1 | /* Copyright (C) 1995-2022 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 (7) |
36 | |
37 | mp_size_t |
38 | (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 differnce 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 | } |
198 | |