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gcc/libgcc/config/libbid/bid128_string.c

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/* Copyright (C) 2007-2016 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
/*****************************************************************************
* BID128_to_string
****************************************************************************/
#define BID_128RES
#include <stdio.h>
#include "bid_internal.h"
#include "bid128_2_str.h"
#include "bid128_2_str_macros.h"
extern int bid128_coeff_2_string (UINT64 X_hi, UINT64 X_lo,
char *char_ptr);
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_to_string (char *str,
UINT128 *
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT128 x;
#else
void
bid128_to_string (char *str, UINT128 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
int ind;
UINT128 C1;
unsigned int k = 0; // pointer in the string
unsigned int d0, d123;
UINT64 HI_18Dig, LO_18Dig, Tmp;
UINT32 MiDi[12], *ptr;
char *c_ptr_start, *c_ptr;
int midi_ind, k_lcv, len;
#if DECIMAL_CALL_BY_REFERENCE
x = *px;
#endif
BID_SWAP128(x);
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
str[0] = ((SINT64)x.w[1]<0)? '-':'+';
str[1] = 'S';
str[2] = 'N';
str[3] = 'a';
str[4] = 'N';
str[5] = '\0';
} else { // x is QNaN
str[0] = ((SINT64)x.w[1]<0)? '-':'+';
str[1] = 'Q';
str[2] = 'N';
str[3] = 'a';
str[4] = 'N';
str[5] = '\0';
}
} else { // x is not a NaN, so it must be infinity
if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf
str[0] = '+';
str[1] = 'I';
str[2] = 'n';
str[3] = 'f';
str[4] = '\0';
} else { // x is -inf
str[0] = '-';
str[1] = 'I';
str[2] = 'n';
str[3] = 'f';
str[4] = '\0';
}
}
return;
} else if (((x.w[1] & MASK_COEFF) == 0x0ull) && (x.w[0] == 0x0ull)) {
// x is 0
len = 0;
//determine if +/-
if (x.w[1] & MASK_SIGN)
str[len++] = '-';
else
str[len++] = '+';
str[len++] = '0';
str[len++] = 'E';
// extract the exponent and print
exp = (int) (((x.w[1] & MASK_EXP) >> 49) - 6176);
if(exp > (((0x5ffe)>>1) - (6176))) {
exp = (int) ((((x.w[1]<<2) & MASK_EXP) >> 49) - 6176);
}
if (exp >= 0) {
str[len++] = '+';
len += sprintf (str + len, "%u", exp);// should not use sprintf (should
// use sophisticated algorithm, since we know range of exp is limited)
str[len++] = '\0';
} else {
len += sprintf (str + len, "%d", exp);// should not use sprintf (should
// use sophisticated algorithm, since we know range of exp is limited)
str[len++] = '\0';
}
return;
} else { // x is not special and is not zero
// unpack x
x_sign = x.w[1] & MASK_SIGN;// 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP;// biased and shifted left 49 bit positions
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)
x_exp = (x.w[1]<<2) & MASK_EXP;// biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
exp = (x_exp >> 49) - 6176;
// determine sign's representation as a char
if (x_sign)
str[k++] = '-';// negative number
else
str[k++] = '+';// positive number
// determine coefficient's representation as a decimal string
// if zero or non-canonical, set coefficient to '0'
if ((C1.w[1] > 0x0001ed09bead87c0ull) ||
(C1.w[1] == 0x0001ed09bead87c0ull &&
(C1.w[0] > 0x378d8e63ffffffffull)) ||
((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
((C1.w[1] == 0) && (C1.w[0] == 0))) {
str[k++] = '0';
} else {
/* ****************************************************
This takes a bid coefficient in C1.w[1],C1.w[0]
and put the converted character sequence at location
starting at &(str[k]). The function returns the number
of MiDi returned. Note that the character sequence
does not have leading zeros EXCEPT when the input is of
zero value. It will then output 1 character '0'
The algorithm essentailly tries first to get a sequence of
Millenial Digits "MiDi" and then uses table lookup to get the
character strings of these MiDis.
**************************************************** */
/* Algorithm first decompose possibly 34 digits in hi and lo
18 digits. (The high can have at most 16 digits). It then
uses macro that handle 18 digit portions.
The first step is to get hi and lo such that
2^(64) C1.w[1] + C1.w[0] = hi * 10^18 + lo, 0 <= lo < 10^18.
We use a table lookup method to obtain the hi and lo 18 digits.
[C1.w[1],C1.w[0]] = c_8 2^(107) + c_7 2^(101) + ... + c_0 2^(59) + d
where 0 <= d < 2^59 and each c_j has 6 bits. Because d fits in
18 digits, we set hi = 0, and lo = d to begin with.
We then retrieve from a table, for j = 0, 1, ..., 8
that gives us A and B where c_j 2^(59+6j) = A * 10^18 + B.
hi += A ; lo += B; After each accumulation into lo, we normalize
immediately. So at the end, we have the decomposition as we need. */
Tmp = C1.w[0] >> 59;
LO_18Dig = (C1.w[0] << 5) >> 5;
Tmp += (C1.w[1] << 5);
HI_18Dig = 0;
k_lcv = 0;
// Tmp = {C1.w[1]{49:0}, C1.w[0]{63:59}}
// Lo_18Dig = {C1.w[0]{58:0}}
while (Tmp) {
midi_ind = (int) (Tmp & 0x000000000000003FLL);
midi_ind <<= 1;
Tmp >>= 6;
HI_18Dig += mod10_18_tbl[k_lcv][midi_ind++];
LO_18Dig += mod10_18_tbl[k_lcv++][midi_ind];
__L0_Normalize_10to18 (HI_18Dig, LO_18Dig);
}
ptr = MiDi;
if (HI_18Dig == 0LL) {
__L1_Split_MiDi_6_Lead (LO_18Dig, ptr);
} else {
__L1_Split_MiDi_6_Lead (HI_18Dig, ptr);
__L1_Split_MiDi_6 (LO_18Dig, ptr);
}
len = ptr - MiDi;
c_ptr_start = &(str[k]);
c_ptr = c_ptr_start;
/* now convert the MiDi into character strings */
__L0_MiDi2Str_Lead (MiDi[0], c_ptr);
for (k_lcv = 1; k_lcv < len; k_lcv++) {
__L0_MiDi2Str (MiDi[k_lcv], c_ptr);
}
k = k + (c_ptr - c_ptr_start);
}
// print E and sign of exponent
str[k++] = 'E';
if (exp < 0) {
exp = -exp;
str[k++] = '-';
} else {
str[k++] = '+';
}
// determine exponent's representation as a decimal string
// d0 = exp / 1000;
// Use Property 1
d0 = (exp * 0x418a) >> 24;// 0x418a * 2^-24 = (10^(-3))RP,15
d123 = exp - 1000 * d0;
if (d0) { // 1000 <= exp <= 6144 => 4 digits to return
str[k++] = d0 + 0x30;// ASCII for decimal digit d0
ind = 3 * d123;
str[k++] = char_table3[ind];
str[k++] = char_table3[ind + 1];
str[k++] = char_table3[ind + 2];
} else { // 0 <= exp <= 999 => d0 = 0
if (d123 < 10) { // 0 <= exp <= 9 => 1 digit to return
str[k++] = d123 + 0x30;// ASCII
} else if (d123 < 100) { // 10 <= exp <= 99 => 2 digits to return
ind = 2 * (d123 - 10);
str[k++] = char_table2[ind];
str[k++] = char_table2[ind + 1];
} else { // 100 <= exp <= 999 => 3 digits to return
ind = 3 * d123;
str[k++] = char_table3[ind];
str[k++] = char_table3[ind + 1];
str[k++] = char_table3[ind + 2];
}
}
str[k] = '\0';
}
return;
}
#define MAX_FORMAT_DIGITS_128 34
#define MAX_STRING_DIGITS_128 100
#define MAX_SEARCH MAX_STRING_DIGITS_128-MAX_FORMAT_DIGITS_128-1
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_from_string (UINT128 * pres,
char *ps _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#else
UINT128
bid128_from_string (char *ps _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT128 CX, res;
UINT64 sign_x, coeff_high, coeff_low, coeff2, coeff_l2, carry = 0x0ull,
scale_high, right_radix_leading_zeros;
int ndigits_before, ndigits_after, ndigits_total, dec_expon, sgn_exp,
i, d2, rdx_pt_enc;
char c, buffer[MAX_STRING_DIGITS_128];
int save_rnd_mode;
int save_fpsf;
#if DECIMAL_CALL_BY_REFERENCE
#if !DECIMAL_GLOBAL_ROUNDING
_IDEC_round rnd_mode = *prnd_mode;
#endif
#endif
save_rnd_mode = rnd_mode; // dummy
save_fpsf = *pfpsf; // dummy
right_radix_leading_zeros = rdx_pt_enc = 0;
// if null string, return NaN
if (!ps) {
res.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// eliminate leading white space
while ((*ps == ' ') || (*ps == '\t'))
ps++;
// c gets first character
c = *ps;
// if c is null or not equal to a (radix point, negative sign,
// positive sign, or number) it might be SNaN, sNaN, Infinity
if (!c
|| (c != '.' && c != '-' && c != '+'
&& ((unsigned) (c - '0') > 9))) {
res.w[0] = 0;
// Infinity?
if ((tolower_macro (ps[0]) == 'i' && tolower_macro (ps[1]) == 'n'
&& tolower_macro (ps[2]) == 'f')
&& (!ps[3]
|| (tolower_macro (ps[3]) == 'i'
&& tolower_macro (ps[4]) == 'n'
&& tolower_macro (ps[5]) == 'i'
&& tolower_macro (ps[6]) == 't'
&& tolower_macro (ps[7]) == 'y' && !ps[8])
)) {
res.w[1] = 0x7800000000000000ull;
BID_RETURN (res);
}
// return sNaN
if (tolower_macro (ps[0]) == 's' && tolower_macro (ps[1]) == 'n' &&
tolower_macro (ps[2]) == 'a' && tolower_macro (ps[3]) == 'n') {
// case insensitive check for snan
res.w[1] = 0x7e00000000000000ull;
BID_RETURN (res);
} else {
// return qNaN
res.w[1] = 0x7c00000000000000ull;
BID_RETURN (res);
}
}
// if +Inf, -Inf, +Infinity, or -Infinity (case insensitive check for inf)
if ((tolower_macro (ps[1]) == 'i' && tolower_macro (ps[2]) == 'n' &&
tolower_macro (ps[3]) == 'f') && (!ps[4] ||
(tolower_macro (ps[4]) == 'i' && tolower_macro (ps[5]) == 'n' &&
tolower_macro (ps[6]) == 'i' && tolower_macro (ps[7]) == 't' &&
tolower_macro (ps[8]) == 'y' && !ps[9]))) { // ci check for infinity
res.w[0] = 0;
if (c == '+')
res.w[1] = 0x7800000000000000ull;
else if (c == '-')
res.w[1] = 0xf800000000000000ull;
else
res.w[1] = 0x7c00000000000000ull;
BID_RETURN (res);
}
// if +sNaN, +SNaN, -sNaN, or -SNaN
if (tolower_macro (ps[1]) == 's' && tolower_macro (ps[2]) == 'n'
&& tolower_macro (ps[3]) == 'a' && tolower_macro (ps[4]) == 'n') {
res.w[0] = 0;
if (c == '-')
res.w[1] = 0xfe00000000000000ull;
else
res.w[1] = 0x7e00000000000000ull;
BID_RETURN (res);
}
// set up sign_x to be OR'ed with the upper word later
if (c == '-')
sign_x = 0x8000000000000000ull;
else
sign_x = 0;
// go to next character if leading sign
if (c == '-' || c == '+')
ps++;
c = *ps;
// if c isn't a decimal point or a decimal digit, return NaN
if (c != '.' && ((unsigned) (c - '0') > 9)) {
res.w[1] = 0x7c00000000000000ull | sign_x;
res.w[0] = 0;
BID_RETURN (res);
}
// detect zero (and eliminate/ignore leading zeros)
if (*(ps) == '0') {
// if all numbers are zeros (with possibly 1 radix point, the number is zero
// should catch cases such as: 000.0
while (*ps == '0') {
ps++;
// for numbers such as 0.0000000000000000000000000000000000001001,
// we want to count the leading zeros
if (rdx_pt_enc) {
right_radix_leading_zeros++;
}
// if this character is a radix point, make sure we haven't already
// encountered one
if (*(ps) == '.') {
if (rdx_pt_enc == 0) {
rdx_pt_enc = 1;
// if this is the first radix point, and the next character is NULL,
// we have a zero
if (!*(ps + 1)) {
res.w[1] =
(0x3040000000000000ull -
(right_radix_leading_zeros << 49)) | sign_x;
res.w[0] = 0;
BID_RETURN (res);
}
ps = ps + 1;
} else {
// if 2 radix points, return NaN
res.w[1] = 0x7c00000000000000ull | sign_x;
res.w[0] = 0;
BID_RETURN (res);
}
} else if (!*(ps)) {
//res.w[1] = 0x3040000000000000ull | sign_x;
res.w[1] =
(0x3040000000000000ull -
(right_radix_leading_zeros << 49)) | sign_x;
res.w[0] = 0;
BID_RETURN (res);
}
}
}
c = *ps;
// initialize local variables
ndigits_before = ndigits_after = ndigits_total = 0;
sgn_exp = 0;
// pstart_coefficient = ps;
if (!rdx_pt_enc) {
// investigate string (before radix point)
while ((unsigned) (c - '0') <= 9
&& ndigits_before < MAX_STRING_DIGITS_128) {
buffer[ndigits_before] = c;
ps++;
c = *ps;
ndigits_before++;
}
ndigits_total = ndigits_before;
if (c == '.') {
ps++;
if ((c = *ps)) {
// 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;
}
}
} 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);
}
}
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