1 /* Copyright (C) 1995-2023 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3
4 The GNU C Library is free software; you can redistribute it and/or
5 modify it under the terms of the GNU Lesser General Public
6 License as published by the Free Software Foundation; either
7 version 2.1 of the License, or (at your option) any later version.
8
9 The GNU C Library is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 Lesser General Public License for more details.
13
14 You should have received a copy of the GNU Lesser General Public
15 License along with the GNU C Library; if not, see
16 <https://www.gnu.org/licenses/>. */
17
18 #include "gmp.h"
19 #include "gmp-impl.h"
20 #include "longlong.h"
21 #include <ieee754.h>
22 #include <float.h>
23 #include <math.h>
24 #include <stdlib.h>
25
26 /* Convert a `long double' in IBM extended format to a multi-precision
27 integer representing the significand scaled up by its number of
28 bits (106 for long double) and an integral power of two (MPN
29 frexpl). */
30
31
32 /* When signs differ, the actual value is the difference between the
33 significant double and the less significant double. Sometimes a
34 bit can be lost when we borrow from the significant mantissa. */
35 #define EXTRA_INTERNAL_PRECISION (7)
36
37 mp_size_t
38 __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
39 int *expt, int *is_neg,
40 long double value)
41 {
42 union ibm_extended_long_double u;
43 unsigned long long hi, lo;
44 int ediff;
45
46 u.ld = value;
47
48 *is_neg = u.d[0].ieee.negative;
49 *expt = (int) u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
50
51 lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
52 hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
53
54 /* Hold 7 extra bits of precision in the mantissa. This allows
55 the normalizing shifts below to prevent losing precision when
56 the signs differ and the exponents are sufficiently far apart. */
57 lo <<= EXTRA_INTERNAL_PRECISION;
58
59 /* If the lower double is not a denormal or zero then set the hidden
60 53rd bit. */
61 if (u.d[1].ieee.exponent != 0)
62 lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION);
63 else
64 lo = lo << 1;
65
66 /* The lower double is normalized separately from the upper. We may
67 need to adjust the lower manitissa to reflect this. */
68 ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
69 if (ediff > 0)
70 {
71 if (ediff < 64)
72 lo = lo >> ediff;
73 else
74 lo = 0;
75 }
76 else if (ediff < 0)
77 lo = lo << -ediff;
78
79 /* The high double may be rounded and the low double reflects the
80 difference between the long double and the rounded high double
81 value. This is indicated by a difference between the signs of the
82 high and low doubles. */
83 if (u.d[0].ieee.negative != u.d[1].ieee.negative
84 && lo != 0)
85 {
86 lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo;
87 if (hi == 0)
88 {
89 /* we have a borrow from the hidden bit, so shift left 1. */
90 hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION));
91 lo = 0x0fffffffffffffffLL & (lo << 1);
92 (*expt)--;
93 }
94 else
95 hi--;
96 }
97 #if BITS_PER_MP_LIMB == 32
98 /* Combine the mantissas to be contiguous. */
99 res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION;
100 res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION));
101 res_ptr[2] = hi >> 11;
102 res_ptr[3] = hi >> (32 + 11);
103 #define N 4
104 #elif BITS_PER_MP_LIMB == 64
105 /* Combine the two mantissas to be contiguous. */
106 res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION);
107 res_ptr[1] = hi >> 11;
108 #define N 2
109 #else
110 #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
111 #endif
112 /* The format does not fill the last limb. There are some zeros. */
113 #define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \
114 - (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB)))
115
116 if (u.d[0].ieee.exponent == 0)
117 {
118 /* A biased exponent of zero is a special case.
119 Either it is a zero or it is a denormal number. */
120 if (res_ptr[0] == 0 && res_ptr[1] == 0
121 && res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */
122 /* It's zero. */
123 *expt = 0;
124 else
125 {
126 /* It is a denormal number, meaning it has no implicit leading
127 one bit, and its exponent is in fact the format minimum. We
128 use DBL_MIN_EXP instead of LDBL_MIN_EXP below because the
129 latter describes the properties of both parts together, but
130 the exponent is computed from the high part only. */
131 int cnt;
132
133 #if N == 2
134 if (res_ptr[N - 1] != 0)
135 {
136 count_leading_zeros (cnt, res_ptr[N - 1]);
137 cnt -= NUM_LEADING_ZEROS;
138 res_ptr[N - 1] = res_ptr[N - 1] << cnt
139 | (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt));
140 res_ptr[0] <<= cnt;
141 *expt = DBL_MIN_EXP - 1 - cnt;
142 }
143 else
144 {
145 count_leading_zeros (cnt, res_ptr[0]);
146 if (cnt >= NUM_LEADING_ZEROS)
147 {
148 res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS);
149 res_ptr[0] = 0;
150 }
151 else
152 {
153 res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt);
154 res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt);
155 }
156 *expt = DBL_MIN_EXP - 1
157 - (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt;
158 }
159 #else
160 int j, k, l;
161
162 for (j = N - 1; j > 0; j--)
163 if (res_ptr[j] != 0)
164 break;
165
166 count_leading_zeros (cnt, res_ptr[j]);
167 cnt -= NUM_LEADING_ZEROS;
168 l = N - 1 - j;
169 if (cnt < 0)
170 {
171 cnt += BITS_PER_MP_LIMB;
172 l--;
173 }
174 if (!cnt)
175 for (k = N - 1; k >= l; k--)
176 res_ptr[k] = res_ptr[k-l];
177 else
178 {
179 for (k = N - 1; k > l; k--)
180 res_ptr[k] = res_ptr[k-l] << cnt
181 | res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt);
182 res_ptr[k--] = res_ptr[0] << cnt;
183 }
184
185 for (; k >= 0; k--)
186 res_ptr[k] = 0;
187 *expt = DBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt;
188 #endif
189 }
190 }
191 else
192 /* Add the implicit leading one bit for a normalized number. */
193 res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1
194 - ((N - 1) * BITS_PER_MP_LIMB));
195
196 return N;
197 }