1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
|
/* mpfr_subnormalize -- Subnormalize a floating point number
emulating sub-normal numbers.
Copyright 2005, 2006, 2007 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
This file is part of the MPFR Library.
The MPFR 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 MPFR 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 MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include "mpfr-impl.h"
/* For GMP_RNDN, we can have a problem of double rounding.
In such a case, this table helps to conclude what to do (y positive):
Rounding Bit | Sticky Bit | inexact | Action | new inexact
0 | ? | ? | Trunc | sticky
1 | 0 | -1 | Trunc |
1 | 0 | 0 | Trunc if even |
1 | 0 | 1 | AddOneUlp |
1 | 1 | ? | AddOneUlp |
For other rounding mode, there isn't such a problem.
Just round it again and merge the inexact flags.
*/
int
mpfr_subnormalize (mpfr_ptr y, int old_inexact, mp_rnd_t rnd)
{
int inexact = 0;
MPFR_ASSERTD ((mpfr_uexp_t) __gmpfr_emax - __gmpfr_emin >= MPFR_PREC (y));
/* The subnormal exponent range are from:
mpfr_emin to mpfr_emin + MPFR_PREC(y) - 1 */
if (MPFR_LIKELY (MPFR_IS_SINGULAR (y)
|| (MPFR_GET_EXP (y) >=
__gmpfr_emin + (mp_exp_t) MPFR_PREC (y) - 1)))
inexact = old_inexact;
/* We have to emulate one bit rounding if EXP(y) = emin */
else if (MPFR_GET_EXP (y) == __gmpfr_emin)
{
/* If this is a power of 2, we don't need rounding.
It handles cases when rouding away and y=0.1*2^emin */
if (mpfr_powerof2_raw (y))
inexact = old_inexact;
/* We keep the same sign for y.
Assuming Y is the real value and y the approximation
and since y is not a power of 2: 0.5*2^emin < Y < 1*2^emin
We also know the direction of the error thanks to inexact flag */
else if (rnd == GMP_RNDN)
{
mp_limb_t *mant, rb ,sb;
mp_size_t s;
/* We need the rounding bit and the sticky bit. Read them
and use the previous table to conclude. */
s = MPFR_LIMB_SIZE (y) - 1;
mant = MPFR_MANT (y) + s;
rb = *mant & (MPFR_LIMB_HIGHBIT>>1);
if (rb == 0)
goto set_min;
sb = *mant & ((MPFR_LIMB_HIGHBIT>>1)-1);
while (sb == 0 && s-- != 0)
sb = *--mant;
if (sb != 0)
goto set_min_p1;
/* Rounding bit is 1 and sticky bit is 0.
We need to examine old inexact flag to conclude. */
if (old_inexact * MPFR_SIGN (y) < 0)
goto set_min;
/* If inexact != 0, return 0.1*2^emin+1.
Otherwise, rounding bit = 1, sticky bit = 0 and inexact = 0
So we have 0.1100000000000000000000000*2^emin exactly!!!
we choose to return 0.1*2^emin+1 which minimizes the relative
error. */
goto set_min_p1;
}
else if (MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y)))
{
set_min:
mpfr_setmin (y, __gmpfr_emin);
inexact = -MPFR_SIGN (y);
}
else
{
set_min_p1:
mpfr_setmin (y, __gmpfr_emin+1);
inexact = MPFR_SIGN (y);
}
}
else /* Hard case: It is more or less the same problem than mpfr_cache */
{
mpfr_t dest;
mp_prec_t q;
int sign;
/* Compute the intermediary precision */
q = (mpfr_uexp_t) MPFR_GET_EXP (y) - __gmpfr_emin + 1;
mpfr_init2 (dest, q);
/* Round y in dest */
sign = MPFR_SIGN (y);
MPFR_SET_EXP (dest, MPFR_GET_EXP (y));
MPFR_SET_SIGN (dest, sign);
MPFR_RNDRAW_EVEN (inexact, dest,
MPFR_MANT (y), MPFR_PREC (y), rnd, sign,
MPFR_SET_EXP (dest, MPFR_GET_EXP (dest)+1));
if (MPFR_LIKELY (old_inexact != 0))
{
if (MPFR_UNLIKELY(rnd==GMP_RNDN && (inexact == MPFR_EVEN_INEX
|| inexact == -MPFR_EVEN_INEX)))
{
if (old_inexact*inexact*MPFR_INT_SIGN (y) > 0)
{
if (inexact < 0)
mpfr_nexttoinf (dest);
else
mpfr_nexttozero (dest);
inexact = -inexact;
}
}
else if (MPFR_UNLIKELY (inexact == 0))
inexact = old_inexact;
}
old_inexact = mpfr_set (y, dest, rnd);
MPFR_ASSERTD (old_inexact == 0);
mpfr_clear (dest);
}
return inexact;
}
|
