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f1717362 | 1 | /* Copyright (C) 2007-2016 Free Software Foundation, Inc. |
9b6b0236 | 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 |
9b6b0236 | 8 | version. |
9 | ||
9b6b0236 | 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/>. */ | |
9b6b0236 | 23 | |
24 | #ifndef __BIDECIMAL_H | |
25 | #define __BIDECIMAL_H | |
26 | ||
27 | #include "bid_conf.h" | |
28 | #include "bid_functions.h" | |
29 | ||
9b6b0236 | 30 | #define __BID_INLINE__ static __inline |
31 | ||
32 | /********************************************************************* | |
33 | * | |
34 | * Logical Shift Macros | |
35 | * | |
36 | *********************************************************************/ | |
37 | ||
38 | #define __shr_128(Q, A, k) \ | |
39 | { \ | |
40 | (Q).w[0] = (A).w[0] >> k; \ | |
41 | (Q).w[0] |= (A).w[1] << (64-k); \ | |
42 | (Q).w[1] = (A).w[1] >> k; \ | |
43 | } | |
44 | ||
45 | #define __shr_128_long(Q, A, k) \ | |
46 | { \ | |
47 | if((k)<64) { \ | |
48 | (Q).w[0] = (A).w[0] >> k; \ | |
49 | (Q).w[0] |= (A).w[1] << (64-k); \ | |
50 | (Q).w[1] = (A).w[1] >> k; \ | |
51 | } \ | |
52 | else { \ | |
53 | (Q).w[0] = (A).w[1]>>((k)-64); \ | |
54 | (Q).w[1] = 0; \ | |
55 | } \ | |
56 | } | |
57 | ||
58 | #define __shl_128_long(Q, A, k) \ | |
59 | { \ | |
60 | if((k)<64) { \ | |
61 | (Q).w[1] = (A).w[1] << k; \ | |
62 | (Q).w[1] |= (A).w[0] >> (64-k); \ | |
63 | (Q).w[0] = (A).w[0] << k; \ | |
64 | } \ | |
65 | else { \ | |
66 | (Q).w[1] = (A).w[0]<<((k)-64); \ | |
67 | (Q).w[0] = 0; \ | |
68 | } \ | |
69 | } | |
70 | ||
71 | #define __low_64(Q) (Q).w[0] | |
72 | /********************************************************************* | |
73 | * | |
74 | * String Macros | |
75 | * | |
76 | *********************************************************************/ | |
77 | #define tolower_macro(x) (((unsigned char)((x)-'A')<=('Z'-'A'))?((x)-'A'+'a'):(x)) | |
78 | /********************************************************************* | |
79 | * | |
80 | * Compare Macros | |
81 | * | |
82 | *********************************************************************/ | |
83 | // greater than | |
84 | // return 0 if A<=B | |
85 | // non-zero if A>B | |
86 | #define __unsigned_compare_gt_128(A, B) \ | |
87 | ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>B.w[0]))) | |
88 | // greater-or-equal | |
89 | #define __unsigned_compare_ge_128(A, B) \ | |
90 | ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>=B.w[0]))) | |
91 | #define __test_equal_128(A, B) (((A).w[1]==(B).w[1]) && ((A).w[0]==(B).w[0])) | |
92 | // tighten exponent range | |
93 | #define __tight_bin_range_128(bp, P, bin_expon) \ | |
94 | { \ | |
95 | UINT64 M; \ | |
96 | M = 1; \ | |
97 | (bp) = (bin_expon); \ | |
98 | if((bp)<63) { \ | |
99 | M <<= ((bp)+1); \ | |
100 | if((P).w[0] >= M) (bp)++; } \ | |
101 | else if((bp)>64) { \ | |
102 | M <<= ((bp)+1-64); \ | |
103 | if(((P).w[1]>M) ||((P).w[1]==M && (P).w[0]))\ | |
104 | (bp)++; } \ | |
105 | else if((P).w[1]) (bp)++; \ | |
106 | } | |
107 | /********************************************************************* | |
108 | * | |
109 | * Add/Subtract Macros | |
110 | * | |
111 | *********************************************************************/ | |
112 | // add 64-bit value to 128-bit | |
113 | #define __add_128_64(R128, A128, B64) \ | |
114 | { \ | |
115 | UINT64 R64H; \ | |
116 | R64H = (A128).w[1]; \ | |
117 | (R128).w[0] = (B64) + (A128).w[0]; \ | |
118 | if((R128).w[0] < (B64)) \ | |
119 | R64H ++; \ | |
120 | (R128).w[1] = R64H; \ | |
121 | } | |
122 | // subtract 64-bit value from 128-bit | |
123 | #define __sub_128_64(R128, A128, B64) \ | |
124 | { \ | |
125 | UINT64 R64H; \ | |
126 | R64H = (A128).w[1]; \ | |
127 | if((A128).w[0] < (B64)) \ | |
128 | R64H --; \ | |
129 | (R128).w[1] = R64H; \ | |
130 | (R128).w[0] = (A128).w[0] - (B64); \ | |
131 | } | |
132 | // add 128-bit value to 128-bit | |
133 | // assume no carry-out | |
134 | #define __add_128_128(R128, A128, B128) \ | |
135 | { \ | |
136 | UINT128 Q128; \ | |
137 | Q128.w[1] = (A128).w[1]+(B128).w[1]; \ | |
138 | Q128.w[0] = (B128).w[0] + (A128).w[0]; \ | |
139 | if(Q128.w[0] < (B128).w[0]) \ | |
140 | Q128.w[1] ++; \ | |
141 | (R128).w[1] = Q128.w[1]; \ | |
142 | (R128).w[0] = Q128.w[0]; \ | |
143 | } | |
144 | #define __sub_128_128(R128, A128, B128) \ | |
145 | { \ | |
146 | UINT128 Q128; \ | |
147 | Q128.w[1] = (A128).w[1]-(B128).w[1]; \ | |
148 | Q128.w[0] = (A128).w[0] - (B128).w[0]; \ | |
149 | if((A128).w[0] < (B128).w[0]) \ | |
150 | Q128.w[1] --; \ | |
151 | (R128).w[1] = Q128.w[1]; \ | |
152 | (R128).w[0] = Q128.w[0]; \ | |
153 | } | |
154 | #define __add_carry_out(S, CY, X, Y) \ | |
155 | { \ | |
156 | UINT64 X1=X; \ | |
157 | S = X + Y; \ | |
158 | CY = (S<X1) ? 1 : 0; \ | |
159 | } | |
160 | #define __add_carry_in_out(S, CY, X, Y, CI) \ | |
161 | { \ | |
162 | UINT64 X1; \ | |
163 | X1 = X + CI; \ | |
164 | S = X1 + Y; \ | |
165 | CY = ((S<X1) || (X1<CI)) ? 1 : 0; \ | |
166 | } | |
167 | #define __sub_borrow_out(S, CY, X, Y) \ | |
168 | { \ | |
169 | UINT64 X1=X; \ | |
170 | S = X - Y; \ | |
171 | CY = (S>X1) ? 1 : 0; \ | |
172 | } | |
173 | #define __sub_borrow_in_out(S, CY, X, Y, CI) \ | |
174 | { \ | |
175 | UINT64 X1, X0=X; \ | |
176 | X1 = X - CI; \ | |
177 | S = X1 - Y; \ | |
178 | CY = ((S>X1) || (X1>X0)) ? 1 : 0; \ | |
179 | } | |
180 | // increment C128 and check for rounding overflow: | |
181 | // if (C_128) = 10^34 then (C_128) = 10^33 and increment the exponent | |
182 | #define INCREMENT(C_128, exp) \ | |
183 | { \ | |
184 | C_128.w[0]++; \ | |
185 | if (C_128.w[0] == 0) C_128.w[1]++; \ | |
186 | if (C_128.w[1] == 0x0001ed09bead87c0ull && \ | |
187 | C_128.w[0] == 0x378d8e6400000000ull) { \ | |
188 | exp++; \ | |
189 | C_128.w[1] = 0x0000314dc6448d93ull; \ | |
190 | C_128.w[0] = 0x38c15b0a00000000ull; \ | |
191 | } \ | |
192 | } | |
193 | // decrement C128 and check for rounding underflow, but only at the | |
194 | // boundary: if C_128 = 10^33 - 1 and exp > 0 then C_128 = 10^34 - 1 | |
195 | // and decrement the exponent | |
196 | #define DECREMENT(C_128, exp) \ | |
197 | { \ | |
198 | C_128.w[0]--; \ | |
199 | if (C_128.w[0] == 0xffffffffffffffffull) C_128.w[1]--; \ | |
200 | if (C_128.w[1] == 0x0000314dc6448d93ull && \ | |
201 | C_128.w[0] == 0x38c15b09ffffffffull && exp > 0) { \ | |
202 | exp--; \ | |
203 | C_128.w[1] = 0x0001ed09bead87c0ull; \ | |
204 | C_128.w[0] = 0x378d8e63ffffffffull; \ | |
205 | } \ | |
206 | } | |
84d1fc49 | 207 | |
9b6b0236 | 208 | /********************************************************************* |
209 | * | |
210 | * Multiply Macros | |
211 | * | |
212 | *********************************************************************/ | |
213 | #define __mul_64x64_to_64(P64, CX, CY) (P64) = (CX) * (CY) | |
214 | /*************************************** | |
215 | * Signed, Full 64x64-bit Multiply | |
216 | ***************************************/ | |
217 | #define __imul_64x64_to_128(P, CX, CY) \ | |
218 | { \ | |
219 | UINT64 SX, SY; \ | |
220 | __mul_64x64_to_128(P, CX, CY); \ | |
221 | \ | |
222 | SX = ((SINT64)(CX))>>63; \ | |
223 | SY = ((SINT64)(CY))>>63; \ | |
224 | SX &= CY; SY &= CX; \ | |
225 | \ | |
226 | (P).w[1] = (P).w[1] - SX - SY; \ | |
227 | } | |
228 | /*************************************** | |
229 | * Signed, Full 64x128-bit Multiply | |
230 | ***************************************/ | |
231 | #define __imul_64x128_full(Ph, Ql, A, B) \ | |
232 | { \ | |
233 | UINT128 ALBL, ALBH, QM2, QM; \ | |
234 | \ | |
235 | __imul_64x64_to_128(ALBH, (A), (B).w[1]); \ | |
236 | __imul_64x64_to_128(ALBL, (A), (B).w[0]); \ | |
237 | \ | |
238 | (Ql).w[0] = ALBL.w[0]; \ | |
239 | QM.w[0] = ALBL.w[1]; \ | |
240 | QM.w[1] = ((SINT64)ALBL.w[1])>>63; \ | |
241 | __add_128_128(QM2, ALBH, QM); \ | |
242 | (Ql).w[1] = QM2.w[0]; \ | |
243 | Ph = QM2.w[1]; \ | |
244 | } | |
245 | /***************************************************** | |
246 | * Unsigned Multiply Macros | |
247 | *****************************************************/ | |
248 | // get full 64x64bit product | |
249 | // | |
250 | #define __mul_64x64_to_128(P, CX, CY) \ | |
251 | { \ | |
252 | UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ | |
253 | CXH = (CX) >> 32; \ | |
254 | CXL = (UINT32)(CX); \ | |
255 | CYH = (CY) >> 32; \ | |
256 | CYL = (UINT32)(CY); \ | |
257 | \ | |
258 | PM = CXH*CYL; \ | |
259 | PH = CXH*CYH; \ | |
260 | PL = CXL*CYL; \ | |
261 | PM2 = CXL*CYH; \ | |
262 | PH += (PM>>32); \ | |
263 | PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ | |
264 | \ | |
265 | (P).w[1] = PH + (PM>>32); \ | |
266 | (P).w[0] = (PM<<32)+(UINT32)PL; \ | |
267 | } | |
268 | // get full 64x64bit product | |
269 | // Note: | |
270 | // This macro is used for CX < 2^61, CY < 2^61 | |
271 | // | |
272 | #define __mul_64x64_to_128_fast(P, CX, CY) \ | |
273 | { \ | |
274 | UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ | |
275 | CXH = (CX) >> 32; \ | |
276 | CXL = (UINT32)(CX); \ | |
277 | CYH = (CY) >> 32; \ | |
278 | CYL = (UINT32)(CY); \ | |
279 | \ | |
280 | PM = CXH*CYL; \ | |
281 | PL = CXL*CYL; \ | |
282 | PH = CXH*CYH; \ | |
283 | PM += CXL*CYH; \ | |
284 | PM += (PL>>32); \ | |
285 | \ | |
286 | (P).w[1] = PH + (PM>>32); \ | |
287 | (P).w[0] = (PM<<32)+(UINT32)PL; \ | |
288 | } | |
289 | // used for CX< 2^60 | |
290 | #define __sqr64_fast(P, CX) \ | |
291 | { \ | |
292 | UINT64 CXH, CXL, PL, PH, PM; \ | |
293 | CXH = (CX) >> 32; \ | |
294 | CXL = (UINT32)(CX); \ | |
295 | \ | |
296 | PM = CXH*CXL; \ | |
297 | PL = CXL*CXL; \ | |
298 | PH = CXH*CXH; \ | |
299 | PM += PM; \ | |
300 | PM += (PL>>32); \ | |
301 | \ | |
302 | (P).w[1] = PH + (PM>>32); \ | |
303 | (P).w[0] = (PM<<32)+(UINT32)PL; \ | |
304 | } | |
305 | // get full 64x64bit product | |
306 | // Note: | |
307 | // This implementation is used for CX < 2^61, CY < 2^61 | |
308 | // | |
309 | #define __mul_64x64_to_64_high_fast(P, CX, CY) \ | |
310 | { \ | |
311 | UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ | |
312 | CXH = (CX) >> 32; \ | |
313 | CXL = (UINT32)(CX); \ | |
314 | CYH = (CY) >> 32; \ | |
315 | CYL = (UINT32)(CY); \ | |
316 | \ | |
317 | PM = CXH*CYL; \ | |
318 | PL = CXL*CYL; \ | |
319 | PH = CXH*CYH; \ | |
320 | PM += CXL*CYH; \ | |
321 | PM += (PL>>32); \ | |
322 | \ | |
323 | (P) = PH + (PM>>32); \ | |
324 | } | |
325 | // get full 64x64bit product | |
326 | // | |
327 | #define __mul_64x64_to_128_full(P, CX, CY) \ | |
328 | { \ | |
329 | UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ | |
330 | CXH = (CX) >> 32; \ | |
331 | CXL = (UINT32)(CX); \ | |
332 | CYH = (CY) >> 32; \ | |
333 | CYL = (UINT32)(CY); \ | |
334 | \ | |
335 | PM = CXH*CYL; \ | |
336 | PH = CXH*CYH; \ | |
337 | PL = CXL*CYL; \ | |
338 | PM2 = CXL*CYH; \ | |
339 | PH += (PM>>32); \ | |
340 | PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ | |
341 | \ | |
342 | (P).w[1] = PH + (PM>>32); \ | |
343 | (P).w[0] = (PM<<32)+(UINT32)PL; \ | |
344 | } | |
345 | #define __mul_128x128_high(Q, A, B) \ | |
346 | { \ | |
347 | UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ | |
348 | \ | |
349 | __mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ | |
350 | __mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ | |
351 | __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ | |
352 | __mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ | |
353 | \ | |
354 | __add_128_128(QM, ALBH, AHBL); \ | |
355 | __add_128_64(QM2, QM, ALBL.w[1]); \ | |
356 | __add_128_64((Q), AHBH, QM2.w[1]); \ | |
357 | } | |
358 | #define __mul_128x128_full(Qh, Ql, A, B) \ | |
359 | { \ | |
360 | UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ | |
361 | \ | |
362 | __mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ | |
363 | __mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ | |
364 | __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ | |
365 | __mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ | |
366 | \ | |
367 | __add_128_128(QM, ALBH, AHBL); \ | |
368 | (Ql).w[0] = ALBL.w[0]; \ | |
369 | __add_128_64(QM2, QM, ALBL.w[1]); \ | |
370 | __add_128_64((Qh), AHBH, QM2.w[1]); \ | |
371 | (Ql).w[1] = QM2.w[0]; \ | |
372 | } | |
373 | #define __mul_128x128_low(Ql, A, B) \ | |
374 | { \ | |
375 | UINT128 ALBL; \ | |
376 | UINT64 QM64; \ | |
377 | \ | |
378 | __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ | |
379 | QM64 = (B).w[0]*(A).w[1] + (A).w[0]*(B).w[1]; \ | |
380 | \ | |
381 | (Ql).w[0] = ALBL.w[0]; \ | |
382 | (Ql).w[1] = QM64 + ALBL.w[1]; \ | |
383 | } | |
384 | #define __mul_64x128_low(Ql, A, B) \ | |
385 | { \ | |
386 | UINT128 ALBL, ALBH, QM2; \ | |
387 | __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ | |
388 | __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ | |
389 | (Ql).w[0] = ALBL.w[0]; \ | |
390 | __add_128_64(QM2, ALBH, ALBL.w[1]); \ | |
391 | (Ql).w[1] = QM2.w[0]; \ | |
392 | } | |
393 | #define __mul_64x128_full(Ph, Ql, A, B) \ | |
394 | { \ | |
395 | UINT128 ALBL, ALBH, QM2; \ | |
396 | \ | |
397 | __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ | |
398 | __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ | |
399 | \ | |
400 | (Ql).w[0] = ALBL.w[0]; \ | |
401 | __add_128_64(QM2, ALBH, ALBL.w[1]); \ | |
402 | (Ql).w[1] = QM2.w[0]; \ | |
403 | Ph = QM2.w[1]; \ | |
404 | } | |
405 | #define __mul_64x128_to_192(Q, A, B) \ | |
406 | { \ | |
407 | UINT128 ALBL, ALBH, QM2; \ | |
408 | \ | |
409 | __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ | |
410 | __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ | |
411 | \ | |
412 | (Q).w[0] = ALBL.w[0]; \ | |
413 | __add_128_64(QM2, ALBH, ALBL.w[1]); \ | |
414 | (Q).w[1] = QM2.w[0]; \ | |
415 | (Q).w[2] = QM2.w[1]; \ | |
416 | } | |
417 | #define __mul_64x128_to192(Q, A, B) \ | |
418 | { \ | |
419 | UINT128 ALBL, ALBH, QM2; \ | |
420 | \ | |
421 | __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ | |
422 | __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ | |
423 | \ | |
424 | (Q).w[0] = ALBL.w[0]; \ | |
425 | __add_128_64(QM2, ALBH, ALBL.w[1]); \ | |
426 | (Q).w[1] = QM2.w[0]; \ | |
427 | (Q).w[2] = QM2.w[1]; \ | |
428 | } | |
429 | #define __mul_128x128_to_256(P256, A, B) \ | |
430 | { \ | |
431 | UINT128 Qll, Qlh; \ | |
432 | UINT64 Phl, Phh, CY1, CY2; \ | |
433 | \ | |
434 | __mul_64x128_full(Phl, Qll, A.w[0], B); \ | |
435 | __mul_64x128_full(Phh, Qlh, A.w[1], B); \ | |
436 | (P256).w[0] = Qll.w[0]; \ | |
437 | __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ | |
438 | __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ | |
439 | (P256).w[3] = Phh + CY2; \ | |
440 | } | |
441 | // | |
442 | // For better performance, will check A.w[1] against 0, | |
443 | // but not B.w[1] | |
444 | // Use this macro accordingly | |
445 | #define __mul_128x128_to_256_check_A(P256, A, B) \ | |
446 | { \ | |
447 | UINT128 Qll, Qlh; \ | |
448 | UINT64 Phl, Phh, CY1, CY2; \ | |
449 | \ | |
450 | __mul_64x128_full(Phl, Qll, A.w[0], B); \ | |
451 | (P256).w[0] = Qll.w[0]; \ | |
452 | if(A.w[1]) { \ | |
453 | __mul_64x128_full(Phh, Qlh, A.w[1], B); \ | |
454 | __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ | |
455 | __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ | |
456 | (P256).w[3] = Phh + CY2; } \ | |
457 | else { \ | |
458 | (P256).w[1] = Qll.w[1]; \ | |
459 | (P256).w[2] = Phl; \ | |
460 | (P256).w[3] = 0; } \ | |
461 | } | |
462 | #define __mul_64x192_to_256(lP, lA, lB) \ | |
463 | { \ | |
464 | UINT128 lP0,lP1,lP2; \ | |
465 | UINT64 lC; \ | |
466 | __mul_64x64_to_128(lP0, lA, (lB).w[0]); \ | |
467 | __mul_64x64_to_128(lP1, lA, (lB).w[1]); \ | |
468 | __mul_64x64_to_128(lP2, lA, (lB).w[2]); \ | |
469 | (lP).w[0] = lP0.w[0]; \ | |
470 | __add_carry_out((lP).w[1],lC,lP1.w[0],lP0.w[1]); \ | |
471 | __add_carry_in_out((lP).w[2],lC,lP2.w[0],lP1.w[1],lC); \ | |
472 | (lP).w[3] = lP2.w[1] + lC; \ | |
473 | } | |
474 | #define __mul_64x256_to_320(P, A, B) \ | |
475 | { \ | |
476 | UINT128 lP0,lP1,lP2,lP3; \ | |
477 | UINT64 lC; \ | |
478 | __mul_64x64_to_128(lP0, A, (B).w[0]); \ | |
479 | __mul_64x64_to_128(lP1, A, (B).w[1]); \ | |
480 | __mul_64x64_to_128(lP2, A, (B).w[2]); \ | |
481 | __mul_64x64_to_128(lP3, A, (B).w[3]); \ | |
482 | (P).w[0] = lP0.w[0]; \ | |
483 | __add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ | |
484 | __add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ | |
485 | __add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ | |
486 | (P).w[4] = lP3.w[1] + lC; \ | |
487 | } | |
488 | #define __mul_192x192_to_384(P, A, B) \ | |
489 | { \ | |
490 | UINT256 P0,P1,P2; \ | |
491 | UINT64 CY; \ | |
492 | __mul_64x192_to_256(P0, (A).w[0], B); \ | |
493 | __mul_64x192_to_256(P1, (A).w[1], B); \ | |
494 | __mul_64x192_to_256(P2, (A).w[2], B); \ | |
495 | (P).w[0] = P0.w[0]; \ | |
496 | __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ | |
497 | __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ | |
498 | __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ | |
499 | (P).w[4] = P1.w[3] + CY; \ | |
500 | __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ | |
501 | __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ | |
502 | __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ | |
503 | (P).w[5] = P2.w[3] + CY; \ | |
504 | } | |
505 | #define __mul_64x320_to_384(P, A, B) \ | |
506 | { \ | |
507 | UINT128 lP0,lP1,lP2,lP3,lP4; \ | |
508 | UINT64 lC; \ | |
509 | __mul_64x64_to_128(lP0, A, (B).w[0]); \ | |
510 | __mul_64x64_to_128(lP1, A, (B).w[1]); \ | |
511 | __mul_64x64_to_128(lP2, A, (B).w[2]); \ | |
512 | __mul_64x64_to_128(lP3, A, (B).w[3]); \ | |
513 | __mul_64x64_to_128(lP4, A, (B).w[4]); \ | |
514 | (P).w[0] = lP0.w[0]; \ | |
515 | __add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ | |
516 | __add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ | |
517 | __add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ | |
518 | __add_carry_in_out((P).w[4],lC,lP4.w[0],lP3.w[1],lC); \ | |
519 | (P).w[5] = lP4.w[1] + lC; \ | |
520 | } | |
521 | // A*A | |
522 | // Full 128x128-bit product | |
523 | #define __sqr128_to_256(P256, A) \ | |
524 | { \ | |
525 | UINT128 Qll, Qlh, Qhh; \ | |
526 | UINT64 TMP_C1, TMP_C2; \ | |
527 | \ | |
528 | __mul_64x64_to_128(Qhh, A.w[1], A.w[1]); \ | |
529 | __mul_64x64_to_128(Qlh, A.w[0], A.w[1]); \ | |
530 | Qhh.w[1] += (Qlh.w[1]>>63); \ | |
531 | Qlh.w[1] = (Qlh.w[1]+Qlh.w[1])|(Qlh.w[0]>>63); \ | |
532 | Qlh.w[0] += Qlh.w[0]; \ | |
533 | __mul_64x64_to_128(Qll, A.w[0], A.w[0]); \ | |
534 | \ | |
535 | __add_carry_out((P256).w[1],TMP_C1, Qlh.w[0], Qll.w[1]); \ | |
536 | (P256).w[0] = Qll.w[0]; \ | |
537 | __add_carry_in_out((P256).w[2],TMP_C2, Qlh.w[1], Qhh.w[0], TMP_C1); \ | |
538 | (P256).w[3] = Qhh.w[1]+TMP_C2; \ | |
539 | } | |
540 | #define __mul_128x128_to_256_low_high(PQh, PQl, A, B) \ | |
541 | { \ | |
542 | UINT128 Qll, Qlh; \ | |
543 | UINT64 Phl, Phh, C1, C2; \ | |
544 | \ | |
545 | __mul_64x128_full(Phl, Qll, A.w[0], B); \ | |
546 | __mul_64x128_full(Phh, Qlh, A.w[1], B); \ | |
547 | (PQl).w[0] = Qll.w[0]; \ | |
548 | __add_carry_out((PQl).w[1],C1, Qlh.w[0], Qll.w[1]); \ | |
549 | __add_carry_in_out((PQh).w[0],C2, Qlh.w[1], Phl, C1); \ | |
550 | (PQh).w[1] = Phh + C2; \ | |
551 | } | |
552 | #define __mul_256x256_to_512(P, A, B) \ | |
553 | { \ | |
554 | UINT512 P0,P1,P2,P3; \ | |
555 | UINT64 CY; \ | |
556 | __mul_64x256_to_320(P0, (A).w[0], B); \ | |
557 | __mul_64x256_to_320(P1, (A).w[1], B); \ | |
558 | __mul_64x256_to_320(P2, (A).w[2], B); \ | |
559 | __mul_64x256_to_320(P3, (A).w[3], B); \ | |
560 | (P).w[0] = P0.w[0]; \ | |
561 | __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ | |
562 | __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ | |
563 | __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ | |
564 | __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ | |
565 | (P).w[5] = P1.w[4] + CY; \ | |
566 | __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ | |
567 | __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ | |
568 | __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ | |
569 | __add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ | |
570 | (P).w[6] = P2.w[4] + CY; \ | |
571 | __add_carry_out((P).w[3],CY,P3.w[0],(P).w[3]); \ | |
572 | __add_carry_in_out((P).w[4],CY,P3.w[1],(P).w[4],CY); \ | |
573 | __add_carry_in_out((P).w[5],CY,P3.w[2],(P).w[5],CY); \ | |
574 | __add_carry_in_out((P).w[6],CY,P3.w[3],(P).w[6],CY); \ | |
575 | (P).w[7] = P3.w[4] + CY; \ | |
576 | } | |
577 | #define __mul_192x256_to_448(P, A, B) \ | |
578 | { \ | |
579 | UINT512 P0,P1,P2; \ | |
580 | UINT64 CY; \ | |
581 | __mul_64x256_to_320(P0, (A).w[0], B); \ | |
582 | __mul_64x256_to_320(P1, (A).w[1], B); \ | |
583 | __mul_64x256_to_320(P2, (A).w[2], B); \ | |
584 | (P).w[0] = P0.w[0]; \ | |
585 | __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ | |
586 | __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ | |
587 | __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ | |
588 | __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ | |
589 | (P).w[5] = P1.w[4] + CY; \ | |
590 | __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ | |
591 | __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ | |
592 | __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ | |
593 | __add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ | |
594 | (P).w[6] = P2.w[4] + CY; \ | |
595 | } | |
596 | #define __mul_320x320_to_640(P, A, B) \ | |
597 | { \ | |
598 | UINT512 P0,P1,P2,P3; \ | |
599 | UINT64 CY; \ | |
600 | __mul_256x256_to_512((P), (A), B); \ | |
601 | __mul_64x256_to_320(P1, (A).w[4], B); \ | |
602 | __mul_64x256_to_320(P2, (B).w[4], A); \ | |
603 | __mul_64x64_to_128(P3, (A).w[4], (B).w[4]); \ | |
604 | __add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ | |
605 | __add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ | |
606 | __add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ | |
607 | __add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ | |
608 | __add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ | |
609 | P3.w[1] += CY; \ | |
610 | __add_carry_out((P).w[4],CY,(P).w[4],P0.w[0]); \ | |
611 | __add_carry_in_out((P).w[5],CY,(P).w[5],P0.w[1],CY); \ | |
612 | __add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[2],CY); \ | |
613 | __add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[3],CY); \ | |
614 | __add_carry_in_out((P).w[8],CY,P3.w[0],P0.w[4],CY); \ | |
615 | (P).w[9] = P3.w[1] + CY; \ | |
616 | } | |
617 | #define __mul_384x384_to_768(P, A, B) \ | |
618 | { \ | |
619 | UINT512 P0,P1,P2,P3; \ | |
620 | UINT64 CY; \ | |
621 | __mul_320x320_to_640((P), (A), B); \ | |
622 | __mul_64x320_to_384(P1, (A).w[5], B); \ | |
623 | __mul_64x320_to_384(P2, (B).w[5], A); \ | |
624 | __mul_64x64_to_128(P3, (A).w[5], (B).w[5]); \ | |
625 | __add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ | |
626 | __add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ | |
627 | __add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ | |
628 | __add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ | |
629 | __add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ | |
630 | __add_carry_in_out((P0).w[5],CY,P1.w[5],P2.w[5],CY); \ | |
631 | P3.w[1] += CY; \ | |
632 | __add_carry_out((P).w[5],CY,(P).w[5],P0.w[0]); \ | |
633 | __add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[1],CY); \ | |
634 | __add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[2],CY); \ | |
635 | __add_carry_in_out((P).w[8],CY,(P).w[8],P0.w[3],CY); \ | |
636 | __add_carry_in_out((P).w[9],CY,(P).w[9],P0.w[4],CY); \ | |
637 | __add_carry_in_out((P).w[10],CY,P3.w[0],P0.w[5],CY); \ | |
638 | (P).w[11] = P3.w[1] + CY; \ | |
639 | } | |
640 | #define __mul_64x128_short(Ql, A, B) \ | |
641 | { \ | |
642 | UINT64 ALBH_L; \ | |
643 | \ | |
644 | __mul_64x64_to_64(ALBH_L, (A),(B).w[1]); \ | |
645 | __mul_64x64_to_128((Ql), (A), (B).w[0]); \ | |
646 | \ | |
647 | (Ql).w[1] += ALBH_L; \ | |
648 | } | |
649 | #define __scale128_10(D,_TMP) \ | |
650 | { \ | |
651 | UINT128 _TMP2,_TMP8; \ | |
652 | _TMP2.w[1] = (_TMP.w[1]<<1)|(_TMP.w[0]>>63); \ | |
653 | _TMP2.w[0] = _TMP.w[0]<<1; \ | |
654 | _TMP8.w[1] = (_TMP.w[1]<<3)|(_TMP.w[0]>>61); \ | |
655 | _TMP8.w[0] = _TMP.w[0]<<3; \ | |
656 | __add_128_128(D, _TMP2, _TMP8); \ | |
657 | } | |
658 | // 64x64-bit product | |
659 | #define __mul_64x64_to_128MACH(P128, CX64, CY64) \ | |
660 | { \ | |
661 | UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ | |
662 | CXH = (CX64) >> 32; \ | |
663 | CXL = (UINT32)(CX64); \ | |
664 | CYH = (CY64) >> 32; \ | |
665 | CYL = (UINT32)(CY64); \ | |
666 | PM = CXH*CYL; \ | |
667 | PH = CXH*CYH; \ | |
668 | PL = CXL*CYL; \ | |
669 | PM2 = CXL*CYH; \ | |
670 | PH += (PM>>32); \ | |
671 | PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ | |
672 | (P128).w[1] = PH + (PM>>32); \ | |
673 | (P128).w[0] = (PM<<32)+(UINT32)PL; \ | |
674 | } | |
675 | // 64x64-bit product | |
676 | #define __mul_64x64_to_128HIGH(P64, CX64, CY64) \ | |
677 | { \ | |
678 | UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ | |
679 | CXH = (CX64) >> 32; \ | |
680 | CXL = (UINT32)(CX64); \ | |
681 | CYH = (CY64) >> 32; \ | |
682 | CYL = (UINT32)(CY64); \ | |
683 | PM = CXH*CYL; \ | |
684 | PH = CXH*CYH; \ | |
685 | PL = CXL*CYL; \ | |
686 | PM2 = CXL*CYH; \ | |
687 | PH += (PM>>32); \ | |
688 | PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ | |
689 | P64 = PH + (PM>>32); \ | |
690 | } | |
691 | #define __mul_128x64_to_128(Q128, A64, B128) \ | |
692 | { \ | |
693 | UINT64 ALBH_L; \ | |
694 | ALBH_L = (A64) * (B128).w[1]; \ | |
695 | __mul_64x64_to_128MACH((Q128), (A64), (B128).w[0]); \ | |
696 | (Q128).w[1] += ALBH_L; \ | |
697 | } | |
698 | // might simplify by calculating just QM2.w[0] | |
699 | #define __mul_64x128_to_128(Ql, A, B) \ | |
700 | { \ | |
701 | UINT128 ALBL, ALBH, QM2; \ | |
702 | __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ | |
703 | __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ | |
704 | (Ql).w[0] = ALBL.w[0]; \ | |
705 | __add_128_64(QM2, ALBH, ALBL.w[1]); \ | |
706 | (Ql).w[1] = QM2.w[0]; \ | |
707 | } | |
708 | /********************************************************************* | |
709 | * | |
710 | * BID Pack/Unpack Macros | |
711 | * | |
712 | *********************************************************************/ | |
713 | ///////////////////////////////////////// | |
714 | // BID64 definitions | |
715 | //////////////////////////////////////// | |
716 | #define DECIMAL_MAX_EXPON_64 767 | |
717 | #define DECIMAL_EXPONENT_BIAS 398 | |
718 | #define MAX_FORMAT_DIGITS 16 | |
719 | ///////////////////////////////////////// | |
720 | // BID128 definitions | |
721 | //////////////////////////////////////// | |
722 | #define DECIMAL_MAX_EXPON_128 12287 | |
723 | #define DECIMAL_EXPONENT_BIAS_128 6176 | |
724 | #define MAX_FORMAT_DIGITS_128 34 | |
725 | ///////////////////////////////////////// | |
726 | // BID32 definitions | |
727 | //////////////////////////////////////// | |
728 | #define DECIMAL_MAX_EXPON_32 191 | |
729 | #define DECIMAL_EXPONENT_BIAS_32 101 | |
730 | #define MAX_FORMAT_DIGITS_32 7 | |
731 | //////////////////////////////////////// | |
732 | // Constant Definitions | |
733 | /////////////////////////////////////// | |
734 | #define SPECIAL_ENCODING_MASK64 0x6000000000000000ull | |
735 | #define INFINITY_MASK64 0x7800000000000000ull | |
84d1fc49 | 736 | #define SINFINITY_MASK64 0xf800000000000000ull |
737 | #define SSNAN_MASK64 0xfc00000000000000ull | |
9b6b0236 | 738 | #define NAN_MASK64 0x7c00000000000000ull |
739 | #define SNAN_MASK64 0x7e00000000000000ull | |
740 | #define QUIET_MASK64 0xfdffffffffffffffull | |
741 | #define LARGE_COEFF_MASK64 0x0007ffffffffffffull | |
742 | #define LARGE_COEFF_HIGH_BIT64 0x0020000000000000ull | |
743 | #define SMALL_COEFF_MASK64 0x001fffffffffffffull | |
744 | #define EXPONENT_MASK64 0x3ff | |
745 | #define EXPONENT_SHIFT_LARGE64 51 | |
746 | #define EXPONENT_SHIFT_SMALL64 53 | |
747 | #define LARGEST_BID64 0x77fb86f26fc0ffffull | |
748 | #define SMALLEST_BID64 0xf7fb86f26fc0ffffull | |
749 | #define SMALL_COEFF_MASK128 0x0001ffffffffffffull | |
750 | #define LARGE_COEFF_MASK128 0x00007fffffffffffull | |
751 | #define EXPONENT_MASK128 0x3fff | |
752 | #define LARGEST_BID128_HIGH 0x5fffed09bead87c0ull | |
753 | #define LARGEST_BID128_LOW 0x378d8e63ffffffffull | |
754 | #define SPECIAL_ENCODING_MASK32 0x60000000ul | |
755 | #define INFINITY_MASK32 0x78000000ul | |
756 | #define LARGE_COEFF_MASK32 0x007ffffful | |
757 | #define LARGE_COEFF_HIGH_BIT32 0x00800000ul | |
758 | #define SMALL_COEFF_MASK32 0x001ffffful | |
759 | #define EXPONENT_MASK32 0xff | |
760 | #define LARGEST_BID32 0x77f8967f | |
84d1fc49 | 761 | #define NAN_MASK32 0x7c000000 |
762 | #define SNAN_MASK32 0x7e000000 | |
9b6b0236 | 763 | #define MASK_BINARY_EXPONENT 0x7ff0000000000000ull |
764 | #define BINARY_EXPONENT_BIAS 0x3ff | |
765 | #define UPPER_EXPON_LIMIT 51 | |
766 | // data needed for BID pack/unpack macros | |
84d1fc49 | 767 | extern UINT64 round_const_table[][19]; |
768 | extern UINT128 reciprocals10_128[]; | |
769 | extern int recip_scale[]; | |
770 | extern UINT128 power10_table_128[]; | |
771 | extern int estimate_decimal_digits[]; | |
772 | extern int estimate_bin_expon[]; | |
773 | extern UINT64 power10_index_binexp[]; | |
774 | extern int short_recip_scale[]; | |
775 | extern UINT64 reciprocals10_64[]; | |
776 | extern UINT128 power10_index_binexp_128[]; | |
777 | extern UINT128 round_const_table_128[][36]; | |
9b6b0236 | 778 | |
779 | ||
780 | ////////////////////////////////////////////// | |
781 | // Status Flag Handling | |
782 | ///////////////////////////////////////////// | |
783 | #define __set_status_flags(fpsc, status) *(fpsc) |= status | |
784 | #define is_inexact(fpsc) ((*(fpsc))&INEXACT_EXCEPTION) | |
785 | ||
786 | __BID_INLINE__ UINT64 | |
787 | unpack_BID64 (UINT64 * psign_x, int *pexponent_x, | |
788 | UINT64 * pcoefficient_x, UINT64 x) { | |
789 | UINT64 tmp, coeff; | |
790 | ||
791 | *psign_x = x & 0x8000000000000000ull; | |
792 | ||
793 | if ((x & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) { | |
794 | // special encodings | |
795 | // coefficient | |
796 | coeff = (x & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64; | |
797 | ||
798 | if ((x & INFINITY_MASK64) == INFINITY_MASK64) { | |
84d1fc49 | 799 | *pexponent_x = 0; |
800 | *pcoefficient_x = x & 0xfe03ffffffffffffull; | |
801 | if ((x & 0x0003ffffffffffffull) >= 1000000000000000ull) | |
802 | *pcoefficient_x = x & 0xfe00000000000000ull; | |
803 | if ((x & NAN_MASK64) == INFINITY_MASK64) | |
804 | *pcoefficient_x = x & SINFINITY_MASK64; | |
9b6b0236 | 805 | return 0; // NaN or Infinity |
806 | } | |
807 | // check for non-canonical values | |
808 | if (coeff >= 10000000000000000ull) | |
809 | coeff = 0; | |
810 | *pcoefficient_x = coeff; | |
811 | // get exponent | |
812 | tmp = x >> EXPONENT_SHIFT_LARGE64; | |
813 | *pexponent_x = (int) (tmp & EXPONENT_MASK64); | |
84d1fc49 | 814 | return coeff; |
9b6b0236 | 815 | } |
816 | // exponent | |
817 | tmp = x >> EXPONENT_SHIFT_SMALL64; | |
818 | *pexponent_x = (int) (tmp & EXPONENT_MASK64); | |
819 | // coefficient | |
820 | *pcoefficient_x = (x & SMALL_COEFF_MASK64); | |
821 | ||
822 | return *pcoefficient_x; | |
823 | } | |
824 | ||
825 | // | |
826 | // BID64 pack macro (general form) | |
827 | // | |
828 | __BID_INLINE__ UINT64 | |
829 | get_BID64 (UINT64 sgn, int expon, UINT64 coeff, int rmode, | |
830 | unsigned *fpsc) { | |
831 | UINT128 Stemp, Q_low; | |
832 | UINT64 QH, r, mask, C64, remainder_h, CY, carry; | |
833 | int extra_digits, amount, amount2; | |
834 | unsigned status; | |
835 | ||
836 | if (coeff > 9999999999999999ull) { | |
837 | expon++; | |
838 | coeff = 1000000000000000ull; | |
839 | } | |
840 | // check for possible underflow/overflow | |
841 | if (((unsigned) expon) >= 3 * 256) { | |
842 | if (expon < 0) { | |
843 | // underflow | |
844 | if (expon + MAX_FORMAT_DIGITS < 0) { | |
845 | #ifdef SET_STATUS_FLAGS | |
846 | __set_status_flags (fpsc, | |
847 | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
848 | #endif | |
849 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
850 | #ifndef IEEE_ROUND_NEAREST | |
851 | if (rmode == ROUNDING_DOWN && sgn) | |
852 | return 0x8000000000000001ull; | |
853 | if (rmode == ROUNDING_UP && !sgn) | |
854 | return 1ull; | |
855 | #endif | |
856 | #endif | |
857 | // result is 0 | |
858 | return sgn; | |
859 | } | |
860 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
861 | #ifndef IEEE_ROUND_NEAREST | |
862 | if (sgn && (unsigned) (rmode - 1) < 2) | |
863 | rmode = 3 - rmode; | |
864 | #endif | |
865 | #endif | |
866 | // get digits to be shifted out | |
867 | extra_digits = -expon; | |
84d1fc49 | 868 | coeff += round_const_table[rmode][extra_digits]; |
9b6b0236 | 869 | |
870 | // get coeff*(2^M[extra_digits])/10^extra_digits | |
871 | __mul_64x128_full (QH, Q_low, coeff, | |
84d1fc49 | 872 | reciprocals10_128[extra_digits]); |
9b6b0236 | 873 | |
874 | // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 | |
84d1fc49 | 875 | amount = recip_scale[extra_digits]; |
9b6b0236 | 876 | |
877 | C64 = QH >> amount; | |
878 | ||
879 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
880 | #ifndef IEEE_ROUND_NEAREST | |
84d1fc49 | 881 | if (rmode == 0) //ROUNDING_TO_NEAREST |
9b6b0236 | 882 | #endif |
883 | if (C64 & 1) { | |
884 | // check whether fractional part of initial_P/10^extra_digits is exactly .5 | |
885 | ||
886 | // get remainder | |
887 | amount2 = 64 - amount; | |
888 | remainder_h = 0; | |
889 | remainder_h--; | |
890 | remainder_h >>= amount2; | |
891 | remainder_h = remainder_h & QH; | |
892 | ||
893 | if (!remainder_h | |
84d1fc49 | 894 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
895 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 896 | && Q_low.w[0] < |
84d1fc49 | 897 | reciprocals10_128[extra_digits].w[0]))) { |
9b6b0236 | 898 | C64--; |
899 | } | |
900 | } | |
901 | #endif | |
902 | ||
903 | #ifdef SET_STATUS_FLAGS | |
904 | ||
905 | if (is_inexact (fpsc)) | |
906 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); | |
907 | else { | |
908 | status = INEXACT_EXCEPTION; | |
909 | // get remainder | |
910 | remainder_h = QH << (64 - amount); | |
911 | ||
912 | switch (rmode) { | |
913 | case ROUNDING_TO_NEAREST: | |
914 | case ROUNDING_TIES_AWAY: | |
915 | // test whether fractional part is 0 | |
916 | if (remainder_h == 0x8000000000000000ull | |
84d1fc49 | 917 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
918 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 919 | && Q_low.w[0] < |
84d1fc49 | 920 | reciprocals10_128[extra_digits].w[0]))) |
9b6b0236 | 921 | status = EXACT_STATUS; |
922 | break; | |
923 | case ROUNDING_DOWN: | |
924 | case ROUNDING_TO_ZERO: | |
925 | if (!remainder_h | |
84d1fc49 | 926 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
927 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 928 | && Q_low.w[0] < |
84d1fc49 | 929 | reciprocals10_128[extra_digits].w[0]))) |
9b6b0236 | 930 | status = EXACT_STATUS; |
931 | break; | |
932 | default: | |
933 | // round up | |
934 | __add_carry_out (Stemp.w[0], CY, Q_low.w[0], | |
84d1fc49 | 935 | reciprocals10_128[extra_digits].w[0]); |
9b6b0236 | 936 | __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], |
84d1fc49 | 937 | reciprocals10_128[extra_digits].w[1], CY); |
9b6b0236 | 938 | if ((remainder_h >> (64 - amount)) + carry >= |
939 | (((UINT64) 1) << amount)) | |
940 | status = EXACT_STATUS; | |
941 | } | |
942 | ||
943 | if (status != EXACT_STATUS) | |
944 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); | |
945 | } | |
946 | ||
947 | #endif | |
948 | ||
949 | return sgn | C64; | |
950 | } | |
951 | while (coeff < 1000000000000000ull && expon >= 3 * 256) { | |
952 | expon--; | |
953 | coeff = (coeff << 3) + (coeff << 1); | |
954 | } | |
955 | if (expon > DECIMAL_MAX_EXPON_64) { | |
956 | #ifdef SET_STATUS_FLAGS | |
957 | __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
958 | #endif | |
959 | // overflow | |
960 | r = sgn | INFINITY_MASK64; | |
961 | switch (rmode) { | |
962 | case ROUNDING_DOWN: | |
963 | if (!sgn) | |
964 | r = LARGEST_BID64; | |
965 | break; | |
966 | case ROUNDING_TO_ZERO: | |
967 | r = sgn | LARGEST_BID64; | |
968 | break; | |
969 | case ROUNDING_UP: | |
970 | // round up | |
971 | if (sgn) | |
972 | r = SMALLEST_BID64; | |
973 | } | |
974 | return r; | |
975 | } | |
976 | } | |
977 | ||
978 | mask = 1; | |
979 | mask <<= EXPONENT_SHIFT_SMALL64; | |
980 | ||
981 | // check whether coefficient fits in 10*5+3 bits | |
982 | if (coeff < mask) { | |
983 | r = expon; | |
984 | r <<= EXPONENT_SHIFT_SMALL64; | |
985 | r |= (coeff | sgn); | |
986 | return r; | |
987 | } | |
988 | // special format | |
989 | ||
990 | // eliminate the case coeff==10^16 after rounding | |
991 | if (coeff == 10000000000000000ull) { | |
992 | r = expon + 1; | |
993 | r <<= EXPONENT_SHIFT_SMALL64; | |
994 | r |= (1000000000000000ull | sgn); | |
995 | return r; | |
996 | } | |
997 | ||
998 | r = expon; | |
999 | r <<= EXPONENT_SHIFT_LARGE64; | |
1000 | r |= (sgn | SPECIAL_ENCODING_MASK64); | |
1001 | // add coeff, without leading bits | |
1002 | mask = (mask >> 2) - 1; | |
1003 | coeff &= mask; | |
1004 | r |= coeff; | |
1005 | ||
1006 | return r; | |
1007 | } | |
1008 | ||
1009 | ||
1010 | ||
1011 | ||
1012 | // | |
1013 | // No overflow/underflow checking | |
1014 | // | |
1015 | __BID_INLINE__ UINT64 | |
1016 | fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { | |
1017 | UINT64 r, mask; | |
1018 | ||
1019 | mask = 1; | |
1020 | mask <<= EXPONENT_SHIFT_SMALL64; | |
1021 | ||
1022 | // check whether coefficient fits in 10*5+3 bits | |
1023 | if (coeff < mask) { | |
1024 | r = expon; | |
1025 | r <<= EXPONENT_SHIFT_SMALL64; | |
1026 | r |= (coeff | sgn); | |
1027 | return r; | |
1028 | } | |
1029 | // special format | |
1030 | ||
1031 | // eliminate the case coeff==10^16 after rounding | |
1032 | if (coeff == 10000000000000000ull) { | |
1033 | r = expon + 1; | |
1034 | r <<= EXPONENT_SHIFT_SMALL64; | |
1035 | r |= (1000000000000000ull | sgn); | |
1036 | return r; | |
1037 | } | |
1038 | ||
1039 | r = expon; | |
1040 | r <<= EXPONENT_SHIFT_LARGE64; | |
1041 | r |= (sgn | SPECIAL_ENCODING_MASK64); | |
1042 | // add coeff, without leading bits | |
1043 | mask = (mask >> 2) - 1; | |
1044 | coeff &= mask; | |
1045 | r |= coeff; | |
1046 | ||
1047 | return r; | |
1048 | } | |
1049 | ||
1050 | ||
1051 | // | |
1052 | // no underflow checking | |
1053 | // | |
1054 | __BID_INLINE__ UINT64 | |
1055 | fast_get_BID64_check_OF (UINT64 sgn, int expon, UINT64 coeff, int rmode, | |
1056 | unsigned *fpsc) { | |
1057 | UINT64 r, mask; | |
1058 | ||
1059 | if (((unsigned) expon) >= 3 * 256 - 1) { | |
1060 | if ((expon == 3 * 256 - 1) && coeff == 10000000000000000ull) { | |
1061 | expon = 3 * 256; | |
1062 | coeff = 1000000000000000ull; | |
1063 | } | |
1064 | ||
1065 | if (((unsigned) expon) >= 3 * 256) { | |
1066 | while (coeff < 1000000000000000ull && expon >= 3 * 256) { | |
1067 | expon--; | |
1068 | coeff = (coeff << 3) + (coeff << 1); | |
1069 | } | |
1070 | if (expon > DECIMAL_MAX_EXPON_64) { | |
1071 | #ifdef SET_STATUS_FLAGS | |
1072 | __set_status_flags (fpsc, | |
1073 | OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1074 | #endif | |
1075 | // overflow | |
1076 | r = sgn | INFINITY_MASK64; | |
1077 | switch (rmode) { | |
1078 | case ROUNDING_DOWN: | |
1079 | if (!sgn) | |
1080 | r = LARGEST_BID64; | |
1081 | break; | |
1082 | case ROUNDING_TO_ZERO: | |
1083 | r = sgn | LARGEST_BID64; | |
1084 | break; | |
1085 | case ROUNDING_UP: | |
1086 | // round up | |
1087 | if (sgn) | |
1088 | r = SMALLEST_BID64; | |
1089 | } | |
1090 | return r; | |
1091 | } | |
1092 | } | |
1093 | } | |
1094 | ||
1095 | mask = 1; | |
1096 | mask <<= EXPONENT_SHIFT_SMALL64; | |
1097 | ||
1098 | // check whether coefficient fits in 10*5+3 bits | |
1099 | if (coeff < mask) { | |
1100 | r = expon; | |
1101 | r <<= EXPONENT_SHIFT_SMALL64; | |
1102 | r |= (coeff | sgn); | |
1103 | return r; | |
1104 | } | |
1105 | // special format | |
1106 | ||
1107 | // eliminate the case coeff==10^16 after rounding | |
1108 | if (coeff == 10000000000000000ull) { | |
1109 | r = expon + 1; | |
1110 | r <<= EXPONENT_SHIFT_SMALL64; | |
1111 | r |= (1000000000000000ull | sgn); | |
1112 | return r; | |
1113 | } | |
1114 | ||
1115 | r = expon; | |
1116 | r <<= EXPONENT_SHIFT_LARGE64; | |
1117 | r |= (sgn | SPECIAL_ENCODING_MASK64); | |
1118 | // add coeff, without leading bits | |
1119 | mask = (mask >> 2) - 1; | |
1120 | coeff &= mask; | |
1121 | r |= coeff; | |
1122 | ||
1123 | return r; | |
1124 | } | |
1125 | ||
1126 | ||
1127 | // | |
1128 | // No overflow/underflow checking | |
1129 | // or checking for coefficients equal to 10^16 (after rounding) | |
1130 | // | |
1131 | __BID_INLINE__ UINT64 | |
1132 | very_fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { | |
1133 | UINT64 r, mask; | |
1134 | ||
1135 | mask = 1; | |
1136 | mask <<= EXPONENT_SHIFT_SMALL64; | |
1137 | ||
1138 | // check whether coefficient fits in 10*5+3 bits | |
1139 | if (coeff < mask) { | |
1140 | r = expon; | |
1141 | r <<= EXPONENT_SHIFT_SMALL64; | |
1142 | r |= (coeff | sgn); | |
1143 | return r; | |
1144 | } | |
1145 | // special format | |
1146 | r = expon; | |
1147 | r <<= EXPONENT_SHIFT_LARGE64; | |
1148 | r |= (sgn | SPECIAL_ENCODING_MASK64); | |
1149 | // add coeff, without leading bits | |
1150 | mask = (mask >> 2) - 1; | |
1151 | coeff &= mask; | |
1152 | r |= coeff; | |
1153 | ||
1154 | return r; | |
1155 | } | |
1156 | ||
1157 | // | |
1158 | // No overflow/underflow checking or checking for coefficients above 2^53 | |
1159 | // | |
1160 | __BID_INLINE__ UINT64 | |
1161 | very_fast_get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff) { | |
1162 | // no UF/OF | |
1163 | UINT64 r; | |
1164 | ||
1165 | r = expon; | |
1166 | r <<= EXPONENT_SHIFT_SMALL64; | |
1167 | r |= (coeff | sgn); | |
1168 | return r; | |
1169 | } | |
1170 | ||
1171 | ||
1172 | // | |
1173 | // This pack macro is used when underflow is known to occur | |
1174 | // | |
1175 | __BID_INLINE__ UINT64 | |
1176 | get_BID64_UF (UINT64 sgn, int expon, UINT64 coeff, UINT64 R, int rmode, | |
1177 | unsigned *fpsc) { | |
1178 | UINT128 C128, Q_low, Stemp; | |
1179 | UINT64 C64, remainder_h, QH, carry, CY; | |
1180 | int extra_digits, amount, amount2; | |
1181 | unsigned status; | |
1182 | ||
1183 | // underflow | |
1184 | if (expon + MAX_FORMAT_DIGITS < 0) { | |
1185 | #ifdef SET_STATUS_FLAGS | |
1186 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1187 | #endif | |
1188 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1189 | #ifndef IEEE_ROUND_NEAREST | |
1190 | if (rmode == ROUNDING_DOWN && sgn) | |
1191 | return 0x8000000000000001ull; | |
1192 | if (rmode == ROUNDING_UP && !sgn) | |
1193 | return 1ull; | |
1194 | #endif | |
1195 | #endif | |
1196 | // result is 0 | |
1197 | return sgn; | |
1198 | } | |
1199 | // 10*coeff | |
1200 | coeff = (coeff << 3) + (coeff << 1); | |
1201 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1202 | #ifndef IEEE_ROUND_NEAREST | |
1203 | if (sgn && (unsigned) (rmode - 1) < 2) | |
1204 | rmode = 3 - rmode; | |
1205 | #endif | |
1206 | #endif | |
1207 | if (R) | |
1208 | coeff |= 1; | |
1209 | // get digits to be shifted out | |
1210 | extra_digits = 1 - expon; | |
84d1fc49 | 1211 | C128.w[0] = coeff + round_const_table[rmode][extra_digits]; |
9b6b0236 | 1212 | |
1213 | // get coeff*(2^M[extra_digits])/10^extra_digits | |
1214 | __mul_64x128_full (QH, Q_low, C128.w[0], | |
84d1fc49 | 1215 | reciprocals10_128[extra_digits]); |
9b6b0236 | 1216 | |
1217 | // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 | |
84d1fc49 | 1218 | amount = recip_scale[extra_digits]; |
9b6b0236 | 1219 | |
1220 | C64 = QH >> amount; | |
1221 | //__shr_128(C128, Q_high, amount); | |
1222 | ||
1223 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1224 | #ifndef IEEE_ROUND_NEAREST | |
84d1fc49 | 1225 | if (rmode == 0) //ROUNDING_TO_NEAREST |
9b6b0236 | 1226 | #endif |
1227 | if (C64 & 1) { | |
1228 | // check whether fractional part of initial_P/10^extra_digits is exactly .5 | |
1229 | ||
1230 | // get remainder | |
1231 | amount2 = 64 - amount; | |
1232 | remainder_h = 0; | |
1233 | remainder_h--; | |
1234 | remainder_h >>= amount2; | |
1235 | remainder_h = remainder_h & QH; | |
1236 | ||
1237 | if (!remainder_h | |
84d1fc49 | 1238 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
1239 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 1240 | && Q_low.w[0] < |
84d1fc49 | 1241 | reciprocals10_128[extra_digits].w[0]))) { |
9b6b0236 | 1242 | C64--; |
1243 | } | |
1244 | } | |
1245 | #endif | |
1246 | ||
1247 | #ifdef SET_STATUS_FLAGS | |
1248 | ||
1249 | if (is_inexact (fpsc)) | |
1250 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); | |
1251 | else { | |
1252 | status = INEXACT_EXCEPTION; | |
1253 | // get remainder | |
1254 | remainder_h = QH << (64 - amount); | |
1255 | ||
1256 | switch (rmode) { | |
1257 | case ROUNDING_TO_NEAREST: | |
1258 | case ROUNDING_TIES_AWAY: | |
1259 | // test whether fractional part is 0 | |
1260 | if (remainder_h == 0x8000000000000000ull | |
84d1fc49 | 1261 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
1262 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 1263 | && Q_low.w[0] < |
84d1fc49 | 1264 | reciprocals10_128[extra_digits].w[0]))) |
9b6b0236 | 1265 | status = EXACT_STATUS; |
1266 | break; | |
1267 | case ROUNDING_DOWN: | |
1268 | case ROUNDING_TO_ZERO: | |
1269 | if (!remainder_h | |
84d1fc49 | 1270 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
1271 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 1272 | && Q_low.w[0] < |
84d1fc49 | 1273 | reciprocals10_128[extra_digits].w[0]))) |
9b6b0236 | 1274 | status = EXACT_STATUS; |
1275 | break; | |
1276 | default: | |
1277 | // round up | |
1278 | __add_carry_out (Stemp.w[0], CY, Q_low.w[0], | |
84d1fc49 | 1279 | reciprocals10_128[extra_digits].w[0]); |
9b6b0236 | 1280 | __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], |
84d1fc49 | 1281 | reciprocals10_128[extra_digits].w[1], CY); |
9b6b0236 | 1282 | if ((remainder_h >> (64 - amount)) + carry >= |
1283 | (((UINT64) 1) << amount)) | |
1284 | status = EXACT_STATUS; | |
1285 | } | |
1286 | ||
1287 | if (status != EXACT_STATUS) | |
1288 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); | |
1289 | } | |
1290 | ||
1291 | #endif | |
1292 | ||
1293 | return sgn | C64; | |
1294 | ||
1295 | } | |
1296 | ||
1297 | ||
1298 | ||
1299 | // | |
1300 | // This pack macro doesnot check for coefficients above 2^53 | |
1301 | // | |
1302 | __BID_INLINE__ UINT64 | |
1303 | get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff, | |
1304 | int rmode, unsigned *fpsc) { | |
1305 | UINT128 C128, Q_low, Stemp; | |
1306 | UINT64 r, mask, C64, remainder_h, QH, carry, CY; | |
1307 | int extra_digits, amount, amount2; | |
1308 | unsigned status; | |
1309 | ||
1310 | // check for possible underflow/overflow | |
1311 | if (((unsigned) expon) >= 3 * 256) { | |
1312 | if (expon < 0) { | |
1313 | // underflow | |
1314 | if (expon + MAX_FORMAT_DIGITS < 0) { | |
1315 | #ifdef SET_STATUS_FLAGS | |
1316 | __set_status_flags (fpsc, | |
1317 | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1318 | #endif | |
1319 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1320 | #ifndef IEEE_ROUND_NEAREST | |
1321 | if (rmode == ROUNDING_DOWN && sgn) | |
1322 | return 0x8000000000000001ull; | |
1323 | if (rmode == ROUNDING_UP && !sgn) | |
1324 | return 1ull; | |
1325 | #endif | |
1326 | #endif | |
1327 | // result is 0 | |
1328 | return sgn; | |
1329 | } | |
1330 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1331 | #ifndef IEEE_ROUND_NEAREST | |
1332 | if (sgn && (unsigned) (rmode - 1) < 2) | |
1333 | rmode = 3 - rmode; | |
1334 | #endif | |
1335 | #endif | |
1336 | // get digits to be shifted out | |
1337 | extra_digits = -expon; | |
84d1fc49 | 1338 | C128.w[0] = coeff + round_const_table[rmode][extra_digits]; |
9b6b0236 | 1339 | |
1340 | // get coeff*(2^M[extra_digits])/10^extra_digits | |
1341 | __mul_64x128_full (QH, Q_low, C128.w[0], | |
84d1fc49 | 1342 | reciprocals10_128[extra_digits]); |
9b6b0236 | 1343 | |
1344 | // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 | |
84d1fc49 | 1345 | amount = recip_scale[extra_digits]; |
9b6b0236 | 1346 | |
1347 | C64 = QH >> amount; | |
1348 | ||
1349 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1350 | #ifndef IEEE_ROUND_NEAREST | |
84d1fc49 | 1351 | if (rmode == 0) //ROUNDING_TO_NEAREST |
9b6b0236 | 1352 | #endif |
1353 | if (C64 & 1) { | |
1354 | // check whether fractional part of initial_P/10^extra_digits is exactly .5 | |
1355 | ||
1356 | // get remainder | |
1357 | amount2 = 64 - amount; | |
1358 | remainder_h = 0; | |
1359 | remainder_h--; | |
1360 | remainder_h >>= amount2; | |
1361 | remainder_h = remainder_h & QH; | |
1362 | ||
1363 | if (!remainder_h | |
84d1fc49 | 1364 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
1365 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 1366 | && Q_low.w[0] < |
84d1fc49 | 1367 | reciprocals10_128[extra_digits].w[0]))) { |
9b6b0236 | 1368 | C64--; |
1369 | } | |
1370 | } | |
1371 | #endif | |
1372 | ||
1373 | #ifdef SET_STATUS_FLAGS | |
1374 | ||
1375 | if (is_inexact (fpsc)) | |
1376 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); | |
1377 | else { | |
1378 | status = INEXACT_EXCEPTION; | |
1379 | // get remainder | |
1380 | remainder_h = QH << (64 - amount); | |
1381 | ||
1382 | switch (rmode) { | |
1383 | case ROUNDING_TO_NEAREST: | |
1384 | case ROUNDING_TIES_AWAY: | |
1385 | // test whether fractional part is 0 | |
1386 | if (remainder_h == 0x8000000000000000ull | |
84d1fc49 | 1387 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
1388 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 1389 | && Q_low.w[0] < |
84d1fc49 | 1390 | reciprocals10_128[extra_digits].w[0]))) |
9b6b0236 | 1391 | status = EXACT_STATUS; |
1392 | break; | |
1393 | case ROUNDING_DOWN: | |
1394 | case ROUNDING_TO_ZERO: | |
1395 | if (!remainder_h | |
84d1fc49 | 1396 | && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] |
1397 | || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] | |
9b6b0236 | 1398 | && Q_low.w[0] < |
84d1fc49 | 1399 | reciprocals10_128[extra_digits].w[0]))) |
9b6b0236 | 1400 | status = EXACT_STATUS; |
1401 | break; | |
1402 | default: | |
1403 | // round up | |
1404 | __add_carry_out (Stemp.w[0], CY, Q_low.w[0], | |
84d1fc49 | 1405 | reciprocals10_128[extra_digits].w[0]); |
9b6b0236 | 1406 | __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], |
84d1fc49 | 1407 | reciprocals10_128[extra_digits].w[1], CY); |
9b6b0236 | 1408 | if ((remainder_h >> (64 - amount)) + carry >= |
1409 | (((UINT64) 1) << amount)) | |
1410 | status = EXACT_STATUS; | |
1411 | } | |
1412 | ||
1413 | if (status != EXACT_STATUS) | |
1414 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); | |
1415 | } | |
1416 | ||
1417 | #endif | |
1418 | ||
1419 | return sgn | C64; | |
1420 | } | |
1421 | ||
1422 | while (coeff < 1000000000000000ull && expon >= 3 * 256) { | |
1423 | expon--; | |
1424 | coeff = (coeff << 3) + (coeff << 1); | |
1425 | } | |
1426 | if (expon > DECIMAL_MAX_EXPON_64) { | |
1427 | #ifdef SET_STATUS_FLAGS | |
1428 | __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1429 | #endif | |
1430 | // overflow | |
1431 | r = sgn | INFINITY_MASK64; | |
1432 | switch (rmode) { | |
1433 | case ROUNDING_DOWN: | |
1434 | if (!sgn) | |
1435 | r = LARGEST_BID64; | |
1436 | break; | |
1437 | case ROUNDING_TO_ZERO: | |
1438 | r = sgn | LARGEST_BID64; | |
1439 | break; | |
1440 | case ROUNDING_UP: | |
1441 | // round up | |
1442 | if (sgn) | |
1443 | r = SMALLEST_BID64; | |
1444 | } | |
1445 | return r; | |
1446 | } else { | |
1447 | mask = 1; | |
1448 | mask <<= EXPONENT_SHIFT_SMALL64; | |
1449 | if (coeff >= mask) { | |
1450 | r = expon; | |
1451 | r <<= EXPONENT_SHIFT_LARGE64; | |
1452 | r |= (sgn | SPECIAL_ENCODING_MASK64); | |
1453 | // add coeff, without leading bits | |
1454 | mask = (mask >> 2) - 1; | |
1455 | coeff &= mask; | |
1456 | r |= coeff; | |
1457 | return r; | |
1458 | } | |
1459 | } | |
1460 | } | |
1461 | ||
1462 | r = expon; | |
1463 | r <<= EXPONENT_SHIFT_SMALL64; | |
1464 | r |= (coeff | sgn); | |
1465 | ||
1466 | return r; | |
1467 | } | |
1468 | ||
1469 | ||
1470 | /***************************************************************************** | |
1471 | * | |
1472 | * BID128 pack/unpack macros | |
1473 | * | |
1474 | *****************************************************************************/ | |
1475 | ||
1476 | // | |
1477 | // Macro for handling BID128 underflow | |
1478 | // sticky bit given as additional argument | |
1479 | // | |
1480 | __BID_INLINE__ UINT128 * | |
1481 | handle_UF_128_rem (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, | |
1482 | UINT64 R, unsigned *prounding_mode, unsigned *fpsc) { | |
1483 | UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CQ2, CQ8; | |
1484 | UINT64 carry, CY; | |
1485 | int ed2, amount; | |
1486 | unsigned rmode, status; | |
1487 | ||
1488 | // UF occurs | |
1489 | if (expon + MAX_FORMAT_DIGITS_128 < 0) { | |
1490 | #ifdef SET_STATUS_FLAGS | |
1491 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1492 | #endif | |
1493 | pres->w[1] = sgn; | |
1494 | pres->w[0] = 0; | |
1495 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1496 | #ifndef IEEE_ROUND_NEAREST | |
1497 | if ((sgn && *prounding_mode == ROUNDING_DOWN) | |
1498 | || (!sgn && *prounding_mode == ROUNDING_UP)) | |
1499 | pres->w[0] = 1ull; | |
1500 | #endif | |
1501 | #endif | |
1502 | return pres; | |
1503 | } | |
1504 | // CQ *= 10 | |
1505 | CQ2.w[1] = (CQ.w[1] << 1) | (CQ.w[0] >> 63); | |
1506 | CQ2.w[0] = CQ.w[0] << 1; | |
1507 | CQ8.w[1] = (CQ.w[1] << 3) | (CQ.w[0] >> 61); | |
1508 | CQ8.w[0] = CQ.w[0] << 3; | |
1509 | __add_128_128 (CQ, CQ2, CQ8); | |
1510 | ||
1511 | // add remainder | |
1512 | if (R) | |
1513 | CQ.w[0] |= 1; | |
1514 | ||
1515 | ed2 = 1 - expon; | |
1516 | // add rounding constant to CQ | |
1517 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1518 | #ifndef IEEE_ROUND_NEAREST | |
1519 | rmode = *prounding_mode; | |
1520 | if (sgn && (unsigned) (rmode - 1) < 2) | |
1521 | rmode = 3 - rmode; | |
1522 | #else | |
1523 | rmode = 0; | |
1524 | #endif | |
1525 | #else | |
1526 | rmode = 0; | |
1527 | #endif | |
84d1fc49 | 1528 | T128 = round_const_table_128[rmode][ed2]; |
9b6b0236 | 1529 | __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); |
1530 | CQ.w[1] = CQ.w[1] + T128.w[1] + carry; | |
1531 | ||
84d1fc49 | 1532 | TP128 = reciprocals10_128[ed2]; |
9b6b0236 | 1533 | __mul_128x128_full (Qh, Ql, CQ, TP128); |
84d1fc49 | 1534 | amount = recip_scale[ed2]; |
9b6b0236 | 1535 | |
1536 | if (amount >= 64) { | |
1537 | CQ.w[0] = Qh.w[1] >> (amount - 64); | |
1538 | CQ.w[1] = 0; | |
1539 | } else { | |
1540 | __shr_128 (CQ, Qh, amount); | |
1541 | } | |
1542 | ||
1543 | expon = 0; | |
1544 | ||
1545 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1546 | #ifndef IEEE_ROUND_NEAREST | |
1547 | if (!(*prounding_mode)) | |
1548 | #endif | |
1549 | if (CQ.w[0] & 1) { | |
1550 | // check whether fractional part of initial_P/10^ed1 is exactly .5 | |
1551 | ||
1552 | // get remainder | |
1553 | __shl_128_long (Qh1, Qh, (128 - amount)); | |
1554 | ||
1555 | if (!Qh1.w[1] && !Qh1.w[0] | |
84d1fc49 | 1556 | && (Ql.w[1] < reciprocals10_128[ed2].w[1] |
1557 | || (Ql.w[1] == reciprocals10_128[ed2].w[1] | |
1558 | && Ql.w[0] < reciprocals10_128[ed2].w[0]))) { | |
9b6b0236 | 1559 | CQ.w[0]--; |
1560 | } | |
1561 | } | |
1562 | #endif | |
1563 | ||
1564 | #ifdef SET_STATUS_FLAGS | |
1565 | ||
1566 | if (is_inexact (fpsc)) | |
1567 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); | |
1568 | else { | |
1569 | status = INEXACT_EXCEPTION; | |
1570 | // get remainder | |
1571 | __shl_128_long (Qh1, Qh, (128 - amount)); | |
1572 | ||
1573 | switch (rmode) { | |
1574 | case ROUNDING_TO_NEAREST: | |
1575 | case ROUNDING_TIES_AWAY: | |
1576 | // test whether fractional part is 0 | |
1577 | if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) | |
84d1fc49 | 1578 | && (Ql.w[1] < reciprocals10_128[ed2].w[1] |
1579 | || (Ql.w[1] == reciprocals10_128[ed2].w[1] | |
1580 | && Ql.w[0] < reciprocals10_128[ed2].w[0]))) | |
9b6b0236 | 1581 | status = EXACT_STATUS; |
1582 | break; | |
1583 | case ROUNDING_DOWN: | |
1584 | case ROUNDING_TO_ZERO: | |
1585 | if ((!Qh1.w[1]) && (!Qh1.w[0]) | |
84d1fc49 | 1586 | && (Ql.w[1] < reciprocals10_128[ed2].w[1] |
1587 | || (Ql.w[1] == reciprocals10_128[ed2].w[1] | |
1588 | && Ql.w[0] < reciprocals10_128[ed2].w[0]))) | |
9b6b0236 | 1589 | status = EXACT_STATUS; |
1590 | break; | |
1591 | default: | |
1592 | // round up | |
1593 | __add_carry_out (Stemp.w[0], CY, Ql.w[0], | |
84d1fc49 | 1594 | reciprocals10_128[ed2].w[0]); |
9b6b0236 | 1595 | __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], |
84d1fc49 | 1596 | reciprocals10_128[ed2].w[1], CY); |
9b6b0236 | 1597 | __shr_128_long (Qh, Qh1, (128 - amount)); |
1598 | Tmp.w[0] = 1; | |
1599 | Tmp.w[1] = 0; | |
1600 | __shl_128_long (Tmp1, Tmp, amount); | |
1601 | Qh.w[0] += carry; | |
1602 | if (Qh.w[0] < carry) | |
1603 | Qh.w[1]++; | |
1604 | if (__unsigned_compare_ge_128 (Qh, Tmp1)) | |
1605 | status = EXACT_STATUS; | |
1606 | } | |
1607 | ||
1608 | if (status != EXACT_STATUS) | |
1609 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); | |
1610 | } | |
1611 | ||
1612 | #endif | |
1613 | ||
1614 | pres->w[1] = sgn | CQ.w[1]; | |
1615 | pres->w[0] = CQ.w[0]; | |
1616 | ||
1617 | return pres; | |
1618 | ||
1619 | } | |
1620 | ||
1621 | ||
1622 | // | |
1623 | // Macro for handling BID128 underflow | |
1624 | // | |
1625 | __BID_INLINE__ UINT128 * | |
1626 | handle_UF_128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, | |
1627 | unsigned *prounding_mode, unsigned *fpsc) { | |
1628 | UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1; | |
1629 | UINT64 carry, CY; | |
1630 | int ed2, amount; | |
1631 | unsigned rmode, status; | |
1632 | ||
1633 | // UF occurs | |
1634 | if (expon + MAX_FORMAT_DIGITS_128 < 0) { | |
1635 | #ifdef SET_STATUS_FLAGS | |
1636 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1637 | #endif | |
1638 | pres->w[1] = sgn; | |
1639 | pres->w[0] = 0; | |
1640 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1641 | #ifndef IEEE_ROUND_NEAREST | |
1642 | if ((sgn && *prounding_mode == ROUNDING_DOWN) | |
1643 | || (!sgn && *prounding_mode == ROUNDING_UP)) | |
1644 | pres->w[0] = 1ull; | |
1645 | #endif | |
1646 | #endif | |
1647 | return pres; | |
1648 | } | |
1649 | ||
1650 | ed2 = 0 - expon; | |
1651 | // add rounding constant to CQ | |
1652 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1653 | #ifndef IEEE_ROUND_NEAREST | |
1654 | rmode = *prounding_mode; | |
1655 | if (sgn && (unsigned) (rmode - 1) < 2) | |
1656 | rmode = 3 - rmode; | |
1657 | #else | |
1658 | rmode = 0; | |
1659 | #endif | |
1660 | #else | |
1661 | rmode = 0; | |
1662 | #endif | |
1663 | ||
84d1fc49 | 1664 | T128 = round_const_table_128[rmode][ed2]; |
9b6b0236 | 1665 | __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); |
1666 | CQ.w[1] = CQ.w[1] + T128.w[1] + carry; | |
1667 | ||
84d1fc49 | 1668 | TP128 = reciprocals10_128[ed2]; |
9b6b0236 | 1669 | __mul_128x128_full (Qh, Ql, CQ, TP128); |
84d1fc49 | 1670 | amount = recip_scale[ed2]; |
9b6b0236 | 1671 | |
1672 | if (amount >= 64) { | |
1673 | CQ.w[0] = Qh.w[1] >> (amount - 64); | |
1674 | CQ.w[1] = 0; | |
1675 | } else { | |
1676 | __shr_128 (CQ, Qh, amount); | |
1677 | } | |
1678 | ||
1679 | expon = 0; | |
1680 | ||
1681 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1682 | #ifndef IEEE_ROUND_NEAREST | |
1683 | if (!(*prounding_mode)) | |
1684 | #endif | |
1685 | if (CQ.w[0] & 1) { | |
1686 | // check whether fractional part of initial_P/10^ed1 is exactly .5 | |
1687 | ||
1688 | // get remainder | |
1689 | __shl_128_long (Qh1, Qh, (128 - amount)); | |
1690 | ||
1691 | if (!Qh1.w[1] && !Qh1.w[0] | |
84d1fc49 | 1692 | && (Ql.w[1] < reciprocals10_128[ed2].w[1] |
1693 | || (Ql.w[1] == reciprocals10_128[ed2].w[1] | |
1694 | && Ql.w[0] < reciprocals10_128[ed2].w[0]))) { | |
9b6b0236 | 1695 | CQ.w[0]--; |
1696 | } | |
1697 | } | |
1698 | #endif | |
1699 | ||
1700 | #ifdef SET_STATUS_FLAGS | |
1701 | ||
1702 | if (is_inexact (fpsc)) | |
1703 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); | |
1704 | else { | |
1705 | status = INEXACT_EXCEPTION; | |
1706 | // get remainder | |
1707 | __shl_128_long (Qh1, Qh, (128 - amount)); | |
1708 | ||
1709 | switch (rmode) { | |
1710 | case ROUNDING_TO_NEAREST: | |
1711 | case ROUNDING_TIES_AWAY: | |
1712 | // test whether fractional part is 0 | |
1713 | if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) | |
84d1fc49 | 1714 | && (Ql.w[1] < reciprocals10_128[ed2].w[1] |
1715 | || (Ql.w[1] == reciprocals10_128[ed2].w[1] | |
1716 | && Ql.w[0] < reciprocals10_128[ed2].w[0]))) | |
9b6b0236 | 1717 | status = EXACT_STATUS; |
1718 | break; | |
1719 | case ROUNDING_DOWN: | |
1720 | case ROUNDING_TO_ZERO: | |
1721 | if ((!Qh1.w[1]) && (!Qh1.w[0]) | |
84d1fc49 | 1722 | && (Ql.w[1] < reciprocals10_128[ed2].w[1] |
1723 | || (Ql.w[1] == reciprocals10_128[ed2].w[1] | |
1724 | && Ql.w[0] < reciprocals10_128[ed2].w[0]))) | |
9b6b0236 | 1725 | status = EXACT_STATUS; |
1726 | break; | |
1727 | default: | |
1728 | // round up | |
1729 | __add_carry_out (Stemp.w[0], CY, Ql.w[0], | |
84d1fc49 | 1730 | reciprocals10_128[ed2].w[0]); |
9b6b0236 | 1731 | __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], |
84d1fc49 | 1732 | reciprocals10_128[ed2].w[1], CY); |
9b6b0236 | 1733 | __shr_128_long (Qh, Qh1, (128 - amount)); |
1734 | Tmp.w[0] = 1; | |
1735 | Tmp.w[1] = 0; | |
1736 | __shl_128_long (Tmp1, Tmp, amount); | |
1737 | Qh.w[0] += carry; | |
1738 | if (Qh.w[0] < carry) | |
1739 | Qh.w[1]++; | |
1740 | if (__unsigned_compare_ge_128 (Qh, Tmp1)) | |
1741 | status = EXACT_STATUS; | |
1742 | } | |
1743 | ||
1744 | if (status != EXACT_STATUS) | |
1745 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); | |
1746 | } | |
1747 | ||
1748 | #endif | |
1749 | ||
1750 | pres->w[1] = sgn | CQ.w[1]; | |
1751 | pres->w[0] = CQ.w[0]; | |
1752 | ||
1753 | return pres; | |
1754 | ||
1755 | } | |
1756 | ||
1757 | ||
1758 | ||
1759 | // | |
1760 | // BID128 unpack, input passed by value | |
1761 | // | |
1762 | __BID_INLINE__ UINT64 | |
1763 | unpack_BID128_value (UINT64 * psign_x, int *pexponent_x, | |
84d1fc49 | 1764 | UINT128 * pcoefficient_x, UINT128 x) { |
9b6b0236 | 1765 | UINT128 coeff, T33, T34; |
1766 | UINT64 ex; | |
1767 | ||
1768 | *psign_x = (x.w[1]) & 0x8000000000000000ull; | |
1769 | ||
1770 | // special encodings | |
1771 | if ((x.w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { | |
1772 | if ((x.w[1] & INFINITY_MASK64) < INFINITY_MASK64) { | |
1773 | // non-canonical input | |
1774 | pcoefficient_x->w[0] = 0; | |
1775 | pcoefficient_x->w[1] = 0; | |
1776 | ex = (x.w[1]) >> 47; | |
1777 | *pexponent_x = ((int) ex) & EXPONENT_MASK128; | |
1778 | return 0; | |
1779 | } | |
1780 | // 10^33 | |
84d1fc49 | 1781 | T33 = power10_table_128[33]; |
1782 | /*coeff.w[0] = x.w[0]; | |
1783 | coeff.w[1] = (x.w[1]) & LARGE_COEFF_MASK128; | |
1784 | pcoefficient_x->w[0] = x.w[0]; | |
1785 | pcoefficient_x->w[1] = x.w[1]; | |
1786 | if (__unsigned_compare_ge_128 (coeff, T33)) // non-canonical | |
1787 | pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); */ | |
1788 | ||
9b6b0236 | 1789 | pcoefficient_x->w[0] = x.w[0]; |
84d1fc49 | 1790 | pcoefficient_x->w[1] = (x.w[1]) & 0x00003fffffffffffull; |
1791 | if (__unsigned_compare_ge_128 ((*pcoefficient_x), T33)) // non-canonical | |
1792 | { | |
1793 | pcoefficient_x->w[1] = (x.w[1]) & 0xfe00000000000000ull; | |
1794 | pcoefficient_x->w[0] = 0; | |
1795 | } else | |
1796 | pcoefficient_x->w[1] = (x.w[1]) & 0xfe003fffffffffffull; | |
1797 | if ((x.w[1] & NAN_MASK64) == INFINITY_MASK64) { | |
1798 | pcoefficient_x->w[0] = 0; | |
1799 | pcoefficient_x->w[1] = x.w[1] & SINFINITY_MASK64; | |
1800 | } | |
1801 | *pexponent_x = 0; | |
1802 | return 0; // NaN or Infinity | |
9b6b0236 | 1803 | } |
1804 | ||
1805 | coeff.w[0] = x.w[0]; | |
1806 | coeff.w[1] = (x.w[1]) & SMALL_COEFF_MASK128; | |
1807 | ||
1808 | // 10^34 | |
84d1fc49 | 1809 | T34 = power10_table_128[34]; |
9b6b0236 | 1810 | // check for non-canonical values |
1811 | if (__unsigned_compare_ge_128 (coeff, T34)) | |
1812 | coeff.w[0] = coeff.w[1] = 0; | |
1813 | ||
1814 | pcoefficient_x->w[0] = coeff.w[0]; | |
1815 | pcoefficient_x->w[1] = coeff.w[1]; | |
1816 | ||
1817 | ex = (x.w[1]) >> 49; | |
1818 | *pexponent_x = ((int) ex) & EXPONENT_MASK128; | |
1819 | ||
1820 | return coeff.w[0] | coeff.w[1]; | |
1821 | } | |
1822 | ||
1823 | ||
1824 | // | |
1825 | // BID128 unpack, input pased by reference | |
1826 | // | |
1827 | __BID_INLINE__ UINT64 | |
1828 | unpack_BID128 (UINT64 * psign_x, int *pexponent_x, | |
1829 | UINT128 * pcoefficient_x, UINT128 * px) { | |
1830 | UINT128 coeff, T33, T34; | |
1831 | UINT64 ex; | |
1832 | ||
1833 | *psign_x = (px->w[1]) & 0x8000000000000000ull; | |
1834 | ||
1835 | // special encodings | |
1836 | if ((px->w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { | |
1837 | if ((px->w[1] & INFINITY_MASK64) < INFINITY_MASK64) { | |
1838 | // non-canonical input | |
1839 | pcoefficient_x->w[0] = 0; | |
1840 | pcoefficient_x->w[1] = 0; | |
1841 | ex = (px->w[1]) >> 47; | |
1842 | *pexponent_x = ((int) ex) & EXPONENT_MASK128; | |
1843 | return 0; | |
1844 | } | |
1845 | // 10^33 | |
84d1fc49 | 1846 | T33 = power10_table_128[33]; |
9b6b0236 | 1847 | coeff.w[0] = px->w[0]; |
1848 | coeff.w[1] = (px->w[1]) & LARGE_COEFF_MASK128; | |
1849 | pcoefficient_x->w[0] = px->w[0]; | |
1850 | pcoefficient_x->w[1] = px->w[1]; | |
84d1fc49 | 1851 | if (__unsigned_compare_ge_128 (coeff, T33)) { // non-canonical |
9b6b0236 | 1852 | pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); |
84d1fc49 | 1853 | pcoefficient_x->w[0] = 0; |
1854 | } | |
1855 | *pexponent_x = 0; | |
1856 | return 0; // NaN or Infinity | |
9b6b0236 | 1857 | } |
1858 | ||
1859 | coeff.w[0] = px->w[0]; | |
1860 | coeff.w[1] = (px->w[1]) & SMALL_COEFF_MASK128; | |
1861 | ||
1862 | // 10^34 | |
84d1fc49 | 1863 | T34 = power10_table_128[34]; |
9b6b0236 | 1864 | // check for non-canonical values |
1865 | if (__unsigned_compare_ge_128 (coeff, T34)) | |
1866 | coeff.w[0] = coeff.w[1] = 0; | |
1867 | ||
1868 | pcoefficient_x->w[0] = coeff.w[0]; | |
1869 | pcoefficient_x->w[1] = coeff.w[1]; | |
1870 | ||
1871 | ex = (px->w[1]) >> 49; | |
1872 | *pexponent_x = ((int) ex) & EXPONENT_MASK128; | |
1873 | ||
1874 | return coeff.w[0] | coeff.w[1]; | |
1875 | } | |
1876 | ||
1877 | // | |
1878 | // Pack macro checks for overflow, but not underflow | |
1879 | // | |
1880 | __BID_INLINE__ UINT128 * | |
1881 | get_BID128_very_fast_OF (UINT128 * pres, UINT64 sgn, int expon, | |
1882 | UINT128 coeff, unsigned *prounding_mode, | |
1883 | unsigned *fpsc) { | |
1884 | UINT128 T; | |
1885 | UINT64 tmp, tmp2; | |
1886 | ||
1887 | if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { | |
1888 | ||
1889 | if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { | |
84d1fc49 | 1890 | T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; |
9b6b0236 | 1891 | while (__unsigned_compare_gt_128 (T, coeff) |
1892 | && expon > DECIMAL_MAX_EXPON_128) { | |
1893 | coeff.w[1] = | |
1894 | (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + | |
1895 | (coeff.w[0] >> 63); | |
1896 | tmp2 = coeff.w[0] << 3; | |
1897 | coeff.w[0] = (coeff.w[0] << 1) + tmp2; | |
1898 | if (coeff.w[0] < tmp2) | |
1899 | coeff.w[1]++; | |
1900 | ||
1901 | expon--; | |
1902 | } | |
1903 | } | |
1904 | if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { | |
1905 | // OF | |
1906 | #ifdef SET_STATUS_FLAGS | |
1907 | __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
1908 | #endif | |
1909 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
1910 | #ifndef IEEE_ROUND_NEAREST | |
1911 | if (*prounding_mode == ROUNDING_TO_ZERO | |
1912 | || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn | |
1913 | && | |
1914 | *prounding_mode | |
1915 | == | |
1916 | ROUNDING_DOWN)) | |
1917 | { | |
1918 | pres->w[1] = sgn | LARGEST_BID128_HIGH; | |
1919 | pres->w[0] = LARGEST_BID128_LOW; | |
1920 | } else | |
1921 | #endif | |
1922 | #endif | |
1923 | { | |
1924 | pres->w[1] = sgn | INFINITY_MASK64; | |
1925 | pres->w[0] = 0; | |
1926 | } | |
1927 | return pres; | |
1928 | } | |
1929 | } | |
1930 | ||
1931 | pres->w[0] = coeff.w[0]; | |
1932 | tmp = expon; | |
1933 | tmp <<= 49; | |
1934 | pres->w[1] = sgn | tmp | coeff.w[1]; | |
1935 | ||
1936 | return pres; | |
1937 | } | |
1938 | ||
1939 | ||
1940 | // | |
1941 | // No overflow/underflow checks | |
1942 | // No checking for coefficient == 10^34 (rounding artifact) | |
1943 | // | |
1944 | __BID_INLINE__ UINT128 * | |
1945 | get_BID128_very_fast (UINT128 * pres, UINT64 sgn, int expon, | |
1946 | UINT128 coeff) { | |
1947 | UINT64 tmp; | |
1948 | ||
1949 | pres->w[0] = coeff.w[0]; | |
1950 | tmp = expon; | |
1951 | tmp <<= 49; | |
1952 | pres->w[1] = sgn | tmp | coeff.w[1]; | |
1953 | ||
1954 | return pres; | |
1955 | } | |
1956 | ||
1957 | // | |
1958 | // No overflow/underflow checks | |
1959 | // | |
1960 | __BID_INLINE__ UINT128 * | |
1961 | get_BID128_fast (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { | |
1962 | UINT64 tmp; | |
1963 | ||
1964 | // coeff==10^34? | |
1965 | if (coeff.w[1] == 0x0001ed09bead87c0ull | |
1966 | && coeff.w[0] == 0x378d8e6400000000ull) { | |
1967 | expon++; | |
1968 | // set coefficient to 10^33 | |
1969 | coeff.w[1] = 0x0000314dc6448d93ull; | |
1970 | coeff.w[0] = 0x38c15b0a00000000ull; | |
1971 | } | |
1972 | ||
1973 | pres->w[0] = coeff.w[0]; | |
1974 | tmp = expon; | |
1975 | tmp <<= 49; | |
1976 | pres->w[1] = sgn | tmp | coeff.w[1]; | |
1977 | ||
1978 | return pres; | |
1979 | } | |
1980 | ||
1981 | // | |
1982 | // General BID128 pack macro | |
1983 | // | |
1984 | __BID_INLINE__ UINT128 * | |
1985 | get_BID128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff, | |
1986 | unsigned *prounding_mode, unsigned *fpsc) { | |
1987 | UINT128 T; | |
1988 | UINT64 tmp, tmp2; | |
1989 | ||
1990 | // coeff==10^34? | |
1991 | if (coeff.w[1] == 0x0001ed09bead87c0ull | |
1992 | && coeff.w[0] == 0x378d8e6400000000ull) { | |
1993 | expon++; | |
1994 | // set coefficient to 10^33 | |
1995 | coeff.w[1] = 0x0000314dc6448d93ull; | |
1996 | coeff.w[0] = 0x38c15b0a00000000ull; | |
1997 | } | |
1998 | // check OF, UF | |
84d1fc49 | 1999 | if (expon < 0 || expon > DECIMAL_MAX_EXPON_128) { |
9b6b0236 | 2000 | // check UF |
84d1fc49 | 2001 | if (expon < 0) { |
9b6b0236 | 2002 | return handle_UF_128 (pres, sgn, expon, coeff, prounding_mode, |
2003 | fpsc); | |
84d1fc49 | 2004 | } |
9b6b0236 | 2005 | |
2006 | if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { | |
84d1fc49 | 2007 | T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; |
9b6b0236 | 2008 | while (__unsigned_compare_gt_128 (T, coeff) |
2009 | && expon > DECIMAL_MAX_EXPON_128) { | |
2010 | coeff.w[1] = | |
2011 | (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + | |
2012 | (coeff.w[0] >> 63); | |
2013 | tmp2 = coeff.w[0] << 3; | |
2014 | coeff.w[0] = (coeff.w[0] << 1) + tmp2; | |
2015 | if (coeff.w[0] < tmp2) | |
2016 | coeff.w[1]++; | |
2017 | ||
2018 | expon--; | |
2019 | } | |
2020 | } | |
84d1fc49 | 2021 | if (expon > DECIMAL_MAX_EXPON_128) { |
2022 | if (!(coeff.w[1] | coeff.w[0])) { | |
2023 | pres->w[1] = sgn | (((UINT64) DECIMAL_MAX_EXPON_128) << 49); | |
2024 | pres->w[0] = 0; | |
2025 | return pres; | |
2026 | } | |
9b6b0236 | 2027 | // OF |
2028 | #ifdef SET_STATUS_FLAGS | |
2029 | __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
2030 | #endif | |
2031 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
2032 | #ifndef IEEE_ROUND_NEAREST | |
2033 | if (*prounding_mode == ROUNDING_TO_ZERO | |
2034 | || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn | |
2035 | && | |
2036 | *prounding_mode | |
2037 | == | |
2038 | ROUNDING_DOWN)) | |
2039 | { | |
2040 | pres->w[1] = sgn | LARGEST_BID128_HIGH; | |
2041 | pres->w[0] = LARGEST_BID128_LOW; | |
2042 | } else | |
2043 | #endif | |
2044 | #endif | |
2045 | { | |
2046 | pres->w[1] = sgn | INFINITY_MASK64; | |
2047 | pres->w[0] = 0; | |
2048 | } | |
2049 | return pres; | |
2050 | } | |
2051 | } | |
2052 | ||
2053 | pres->w[0] = coeff.w[0]; | |
2054 | tmp = expon; | |
2055 | tmp <<= 49; | |
2056 | pres->w[1] = sgn | tmp | coeff.w[1]; | |
2057 | ||
2058 | return pres; | |
2059 | } | |
2060 | ||
2061 | ||
2062 | // | |
2063 | // Macro used for conversions from string | |
2064 | // (no additional arguments given for rounding mode, status flags) | |
2065 | // | |
2066 | __BID_INLINE__ UINT128 * | |
2067 | get_BID128_string (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { | |
2068 | UINT128 D2, D8; | |
2069 | UINT64 tmp; | |
2070 | unsigned rmode = 0, status; | |
2071 | ||
2072 | // coeff==10^34? | |
2073 | if (coeff.w[1] == 0x0001ed09bead87c0ull | |
2074 | && coeff.w[0] == 0x378d8e6400000000ull) { | |
2075 | expon++; | |
2076 | // set coefficient to 10^33 | |
2077 | coeff.w[1] = 0x0000314dc6448d93ull; | |
2078 | coeff.w[0] = 0x38c15b0a00000000ull; | |
2079 | } | |
2080 | // check OF, UF | |
2081 | if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { | |
2082 | // check UF | |
2083 | if (expon < 0) | |
2084 | return handle_UF_128 (pres, sgn, expon, coeff, &rmode, &status); | |
2085 | ||
2086 | // OF | |
2087 | ||
2088 | if (expon < DECIMAL_MAX_EXPON_128 + 34) { | |
2089 | while (expon > DECIMAL_MAX_EXPON_128 && | |
84d1fc49 | 2090 | (coeff.w[1] < power10_table_128[33].w[1] || |
2091 | (coeff.w[1] == power10_table_128[33].w[1] | |
2092 | && coeff.w[0] < power10_table_128[33].w[0]))) { | |
9b6b0236 | 2093 | D2.w[1] = (coeff.w[1] << 1) | (coeff.w[0] >> 63); |
2094 | D2.w[0] = coeff.w[0] << 1; | |
2095 | D8.w[1] = (coeff.w[1] << 3) | (coeff.w[0] >> 61); | |
2096 | D8.w[0] = coeff.w[0] << 3; | |
2097 | ||
2098 | __add_128_128 (coeff, D2, D8); | |
2099 | expon--; | |
2100 | } | |
2101 | } else if (!(coeff.w[0] | coeff.w[1])) | |
2102 | expon = DECIMAL_MAX_EXPON_128; | |
2103 | ||
2104 | if (expon > DECIMAL_MAX_EXPON_128) { | |
2105 | pres->w[1] = sgn | INFINITY_MASK64; | |
2106 | pres->w[0] = 0; | |
2107 | switch (rmode) { | |
2108 | case ROUNDING_DOWN: | |
2109 | if (!sgn) { | |
2110 | pres->w[1] = LARGEST_BID128_HIGH; | |
2111 | pres->w[0] = LARGEST_BID128_LOW; | |
2112 | } | |
2113 | break; | |
2114 | case ROUNDING_TO_ZERO: | |
2115 | pres->w[1] = sgn | LARGEST_BID128_HIGH; | |
2116 | pres->w[0] = LARGEST_BID128_LOW; | |
2117 | break; | |
2118 | case ROUNDING_UP: | |
2119 | // round up | |
2120 | if (sgn) { | |
2121 | pres->w[1] = sgn | LARGEST_BID128_HIGH; | |
2122 | pres->w[0] = LARGEST_BID128_LOW; | |
2123 | } | |
2124 | break; | |
2125 | } | |
2126 | ||
2127 | return pres; | |
2128 | } | |
2129 | } | |
2130 | ||
2131 | pres->w[0] = coeff.w[0]; | |
2132 | tmp = expon; | |
2133 | tmp <<= 49; | |
2134 | pres->w[1] = sgn | tmp | coeff.w[1]; | |
2135 | ||
2136 | return pres; | |
2137 | } | |
2138 | ||
2139 | ||
2140 | ||
2141 | /***************************************************************************** | |
2142 | * | |
2143 | * BID32 pack/unpack macros | |
2144 | * | |
2145 | *****************************************************************************/ | |
2146 | ||
2147 | ||
2148 | __BID_INLINE__ UINT32 | |
2149 | unpack_BID32 (UINT32 * psign_x, int *pexponent_x, | |
2150 | UINT32 * pcoefficient_x, UINT32 x) { | |
2151 | UINT32 tmp; | |
2152 | ||
2153 | *psign_x = x & 0x80000000; | |
2154 | ||
2155 | if ((x & SPECIAL_ENCODING_MASK32) == SPECIAL_ENCODING_MASK32) { | |
2156 | // special encodings | |
84d1fc49 | 2157 | if ((x & INFINITY_MASK32) == INFINITY_MASK32) { |
2158 | *pcoefficient_x = x & 0xfe0fffff; | |
2159 | if ((x & 0x000fffff) >= 1000000) | |
2160 | *pcoefficient_x = x & 0xfe000000; | |
2161 | if ((x & NAN_MASK32) == INFINITY_MASK32) | |
2162 | *pcoefficient_x = x & 0xf8000000; | |
2163 | *pexponent_x = 0; | |
9b6b0236 | 2164 | return 0; // NaN or Infinity |
84d1fc49 | 2165 | } |
9b6b0236 | 2166 | // coefficient |
2167 | *pcoefficient_x = (x & SMALL_COEFF_MASK32) | LARGE_COEFF_HIGH_BIT32; | |
2168 | // check for non-canonical value | |
2169 | if (*pcoefficient_x >= 10000000) | |
2170 | *pcoefficient_x = 0; | |
2171 | // get exponent | |
2172 | tmp = x >> 21; | |
2173 | *pexponent_x = tmp & EXPONENT_MASK32; | |
2174 | return 1; | |
2175 | } | |
2176 | // exponent | |
2177 | tmp = x >> 23; | |
2178 | *pexponent_x = tmp & EXPONENT_MASK32; | |
2179 | // coefficient | |
2180 | *pcoefficient_x = (x & LARGE_COEFF_MASK32); | |
2181 | ||
2182 | return *pcoefficient_x; | |
2183 | } | |
2184 | ||
2185 | // | |
2186 | // General pack macro for BID32 | |
2187 | // | |
2188 | __BID_INLINE__ UINT32 | |
2189 | get_BID32 (UINT32 sgn, int expon, UINT64 coeff, int rmode, | |
2190 | unsigned *fpsc) { | |
2191 | UINT128 Q; | |
2192 | UINT64 C64, remainder_h, carry, Stemp; | |
2193 | UINT32 r, mask; | |
2194 | int extra_digits, amount, amount2; | |
2195 | unsigned status; | |
2196 | ||
2197 | if (coeff > 9999999ull) { | |
2198 | expon++; | |
2199 | coeff = 1000000ull; | |
2200 | } | |
2201 | // check for possible underflow/overflow | |
2202 | if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { | |
2203 | if (expon < 0) { | |
2204 | // underflow | |
2205 | if (expon + MAX_FORMAT_DIGITS_32 < 0) { | |
2206 | #ifdef SET_STATUS_FLAGS | |
2207 | __set_status_flags (fpsc, | |
2208 | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
2209 | #endif | |
2210 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
2211 | #ifndef IEEE_ROUND_NEAREST | |
2212 | if (rmode == ROUNDING_DOWN && sgn) | |
2213 | return 0x80000001; | |
2214 | if (rmode == ROUNDING_UP && !sgn) | |
2215 | return 1; | |
2216 | #endif | |
2217 | #endif | |
2218 | // result is 0 | |
2219 | return sgn; | |
2220 | } | |
2221 | // get digits to be shifted out | |
2222 | #ifdef IEEE_ROUND_NEAREST_TIES_AWAY | |
2223 | rmode = 0; | |
2224 | #endif | |
2225 | #ifdef IEEE_ROUND_NEAREST | |
2226 | rmode = 0; | |
84d1fc49 | 2227 | #endif |
2228 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
2229 | #ifndef IEEE_ROUND_NEAREST | |
2230 | if (sgn && (unsigned) (rmode - 1) < 2) | |
2231 | rmode = 3 - rmode; | |
2232 | #endif | |
9b6b0236 | 2233 | #endif |
2234 | ||
2235 | extra_digits = -expon; | |
84d1fc49 | 2236 | coeff += round_const_table[rmode][extra_digits]; |
9b6b0236 | 2237 | |
2238 | // get coeff*(2^M[extra_digits])/10^extra_digits | |
84d1fc49 | 2239 | __mul_64x64_to_128 (Q, coeff, reciprocals10_64[extra_digits]); |
9b6b0236 | 2240 | |
2241 | // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 | |
84d1fc49 | 2242 | amount = short_recip_scale[extra_digits]; |
9b6b0236 | 2243 | |
2244 | C64 = Q.w[1] >> amount; | |
2245 | ||
2246 | #ifndef IEEE_ROUND_NEAREST_TIES_AWAY | |
2247 | #ifndef IEEE_ROUND_NEAREST | |
84d1fc49 | 2248 | if (rmode == 0) //ROUNDING_TO_NEAREST |
9b6b0236 | 2249 | #endif |
2250 | if (C64 & 1) { | |
2251 | // check whether fractional part of initial_P/10^extra_digits is exactly .5 | |
2252 | ||
2253 | // get remainder | |
2254 | amount2 = 64 - amount; | |
2255 | remainder_h = 0; | |
2256 | remainder_h--; | |
2257 | remainder_h >>= amount2; | |
2258 | remainder_h = remainder_h & Q.w[1]; | |
2259 | ||
84d1fc49 | 2260 | if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) { |
9b6b0236 | 2261 | C64--; |
2262 | } | |
2263 | } | |
2264 | #endif | |
2265 | ||
2266 | #ifdef SET_STATUS_FLAGS | |
2267 | ||
2268 | if (is_inexact (fpsc)) | |
2269 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); | |
2270 | else { | |
2271 | status = INEXACT_EXCEPTION; | |
2272 | // get remainder | |
2273 | remainder_h = Q.w[1] << (64 - amount); | |
2274 | ||
2275 | switch (rmode) { | |
2276 | case ROUNDING_TO_NEAREST: | |
2277 | case ROUNDING_TIES_AWAY: | |
2278 | // test whether fractional part is 0 | |
2279 | if (remainder_h == 0x8000000000000000ull | |
84d1fc49 | 2280 | && (Q.w[0] < reciprocals10_64[extra_digits])) |
9b6b0236 | 2281 | status = EXACT_STATUS; |
2282 | break; | |
2283 | case ROUNDING_DOWN: | |
2284 | case ROUNDING_TO_ZERO: | |
84d1fc49 | 2285 | if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) |
9b6b0236 | 2286 | status = EXACT_STATUS; |
2287 | break; | |
2288 | default: | |
2289 | // round up | |
2290 | __add_carry_out (Stemp, carry, Q.w[0], | |
84d1fc49 | 2291 | reciprocals10_64[extra_digits]); |
9b6b0236 | 2292 | if ((remainder_h >> (64 - amount)) + carry >= |
2293 | (((UINT64) 1) << amount)) | |
2294 | status = EXACT_STATUS; | |
2295 | } | |
2296 | ||
2297 | if (status != EXACT_STATUS) | |
2298 | __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); | |
2299 | } | |
2300 | ||
2301 | #endif | |
2302 | ||
2303 | return sgn | (UINT32) C64; | |
2304 | } | |
2305 | ||
2306 | while (coeff < 1000000 && expon > DECIMAL_MAX_EXPON_32) { | |
2307 | coeff = (coeff << 3) + (coeff << 1); | |
2308 | expon--; | |
2309 | } | |
2310 | if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { | |
2311 | __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); | |
2312 | // overflow | |
2313 | r = sgn | INFINITY_MASK32; | |
2314 | switch (rmode) { | |
2315 | case ROUNDING_DOWN: | |
2316 | if (!sgn) | |
2317 | r = LARGEST_BID32; | |
2318 | break; | |
2319 | case ROUNDING_TO_ZERO: | |
2320 | r = sgn | LARGEST_BID32; | |
2321 | break; | |
2322 | case ROUNDING_UP: | |
2323 | // round up | |
2324 | if (sgn) | |
2325 | r = sgn | LARGEST_BID32; | |
2326 | } | |
2327 | return r; | |
2328 | } | |
2329 | } | |
2330 | ||
2331 | mask = 1 << 23; | |
2332 | ||
2333 | // check whether coefficient fits in DECIMAL_COEFF_FIT bits | |
2334 | if (coeff < mask) { | |
2335 | r = expon; | |
2336 | r <<= 23; | |
2337 | r |= ((UINT32) coeff | sgn); | |
2338 | return r; | |
2339 | } | |
2340 | // special format | |
2341 | ||
2342 | r = expon; | |
2343 | r <<= 21; | |
2344 | r |= (sgn | SPECIAL_ENCODING_MASK32); | |
2345 | // add coeff, without leading bits | |
2346 | mask = (1 << 21) - 1; | |
2347 | r |= (((UINT32) coeff) & mask); | |
2348 | ||
2349 | return r; | |
2350 | } | |
2351 | ||
2352 | ||
2353 | ||
2354 | // | |
2355 | // no overflow/underflow checks | |
2356 | // | |
2357 | __BID_INLINE__ UINT32 | |
2358 | very_fast_get_BID32 (UINT32 sgn, int expon, UINT32 coeff) { | |
2359 | UINT32 r, mask; | |
2360 | ||
2361 | mask = 1 << 23; | |
2362 | ||
2363 | // check whether coefficient fits in 10*2+3 bits | |
2364 | if (coeff < mask) { | |
2365 | r = expon; | |
2366 | r <<= 23; | |
2367 | r |= (coeff | sgn); | |
2368 | return r; | |
2369 | } | |
2370 | // special format | |
2371 | r = expon; | |
2372 | r <<= 21; | |
2373 | r |= (sgn | SPECIAL_ENCODING_MASK32); | |
2374 | // add coeff, without leading bits | |
2375 | mask = (1 << 21) - 1; | |
2376 | coeff &= mask; | |
2377 | r |= coeff; | |
2378 | ||
2379 | return r; | |
2380 | } | |
2381 | ||
2382 | ||
2383 | ||
2384 | /************************************************************* | |
2385 | * | |
2386 | *************************************************************/ | |
2387 | typedef | |
2388 | ALIGN (16) | |
2389 | struct { | |
2390 | UINT64 w[6]; | |
2391 | } UINT384; | |
2392 | typedef ALIGN (16) | |
2393 | struct { | |
2394 | UINT64 w[8]; | |
2395 | } UINT512; | |
2396 | ||
2397 | // #define P 34 | |
2398 | #define MASK_STEERING_BITS 0x6000000000000000ull | |
2399 | #define MASK_BINARY_EXPONENT1 0x7fe0000000000000ull | |
2400 | #define MASK_BINARY_SIG1 0x001fffffffffffffull | |
2401 | #define MASK_BINARY_EXPONENT2 0x1ff8000000000000ull | |
2402 | //used to take G[2:w+3] (sec 3.3) | |
2403 | #define MASK_BINARY_SIG2 0x0007ffffffffffffull | |
2404 | //used to mask out G4:T0 (sec 3.3) | |
2405 | #define MASK_BINARY_OR2 0x0020000000000000ull | |
2406 | //used to prefix 8+G4 to T (sec 3.3) | |
2407 | #define UPPER_EXPON_LIMIT 51 | |
2408 | #define MASK_EXP 0x7ffe000000000000ull | |
2409 | #define MASK_SPECIAL 0x7800000000000000ull | |
2410 | #define MASK_NAN 0x7c00000000000000ull | |
2411 | #define MASK_SNAN 0x7e00000000000000ull | |
2412 | #define MASK_ANY_INF 0x7c00000000000000ull | |
2413 | #define MASK_INF 0x7800000000000000ull | |
2414 | #define MASK_SIGN 0x8000000000000000ull | |
2415 | #define MASK_COEFF 0x0001ffffffffffffull | |
2416 | #define BIN_EXP_BIAS (0x1820ull << 49) | |
2417 | ||
2418 | #define EXP_MIN 0x0000000000000000ull | |
2419 | // EXP_MIN = (-6176 + 6176) << 49 | |
2420 | #define EXP_MAX 0x5ffe000000000000ull | |
2421 | // EXP_MAX = (6111 + 6176) << 49 | |
2422 | #define EXP_MAX_P1 0x6000000000000000ull | |
2423 | // EXP_MAX + 1 = (6111 + 6176 + 1) << 49 | |
2424 | #define EXP_P1 0x0002000000000000ull | |
2425 | // EXP_ P1= 1 << 49 | |
2426 | #define expmin -6176 | |
2427 | // min unbiased exponent | |
2428 | #define expmax 6111 | |
2429 | // max unbiased exponent | |
2430 | #define expmin16 -398 | |
2431 | // min unbiased exponent | |
2432 | #define expmax16 369 | |
2433 | // max unbiased exponent | |
2434 | ||
2435 | #define SIGNMASK32 0x80000000 | |
2436 | #define BID64_SIG_MAX 0x002386F26FC0ffffull | |
2437 | #define SIGNMASK64 0x8000000000000000ull | |
2438 | ||
2439 | // typedef unsigned int FPSC; // floating-point status and control | |
2440 | // bit31: | |
2441 | // bit30: | |
2442 | // bit29: | |
2443 | // bit28: | |
2444 | // bit27: | |
2445 | // bit26: | |
2446 | // bit25: | |
2447 | // bit24: | |
2448 | // bit23: | |
2449 | // bit22: | |
2450 | // bit21: | |
2451 | // bit20: | |
2452 | // bit19: | |
2453 | // bit18: | |
2454 | // bit17: | |
2455 | // bit16: | |
2456 | // bit15: | |
2457 | // bit14: RC:2 | |
2458 | // bit13: RC:1 | |
2459 | // bit12: RC:0 | |
2460 | // bit11: PM | |
2461 | // bit10: UM | |
2462 | // bit9: OM | |
2463 | // bit8: ZM | |
2464 | // bit7: DM | |
2465 | // bit6: IM | |
2466 | // bit5: PE | |
2467 | // bit4: UE | |
2468 | // bit3: OE | |
2469 | // bit2: ZE | |
2470 | // bit1: DE | |
2471 | // bit0: IE | |
2472 | ||
2473 | #define ROUNDING_MODE_MASK 0x00007000 | |
2474 | ||
2475 | typedef struct _DEC_DIGITS { | |
2476 | unsigned int digits; | |
2477 | UINT64 threshold_hi; | |
2478 | UINT64 threshold_lo; | |
2479 | unsigned int digits1; | |
2480 | } DEC_DIGITS; | |
2481 | ||
84d1fc49 | 2482 | extern DEC_DIGITS nr_digits[]; |
2483 | extern UINT64 midpoint64[]; | |
2484 | extern UINT128 midpoint128[]; | |
2485 | extern UINT192 midpoint192[]; | |
2486 | extern UINT256 midpoint256[]; | |
2487 | extern UINT64 ten2k64[]; | |
2488 | extern UINT128 ten2k128[]; | |
2489 | extern UINT256 ten2k256[]; | |
2490 | extern UINT128 ten2mk128[]; | |
2491 | extern UINT64 ten2mk64[]; | |
2492 | extern UINT128 ten2mk128trunc[]; | |
2493 | extern int shiftright128[]; | |
2494 | extern UINT64 maskhigh128[]; | |
2495 | extern UINT64 maskhigh128M[]; | |
2496 | extern UINT64 maskhigh192M[]; | |
2497 | extern UINT64 maskhigh256M[]; | |
2498 | extern UINT64 onehalf128[]; | |
2499 | extern UINT64 onehalf128M[]; | |
2500 | extern UINT64 onehalf192M[]; | |
2501 | extern UINT64 onehalf256M[]; | |
2502 | extern UINT128 ten2mk128M[]; | |
2503 | extern UINT128 ten2mk128truncM[]; | |
2504 | extern UINT192 ten2mk192truncM[]; | |
2505 | extern UINT256 ten2mk256truncM[]; | |
2506 | extern int shiftright128M[]; | |
2507 | extern int shiftright192M[]; | |
2508 | extern int shiftright256M[]; | |
2509 | extern UINT192 ten2mk192M[]; | |
2510 | extern UINT256 ten2mk256M[]; | |
2511 | extern unsigned char char_table2[]; | |
2512 | extern unsigned char char_table3[]; | |
2513 | ||
2514 | extern UINT64 ten2m3k64[]; | |
2515 | extern unsigned int shift_ten2m3k64[]; | |
2516 | extern UINT128 ten2m3k128[]; | |
2517 | extern unsigned int shift_ten2m3k128[]; | |
9b6b0236 | 2518 | |
2519 | ||
2520 | ||
2521 | /*************************************************************************** | |
2522 | *************** TABLES FOR GENERAL ROUNDING FUNCTIONS ********************* | |
2523 | ***************************************************************************/ | |
2524 | ||
84d1fc49 | 2525 | extern UINT64 Kx64[]; |
2526 | extern unsigned int Ex64m64[]; | |
2527 | extern UINT64 half64[]; | |
2528 | extern UINT64 mask64[]; | |
2529 | extern UINT64 ten2mxtrunc64[]; | |
2530 | ||
2531 | extern UINT128 Kx128[]; | |
2532 | extern unsigned int Ex128m128[]; | |
2533 | extern UINT64 half128[]; | |
2534 | extern UINT64 mask128[]; | |
2535 | extern UINT128 ten2mxtrunc128[]; | |
2536 | ||
2537 | extern UINT192 Kx192[]; | |
2538 | extern unsigned int Ex192m192[]; | |
2539 | extern UINT64 half192[]; | |
2540 | extern UINT64 mask192[]; | |
2541 | extern UINT192 ten2mxtrunc192[]; | |
2542 | ||
2543 | extern UINT256 Kx256[]; | |
2544 | extern unsigned int Ex256m256[]; | |
2545 | extern UINT64 half256[]; | |
2546 | extern UINT64 mask256[]; | |
2547 | extern UINT256 ten2mxtrunc256[]; | |
9b6b0236 | 2548 | |
2549 | typedef union __bid64_128 { | |
2550 | UINT64 b64; | |
2551 | UINT128 b128; | |
2552 | } BID64_128; | |
2553 | ||
2554 | BID64_128 bid_fma (unsigned int P0, | |
2555 | BID64_128 x1, unsigned int P1, | |
2556 | BID64_128 y1, unsigned int P2, | |
2557 | BID64_128 z1, unsigned int P3, | |
2558 | unsigned int rnd_mode, FPSC * fpsc); | |
2559 | ||
2560 | #define P16 16 | |
2561 | #define P34 34 | |
2562 | ||
2563 | union __int_double { | |
2564 | UINT64 i; | |
2565 | double d; | |
2566 | }; | |
2567 | typedef union __int_double int_double; | |
2568 | ||
2569 | ||
2570 | union __int_float { | |
2571 | UINT32 i; | |
2572 | float d; | |
2573 | }; | |
2574 | typedef union __int_float int_float; | |
2575 | ||
2576 | #define SWAP(A,B,T) {\ | |
2577 | T = A; \ | |
2578 | A = B; \ | |
2579 | B = T; \ | |
2580 | } | |
2581 | ||
2582 | // this macro will find coefficient_x to be in [2^A, 2^(A+1) ) | |
2583 | // ie it knows that it is A bits long | |
2584 | #define NUMBITS(A, coefficient_x, tempx){\ | |
2585 | temp_x.d=(float)coefficient_x;\ | |
2586 | A=((tempx.i >>23) & EXPONENT_MASK32) - 0x7f;\ | |
2587 | } | |
2588 | ||
2589 | enum class_types { | |
2590 | signalingNaN, | |
2591 | quietNaN, | |
2592 | negativeInfinity, | |
2593 | negativeNormal, | |
2594 | negativeSubnormal, | |
2595 | negativeZero, | |
2596 | positiveZero, | |
2597 | positiveSubnormal, | |
2598 | positiveNormal, | |
2599 | positiveInfinity | |
2600 | }; | |
2601 | ||
84d1fc49 | 2602 | typedef union { |
2603 | UINT64 ui64; | |
2604 | double d; | |
2605 | } BID_UI64DOUBLE; | |
9b6b0236 | 2606 | |
84d1fc49 | 2607 | #endif |