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596 lines
16 KiB
C
596 lines
16 KiB
C
/* Copyright (C) 2007-2017 Free Software Foundation, Inc.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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/*****************************************************************************
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* BID64 add
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*****************************************************************************
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*
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* Algorithm description:
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*
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* if(exponent_a < exponent_b)
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* switch a, b
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* diff_expon = exponent_a - exponent_b
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* if(diff_expon > 16)
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* return normalize(a)
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* if(coefficient_a*10^diff_expon guaranteed below 2^62)
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* S = sign_a*coefficient_a*10^diff_expon + sign_b*coefficient_b
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* if(|S|<10^16)
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* return get_BID64(sign(S),exponent_b,|S|)
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* else
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* determine number of extra digits in S (1, 2, or 3)
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* return rounded result
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* else // large exponent difference
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* if(number_digits(coefficient_a*10^diff_expon) +/- 10^16)
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* guaranteed the same as
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* number_digits(coefficient_a*10^diff_expon) )
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* S = normalize(coefficient_a + (sign_a^sign_b)*10^(16-diff_expon))
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* corr = 10^16 + (sign_a^sign_b)*coefficient_b
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* corr*10^exponent_b is rounded so it aligns with S*10^exponent_S
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* return get_BID64(sign_a,exponent(S),S+rounded(corr))
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* else
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* add sign_a*coefficient_a*10^diff_expon, sign_b*coefficient_b
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* in 128-bit integer arithmetic, then round to 16 decimal digits
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*
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*
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****************************************************************************/
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#include "bid_internal.h"
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#if DECIMAL_CALL_BY_REFERENCE
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void bid64_add (UINT64 * pres, UINT64 * px,
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UINT64 *
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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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#else
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UINT64 bid64_add (UINT64 x,
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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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#endif
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_sub (UINT64 * pres, UINT64 * px,
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UINT64 *
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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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UINT64 y = *py;
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#if !DECIMAL_GLOBAL_ROUNDING
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_IDEC_round rnd_mode = *prnd_mode;
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#endif
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// check if y is not NaN
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if (((y & NAN_MASK64) != NAN_MASK64))
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y ^= 0x8000000000000000ull;
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bid64_add (pres, px,
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&y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
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_EXC_INFO_ARG);
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}
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#else
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UINT64
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bid64_sub (UINT64 x,
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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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// check if y is not NaN
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if (((y & NAN_MASK64) != NAN_MASK64))
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y ^= 0x8000000000000000ull;
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return bid64_add (x,
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y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
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_EXC_INFO_ARG);
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}
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#endif
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_add (UINT64 * pres, UINT64 * px,
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UINT64 *
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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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UINT64 x, y;
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#else
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UINT64
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bid64_add (UINT64 x,
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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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#endif
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UINT128 CA, CT, CT_new;
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y, C64_new;
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UINT64 valid_x, valid_y;
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UINT64 res;
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UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab,
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rem_a;
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UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1, carry, tmp;
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int_double tempx;
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int exponent_x, exponent_y, exponent_a, exponent_b, diff_dec_expon;
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int bin_expon_ca, extra_digits, amount, scale_k, scale_ca;
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unsigned rmode, status;
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#if DECIMAL_CALL_BY_REFERENCE
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#if !DECIMAL_GLOBAL_ROUNDING
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_IDEC_round rnd_mode = *prnd_mode;
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#endif
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x = *px;
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y = *py;
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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_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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if (!valid_x) {
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// x is Inf. or NaN
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// test if x is NaN
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if ((x & NAN_MASK64) == NAN_MASK64) {
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#ifdef SET_STATUS_FLAGS
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if (((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
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|| ((y & SNAN_MASK64) == SNAN_MASK64))
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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res = coefficient_x & QUIET_MASK64;
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BID_RETURN (res);
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}
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// x is Infinity?
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if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
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// check if y is Inf
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if (((y & NAN_MASK64) == INFINITY_MASK64)) {
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if (sign_x == (y & 0x8000000000000000ull)) {
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res = coefficient_x;
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BID_RETURN (res);
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}
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// return NaN
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{
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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res = NAN_MASK64;
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BID_RETURN (res);
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}
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}
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// check if y is NaN
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if (((y & NAN_MASK64) == NAN_MASK64)) {
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res = coefficient_y & QUIET_MASK64;
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#ifdef SET_STATUS_FLAGS
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if (((y & SNAN_MASK64) == SNAN_MASK64))
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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BID_RETURN (res);
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}
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// otherwise return +/-Inf
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{
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res = coefficient_x;
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BID_RETURN (res);
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}
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}
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// x is 0
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{
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if (((y & INFINITY_MASK64) != INFINITY_MASK64) && coefficient_y) {
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if (exponent_y <= exponent_x) {
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res = y;
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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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// y is Inf. or NaN?
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if (((y & INFINITY_MASK64) == INFINITY_MASK64)) {
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#ifdef SET_STATUS_FLAGS
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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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#endif
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res = coefficient_y & QUIET_MASK64;
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BID_RETURN (res);
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}
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// y is 0
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if (!coefficient_x) { // x==0
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if (exponent_x <= exponent_y)
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res = ((UINT64) exponent_x) << 53;
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else
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res = ((UINT64) exponent_y) << 53;
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if (sign_x == sign_y)
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res |= sign_x;
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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#ifndef IEEE_ROUND_NEAREST
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if (rnd_mode == ROUNDING_DOWN && sign_x != sign_y)
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res |= 0x8000000000000000ull;
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#endif
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#endif
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BID_RETURN (res);
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} else if (exponent_y >= exponent_x) {
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res = x;
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BID_RETURN (res);
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}
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}
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// sort arguments by exponent
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if (exponent_x < exponent_y) {
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sign_a = sign_y;
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exponent_a = exponent_y;
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coefficient_a = coefficient_y;
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sign_b = sign_x;
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exponent_b = exponent_x;
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coefficient_b = coefficient_x;
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} else {
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sign_a = sign_x;
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exponent_a = exponent_x;
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coefficient_a = coefficient_x;
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sign_b = sign_y;
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exponent_b = exponent_y;
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coefficient_b = coefficient_y;
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}
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// exponent difference
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diff_dec_expon = exponent_a - exponent_b;
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/* get binary coefficients of x and y */
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//--- get number of bits in the coefficients of x and y ---
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// version 2 (original)
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tempx.d = (double) coefficient_a;
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bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
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if (diff_dec_expon > MAX_FORMAT_DIGITS) {
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// normalize a to a 16-digit coefficient
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scale_ca = estimate_decimal_digits[bin_expon_ca];
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if (coefficient_a >= power10_table_128[scale_ca].w[0])
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scale_ca++;
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scale_k = 16 - scale_ca;
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coefficient_a *= power10_table_128[scale_k].w[0];
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diff_dec_expon -= scale_k;
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exponent_a -= scale_k;
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/* get binary 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 = (double) coefficient_a;
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bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
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if (diff_dec_expon > MAX_FORMAT_DIGITS) {
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#ifdef SET_STATUS_FLAGS
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if (coefficient_b) {
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__set_status_flags (pfpsf, INEXACT_EXCEPTION);
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}
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#endif
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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#ifndef IEEE_ROUND_NEAREST
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if (((rnd_mode) & 3) && coefficient_b) // not ROUNDING_TO_NEAREST
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{
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switch (rnd_mode) {
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case ROUNDING_DOWN:
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if (sign_b) {
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coefficient_a -= ((((SINT64) sign_a) >> 63) | 1);
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if (coefficient_a < 1000000000000000ull) {
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exponent_a--;
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coefficient_a = 9999999999999999ull;
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} else if (coefficient_a >= 10000000000000000ull) {
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exponent_a++;
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coefficient_a = 1000000000000000ull;
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}
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}
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break;
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case ROUNDING_UP:
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if (!sign_b) {
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coefficient_a += ((((SINT64) sign_a) >> 63) | 1);
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if (coefficient_a < 1000000000000000ull) {
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exponent_a--;
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coefficient_a = 9999999999999999ull;
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} else if (coefficient_a >= 10000000000000000ull) {
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exponent_a++;
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coefficient_a = 1000000000000000ull;
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}
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}
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break;
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default: // RZ
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if (sign_a != sign_b) {
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coefficient_a--;
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if (coefficient_a < 1000000000000000ull) {
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exponent_a--;
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coefficient_a = 9999999999999999ull;
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}
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}
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break;
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}
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} else
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#endif
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#endif
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// check special case here
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if ((coefficient_a == 1000000000000000ull)
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&& (diff_dec_expon == MAX_FORMAT_DIGITS + 1)
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&& (sign_a ^ sign_b)
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&& (coefficient_b > 5000000000000000ull)) {
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coefficient_a = 9999999999999999ull;
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exponent_a--;
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}
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res =
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fast_get_BID64_check_OF (sign_a, exponent_a, coefficient_a,
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rnd_mode, pfpsf);
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BID_RETURN (res);
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}
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}
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// test whether coefficient_a*10^(exponent_a-exponent_b) may exceed 2^62
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if (bin_expon_ca + estimate_bin_expon[diff_dec_expon] < 60) {
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// coefficient_a*10^(exponent_a-exponent_b)<2^63
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// multiply by 10^(exponent_a-exponent_b)
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coefficient_a *= power10_table_128[diff_dec_expon].w[0];
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// sign mask
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sign_b = ((SINT64) sign_b) >> 63;
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// apply sign to coeff. of b
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coefficient_b = (coefficient_b + sign_b) ^ sign_b;
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// apply sign to coefficient a
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sign_a = ((SINT64) sign_a) >> 63;
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coefficient_a = (coefficient_a + sign_a) ^ sign_a;
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coefficient_a += coefficient_b;
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// get sign
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sign_s = ((SINT64) coefficient_a) >> 63;
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coefficient_a = (coefficient_a + sign_s) ^ sign_s;
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sign_s &= 0x8000000000000000ull;
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// coefficient_a < 10^16 ?
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if (coefficient_a < power10_table_128[MAX_FORMAT_DIGITS].w[0]) {
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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#ifndef IEEE_ROUND_NEAREST
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if (rnd_mode == ROUNDING_DOWN && (!coefficient_a)
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&& sign_a != sign_b)
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sign_s = 0x8000000000000000ull;
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#endif
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#endif
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res = very_fast_get_BID64 (sign_s, exponent_b, coefficient_a);
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BID_RETURN (res);
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}
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// otherwise rounding is necessary
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// already know coefficient_a<10^19
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// coefficient_a < 10^17 ?
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if (coefficient_a < power10_table_128[17].w[0])
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extra_digits = 1;
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else if (coefficient_a < power10_table_128[18].w[0])
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extra_digits = 2;
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else
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extra_digits = 3;
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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#ifndef IEEE_ROUND_NEAREST
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rmode = rnd_mode;
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if (sign_s && (unsigned) (rmode - 1) < 2)
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rmode = 3 - rmode;
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#else
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rmode = 0;
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#endif
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#else
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rmode = 0;
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#endif
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coefficient_a += round_const_table[rmode][extra_digits];
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// get P*(2^M[extra_digits])/10^extra_digits
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__mul_64x64_to_128 (CT, coefficient_a,
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reciprocals10_64[extra_digits]);
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// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
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amount = short_recip_scale[extra_digits];
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C64 = CT.w[1] >> amount;
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} else {
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// coefficient_a*10^(exponent_a-exponent_b) is large
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sign_s = sign_a;
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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#ifndef IEEE_ROUND_NEAREST
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rmode = rnd_mode;
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if (sign_s && (unsigned) (rmode - 1) < 2)
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rmode = 3 - rmode;
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#else
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rmode = 0;
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#endif
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#else
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rmode = 0;
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#endif
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// check whether we can take faster path
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scale_ca = estimate_decimal_digits[bin_expon_ca];
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sign_ab = sign_a ^ sign_b;
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sign_ab = ((SINT64) sign_ab) >> 63;
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// T1 = 10^(16-diff_dec_expon)
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T1 = power10_table_128[16 - diff_dec_expon].w[0];
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// get number of digits in coefficient_a
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if (coefficient_a >= power10_table_128[scale_ca].w[0]) {
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scale_ca++;
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}
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scale_k = 16 - scale_ca;
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// addition
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saved_ca = coefficient_a - T1;
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coefficient_a =
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(SINT64) saved_ca *(SINT64) power10_table_128[scale_k].w[0];
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extra_digits = diff_dec_expon - scale_k;
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// apply sign
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saved_cb = (coefficient_b + sign_ab) ^ sign_ab;
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// add 10^16 and rounding constant
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coefficient_b =
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saved_cb + 10000000000000000ull +
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round_const_table[rmode][extra_digits];
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// get P*(2^M[extra_digits])/10^extra_digits
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__mul_64x64_to_128 (CT, coefficient_b,
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reciprocals10_64[extra_digits]);
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// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
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amount = short_recip_scale[extra_digits];
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C0_64 = CT.w[1] >> amount;
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// result coefficient
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C64 = C0_64 + coefficient_a;
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// filter out difficult (corner) cases
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// this test ensures the number of digits in coefficient_a does not change
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// after adding (the appropriately scaled and rounded) coefficient_b
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if ((UINT64) (C64 - 1000000000000000ull - 1) >
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9000000000000000ull - 2) {
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if (C64 >= 10000000000000000ull) {
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// result has more than 16 digits
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if (!scale_k) {
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// must divide coeff_a by 10
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saved_ca = saved_ca + T1;
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__mul_64x64_to_128 (CA, saved_ca, 0x3333333333333334ull);
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//reciprocals10_64[1]);
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coefficient_a = CA.w[1] >> 1;
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rem_a =
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saved_ca - (coefficient_a << 3) - (coefficient_a << 1);
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coefficient_a = coefficient_a - T1;
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saved_cb += rem_a * power10_table_128[diff_dec_expon].w[0];
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} else
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coefficient_a =
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(SINT64) (saved_ca - T1 -
|
|
(T1 << 3)) * (SINT64) power10_table_128[scale_k -
|
|
1].w[0];
|
|
|
|
extra_digits++;
|
|
coefficient_b =
|
|
saved_cb + 100000000000000000ull +
|
|
round_const_table[rmode][extra_digits];
|
|
|
|
// get P*(2^M[extra_digits])/10^extra_digits
|
|
__mul_64x64_to_128 (CT, coefficient_b,
|
|
reciprocals10_64[extra_digits]);
|
|
|
|
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
|
|
amount = short_recip_scale[extra_digits];
|
|
C0_64 = CT.w[1] >> amount;
|
|
|
|
// result coefficient
|
|
C64 = C0_64 + coefficient_a;
|
|
} else if (C64 <= 1000000000000000ull) {
|
|
// less than 16 digits in result
|
|
coefficient_a =
|
|
(SINT64) saved_ca *(SINT64) power10_table_128[scale_k +
|
|
1].w[0];
|
|
//extra_digits --;
|
|
exponent_b--;
|
|
coefficient_b =
|
|
(saved_cb << 3) + (saved_cb << 1) + 100000000000000000ull +
|
|
round_const_table[rmode][extra_digits];
|
|
|
|
// get P*(2^M[extra_digits])/10^extra_digits
|
|
__mul_64x64_to_128 (CT_new, coefficient_b,
|
|
reciprocals10_64[extra_digits]);
|
|
|
|
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
|
|
amount = short_recip_scale[extra_digits];
|
|
C0_64 = CT_new.w[1] >> amount;
|
|
|
|
// result coefficient
|
|
C64_new = C0_64 + coefficient_a;
|
|
if (C64_new < 10000000000000000ull) {
|
|
C64 = C64_new;
|
|
#ifdef SET_STATUS_FLAGS
|
|
CT = CT_new;
|
|
#endif
|
|
} else
|
|
exponent_b++;
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
|
|
#ifndef IEEE_ROUND_NEAREST
|
|
if (rmode == 0) //ROUNDING_TO_NEAREST
|
|
#endif
|
|
if (C64 & 1) {
|
|
// check whether fractional part of initial_P/10^extra_digits is
|
|
// exactly .5
|
|
// this is the same as fractional part of
|
|
// (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero
|
|
|
|
// get remainder
|
|
remainder_h = CT.w[1] << (64 - amount);
|
|
|
|
// test whether fractional part is 0
|
|
if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) {
|
|
C64--;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
#ifdef SET_STATUS_FLAGS
|
|
status = INEXACT_EXCEPTION;
|
|
|
|
// get remainder
|
|
remainder_h = CT.w[1] << (64 - amount);
|
|
|
|
switch (rmode) {
|
|
case ROUNDING_TO_NEAREST:
|
|
case ROUNDING_TIES_AWAY:
|
|
// test whether fractional part is 0
|
|
if ((remainder_h == 0x8000000000000000ull)
|
|
&& (CT.w[0] < reciprocals10_64[extra_digits]))
|
|
status = EXACT_STATUS;
|
|
break;
|
|
case ROUNDING_DOWN:
|
|
case ROUNDING_TO_ZERO:
|
|
if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits]))
|
|
status = EXACT_STATUS;
|
|
//if(!C64 && rmode==ROUNDING_DOWN) sign_s=sign_y;
|
|
break;
|
|
default:
|
|
// round up
|
|
__add_carry_out (tmp, carry, CT.w[0],
|
|
reciprocals10_64[extra_digits]);
|
|
if ((remainder_h >> (64 - amount)) + carry >=
|
|
(((UINT64) 1) << amount))
|
|
status = EXACT_STATUS;
|
|
break;
|
|
}
|
|
__set_status_flags (pfpsf, status);
|
|
|
|
#endif
|
|
|
|
res =
|
|
fast_get_BID64_check_OF (sign_s, exponent_b + extra_digits, C64,
|
|
rnd_mode, pfpsf);
|
|
BID_RETURN (res);
|
|
}
|