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/* Copyright (C) 1995-2021 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C 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 2.1 of the License, or (at your option) any later version.
The GNU C 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 C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include <ieee754.h>
#include <float.h>
#include <math.h>
#include <stdlib.h>
/* Convert a `long double' in IBM extended format to a multi-precision
integer representing the significand scaled up by its number of
bits (106 for long double) and an integral power of two (MPN
frexpl). */
/* When signs differ, the actual value is the difference between the
significant double and the less significant double. Sometimes a
bit can be lost when we borrow from the significant mantissa. */
#define EXTRA_INTERNAL_PRECISION (7)
mp_size_t
__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
int *expt, int *is_neg,
long double value)
{
union ibm_extended_long_double u;
unsigned long long hi, lo;
int ediff;
u.ld = value;
*is_neg = u.d[0].ieee.negative;
*expt = (int) u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
/* Hold 7 extra bits of precision in the mantissa. This allows
the normalizing shifts below to prevent losing precision when
the signs differ and the exponents are sufficiently far apart. */
lo <<= EXTRA_INTERNAL_PRECISION;
/* If the lower double is not a denormal or zero then set the hidden
53rd bit. */
if (u.d[1].ieee.exponent != 0)
lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION);
else
lo = lo << 1;
/* The lower double is normalized separately from the upper. We may
need to adjust the lower manitissa to reflect this. */
ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
if (ediff > 0)
{
if (ediff < 64)
lo = lo >> ediff;
else
lo = 0;
}
else if (ediff < 0)
lo = lo << -ediff;
/* The high double may be rounded and the low double reflects the
difference between the long double and the rounded high double
value. This is indicated by a differnce between the signs of the
high and low doubles. */
if (u.d[0].ieee.negative != u.d[1].ieee.negative
&& lo != 0)
{
lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo;
if (hi == 0)
{
/* we have a borrow from the hidden bit, so shift left 1. */
hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION));
lo = 0x0fffffffffffffffLL & (lo << 1);
(*expt)--;
}
else
hi--;
}
#if BITS_PER_MP_LIMB == 32
/* Combine the mantissas to be contiguous. */
res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION;
res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION));
res_ptr[2] = hi >> 11;
res_ptr[3] = hi >> (32 + 11);
#define N 4
#elif BITS_PER_MP_LIMB == 64
/* Combine the two mantissas to be contiguous. */
res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION);
res_ptr[1] = hi >> 11;
#define N 2
#else
#error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
#endif
/* The format does not fill the last limb. There are some zeros. */
#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \
- (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB)))
if (u.d[0].ieee.exponent == 0)
{
/* A biased exponent of zero is a special case.
Either it is a zero or it is a denormal number. */
if (res_ptr[0] == 0 && res_ptr[1] == 0
&& res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */
/* It's zero. */
*expt = 0;
else
{
/* It is a denormal number, meaning it has no implicit leading
one bit, and its exponent is in fact the format minimum. We
use DBL_MIN_EXP instead of LDBL_MIN_EXP below because the
latter describes the properties of both parts together, but
the exponent is computed from the high part only. */
int cnt;
#if N == 2
if (res_ptr[N - 1] != 0)
{
count_leading_zeros (cnt, res_ptr[N - 1]);
cnt -= NUM_LEADING_ZEROS;
res_ptr[N - 1] = res_ptr[N - 1] << cnt
| (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt));
res_ptr[0] <<= cnt;
*expt = DBL_MIN_EXP - 1 - cnt;
}
else
{
count_leading_zeros (cnt, res_ptr[0]);
if (cnt >= NUM_LEADING_ZEROS)
{
res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS);
res_ptr[0] = 0;
}
else
{
res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt);
res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt);
}
*expt = DBL_MIN_EXP - 1
- (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt;
}
#else
int j, k, l;
for (j = N - 1; j > 0; j--)
if (res_ptr[j] != 0)
break;
count_leading_zeros (cnt, res_ptr[j]);
cnt -= NUM_LEADING_ZEROS;
l = N - 1 - j;
if (cnt < 0)
{
cnt += BITS_PER_MP_LIMB;
l--;
}
if (!cnt)
for (k = N - 1; k >= l; k--)
res_ptr[k] = res_ptr[k-l];
else
{
for (k = N - 1; k > l; k--)
res_ptr[k] = res_ptr[k-l] << cnt
| res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt);
res_ptr[k--] = res_ptr[0] << cnt;
}
for (; k >= 0; k--)
res_ptr[k] = 0;
*expt = DBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt;
#endif
}
}
else
/* Add the implicit leading one bit for a normalized number. */
res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1
- ((N - 1) * BITS_PER_MP_LIMB));
return N;
}
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