198 lines
6.0 KiB
C
198 lines
6.0 KiB
C
/* Copyright (C) 1995-2022 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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#include <ieee754.h>
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#include <float.h>
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#include <math.h>
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#include <stdlib.h>
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/* Convert a `long double' in IBM extended format to a multi-precision
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integer representing the significand scaled up by its number of
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bits (106 for long double) and an integral power of two (MPN
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frexpl). */
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/* When signs differ, the actual value is the difference between the
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significant double and the less significant double. Sometimes a
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bit can be lost when we borrow from the significant mantissa. */
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#define EXTRA_INTERNAL_PRECISION (7)
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mp_size_t
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__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
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int *expt, int *is_neg,
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long double value)
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{
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union ibm_extended_long_double u;
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unsigned long long hi, lo;
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int ediff;
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u.ld = value;
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*is_neg = u.d[0].ieee.negative;
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*expt = (int) u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
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lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
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hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
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/* Hold 7 extra bits of precision in the mantissa. This allows
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the normalizing shifts below to prevent losing precision when
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the signs differ and the exponents are sufficiently far apart. */
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lo <<= EXTRA_INTERNAL_PRECISION;
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/* If the lower double is not a denormal or zero then set the hidden
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53rd bit. */
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if (u.d[1].ieee.exponent != 0)
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lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION);
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else
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lo = lo << 1;
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/* The lower double is normalized separately from the upper. We may
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need to adjust the lower manitissa to reflect this. */
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ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
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if (ediff > 0)
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{
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if (ediff < 64)
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lo = lo >> ediff;
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else
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lo = 0;
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}
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else if (ediff < 0)
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lo = lo << -ediff;
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/* The high double may be rounded and the low double reflects the
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difference between the long double and the rounded high double
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value. This is indicated by a differnce between the signs of the
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high and low doubles. */
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if (u.d[0].ieee.negative != u.d[1].ieee.negative
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&& lo != 0)
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{
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lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo;
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if (hi == 0)
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{
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/* we have a borrow from the hidden bit, so shift left 1. */
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hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION));
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lo = 0x0fffffffffffffffLL & (lo << 1);
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(*expt)--;
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}
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else
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hi--;
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}
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#if BITS_PER_MP_LIMB == 32
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/* Combine the mantissas to be contiguous. */
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res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION;
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res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION));
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res_ptr[2] = hi >> 11;
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res_ptr[3] = hi >> (32 + 11);
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#define N 4
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#elif BITS_PER_MP_LIMB == 64
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/* Combine the two mantissas to be contiguous. */
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res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION);
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res_ptr[1] = hi >> 11;
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#define N 2
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#else
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#error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
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#endif
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/* The format does not fill the last limb. There are some zeros. */
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#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \
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- (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB)))
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if (u.d[0].ieee.exponent == 0)
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{
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/* A biased exponent of zero is a special case.
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Either it is a zero or it is a denormal number. */
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if (res_ptr[0] == 0 && res_ptr[1] == 0
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&& res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */
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/* It's zero. */
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*expt = 0;
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else
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{
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/* It is a denormal number, meaning it has no implicit leading
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one bit, and its exponent is in fact the format minimum. We
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use DBL_MIN_EXP instead of LDBL_MIN_EXP below because the
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latter describes the properties of both parts together, but
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the exponent is computed from the high part only. */
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int cnt;
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#if N == 2
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if (res_ptr[N - 1] != 0)
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{
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count_leading_zeros (cnt, res_ptr[N - 1]);
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cnt -= NUM_LEADING_ZEROS;
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res_ptr[N - 1] = res_ptr[N - 1] << cnt
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| (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt));
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res_ptr[0] <<= cnt;
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*expt = DBL_MIN_EXP - 1 - cnt;
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}
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else
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{
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count_leading_zeros (cnt, res_ptr[0]);
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if (cnt >= NUM_LEADING_ZEROS)
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{
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res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS);
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res_ptr[0] = 0;
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}
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else
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{
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res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt);
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res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt);
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}
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*expt = DBL_MIN_EXP - 1
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- (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt;
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}
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#else
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int j, k, l;
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for (j = N - 1; j > 0; j--)
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if (res_ptr[j] != 0)
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break;
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count_leading_zeros (cnt, res_ptr[j]);
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cnt -= NUM_LEADING_ZEROS;
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l = N - 1 - j;
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if (cnt < 0)
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{
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cnt += BITS_PER_MP_LIMB;
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l--;
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}
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if (!cnt)
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for (k = N - 1; k >= l; k--)
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res_ptr[k] = res_ptr[k-l];
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else
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{
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for (k = N - 1; k > l; k--)
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res_ptr[k] = res_ptr[k-l] << cnt
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| res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt);
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res_ptr[k--] = res_ptr[0] << cnt;
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}
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for (; k >= 0; k--)
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res_ptr[k] = 0;
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*expt = DBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt;
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#endif
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}
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}
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else
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/* Add the implicit leading one bit for a normalized number. */
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res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1
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- ((N - 1) * BITS_PER_MP_LIMB));
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return N;
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}
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