465 lines
14 KiB
C
465 lines
14 KiB
C
/* Copyright (C) 2007 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 2, or (at your option) any later
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version.
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In addition to the permissions in the GNU General Public License, the
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Free Software Foundation gives you unlimited permission to link the
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compiled version of this file into combinations with other programs,
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and to distribute those combinations without any restriction coming
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from the use of this file. (The General Public License restrictions
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do apply in other respects; for example, they cover modification of
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the file, and distribution when not linked into a combine
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executable.)
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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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You should have received a copy of the GNU General Public License
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along with GCC; see the file COPYING. If not, write to the Free
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
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02110-1301, USA. */
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#define BID_128RES
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#include "div_macros.h"
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extern UINT32 __bid_convert_table[5][128][2];
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extern SINT8 __bid_factors[][2];
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extern UINT8 __bid_packed_10000_zeros[];
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BID128_FUNCTION_ARG2(__bid128_div, x, y)
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UINT256 CA4, CA4r, P256;
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UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, Ql, res;
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UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, X, PD;
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int_float fx, fy, f64;
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UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
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int exponent_x = 0, exponent_y, bin_index, bin_expon, diff_expon, ed2,
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digits_q, amount;
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int nzeros, i, j, k, d5;
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unsigned rmode;
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// unpack arguments, check for NaN or Infinity
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if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
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// test if x is NaN
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if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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#ifdef SET_STATUS_FLAGS
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if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
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(y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull)
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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res.w[1] = (x.w[1]) & QUIET_MASK64;
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res.w[0] = x.w[0];
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BID_RETURN (res);
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}
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// x is Infinity?
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if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
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// check if y is Inf.
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if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
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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.w[1] = 0x7c00000000000000ull;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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// y is NaN?
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if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull))
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// return NaN
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{
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// return +/-Inf
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res.w[1] = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) |
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0x7800000000000000ull;
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res.w[0] = 0;
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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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if ((y.w[1] & 0x7800000000000000ull) < 0x7800000000000000ull) {
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if ((!y.w[0]) && !(y.w[1] & 0x0001ffffffffffffull)) {
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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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// x=y=0, return NaN
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res.w[1] = 0x7c00000000000000ull;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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// return 0
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res.w[1] = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull;
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X = ((y.w[1]) << 1) >> 50;
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exponent_x = exponent_x - (int) X + DECIMAL_EXPONENT_BIAS_128;
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if (exponent_x > DECIMAL_MAX_EXPON_128)
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exponent_x = DECIMAL_MAX_EXPON_128;
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else if (exponent_x < 0)
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exponent_x = 0;
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res.w[1] |= (((UINT64) exponent_x) << 49);
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res.w[0] = 0;
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BID_RETURN (res);
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}
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}
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if (!unpack_BID128_value (&sign_y, &exponent_y, &CY, 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.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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#ifdef SET_STATUS_FLAGS
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if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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res.w[1] = y.w[1] & QUIET_MASK64;
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res.w[0] = y.w[0];
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BID_RETURN (res);
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}
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// y is Infinity?
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if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
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// return +/-0
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res.w[1] = sign_x ^ sign_y;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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// y is 0, return +/-Inf
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
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#endif
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res.w[1] =
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((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128;
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if (__unsigned_compare_gt_128 (CY, CX)) {
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// CX < CY
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// 2^64
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f64.i = 0x5f800000;
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// fx ~ CX, fy ~ CY
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fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
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fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
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// expon_cy - expon_cx
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bin_index = (fy.i - fx.i) >> 23;
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if (CX.w[1]) {
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T = __bid_power10_index_binexp_128[bin_index].w[0];
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__mul_64x128_short (CA, T, CX);
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} else {
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T128 = __bid_power10_index_binexp_128[bin_index];
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__mul_64x128_short (CA, CX.w[0], T128);
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}
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ed2 = 33;
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if (__unsigned_compare_gt_128 (CY, CA))
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ed2++;
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T128 = __bid_power10_table_128[ed2];
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__mul_128x128_to_256 (CA4, CA, T128);
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ed2 += __bid_estimate_decimal_digits[bin_index];
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CQ.w[0] = CQ.w[1] = 0;
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diff_expon = diff_expon - ed2;
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} else {
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// get CQ = CX/CY
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__div_128_by_128 (&CQ, &CR, CX, CY);
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if (!CR.w[1] && !CR.w[0]) {
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get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,
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pfpsf);
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BID_RETURN (res);
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}
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// get number of decimal digits in CQ
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// 2^64
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f64.i = 0x5f800000;
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fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
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// binary expon. of CQ
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bin_expon = (fx.i - 0x3f800000) >> 23;
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digits_q = __bid_estimate_decimal_digits[bin_expon];
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TP128.w[0] = __bid_power10_index_binexp_128[bin_expon].w[0];
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TP128.w[1] = __bid_power10_index_binexp_128[bin_expon].w[1];
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if (__unsigned_compare_ge_128 (CQ, TP128))
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digits_q++;
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ed2 = 34 - digits_q;
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T128.w[0] = __bid_power10_table_128[ed2].w[0];
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T128.w[1] = __bid_power10_table_128[ed2].w[1];
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__mul_128x128_to_256 (CA4, CR, T128);
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diff_expon = diff_expon - ed2;
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__mul_128x128_low (CQ, CQ, T128);
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}
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__div_256_by_128 (&CQ, &CA4, CY);
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#ifdef SET_STATUS_FLAGS
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if (CA4.w[0] || CA4.w[1]) {
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// set status flags
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__set_status_flags (pfpsf, INEXACT_EXCEPTION);
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}
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#ifndef LEAVE_TRAILING_ZEROS
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else
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#endif
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#else
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#ifndef LEAVE_TRAILING_ZEROS
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if (!CA4.w[0] && !CA4.w[1])
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#endif
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#endif
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#ifndef LEAVE_TRAILING_ZEROS
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// check whether result is exact
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{
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// check whether CX, CY are short
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if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
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i = (int) CY.w[0] - 1;
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j = (int) CX.w[0] - 1;
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// difference in powers of 2 __bid_factors for Y and X
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nzeros = ed2 - __bid_factors[i][0] + __bid_factors[j][0];
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// difference in powers of 5 __bid_factors
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d5 = ed2 - __bid_factors[i][1] + __bid_factors[j][1];
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if (d5 < nzeros)
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nzeros = d5;
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// get P*(2^M[extra_digits])/10^extra_digits
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__mul_128x128_full (Qh, Ql, CQ, __bid_reciprocals10_128[nzeros]);
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// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
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amount = __bid_recip_scale[nzeros];
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__shr_128_long (CQ, Qh, amount);
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diff_expon += nzeros;
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} else {
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// decompose Q as Qh*10^17 + Ql
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//T128 = __bid_reciprocals10_128[17];
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T128.w[0] = 0x44909befeb9fad49ull;
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T128.w[1] = 0x000b877aa3236a4bull;
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__mul_128x128_to_256 (P256, CQ, T128);
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//amount = __bid_recip_scale[17];
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Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44));
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Q_low = CQ.w[0] - Q_high * 100000000000000000ull;
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if (!Q_low) {
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diff_expon += 17;
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tdigit[0] = Q_high & 0x3ffffff;
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tdigit[1] = 0;
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QX = Q_high >> 26;
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QX32 = QX;
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nzeros = 0;
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for (j = 0; QX32; j++, QX32 >>= 7) {
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k = (QX32 & 127);
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tdigit[0] += __bid_convert_table[j][k][0];
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tdigit[1] += __bid_convert_table[j][k][1];
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if (tdigit[0] >= 100000000) {
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tdigit[0] -= 100000000;
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tdigit[1]++;
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}
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}
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if (tdigit[1] >= 100000000) {
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tdigit[1] -= 100000000;
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if (tdigit[1] >= 100000000)
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tdigit[1] -= 100000000;
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}
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digit = tdigit[0];
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if (!digit && !tdigit[1])
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nzeros += 16;
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else {
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if (!digit) {
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nzeros += 8;
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digit = tdigit[1];
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}
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// decompose digit
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PD = (UINT64) digit *0x068DB8BBull;
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digit_h = (UINT32) (PD >> 40);
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digit_low = digit - digit_h * 10000;
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if (!digit_low)
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nzeros += 4;
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else
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digit_h = digit_low;
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if (!(digit_h & 1))
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nzeros +=
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3 & (UINT32) (__bid_packed_10000_zeros[digit_h >> 3] >>
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(digit_h & 7));
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}
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if (nzeros) {
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__mul_64x64_to_128 (CQ, Q_high, __bid_reciprocals10_64[nzeros]);
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// now get P/10^extra_digits: shift C64 right by M[extra_digits]-64
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amount = __bid_short_recip_scale[nzeros];
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CQ.w[0] = CQ.w[1] >> amount;
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} else
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CQ.w[0] = Q_high;
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CQ.w[1] = 0;
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diff_expon += nzeros;
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} else {
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tdigit[0] = Q_low & 0x3ffffff;
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tdigit[1] = 0;
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QX = Q_low >> 26;
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QX32 = QX;
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nzeros = 0;
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for (j = 0; QX32; j++, QX32 >>= 7) {
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k = (QX32 & 127);
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tdigit[0] += __bid_convert_table[j][k][0];
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tdigit[1] += __bid_convert_table[j][k][1];
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if (tdigit[0] >= 100000000) {
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tdigit[0] -= 100000000;
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tdigit[1]++;
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}
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}
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if (tdigit[1] >= 100000000) {
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tdigit[1] -= 100000000;
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if (tdigit[1] >= 100000000)
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tdigit[1] -= 100000000;
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}
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digit = tdigit[0];
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if (!digit && !tdigit[1])
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nzeros += 16;
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else {
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if (!digit) {
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nzeros += 8;
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digit = tdigit[1];
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}
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// decompose digit
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PD = (UINT64) digit *0x068DB8BBull;
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digit_h = (UINT32) (PD >> 40);
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digit_low = digit - digit_h * 10000;
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if (!digit_low)
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nzeros += 4;
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else
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digit_h = digit_low;
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if (!(digit_h & 1))
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nzeros +=
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3 & (UINT32) (__bid_packed_10000_zeros[digit_h >> 3] >>
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(digit_h & 7));
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}
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if (nzeros) {
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// get P*(2^M[extra_digits])/10^extra_digits
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__mul_128x128_full (Qh, Ql, CQ, __bid_reciprocals10_128[nzeros]);
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//now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
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amount = __bid_recip_scale[nzeros];
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__shr_128 (CQ, Qh, amount);
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}
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diff_expon += nzeros;
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}
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}
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get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,
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pfpsf);
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BID_RETURN (res);
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}
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#endif
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if (diff_expon >= 0) {
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#ifdef IEEE_ROUND_NEAREST
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// rounding
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// 2*CA4 - CY
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CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
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CA4r.w[0] = CA4.w[0] + CA4.w[0];
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__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
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CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
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D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
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carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
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CQ.w[0] += carry64;
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if (CQ.w[0] < carry64)
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CQ.w[1]++;
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#else
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#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
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// rounding
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// 2*CA4 - CY
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CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
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CA4r.w[0] = CA4.w[0] + CA4.w[0];
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__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
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CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
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D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
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carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
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CQ.w[0] += carry64;
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if (CQ.w[0] < carry64)
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CQ.w[1]++;
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#else
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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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switch (rmode) {
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case ROUNDING_TO_NEAREST: // round to nearest code
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// rounding
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// 2*CA4 - CY
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CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
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CA4r.w[0] = CA4.w[0] + CA4.w[0];
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__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
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CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
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D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
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carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
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CQ.w[0] += carry64;
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if (CQ.w[0] < carry64)
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CQ.w[1]++;
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break;
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case ROUNDING_TIES_AWAY:
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// rounding
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// 2*CA4 - CY
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CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
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CA4r.w[0] = CA4.w[0] + CA4.w[0];
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__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
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CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
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D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
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carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
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CQ.w[0] += carry64;
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if (CQ.w[0] < carry64)
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CQ.w[1]++;
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break;
|
|
case ROUNDING_DOWN:
|
|
case ROUNDING_TO_ZERO:
|
|
break;
|
|
default: // rounding up
|
|
CQ.w[0]++;
|
|
if (!CQ.w[0])
|
|
CQ.w[1]++;
|
|
break;
|
|
}
|
|
#endif
|
|
#endif
|
|
|
|
} else {
|
|
#ifdef SET_STATUS_FLAGS
|
|
if (CA4.w[0] || CA4.w[1]) {
|
|
// set status flags
|
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
|
}
|
|
#endif
|
|
|
|
handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ,
|
|
CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf);
|
|
BID_RETURN (res);
|
|
|
|
}
|
|
|
|
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf);
|
|
BID_RETURN (res);
|
|
|
|
}
|