673 lines
19 KiB
C
673 lines
19 KiB
C
/* Copyright (C) 2007-2016 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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* BID128_to_string
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****************************************************************************/
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#define BID_128RES
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#include <stdio.h>
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#include "bid_internal.h"
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#include "bid128_2_str.h"
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#include "bid128_2_str_macros.h"
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extern int bid128_coeff_2_string (UINT64 X_hi, UINT64 X_lo,
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char *char_ptr);
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_to_string (char *str,
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UINT128 *
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px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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UINT128 x;
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#else
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void
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bid128_to_string (char *str, UINT128 x
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_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT64 x_sign;
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UINT64 x_exp;
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int exp; // unbiased exponent
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// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
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int ind;
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UINT128 C1;
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unsigned int k = 0; // pointer in the string
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unsigned int d0, d123;
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UINT64 HI_18Dig, LO_18Dig, Tmp;
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UINT32 MiDi[12], *ptr;
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char *c_ptr_start, *c_ptr;
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int midi_ind, k_lcv, len;
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#if DECIMAL_CALL_BY_REFERENCE
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x = *px;
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#endif
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BID_SWAP128(x);
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// check for NaN or Infinity
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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// x is special
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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// set invalid flag
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str[0] = ((SINT64)x.w[1]<0)? '-':'+';
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str[1] = 'S';
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str[2] = 'N';
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str[3] = 'a';
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str[4] = 'N';
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str[5] = '\0';
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} else { // x is QNaN
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str[0] = ((SINT64)x.w[1]<0)? '-':'+';
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str[1] = 'Q';
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str[2] = 'N';
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str[3] = 'a';
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str[4] = 'N';
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str[5] = '\0';
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}
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} else { // x is not a NaN, so it must be infinity
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if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
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str[0] = '+';
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str[1] = 'I';
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str[2] = 'n';
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str[3] = 'f';
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str[4] = '\0';
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} else { // x is -inf
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str[0] = '-';
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str[1] = 'I';
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str[2] = 'n';
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str[3] = 'f';
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str[4] = '\0';
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}
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}
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return;
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} else if (((x.w[1] & MASK_COEFF) == 0x0ull) && (x.w[0] == 0x0ull)) {
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// x is 0
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len = 0;
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//determine if +/-
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if (x.w[1] & MASK_SIGN)
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str[len++] = '-';
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else
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str[len++] = '+';
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str[len++] = '0';
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str[len++] = 'E';
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// extract the exponent and print
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exp = (int) (((x.w[1] & MASK_EXP) >> 49) - 6176);
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if(exp > (((0x5ffe)>>1) - (6176))) {
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exp = (int) ((((x.w[1]<<2) & MASK_EXP) >> 49) - 6176);
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}
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if (exp >= 0) {
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str[len++] = '+';
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len += sprintf (str + len, "%u", exp);// should not use sprintf (should
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// use sophisticated algorithm, since we know range of exp is limited)
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str[len++] = '\0';
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} else {
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len += sprintf (str + len, "%d", exp);// should not use sprintf (should
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// use sophisticated algorithm, since we know range of exp is limited)
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str[len++] = '\0';
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}
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return;
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} else { // x is not special and is not zero
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// unpack x
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x_sign = x.w[1] & MASK_SIGN;// 0 for positive, MASK_SIGN for negative
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x_exp = x.w[1] & MASK_EXP;// biased and shifted left 49 bit positions
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if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)
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x_exp = (x.w[1]<<2) & MASK_EXP;// biased and shifted left 49 bit positions
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C1.w[1] = x.w[1] & MASK_COEFF;
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C1.w[0] = x.w[0];
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exp = (x_exp >> 49) - 6176;
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// determine sign's representation as a char
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if (x_sign)
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str[k++] = '-';// negative number
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else
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str[k++] = '+';// positive number
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// determine coefficient's representation as a decimal string
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// if zero or non-canonical, set coefficient to '0'
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if ((C1.w[1] > 0x0001ed09bead87c0ull) ||
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(C1.w[1] == 0x0001ed09bead87c0ull &&
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(C1.w[0] > 0x378d8e63ffffffffull)) ||
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((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
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((C1.w[1] == 0) && (C1.w[0] == 0))) {
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str[k++] = '0';
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} else {
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/* ****************************************************
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This takes a bid coefficient in C1.w[1],C1.w[0]
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and put the converted character sequence at location
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starting at &(str[k]). The function returns the number
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of MiDi returned. Note that the character sequence
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does not have leading zeros EXCEPT when the input is of
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zero value. It will then output 1 character '0'
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The algorithm essentailly tries first to get a sequence of
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Millenial Digits "MiDi" and then uses table lookup to get the
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character strings of these MiDis.
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**************************************************** */
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/* Algorithm first decompose possibly 34 digits in hi and lo
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18 digits. (The high can have at most 16 digits). It then
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uses macro that handle 18 digit portions.
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The first step is to get hi and lo such that
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2^(64) C1.w[1] + C1.w[0] = hi * 10^18 + lo, 0 <= lo < 10^18.
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We use a table lookup method to obtain the hi and lo 18 digits.
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[C1.w[1],C1.w[0]] = c_8 2^(107) + c_7 2^(101) + ... + c_0 2^(59) + d
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where 0 <= d < 2^59 and each c_j has 6 bits. Because d fits in
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18 digits, we set hi = 0, and lo = d to begin with.
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We then retrieve from a table, for j = 0, 1, ..., 8
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that gives us A and B where c_j 2^(59+6j) = A * 10^18 + B.
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hi += A ; lo += B; After each accumulation into lo, we normalize
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immediately. So at the end, we have the decomposition as we need. */
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Tmp = C1.w[0] >> 59;
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LO_18Dig = (C1.w[0] << 5) >> 5;
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Tmp += (C1.w[1] << 5);
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HI_18Dig = 0;
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k_lcv = 0;
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// Tmp = {C1.w[1]{49:0}, C1.w[0]{63:59}}
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// Lo_18Dig = {C1.w[0]{58:0}}
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while (Tmp) {
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midi_ind = (int) (Tmp & 0x000000000000003FLL);
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midi_ind <<= 1;
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Tmp >>= 6;
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HI_18Dig += mod10_18_tbl[k_lcv][midi_ind++];
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LO_18Dig += mod10_18_tbl[k_lcv++][midi_ind];
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__L0_Normalize_10to18 (HI_18Dig, LO_18Dig);
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}
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ptr = MiDi;
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if (HI_18Dig == 0LL) {
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__L1_Split_MiDi_6_Lead (LO_18Dig, ptr);
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} else {
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__L1_Split_MiDi_6_Lead (HI_18Dig, ptr);
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__L1_Split_MiDi_6 (LO_18Dig, ptr);
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}
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len = ptr - MiDi;
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c_ptr_start = &(str[k]);
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c_ptr = c_ptr_start;
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/* now convert the MiDi into character strings */
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__L0_MiDi2Str_Lead (MiDi[0], c_ptr);
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for (k_lcv = 1; k_lcv < len; k_lcv++) {
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__L0_MiDi2Str (MiDi[k_lcv], c_ptr);
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}
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k = k + (c_ptr - c_ptr_start);
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}
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// print E and sign of exponent
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str[k++] = 'E';
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if (exp < 0) {
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exp = -exp;
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str[k++] = '-';
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} else {
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str[k++] = '+';
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}
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// determine exponent's representation as a decimal string
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// d0 = exp / 1000;
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// Use Property 1
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d0 = (exp * 0x418a) >> 24;// 0x418a * 2^-24 = (10^(-3))RP,15
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d123 = exp - 1000 * d0;
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if (d0) { // 1000 <= exp <= 6144 => 4 digits to return
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str[k++] = d0 + 0x30;// ASCII for decimal digit d0
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ind = 3 * d123;
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str[k++] = char_table3[ind];
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str[k++] = char_table3[ind + 1];
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str[k++] = char_table3[ind + 2];
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} else { // 0 <= exp <= 999 => d0 = 0
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if (d123 < 10) { // 0 <= exp <= 9 => 1 digit to return
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str[k++] = d123 + 0x30;// ASCII
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} else if (d123 < 100) { // 10 <= exp <= 99 => 2 digits to return
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ind = 2 * (d123 - 10);
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str[k++] = char_table2[ind];
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str[k++] = char_table2[ind + 1];
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} else { // 100 <= exp <= 999 => 3 digits to return
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ind = 3 * d123;
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str[k++] = char_table3[ind];
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str[k++] = char_table3[ind + 1];
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str[k++] = char_table3[ind + 2];
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}
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}
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str[k] = '\0';
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}
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return;
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}
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#define MAX_FORMAT_DIGITS_128 34
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#define MAX_STRING_DIGITS_128 100
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#define MAX_SEARCH MAX_STRING_DIGITS_128-MAX_FORMAT_DIGITS_128-1
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_from_string (UINT128 * pres,
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char *ps _RND_MODE_PARAM _EXC_FLAGS_PARAM
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_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#else
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UINT128
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bid128_from_string (char *ps _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 CX, res;
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UINT64 sign_x, coeff_high, coeff_low, coeff2, coeff_l2, carry = 0x0ull,
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scale_high, right_radix_leading_zeros;
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int ndigits_before, ndigits_after, ndigits_total, dec_expon, sgn_exp,
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i, d2, rdx_pt_enc;
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char c, buffer[MAX_STRING_DIGITS_128];
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int save_rnd_mode;
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int save_fpsf;
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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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#endif
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save_rnd_mode = rnd_mode; // dummy
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save_fpsf = *pfpsf; // dummy
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right_radix_leading_zeros = rdx_pt_enc = 0;
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// if null string, return NaN
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if (!ps) {
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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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// eliminate leading white space
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while ((*ps == ' ') || (*ps == '\t'))
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ps++;
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// c gets first character
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c = *ps;
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// if c is null or not equal to a (radix point, negative sign,
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// positive sign, or number) it might be SNaN, sNaN, Infinity
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if (!c
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|| (c != '.' && c != '-' && c != '+'
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&& ((unsigned) (c - '0') > 9))) {
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res.w[0] = 0;
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// Infinity?
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if ((tolower_macro (ps[0]) == 'i' && tolower_macro (ps[1]) == 'n'
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&& tolower_macro (ps[2]) == 'f')
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&& (!ps[3]
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|| (tolower_macro (ps[3]) == 'i'
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&& tolower_macro (ps[4]) == 'n'
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&& tolower_macro (ps[5]) == 'i'
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&& tolower_macro (ps[6]) == 't'
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&& tolower_macro (ps[7]) == 'y' && !ps[8])
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)) {
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res.w[1] = 0x7800000000000000ull;
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BID_RETURN (res);
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}
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// return sNaN
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if (tolower_macro (ps[0]) == 's' && tolower_macro (ps[1]) == 'n' &&
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tolower_macro (ps[2]) == 'a' && tolower_macro (ps[3]) == 'n') {
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// case insensitive check for snan
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res.w[1] = 0x7e00000000000000ull;
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BID_RETURN (res);
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} else {
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// return qNaN
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res.w[1] = 0x7c00000000000000ull;
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BID_RETURN (res);
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}
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}
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// if +Inf, -Inf, +Infinity, or -Infinity (case insensitive check for inf)
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if ((tolower_macro (ps[1]) == 'i' && tolower_macro (ps[2]) == 'n' &&
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tolower_macro (ps[3]) == 'f') && (!ps[4] ||
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(tolower_macro (ps[4]) == 'i' && tolower_macro (ps[5]) == 'n' &&
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tolower_macro (ps[6]) == 'i' && tolower_macro (ps[7]) == 't' &&
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tolower_macro (ps[8]) == 'y' && !ps[9]))) { // ci check for infinity
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res.w[0] = 0;
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if (c == '+')
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res.w[1] = 0x7800000000000000ull;
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else if (c == '-')
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res.w[1] = 0xf800000000000000ull;
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else
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res.w[1] = 0x7c00000000000000ull;
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BID_RETURN (res);
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}
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// if +sNaN, +SNaN, -sNaN, or -SNaN
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if (tolower_macro (ps[1]) == 's' && tolower_macro (ps[2]) == 'n'
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&& tolower_macro (ps[3]) == 'a' && tolower_macro (ps[4]) == 'n') {
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res.w[0] = 0;
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if (c == '-')
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res.w[1] = 0xfe00000000000000ull;
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else
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res.w[1] = 0x7e00000000000000ull;
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BID_RETURN (res);
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}
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// set up sign_x to be OR'ed with the upper word later
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if (c == '-')
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sign_x = 0x8000000000000000ull;
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else
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sign_x = 0;
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// go to next character if leading sign
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if (c == '-' || c == '+')
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ps++;
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c = *ps;
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// if c isn't a decimal point or a decimal digit, return NaN
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if (c != '.' && ((unsigned) (c - '0') > 9)) {
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res.w[1] = 0x7c00000000000000ull | sign_x;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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// detect zero (and eliminate/ignore leading zeros)
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if (*(ps) == '0') {
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// if all numbers are zeros (with possibly 1 radix point, the number is zero
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// should catch cases such as: 000.0
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while (*ps == '0') {
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ps++;
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// for numbers such as 0.0000000000000000000000000000000000001001,
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// we want to count the leading zeros
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if (rdx_pt_enc) {
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right_radix_leading_zeros++;
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}
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// if this character is a radix point, make sure we haven't already
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// encountered one
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if (*(ps) == '.') {
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if (rdx_pt_enc == 0) {
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rdx_pt_enc = 1;
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// if this is the first radix point, and the next character is NULL,
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// we have a zero
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if (!*(ps + 1)) {
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res.w[1] =
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(0x3040000000000000ull -
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(right_radix_leading_zeros << 49)) | sign_x;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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ps = ps + 1;
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} else {
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// if 2 radix points, return NaN
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res.w[1] = 0x7c00000000000000ull | sign_x;
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res.w[0] = 0;
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BID_RETURN (res);
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}
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} else if (!*(ps)) {
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//res.w[1] = 0x3040000000000000ull | sign_x;
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res.w[1] =
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(0x3040000000000000ull -
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(right_radix_leading_zeros << 49)) | sign_x;
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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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}
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c = *ps;
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// initialize local variables
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ndigits_before = ndigits_after = ndigits_total = 0;
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sgn_exp = 0;
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// pstart_coefficient = ps;
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if (!rdx_pt_enc) {
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// investigate string (before radix point)
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while ((unsigned) (c - '0') <= 9
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&& ndigits_before < MAX_STRING_DIGITS_128) {
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buffer[ndigits_before] = c;
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ps++;
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c = *ps;
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ndigits_before++;
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}
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ndigits_total = ndigits_before;
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if (c == '.') {
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ps++;
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if ((c = *ps)) {
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// investigate string (after radix point)
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while ((unsigned) (c - '0') <= 9
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&& ndigits_total < MAX_STRING_DIGITS_128) {
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buffer[ndigits_total] = c;
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ps++;
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c = *ps;
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|
ndigits_total++;
|
|
}
|
|
ndigits_after = ndigits_total - ndigits_before;
|
|
}
|
|
}
|
|
} else {
|
|
// we encountered a radix point while detecting zeros
|
|
//if (c = *ps){
|
|
|
|
c = *ps;
|
|
ndigits_total = 0;
|
|
// investigate string (after radix point)
|
|
while ((unsigned) (c - '0') <= 9
|
|
&& ndigits_total < MAX_STRING_DIGITS_128) {
|
|
buffer[ndigits_total] = c;
|
|
ps++;
|
|
c = *ps;
|
|
ndigits_total++;
|
|
}
|
|
ndigits_after = ndigits_total - ndigits_before;
|
|
}
|
|
|
|
// get exponent
|
|
dec_expon = 0;
|
|
if (ndigits_total < MAX_STRING_DIGITS_128) {
|
|
if (c) {
|
|
if (c != 'e' && c != 'E') {
|
|
// return NaN
|
|
res.w[1] = 0x7c00000000000000ull;
|
|
res.w[0] = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
ps++;
|
|
c = *ps;
|
|
|
|
if (((unsigned) (c - '0') > 9)
|
|
&& ((c != '+' && c != '-') || (unsigned) (ps[1] - '0') > 9)) {
|
|
// return NaN
|
|
res.w[1] = 0x7c00000000000000ull;
|
|
res.w[0] = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
if (c == '-') {
|
|
sgn_exp = -1;
|
|
ps++;
|
|
c = *ps;
|
|
} else if (c == '+') {
|
|
ps++;
|
|
c = *ps;
|
|
}
|
|
|
|
dec_expon = c - '0';
|
|
i = 1;
|
|
ps++;
|
|
c = *ps - '0';
|
|
while (((unsigned) c) <= 9 && i < 7) {
|
|
d2 = dec_expon + dec_expon;
|
|
dec_expon = (d2 << 2) + d2 + c;
|
|
ps++;
|
|
c = *ps - '0';
|
|
i++;
|
|
}
|
|
}
|
|
|
|
dec_expon = (dec_expon + sgn_exp) ^ sgn_exp;
|
|
}
|
|
|
|
|
|
if (ndigits_total <= MAX_FORMAT_DIGITS_128) {
|
|
dec_expon +=
|
|
DECIMAL_EXPONENT_BIAS_128 - ndigits_after -
|
|
right_radix_leading_zeros;
|
|
if (dec_expon < 0) {
|
|
res.w[1] = 0 | sign_x;
|
|
res.w[0] = 0;
|
|
}
|
|
if (ndigits_total == 0) {
|
|
CX.w[0] = 0;
|
|
CX.w[1] = 0;
|
|
} else if (ndigits_total <= 19) {
|
|
coeff_high = buffer[0] - '0';
|
|
for (i = 1; i < ndigits_total; i++) {
|
|
coeff2 = coeff_high + coeff_high;
|
|
coeff_high = (coeff2 << 2) + coeff2 + buffer[i] - '0';
|
|
}
|
|
CX.w[0] = coeff_high;
|
|
CX.w[1] = 0;
|
|
} else {
|
|
coeff_high = buffer[0] - '0';
|
|
for (i = 1; i < ndigits_total - 17; i++) {
|
|
coeff2 = coeff_high + coeff_high;
|
|
coeff_high = (coeff2 << 2) + coeff2 + buffer[i] - '0';
|
|
}
|
|
coeff_low = buffer[i] - '0';
|
|
i++;
|
|
for (; i < ndigits_total; i++) {
|
|
coeff_l2 = coeff_low + coeff_low;
|
|
coeff_low = (coeff_l2 << 2) + coeff_l2 + buffer[i] - '0';
|
|
}
|
|
// now form the coefficient as coeff_high*10^19+coeff_low+carry
|
|
scale_high = 100000000000000000ull;
|
|
__mul_64x64_to_128_fast (CX, coeff_high, scale_high);
|
|
|
|
CX.w[0] += coeff_low;
|
|
if (CX.w[0] < coeff_low)
|
|
CX.w[1]++;
|
|
}
|
|
get_BID128 (&res, sign_x, dec_expon, CX,&rnd_mode,pfpsf);
|
|
BID_RETURN (res);
|
|
} else {
|
|
// simply round using the digits that were read
|
|
|
|
dec_expon +=
|
|
ndigits_before + DECIMAL_EXPONENT_BIAS_128 -
|
|
MAX_FORMAT_DIGITS_128 - right_radix_leading_zeros;
|
|
|
|
if (dec_expon < 0) {
|
|
res.w[1] = 0 | sign_x;
|
|
res.w[0] = 0;
|
|
}
|
|
|
|
coeff_high = buffer[0] - '0';
|
|
for (i = 1; i < MAX_FORMAT_DIGITS_128 - 17; i++) {
|
|
coeff2 = coeff_high + coeff_high;
|
|
coeff_high = (coeff2 << 2) + coeff2 + buffer[i] - '0';
|
|
}
|
|
coeff_low = buffer[i] - '0';
|
|
i++;
|
|
for (; i < MAX_FORMAT_DIGITS_128; i++) {
|
|
coeff_l2 = coeff_low + coeff_low;
|
|
coeff_low = (coeff_l2 << 2) + coeff_l2 + buffer[i] - '0';
|
|
}
|
|
switch(rnd_mode) {
|
|
case ROUNDING_TO_NEAREST:
|
|
carry = ((unsigned) ('4' - buffer[i])) >> 31;
|
|
if ((buffer[i] == '5' && !(coeff_low & 1)) || dec_expon < 0) {
|
|
if (dec_expon >= 0) {
|
|
carry = 0;
|
|
i++;
|
|
}
|
|
for (; i < ndigits_total; i++) {
|
|
if (buffer[i] > '0') {
|
|
carry = 1;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
break;
|
|
|
|
case ROUNDING_DOWN:
|
|
if(sign_x)
|
|
for (; i < ndigits_total; i++) {
|
|
if (buffer[i] > '0') {
|
|
carry = 1;
|
|
break;
|
|
}
|
|
}
|
|
break;
|
|
case ROUNDING_UP:
|
|
if(!sign_x)
|
|
for (; i < ndigits_total; i++) {
|
|
if (buffer[i] > '0') {
|
|
carry = 1;
|
|
break;
|
|
}
|
|
}
|
|
break;
|
|
case ROUNDING_TO_ZERO:
|
|
carry=0;
|
|
break;
|
|
case ROUNDING_TIES_AWAY:
|
|
carry = ((unsigned) ('4' - buffer[i])) >> 31;
|
|
if (dec_expon < 0) {
|
|
for (; i < ndigits_total; i++) {
|
|
if (buffer[i] > '0') {
|
|
carry = 1;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
break;
|
|
|
|
|
|
}
|
|
// now form the coefficient as coeff_high*10^17+coeff_low+carry
|
|
scale_high = 100000000000000000ull;
|
|
if (dec_expon < 0) {
|
|
if (dec_expon > -MAX_FORMAT_DIGITS_128) {
|
|
scale_high = 1000000000000000000ull;
|
|
coeff_low = (coeff_low << 3) + (coeff_low << 1);
|
|
dec_expon--;
|
|
}
|
|
if (dec_expon == -MAX_FORMAT_DIGITS_128
|
|
&& coeff_high > 50000000000000000ull)
|
|
carry = 0;
|
|
}
|
|
|
|
__mul_64x64_to_128_fast (CX, coeff_high, scale_high);
|
|
|
|
coeff_low += carry;
|
|
CX.w[0] += coeff_low;
|
|
if (CX.w[0] < coeff_low)
|
|
CX.w[1]++;
|
|
|
|
|
|
get_BID128(&res, sign_x, dec_expon, CX, &rnd_mode, pfpsf);
|
|
BID_RETURN (res);
|
|
}
|
|
}
|