aboutsummaryrefslogtreecommitdiff
path: root/soft-fp/extended.h
blob: c8b1583086547782428c268f85624ea0216f5c3e (plain)
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
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
/* Software floating-point emulation.
   Definitions for IEEE Extended Precision.
   Copyright (C) 1999-2013 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Jakub Jelinek (jj@ultra.linux.cz).

   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/>.  */

#if _FP_W_TYPE_SIZE < 32
#error "Here's a nickel, kid. Go buy yourself a real computer."
#endif

#if _FP_W_TYPE_SIZE < 64
#define _FP_FRACTBITS_E         (4*_FP_W_TYPE_SIZE)
#define _FP_FRACTBITS_DW_E	(8*_FP_W_TYPE_SIZE)
#else
#define _FP_FRACTBITS_E		(2*_FP_W_TYPE_SIZE)
#define _FP_FRACTBITS_DW_E	(4*_FP_W_TYPE_SIZE)
#endif

#define _FP_FRACBITS_E		64
#define _FP_FRACXBITS_E		(_FP_FRACTBITS_E - _FP_FRACBITS_E)
#define _FP_WFRACBITS_E		(_FP_WORKBITS + _FP_FRACBITS_E)
#define _FP_WFRACXBITS_E	(_FP_FRACTBITS_E - _FP_WFRACBITS_E)
#define _FP_EXPBITS_E		15
#define _FP_EXPBIAS_E		16383
#define _FP_EXPMAX_E		32767

#define _FP_QNANBIT_E		\
	((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
#define _FP_QNANBIT_SH_E		\
	((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
#define _FP_IMPLBIT_E		\
	((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
#define _FP_IMPLBIT_SH_E		\
	((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
#define _FP_OVERFLOW_E		\
	((_FP_W_TYPE)1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))

#define _FP_WFRACBITS_DW_E	(2 * _FP_WFRACBITS_E)
#define _FP_WFRACXBITS_DW_E	(_FP_FRACTBITS_DW_E - _FP_WFRACBITS_DW_E)
#define _FP_HIGHBIT_DW_E	\
  ((_FP_W_TYPE)1 << (_FP_WFRACBITS_DW_E - 1) % _FP_W_TYPE_SIZE)

typedef float XFtype __attribute__((mode(XF)));

#if _FP_W_TYPE_SIZE < 64

union _FP_UNION_E
{
   XFtype flt;
   struct _FP_STRUCT_LAYOUT
   {
#if __BYTE_ORDER == __BIG_ENDIAN
      unsigned long pad1 : _FP_W_TYPE_SIZE;
      unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
      unsigned long sign : 1;
      unsigned long exp : _FP_EXPBITS_E;
      unsigned long frac1 : _FP_W_TYPE_SIZE;
      unsigned long frac0 : _FP_W_TYPE_SIZE;
#else
      unsigned long frac0 : _FP_W_TYPE_SIZE;
      unsigned long frac1 : _FP_W_TYPE_SIZE;
      unsigned exp : _FP_EXPBITS_E;
      unsigned sign : 1;
#endif /* not bigendian */
   } bits __attribute__((packed));
};


#define FP_DECL_E(X)		_FP_DECL(4,X)

#define FP_UNPACK_RAW_E(X, val)				\
  do {							\
    union _FP_UNION_E _flo; _flo.flt = (val);		\
							\
    X##_f[2] = 0; X##_f[3] = 0;				\
    X##_f[0] = _flo.bits.frac0;				\
    X##_f[1] = _flo.bits.frac1;				\
    X##_e  = _flo.bits.exp;				\
    X##_s  = _flo.bits.sign;				\
  } while (0)

#define FP_UNPACK_RAW_EP(X, val)			\
  do {							\
    union _FP_UNION_E *_flo =				\
    (union _FP_UNION_E *)(val);				\
							\
    X##_f[2] = 0; X##_f[3] = 0;				\
    X##_f[0] = _flo->bits.frac0;			\
    X##_f[1] = _flo->bits.frac1;			\
    X##_e  = _flo->bits.exp;				\
    X##_s  = _flo->bits.sign;				\
  } while (0)

#define FP_PACK_RAW_E(val, X)				\
  do {							\
    union _FP_UNION_E _flo;				\
							\
    if (X##_e) X##_f[1] |= _FP_IMPLBIT_E;		\
    else X##_f[1] &= ~(_FP_IMPLBIT_E);			\
    _flo.bits.frac0 = X##_f[0];				\
    _flo.bits.frac1 = X##_f[1];				\
    _flo.bits.exp   = X##_e;				\
    _flo.bits.sign  = X##_s;				\
							\
    (val) = _flo.flt;					\
  } while (0)

#define FP_PACK_RAW_EP(val, X)				\
  do {							\
    if (!FP_INHIBIT_RESULTS)				\
      {							\
	union _FP_UNION_E *_flo =			\
	  (union _FP_UNION_E *)(val);			\
							\
	if (X##_e) X##_f[1] |= _FP_IMPLBIT_E;		\
	else X##_f[1] &= ~(_FP_IMPLBIT_E);		\
	_flo->bits.frac0 = X##_f[0];			\
	_flo->bits.frac1 = X##_f[1];			\
	_flo->bits.exp   = X##_e;			\
	_flo->bits.sign  = X##_s;			\
      }							\
  } while (0)

#define FP_UNPACK_E(X,val)		\
  do {					\
    FP_UNPACK_RAW_E(X,val);		\
    _FP_UNPACK_CANONICAL(E,4,X);	\
  } while (0)

#define FP_UNPACK_EP(X,val)		\
  do {					\
    FP_UNPACK_RAW_EP(X,val);		\
    _FP_UNPACK_CANONICAL(E,4,X);	\
  } while (0)

#define FP_UNPACK_SEMIRAW_E(X,val)	\
  do {					\
    FP_UNPACK_RAW_E(X,val);		\
    _FP_UNPACK_SEMIRAW(E,4,X);		\
  } while (0)

#define FP_UNPACK_SEMIRAW_EP(X,val)	\
  do {					\
    FP_UNPACK_RAW_EP(X,val);		\
    _FP_UNPACK_SEMIRAW(E,4,X);		\
  } while (0)

#define FP_PACK_E(val,X)		\
  do {					\
    _FP_PACK_CANONICAL(E,4,X);		\
    FP_PACK_RAW_E(val,X);		\
  } while (0)

#define FP_PACK_EP(val,X)		\
  do {					\
    _FP_PACK_CANONICAL(E,4,X);		\
    FP_PACK_RAW_EP(val,X);		\
  } while (0)

#define FP_PACK_SEMIRAW_E(val,X)	\
  do {					\
    _FP_PACK_SEMIRAW(E,4,X);		\
    FP_PACK_RAW_E(val,X);		\
  } while (0)

#define FP_PACK_SEMIRAW_EP(val,X)	\
  do {					\
    _FP_PACK_SEMIRAW(E,4,X);		\
    FP_PACK_RAW_EP(val,X);		\
  } while (0)

#define FP_ISSIGNAN_E(X)	_FP_ISSIGNAN(E,4,X)
#define FP_NEG_E(R,X)		_FP_NEG(E,4,R,X)
#define FP_ADD_E(R,X,Y)		_FP_ADD(E,4,R,X,Y)
#define FP_SUB_E(R,X,Y)		_FP_SUB(E,4,R,X,Y)
#define FP_MUL_E(R,X,Y)		_FP_MUL(E,4,R,X,Y)
#define FP_DIV_E(R,X,Y)		_FP_DIV(E,4,R,X,Y)
#define FP_SQRT_E(R,X)		_FP_SQRT(E,4,R,X)
#define FP_FMA_E(R,X,Y,Z)	_FP_FMA(E,4,8,R,X,Y,Z)

/*
 * Square root algorithms:
 * We have just one right now, maybe Newton approximation
 * should be added for those machines where division is fast.
 * This has special _E version because standard _4 square
 * root would not work (it has to start normally with the
 * second word and not the first), but as we have to do it
 * anyway, we optimize it by doing most of the calculations
 * in two UWtype registers instead of four.
 */

#define _FP_SQRT_MEAT_E(R, S, T, X, q)			\
  do {							\
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);		\
    _FP_FRAC_SRL_4(X, (_FP_WORKBITS));			\
    while (q)						\
      {							\
	T##_f[1] = S##_f[1] + q;			\
	if (T##_f[1] <= X##_f[1])			\
	  {						\
	    S##_f[1] = T##_f[1] + q;			\
	    X##_f[1] -= T##_f[1];			\
	    R##_f[1] += q;				\
	  }						\
	_FP_FRAC_SLL_2(X, 1);				\
	q >>= 1;					\
      }							\
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);		\
    while (q)						\
      {							\
	T##_f[0] = S##_f[0] + q;			\
	T##_f[1] = S##_f[1];				\
	if (T##_f[1] < X##_f[1] || 			\
	    (T##_f[1] == X##_f[1] &&			\
	     T##_f[0] <= X##_f[0]))			\
	  {						\
	    S##_f[0] = T##_f[0] + q;			\
	    S##_f[1] += (T##_f[0] > S##_f[0]);		\
	    _FP_FRAC_DEC_2(X, T);			\
	    R##_f[0] += q;				\
	  }						\
	_FP_FRAC_SLL_2(X, 1);				\
	q >>= 1;					\
      }							\
    _FP_FRAC_SLL_4(R, (_FP_WORKBITS));			\
    if (X##_f[0] | X##_f[1])				\
      {							\
	if (S##_f[1] < X##_f[1] || 			\
	    (S##_f[1] == X##_f[1] &&			\
	     S##_f[0] < X##_f[0]))			\
	  R##_f[0] |= _FP_WORK_ROUND;			\
	R##_f[0] |= _FP_WORK_STICKY;			\
      }							\
  } while (0)

#define FP_CMP_E(r,X,Y,un)	_FP_CMP(E,4,r,X,Y,un)
#define FP_CMP_EQ_E(r,X,Y)	_FP_CMP_EQ(E,4,r,X,Y)
#define FP_CMP_UNORD_E(r,X,Y)	_FP_CMP_UNORD(E,4,r,X,Y)

#define FP_TO_INT_E(r,X,rsz,rsg)	_FP_TO_INT(E,4,r,X,rsz,rsg)
#define FP_FROM_INT_E(X,r,rs,rt)	_FP_FROM_INT(E,4,X,r,rs,rt)

#define _FP_FRAC_HIGH_E(X)	(X##_f[2])
#define _FP_FRAC_HIGH_RAW_E(X)	(X##_f[1])

#define _FP_FRAC_HIGH_DW_E(X)	(X##_f[4])

#else   /* not _FP_W_TYPE_SIZE < 64 */
union _FP_UNION_E
{
  XFtype flt;
  struct _FP_STRUCT_LAYOUT {
#if __BYTE_ORDER == __BIG_ENDIAN
    _FP_W_TYPE pad  : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
    unsigned sign   : 1;
    unsigned exp    : _FP_EXPBITS_E;
    _FP_W_TYPE frac : _FP_W_TYPE_SIZE;
#else
    _FP_W_TYPE frac : _FP_W_TYPE_SIZE;
    unsigned exp    : _FP_EXPBITS_E;
    unsigned sign   : 1;
#endif
  } bits;
};

#define FP_DECL_E(X)		_FP_DECL(2,X)

#define FP_UNPACK_RAW_E(X, val)					\
  do {								\
    union _FP_UNION_E _flo; _flo.flt = (val);			\
								\
    X##_f0 = _flo.bits.frac;					\
    X##_f1 = 0;							\
    X##_e = _flo.bits.exp;					\
    X##_s = _flo.bits.sign;					\
  } while (0)

#define FP_UNPACK_RAW_EP(X, val)				\
  do {								\
    union _FP_UNION_E *_flo =					\
      (union _FP_UNION_E *)(val);				\
								\
    X##_f0 = _flo->bits.frac;					\
    X##_f1 = 0;							\
    X##_e = _flo->bits.exp;					\
    X##_s = _flo->bits.sign;					\
  } while (0)

#define FP_PACK_RAW_E(val, X)					\
  do {								\
    union _FP_UNION_E _flo;					\
								\
    if (X##_e) X##_f0 |= _FP_IMPLBIT_E;				\
    else X##_f0 &= ~(_FP_IMPLBIT_E);				\
    _flo.bits.frac = X##_f0;					\
    _flo.bits.exp  = X##_e;					\
    _flo.bits.sign = X##_s;					\
								\
    (val) = _flo.flt;						\
  } while (0)

#define FP_PACK_RAW_EP(fs, val, X)				\
  do {								\
    if (!FP_INHIBIT_RESULTS)					\
      {								\
	union _FP_UNION_E *_flo =				\
	  (union _FP_UNION_E *)(val);				\
								\
	if (X##_e) X##_f0 |= _FP_IMPLBIT_E;			\
	else X##_f0 &= ~(_FP_IMPLBIT_E);			\
	_flo->bits.frac = X##_f0;				\
	_flo->bits.exp  = X##_e;				\
	_flo->bits.sign = X##_s;				\
      }								\
  } while (0)


#define FP_UNPACK_E(X,val)		\
  do {					\
    FP_UNPACK_RAW_E(X,val);		\
    _FP_UNPACK_CANONICAL(E,2,X);	\
  } while (0)

#define FP_UNPACK_EP(X,val)		\
  do {					\
    FP_UNPACK_RAW_EP(X,val);		\
    _FP_UNPACK_CANONICAL(E,2,X);	\
  } while (0)

#define FP_UNPACK_SEMIRAW_E(X,val)	\
  do {					\
    FP_UNPACK_RAW_E(X,val);		\
    _FP_UNPACK_SEMIRAW(E,2,X);		\
  } while (0)

#define FP_UNPACK_SEMIRAW_EP(X,val)	\
  do {					\
    FP_UNPACK_RAW_EP(X,val);		\
    _FP_UNPACK_SEMIRAW(E,2,X);		\
  } while (0)

#define FP_PACK_E(val,X)		\
  do {					\
    _FP_PACK_CANONICAL(E,2,X);		\
    FP_PACK_RAW_E(val,X);		\
  } while (0)

#define FP_PACK_EP(val,X)		\
  do {					\
    _FP_PACK_CANONICAL(E,2,X);		\
    FP_PACK_RAW_EP(val,X);		\
  } while (0)

#define FP_PACK_SEMIRAW_E(val,X)	\
  do {					\
    _FP_PACK_SEMIRAW(E,2,X);		\
    FP_PACK_RAW_E(val,X);		\
  } while (0)

#define FP_PACK_SEMIRAW_EP(val,X)	\
  do {					\
    _FP_PACK_SEMIRAW(E,2,X);		\
    FP_PACK_RAW_EP(val,X);		\
  } while (0)

#define FP_ISSIGNAN_E(X)	_FP_ISSIGNAN(E,2,X)
#define FP_NEG_E(R,X)		_FP_NEG(E,2,R,X)
#define FP_ADD_E(R,X,Y)		_FP_ADD(E,2,R,X,Y)
#define FP_SUB_E(R,X,Y)		_FP_SUB(E,2,R,X,Y)
#define FP_MUL_E(R,X,Y)		_FP_MUL(E,2,R,X,Y)
#define FP_DIV_E(R,X,Y)		_FP_DIV(E,2,R,X,Y)
#define FP_SQRT_E(R,X)		_FP_SQRT(E,2,R,X)
#define FP_FMA_E(R,X,Y,Z)	_FP_FMA(E,2,4,R,X,Y,Z)

/*
 * Square root algorithms:
 * We have just one right now, maybe Newton approximation
 * should be added for those machines where division is fast.
 * We optimize it by doing most of the calculations
 * in one UWtype registers instead of two, although we don't
 * have to.
 */
#define _FP_SQRT_MEAT_E(R, S, T, X, q)			\
  do {							\
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);		\
    _FP_FRAC_SRL_2(X, (_FP_WORKBITS));			\
    while (q)						\
      {							\
        T##_f0 = S##_f0 + q;				\
        if (T##_f0 <= X##_f0)				\
          {						\
            S##_f0 = T##_f0 + q;			\
            X##_f0 -= T##_f0;				\
            R##_f0 += q;				\
          }						\
        _FP_FRAC_SLL_1(X, 1);				\
        q >>= 1;					\
      }							\
    _FP_FRAC_SLL_2(R, (_FP_WORKBITS));			\
    if (X##_f0)						\
      {							\
	if (S##_f0 < X##_f0)				\
	  R##_f0 |= _FP_WORK_ROUND;			\
	R##_f0 |= _FP_WORK_STICKY;			\
      }							\
  } while (0)

#define FP_CMP_E(r,X,Y,un)	_FP_CMP(E,2,r,X,Y,un)
#define FP_CMP_EQ_E(r,X,Y)	_FP_CMP_EQ(E,2,r,X,Y)
#define FP_CMP_UNORD_E(r,X,Y)	_FP_CMP_UNORD(E,2,r,X,Y)

#define FP_TO_INT_E(r,X,rsz,rsg)	_FP_TO_INT(E,2,r,X,rsz,rsg)
#define FP_FROM_INT_E(X,r,rs,rt)	_FP_FROM_INT(E,2,X,r,rs,rt)

#define _FP_FRAC_HIGH_E(X)	(X##_f1)
#define _FP_FRAC_HIGH_RAW_E(X)	(X##_f0)

#define _FP_FRAC_HIGH_DW_E(X)	(X##_f[2])

#endif /* not _FP_W_TYPE_SIZE < 64 */