|
digit_low = digit - digit_h * 10000;
|
digit_low = digit - digit_h * 10000;
|
|
|
if (!digit_low)
|
if (!digit_low)
|
nzeros += 4;
|
nzeros += 4;
|
else
|
else
|
digit_h = digit_low;
|
digit_h = digit_low;
|
|
|
if (!(digit_h & 1))
|
if (!(digit_h & 1))
|
nzeros +=
|
nzeros +=
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
|
(digit_h & 7));
|
(digit_h & 7));
|
}
|
}
|
|
|
if (nzeros) {
|
if (nzeros) {
|
// get P*(2^M[extra_digits])/10^extra_digits
|
// get P*(2^M[extra_digits])/10^extra_digits
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
|
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
amount = recip_scale[nzeros];
|
amount = recip_scale[nzeros];
|
__shr_128 (CQ, Qh, amount);
|
__shr_128 (CQ, Qh, amount);
|
}
|
}
|
diff_expon += nzeros;
|
diff_expon += nzeros;
|
|
|
}
|
}
|
}
|
}
|
}
|
}
|
if(diff_expon>=0){
|
if(diff_expon>=0){
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
|
rnd_mode, pfpsf);
|
rnd_mode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
}
|
}
|
#endif
|
#endif
|
|
|
if(diff_expon>=0) {
|
if(diff_expon>=0) {
|
|
|
#ifdef IEEE_ROUND_NEAREST
|
#ifdef IEEE_ROUND_NEAREST
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
|
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
|
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
//if(CQ.w[0]<carry64)
|
//if(CQ.w[0]<carry64)
|
//CQ.w[1] ++;
|
//CQ.w[1] ++;
|
#else
|
#else
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
|
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
|
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
#else
|
#else
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
|
rmode = 3 - rmode;
|
rmode = 3 - rmode;
|
switch (rmode) {
|
switch (rmode) {
|
case ROUNDING_TO_NEAREST: // round to nearest code
|
case ROUNDING_TO_NEAREST: // round to nearest code
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
case ROUNDING_TIES_AWAY:
|
case ROUNDING_TIES_AWAY:
|
// rounding
|
// rounding
|
// 2*CA4 - CY
|
// 2*CA4 - CY
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
CA4r.w[0] = CA4.w[0] + CA4.w[0];
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
|
CQ.w[0] += carry64;
|
CQ.w[0] += carry64;
|
if (CQ.w[0] < carry64)
|
if (CQ.w[0] < carry64)
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
case ROUNDING_DOWN:
|
case ROUNDING_DOWN:
|
case ROUNDING_TO_ZERO:
|
case ROUNDING_TO_ZERO:
|
break;
|
break;
|
default: // rounding up
|
default: // rounding up
|
CQ.w[0]++;
|
CQ.w[0]++;
|
if (!CQ.w[0])
|
if (!CQ.w[0])
|
CQ.w[1]++;
|
CQ.w[1]++;
|
break;
|
break;
|
}
|
}
|
#endif
|
#endif
|
#endif
|
#endif
|
|
|
|
|
res =
|
res =
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
|
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
|
pfpsf);
|
pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else {
|
} else {
|
// UF occurs
|
// UF occurs
|
|
|
#ifdef SET_STATUS_FLAGS
|
#ifdef SET_STATUS_FLAGS
|
if ((diff_expon + 16 < 0)) {
|
if ((diff_expon + 16 < 0)) {
|
// set status flags
|
// set status flags
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
}
|
}
|
#endif
|
#endif
|
rmode = rnd_mode;
|
rmode = rnd_mode;
|
res =
|
res =
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
|
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
#endif
|
#endif
|
BID_RETURN (res);
|
BID_RETURN (res);
|
|
|
}
|
}
|
|
|
}
|
}
|
|
|
