| blob | b9b06b4c6ea16f144cd7fa0b814770f3b272e085 |
1 /*
2 * Basic two-word fraction declaration and manipulation.
3 */
5 #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1
6 #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
7 #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
8 #define _FP_FRAC_HIGH_2(X) (X##_f1)
9 #define _FP_FRAC_LOW_2(X) (X##_f0)
10 #define _FP_FRAC_WORD_2(X,w) (X##_f##w)
12 #define _FP_FRAC_SLL_2(X,N) \
13 do { \
14 if ((N) < _FP_W_TYPE_SIZE) \
15 { \
16 if (__builtin_constant_p(N) && (N) == 1) \
17 { \
18 X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \
19 X##_f0 += X##_f0; \
20 } \
21 else \
22 { \
23 X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
24 X##_f0 <<= (N); \
25 } \
26 } \
27 else \
28 { \
29 X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
30 X##_f0 = 0; \
31 } \
32 } while (0)
34 #define _FP_FRAC_SRL_2(X,N) \
35 do { \
36 if ((N) < _FP_W_TYPE_SIZE) \
37 { \
38 X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
39 X##_f1 >>= (N); \
40 } \
41 else \
42 { \
43 X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
44 X##_f1 = 0; \
45 } \
46 } while (0)
48 /* Right shift with sticky-lsb. */
49 #define _FP_FRAC_SRS_2(X,N,sz) \
50 do { \
51 if ((N) < _FP_W_TYPE_SIZE) \
52 { \
53 X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \
54 (__builtin_constant_p(N) && (N) == 1 \
55 ? X##_f0 & 1 \
56 : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
57 X##_f1 >>= (N); \
58 } \
59 else \
60 { \
61 X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \
62 (((X##_f1 << (sz - (N))) | X##_f0) != 0)); \
63 X##_f1 = 0; \
64 } \
65 } while (0)
67 #define _FP_FRAC_ADDI_2(X,I) \
68 __FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
70 #define _FP_FRAC_ADD_2(R,X,Y) \
71 __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
73 #define _FP_FRAC_SUB_2(R,X,Y) \
74 __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
76 #define _FP_FRAC_CLZ_2(R,X) \
77 do { \
78 if (X##_f1) \
79 __FP_CLZ(R,X##_f1); \
80 else \
81 { \
82 __FP_CLZ(R,X##_f0); \
83 R += _FP_W_TYPE_SIZE; \
84 } \
85 } while(0)
87 /* Predicates */
88 #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
89 #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
90 #define _FP_FRAC_OVERP_2(fs,X) (X##_f1 & _FP_OVERFLOW_##fs)
91 #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
92 #define _FP_FRAC_GT_2(X, Y) \
93 ((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
94 #define _FP_FRAC_GE_2(X, Y) \
95 ((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
97 #define _FP_ZEROFRAC_2 0, 0
98 #define _FP_MINFRAC_2 0, 1
100 /*
101 * Internals
102 */
104 #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
106 #define __FP_CLZ_2(R, xh, xl) \
107 do { \
108 if (xh) \
109 __FP_CLZ(R,xl); \
110 else \
111 { \
112 __FP_CLZ(R,xl); \
113 R += _FP_W_TYPE_SIZE; \
114 } \
115 } while(0)
117 #if 0
119 #ifndef __FP_FRAC_ADDI_2
120 #define __FP_FRAC_ADDI_2(xh, xl, i) \
121 (xh += ((xl += i) < i))
122 #endif
123 #ifndef __FP_FRAC_ADD_2
124 #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
125 (rh = xh + yh + ((rl = xl + yl) < xl))
126 #endif
127 #ifndef __FP_FRAC_SUB_2
128 #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
129 (rh = xh - yh - ((rl = xl - yl) > xl))
130 #endif
132 #else
134 #undef __FP_FRAC_ADDI_2
135 #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
136 #undef __FP_FRAC_ADD_2
137 #define __FP_FRAC_ADD_2 add_ssaaaa
138 #undef __FP_FRAC_SUB_2
139 #define __FP_FRAC_SUB_2 sub_ddmmss
141 #endif
143 /*
144 * Unpack the raw bits of a native fp value. Do not classify or
145 * normalize the data.
146 */
148 #define _FP_UNPACK_RAW_2(fs, X, val) \
149 do { \
150 union _FP_UNION_##fs _flo; _flo.flt = (val); \
151 \
152 X##_f0 = _flo.bits.frac0; \
153 X##_f1 = _flo.bits.frac1; \
154 X##_e = _flo.bits.exp; \
155 X##_s = _flo.bits.sign; \
156 } while (0)
159 /*
160 * Repack the raw bits of a native fp value.
161 */
163 #define _FP_PACK_RAW_2(fs, val, X) \
164 do { \
165 union _FP_UNION_##fs _flo; \
166 \
167 _flo.bits.frac0 = X##_f0; \
168 _flo.bits.frac1 = X##_f1; \
169 _flo.bits.exp = X##_e; \
170 _flo.bits.sign = X##_s; \
171 \
172 (val) = _flo.flt; \
173 } while (0)
176 /*
177 * Multiplication algorithms:
178 */
180 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
182 #define _FP_MUL_MEAT_2_wide(fs, R, X, Y, doit) \
183 do { \
184 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
185 \
186 doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
187 doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
188 doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
189 doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
190 \
191 __FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
192 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
193 0, _b_f1, _b_f0, 0, \
194 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
195 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
196 __FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
197 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
198 0, _c_f1, _c_f0, 0, \
199 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
200 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
201 \
202 /* Normalize since we know where the msb of the multiplicands \
203 were (bit B), we know that the msb of the of the product is \
205 _FP_FRAC_SRS_4(_z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs); \
206 R##_f0 = _FP_FRAC_WORD_4(_z,0); \
207 R##_f1 = _FP_FRAC_WORD_4(_z,1); \
208 } while (0)
210 /* This next macro appears to be totally broken. Fortunately nowhere
211 * seems to use it :-> The problem is that we define _z[4] but
212 * then use it in _FP_FRAC_SRS_4, which will attempt to access
213 * _z_f[n] which will cause an error. The fix probably involves
214 * declaring it with _FP_FRAC_DECL_4, see previous macro. -- PMM 02/1998
215 */
216 #define _FP_MUL_MEAT_2_gmp(fs, R, X, Y) \
217 do { \
218 _FP_W_TYPE _x[2], _y[2], _z[4]; \
219 _x[0] = X##_f0; _x[1] = X##_f1; \
220 _y[0] = Y##_f0; _y[1] = Y##_f1; \
221 \
222 mpn_mul_n(_z, _x, _y, 2); \
223 \
224 /* Normalize since we know where the msb of the multiplicands \
225 were (bit B), we know that the msb of the of the product is \
227 _FP_FRAC_SRS_4(_z, _FP_WFRACBITS##_fs-1, 2*_FP_WFRACBITS_##fs); \
228 R##_f0 = _z[0]; \
229 R##_f1 = _z[1]; \
230 } while (0)
233 /*
234 * Division algorithms:
235 * This seems to be giving me difficulties -- PMM
236 * Look, NetBSD seems to be able to comment algorithms. Can't you?
237 * I've thrown printks at the problem.
238 * This now appears to work, but I still don't really know why.
239 * Also, I don't think the result is properly normalised...
240 */
242 #define _FP_DIV_MEAT_2_udiv_64(fs, R, X, Y) \
243 do { \
244 extern void _fp_udivmodti4(_FP_W_TYPE q[2], _FP_W_TYPE r[2], \
245 _FP_W_TYPE n1, _FP_W_TYPE n0, \
246 _FP_W_TYPE d1, _FP_W_TYPE d0); \
247 _FP_W_TYPE _n_f3, _n_f2, _n_f1, _n_f0, _r_f1, _r_f0; \
248 _FP_W_TYPE _q_f1, _q_f0, _m_f1, _m_f0; \
249 _FP_W_TYPE _rmem[2], _qmem[2]; \
250 /* I think this check is to ensure that the result is normalised. \
251 * Assuming X,Y normalised (ie in [1.0,2.0)) X/Y will be in \
252 * [0.5,2.0). Furthermore, it will be less than 1.0 iff X < Y. \
253 * In this case we tweak things. (this is based on comments in \
254 * the NetBSD FPU emulation code. ) \
255 * We know X,Y are normalised because we ensure this as part of \
256 * the unpacking process. -- PMM \
258 if (_FP_FRAC_GT_2(X, Y)) \
259 { \
261 _n_f3 = X##_f1 >> 1; \
262 _n_f2 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
263 _n_f1 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
264 _n_f0 = 0; \
265 } \
266 else \
267 { \
268 R##_e--; \
269 _n_f3 = X##_f1; \
270 _n_f2 = X##_f0; \
271 _n_f1 = _n_f0 = 0; \
272 } \
273 \
274 /* Normalize, i.e. make the most significant bit of the \
277 \
278 /* Do the 256/128 bit division given the 128-bit _fp_udivmodtf4 \
280 \
281 _fp_udivmodti4(_qmem, _rmem, _n_f3, _n_f2, 0, Y##_f1); \
282 _q_f1 = _qmem[0]; \
283 umul_ppmm(_m_f1, _m_f0, _q_f1, Y##_f0); \
284 _r_f1 = _rmem[0]; \
285 _r_f0 = _n_f1; \
286 if (_FP_FRAC_GT_2(_m, _r)) \
287 { \
288 _q_f1--; \
289 _FP_FRAC_ADD_2(_r, _r, Y); \
290 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
291 { \
292 _q_f1--; \
293 _FP_FRAC_ADD_2(_r, _r, Y); \
294 } \
295 } \
296 _FP_FRAC_SUB_2(_r, _r, _m); \
297 \
298 _fp_udivmodti4(_qmem, _rmem, _r_f1, _r_f0, 0, Y##_f1); \
299 _q_f0 = _qmem[0]; \
300 umul_ppmm(_m_f1, _m_f0, _q_f0, Y##_f0); \
301 _r_f1 = _rmem[0]; \
302 _r_f0 = _n_f0; \
303 if (_FP_FRAC_GT_2(_m, _r)) \
304 { \
305 _q_f0--; \
306 _FP_FRAC_ADD_2(_r, _r, Y); \
307 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
308 { \
309 _q_f0--; \
310 _FP_FRAC_ADD_2(_r, _r, Y); \
311 } \
312 } \
313 _FP_FRAC_SUB_2(_r, _r, _m); \
314 \
315 R##_f1 = _q_f1; \
316 R##_f0 = _q_f0 | ((_r_f1 | _r_f0) != 0); \
317 /* adjust so answer is normalized again. I'm not sure what the \
318 * final sz param should be. In practice it's never used since \
319 * N is 1 which is always going to be < _FP_W_TYPE_SIZE... \
322 } while (0)
325 #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
326 do { \
327 _FP_W_TYPE _x[4], _y[2], _z[4]; \
328 _y[0] = Y##_f0; _y[1] = Y##_f1; \
329 _x[0] = _x[3] = 0; \
330 if (_FP_FRAC_GT_2(X, Y)) \
331 { \
332 R##_e++; \
333 _x[1] = (X##_f0 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE) | \
334 X##_f1 >> (_FP_W_TYPE_SIZE - \
335 (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE))); \
336 _x[2] = X##_f1 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE); \
337 } \
338 else \
339 { \
340 _x[1] = (X##_f0 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE) | \
341 X##_f1 >> (_FP_W_TYPE_SIZE - \
342 (_FP_WFRACBITS - _FP_W_TYPE_SIZE))); \
343 _x[2] = X##_f1 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE); \
344 } \
345 \
346 (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
347 R##_f1 = _z[1]; \
348 R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \
349 } while (0)
352 /*
353 * Square root algorithms:
354 * We have just one right now, maybe Newton approximation
355 * should be added for those machines where division is fast.
356 */
358 #define _FP_SQRT_MEAT_2(R, S, T, X, q) \
359 do { \
360 while (q) \
361 { \
362 T##_f1 = S##_f1 + q; \
363 if (T##_f1 <= X##_f1) \
364 { \
365 S##_f1 = T##_f1 + q; \
366 X##_f1 -= T##_f1; \
367 R##_f1 += q; \
368 } \
369 _FP_FRAC_SLL_2(X, 1); \
370 q >>= 1; \
371 } \
372 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
373 while (q) \
374 { \
375 T##_f0 = S##_f0 + q; \
376 T##_f1 = S##_f1; \
377 if (T##_f1 < X##_f1 || \
378 (T##_f1 == X##_f1 && T##_f0 < X##_f0)) \
379 { \
380 S##_f0 = T##_f0 + q; \
381 if (((_FP_WS_TYPE)T##_f0) < 0 && \
382 ((_FP_WS_TYPE)S##_f0) >= 0) \
383 S##_f1++; \
384 _FP_FRAC_SUB_2(X, X, T); \
385 R##_f0 += q; \
386 } \
387 _FP_FRAC_SLL_2(X, 1); \
388 q >>= 1; \
389 } \
390 } while (0)
393 /*
394 * Assembly/disassembly for converting to/from integral types.
395 * No shifting or overflow handled here.
396 */
398 #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
399 do { \
400 if (rsize <= _FP_W_TYPE_SIZE) \
401 r = X##_f0; \
402 else \
403 { \
404 r = X##_f1; \
405 r <<= _FP_W_TYPE_SIZE; \
406 r += X##_f0; \
407 } \
408 } while (0)
410 #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
411 do { \
412 X##_f0 = r; \
413 X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
414 } while (0)
416 /*
417 * Convert FP values between word sizes
418 */
420 #define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \
421 do { \
422 _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
423 _FP_WFRACBITS_##sfs); \
424 D##_f = S##_f0; \
425 } while (0)
427 #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \
428 do { \
429 D##_f0 = S##_f; \
430 D##_f1 = 0; \
431 _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
432 } while (0)