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375 lines
11 KiB
C
375 lines
11 KiB
C
/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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/*****************************************************************************
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* BID64 multiply
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*****************************************************************************
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*
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* Algorithm description:
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*
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* if(number_digits(coefficient_x)+number_digits(coefficient_y) guaranteed
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* below 16)
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* return get_BID64(sign_x^sign_y, exponent_x + exponent_y - dec_bias,
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* coefficient_x*coefficient_y)
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* else
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* get long product: coefficient_x*coefficient_y
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* determine number of digits to round off (extra_digits)
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* rounding is performed as a 128x128-bit multiplication by
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* 2^M[extra_digits]/10^extra_digits, followed by a shift
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* M[extra_digits] is sufficiently large for required accuracy
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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
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bid64_mul (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_mul (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 P, PU, C128, Q_high, Q_low, Stemp;
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y;
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UINT64 C64, remainder_h, carry, CY, res;
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UINT64 valid_x, valid_y;
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int_double tempx, tempy;
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int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy,
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bin_expon_product;
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int rmode, digits_p, bp, amount, amount2, final_exponent, round_up;
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unsigned status, uf_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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#ifdef SET_STATUS_FLAGS
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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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#endif
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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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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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BID_RETURN (coefficient_x & QUIET_MASK64);
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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 0
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if (((y & INFINITY_MASK64) != INFINITY_MASK64)
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&& !coefficient_y) {
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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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// y==0 , return NaN
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BID_RETURN (NAN_MASK64);
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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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// y==NaN , return NaN
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BID_RETURN (coefficient_y & QUIET_MASK64);
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// otherwise return +/-Inf
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64);
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}
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// x is 0
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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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exponent_y = ((UINT32) (y >> 51)) & 0x3ff;
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else
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exponent_y = ((UINT32) (y >> 53)) & 0x3ff;
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sign_y = y & 0x8000000000000000ull;
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exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS;
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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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else if (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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}
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}
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if (!valid_y) {
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// y is Inf. or NaN
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// test if y is NaN
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if ((y & NAN_MASK64) == NAN_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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BID_RETURN (coefficient_y & QUIET_MASK64);
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}
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// y is Infinity?
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
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// check if x is 0
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if (!coefficient_x) {
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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// x==0, return NaN
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BID_RETURN (NAN_MASK64);
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}
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// otherwise return +/-Inf
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64);
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}
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// y is 0
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exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS;
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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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else if (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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}
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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_x;
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bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52);
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tempy.d = (double) coefficient_y;
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bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52);
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// magnitude estimate for coefficient_x*coefficient_y is
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// 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx)
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bin_expon_product = bin_expon_cx + bin_expon_cy;
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// check if coefficient_x*coefficient_y<2^(10*k+3)
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// equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1
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if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) {
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// easy multiply
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C64 = coefficient_x * coefficient_y;
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res =
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get_BID64_small_mantissa (sign_x ^ sign_y,
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exponent_x + exponent_y -
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DECIMAL_EXPONENT_BIAS, C64, rnd_mode,
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pfpsf);
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BID_RETURN (res);
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} else {
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uf_status = 0;
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// get 128-bit product: coefficient_x*coefficient_y
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__mul_64x64_to_128 (P, coefficient_x, coefficient_y);
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// tighten binary range of P: leading bit is 2^bp
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// unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1
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bin_expon_product -= 2 * BINARY_EXPONENT_BIAS;
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__tight_bin_range_128 (bp, P, bin_expon_product);
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// get number of decimal digits in the product
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digits_p = estimate_decimal_digits[bp];
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if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P)))
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digits_p++; // if power10_table_128[digits_p] <= P
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// determine number of decimal digits to be rounded out
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extra_digits = digits_p - MAX_FORMAT_DIGITS;
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final_exponent =
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exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS;
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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_x ^ sign_y && (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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round_up = 0;
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if (((unsigned) final_exponent) >= 3 * 256) {
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if (final_exponent < 0) {
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// underflow
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if (final_exponent + 16 < 0) {
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res = sign_x ^ sign_y;
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__set_status_flags (pfpsf,
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UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
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if (rmode == ROUNDING_UP)
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res |= 1;
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BID_RETURN (res);
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}
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uf_status = UNDERFLOW_EXCEPTION;
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if (final_exponent == -1) {
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__add_128_64 (PU, P, round_const_table[rmode][extra_digits]);
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if (__unsigned_compare_ge_128
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(PU, power10_table_128[extra_digits + 16]))
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uf_status = 0;
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}
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extra_digits -= final_exponent;
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final_exponent = 0;
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if (extra_digits > 17) {
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__mul_128x128_full (Q_high, Q_low, P, reciprocals10_128[16]);
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amount = recip_scale[16];
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__shr_128 (P, Q_high, amount);
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// get sticky bits
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amount2 = 64 - amount;
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remainder_h = 0;
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remainder_h--;
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remainder_h >>= amount2;
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remainder_h = remainder_h & Q_high.w[0];
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extra_digits -= 16;
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if (remainder_h || (Q_low.w[1] > reciprocals10_128[16].w[1]
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|| (Q_low.w[1] ==
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reciprocals10_128[16].w[1]
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&& Q_low.w[0] >=
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reciprocals10_128[16].w[0]))) {
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round_up = 1;
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__set_status_flags (pfpsf,
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UNDERFLOW_EXCEPTION |
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INEXACT_EXCEPTION);
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P.w[0] = (P.w[0] << 3) + (P.w[0] << 1);
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P.w[0] |= 1;
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extra_digits++;
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}
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}
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} else {
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res =
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fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent,
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1000000000000000ull, rnd_mode,
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pfpsf);
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BID_RETURN (res);
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}
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}
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if (extra_digits > 0) {
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// will divide by 10^(digits_p - 16)
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// add a constant to P, depending on rounding mode
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// 0.5*10^(digits_p - 16) for round-to-nearest
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__add_128_64 (P, P, round_const_table[rmode][extra_digits]);
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// get P*(2^M[extra_digits])/10^extra_digits
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__mul_128x128_full (Q_high, Q_low, P,
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reciprocals10_128[extra_digits]);
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// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
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amount = recip_scale[extra_digits];
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__shr_128 (C128, Q_high, amount);
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C64 = __low_64 (C128);
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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#ifndef IEEE_ROUND_NEAREST
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if (rmode == 0) //ROUNDING_TO_NEAREST
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#endif
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if ((C64 & 1) && !round_up) {
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// check whether fractional part of initial_P/10^extra_digits
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// is exactly .5
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// this is the same as fractional part of
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// (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero
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// get remainder
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remainder_h = Q_high.w[0] << (64 - amount);
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// test whether fractional part is 0
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if (!remainder_h
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&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
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|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
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&& Q_low.w[0] <
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reciprocals10_128[extra_digits].w[0]))) {
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C64--;
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}
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}
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#endif
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#ifdef SET_STATUS_FLAGS
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status = INEXACT_EXCEPTION | uf_status;
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// get remainder
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remainder_h = Q_high.w[0] << (64 - amount);
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switch (rmode) {
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case ROUNDING_TO_NEAREST:
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case ROUNDING_TIES_AWAY:
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// test whether fractional part is 0
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if (remainder_h == 0x8000000000000000ull
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&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
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|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
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&& Q_low.w[0] <
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reciprocals10_128[extra_digits].w[0])))
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status = EXACT_STATUS;
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break;
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case ROUNDING_DOWN:
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case ROUNDING_TO_ZERO:
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if (!remainder_h
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&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
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|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
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&& Q_low.w[0] <
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reciprocals10_128[extra_digits].w[0])))
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status = EXACT_STATUS;
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break;
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default:
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// round up
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__add_carry_out (Stemp.w[0], CY, Q_low.w[0],
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reciprocals10_128[extra_digits].w[0]);
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__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
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reciprocals10_128[extra_digits].w[1], CY);
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if ((remainder_h >> (64 - amount)) + carry >=
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(((UINT64) 1) << amount))
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status = EXACT_STATUS;
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}
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__set_status_flags (pfpsf, status);
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#endif
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// convert to BID and return
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res =
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fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, C64,
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rmode, pfpsf);
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BID_RETURN (res);
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}
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// go to convert_format and exit
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C64 = __low_64 (P);
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res =
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get_BID64 (sign_x ^ sign_y,
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exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64,
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rmode, pfpsf);
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BID_RETURN (res);
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}
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}
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