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 <ieee754.h> |
19 | #include <errno.h> |
20 | #include <float.h> |
21 | #include <math.h> |
22 | |
23 | #include "gmp.h" |
24 | #include "gmp-impl.h" |
25 | |
26 | /* Convert a multi-precision integer of the needed number of bits (106 |
27 | for long double) and an integral power of two to a `long double' in |
28 | IBM extended format. */ |
29 | |
30 | long double |
31 | __mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign) |
32 | { |
33 | union ibm_extended_long_double u; |
34 | unsigned long lzcount; |
35 | unsigned long long hi, lo; |
36 | int exponent2; |
37 | |
38 | u.d[0].ieee.negative = sign; |
39 | u.d[1].ieee.negative = sign; |
40 | u.d[0].ieee.exponent = expt + IEEE754_DOUBLE_BIAS; |
41 | u.d[1].ieee.exponent = 0; |
42 | exponent2 = expt - 53 + IEEE754_DOUBLE_BIAS; |
43 | |
44 | #if BITS_PER_MP_LIMB == 32 |
45 | /* The low order 53 bits (52 + hidden) go into the lower double */ |
46 | lo = frac_ptr[0]; |
47 | lo |= (frac_ptr[1] & ((1LL << (53 - 32)) - 1)) << 32; |
48 | /* The high order 53 bits (52 + hidden) go into the upper double */ |
49 | hi = (frac_ptr[1] >> (53 - 32)) & ((1 << 11) - 1); |
50 | hi |= ((unsigned long long) frac_ptr[2]) << 11; |
51 | hi |= ((unsigned long long) frac_ptr[3]) << (32 + 11); |
52 | #elif BITS_PER_MP_LIMB == 64 |
53 | /* The low order 53 bits (52 + hidden) go into the lower double */ |
54 | lo = frac_ptr[0] & (((mp_limb_t) 1 << 53) - 1); |
55 | /* The high order 53 bits (52 + hidden) go into the upper double */ |
56 | hi = (frac_ptr[0] >> 53) & (((mp_limb_t) 1 << 11) - 1); |
57 | hi |= (frac_ptr[1] << 11); |
58 | #else |
59 | #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for" |
60 | #endif |
61 | |
62 | if ((hi & (1LL << 52)) == 0 && (hi | lo) != 0) |
63 | { |
64 | /* denormal number */ |
65 | unsigned long long val = hi ? hi : lo; |
66 | |
67 | if (sizeof (val) == sizeof (long)) |
68 | lzcount = __builtin_clzl (val); |
69 | else if ((val >> 32) != 0) |
70 | lzcount = __builtin_clzl ((long) (val >> 32)); |
71 | else |
72 | lzcount = __builtin_clzl ((long) val) + 32; |
73 | if (hi) |
74 | lzcount = lzcount - (64 - 53); |
75 | else |
76 | lzcount = lzcount + 53 - (64 - 53); |
77 | |
78 | if (lzcount > u.d[0].ieee.exponent) |
79 | { |
80 | lzcount = u.d[0].ieee.exponent; |
81 | u.d[0].ieee.exponent = 0; |
82 | exponent2 -= lzcount; |
83 | } |
84 | else |
85 | { |
86 | u.d[0].ieee.exponent -= (lzcount - 1); |
87 | exponent2 -= (lzcount - 1); |
88 | } |
89 | |
90 | if (lzcount <= 53) |
91 | { |
92 | hi = (hi << lzcount) | (lo >> (53 - lzcount)); |
93 | lo = (lo << lzcount) & ((1LL << 53) - 1); |
94 | } |
95 | else |
96 | { |
97 | hi = lo << (lzcount - 53); |
98 | lo = 0; |
99 | } |
100 | } |
101 | |
102 | if (lo != 0) |
103 | { |
104 | /* hidden bit of low double controls rounding of the high double. |
105 | If hidden is '1' and either the explicit mantissa is non-zero |
106 | or hi is odd, then round up hi and adjust lo (2nd mantissa) |
107 | plus change the sign of the low double to compensate. */ |
108 | if ((lo & (1LL << 52)) != 0 |
109 | && ((hi & 1) != 0 || (lo & ((1LL << 52) - 1)) != 0)) |
110 | { |
111 | hi++; |
112 | if ((hi & (1LL << 53)) != 0) |
113 | { |
114 | hi >>= 1; |
115 | u.d[0].ieee.exponent++; |
116 | if (u.d[0].ieee.exponent == IEEE754_DOUBLE_BIAS + DBL_MAX_EXP) |
117 | { |
118 | /* Overflow. The appropriate overflowed result must |
119 | be produced (if an infinity, that means the low |
120 | part must be zero). */ |
121 | __set_errno (ERANGE); |
122 | return (sign ? -LDBL_MAX : LDBL_MAX) * LDBL_MAX; |
123 | } |
124 | } |
125 | u.d[1].ieee.negative = !sign; |
126 | lo = (1LL << 53) - lo; |
127 | } |
128 | |
129 | /* Normalize the low double. Shift the mantissa left until |
130 | the hidden bit is '1' and adjust the exponent accordingly. */ |
131 | |
132 | if (sizeof (lo) == sizeof (long)) |
133 | lzcount = __builtin_clzl (lo); |
134 | else if ((lo >> 32) != 0) |
135 | lzcount = __builtin_clzl ((long) (lo >> 32)); |
136 | else |
137 | lzcount = __builtin_clzl ((long) lo) + 32; |
138 | lzcount = lzcount - (64 - 53); |
139 | lo <<= lzcount; |
140 | exponent2 -= lzcount; |
141 | |
142 | if (exponent2 > 0) |
143 | u.d[1].ieee.exponent = exponent2; |
144 | else if (exponent2 > -53) |
145 | lo >>= 1 - exponent2; |
146 | else |
147 | lo = 0; |
148 | } |
149 | else |
150 | u.d[1].ieee.negative = 0; |
151 | |
152 | u.d[1].ieee.mantissa1 = lo; |
153 | u.d[1].ieee.mantissa0 = lo >> 32; |
154 | u.d[0].ieee.mantissa1 = hi; |
155 | u.d[0].ieee.mantissa0 = hi >> 32; |
156 | |
157 | return u.ld; |
158 | } |
159 | |