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
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
|
/* -----------------------------------------------------------------------------
*
* (c) Lennart Augustsson
* (c) The GHC Team, 1998-2000
*
* Support for floating-point <-> gmp integer primitives
*
* ---------------------------------------------------------------------------*/
/* TODO: do we need PosixSource.h ? it lives in rts/ not public includes/ */
/* #include "PosixSource.h" */
#include "Rts.h"
#include "gmp.h"
#include "GmpDerivedConstants.h"
#include <math.h>
#define IEEE_FLOATING_POINT 1
/*
* Encoding and decoding Doubles. Code based on the HBC code
* (lib/fltcode.c).
*/
#define SIZEOF_LIMB_T SIZEOF_MP_LIMB_T
#if SIZEOF_LIMB_T == 4
#define GMP_BASE 4294967296.0
#define LIMBBITS_LOG_2 5
#elif SIZEOF_LIMB_T == 8
#define GMP_BASE 18446744073709551616.0
#define LIMBBITS_LOG_2 6
#else
#error Cannot cope with SIZEOF_LIMB_T -- please add definition of GMP_BASE
#endif
#define DNBIGIT ((SIZEOF_DOUBLE+SIZEOF_LIMB_T-1)/SIZEOF_LIMB_T)
#define FNBIGIT ((SIZEOF_FLOAT +SIZEOF_LIMB_T-1)/SIZEOF_LIMB_T)
#if IEEE_FLOATING_POINT
#define MY_DMINEXP ((DBL_MIN_EXP) - (DBL_MANT_DIG) - 1)
/* DMINEXP is defined in values.h on Linux (for example) */
#define DHIGHBIT 0x00100000
#define DMSBIT 0x80000000
#define MY_FMINEXP ((FLT_MIN_EXP) - (FLT_MANT_DIG) - 1)
#define FHIGHBIT 0x00800000
#define FMSBIT 0x80000000
#endif
#if defined(WORDS_BIGENDIAN) || defined(FLOAT_WORDS_BIGENDIAN)
#define L 1
#define H 0
#else
#define L 0
#define H 1
#endif
#define __abs(a) (( (a) >= 0 ) ? (a) : (-(a)))
StgDouble
integer_cbits_encodeDouble (I_ size, StgByteArray ba, I_ e) /* result = s * 2^e */
{
StgDouble r;
const mp_limb_t *const arr = (const mp_limb_t *)ba;
I_ i;
/* Convert MP_INT to a double; knows a lot about internal rep! */
i = __abs(size)-1;
if ((i < 15) || (e >= 0)) /* overflows only if the final result does */
{
/* This would cause overflow if a large MP_INT is passed, even if the
* exponent would scale it back into range, so we do it only when it's safe. */
for(r = 0.0; i >= 0; i--)
r = (r * GMP_BASE) + arr[i];
} else { /* possibly more than 1024 bits in the MP_INT, but gets scaled down */
/* Find the first nonzero limb; normally it would be the first */
r = 0.0;
while((i >= 0) && (r == 0.0))
{
r = arr[i--];
}
if (i >= 0)
r = (r * GMP_BASE) + arr[i];
#if SIZEOF_LIMB_T < 8
if (i > 0)
r = (r * GMP_BASE) + arr[--i];
#endif
/* Now we have at least the 65 leading bits of the MP_INT or all of it.
* Any further bits would be rounded down, so from now on everything is
* multiplication by powers of 2.
* If i is positive, arr contains i limbs we haven't looked at yet, so
* adjust the exponent by i*8*SIZEOF_LIMB_T. Unfortunately, we must
* beware of overflow, so we can't simply add this to e. */
if (i > 0)
{
/* first add the number of whole limbs that would be cancelled */
i = i + e / (8 * SIZEOF_LIMB_T);
/* check for overflow */
if ((i > 0) && ((i >> (8*sizeof(I_) - 1 - LIMBBITS_LOG_2)) > 0))
{
/* overflow, give e a large dummy value */
e = 2147483647;
} else {
/* no overflow, get the exact value */
e = i * (8 * SIZEOF_LIMB_T) + (e % (8 * SIZEOF_LIMB_T));
}
}
}
/* Now raise to the exponent */
if ( r != 0.0 ) /* Lennart suggests this avoids a bug in MIPS's ldexp */
r = ldexp(r, e);
/* sign is encoded in the size */
if (size < 0)
r = -r;
return r;
}
StgFloat
integer_cbits_encodeFloat (I_ size, StgByteArray ba, I_ e) /* result = s * 2^e */
{
StgFloat r;
const mp_limb_t *arr = (const mp_limb_t *)ba;
I_ i;
/* Convert MP_INT to a float; knows a lot about internal rep! */
i = __abs(size)-1;
/* just in case StgFloat is a double, check sizes */
#if SIZEOF_FLOAT == 4
if ((i < 2) || (e >= 0))
#else
if ((i < 15) || (e >= 0))
#endif
{
for(r = 0.0; i >= 0; i--)
r = (r * GMP_BASE) + arr[i];
} else {
/* Find the first nonzero limb; normally it would be the first */
r = 0.0;
while((i >= 0) && (r == 0.0))
{
r = arr[i--];
}
if (i >= 0)
r = (r * GMP_BASE) + arr[i];
#if (SIZEOF_LIMB_T < 8) && (SIZEOF_FLOAT > 4)
if (i > 0)
r = (r * GMP_BASE) + arr[--i];
#endif
/* Now we have enough leading bits of the MP_INT.
* Any further bits would be rounded down, so from now on everything is
* multiplication by powers of 2.
* If i is positive, arr contains i limbs we haven't looked at yet, so
* adjust the exponent by i*8*SIZEOF_LIMB_T. Unfortunately, we must
* beware of overflow, so we can't simply add this to e. */
if (i > 0)
{
/* first add the number of whole limbs that would be cancelled */
i = i + e / (8 * SIZEOF_LIMB_T);
/* check for overflow */
if ((i > 0) && ((i >> (8*sizeof(I_) - 1 - LIMBBITS_LOG_2)) > 0))
{
/* overflow, give e a large dummy value */
e = 2147483647;
} else {
/* no overflow, get the exact value */
e = i * (8 * SIZEOF_LIMB_T) + (e % (8 * SIZEOF_LIMB_T));
}
}
}
/* Now raise to the exponent */
if ( r != 0.0 ) /* Lennart suggests this avoids a bug in MIPS's ldexp */
r = ldexp(r, e);
/* sign is encoded in the size */
if (size < 0)
r = -r;
return r;
}
/* This only supports IEEE floating point */
void
integer_cbits_decodeDouble (MP_INT *man, I_ *exp, StgDouble dbl)
{
/* Do some bit fiddling on IEEE */
unsigned int low, high; /* assuming 32 bit ints */
int sign, iexp;
union { double d; unsigned int i[2]; } u; /* assuming 32 bit ints, 64 bit double */
ASSERT(sizeof(unsigned int ) == 4 );
ASSERT(sizeof(dbl ) == SIZEOF_DOUBLE);
ASSERT(sizeof(man->_mp_d[0]) == SIZEOF_LIMB_T);
ASSERT(DNBIGIT*SIZEOF_LIMB_T >= SIZEOF_DOUBLE);
u.d = dbl; /* grab chunks of the double */
low = u.i[L];
high = u.i[H];
/* we know the MP_INT* passed in has size zero, so we realloc
no matter what.
*/
man->_mp_alloc = DNBIGIT;
if (low == 0 && (high & ~DMSBIT) == 0) {
man->_mp_size = 0;
*exp = 0L;
} else {
man->_mp_size = DNBIGIT;
iexp = ((high >> 20) & 0x7ff) + MY_DMINEXP;
sign = high;
high &= DHIGHBIT-1;
if (iexp != MY_DMINEXP) /* don't add hidden bit to denorms */
high |= DHIGHBIT;
else {
iexp++;
/* A denorm, normalize the mantissa */
while (! (high & DHIGHBIT)) {
high <<= 1;
if (low & DMSBIT)
high++;
low <<= 1;
iexp--;
}
}
*exp = (I_) iexp;
#if DNBIGIT == 2
man->_mp_d[0] = (mp_limb_t)low;
man->_mp_d[1] = (mp_limb_t)high;
#else
#if DNBIGIT == 1
man->_mp_d[0] = ((mp_limb_t)high) << 32 | (mp_limb_t)low;
#else
#error Cannot cope with DNBIGIT
#endif
#endif
if (sign < 0)
man->_mp_size = -man->_mp_size;
}
}
|
