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f1717362 | 1 | /* Copyright (C) 2007-2016 Free Software Foundation, Inc. |
84d1fc49 | 2 | |
3 | This file is part of GCC. | |
4 | ||
5 | GCC is free software; you can redistribute it and/or modify it under | |
6 | the terms of the GNU General Public License as published by the Free | |
6bc9506f | 7 | Software Foundation; either version 3, or (at your option) any later |
84d1fc49 | 8 | version. |
9 | ||
84d1fc49 | 10 | GCC is distributed in the hope that it will be useful, but WITHOUT ANY |
11 | WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
12 | FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
13 | for more details. | |
14 | ||
6bc9506f | 15 | Under Section 7 of GPL version 3, you are granted additional |
16 | permissions described in the GCC Runtime Library Exception, version | |
17 | 3.1, as published by the Free Software Foundation. | |
18 | ||
19 | You should have received a copy of the GNU General Public License and | |
20 | a copy of the GCC Runtime Library Exception along with this program; | |
21 | see the files COPYING3 and COPYING.RUNTIME respectively. If not, see | |
22 | <http://www.gnu.org/licenses/>. */ | |
84d1fc49 | 23 | |
24 | #define DECNUMDIGITS 34 // work with up to 34 digits | |
25 | ||
26 | #include "bid_internal.h" | |
27 | #include "bid_b2d.h" | |
28 | ||
29 | UINT32 | |
30 | bid_to_bid32 (UINT32 ba) { | |
31 | UINT32 res; | |
32 | UINT32 sign, comb, exp; | |
33 | UINT32 trailing; | |
34 | UINT32 bcoeff; | |
35 | ||
36 | sign = (ba & 0x80000000ul); | |
37 | comb = (ba & 0x7ff00000ul) >> 20; | |
38 | trailing = (ba & 0x000ffffful); | |
39 | ||
40 | if ((comb & 0x780) == 0x780) { | |
41 | ba &= 0xfff0000ul; | |
42 | return ba; | |
43 | } else { | |
44 | if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11 | |
45 | exp = (comb >> 1) & 0xff; | |
46 | bcoeff = ((8 + (comb & 1)) << 20) | trailing; | |
47 | } else { | |
48 | exp = (comb >> 3) & 0xff; | |
49 | bcoeff = ((comb & 7) << 20) | trailing; | |
50 | } | |
51 | if (bcoeff >= 10000000) | |
52 | bcoeff = 0; | |
53 | res = very_fast_get_BID32 (sign, exp, bcoeff); | |
54 | } | |
55 | return res; | |
56 | } | |
57 | ||
58 | UINT64 | |
59 | bid_to_bid64 (UINT64 ba) { | |
60 | UINT64 res; | |
61 | UINT64 sign, comb, exp; | |
62 | UINT64 trailing; | |
63 | UINT64 bcoeff; | |
64 | ||
65 | sign = (ba & 0x8000000000000000ull); | |
66 | comb = (ba & 0x7ffc000000000000ull) >> 50; | |
67 | trailing = (ba & 0x0003ffffffffffffull); | |
68 | ||
69 | if ((comb & 0x1e00) == 0x1e00) { | |
70 | ba &= 0xfff000000000000ULL; | |
71 | return ba; | |
72 | } else { | |
73 | if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11 | |
74 | exp = (comb >> 1) & 0x3ff; | |
75 | bcoeff = ((8 + (comb & 1)) << 50) | trailing; | |
76 | } else { | |
77 | exp = (comb >> 3) & 0x3ff; | |
78 | bcoeff = ((comb & 7) << 50) | trailing; | |
79 | } | |
80 | if (bcoeff >= 10000000000000000ull) | |
81 | bcoeff = 0ull; | |
82 | res = very_fast_get_BID64 (sign, exp, bcoeff); | |
83 | } | |
84 | return res; | |
85 | } | |
86 | ||
87 | #if DECIMAL_CALL_BY_REFERENCE | |
88 | void | |
89 | bid_to_dpd32 (UINT32 * pres, UINT32 * pba) { | |
90 | UINT32 ba = *pba; | |
91 | #else | |
92 | UINT32 | |
93 | bid_to_dpd32 (UINT32 ba) { | |
94 | #endif | |
95 | UINT32 res; | |
96 | ||
97 | UINT32 sign, comb, exp, trailing; | |
98 | UINT32 b0, b1, b2; | |
99 | UINT32 bcoeff, dcoeff; | |
100 | UINT32 nanb = 0; | |
101 | ||
102 | sign = (ba & 0x80000000); | |
103 | comb = (ba & 0x7ff00000) >> 20; | |
104 | trailing = (ba & 0xfffff); | |
105 | ||
106 | // Detect infinity, and return canonical infinity | |
107 | if ((comb & 0x7c0) == 0x780) { | |
108 | res = sign | 0x78000000; | |
109 | BID_RETURN (res); | |
110 | // Detect NaN, and canonicalize trailing | |
111 | } else if ((comb & 0x7c0) == 0x7c0) { | |
112 | if (trailing > 999999) | |
113 | trailing = 0; | |
114 | nanb = ba & 0xfe000000; | |
115 | exp = 0; | |
116 | bcoeff = trailing; | |
117 | } else { // Normal number | |
118 | if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11 | |
119 | exp = (comb >> 1) & 0xff; | |
120 | bcoeff = ((8 + (comb & 1)) << 20) | trailing; | |
121 | } else { | |
122 | exp = (comb >> 3) & 0xff; | |
123 | bcoeff = ((comb & 7) << 20) | trailing; | |
124 | } | |
125 | // Zero the coefficient if non-canonical (>= 10^7) | |
126 | if (bcoeff >= 10000000) | |
127 | bcoeff = 0; | |
128 | } | |
129 | ||
130 | b0 = bcoeff / 1000000; | |
131 | b1 = (bcoeff / 1000) % 1000; | |
132 | b2 = bcoeff % 1000; | |
133 | dcoeff = (b2d[b1] << 10) | b2d[b2]; | |
134 | ||
135 | if (b0 >= 8) // is b0 8 or 9? | |
136 | res = | |
137 | sign | | |
138 | ((0x600 | ((exp >> 6) << 7) | ((b0 & 1) << 6) | (exp & 0x3f)) << | |
139 | 20) | dcoeff; | |
140 | else // else b0 is 0..7 | |
141 | res = | |
142 | sign | ((((exp >> 6) << 9) | (b0 << 6) | (exp & 0x3f)) << 20) | | |
143 | dcoeff; | |
144 | ||
145 | res |= nanb; | |
146 | ||
147 | BID_RETURN (res); | |
148 | } | |
149 | ||
150 | #if DECIMAL_CALL_BY_REFERENCE | |
151 | void | |
152 | bid_to_dpd64 (UINT64 * pres, UINT64 * pba) { | |
153 | UINT64 ba = *pba; | |
154 | #else | |
155 | UINT64 | |
156 | bid_to_dpd64 (UINT64 ba) { | |
157 | #endif | |
158 | UINT64 res; | |
159 | ||
160 | UINT64 sign, comb, exp; | |
161 | UINT64 trailing; | |
162 | UINT32 b0, b1, b2, b3, b4, b5; | |
163 | UINT64 bcoeff; | |
164 | UINT64 dcoeff; | |
165 | UINT32 yhi, ylo; | |
166 | UINT64 nanb = 0; | |
167 | ||
168 | //printf("arg bid "FMT_LLX16" \n", ba); | |
169 | sign = (ba & 0x8000000000000000ull); | |
170 | comb = (ba & 0x7ffc000000000000ull) >> 50; | |
171 | trailing = (ba & 0x0003ffffffffffffull); | |
172 | ||
173 | // Detect infinity, and return canonical infinity | |
174 | if ((comb & 0x1f00) == 0x1e00) { | |
175 | res = sign | 0x7800000000000000ull; | |
176 | BID_RETURN (res); | |
177 | // Detect NaN, and canonicalize trailing | |
178 | } else if ((comb & 0x1e00) == 0x1e00) { | |
179 | if (trailing > 999999999999999ull) | |
180 | trailing = 0; | |
181 | nanb = ba & 0xfe00000000000000ull; | |
182 | exp = 0; | |
183 | bcoeff = trailing; | |
184 | } else { // Normal number | |
185 | if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11 | |
186 | exp = (comb >> 1) & 0x3ff; | |
187 | bcoeff = ((8 + (comb & 1)) << 50) | trailing; | |
188 | } else { | |
189 | exp = (comb >> 3) & 0x3ff; | |
190 | bcoeff = ((comb & 7) << 50) | trailing; | |
191 | } | |
192 | ||
193 | // Zero the coefficient if it is non-canonical (>= 10^16) | |
194 | if (bcoeff >= 10000000000000000ull) | |
195 | bcoeff = 0; | |
196 | } | |
197 | ||
198 | // Floor(2^61 / 10^9) | |
199 | #define D61 (2305843009ull) | |
200 | ||
201 | // Multipy the binary coefficient by ceil(2^64 / 1000), and take the upper | |
202 | // 64-bits in order to compute a division by 1000. | |
203 | ||
204 | #if 1 | |
205 | yhi = | |
206 | ((UINT64) D61 * | |
207 | (UINT64) (UINT32) (bcoeff >> (UINT64) 27)) >> (UINT64) 34; | |
208 | ylo = bcoeff - 1000000000ull * yhi; | |
209 | if (ylo >= 1000000000) { | |
210 | ylo = ylo - 1000000000; | |
211 | yhi = yhi + 1; | |
212 | } | |
213 | #else | |
214 | yhi = bcoeff / 1000000000ull; | |
215 | ylo = bcoeff % 1000000000ull; | |
216 | #endif | |
217 | ||
218 | // yhi = ABBBCCC ylo = DDDEEEFFF | |
219 | b5 = ylo % 1000; // b5 = FFF | |
220 | b3 = ylo / 1000000; // b3 = DDD | |
221 | b4 = (ylo / 1000) - (1000 * b3); // b4 = EEE | |
222 | b2 = yhi % 1000; // b2 = CCC | |
223 | b0 = yhi / 1000000; // b0 = A | |
224 | b1 = (yhi / 1000) - (1000 * b0); // b1 = BBB | |
225 | ||
226 | dcoeff = b2d[b5] | b2d2[b4] | b2d3[b3] | b2d4[b2] | b2d5[b1]; | |
227 | ||
228 | if (b0 >= 8) // is b0 8 or 9? | |
229 | res = | |
230 | sign | | |
231 | ((0x1800 | ((exp >> 8) << 9) | ((b0 & 1) << 8) | (exp & 0xff)) << | |
232 | 50) | dcoeff; | |
233 | else // else b0 is 0..7 | |
234 | res = | |
235 | sign | ((((exp >> 8) << 11) | (b0 << 8) | (exp & 0xff)) << 50) | | |
236 | dcoeff; | |
237 | ||
238 | res |= nanb; | |
239 | ||
240 | BID_RETURN (res); | |
241 | } | |
242 | ||
243 | #if DECIMAL_CALL_BY_REFERENCE | |
244 | void | |
245 | dpd_to_bid32 (UINT32 * pres, UINT32 * pda) { | |
246 | UINT32 da = *pda; | |
247 | #else | |
248 | UINT32 | |
249 | dpd_to_bid32 (UINT32 da) { | |
250 | #endif | |
251 | UINT32 in = *(UINT32 *) & da; | |
252 | UINT32 res; | |
253 | ||
254 | UINT32 sign, comb, exp; | |
255 | UINT32 trailing; | |
256 | UINT32 d0 = 0, d1, d2; | |
257 | UINT64 bcoeff; | |
258 | UINT32 nanb = 0; | |
259 | ||
260 | sign = (in & 0x80000000); | |
261 | comb = (in & 0x7ff00000) >> 20; | |
262 | trailing = (in & 0x000fffff); | |
263 | ||
264 | if ((comb & 0x7e0) == 0x780) { // G0..G4 = 1111 -> Inf | |
265 | res = in & 0xf8000000; | |
266 | BID_RETURN (res); | |
267 | } else if ((comb & 0x7c0) == 0x7c0) { // G0..G5 = 11111 -> NaN | |
268 | nanb = in & 0xfe000000; | |
269 | exp = 0; | |
270 | } else { // Normal number | |
271 | if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> d0 = 8 + G4 | |
272 | d0 = ((comb >> 6) & 1) | 8; | |
273 | exp = ((comb & 0x180) >> 1) | (comb & 0x3f); | |
274 | } else { | |
275 | d0 = (comb >> 6) & 0x7; | |
276 | exp = ((comb & 0x600) >> 3) | (comb & 0x3f); | |
277 | } | |
278 | } | |
279 | d1 = d2b2[(trailing >> 10) & 0x3ff]; | |
280 | d2 = d2b[(trailing) & 0x3ff]; | |
281 | ||
282 | bcoeff = d2 + d1 + (1000000 * d0); | |
283 | if (bcoeff < 0x800000) { | |
284 | res = (exp << 23) | bcoeff | sign; | |
285 | } else { | |
286 | res = (exp << 21) | sign | 0x60000000 | (bcoeff & 0x1fffff); | |
287 | } | |
288 | ||
289 | res |= nanb; | |
290 | ||
291 | BID_RETURN (res); | |
292 | } | |
293 | ||
294 | #if DECIMAL_CALL_BY_REFERENCE | |
295 | void | |
296 | dpd_to_bid64 (UINT64 * pres, UINT64 * pda) { | |
297 | UINT64 da = *pda; | |
298 | #else | |
299 | UINT64 | |
300 | dpd_to_bid64 (UINT64 da) { | |
301 | #endif | |
302 | UINT64 in = *(UINT64 *) & da; | |
303 | UINT64 res; | |
304 | ||
305 | UINT64 sign, comb, exp; | |
306 | UINT64 trailing; | |
307 | // UINT64 d0, d1, d2, d3, d4, d5; | |
308 | ||
309 | UINT64 d1, d2; | |
310 | UINT32 d0, d3, d4, d5; | |
311 | UINT64 bcoeff; | |
312 | UINT64 nanb = 0; | |
313 | ||
314 | //printf("arg dpd "FMT_LLX16" \n", in); | |
315 | sign = (in & 0x8000000000000000ull); | |
316 | comb = (in & 0x7ffc000000000000ull) >> 50; | |
317 | trailing = (in & 0x0003ffffffffffffull); | |
318 | ||
319 | if ((comb & 0x1f00) == 0x1e00) { // G0..G4 = 1111 -> Inf | |
320 | res = in & 0xf800000000000000ull; | |
321 | BID_RETURN (res); | |
322 | } else if ((comb & 0x1f00) == 0x1f00) { // G0..G5 = 11111 -> NaN | |
323 | nanb = in & 0xfe00000000000000ull; | |
324 | exp = 0; | |
325 | d0 = 0; | |
326 | } else { // Normal number | |
327 | if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> d0 = 8 + G4 | |
328 | d0 = ((comb >> 8) & 1) | 8; | |
329 | // d0 = (comb & 0x0100 ? 9 : 8); | |
330 | exp = (comb & 0x600) >> 1; | |
331 | // exp = (comb & 0x0400 ? 1 : 0) * 0x200 + (comb & 0x0200 ? 1 : 0) * 0x100; // exp leading bits are G2..G3 | |
332 | } else { | |
333 | d0 = (comb >> 8) & 0x7; | |
334 | exp = (comb & 0x1800) >> 3; | |
335 | // exp = (comb & 0x1000 ? 1 : 0) * 0x200 + (comb & 0x0800 ? 1 : 0) * 0x100; // exp loading bits are G0..G1 | |
336 | } | |
337 | } | |
338 | d1 = d2b5[(trailing >> 40) & 0x3ff]; | |
339 | d2 = d2b4[(trailing >> 30) & 0x3ff]; | |
340 | d3 = d2b3[(trailing >> 20) & 0x3ff]; | |
341 | d4 = d2b2[(trailing >> 10) & 0x3ff]; | |
342 | d5 = d2b[(trailing) & 0x3ff]; | |
343 | ||
344 | bcoeff = (d5 + d4 + d3) + d2 + d1 + (1000000000000000ull * d0); | |
345 | exp += (comb & 0xff); | |
346 | res = very_fast_get_BID64 (sign, exp, bcoeff); | |
347 | ||
348 | res |= nanb; | |
349 | ||
350 | BID_RETURN (res); | |
351 | } | |
352 | ||
353 | #if DECIMAL_CALL_BY_REFERENCE | |
354 | void | |
355 | bid_to_dpd128 (UINT128 * pres, UINT128 * pba) { | |
356 | UINT128 ba = *pba; | |
357 | #else | |
358 | UINT128 | |
359 | bid_to_dpd128 (UINT128 ba) { | |
360 | #endif | |
361 | UINT128 res; | |
362 | ||
363 | UINT128 sign; | |
364 | UINT32 comb, exp; | |
365 | UINT128 trailing; | |
366 | UINT128 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11; | |
367 | UINT128 bcoeff; | |
368 | UINT128 dcoeff; | |
369 | UINT64 nanb = 0; | |
370 | ||
371 | sign.w[1] = (ba.w[HIGH_128W] & 0x8000000000000000ull); | |
372 | sign.w[0] = 0; | |
373 | comb = (ba.w[HIGH_128W] & 0x7fffc00000000000ull) >> 46; | |
374 | trailing.w[1] = (ba.w[HIGH_128W] & 0x00003fffffffffffull); | |
375 | trailing.w[0] = ba.w[LOW_128W]; | |
376 | exp = 0; | |
377 | ||
378 | if ((comb & 0x1f000) == 0x1e000) { // G0..G4 = 1111 -> Inf | |
379 | res.w[HIGH_128W] = ba.w[HIGH_128W] & 0xf800000000000000ull; | |
380 | res.w[LOW_128W] = 0; | |
381 | BID_RETURN (res); | |
382 | // Detect NaN, and canonicalize trailing | |
383 | } else if ((comb & 0x1f000) == 0x1f000) { | |
384 | if ((trailing.w[1] > 0x0000314dc6448d93ULL) || // significand is non-canonical | |
385 | ((trailing.w[1] == 0x0000314dc6448d93ULL) | |
386 | && (trailing.w[0] >= 0x38c15b0a00000000ULL)) | |
387 | // significand is non-canonical | |
388 | ) { | |
389 | trailing.w[1] = trailing.w[0] = 0ull; | |
390 | } | |
391 | bcoeff.w[1] = trailing.w[1]; | |
392 | bcoeff.w[0] = trailing.w[0]; | |
393 | nanb = ba.w[HIGH_128W] & 0xfe00000000000000ull; | |
394 | exp = 0; | |
395 | } else { // Normal number | |
396 | if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11 | |
397 | exp = (comb >> 1) & 0x3fff; | |
398 | bcoeff.w[1] = | |
399 | ((UINT64) (8 + (comb & 1)) << (UINT64) 46) | trailing.w[1]; | |
400 | bcoeff.w[0] = trailing.w[0]; | |
401 | } else { | |
402 | exp = (comb >> 3) & 0x3fff; | |
403 | bcoeff.w[1] = | |
404 | ((UINT64) (comb & 7) << (UINT64) 46) | trailing.w[1]; | |
405 | bcoeff.w[0] = trailing.w[0]; | |
406 | } | |
407 | // Zero the coefficient if non-canonical (>= 10^34) | |
408 | if (bcoeff.w[1] > 0x1ed09bead87c0ull || | |
409 | (bcoeff.w[1] == 0x1ed09bead87c0ull | |
410 | && bcoeff.w[0] >= 0x378D8E6400000000ull)) { | |
411 | bcoeff.w[0] = bcoeff.w[1] = 0; | |
412 | } | |
413 | } | |
414 | // Constant 2^128 / 1000 + 1 | |
415 | { | |
416 | UINT128 t; | |
417 | UINT64 t2; | |
418 | UINT128 d1000; | |
419 | UINT128 b11, b10, b9, b8, b7, b6, b5, b4, b3, b2, b1; | |
420 | d1000.w[1] = 0x4189374BC6A7EFull; | |
421 | d1000.w[0] = 0x9DB22D0E56041894ull; | |
422 | __mul_128x128_high (b11, bcoeff, d1000); | |
423 | __mul_128x128_high (b10, b11, d1000); | |
424 | __mul_128x128_high (b9, b10, d1000); | |
425 | __mul_128x128_high (b8, b9, d1000); | |
426 | __mul_128x128_high (b7, b8, d1000); | |
427 | __mul_128x128_high (b6, b7, d1000); | |
428 | __mul_128x128_high (b5, b6, d1000); | |
429 | __mul_128x128_high (b4, b5, d1000); | |
430 | __mul_128x128_high (b3, b4, d1000); | |
431 | __mul_128x128_high (b2, b3, d1000); | |
432 | __mul_128x128_high (b1, b2, d1000); | |
433 | ||
434 | ||
435 | __mul_64x128_full (t2, t, 1000ull, b11); | |
436 | __sub_128_128 (d11, bcoeff, t); | |
437 | __mul_64x128_full (t2, t, 1000ull, b10); | |
438 | __sub_128_128 (d10, b11, t); | |
439 | __mul_64x128_full (t2, t, 1000ull, b9); | |
440 | __sub_128_128 (d9, b10, t); | |
441 | __mul_64x128_full (t2, t, 1000ull, b8); | |
442 | __sub_128_128 (d8, b9, t); | |
443 | __mul_64x128_full (t2, t, 1000ull, b7); | |
444 | __sub_128_128 (d7, b8, t); | |
445 | __mul_64x128_full (t2, t, 1000ull, b6); | |
446 | __sub_128_128 (d6, b7, t); | |
447 | __mul_64x128_full (t2, t, 1000ull, b5); | |
448 | __sub_128_128 (d5, b6, t); | |
449 | __mul_64x128_full (t2, t, 1000ull, b4); | |
450 | __sub_128_128 (d4, b5, t); | |
451 | __mul_64x128_full (t2, t, 1000ull, b3); | |
452 | __sub_128_128 (d3, b4, t); | |
453 | __mul_64x128_full (t2, t, 1000ull, b2); | |
454 | __sub_128_128 (d2, b3, t); | |
455 | __mul_64x128_full (t2, t, 1000ull, b1); | |
456 | __sub_128_128 (d1, b2, t); | |
457 | d0 = b1; | |
458 | ||
459 | } | |
460 | ||
461 | dcoeff.w[0] = b2d[d11.w[0]] | (b2d[d10.w[0]] << 10) | | |
462 | (b2d[d9.w[0]] << 20) | (b2d[d8.w[0]] << 30) | (b2d[d7.w[0]] << 40) | | |
463 | (b2d[d6.w[0]] << 50) | (b2d[d5.w[0]] << 60); | |
464 | dcoeff.w[1] = | |
465 | (b2d[d5.w[0]] >> 4) | (b2d[d4.w[0]] << 6) | (b2d[d3.w[0]] << 16) | | |
466 | (b2d[d2.w[0]] << 26) | (b2d[d1.w[0]] << 36); | |
467 | ||
468 | res.w[0] = dcoeff.w[0]; | |
469 | if (d0.w[0] >= 8) { | |
470 | res.w[1] = | |
471 | sign. | |
472 | w[1] | | |
473 | ((0x18000 | ((exp >> 12) << 13) | ((d0.w[0] & 1) << 12) | | |
474 | (exp & 0xfff)) << 46) | dcoeff.w[1]; | |
475 | } else { | |
476 | res.w[1] = | |
477 | sign. | |
478 | w[1] | ((((exp >> 12) << 15) | (d0.w[0] << 12) | (exp & 0xfff)) | |
479 | << 46) | dcoeff.w[1]; | |
480 | } | |
481 | ||
482 | res.w[1] |= nanb; | |
483 | ||
484 | BID_SWAP128 (res); | |
485 | BID_RETURN (res); | |
486 | } | |
487 | ||
488 | #if DECIMAL_CALL_BY_REFERENCE | |
489 | void | |
490 | dpd_to_bid128 (UINT128 * pres, UINT128 * pda) { | |
491 | UINT128 da = *pda; | |
492 | #else | |
493 | UINT128 | |
494 | dpd_to_bid128 (UINT128 da) { | |
495 | #endif | |
496 | UINT128 in = *(UINT128 *) & da; | |
497 | UINT128 res; | |
498 | ||
499 | UINT128 sign; | |
500 | UINT64 exp, comb; | |
501 | UINT128 trailing; | |
502 | UINT64 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11; | |
503 | UINT128 bcoeff; | |
504 | UINT64 tl, th; | |
505 | UINT64 nanb = 0; | |
506 | ||
507 | sign.w[1] = (in.w[HIGH_128W] & 0x8000000000000000ull); | |
508 | sign.w[0] = 0; | |
509 | comb = (in.w[HIGH_128W] & 0x7fffc00000000000ull) >> 46; | |
510 | trailing.w[1] = (in.w[HIGH_128W] & 0x00003fffffffffffull); | |
511 | trailing.w[0] = in.w[LOW_128W]; | |
512 | exp = 0; | |
513 | ||
514 | if ((comb & 0x1f000) == 0x1e000) { // G0..G4 = 1111 -> Inf | |
515 | res.w[HIGH_128W] = in.w[HIGH_128W] & 0xf800000000000000ull; | |
516 | res.w[LOW_128W] = 0ull; | |
517 | BID_RETURN (res); | |
518 | } else if ((comb & 0x1f000) == 0x1f000) { // G0..G4 = 11111 -> NaN | |
519 | nanb = in.w[HIGH_128W] & 0xfe00000000000000ull; | |
520 | exp = 0; | |
521 | d0 = 0; | |
522 | } else { // Normal number | |
523 | if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> d0 = 8 + G4 | |
524 | d0 = 8 + (comb & 0x01000 ? 1 : 0); | |
525 | exp = | |
526 | (comb & 0x04000 ? 1 : 0) * 0x2000 + | |
527 | (comb & 0x02000 ? 1 : 0) * 0x1000; | |
528 | // exp leading bits are G2..G3 | |
529 | } else { | |
530 | d0 = | |
531 | 4 * (comb & 0x04000 ? 1 : 0) + 2 * (comb & 0x2000 ? 1 : 0) + | |
532 | (comb & 0x1000 ? 1 : 0); | |
533 | exp = | |
534 | (comb & 0x10000 ? 1 : 0) * 0x2000 + | |
535 | (comb & 0x08000 ? 1 : 0) * 0x1000; | |
536 | // exp loading bits are G0..G1 | |
537 | } | |
538 | } | |
539 | ||
540 | d11 = d2b[(trailing.w[0]) & 0x3ff]; | |
541 | d10 = d2b[(trailing.w[0] >> 10) & 0x3ff]; | |
542 | d9 = d2b[(trailing.w[0] >> 20) & 0x3ff]; | |
543 | d8 = d2b[(trailing.w[0] >> 30) & 0x3ff]; | |
544 | d7 = d2b[(trailing.w[0] >> 40) & 0x3ff]; | |
545 | d6 = d2b[(trailing.w[0] >> 50) & 0x3ff]; | |
546 | d5 = d2b[(trailing.w[0] >> 60) | ((trailing.w[1] & 0x3f) << 4)]; | |
547 | d4 = d2b[(trailing.w[1] >> 6) & 0x3ff]; | |
548 | d3 = d2b[(trailing.w[1] >> 16) & 0x3ff]; | |
549 | d2 = d2b[(trailing.w[1] >> 26) & 0x3ff]; | |
550 | d1 = d2b[(trailing.w[1] >> 36) & 0x3ff]; | |
551 | ||
552 | tl = | |
553 | d11 + (d10 * 1000ull) + (d9 * 1000000ull) + (d8 * 1000000000ull) + | |
554 | (d7 * 1000000000000ull) + (d6 * 1000000000000000ull); | |
555 | th = | |
556 | d5 + (d4 * 1000ull) + (d3 * 1000000ull) + (d2 * 1000000000ull) + | |
557 | (d1 * 1000000000000ull) + (d0 * 1000000000000000ull); | |
558 | __mul_64x64_to_128 (bcoeff, th, 1000000000000000000ull); | |
559 | __add_128_64 (bcoeff, bcoeff, tl); | |
560 | ||
561 | if (!nanb) | |
562 | exp += (comb & 0xfff); | |
563 | ||
564 | res.w[0] = bcoeff.w[0]; | |
565 | res.w[1] = (exp << 49) | sign.w[1] | bcoeff.w[1]; | |
566 | ||
567 | res.w[1] |= nanb; | |
568 | ||
569 | BID_SWAP128 (res); | |
570 | BID_RETURN (res); | |
571 | } | |
572 | ||
573 | UINT128 | |
574 | bid_to_bid128 (UINT128 bq) { | |
575 | UINT128 res; | |
576 | UINT64 sign, comb, exp; | |
577 | UINT64 trailing; | |
578 | UINT64 bcoeff; | |
579 | ||
580 | UINT128 rq; | |
581 | UINT128 qcoeff; | |
582 | UINT64 ba, bb; | |
583 | ||
584 | ba = *((UINT64 *) & bq + HIGH_128W); | |
585 | bb = *((UINT64 *) & bq + LOW_128W); | |
586 | ||
587 | sign = (ba & 0x8000000000000000ull); | |
588 | comb = (ba & 0x7fffc00000000000ull) >> 46; | |
589 | trailing = (ba & 0x00003fffffffffffull); | |
590 | ||
591 | if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11 | |
592 | exp = (comb >> 1) & 0x3fff; | |
593 | bcoeff = ((8 + (comb & 1)) << 46) | trailing; | |
594 | } else { | |
595 | exp = (comb >> 3) & 0x3fff; | |
596 | bcoeff = ((comb & 7) << 46) | trailing; | |
597 | } | |
598 | ||
599 | if ((comb & 0x1f000) == 0x1f000) { //NaN | |
600 | ba &= 0xfe003fffffffffffULL; // make exponent 0 | |
601 | bcoeff &= 0x00003fffffffffffull; // NaN payloat is only T. | |
602 | if ((bcoeff > 0x0000314dc6448d93ULL) || // significand is non-canonical | |
603 | ((bcoeff == 0x0000314dc6448d93ULL) | |
604 | && (bb >= 0x38c15b0a00000000ULL)) | |
605 | // significand is non-canonical | |
606 | ) { | |
607 | bcoeff = 0ull; | |
608 | ba &= ~0x00003fffffffffffull; | |
609 | bb = 0ull; | |
610 | } | |
611 | *((UINT64 *) & rq + HIGH_128W) = ba; | |
612 | *((UINT64 *) & rq + LOW_128W) = bb; | |
613 | return rq; | |
614 | } else if ((comb & 0x1e000) == 0x1e000) { //Inf | |
615 | ba &= 0xf800000000000000ULL; // make exponent and significand 0 | |
616 | bb = 0; | |
617 | *((UINT64 *) & rq + HIGH_128W) = ba; | |
618 | *((UINT64 *) & rq + LOW_128W) = bb; | |
619 | return rq; | |
620 | } | |
621 | ||
622 | if ((bcoeff > 0x0001ed09bead87c0ull) | |
623 | || ((bcoeff == 0x0001ed09bead87c0ull) | |
624 | && (bb > 0x378d8e63ffffffffull))) { | |
625 | // significand is non-canonical | |
626 | bcoeff = 0ull; | |
627 | bb = 0ull; | |
628 | } | |
629 | ||
630 | *((UINT64 *) & qcoeff + 1) = bcoeff; | |
631 | *((UINT64 *) & qcoeff + 0) = bb; | |
632 | ||
633 | get_BID128_fast (&res, sign, exp, qcoeff); | |
634 | ||
635 | BID_SWAP128 (res); | |
636 | return res; | |
637 | } | |
638 | ||
639 | UINT32 | |
640 | bid32_canonize (UINT32 ba) { | |
641 | FPSC bidrnd; | |
642 | unsigned int rnd = 0; | |
643 | ||
644 | UINT32 res; | |
645 | UINT32 sign, comb, exp; | |
646 | UINT32 trailing; | |
647 | UINT32 bcoeff; | |
648 | ||
649 | sign = (ba & 0x80000000); | |
650 | comb = (ba & 0x7ff00000) >> 20; | |
651 | trailing = (ba & 0x000fffff); | |
652 | ||
653 | if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11 | |
654 | exp = (comb >> 1) & 0xff; | |
655 | bcoeff = ((8 + (comb & 1)) << 20) | trailing; | |
656 | } else { | |
657 | exp = (comb >> 3) & 0xff; | |
658 | bcoeff = ((comb & 7) << 20) | trailing; | |
659 | } | |
660 | ||
661 | if ((comb & 0x7c0) == 0x7c0) { //NaN | |
662 | ba &= 0xfe0fffff; // make exponent 0 | |
663 | bcoeff &= 0x000fffff; // NaN payloat is only T. | |
664 | if (bcoeff >= 1000000) | |
665 | ba &= 0xfff00000; //treat non-canonical significand | |
666 | return ba; | |
667 | } else if ((comb & 0x780) == 0x780) { //Inf | |
668 | ba &= 0xf8000000; // make exponent and significand 0 | |
669 | return ba; | |
670 | } | |
671 | ||
672 | if (bcoeff >= 10000000) | |
673 | bcoeff = 0; | |
674 | rnd = bidrnd = ROUNDING_TO_NEAREST; | |
675 | res = get_BID32 (sign, exp, bcoeff, rnd, &bidrnd); | |
676 | return res; | |
677 | } | |
678 | ||
679 | UINT64 | |
680 | bid64_canonize (UINT64 ba) { | |
681 | UINT64 res; | |
682 | UINT64 sign, comb, exp; | |
683 | UINT64 trailing; | |
684 | UINT64 bcoeff; | |
685 | ||
686 | sign = (ba & 0x8000000000000000ull); | |
687 | comb = (ba & 0x7ffc000000000000ull) >> 50; | |
688 | trailing = (ba & 0x0003ffffffffffffull); | |
689 | ||
690 | ||
691 | if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11 | |
692 | exp = (comb >> 1) & 0x3ff; | |
693 | bcoeff = ((8 + (comb & 1)) << 50) | trailing; | |
694 | } else { | |
695 | exp = (comb >> 3) & 0x3ff; | |
696 | bcoeff = ((comb & 7) << 50) | trailing; | |
697 | } | |
698 | ||
699 | if ((comb & 0x1f00) == 0x1f00) { //NaN | |
700 | ba &= 0xfe03ffffffffffffULL; // make exponent 0 | |
701 | bcoeff &= 0x0003ffffffffffffull; // NaN payloat is only T. | |
702 | if (bcoeff >= 1000000000000000ull) | |
703 | ba &= 0xfe00000000000000ull; // treat non canonical significand and zero G6-G12 | |
704 | return ba; | |
705 | } else if ((comb & 0x1e00) == 0x1e00) { //Inf | |
706 | ba &= 0xf800000000000000ULL; // make exponent and significand 0 | |
707 | return ba; | |
708 | } | |
709 | ||
710 | if (bcoeff >= 10000000000000000ull) { | |
711 | bcoeff = 0ull; | |
712 | } | |
713 | res = very_fast_get_BID64 (sign, exp, bcoeff); | |
714 | return res; | |
715 | } | |
716 | ||
717 | UINT128 | |
718 | bid128_canonize (UINT128 bq) { | |
719 | UINT128 res; | |
720 | UINT64 sign, comb, exp; | |
721 | UINT64 trailing; | |
722 | UINT64 bcoeff; | |
723 | ||
724 | UINT128 rq; | |
725 | UINT128 qcoeff; | |
726 | UINT64 ba, bb; | |
727 | ||
728 | ba = *((UINT64 *) & bq + HIGH_128W); | |
729 | bb = *((UINT64 *) & bq + LOW_128W); | |
730 | ||
731 | sign = (ba & 0x8000000000000000ull); | |
732 | comb = (ba & 0x7fffc00000000000ull) >> 46; | |
733 | trailing = (ba & 0x00003fffffffffffull); | |
734 | ||
735 | if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11 | |
736 | exp = (comb >> 1) & 0x3fff; | |
737 | bcoeff = ((8 + (comb & 1)) << 46) | trailing; | |
738 | } else { | |
739 | exp = (comb >> 3) & 0x3fff; | |
740 | bcoeff = ((comb & 7) << 46) | trailing; | |
741 | } | |
742 | ||
743 | if ((comb & 0x1f000) == 0x1f000) { //NaN | |
744 | ba &= 0xfe003fffffffffffULL; // make exponent 0 | |
745 | bcoeff &= 0x00003fffffffffffull; // NaN payload is only T. | |
746 | ||
747 | if ((bcoeff > 0x0000314dc6448d93ULL) || // significand is non-canonical | |
748 | ((bcoeff == 0x0000314dc6448d93ULL) | |
749 | && (bb >= 0x38c15b0a00000000ULL)) | |
750 | // significand is non-canonical | |
751 | ) { | |
752 | bcoeff = 0ull; | |
753 | ba &= ~0x00003fffffffffffull; | |
754 | bb = 0ull; | |
755 | } | |
756 | *((UINT64 *) & rq + HIGH_128W) = ba; | |
757 | *((UINT64 *) & rq + LOW_128W) = bb; | |
758 | return rq; | |
759 | } else if ((comb & 0x1e000) == 0x1e000) { //Inf | |
760 | ba &= 0xf800000000000000ULL; // make exponent and significand 0 | |
761 | bb = 0; | |
762 | *((UINT64 *) & rq + HIGH_128W) = ba; | |
763 | *((UINT64 *) & rq + LOW_128W) = bb; | |
764 | return rq; | |
765 | } | |
766 | ||
767 | if ((bcoeff > 0x0001ed09bead87c0ull) || // significand is non-canonical | |
768 | ((bcoeff == 0x0001ed09bead87c0ull) | |
769 | && (bb > 0x378d8e63ffffffffull)) | |
770 | // significand is non-canonical | |
771 | ) { | |
772 | bcoeff = 0ull; | |
773 | bb = 0ull; | |
774 | } | |
775 | ||
776 | *((UINT64 *) & qcoeff + 1) = bcoeff; | |
777 | *((UINT64 *) & qcoeff + 0) = bb; | |
778 | ||
779 | get_BID128_fast (&res, sign, exp, qcoeff); | |
780 | BID_SWAP128 (res); | |
781 | return res; | |
782 | } |