/* 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 remainder
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* BID64 remainder
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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(exponent_x < exponent_y)
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* if(exponent_x < exponent_y)
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* scale coefficient_y so exponents are aligned
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* scale coefficient_y so exponents are aligned
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* perform coefficient divide (64-bit integer divide), unless
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* perform coefficient divide (64-bit integer divide), unless
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* coefficient_y is longer than 64 bits (clearly larger
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* coefficient_y is longer than 64 bits (clearly larger
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* than coefficient_x)
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* than coefficient_x)
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* else // exponent_x > exponent_y
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* else // exponent_x > exponent_y
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* use a loop to scale coefficient_x to 18_digits, divide by
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* use a loop to scale coefficient_x to 18_digits, divide by
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* coefficient_y (64-bit integer divide), calculate remainder
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* coefficient_y (64-bit integer divide), calculate remainder
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* as new_coefficient_x and repeat until final remainder is obtained
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* as new_coefficient_x and repeat until final remainder is obtained
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* (when new_exponent_x < exponent_y)
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* (when new_exponent_x < exponent_y)
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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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#define MAX_FORMAT_DIGITS 16
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#define MAX_FORMAT_DIGITS 16
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#define DECIMAL_EXPONENT_BIAS 398
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#define DECIMAL_EXPONENT_BIAS 398
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#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull
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#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull
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#define BINARY_EXPONENT_BIAS 0x3ff
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#define BINARY_EXPONENT_BIAS 0x3ff
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#define UPPER_EXPON_LIMIT 51
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#define UPPER_EXPON_LIMIT 51
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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_rem (UINT64 * pres, UINT64 * px,
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bid64_rem (UINT64 * pres, UINT64 * px,
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UINT64 *
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UINT64 *
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py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _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_rem (UINT64 x,
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bid64_rem (UINT64 x,
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UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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#endif
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UINT128 CY;
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UINT128 CY;
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res;
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res;
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UINT64 Q, R, R2, T, valid_y, valid_x;
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UINT64 Q, R, R2, T, valid_y, valid_x;
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int_float tempx;
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int_float tempx;
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int exponent_x, exponent_y, bin_expon, e_scale;
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int exponent_x, exponent_y, bin_expon, e_scale;
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int digits_x, diff_expon;
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int digits_x, diff_expon;
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#if DECIMAL_CALL_BY_REFERENCE
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#if DECIMAL_CALL_BY_REFERENCE
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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_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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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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// 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 or 0
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// x is Inf. or NaN or 0
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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 & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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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))
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if (((x & SNAN_MASK64) == SNAN_MASK64))
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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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res = coefficient_x & QUIET_MASK64;;
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res = coefficient_x & QUIET_MASK64;;
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BID_RETURN (res);
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BID_RETURN (res);
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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 & 0x7800000000000000ull) == 0x7800000000000000ull) {
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if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
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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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__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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// return NaN
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// return NaN
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res = 0x7c00000000000000ull;
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res = 0x7c00000000000000ull;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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}
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}
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// x is 0
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// x is 0
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// return x if y != 0
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// return x if y != 0
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if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) &&
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if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) &&
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coefficient_y) {
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coefficient_y) {
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if ((y & 0x6000000000000000ull) == 0x6000000000000000ull)
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if ((y & 0x6000000000000000ull) == 0x6000000000000000ull)
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exponent_y = (y >> 51) & 0x3ff;
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exponent_y = (y >> 51) & 0x3ff;
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else
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else
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exponent_y = (y >> 53) & 0x3ff;
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exponent_y = (y >> 53) & 0x3ff;
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if (exponent_y < exponent_x)
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if (exponent_y < exponent_x)
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exponent_x = exponent_y;
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exponent_x = exponent_y;
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x = exponent_x;
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x = exponent_x;
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x <<= 53;
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x <<= 53;
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res = x | sign_x;
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res = x | sign_x;
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BID_RETURN (res);
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BID_RETURN (res);
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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 & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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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))
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if (((y & SNAN_MASK64) == SNAN_MASK64))
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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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res = coefficient_y & QUIET_MASK64;;
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res = coefficient_y & QUIET_MASK64;;
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BID_RETURN (res);
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BID_RETURN (res);
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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 & 0x7800000000000000ull) == 0x7800000000000000ull) {
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if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
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res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x);
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res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x);
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// y is 0, return NaN
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// y is 0, return NaN
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{
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{
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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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res = 0x7c00000000000000ull;
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res = 0x7c00000000000000ull;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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}
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}
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diff_expon = exponent_x - exponent_y;
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diff_expon = exponent_x - exponent_y;
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if (diff_expon <= 0) {
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if (diff_expon <= 0) {
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diff_expon = -diff_expon;
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diff_expon = -diff_expon;
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if (diff_expon > 16) {
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if (diff_expon > 16) {
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// |x|<|y| in this case
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// |x|<|y| in this case
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res = x;
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res = x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// set exponent of y to exponent_x, scale coefficient_y
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// set exponent of y to exponent_x, scale coefficient_y
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T = power10_table_128[diff_expon].w[0];
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T = power10_table_128[diff_expon].w[0];
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__mul_64x64_to_128 (CY, coefficient_y, T);
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__mul_64x64_to_128 (CY, coefficient_y, T);
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if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) {
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if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) {
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res = x;
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res = x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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Q = coefficient_x / CY.w[0];
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Q = coefficient_x / CY.w[0];
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R = coefficient_x - Q * CY.w[0];
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R = coefficient_x - Q * CY.w[0];
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R2 = R + R;
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R2 = R + R;
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if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) {
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if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) {
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R = CY.w[0] - R;
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R = CY.w[0] - R;
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sign_x ^= 0x8000000000000000ull;
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sign_x ^= 0x8000000000000000ull;
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}
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}
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res = very_fast_get_BID64 (sign_x, exponent_x, R);
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res = very_fast_get_BID64 (sign_x, exponent_x, R);
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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while (diff_expon > 0) {
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while (diff_expon > 0) {
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// get number of digits in coeff_x
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// get number of digits in coeff_x
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tempx.d = (float) coefficient_x;
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tempx.d = (float) coefficient_x;
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bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f;
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bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f;
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digits_x = estimate_decimal_digits[bin_expon];
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digits_x = estimate_decimal_digits[bin_expon];
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// will not use this test, dividend will have 18 or 19 digits
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// will not use this test, dividend will have 18 or 19 digits
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//if(coefficient_x >= power10_table_128[digits_x].w[0])
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//if(coefficient_x >= power10_table_128[digits_x].w[0])
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// digits_x++;
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// digits_x++;
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e_scale = 18 - digits_x;
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e_scale = 18 - digits_x;
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if (diff_expon >= e_scale) {
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if (diff_expon >= e_scale) {
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diff_expon -= e_scale;
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diff_expon -= e_scale;
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} else {
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} else {
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e_scale = diff_expon;
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e_scale = diff_expon;
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diff_expon = 0;
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diff_expon = 0;
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}
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}
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// scale dividend to 18 or 19 digits
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// scale dividend to 18 or 19 digits
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coefficient_x *= power10_table_128[e_scale].w[0];
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coefficient_x *= power10_table_128[e_scale].w[0];
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// quotient
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// quotient
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Q = coefficient_x / coefficient_y;
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Q = coefficient_x / coefficient_y;
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// remainder
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// remainder
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coefficient_x -= Q * coefficient_y;
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coefficient_x -= Q * coefficient_y;
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// check for remainder == 0
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// check for remainder == 0
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if (!coefficient_x) {
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if (!coefficient_x) {
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res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0);
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res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0);
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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}
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}
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R2 = coefficient_x + coefficient_x;
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R2 = coefficient_x + coefficient_x;
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if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) {
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if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) {
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coefficient_x = coefficient_y - coefficient_x;
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coefficient_x = coefficient_y - coefficient_x;
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sign_x ^= 0x8000000000000000ull;
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sign_x ^= 0x8000000000000000ull;
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}
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}
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res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x);
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res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x);
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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