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
|
/*
* Basic two-word fraction declaration and manipulation.
*/
#define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1
#define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
#define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
#define _FP_FRAC_HIGH_2(X) (X##_f1)
#define _FP_FRAC_LOW_2(X) (X##_f0)
#define _FP_FRAC_WORD_2(X,w) (X##_f##w)
#define _FP_FRAC_SLL_2(X,N) \
do { \
if ((N) < _FP_W_TYPE_SIZE) \
{ \
if (__builtin_constant_p(N) && (N) == 1) \
{ \
X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \
X##_f0 += X##_f0; \
} \
else \
{ \
X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
X##_f0 <<= (N); \
} \
} \
else \
{ \
X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
X##_f0 = 0; \
} \
} while (0)
#define _FP_FRAC_SRL_2(X,N) \
do { \
if ((N) < _FP_W_TYPE_SIZE) \
{ \
X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
X##_f1 >>= (N); \
} \
else \
{ \
X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
X##_f1 = 0; \
} \
} while (0)
/* Right shift with sticky-lsb. */
#define _FP_FRAC_SRS_2(X,N,sz) \
do { \
if ((N) < _FP_W_TYPE_SIZE) \
{ \
X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \
(__builtin_constant_p(N) && (N) == 1 \
? X##_f0 & 1 \
: (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
X##_f1 >>= (N); \
} \
else \
{ \
X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \
(((X##_f1 << (2 * _FP_W_TYPE_SIZE - (N))) | \
X##_f0) != 0)); \
X##_f1 = 0; \
} \
} while (0)
#define _FP_FRAC_ADDI_2(X,I) \
__FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
#define _FP_FRAC_ADD_2(R,X,Y) \
__FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
#define _FP_FRAC_SUB_2(R,X,Y) \
__FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
#define _FP_FRAC_CLZ_2(R,X) \
do { \
if (X##_f1) \
__FP_CLZ(R,X##_f1); \
else \
{ \
__FP_CLZ(R,X##_f0); \
R += _FP_W_TYPE_SIZE; \
} \
} while(0)
/* Predicates */
#define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
#define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
#define _FP_FRAC_OVERP_2(fs,X) (X##_f1 & _FP_OVERFLOW_##fs)
#define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
#define _FP_FRAC_GT_2(X, Y) \
((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
#define _FP_FRAC_GE_2(X, Y) \
((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
#define _FP_ZEROFRAC_2 0, 0
#define _FP_MINFRAC_2 0, 1
/*
* Internals
*/
#define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
#define __FP_CLZ_2(R, xh, xl) \
do { \
if (xh) \
__FP_CLZ(R,xl); \
else \
{ \
__FP_CLZ(R,xl); \
R += _FP_W_TYPE_SIZE; \
} \
} while(0)
#if 0
#ifndef __FP_FRAC_ADDI_2
#define __FP_FRAC_ADDI_2(xh, xl, i) \
(xh += ((xl += i) < i))
#endif
#ifndef __FP_FRAC_ADD_2
#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
(rh = xh + yh + ((rl = xl + yl) < xl))
#endif
#ifndef __FP_FRAC_SUB_2
#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
(rh = xh - yh - ((rl = xl - yl) > xl))
#endif
#else
#undef __FP_FRAC_ADDI_2
#define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
#undef __FP_FRAC_ADD_2
#define __FP_FRAC_ADD_2 add_ssaaaa
#undef __FP_FRAC_SUB_2
#define __FP_FRAC_SUB_2 sub_ddmmss
#endif
/*
* Unpack the raw bits of a native fp value. Do not classify or
* normalize the data.
*/
#define _FP_UNPACK_RAW_2(fs, X, val) \
do { \
union _FP_UNION_##fs _flo; _flo.flt = (val); \
\
X##_f0 = _flo.bits.frac0; \
X##_f1 = _flo.bits.frac1; \
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_2(fs, val, X) \
do { \
union _FP_UNION_##fs _flo; \
\
_flo.bits.frac0 = X##_f0; \
_flo.bits.frac1 = X##_f1; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} while (0)
/*
* Multiplication algorithms:
*/
/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
#define _FP_MUL_MEAT_2_wide(fs, R, X, Y, doit) \
do { \
_FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
\
doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
\
__FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
0, _b_f1, _b_f0, 0, \
_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
__FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
0, _c_f1, _c_f0, 0, \
_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
\
/* 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_4(_z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs); \
R##_f0 = _FP_FRAC_WORD_4(_z,0); \
R##_f1 = _FP_FRAC_WORD_4(_z,1); \
} while (0)
/* This next macro appears to be totally broken. Fortunately nowhere
* seems to use it :-> The problem is that we define _z[4] but
* then use it in _FP_FRAC_SRS_4, which will attempt to access
* _z_f[n] which will cause an error. The fix probably involves
* declaring it with _FP_FRAC_DECL_4, see previous macro. -- PMM 02/1998
*/
#define _FP_MUL_MEAT_2_gmp(fs, R, X, Y) \
do { \
_FP_W_TYPE _x[2], _y[2], _z[4]; \
_x[0] = X##_f0; _x[1] = X##_f1; \
_y[0] = Y##_f0; _y[1] = Y##_f1; \
\
mpn_mul_n(_z, _x, _y, 2); \
\
/* 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_4(_z, _FP_WFRACBITS##_fs-1, 2*_FP_WFRACBITS_##fs); \
R##_f0 = _z[0]; \
R##_f1 = _z[1]; \
} while (0)
/*
* Division algorithms:
* This seems to be giving me difficulties -- PMM
* Look, NetBSD seems to be able to comment algorithms. Can't you?
* I've thrown printks at the problem.
* This now appears to work, but I still don't really know why.
* Also, I don't think the result is properly normalised...
*/
#define _FP_DIV_MEAT_2_udiv_64(fs, R, X, Y) \
do { \
extern void _fp_udivmodti4(_FP_W_TYPE q[2], _FP_W_TYPE r[2], \
_FP_W_TYPE n1, _FP_W_TYPE n0, \
_FP_W_TYPE d1, _FP_W_TYPE d0); \
_FP_W_TYPE _n_f3, _n_f2, _n_f1, _n_f0, _r_f1, _r_f0; \
_FP_W_TYPE _q_f1, _q_f0, _m_f1, _m_f0; \
_FP_W_TYPE _rmem[2], _qmem[2]; \
/* I think this check is to ensure that the result is normalised. \
* Assuming X,Y normalised (ie in [1.0,2.0)) X/Y will be in \
* [0.5,2.0). Furthermore, it will be less than 1.0 iff X < Y. \
* In this case we tweak things. (this is based on comments in \
* the NetBSD FPU emulation code. ) \
* We know X,Y are normalised because we ensure this as part of \
* the unpacking process. -- PMM \
*/ \
if (_FP_FRAC_GT_2(X, Y)) \
{ \
/* R##_e++; */ \
_n_f3 = X##_f1 >> 1; \
_n_f2 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
_n_f1 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
_n_f0 = 0; \
} \
else \
{ \
R##_e--; \
_n_f3 = X##_f1; \
_n_f2 = X##_f0; \
_n_f1 = _n_f0 = 0; \
} \
\
/* Normalize, i.e. make the most significant bit of the \
denominator set. CHANGED: - 1 to nothing -- PMM */ \
_FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs /* -1 */); \
\
/* Do the 256/128 bit division given the 128-bit _fp_udivmodtf4 \
primitive snagged from libgcc2.c. */ \
\
_fp_udivmodti4(_qmem, _rmem, _n_f3, _n_f2, 0, Y##_f1); \
_q_f1 = _qmem[0]; \
umul_ppmm(_m_f1, _m_f0, _q_f1, Y##_f0); \
_r_f1 = _rmem[0]; \
_r_f0 = _n_f1; \
if (_FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f1--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f1--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
} \
} \
_FP_FRAC_SUB_2(_r, _r, _m); \
\
_fp_udivmodti4(_qmem, _rmem, _r_f1, _r_f0, 0, Y##_f1); \
_q_f0 = _qmem[0]; \
umul_ppmm(_m_f1, _m_f0, _q_f0, Y##_f0); \
_r_f1 = _rmem[0]; \
_r_f0 = _n_f0; \
if (_FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f0--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f0--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
} \
} \
_FP_FRAC_SUB_2(_r, _r, _m); \
\
R##_f1 = _q_f1; \
R##_f0 = _q_f0 | ((_r_f1 | _r_f0) != 0); \
/* adjust so answer is normalized again. I'm not sure what the \
* final sz param should be. In practice it's never used since \
* N is 1 which is always going to be < _FP_W_TYPE_SIZE... \
*/ \
/* _FP_FRAC_SRS_2(R,1,_FP_WFRACBITS_##fs); */ \
} while (0)
#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
do { \
_FP_W_TYPE _x[4], _y[2], _z[4]; \
_y[0] = Y##_f0; _y[1] = Y##_f1; \
_x[0] = _x[3] = 0; \
if (_FP_FRAC_GT_2(X, Y)) \
{ \
R##_e++; \
_x[1] = (X##_f0 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE) | \
X##_f1 >> (_FP_W_TYPE_SIZE - \
(_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE))); \
_x[2] = X##_f1 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE); \
} \
else \
{ \
_x[1] = (X##_f0 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE) | \
X##_f1 >> (_FP_W_TYPE_SIZE - \
(_FP_WFRACBITS - _FP_W_TYPE_SIZE))); \
_x[2] = X##_f1 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE); \
} \
\
(void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
R##_f1 = _z[1]; \
R##_f0 = _z[0] | ((_x[0] | _x[1]) != 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_2(R, S, T, X, q) \
do { \
while (q) \
{ \
T##_f1 = S##_f1 + q; \
if (T##_f1 <= X##_f1) \
{ \
S##_f1 = T##_f1 + q; \
X##_f1 -= T##_f1; \
R##_f1 += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
while (q) \
{ \
T##_f0 = S##_f0 + q; \
T##_f1 = S##_f1; \
if (T##_f1 < X##_f1 || \
(T##_f1 == X##_f1 && T##_f0 < X##_f0)) \
{ \
S##_f0 = T##_f0 + q; \
if (((_FP_WS_TYPE)T##_f0) < 0 && \
((_FP_WS_TYPE)S##_f0) >= 0) \
S##_f1++; \
_FP_FRAC_SUB_2(X, X, T); \
R##_f0 += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
} while (0)
/*
* Assembly/disassembly for converting to/from integral types.
* No shifting or overflow handled here.
*/
#define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
do { \
if (rsize <= _FP_W_TYPE_SIZE) \
r = X##_f0; \
else \
{ \
r = X##_f1; \
r <<= _FP_W_TYPE_SIZE; \
r += X##_f0; \
} \
} while (0)
#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
do { \
X##_f0 = r; \
X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
} while (0)
/*
* Convert FP values between word sizes
*/
#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \
do { \
_FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
_FP_WFRACBITS_##sfs); \
D##_f = S##_f0; \
} while (0)
#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \
do { \
D##_f0 = S##_f; \
D##_f1 = 0; \
_FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
} while (0)
|
