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/* mpfr_get_decimal128 -- convert a multiple precision floating-point number
to an IEEE 754-2008 decimal128 float
See https://gcc.gnu.org/legacy-ml/gcc/2006-06/msg00691.html,
https://gcc.gnu.org/onlinedocs/gcc/Decimal-Float.html,
and TR 24732 <http://www.open-std.org/jtc1/sc22/wg14/www/projects#24732>.
Copyright 2006-2020 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The GNU MPFR Library 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include "mpfr-impl.h"
#include "ieee_floats.h"
#define ISDIGIT(c) ('0' <= c && c <= '9')
#ifdef MPFR_WANT_DECIMAL_FLOATS
#ifndef DEC128_MAX
# define DEC128_MAX 9.999999999999999999999999999999999E6144dl
#endif
/* construct a decimal128 NaN */
static _Decimal128
get_decimal128_nan (void)
{
return (_Decimal128) MPFR_DBL_NAN;
}
/* construct the decimal128 Inf with given sign */
static _Decimal128
get_decimal128_inf (int negative)
{
return (_Decimal128) (negative ? MPFR_DBL_INFM : MPFR_DBL_INFP);
}
/* construct the decimal128 zero with given sign */
static _Decimal128
get_decimal128_zero (int negative)
{
_Decimal128 zero = 0;
return (_Decimal128) (negative ? -zero : zero);
}
/* construct the decimal128 smallest non-zero with given sign:
it is 10^emin * 10^(1-p). Since emax = 6144, emin = 1-emax = -6143,
and p = 34, we get 10^(-6176) */
static _Decimal128
get_decimal128_min (int negative)
{
return negative ? - 1E-6176dl : 1E-6176dl;
}
/* construct the decimal128 largest finite number with given sign */
static _Decimal128
get_decimal128_max (int negative)
{
return negative ? - DEC128_MAX : DEC128_MAX;
}
/* one-to-one conversion:
s is a decimal string representing a number x = m * 10^e which must be
exactly representable in the decimal128 format, i.e.
(a) the mantissa m has at most 34 decimal digits
(b1) -6143 <= e <= 6144 with m integer multiple of 10^(-33), |m| < 10
(b2) or -6176 <= e <= 6111 with m integer, |m| < 10^34.
Assumes s is neither NaN nor +Inf nor -Inf.
s = [-][0-9]+E[-][0-9]+
The decimal128 format (cf table 3.6 of IEEE 754-2008) has the following
parameters:
* k = 128 (number of bits of storage)
* p = 34 (precision in digits)
* emax = 6144
* bias = E-q = 6176
* sign bit has 1 bit
* w+5 = 17 bits (combination field width)
* t = 110 bits (trailing significand width)
We have k = 1 + 5 + w + t = 128.
*/
static _Decimal128
string_to_Decimal128 (char *s) /* portable version */
{
long int exp = 0;
char m[35];
long n = 0; /* mantissa length */
char *endptr[1];
_Decimal128 x = 0;
int sign = 0;
/* read sign */
if (*s == '-')
{
sign = 1;
s ++;
}
/* read mantissa */
while (ISDIGIT (*s))
m[n++] = *s++;
/* as constructed in mpfr_get_decimal128, s cannot have any '.' separator */
/* we will consider an integer mantissa m*10^exp */
MPFR_ASSERTN(n <= 34);
/* s always has an exponent separator 'E' */
MPFR_ASSERTN(*s == 'E');
exp = strtol (s + 1, endptr, 10);
MPFR_ASSERTN(**endptr == '\0');
MPFR_ASSERTN(-6176 <= exp && exp <= (long) (6145 - n));
while (n < 34)
{
m[n++] = '0';
exp --;
}
/* now n=34 and -6176 <= exp <= 6111, cf (b2) */
m[n] = '\0';
/* the number to convert is m[] * 10^exp where the mantissa is a 34-digit
integer */
/* compute biased exponent */
exp += 6176;
MPFR_ASSERTN(exp >= -33);
if (exp < 0)
{
int i;
n = -exp;
/* check the last n digits of the mantissa are zero */
for (i = 1; i <= n; i++)
MPFR_ASSERTN(m[34 - n] == '0');
/* shift the first (34-n) digits to the right */
for (i = 34 - n - 1; i >= 0; i--)
m[i + n] = m[i];
/* zero the first n digits */
for (i = 0; i < n; i ++)
m[i] = '0';
exp = 0;
}
/* the number to convert is m[] * 10^(exp-6176) */
exp -= 6176;
for (n = 0; n < 34; n++)
x = (_Decimal128) 10 * x + (_Decimal128) (m[n] - '0');
/* multiply by 10^exp */
if (exp > 0)
{
_Decimal128 ten = 10;
_Decimal128 ten2 = ten * ten;
_Decimal128 ten4 = ten2 * ten2;
_Decimal128 ten8 = ten4 * ten4;
_Decimal128 ten16 = ten8 * ten8;
_Decimal128 ten32 = ten16 * ten16;
_Decimal128 ten64 = ten32 * ten32;
_Decimal128 ten128 = ten64 * ten64;
_Decimal128 ten256 = ten128 * ten128;
_Decimal128 ten512 = ten256 * ten256;
_Decimal128 ten1024 = ten512 * ten512;
_Decimal128 ten2048 = ten1024 * ten1024;
_Decimal128 ten4096 = ten2048 * ten2048;
if (exp >= 4096)
{
x *= ten4096;
exp -= 4096;
}
if (exp >= 2048)
{
x *= ten2048;
exp -= 2048;
}
if (exp >= 1024)
{
x *= ten1024;
exp -= 1024;
}
if (exp >= 512)
{
x *= ten512;
exp -= 512;
}
if (exp >= 256)
{
x *= ten256;
exp -= 256;
}
if (exp >= 128)
{
x *= ten128;
exp -= 128;
}
if (exp >= 64)
{
x *= ten64;
exp -= 64;
}
if (exp >= 32)
{
x *= ten32;
exp -= 32;
}
if (exp >= 16)
{
x *= ten16;
exp -= 16;
}
if (exp >= 8)
{
x *= ten8;
exp -= 8;
}
if (exp >= 4)
{
x *= ten4;
exp -= 4;
}
if (exp >= 2)
{
x *= ten2;
exp -= 2;
}
if (exp >= 1)
{
x *= ten;
exp -= 1;
}
}
else if (exp < 0)
{
_Decimal128 ten = 10;
_Decimal128 ten2 = ten * ten;
_Decimal128 ten4 = ten2 * ten2;
_Decimal128 ten8 = ten4 * ten4;
_Decimal128 ten16 = ten8 * ten8;
_Decimal128 ten32 = ten16 * ten16;
_Decimal128 ten64 = ten32 * ten32;
_Decimal128 ten128 = ten64 * ten64;
_Decimal128 ten256 = ten128 * ten128;
_Decimal128 ten512 = ten256 * ten256;
_Decimal128 ten1024 = ten512 * ten512;
_Decimal128 ten2048 = ten1024 * ten1024;
_Decimal128 ten4096 = ten2048 * ten2048;
if (exp <= -4096)
{
x /= ten4096;
exp += 4096;
}
if (exp <= -2048)
{
x /= ten2048;
exp += 2048;
}
if (exp <= -1024)
{
x /= ten1024;
exp += 1024;
}
if (exp <= -512)
{
x /= ten512;
exp += 512;
}
if (exp <= -256)
{
x /= ten256;
exp += 256;
}
if (exp <= -128)
{
x /= ten128;
exp += 128;
}
if (exp <= -64)
{
x /= ten64;
exp += 64;
}
if (exp <= -32)
{
x /= ten32;
exp += 32;
}
if (exp <= -16)
{
x /= ten16;
exp += 16;
}
if (exp <= -8)
{
x /= ten8;
exp += 8;
}
if (exp <= -4)
{
x /= ten4;
exp += 4;
}
if (exp <= -2)
{
x /= ten2;
exp += 2;
}
if (exp <= -1)
{
x /= ten;
exp += 1;
}
}
if (sign)
x = -x;
return x;
}
_Decimal128
mpfr_get_decimal128 (mpfr_srcptr src, mpfr_rnd_t rnd_mode)
{
int negative;
mpfr_exp_t e;
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
{
if (MPFR_IS_NAN (src))
return get_decimal128_nan ();
negative = MPFR_IS_NEG (src);
if (MPFR_IS_INF (src))
return get_decimal128_inf (negative);
MPFR_ASSERTD (MPFR_IS_ZERO(src));
return get_decimal128_zero (negative);
}
e = MPFR_GET_EXP (src);
negative = MPFR_IS_NEG (src);
MPFR_UPDATE2_RND_MODE (rnd_mode, MPFR_SIGN (src));
/* now rnd_mode is RNDN, RNDF, RNDA or RNDZ */
/* the smallest decimal128 number is 10^(-6176),
with 2^(-20517) < 10^(-6176) < 2^(-20516) */
if (MPFR_UNLIKELY (e < -20517)) /* src <= 2^(-20518) < 1/2*10^(-6176) */
{
if (rnd_mode != MPFR_RNDA)
return get_decimal128_zero (negative);
else /* RNDA: return the smallest non-zero number */
return get_decimal128_min (negative);
}
/* the largest decimal128 number is just below 10^6145 < 2^20414 */
else if (MPFR_UNLIKELY (e > 20414)) /* then src >= 2^20414 */
{
if (rnd_mode == MPFR_RNDZ)
return get_decimal128_max (negative);
else /* RNDN, RNDA, RNDF: round away */
return get_decimal128_inf (negative);
}
else
{
/* we need to store the sign (1 character), the significand (at most 34
characters), the exponent part (at most 6 characters for "E-6176"),
and the terminating null character, thus we need at least 42
characters in s. */
char s[42];
mpfr_get_str (s, &e, 10, 34, src, rnd_mode);
/* the smallest normal number is 1.000...000E-6143,
which corresponds to s=[0.]1000...000 and e=-6142 */
if (e < -6142)
{
/* the smallest subnormal number is 0.000...001E-6143 = 1E-6176,
which corresponds to s=[0.]1000...000 and e=-6175 */
if (e < -6175)
{
if (rnd_mode == MPFR_RNDN && e == -6176)
{
/* If 0.5E-6176 < |src| < 1E-6176 (smallest subnormal),
src should round to +/- 1E-6176 in MPFR_RNDN. */
mpfr_get_str (s, &e, 10, 1, src, MPFR_RNDA);
return e == -6176 && s[negative] <= '5' ?
get_decimal128_zero (negative) :
get_decimal128_min (negative);
}
if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDN)
return get_decimal128_zero (negative);
else /* RNDA or RNDF: return the smallest non-zero number */
return get_decimal128_min (negative);
}
else
{
mpfr_exp_t e2;
long digits = 34 - (-6142 - e);
/* if e = -6175 then 34 - (-6142 - e) = 1 */
mpfr_get_str (s, &e2, 10, digits, src, rnd_mode);
/* Warning: we can have e2 = e + 1 here, when rounding to
nearest or away from zero. */
s[negative + digits] = 'E';
sprintf (s + negative + digits + 1, "%ld",
(long int)e2 - digits);
return string_to_Decimal128 (s);
}
}
/* the largest number is 9.999...999E+6144,
which corresponds to s=[0.]9999...999 and e=6145 */
else if (e > 6145)
{
if (rnd_mode == MPFR_RNDZ)
return get_decimal128_max (negative);
else /* RNDN, RNDA, RNDF: round away */
return get_decimal128_inf (negative);
}
else /* -6142 <= e <= 6145 */
{
s[34 + negative] = 'E';
sprintf (s + 35 + negative, "%ld", (long int) e - 34);
return string_to_Decimal128 (s);
}
}
}
#endif /* MPFR_WANT_DECIMAL_FLOATS */
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