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
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
|
/* Software floating-point emulation.
Basic one-word fraction declaration and manipulation.
Copyright (C) 1997-2013 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Richard Henderson (rth@cygnus.com),
Jakub Jelinek (jj@ultra.linux.cz),
David S. Miller (davem@redhat.com) and
Peter Maydell (pmaydell@chiark.greenend.org.uk).
The GNU C 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.
In addition to the permissions in the GNU Lesser General Public
License, the Free Software Foundation gives you unlimited
permission to link the compiled version of this file into
combinations with other programs, and to distribute those
combinations without any restriction coming from the use of this
file. (The Lesser General Public License restrictions do apply in
other respects; for example, they cover modification of the file,
and distribution when not linked into a combine executable.)
The GNU C 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 GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f
#define _FP_FRAC_COPY_1(D,S) (D##_f = S##_f)
#define _FP_FRAC_SET_1(X,I) (X##_f = I)
#define _FP_FRAC_HIGH_1(X) (X##_f)
#define _FP_FRAC_LOW_1(X) (X##_f)
#define _FP_FRAC_WORD_1(X,w) (X##_f)
#define _FP_FRAC_ADDI_1(X,I) (X##_f += I)
#define _FP_FRAC_SLL_1(X,N) \
do \
{ \
if (__builtin_constant_p(N) && (N) == 1) \
X##_f += X##_f; \
else \
X##_f <<= (N); \
} \
while (0)
#define _FP_FRAC_SRL_1(X,N) (X##_f >>= N)
/* Right shift with sticky-lsb. */
#define _FP_FRAC_SRST_1(X,S,N,sz) __FP_FRAC_SRST_1(X##_f, S, N, sz)
#define _FP_FRAC_SRS_1(X,N,sz) __FP_FRAC_SRS_1(X##_f, N, sz)
#define __FP_FRAC_SRST_1(X,S,N,sz) \
do \
{ \
S = (__builtin_constant_p(N) && (N) == 1 \
? X & 1 \
: (X << (_FP_W_TYPE_SIZE - (N))) != 0); \
X = X >> (N); \
} \
while (0)
#define __FP_FRAC_SRS_1(X,N,sz) \
(X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1 \
? X & 1 \
: (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
#define _FP_FRAC_ADD_1(R,X,Y) (R##_f = X##_f + Y##_f)
#define _FP_FRAC_SUB_1(R,X,Y) (R##_f = X##_f - Y##_f)
#define _FP_FRAC_DEC_1(X,Y) (X##_f -= Y##_f)
#define _FP_FRAC_CLZ_1(z, X) __FP_CLZ(z, X##_f)
/* Predicates */
#define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE)X##_f < 0)
#define _FP_FRAC_ZEROP_1(X) (X##_f == 0)
#define _FP_FRAC_OVERP_1(fs,X) (X##_f & _FP_OVERFLOW_##fs)
#define _FP_FRAC_CLEAR_OVERP_1(fs,X) (X##_f &= ~_FP_OVERFLOW_##fs)
#define _FP_FRAC_HIGHBIT_DW_1(fs,X) (X##_f & _FP_HIGHBIT_DW_##fs)
#define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f)
#define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f)
#define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f)
#define _FP_ZEROFRAC_1 0
#define _FP_MINFRAC_1 1
#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE)0)
/*
* Unpack the raw bits of a native fp value. Do not classify or
* normalize the data.
*/
#define _FP_UNPACK_RAW_1(fs, X, val) \
do \
{ \
union _FP_UNION_##fs _flo; \
_flo.flt = (val); \
\
X##_f = _flo.bits.frac; \
X##_e = _flo.bits.exp; \
X##_s = _flo.bits.sign; \
} \
while (0)
#define _FP_UNPACK_RAW_1_P(fs, X, val) \
do \
{ \
union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *)(val); \
\
X##_f = _flo->bits.frac; \
X##_e = _flo->bits.exp; \
X##_s = _flo->bits.sign; \
} \
while (0)
/*
* Repack the raw bits of a native fp value.
*/
#define _FP_PACK_RAW_1(fs, val, X) \
do \
{ \
union _FP_UNION_##fs _flo; \
\
_flo.bits.frac = X##_f; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} \
while (0)
#define _FP_PACK_RAW_1_P(fs, val, X) \
do \
{ \
union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *)(val); \
\
_flo->bits.frac = X##_f; \
_flo->bits.exp = X##_e; \
_flo->bits.sign = X##_s; \
} \
while (0)
/*
* Multiplication algorithms:
*/
/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
multiplication immediately. */
#define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \
do \
{ \
R##_f = X##_f * Y##_f; \
} \
while (0)
#define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \
do \
{ \
_FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y); \
/* Normalize since we know where the msb of the multiplicands \
were (bit B), we know that the msb of the of the product is \
at either 2B or 2B-1. */ \
_FP_FRAC_SRS_1(R, wfracbits-1, 2*wfracbits); \
} \
while (0)
/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
#define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \
do \
{ \
doit(R##_f1, R##_f0, X##_f, Y##_f); \
} \
while (0)
#define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \
do \
{ \
_FP_FRAC_DECL_2(_Z); \
_FP_MUL_MEAT_DW_1_wide(wfracbits, _Z, X, Y, doit); \
/* Normalize since we know where the msb of the multiplicands \
were (bit B), we know that the msb of the of the product is \
at either 2B or 2B-1. */ \
_FP_FRAC_SRS_2(_Z, wfracbits-1, 2*wfracbits); \
R##_f = _Z_f0; \
} \
while (0)
/* Finally, a simple widening multiply algorithm. What fun! */
#define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \
do \
{ \
_FP_W_TYPE _xh, _xl, _yh, _yl; \
_FP_FRAC_DECL_2(_a); \
\
/* split the words in half */ \
_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \
_xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \
_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \
_yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \
\
/* multiply the pieces */ \
R##_f0 = _xl * _yl; \
_a_f0 = _xh * _yl; \
_a_f1 = _xl * _yh; \
R##_f1 = _xh * _yh; \
\
/* reassemble into two full words */ \
if ((_a_f0 += _a_f1) < _a_f1) \
R##_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2); \
_a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2); \
_a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2); \
_FP_FRAC_ADD_2(R, R, _a); \
} \
while (0)
#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \
do \
{ \
_FP_FRAC_DECL_2(_z); \
_FP_MUL_MEAT_DW_1_hard(wfracbits, _z, X, Y); \
\
/* normalize */ \
_FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits); \
R##_f = _z_f0; \
} \
while (0)
/*
* Division algorithms:
*/
/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
division immediately. Give this macro either _FP_DIV_HELP_imm for
C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you
choose will depend on what the compiler does with divrem4. */
#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \
do \
{ \
_FP_W_TYPE _q, _r; \
X##_f <<= (X##_f < Y##_f \
? R##_e--, _FP_WFRACBITS_##fs \
: _FP_WFRACBITS_##fs - 1); \
doit(_q, _r, X##_f, Y##_f); \
R##_f = _q | (_r != 0); \
} \
while (0)
/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
that may be useful in this situation. This first is for a primitive
that requires normalization, the second for one that does not. Look
for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */
#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \
do \
{ \
_FP_W_TYPE _nh, _nl, _q, _r, _y; \
\
/* Normalize Y -- i.e. make the most significant bit set. */ \
_y = Y##_f << _FP_WFRACXBITS_##fs; \
\
/* Shift X op correspondingly high, that is, up one full word. */ \
if (X##_f < Y##_f) \
{ \
R##_e--; \
_nl = 0; \
_nh = X##_f; \
} \
else \
{ \
_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \
_nh = X##_f >> 1; \
} \
\
udiv_qrnnd(_q, _r, _nh, _nl, _y); \
R##_f = _q | (_r != 0); \
} \
while (0)
#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \
do \
{ \
_FP_W_TYPE _nh, _nl, _q, _r; \
if (X##_f < Y##_f) \
{ \
R##_e--; \
_nl = X##_f << _FP_WFRACBITS_##fs; \
_nh = X##_f >> _FP_WFRACXBITS_##fs; \
} \
else \
{ \
_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \
_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
} \
udiv_qrnnd(_q, _r, _nh, _nl, Y##_f); \
R##_f = _q | (_r != 0); \
} \
while (0)
/*
* Square root algorithms:
* We have just one right now, maybe Newton approximation
* should be added for those machines where division is fast.
*/
#define _FP_SQRT_MEAT_1(R, S, T, X, q) \
do \
{ \
while (q != _FP_WORK_ROUND) \
{ \
T##_f = S##_f + q; \
if (T##_f <= X##_f) \
{ \
S##_f = T##_f + q; \
X##_f -= T##_f; \
R##_f += q; \
} \
_FP_FRAC_SLL_1(X, 1); \
q >>= 1; \
} \
if (X##_f) \
{ \
if (S##_f < X##_f) \
R##_f |= _FP_WORK_ROUND; \
R##_f |= _FP_WORK_STICKY; \
} \
} \
while (0)
/*
* Assembly/disassembly for converting to/from integral types.
* No shifting or overflow handled here.
*/
#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) (r = X##_f)
#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = r)
/*
* Convert FP values between word sizes
*/
#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f)
|
