projects / thirdparty / gcc.git / blame
| Commit | Line | Data |
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| 748086b7 | 1 | /* Copyright (C) 2007, 2009 Free Software Foundation, Inc. |
| 200359e8 L |
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 | |
| 748086b7 | 7 | Software Foundation; either version 3, or (at your option) any later |
| 200359e8 L |
8 | version. |
| 9 | ||
| 200359e8 L |
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 | ||
| 748086b7 JJ |
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/>. */ | |
| 200359e8 | 23 | |
| b2a00c89 L |
24 | #include "bid_internal.h" |
| 25 | ||
| 26 | ||
| 27 | #if DECIMAL_CALL_BY_REFERENCE | |
| 28 | void | |
| 29 | bid64dq_add (UINT64 * pres, UINT64 * px, UINT128 * py | |
| 30 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 31 | _EXC_INFO_PARAM) { | |
| 32 | UINT64 x = *px; | |
| 33 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 34 | unsigned int rnd_mode = *prnd_mode; | |
| 35 | #endif | |
| 36 | #else | |
| 37 | UINT64 | |
| 38 | bid64dq_add (UINT64 x, UINT128 y | |
| 39 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 40 | _EXC_INFO_PARAM) { | |
| 41 | #endif | |
| 42 | UINT64 res = 0xbaddbaddbaddbaddull; | |
| 43 | UINT128 x1; | |
| 44 | ||
| 45 | #if DECIMAL_CALL_BY_REFERENCE | |
| 46 | bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 47 | bid64qq_add (&res, &x1, py | |
| 48 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 49 | _EXC_INFO_ARG); | |
| 50 | #else | |
| 51 | x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 52 | res = bid64qq_add (x1, y | |
| 53 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 54 | _EXC_INFO_ARG); | |
| 55 | #endif | |
| 56 | BID_RETURN (res); | |
| 57 | } | |
| 58 | ||
| 59 | ||
| 60 | #if DECIMAL_CALL_BY_REFERENCE | |
| 61 | void | |
| 62 | bid64qd_add (UINT64 * pres, UINT128 * px, UINT64 * py | |
| 63 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 64 | _EXC_INFO_PARAM) { | |
| 65 | UINT64 y = *py; | |
| 66 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 67 | unsigned int rnd_mode = *prnd_mode; | |
| 68 | #endif | |
| 69 | #else | |
| 70 | UINT64 | |
| 71 | bid64qd_add (UINT128 x, UINT64 y | |
| 72 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 73 | _EXC_INFO_PARAM) { | |
| 74 | #endif | |
| 75 | UINT64 res = 0xbaddbaddbaddbaddull; | |
| 76 | UINT128 y1; | |
| 77 | ||
| 78 | #if DECIMAL_CALL_BY_REFERENCE | |
| 79 | bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 80 | bid64qq_add (&res, px, &y1 | |
| 81 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 82 | _EXC_INFO_ARG); | |
| 83 | #else | |
| 84 | y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 85 | res = bid64qq_add (x, y1 | |
| 86 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 87 | _EXC_INFO_ARG); | |
| 88 | #endif | |
| 89 | BID_RETURN (res); | |
| 90 | } | |
| 91 | ||
| 92 | ||
| 93 | #if DECIMAL_CALL_BY_REFERENCE | |
| 94 | void | |
| 95 | bid64qq_add (UINT64 * pres, UINT128 * px, UINT128 * py | |
| 96 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 97 | _EXC_INFO_PARAM) { | |
| 98 | UINT128 x = *px, y = *py; | |
| 99 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 100 | unsigned int rnd_mode = *prnd_mode; | |
| 101 | #endif | |
| 102 | #else | |
| 103 | UINT64 | |
| 104 | bid64qq_add (UINT128 x, UINT128 y | |
| 105 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 106 | _EXC_INFO_PARAM) { | |
| 107 | #endif | |
| 108 | ||
| 109 | UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull} | |
| 110 | }; | |
| 111 | UINT64 res = 0xbaddbaddbaddbaddull; | |
| 112 | ||
| 113 | BID_SWAP128 (one); | |
| 114 | #if DECIMAL_CALL_BY_REFERENCE | |
| 115 | bid64qqq_fma (&res, &one, &x, &y | |
| 116 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 117 | _EXC_INFO_ARG); | |
| 118 | #else | |
| 119 | res = bid64qqq_fma (one, x, y | |
| 120 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 121 | _EXC_INFO_ARG); | |
| 122 | #endif | |
| 123 | BID_RETURN (res); | |
| 124 | } | |
| 125 | ||
| 126 | ||
| 127 | #if DECIMAL_CALL_BY_REFERENCE | |
| 128 | void | |
| 129 | bid128dd_add (UINT128 * pres, UINT64 * px, UINT64 * py | |
| 130 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 131 | _EXC_INFO_PARAM) { | |
| 132 | UINT64 x = *px, y = *py; | |
| 133 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 134 | unsigned int rnd_mode = *prnd_mode; | |
| 135 | #endif | |
| 136 | #else | |
| 137 | UINT128 | |
| 138 | bid128dd_add (UINT64 x, UINT64 y | |
| 139 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 140 | _EXC_INFO_PARAM) { | |
| 141 | #endif | |
| 142 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} | |
| 143 | }; | |
| 144 | UINT128 x1, y1; | |
| 145 | ||
| 146 | #if DECIMAL_CALL_BY_REFERENCE | |
| 147 | bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 148 | bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 149 | bid128_add (&res, &x1, &y1 | |
| 150 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 151 | _EXC_INFO_ARG); | |
| 152 | #else | |
| 153 | x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 154 | y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 155 | res = bid128_add (x1, y1 | |
| 156 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 157 | _EXC_INFO_ARG); | |
| 158 | #endif | |
| 159 | BID_RETURN (res); | |
| 160 | } | |
| 161 | ||
| 162 | ||
| 163 | #if DECIMAL_CALL_BY_REFERENCE | |
| 164 | void | |
| 165 | bid128dq_add (UINT128 * pres, UINT64 * px, UINT128 * py | |
| 166 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 167 | _EXC_INFO_PARAM) { | |
| 168 | UINT64 x = *px; | |
| 169 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 170 | unsigned int rnd_mode = *prnd_mode; | |
| 171 | #endif | |
| 172 | #else | |
| 173 | UINT128 | |
| 174 | bid128dq_add (UINT64 x, UINT128 y | |
| 175 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 176 | _EXC_INFO_PARAM) { | |
| 177 | #endif | |
| 178 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} | |
| 179 | }; | |
| 180 | UINT128 x1; | |
| 181 | ||
| 182 | #if DECIMAL_CALL_BY_REFERENCE | |
| 183 | bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 184 | bid128_add (&res, &x1, py | |
| 185 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 186 | _EXC_INFO_ARG); | |
| 187 | #else | |
| 188 | x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 189 | res = bid128_add (x1, y | |
| 190 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 191 | _EXC_INFO_ARG); | |
| 192 | #endif | |
| 193 | BID_RETURN (res); | |
| 194 | } | |
| 195 | ||
| 196 | ||
| 197 | #if DECIMAL_CALL_BY_REFERENCE | |
| 198 | void | |
| 199 | bid128qd_add (UINT128 * pres, UINT128 * px, UINT64 * py | |
| 200 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 201 | _EXC_INFO_PARAM) { | |
| 202 | UINT64 y = *py; | |
| 203 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 204 | unsigned int rnd_mode = *prnd_mode; | |
| 205 | #endif | |
| 206 | #else | |
| 207 | UINT128 | |
| 208 | bid128qd_add (UINT128 x, UINT64 y | |
| 209 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 210 | _EXC_INFO_PARAM) { | |
| 211 | #endif | |
| 212 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} | |
| 213 | }; | |
| 214 | UINT128 y1; | |
| 215 | ||
| 216 | #if DECIMAL_CALL_BY_REFERENCE | |
| 217 | bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 218 | bid128_add (&res, px, &y1 | |
| 219 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 220 | _EXC_INFO_ARG); | |
| 221 | #else | |
| 222 | y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 223 | res = bid128_add (x, y1 | |
| 224 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 225 | _EXC_INFO_ARG); | |
| 226 | #endif | |
| 227 | BID_RETURN (res); | |
| 228 | } | |
| 229 | ||
| 230 | ||
| 231 | // bid128_add stands for bid128qq_add | |
| 232 | ||
| 233 | ||
| 200359e8 | 234 | /***************************************************************************** |
| b2a00c89 | 235 | * BID64/BID128 sub |
| 200359e8 L |
236 | ****************************************************************************/ |
| 237 | ||
| b2a00c89 L |
238 | #if DECIMAL_CALL_BY_REFERENCE |
| 239 | void | |
| 240 | bid64dq_sub (UINT64 * pres, UINT64 * px, UINT128 * py | |
| 241 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 242 | _EXC_INFO_PARAM) { | |
| 243 | UINT64 x = *px; | |
| 244 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 245 | unsigned int rnd_mode = *prnd_mode; | |
| 246 | #endif | |
| 247 | #else | |
| 248 | UINT64 | |
| 249 | bid64dq_sub (UINT64 x, UINT128 y | |
| 250 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 251 | _EXC_INFO_PARAM) { | |
| 252 | #endif | |
| 253 | UINT64 res = 0xbaddbaddbaddbaddull; | |
| 254 | UINT128 x1; | |
| 255 | ||
| 256 | #if DECIMAL_CALL_BY_REFERENCE | |
| 257 | bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 258 | bid64qq_sub (&res, &x1, py | |
| 259 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 260 | _EXC_INFO_ARG); | |
| 261 | #else | |
| 262 | x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 263 | res = bid64qq_sub (x1, y | |
| 264 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 265 | _EXC_INFO_ARG); | |
| 266 | #endif | |
| 267 | BID_RETURN (res); | |
| 268 | } | |
| 269 | ||
| 270 | ||
| 271 | #if DECIMAL_CALL_BY_REFERENCE | |
| 272 | void | |
| 273 | bid64qd_sub (UINT64 * pres, UINT128 * px, UINT64 * py | |
| 274 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 275 | _EXC_INFO_PARAM) { | |
| 276 | UINT64 y = *py; | |
| 277 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 278 | unsigned int rnd_mode = *prnd_mode; | |
| 279 | #endif | |
| 280 | #else | |
| 281 | UINT64 | |
| 282 | bid64qd_sub (UINT128 x, UINT64 y | |
| 283 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 284 | _EXC_INFO_PARAM) { | |
| 285 | #endif | |
| 286 | UINT64 res = 0xbaddbaddbaddbaddull; | |
| 287 | UINT128 y1; | |
| 288 | ||
| 289 | #if DECIMAL_CALL_BY_REFERENCE | |
| 290 | bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 291 | bid64qq_sub (&res, px, &y1 | |
| 292 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 293 | _EXC_INFO_ARG); | |
| 294 | #else | |
| 295 | y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 296 | res = bid64qq_sub (x, y1 | |
| 297 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 298 | _EXC_INFO_ARG); | |
| 299 | #endif | |
| 300 | BID_RETURN (res); | |
| 301 | } | |
| 302 | ||
| 200359e8 L |
303 | |
| 304 | #if DECIMAL_CALL_BY_REFERENCE | |
| 305 | void | |
| b2a00c89 L |
306 | bid64qq_sub (UINT64 * pres, UINT128 * px, UINT128 * py |
| 307 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 308 | _EXC_INFO_PARAM) { | |
| 200359e8 L |
309 | UINT128 x = *px, y = *py; |
| 310 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 311 | unsigned int rnd_mode = *prnd_mode; | |
| 312 | #endif | |
| 313 | #else | |
| b2a00c89 L |
314 | UINT64 |
| 315 | bid64qq_sub (UINT128 x, UINT128 y | |
| 316 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 317 | _EXC_INFO_PARAM) { | |
| 318 | #endif | |
| 319 | ||
| 320 | UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull} | |
| 321 | }; | |
| 322 | UINT64 res = 0xbaddbaddbaddbaddull; | |
| 323 | UINT64 y_sign; | |
| 324 | ||
| 325 | BID_SWAP128 (one); | |
| 326 | if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) { // y is not NAN | |
| 327 | // change its sign | |
| 328 | y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative | |
| 329 | if (y_sign) | |
| 330 | y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull; | |
| 331 | else | |
| 332 | y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull; | |
| 333 | } | |
| 334 | #if DECIMAL_CALL_BY_REFERENCE | |
| 335 | bid64qqq_fma (&res, &one, &x, &y | |
| 336 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 337 | _EXC_INFO_ARG); | |
| 338 | #else | |
| 339 | res = bid64qqq_fma (one, x, y | |
| 340 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 341 | _EXC_INFO_ARG); | |
| 342 | #endif | |
| 343 | BID_RETURN (res); | |
| 344 | } | |
| 345 | ||
| 346 | ||
| 347 | #if DECIMAL_CALL_BY_REFERENCE | |
| 348 | void | |
| 349 | bid128dd_sub (UINT128 * pres, UINT64 * px, UINT64 * py | |
| 350 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 351 | _EXC_INFO_PARAM) { | |
| 352 | UINT64 x = *px, y = *py; | |
| 353 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 354 | unsigned int rnd_mode = *prnd_mode; | |
| 355 | #endif | |
| 356 | #else | |
| 200359e8 | 357 | UINT128 |
| b2a00c89 L |
358 | bid128dd_sub (UINT64 x, UINT64 y |
| 359 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 360 | _EXC_INFO_PARAM) { | |
| 200359e8 | 361 | #endif |
| b2a00c89 L |
362 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} |
| 363 | }; | |
| 364 | UINT128 x1, y1; | |
| 200359e8 | 365 | |
| b2a00c89 L |
366 | #if DECIMAL_CALL_BY_REFERENCE |
| 367 | bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 368 | bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 369 | bid128_sub (&res, &x1, &y1 | |
| 370 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 371 | _EXC_INFO_ARG); | |
| 372 | #else | |
| 373 | x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 374 | y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 375 | res = bid128_sub (x1, y1 | |
| 376 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 377 | _EXC_INFO_ARG); | |
| 378 | #endif | |
| 379 | BID_RETURN (res); | |
| 380 | } | |
| 381 | ||
| 382 | ||
| 383 | #if DECIMAL_CALL_BY_REFERENCE | |
| 384 | void | |
| 385 | bid128dq_sub (UINT128 * pres, UINT64 * px, UINT128 * py | |
| 386 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 387 | _EXC_INFO_PARAM) { | |
| 388 | UINT64 x = *px; | |
| 389 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 390 | unsigned int rnd_mode = *prnd_mode; | |
| 391 | #endif | |
| 392 | #else | |
| 393 | UINT128 | |
| 394 | bid128dq_sub (UINT64 x, UINT128 y | |
| 395 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 396 | _EXC_INFO_PARAM) { | |
| 397 | #endif | |
| 398 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} | |
| 399 | }; | |
| 400 | UINT128 x1; | |
| 401 | ||
| 402 | #if DECIMAL_CALL_BY_REFERENCE | |
| 403 | bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 404 | bid128_sub (&res, &x1, py | |
| 405 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 406 | _EXC_INFO_ARG); | |
| 407 | #else | |
| 408 | x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 409 | res = bid128_sub (x1, y | |
| 410 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 411 | _EXC_INFO_ARG); | |
| 412 | #endif | |
| 413 | BID_RETURN (res); | |
| 414 | } | |
| 415 | ||
| 416 | ||
| 417 | #if DECIMAL_CALL_BY_REFERENCE | |
| 418 | void | |
| 419 | bid128qd_sub (UINT128 * pres, UINT128 * px, UINT64 * py | |
| 420 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 421 | _EXC_INFO_PARAM) { | |
| 422 | UINT64 y = *py; | |
| 423 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 424 | unsigned int rnd_mode = *prnd_mode; | |
| 425 | #endif | |
| 426 | #else | |
| 427 | UINT128 | |
| 428 | bid128qd_sub (UINT128 x, UINT64 y | |
| 429 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 430 | _EXC_INFO_PARAM) { | |
| 431 | #endif | |
| 432 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} | |
| 433 | }; | |
| 434 | UINT128 y1; | |
| 435 | ||
| 436 | #if DECIMAL_CALL_BY_REFERENCE | |
| 437 | bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 438 | bid128_sub (&res, px, &y1 | |
| 439 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 440 | _EXC_INFO_ARG); | |
| 441 | #else | |
| 442 | y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); | |
| 443 | res = bid128_sub (x, y1 | |
| 444 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 445 | _EXC_INFO_ARG); | |
| 446 | #endif | |
| 447 | BID_RETURN (res); | |
| 448 | } | |
| 449 | ||
| 450 | #if DECIMAL_CALL_BY_REFERENCE | |
| 451 | void | |
| 452 | bid128_add (UINT128 * pres, UINT128 * px, UINT128 * py | |
| 453 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 454 | _EXC_INFO_PARAM) { | |
| 455 | UINT128 x = *px, y = *py; | |
| 456 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 457 | unsigned int rnd_mode = *prnd_mode; | |
| 458 | #endif | |
| 459 | #else | |
| 460 | UINT128 | |
| 461 | bid128_add (UINT128 x, UINT128 y | |
| 462 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 463 | _EXC_INFO_PARAM) { | |
| 464 | #endif | |
| 465 | UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} | |
| 466 | }; | |
| 200359e8 | 467 | UINT64 x_sign, y_sign, tmp_sign; |
| b2a00c89 | 468 | UINT64 x_exp, y_exp, tmp_exp; // e1 = x_exp, e2 = y_exp |
| 200359e8 L |
469 | UINT64 C1_hi, C2_hi, tmp_signif_hi; |
| 470 | UINT64 C1_lo, C2_lo, tmp_signif_lo; | |
| b2a00c89 L |
471 | // Note: C1.w[1], C1.w[0] represent C1_hi, C1_lo (all UINT64) |
| 472 | // Note: C2.w[1], C2.w[0] represent C2_hi, C2_lo (all UINT64) | |
| 200359e8 L |
473 | UINT64 tmp64, tmp64A, tmp64B; |
| 474 | BID_UI64DOUBLE tmp1, tmp2; | |
| 475 | int x_nr_bits, y_nr_bits; | |
| 476 | int q1, q2, delta, scale, x1, ind, shift, tmp_inexact = 0; | |
| 477 | UINT64 halfulp64; | |
| 478 | UINT128 halfulp128; | |
| 479 | UINT128 C1, C2; | |
| b2a00c89 L |
480 | UINT128 ten2m1; |
| 481 | UINT128 highf2star; // top 128 bits in f2*; low 128 bits in R256[1], R256[0] | |
| 200359e8 L |
482 | UINT256 P256, Q256, R256; |
| 483 | int is_inexact = 0, is_midpoint_lt_even = 0, is_midpoint_gt_even = 0; | |
| 484 | int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; | |
| 485 | int second_pass = 0; | |
| 486 | ||
| b2a00c89 L |
487 | BID_SWAP128 (x); |
| 488 | BID_SWAP128 (y); | |
| 489 | x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative | |
| 490 | y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative | |
| 491 | ||
| 200359e8 L |
492 | // check for NaN or Infinity |
| 493 | if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) | |
| 494 | || ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) { | |
| 495 | // x is special or y is special | |
| b2a00c89 L |
496 | if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| 497 | // check first for non-canonical NaN payload | |
| 498 | if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || | |
| 499 | (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) | |
| 500 | && (x.w[0] > 0x38c15b09ffffffffull))) { | |
| 501 | x.w[1] = x.w[1] & 0xffffc00000000000ull; | |
| 502 | x.w[0] = 0x0ull; | |
| 200359e8 | 503 | } |
| b2a00c89 L |
504 | if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| 505 | // set invalid flag | |
| 506 | *pfpsf |= INVALID_EXCEPTION; | |
| 507 | // return quiet (x) | |
| 508 | res.w[1] = x.w[1] & 0xfc003fffffffffffull; | |
| 509 | // clear out also G[6]-G[16] | |
| 510 | res.w[0] = x.w[0]; | |
| 511 | } else { // x is QNaN | |
| 512 | // return x | |
| 513 | res.w[1] = x.w[1] & 0xfc003fffffffffffull; | |
| 514 | // clear out G[6]-G[16] | |
| 515 | res.w[0] = x.w[0]; | |
| 516 | // if y = SNaN signal invalid exception | |
| 517 | if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { | |
| 518 | // set invalid flag | |
| 519 | *pfpsf |= INVALID_EXCEPTION; | |
| 520 | } | |
| 521 | } | |
| 522 | BID_SWAP128 (res); | |
| 200359e8 | 523 | BID_RETURN (res); |
| b2a00c89 L |
524 | } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN |
| 525 | // check first for non-canonical NaN payload | |
| 526 | if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || | |
| 527 | (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) | |
| 528 | && (y.w[0] > 0x38c15b09ffffffffull))) { | |
| 529 | y.w[1] = y.w[1] & 0xffffc00000000000ull; | |
| 530 | y.w[0] = 0x0ull; | |
| 531 | } | |
| 532 | if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN | |
| 533 | // set invalid flag | |
| 534 | *pfpsf |= INVALID_EXCEPTION; | |
| 535 | // return quiet (y) | |
| 536 | res.w[1] = y.w[1] & 0xfc003fffffffffffull; | |
| 537 | // clear out also G[6]-G[16] | |
| 538 | res.w[0] = y.w[0]; | |
| 539 | } else { // y is QNaN | |
| 540 | // return y | |
| 541 | res.w[1] = y.w[1] & 0xfc003fffffffffffull; | |
| 542 | // clear out G[6]-G[16] | |
| 543 | res.w[0] = y.w[0]; | |
| 200359e8 | 544 | } |
| b2a00c89 | 545 | BID_SWAP128 (res); |
| 200359e8 | 546 | BID_RETURN (res); |
| b2a00c89 L |
547 | } else { // neither x not y is NaN; at least one is infinity |
| 548 | if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x is infinity | |
| 549 | if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y is infinity | |
| 550 | // if same sign, return either of them | |
| 551 | if ((x.w[1] & MASK_SIGN) == (y.w[1] & MASK_SIGN)) { | |
| 552 | res.w[1] = x_sign | MASK_INF; | |
| 553 | res.w[0] = 0x0ull; | |
| 554 | } else { // x and y are infinities of opposite signs | |
| 555 | // set invalid flag | |
| 556 | *pfpsf |= INVALID_EXCEPTION; | |
| 557 | // return QNaN Indefinite | |
| 558 | res.w[1] = 0x7c00000000000000ull; | |
| 559 | res.w[0] = 0x0000000000000000ull; | |
| 560 | } | |
| 561 | } else { // y is 0 or finite | |
| 562 | // return x | |
| 563 | res.w[1] = x_sign | MASK_INF; | |
| 564 | res.w[0] = 0x0ull; | |
| 565 | } | |
| 566 | } else { // x is not NaN or infinity, so y must be infinity | |
| 567 | res.w[1] = y_sign | MASK_INF; | |
| 568 | res.w[0] = 0x0ull; | |
| 200359e8 | 569 | } |
| b2a00c89 | 570 | BID_SWAP128 (res); |
| 200359e8 L |
571 | BID_RETURN (res); |
| 572 | } | |
| 573 | } | |
| 574 | // unpack the arguments | |
| b2a00c89 | 575 | |
| 200359e8 | 576 | // unpack x |
| 200359e8 L |
577 | C1_hi = x.w[1] & MASK_COEFF; |
| 578 | C1_lo = x.w[0]; | |
| 200359e8 L |
579 | // test for non-canonical values: |
| 580 | // - values whose encoding begins with x00, x01, or x10 and whose | |
| 581 | // coefficient is larger than 10^34 -1, or | |
| 582 | // - values whose encoding begins with x1100, x1101, x1110 (if NaNs | |
| 583 | // and infinitis were eliminated already this test is reduced to | |
| 584 | // checking for x10x) | |
| 585 | ||
| b2a00c89 L |
586 | // x is not infinity; check for non-canonical values - treated as zero |
| 587 | if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { | |
| 588 | // G0_G1=11; non-canonical | |
| 589 | x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits | |
| 590 | C1_hi = 0; // significand high | |
| 591 | C1_lo = 0; // significand low | |
| 592 | } else { // G0_G1 != 11 | |
| 593 | x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits | |
| 594 | if (C1_hi > 0x0001ed09bead87c0ull || | |
| 595 | (C1_hi == 0x0001ed09bead87c0ull | |
| 596 | && C1_lo > 0x378d8e63ffffffffull)) { | |
| 597 | // x is non-canonical if coefficient is larger than 10^34 -1 | |
| 598 | C1_hi = 0; | |
| 599 | C1_lo = 0; | |
| 600 | } else { // canonical | |
| 601 | ; | |
| 200359e8 | 602 | } |
| 200359e8 | 603 | } |
| b2a00c89 L |
604 | |
| 605 | // unpack y | |
| 606 | C2_hi = y.w[1] & MASK_COEFF; | |
| 607 | C2_lo = y.w[0]; | |
| 608 | // y is not infinity; check for non-canonical values - treated as zero | |
| 609 | if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { | |
| 610 | // G0_G1=11; non-canonical | |
| 611 | y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits | |
| 612 | C2_hi = 0; // significand high | |
| 613 | C2_lo = 0; // significand low | |
| 614 | } else { // G0_G1 != 11 | |
| 615 | y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits | |
| 616 | if (C2_hi > 0x0001ed09bead87c0ull || | |
| 617 | (C2_hi == 0x0001ed09bead87c0ull | |
| 618 | && C2_lo > 0x378d8e63ffffffffull)) { | |
| 619 | // y is non-canonical if coefficient is larger than 10^34 -1 | |
| 620 | C2_hi = 0; | |
| 621 | C2_lo = 0; | |
| 622 | } else { // canonical | |
| 623 | ; | |
| 200359e8 | 624 | } |
| 200359e8 L |
625 | } |
| 626 | ||
| 627 | if ((C1_hi == 0x0ull) && (C1_lo == 0x0ull)) { | |
| 628 | // x is 0 and y is not special | |
| 629 | // if y is 0 return 0 with the smaller exponent | |
| 630 | if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) { | |
| 631 | if (x_exp < y_exp) | |
| b2a00c89 | 632 | res.w[1] = x_exp; |
| 200359e8 | 633 | else |
| b2a00c89 | 634 | res.w[1] = y_exp; |
| 200359e8 | 635 | if (x_sign && y_sign) |
| b2a00c89 | 636 | res.w[1] = res.w[1] | x_sign; // both negative |
| 200359e8 | 637 | else if (rnd_mode == ROUNDING_DOWN && x_sign != y_sign) |
| b2a00c89 | 638 | res.w[1] = res.w[1] | 0x8000000000000000ull; // -0 |
| 200359e8 L |
639 | // else; // res = +0 |
| 640 | res.w[0] = 0; | |
| 641 | } else { | |
| 642 | // for 0 + y return y, with the preferred exponent | |
| 643 | if (y_exp <= x_exp) { | |
| b2a00c89 L |
644 | res.w[1] = y.w[1]; |
| 645 | res.w[0] = y.w[0]; | |
| 646 | } else { // if y_exp > x_exp | |
| 647 | // return (C2 * 10^scale) * 10^(y_exp - scale) | |
| 648 | // where scale = min (P34-q2, y_exp-x_exp) | |
| 649 | // determine q2 = nr. of decimal digits in y | |
| 650 | // determine first the nr. of bits in y (y_nr_bits) | |
| 651 | ||
| 652 | if (C2_hi == 0) { // y_bits is the nr. of bits in C2_lo | |
| 653 | if (C2_lo >= 0x0020000000000000ull) { // y >= 2^53 | |
| 654 | // split the 64-bit value in two 32-bit halves to avoid | |
| 655 | // rounding errors | |
| 656 | if (C2_lo >= 0x0000000100000000ull) { // y >= 2^32 | |
| 657 | tmp2.d = (double) (C2_lo >> 32); // exact conversion | |
| 658 | y_nr_bits = | |
| 659 | 32 + | |
| 660 | ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 661 | } else { // y < 2^32 | |
| 662 | tmp2.d = (double) (C2_lo); // exact conversion | |
| 663 | y_nr_bits = | |
| 664 | ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 665 | } | |
| 666 | } else { // if y < 2^53 | |
| 667 | tmp2.d = (double) C2_lo; // exact conversion | |
| 668 | y_nr_bits = | |
| 669 | ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 670 | } | |
| 671 | } else { // C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi) | |
| 672 | tmp2.d = (double) C2_hi; // exact conversion | |
| 673 | y_nr_bits = | |
| 674 | 64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 675 | } | |
| 676 | q2 = nr_digits[y_nr_bits].digits; | |
| 677 | if (q2 == 0) { | |
| 678 | q2 = nr_digits[y_nr_bits].digits1; | |
| 679 | if (C2_hi > nr_digits[y_nr_bits].threshold_hi || | |
| 680 | (C2_hi == nr_digits[y_nr_bits].threshold_hi && | |
| 681 | C2_lo >= nr_digits[y_nr_bits].threshold_lo)) | |
| 682 | q2++; | |
| 683 | } | |
| 684 | // return (C2 * 10^scale) * 10^(y_exp - scale) | |
| 685 | // where scale = min (P34-q2, y_exp-x_exp) | |
| 686 | scale = P34 - q2; | |
| 687 | ind = (y_exp - x_exp) >> 49; | |
| 688 | if (ind < scale) | |
| 689 | scale = ind; | |
| 690 | if (scale == 0) { | |
| 691 | res.w[1] = y.w[1]; | |
| 692 | res.w[0] = y.w[0]; | |
| 693 | } else if (q2 <= 19) { // y fits in 64 bits | |
| 694 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 695 | // 64 x 64 C2_lo * ten2k64[scale] | |
| 696 | __mul_64x64_to_128MACH (res, C2_lo, ten2k64[scale]); | |
| 697 | } else { // 10^scale fits in 128 bits | |
| 698 | // 64 x 128 C2_lo * ten2k128[scale - 20] | |
| 699 | __mul_128x64_to_128 (res, C2_lo, ten2k128[scale - 20]); | |
| 700 | } | |
| 701 | } else { // y fits in 128 bits, but 10^scale must fit in 64 bits | |
| 702 | // 64 x 128 ten2k64[scale] * C2 | |
| 703 | C2.w[1] = C2_hi; | |
| 704 | C2.w[0] = C2_lo; | |
| 705 | __mul_128x64_to_128 (res, ten2k64[scale], C2); | |
| 706 | } | |
| 707 | // subtract scale from the exponent | |
| 708 | y_exp = y_exp - ((UINT64) scale << 49); | |
| 709 | res.w[1] = res.w[1] | y_sign | y_exp; | |
| 200359e8 L |
710 | } |
| 711 | } | |
| b2a00c89 | 712 | BID_SWAP128 (res); |
| 200359e8 L |
713 | BID_RETURN (res); |
| 714 | } else if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) { | |
| 715 | // y is 0 and x is not special, and not zero | |
| 716 | // for x + 0 return x, with the preferred exponent | |
| 717 | if (x_exp <= y_exp) { | |
| 718 | res.w[1] = x.w[1]; | |
| 719 | res.w[0] = x.w[0]; | |
| b2a00c89 | 720 | } else { // if x_exp > y_exp |
| 200359e8 L |
721 | // return (C1 * 10^scale) * 10^(x_exp - scale) |
| 722 | // where scale = min (P34-q1, x_exp-y_exp) | |
| 723 | // determine q1 = nr. of decimal digits in x | |
| 724 | // determine first the nr. of bits in x | |
| b2a00c89 L |
725 | if (C1_hi == 0) { // x_bits is the nr. of bits in C1_lo |
| 726 | if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 | |
| 727 | // split the 64-bit value in two 32-bit halves to avoid | |
| 728 | // rounding errors | |
| 729 | if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 | |
| 730 | tmp1.d = (double) (C1_lo >> 32); // exact conversion | |
| 731 | x_nr_bits = | |
| 732 | 32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - | |
| 733 | 0x3ff); | |
| 734 | } else { // x < 2^32 | |
| 735 | tmp1.d = (double) (C1_lo); // exact conversion | |
| 736 | x_nr_bits = | |
| 737 | ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 738 | } | |
| 739 | } else { // if x < 2^53 | |
| 740 | tmp1.d = (double) C1_lo; // exact conversion | |
| 741 | x_nr_bits = | |
| 742 | ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 743 | } | |
| 744 | } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) | |
| 745 | tmp1.d = (double) C1_hi; // exact conversion | |
| 746 | x_nr_bits = | |
| 747 | 64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 200359e8 | 748 | } |
| b2a00c89 | 749 | q1 = nr_digits[x_nr_bits].digits; |
| 200359e8 | 750 | if (q1 == 0) { |
| b2a00c89 L |
751 | q1 = nr_digits[x_nr_bits].digits1; |
| 752 | if (C1_hi > nr_digits[x_nr_bits].threshold_hi || | |
| 753 | (C1_hi == nr_digits[x_nr_bits].threshold_hi && | |
| 754 | C1_lo >= nr_digits[x_nr_bits].threshold_lo)) | |
| 755 | q1++; | |
| 200359e8 L |
756 | } |
| 757 | // return (C1 * 10^scale) * 10^(x_exp - scale) | |
| 758 | // where scale = min (P34-q1, x_exp-y_exp) | |
| 759 | scale = P34 - q1; | |
| 760 | ind = (x_exp - y_exp) >> 49; | |
| 761 | if (ind < scale) | |
| b2a00c89 | 762 | scale = ind; |
| 200359e8 | 763 | if (scale == 0) { |
| b2a00c89 L |
764 | res.w[1] = x.w[1]; |
| 765 | res.w[0] = x.w[0]; | |
| 766 | } else if (q1 <= 19) { // x fits in 64 bits | |
| 767 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 768 | // 64 x 64 C1_lo * ten2k64[scale] | |
| 769 | __mul_64x64_to_128MACH (res, C1_lo, ten2k64[scale]); | |
| 770 | } else { // 10^scale fits in 128 bits | |
| 771 | // 64 x 128 C1_lo * ten2k128[scale - 20] | |
| 772 | __mul_128x64_to_128 (res, C1_lo, ten2k128[scale - 20]); | |
| 773 | } | |
| 774 | } else { // x fits in 128 bits, but 10^scale must fit in 64 bits | |
| 775 | // 64 x 128 ten2k64[scale] * C1 | |
| 776 | C1.w[1] = C1_hi; | |
| 777 | C1.w[0] = C1_lo; | |
| 778 | __mul_128x64_to_128 (res, ten2k64[scale], C1); | |
| 200359e8 L |
779 | } |
| 780 | // subtract scale from the exponent | |
| 781 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 782 | res.w[1] = res.w[1] | x_sign | x_exp; | |
| 783 | } | |
| b2a00c89 | 784 | BID_SWAP128 (res); |
| 200359e8 | 785 | BID_RETURN (res); |
| b2a00c89 | 786 | } else { // x and y are not canonical, not special, and are not zero |
| 200359e8 L |
787 | // note that the result may still be zero, and then it has to have the |
| 788 | // preferred exponent | |
| b2a00c89 | 789 | if (x_exp < y_exp) { // if exp_x < exp_y then swap x and y |
| 200359e8 L |
790 | tmp_sign = x_sign; |
| 791 | tmp_exp = x_exp; | |
| 792 | tmp_signif_hi = C1_hi; | |
| 793 | tmp_signif_lo = C1_lo; | |
| 794 | x_sign = y_sign; | |
| 795 | x_exp = y_exp; | |
| 796 | C1_hi = C2_hi; | |
| 797 | C1_lo = C2_lo; | |
| 798 | y_sign = tmp_sign; | |
| 799 | y_exp = tmp_exp; | |
| 800 | C2_hi = tmp_signif_hi; | |
| 801 | C2_lo = tmp_signif_lo; | |
| 802 | } | |
| 803 | // q1 = nr. of decimal digits in x | |
| 804 | // determine first the nr. of bits in x | |
| b2a00c89 L |
805 | if (C1_hi == 0) { // x_bits is the nr. of bits in C1_lo |
| 806 | if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 | |
| 807 | //split the 64-bit value in two 32-bit halves to avoid rounding errors | |
| 808 | if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 | |
| 809 | tmp1.d = (double) (C1_lo >> 32); // exact conversion | |
| 810 | x_nr_bits = | |
| 811 | 32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 812 | } else { // x < 2^32 | |
| 813 | tmp1.d = (double) (C1_lo); // exact conversion | |
| 814 | x_nr_bits = | |
| 815 | ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 816 | } | |
| 817 | } else { // if x < 2^53 | |
| 818 | tmp1.d = (double) C1_lo; // exact conversion | |
| 819 | x_nr_bits = | |
| 820 | ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 200359e8 | 821 | } |
| b2a00c89 L |
822 | } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) |
| 823 | tmp1.d = (double) C1_hi; // exact conversion | |
| 200359e8 | 824 | x_nr_bits = |
| b2a00c89 | 825 | 64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| 200359e8 L |
826 | } |
| 827 | ||
| b2a00c89 | 828 | q1 = nr_digits[x_nr_bits].digits; |
| 200359e8 | 829 | if (q1 == 0) { |
| b2a00c89 L |
830 | q1 = nr_digits[x_nr_bits].digits1; |
| 831 | if (C1_hi > nr_digits[x_nr_bits].threshold_hi || | |
| 832 | (C1_hi == nr_digits[x_nr_bits].threshold_hi && | |
| 833 | C1_lo >= nr_digits[x_nr_bits].threshold_lo)) | |
| 834 | q1++; | |
| 200359e8 L |
835 | } |
| 836 | // q2 = nr. of decimal digits in y | |
| 837 | // determine first the nr. of bits in y (y_nr_bits) | |
| b2a00c89 L |
838 | if (C2_hi == 0) { // y_bits is the nr. of bits in C2_lo |
| 839 | if (C2_lo >= 0x0020000000000000ull) { // y >= 2^53 | |
| 840 | //split the 64-bit value in two 32-bit halves to avoid rounding errors | |
| 841 | if (C2_lo >= 0x0000000100000000ull) { // y >= 2^32 | |
| 842 | tmp2.d = (double) (C2_lo >> 32); // exact conversion | |
| 843 | y_nr_bits = | |
| 844 | 32 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 845 | } else { // y < 2^32 | |
| 846 | tmp2.d = (double) (C2_lo); // exact conversion | |
| 847 | y_nr_bits = | |
| 848 | ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 849 | } | |
| 850 | } else { // if y < 2^53 | |
| 851 | tmp2.d = (double) C2_lo; // exact conversion | |
| 852 | y_nr_bits = | |
| 853 | ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); | |
| 200359e8 | 854 | } |
| b2a00c89 L |
855 | } else { // C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi) |
| 856 | tmp2.d = (double) C2_hi; // exact conversion | |
| 200359e8 | 857 | y_nr_bits = |
| b2a00c89 | 858 | 64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| 200359e8 L |
859 | } |
| 860 | ||
| b2a00c89 | 861 | q2 = nr_digits[y_nr_bits].digits; |
| 200359e8 | 862 | if (q2 == 0) { |
| b2a00c89 L |
863 | q2 = nr_digits[y_nr_bits].digits1; |
| 864 | if (C2_hi > nr_digits[y_nr_bits].threshold_hi || | |
| 865 | (C2_hi == nr_digits[y_nr_bits].threshold_hi && | |
| 866 | C2_lo >= nr_digits[y_nr_bits].threshold_lo)) | |
| 867 | q2++; | |
| 200359e8 L |
868 | } |
| 869 | ||
| 870 | delta = q1 + (int) (x_exp >> 49) - q2 - (int) (y_exp >> 49); | |
| 871 | ||
| 872 | if (delta >= P34) { | |
| 873 | // round the result directly because 0 < C2 < ulp (C1 * 10^(x_exp-e2)) | |
| 874 | // n = C1 * 10^e1 or n = C1 +/- 10^(q1-P34)) * 10^e1 | |
| 875 | // the result is inexact; the preferred exponent is the least possible | |
| 876 | ||
| 877 | if (delta >= P34 + 1) { | |
| b2a00c89 L |
878 | // for RN the result is the operand with the larger magnitude, |
| 879 | // possibly scaled up by 10^(P34-q1) | |
| 880 | // an overflow cannot occur in this case (rounding to nearest) | |
| 881 | if (q1 < P34) { // scale C1 up by 10^(P34-q1) | |
| 882 | // Note: because delta >= P34+1 it is certain that | |
| 883 | // x_exp - ((UINT64)scale << 49) will stay above e_min | |
| 884 | scale = P34 - q1; | |
| 885 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 886 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 887 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 888 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 889 | } else { // if 20 <= scale <= 33 | |
| 890 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 891 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 892 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 893 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 894 | } | |
| 895 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 896 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 897 | C1.w[1] = C1_hi; | |
| 898 | C1.w[0] = C1_lo; | |
| 899 | // C1 = ten2k64[P34 - q1] * C1 | |
| 900 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 901 | } | |
| 902 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 903 | C1_hi = C1.w[1]; | |
| 904 | C1_lo = C1.w[0]; | |
| 905 | } | |
| 906 | // some special cases arise: if delta = P34 + 1 and C1 = 10^(P34-1) | |
| 907 | // (after scaling) and x_sign != y_sign and C2 > 5*10^(q2-1) => | |
| 908 | // subtract 1 ulp | |
| 909 | // Note: do this only for rounding to nearest; for other rounding | |
| 910 | // modes the correction will be applied next | |
| 911 | if ((rnd_mode == ROUNDING_TO_NEAREST | |
| 912 | || rnd_mode == ROUNDING_TIES_AWAY) && delta == (P34 + 1) | |
| 913 | && C1_hi == 0x0000314dc6448d93ull | |
| 914 | && C1_lo == 0x38c15b0a00000000ull && x_sign != y_sign | |
| 915 | && ((q2 <= 19 && C2_lo > midpoint64[q2 - 1]) || (q2 >= 20 | |
| 916 | && (C2_hi > | |
| 917 | midpoint128 | |
| 918 | [q2 - | |
| 919 | 20]. | |
| 920 | w[1] | |
| 921 | || | |
| 922 | (C2_hi | |
| 923 | == | |
| 924 | midpoint128 | |
| 925 | [q2 - | |
| 926 | 20]. | |
| 927 | w[1] | |
| 928 | && | |
| 929 | C2_lo | |
| 930 | > | |
| 931 | midpoint128 | |
| 932 | [q2 - | |
| 933 | 20]. | |
| 934 | w | |
| 935 | [0]))))) | |
| 936 | { | |
| 937 | // C1 = 10^34 - 1 and decrement x_exp by 1 (no underflow possible) | |
| 938 | C1_hi = 0x0001ed09bead87c0ull; | |
| 939 | C1_lo = 0x378d8e63ffffffffull; | |
| 940 | x_exp = x_exp - EXP_P1; | |
| 941 | } | |
| 942 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 943 | if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || | |
| 944 | (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { | |
| 945 | // add 1 ulp and then check for overflow | |
| 946 | C1_lo = C1_lo + 1; | |
| 947 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 948 | C1_hi = C1_hi + 1; | |
| 949 | } | |
| 950 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 951 | && C1_lo == 0x378d8e6400000000ull) { | |
| 952 | // C1 = 10^34 => rounding overflow | |
| 953 | C1_hi = 0x0000314dc6448d93ull; | |
| 954 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 955 | x_exp = x_exp + EXP_P1; | |
| 956 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 957 | C1_hi = 0x7800000000000000ull; // +inf | |
| 958 | C1_lo = 0x0ull; | |
| 959 | x_exp = 0; // x_sign is preserved | |
| 960 | // set overflow flag (the inexact flag was set too) | |
| 961 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 962 | } | |
| 963 | } | |
| 964 | } else if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || | |
| 965 | (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || | |
| 966 | (rnd_mode == ROUNDING_TO_ZERO | |
| 967 | && x_sign != y_sign)) { | |
| 968 | // subtract 1 ulp from C1 | |
| 969 | // Note: because delta >= P34 + 1 the result cannot be zero | |
| 970 | C1_lo = C1_lo - 1; | |
| 971 | if (C1_lo == 0xffffffffffffffffull) | |
| 972 | C1_hi = C1_hi - 1; | |
| 973 | // if the coefficient is 10^33 - 1 then make it 10^34 - 1 and | |
| 974 | // decrease the exponent by 1 (because delta >= P34 + 1 the | |
| 975 | // exponent will not become less than e_min) | |
| 976 | // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff | |
| 977 | // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff | |
| 978 | if (C1_hi == 0x0000314dc6448d93ull | |
| 979 | && C1_lo == 0x38c15b09ffffffffull) { | |
| 980 | // make C1 = 10^34 - 1 | |
| 981 | C1_hi = 0x0001ed09bead87c0ull; | |
| 982 | C1_lo = 0x378d8e63ffffffffull; | |
| 983 | x_exp = x_exp - EXP_P1; | |
| 984 | } | |
| 985 | } else { | |
| 986 | ; // the result is already correct | |
| 987 | } | |
| 988 | } | |
| 989 | // set the inexact flag | |
| 990 | *pfpsf |= INEXACT_EXCEPTION; | |
| 991 | // assemble the result | |
| 992 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 993 | res.w[0] = C1_lo; | |
| 994 | } else { // delta = P34 | |
| 995 | // in most cases, the smaller operand may be < or = or > 1/2 ulp of the | |
| 996 | // larger operand | |
| 997 | // however, the case C1 = 10^(q1-1) and x_sign != y_sign is special due | |
| 998 | // to accuracy loss after subtraction, and will be treated separately | |
| 999 | if (x_sign == y_sign || (q1 <= 20 | |
| 1000 | && (C1_hi != 0 | |
| 1001 | || C1_lo != ten2k64[q1 - 1])) | |
| 1002 | || (q1 >= 21 && (C1_hi != ten2k128[q1 - 21].w[1] | |
| 1003 | || C1_lo != ten2k128[q1 - 21].w[0]))) { | |
| 1004 | // if x_sign == y_sign or C1 != 10^(q1-1) | |
| 1005 | // compare C2 with 1/2 ulp = 5 * 10^(q2-1), the latter read from table | |
| 1006 | // Note: cases q1<=19 and q1>=20 can be coalesced at some latency cost | |
| 1007 | if (q2 <= 19) { // C2 and 5*10^(q2-1) both fit in 64 bits | |
| 1008 | halfulp64 = midpoint64[q2 - 1]; // 5 * 10^(q2-1) | |
| 1009 | if (C2_lo < halfulp64) { // n2 < 1/2 ulp (n1) | |
| 1010 | // for RN the result is the operand with the larger magnitude, | |
| 1011 | // possibly scaled up by 10^(P34-q1) | |
| 1012 | // an overflow cannot occur in this case (rounding to nearest) | |
| 1013 | if (q1 < P34) { // scale C1 up by 10^(P34-q1) | |
| 1014 | // Note: because delta = P34 it is certain that | |
| 1015 | // x_exp - ((UINT64)scale << 49) will stay above e_min | |
| 1016 | scale = P34 - q1; | |
| 1017 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1018 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 1019 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 1020 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 1021 | } else { // if 20 <= scale <= 33 | |
| 1022 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 1023 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 1024 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 1025 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 1026 | } | |
| 1027 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 1028 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 1029 | C1.w[1] = C1_hi; | |
| 1030 | C1.w[0] = C1_lo; | |
| 1031 | // C1 = ten2k64[P34 - q1] * C1 | |
| 1032 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 1033 | } | |
| 1034 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 1035 | C1_hi = C1.w[1]; | |
| 1036 | C1_lo = C1.w[0]; | |
| 1037 | } | |
| 1038 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 1039 | if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || | |
| 1040 | (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { | |
| 1041 | // add 1 ulp and then check for overflow | |
| 1042 | C1_lo = C1_lo + 1; | |
| 1043 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1044 | C1_hi = C1_hi + 1; | |
| 1045 | } | |
| 1046 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1047 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1048 | // C1 = 10^34 => rounding overflow | |
| 1049 | C1_hi = 0x0000314dc6448d93ull; | |
| 1050 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1051 | x_exp = x_exp + EXP_P1; | |
| 1052 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 1053 | C1_hi = 0x7800000000000000ull; // +inf | |
| 1054 | C1_lo = 0x0ull; | |
| 1055 | x_exp = 0; // x_sign is preserved | |
| 1056 | // set overflow flag (the inexact flag was set too) | |
| 1057 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1058 | } | |
| 1059 | } | |
| 1060 | } else | |
| 1061 | if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) | |
| 1062 | || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) | |
| 1063 | || (rnd_mode == ROUNDING_TO_ZERO | |
| 1064 | && x_sign != y_sign)) { | |
| 1065 | // subtract 1 ulp from C1 | |
| 1066 | // Note: because delta >= P34 + 1 the result cannot be zero | |
| 1067 | C1_lo = C1_lo - 1; | |
| 1068 | if (C1_lo == 0xffffffffffffffffull) | |
| 1069 | C1_hi = C1_hi - 1; | |
| 1070 | // if the coefficient is 10^33-1 then make it 10^34-1 and | |
| 1071 | // decrease the exponent by 1 (because delta >= P34 + 1 the | |
| 1072 | // exponent will not become less than e_min) | |
| 1073 | // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff | |
| 1074 | // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff | |
| 1075 | if (C1_hi == 0x0000314dc6448d93ull | |
| 1076 | && C1_lo == 0x38c15b09ffffffffull) { | |
| 1077 | // make C1 = 10^34 - 1 | |
| 1078 | C1_hi = 0x0001ed09bead87c0ull; | |
| 1079 | C1_lo = 0x378d8e63ffffffffull; | |
| 1080 | x_exp = x_exp - EXP_P1; | |
| 1081 | } | |
| 1082 | } else { | |
| 1083 | ; // the result is already correct | |
| 1084 | } | |
| 1085 | } | |
| 1086 | // set the inexact flag | |
| 1087 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1088 | // assemble the result | |
| 1089 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 1090 | res.w[0] = C1_lo; | |
| 1091 | } else if ((C2_lo == halfulp64) | |
| 1092 | && (q1 < P34 || ((C1_lo & 0x1) == 0))) { | |
| 1093 | // n2 = 1/2 ulp (n1) and C1 is even | |
| 1094 | // the result is the operand with the larger magnitude, | |
| 1095 | // possibly scaled up by 10^(P34-q1) | |
| 1096 | // an overflow cannot occur in this case (rounding to nearest) | |
| 1097 | if (q1 < P34) { // scale C1 up by 10^(P34-q1) | |
| 1098 | // Note: because delta = P34 it is certain that | |
| 1099 | // x_exp - ((UINT64)scale << 49) will stay above e_min | |
| 1100 | scale = P34 - q1; | |
| 1101 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1102 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 1103 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 1104 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 1105 | } else { // if 20 <= scale <= 33 | |
| 1106 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 1107 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 1108 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 1109 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 1110 | } | |
| 1111 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 1112 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 1113 | C1.w[1] = C1_hi; | |
| 1114 | C1.w[0] = C1_lo; | |
| 1115 | // C1 = ten2k64[P34 - q1] * C1 | |
| 1116 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 1117 | } | |
| 1118 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 1119 | C1_hi = C1.w[1]; | |
| 1120 | C1_lo = C1.w[0]; | |
| 1121 | } | |
| 1122 | if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign == y_sign | |
| 1123 | && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_TIES_AWAY | |
| 1124 | && x_sign == y_sign) | |
| 1125 | || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign) | |
| 1126 | || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign)) { | |
| 1127 | // add 1 ulp and then check for overflow | |
| 1128 | C1_lo = C1_lo + 1; | |
| 1129 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1130 | C1_hi = C1_hi + 1; | |
| 1131 | } | |
| 1132 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1133 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1134 | // C1 = 10^34 => rounding overflow | |
| 1135 | C1_hi = 0x0000314dc6448d93ull; | |
| 1136 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1137 | x_exp = x_exp + EXP_P1; | |
| 1138 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 1139 | C1_hi = 0x7800000000000000ull; // +inf | |
| 1140 | C1_lo = 0x0ull; | |
| 1141 | x_exp = 0; // x_sign is preserved | |
| 1142 | // set overflow flag (the inexact flag was set too) | |
| 1143 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1144 | } | |
| 1145 | } | |
| 1146 | } else | |
| 1147 | if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign | |
| 1148 | && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_DOWN | |
| 1149 | && !x_sign && y_sign) | |
| 1150 | || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) | |
| 1151 | || (rnd_mode == ROUNDING_TO_ZERO | |
| 1152 | && x_sign != y_sign)) { | |
| 1153 | // subtract 1 ulp from C1 | |
| 1154 | // Note: because delta >= P34 + 1 the result cannot be zero | |
| 1155 | C1_lo = C1_lo - 1; | |
| 1156 | if (C1_lo == 0xffffffffffffffffull) | |
| 1157 | C1_hi = C1_hi - 1; | |
| 1158 | // if the coefficient is 10^33 - 1 then make it 10^34 - 1 | |
| 1159 | // and decrease the exponent by 1 (because delta >= P34 + 1 | |
| 1160 | // the exponent will not become less than e_min) | |
| 1161 | // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff | |
| 1162 | // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff | |
| 1163 | if (C1_hi == 0x0000314dc6448d93ull | |
| 1164 | && C1_lo == 0x38c15b09ffffffffull) { | |
| 1165 | // make C1 = 10^34 - 1 | |
| 1166 | C1_hi = 0x0001ed09bead87c0ull; | |
| 1167 | C1_lo = 0x378d8e63ffffffffull; | |
| 1168 | x_exp = x_exp - EXP_P1; | |
| 1169 | } | |
| 1170 | } else { | |
| 1171 | ; // the result is already correct | |
| 1172 | } | |
| 1173 | // set the inexact flag | |
| 1174 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1175 | // assemble the result | |
| 1176 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 1177 | res.w[0] = C1_lo; | |
| 1178 | } else { // if C2_lo > halfulp64 || | |
| 1179 | // (C2_lo == halfulp64 && q1 == P34 && ((C1_lo & 0x1) == 1)), i.e. | |
| 1180 | // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd | |
| 1181 | // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0 | |
| 1182 | if (q1 < P34) { // then 1 ulp = 10^(e1+q1-P34) < 10^e1 | |
| 1183 | // Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1 | |
| 1184 | // because q1 < P34 we must first replace C1 by | |
| 1185 | // C1 * 10^(P34-q1), and must decrease the exponent by | |
| 1186 | // (P34-q1) (it will still be at least e_min) | |
| 1187 | scale = P34 - q1; | |
| 1188 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1189 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 1190 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 1191 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 1192 | } else { // if 20 <= scale <= 33 | |
| 1193 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 1194 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 1195 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 1196 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 1197 | } | |
| 1198 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 1199 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 1200 | C1.w[1] = C1_hi; | |
| 1201 | C1.w[0] = C1_lo; | |
| 1202 | // C1 = ten2k64[P34 - q1] * C1 | |
| 1203 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 1204 | } | |
| 1205 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 1206 | C1_hi = C1.w[1]; | |
| 1207 | C1_lo = C1.w[0]; | |
| 1208 | // check for rounding overflow | |
| 1209 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1210 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1211 | // C1 = 10^34 => rounding overflow | |
| 1212 | C1_hi = 0x0000314dc6448d93ull; | |
| 1213 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1214 | x_exp = x_exp + EXP_P1; | |
| 1215 | } | |
| 1216 | } | |
| 1217 | if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign) | |
| 1218 | || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign | |
| 1219 | && C2_lo != halfulp64) | |
| 1220 | || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) | |
| 1221 | || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) | |
| 1222 | || (rnd_mode == ROUNDING_TO_ZERO | |
| 1223 | && x_sign != y_sign)) { | |
| 1224 | // the result is x - 1 | |
| 1225 | // for RN n1 * n2 < 0; underflow not possible | |
| 1226 | C1_lo = C1_lo - 1; | |
| 1227 | if (C1_lo == 0xffffffffffffffffull) | |
| 1228 | C1_hi--; | |
| 1229 | // check if we crossed into the lower decade | |
| 1230 | if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 | |
| 1231 | C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 | |
| 1232 | C1_lo = 0x378d8e63ffffffffull; | |
| 1233 | x_exp = x_exp - EXP_P1; // no underflow, because n1 >> n2 | |
| 1234 | } | |
| 1235 | } else | |
| 1236 | if ((rnd_mode == ROUNDING_TO_NEAREST | |
| 1237 | && x_sign == y_sign) | |
| 1238 | || (rnd_mode == ROUNDING_TIES_AWAY | |
| 1239 | && x_sign == y_sign) | |
| 1240 | || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign) | |
| 1241 | || (rnd_mode == ROUNDING_UP && !x_sign | |
| 1242 | && !y_sign)) { | |
| 1243 | // the result is x + 1 | |
| 1244 | // for RN x_sign = y_sign, i.e. n1*n2 > 0 | |
| 1245 | C1_lo = C1_lo + 1; | |
| 1246 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1247 | C1_hi = C1_hi + 1; | |
| 1248 | } | |
| 1249 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1250 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1251 | // C1 = 10^34 => rounding overflow | |
| 1252 | C1_hi = 0x0000314dc6448d93ull; | |
| 1253 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1254 | x_exp = x_exp + EXP_P1; | |
| 1255 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 1256 | C1_hi = 0x7800000000000000ull; // +inf | |
| 1257 | C1_lo = 0x0ull; | |
| 1258 | x_exp = 0; // x_sign is preserved | |
| 1259 | // set the overflow flag | |
| 1260 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1261 | } | |
| 1262 | } | |
| 1263 | } else { | |
| 1264 | ; // the result is x | |
| 1265 | } | |
| 1266 | // set the inexact flag | |
| 1267 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1268 | // assemble the result | |
| 1269 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 1270 | res.w[0] = C1_lo; | |
| 1271 | } | |
| 1272 | } else { // if q2 >= 20 then 5*10^(q2-1) and C2 (the latter in | |
| 1273 | // most cases) fit only in more than 64 bits | |
| 1274 | halfulp128 = midpoint128[q2 - 20]; // 5 * 10^(q2-1) | |
| 1275 | if ((C2_hi < halfulp128.w[1]) | |
| 1276 | || (C2_hi == halfulp128.w[1] | |
| 1277 | && C2_lo < halfulp128.w[0])) { | |
| 1278 | // n2 < 1/2 ulp (n1) | |
| 1279 | // the result is the operand with the larger magnitude, | |
| 1280 | // possibly scaled up by 10^(P34-q1) | |
| 1281 | // an overflow cannot occur in this case (rounding to nearest) | |
| 1282 | if (q1 < P34) { // scale C1 up by 10^(P34-q1) | |
| 1283 | // Note: because delta = P34 it is certain that | |
| 1284 | // x_exp - ((UINT64)scale << 49) will stay above e_min | |
| 1285 | scale = P34 - q1; | |
| 1286 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1287 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 1288 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 1289 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 1290 | } else { // if 20 <= scale <= 33 | |
| 1291 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 1292 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 1293 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 1294 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 1295 | } | |
| 1296 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 1297 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 1298 | C1.w[1] = C1_hi; | |
| 1299 | C1.w[0] = C1_lo; | |
| 1300 | // C1 = ten2k64[P34 - q1] * C1 | |
| 1301 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 1302 | } | |
| 1303 | C1_hi = C1.w[1]; | |
| 1304 | C1_lo = C1.w[0]; | |
| 1305 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 1306 | } | |
| 1307 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 1308 | if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || | |
| 1309 | (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { | |
| 1310 | // add 1 ulp and then check for overflow | |
| 1311 | C1_lo = C1_lo + 1; | |
| 1312 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1313 | C1_hi = C1_hi + 1; | |
| 1314 | } | |
| 1315 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1316 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1317 | // C1 = 10^34 => rounding overflow | |
| 1318 | C1_hi = 0x0000314dc6448d93ull; | |
| 1319 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1320 | x_exp = x_exp + EXP_P1; | |
| 1321 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 1322 | C1_hi = 0x7800000000000000ull; // +inf | |
| 1323 | C1_lo = 0x0ull; | |
| 1324 | x_exp = 0; // x_sign is preserved | |
| 1325 | // set overflow flag (the inexact flag was set too) | |
| 1326 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1327 | } | |
| 1328 | } | |
| 1329 | } else | |
| 1330 | if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) | |
| 1331 | || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) | |
| 1332 | || (rnd_mode == ROUNDING_TO_ZERO | |
| 1333 | && x_sign != y_sign)) { | |
| 1334 | // subtract 1 ulp from C1 | |
| 1335 | // Note: because delta >= P34 + 1 the result cannot be zero | |
| 1336 | C1_lo = C1_lo - 1; | |
| 1337 | if (C1_lo == 0xffffffffffffffffull) | |
| 1338 | C1_hi = C1_hi - 1; | |
| 1339 | // if the coefficient is 10^33-1 then make it 10^34-1 and | |
| 1340 | // decrease the exponent by 1 (because delta >= P34 + 1 the | |
| 1341 | // exponent will not become less than e_min) | |
| 1342 | // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff | |
| 1343 | // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff | |
| 1344 | if (C1_hi == 0x0000314dc6448d93ull | |
| 1345 | && C1_lo == 0x38c15b09ffffffffull) { | |
| 1346 | // make C1 = 10^34 - 1 | |
| 1347 | C1_hi = 0x0001ed09bead87c0ull; | |
| 1348 | C1_lo = 0x378d8e63ffffffffull; | |
| 1349 | x_exp = x_exp - EXP_P1; | |
| 1350 | } | |
| 1351 | } else { | |
| 1352 | ; // the result is already correct | |
| 1353 | } | |
| 1354 | } | |
| 1355 | // set the inexact flag | |
| 1356 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1357 | // assemble the result | |
| 1358 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 1359 | res.w[0] = C1_lo; | |
| 1360 | } else if ((C2_hi == halfulp128.w[1] | |
| 1361 | && C2_lo == halfulp128.w[0]) | |
| 1362 | && (q1 < P34 || ((C1_lo & 0x1) == 0))) { | |
| 1363 | // midpoint & lsb in C1 is 0 | |
| 1364 | // n2 = 1/2 ulp (n1) and C1 is even | |
| 1365 | // the result is the operand with the larger magnitude, | |
| 1366 | // possibly scaled up by 10^(P34-q1) | |
| 1367 | // an overflow cannot occur in this case (rounding to nearest) | |
| 1368 | if (q1 < P34) { // scale C1 up by 10^(P34-q1) | |
| 1369 | // Note: because delta = P34 it is certain that | |
| 1370 | // x_exp - ((UINT64)scale << 49) will stay above e_min | |
| 1371 | scale = P34 - q1; | |
| 1372 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1373 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 1374 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 1375 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 1376 | } else { // if 20 <= scale <= 33 | |
| 1377 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 1378 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 1379 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 1380 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 1381 | } | |
| 1382 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 1383 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 1384 | C1.w[1] = C1_hi; | |
| 1385 | C1.w[0] = C1_lo; | |
| 1386 | // C1 = ten2k64[P34 - q1] * C1 | |
| 1387 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 1388 | } | |
| 1389 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 1390 | C1_hi = C1.w[1]; | |
| 1391 | C1_lo = C1.w[0]; | |
| 1392 | } | |
| 1393 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 1394 | if ((rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign) | |
| 1395 | || (rnd_mode == ROUNDING_UP && !y_sign)) { | |
| 1396 | // add 1 ulp and then check for overflow | |
| 1397 | C1_lo = C1_lo + 1; | |
| 1398 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1399 | C1_hi = C1_hi + 1; | |
| 1400 | } | |
| 1401 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1402 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1403 | // C1 = 10^34 => rounding overflow | |
| 1404 | C1_hi = 0x0000314dc6448d93ull; | |
| 1405 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1406 | x_exp = x_exp + EXP_P1; | |
| 1407 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 1408 | C1_hi = 0x7800000000000000ull; // +inf | |
| 1409 | C1_lo = 0x0ull; | |
| 1410 | x_exp = 0; // x_sign is preserved | |
| 1411 | // set overflow flag (the inexact flag was set too) | |
| 1412 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1413 | } | |
| 1414 | } | |
| 1415 | } else if ((rnd_mode == ROUNDING_DOWN && y_sign) | |
| 1416 | || (rnd_mode == ROUNDING_TO_ZERO | |
| 1417 | && x_sign != y_sign)) { | |
| 1418 | // subtract 1 ulp from C1 | |
| 1419 | // Note: because delta >= P34 + 1 the result cannot be zero | |
| 1420 | C1_lo = C1_lo - 1; | |
| 1421 | if (C1_lo == 0xffffffffffffffffull) | |
| 1422 | C1_hi = C1_hi - 1; | |
| 1423 | // if the coefficient is 10^33 - 1 then make it 10^34 - 1 | |
| 1424 | // and decrease the exponent by 1 (because delta >= P34 + 1 | |
| 1425 | // the exponent will not become less than e_min) | |
| 1426 | // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff | |
| 1427 | // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff | |
| 1428 | if (C1_hi == 0x0000314dc6448d93ull | |
| 1429 | && C1_lo == 0x38c15b09ffffffffull) { | |
| 1430 | // make C1 = 10^34 - 1 | |
| 1431 | C1_hi = 0x0001ed09bead87c0ull; | |
| 1432 | C1_lo = 0x378d8e63ffffffffull; | |
| 1433 | x_exp = x_exp - EXP_P1; | |
| 1434 | } | |
| 1435 | } else { | |
| 1436 | ; // the result is already correct | |
| 1437 | } | |
| 1438 | } | |
| 1439 | // set the inexact flag | |
| 1440 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1441 | // assemble the result | |
| 1442 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 1443 | res.w[0] = C1_lo; | |
| 1444 | } else { // if C2 > halfulp128 || | |
| 1445 | // (C2 == halfulp128 && q1 == P34 && ((C1 & 0x1) == 1)), i.e. | |
| 1446 | // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd | |
| 1447 | // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0 | |
| 1448 | if (q1 < P34) { // then 1 ulp = 10^(e1+q1-P34) < 10^e1 | |
| 1449 | // Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1 | |
| 1450 | // because q1 < P34 we must first replace C1 by C1*10^(P34-q1), | |
| 1451 | // and must decrease the exponent by (P34-q1) (it will still be | |
| 1452 | // at least e_min) | |
| 1453 | scale = P34 - q1; | |
| 1454 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1455 | // 1 <= q1 <= 19 => 15 <= scale <= 33 | |
| 1456 | if (scale <= 19) { // 10^scale fits in 64 bits | |
| 1457 | __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); | |
| 1458 | } else { // if 20 <= scale <= 33 | |
| 1459 | // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where | |
| 1460 | // (C1 * 10^(scale-19)) fits in 64 bits | |
| 1461 | C1_lo = C1_lo * ten2k64[scale - 19]; | |
| 1462 | __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); | |
| 1463 | } | |
| 1464 | } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits | |
| 1465 | // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits | |
| 1466 | C1.w[1] = C1_hi; | |
| 1467 | C1.w[0] = C1_lo; | |
| 1468 | // C1 = ten2k64[P34 - q1] * C1 | |
| 1469 | __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); | |
| 1470 | } | |
| 1471 | C1_hi = C1.w[1]; | |
| 1472 | C1_lo = C1.w[0]; | |
| 1473 | x_exp = x_exp - ((UINT64) scale << 49); | |
| 1474 | } | |
| 1475 | if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign) | |
| 1476 | || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign | |
| 1477 | && (C2_hi != halfulp128.w[1] | |
| 1478 | || C2_lo != halfulp128.w[0])) | |
| 1479 | || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) | |
| 1480 | || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) | |
| 1481 | || (rnd_mode == ROUNDING_TO_ZERO | |
| 1482 | && x_sign != y_sign)) { | |
| 1483 | // the result is x - 1 | |
| 1484 | // for RN n1 * n2 < 0; underflow not possible | |
| 1485 | C1_lo = C1_lo - 1; | |
| 1486 | if (C1_lo == 0xffffffffffffffffull) | |
| 1487 | C1_hi--; | |
| 1488 | // check if we crossed into the lower decade | |
| 1489 | if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 | |
| 1490 | C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 | |
| 1491 | C1_lo = 0x378d8e63ffffffffull; | |
| 1492 | x_exp = x_exp - EXP_P1; // no underflow, because n1 >> n2 | |
| 1493 | } | |
| 1494 | } else | |
| 1495 | if ((rnd_mode == ROUNDING_TO_NEAREST | |
| 1496 | && x_sign == y_sign) | |
| 1497 | || (rnd_mode == ROUNDING_TIES_AWAY | |
| 1498 | && x_sign == y_sign) | |
| 1499 | || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign) | |
| 1500 | || (rnd_mode == ROUNDING_UP && !x_sign | |
| 1501 | && !y_sign)) { | |
| 1502 | // the result is x + 1 | |
| 1503 | // for RN x_sign = y_sign, i.e. n1*n2 > 0 | |
| 1504 | C1_lo = C1_lo + 1; | |
| 1505 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1506 | C1_hi = C1_hi + 1; | |
| 1507 | } | |
| 1508 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1509 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1510 | // C1 = 10^34 => rounding overflow | |
| 1511 | C1_hi = 0x0000314dc6448d93ull; | |
| 1512 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1513 | x_exp = x_exp + EXP_P1; | |
| 1514 | if (x_exp == EXP_MAX_P1) { // overflow | |
| 1515 | C1_hi = 0x7800000000000000ull; // +inf | |
| 1516 | C1_lo = 0x0ull; | |
| 1517 | x_exp = 0; // x_sign is preserved | |
| 1518 | // set the overflow flag | |
| 1519 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1520 | } | |
| 1521 | } | |
| 1522 | } else { | |
| 1523 | ; // the result is x | |
| 1524 | } | |
| 1525 | // set the inexact flag | |
| 1526 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1527 | // assemble the result | |
| 1528 | res.w[1] = x_sign | x_exp | C1_hi; | |
| 1529 | res.w[0] = C1_lo; | |
| 1530 | } | |
| 1531 | } // end q1 >= 20 | |
| 1532 | // end case where C1 != 10^(q1-1) | |
| 1533 | } else { // C1 = 10^(q1-1) and x_sign != y_sign | |
| 1534 | // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34 | |
| 1535 | // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 | |
| 1536 | // where x1 = q2 - 1, 0 <= x1 <= P34 - 1 | |
| 1537 | // Because C1 = 10^(q1-1) and x_sign != y_sign, C' will have P34 | |
| 1538 | // digits and n = C' * 10^(e2+x1) | |
| 1539 | // If the result has P34+1 digits, redo the steps above with x1+1 | |
| 1540 | // If the result has P34-1 digits or less, redo the steps above with | |
| 1541 | // x1-1 but only if initially x1 >= 1 | |
| 1542 | // NOTE: these two steps can be improved, e.g we could guess if | |
| 1543 | // P34+1 or P34-1 digits will be obtained by adding/subtracting | |
| 1544 | // just the top 64 bits of the two operands | |
| 1545 | // The result cannot be zero, and it cannot overflow | |
| 1546 | x1 = q2 - 1; // 0 <= x1 <= P34-1 | |
| 1547 | // Calculate C1 * 10^(e1-e2-x1) where 1 <= e1-e2-x1 <= P34 | |
| 1548 | // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1 | |
| 1549 | scale = P34 - q1 + 1; // scale=e1-e2-x1 = P34+1-q1; 1<=scale<=P34 | |
| 1550 | // either C1 or 10^(e1-e2-x1) may not fit is 64 bits, | |
| 1551 | // but their product fits with certainty in 128 bits | |
| 1552 | if (scale >= 20) { //10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does | |
| 1553 | __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); | |
| 1554 | } else { // if (scale >= 1 | |
| 1555 | // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits | |
| 1556 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1557 | __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); | |
| 1558 | } else { // q1 >= 20 | |
| 1559 | C1.w[1] = C1_hi; | |
| 1560 | C1.w[0] = C1_lo; | |
| 1561 | __mul_128x64_to_128 (C1, ten2k64[scale], C1); | |
| 1562 | } | |
| 1563 | } | |
| 1564 | tmp64 = C1.w[0]; // C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1) | |
| 1565 | ||
| 1566 | // now round C2 to q2-x1 = 1 decimal digit | |
| 1567 | // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1) | |
| 1568 | ind = x1 - 1; // -1 <= ind <= P34 - 2 | |
| 1569 | if (ind >= 0) { // if (x1 >= 1) | |
| 1570 | C2.w[0] = C2_lo; | |
| 1571 | C2.w[1] = C2_hi; | |
| 1572 | if (ind <= 18) { | |
| 1573 | C2.w[0] = C2.w[0] + midpoint64[ind]; | |
| 1574 | if (C2.w[0] < C2_lo) | |
| 1575 | C2.w[1]++; | |
| 1576 | } else { // 19 <= ind <= 32 | |
| 1577 | C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0]; | |
| 1578 | C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1]; | |
| 1579 | if (C2.w[0] < C2_lo) | |
| 1580 | C2.w[1]++; | |
| 1581 | } | |
| 1582 | // the approximation of 10^(-x1) was rounded up to 118 bits | |
| 1583 | __mul_128x128_to_256 (R256, C2, ten2mk128[ind]); // R256 = C2*, f2* | |
| 1584 | // calculate C2* and f2* | |
| 1585 | // C2* is actually floor(C2*) in this case | |
| 1586 | // C2* and f2* need shifting and masking, as shown by | |
| 1587 | // shiftright128[] and maskhigh128[] | |
| 1588 | // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g. | |
| 1589 | // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 | |
| 1590 | // if (0 < f2* < 10^(-x1)) then | |
| 1591 | // if floor(C1+C2*) is even then C2* = floor(C2*) - logical right | |
| 1592 | // shift; C2* has p decimal digits, correct by Prop. 1) | |
| 1593 | // else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right | |
| 1594 | // shift; C2* has p decimal digits, correct by Pr. 1) | |
| 1595 | // else | |
| 1596 | // C2* = floor(C2*) (logical right shift; C has p decimal digits, | |
| 1597 | // correct by Property 1) | |
| 1598 | // n = C2* * 10^(e2+x1) | |
| 1599 | ||
| 1600 | if (ind <= 2) { | |
| 1601 | highf2star.w[1] = 0x0; | |
| 1602 | highf2star.w[0] = 0x0; // low f2* ok | |
| 1603 | } else if (ind <= 21) { | |
| 1604 | highf2star.w[1] = 0x0; | |
| 1605 | highf2star.w[0] = R256.w[2] & maskhigh128[ind]; // low f2* ok | |
| 1606 | } else { | |
| 1607 | highf2star.w[1] = R256.w[3] & maskhigh128[ind]; | |
| 1608 | highf2star.w[0] = R256.w[2]; // low f2* is ok | |
| 1609 | } | |
| 1610 | // shift right C2* by Ex-128 = shiftright128[ind] | |
| 1611 | if (ind >= 3) { | |
| 1612 | shift = shiftright128[ind]; | |
| 1613 | if (shift < 64) { // 3 <= shift <= 63 | |
| 1614 | R256.w[2] = | |
| 1615 | (R256.w[2] >> shift) | (R256.w[3] << (64 - shift)); | |
| 1616 | R256.w[3] = (R256.w[3] >> shift); | |
| 1617 | } else { // 66 <= shift <= 102 | |
| 1618 | R256.w[2] = (R256.w[3] >> (shift - 64)); | |
| 1619 | R256.w[3] = 0x0ULL; | |
| 1620 | } | |
| 1621 | } | |
| 1622 | // redundant | |
| 1623 | is_inexact_lt_midpoint = 0; | |
| 1624 | is_inexact_gt_midpoint = 0; | |
| 1625 | is_midpoint_lt_even = 0; | |
| 1626 | is_midpoint_gt_even = 0; | |
| 1627 | // determine inexactness of the rounding of C2* | |
| 1628 | // (cannot be followed by a second rounding) | |
| 1629 | // if (0 < f2* - 1/2 < 10^(-x1)) then | |
| 1630 | // the result is exact | |
| 1631 | // else (if f2* - 1/2 > T* then) | |
| 1632 | // the result of is inexact | |
| 1633 | if (ind <= 2) { | |
| 1634 | if (R256.w[1] > 0x8000000000000000ull || | |
| 1635 | (R256.w[1] == 0x8000000000000000ull | |
| 1636 | && R256.w[0] > 0x0ull)) { | |
| 1637 | // f2* > 1/2 and the result may be exact | |
| 1638 | tmp64A = R256.w[1] - 0x8000000000000000ull; // f* - 1/2 | |
| 1639 | if ((tmp64A > ten2mk128trunc[ind].w[1] | |
| 1640 | || (tmp64A == ten2mk128trunc[ind].w[1] | |
| 1641 | && R256.w[0] >= ten2mk128trunc[ind].w[0]))) { | |
| 1642 | // set the inexact flag | |
| 1643 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1644 | // this rounding is applied to C2 only! | |
| 1645 | // x_sign != y_sign | |
| 1646 | is_inexact_gt_midpoint = 1; | |
| 1647 | } // else the result is exact | |
| 1648 | // rounding down, unless a midpoint in [ODD, EVEN] | |
| 1649 | } else { // the result is inexact; f2* <= 1/2 | |
| 1650 | // set the inexact flag | |
| 1651 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1652 | // this rounding is applied to C2 only! | |
| 1653 | // x_sign != y_sign | |
| 1654 | is_inexact_lt_midpoint = 1; | |
| 1655 | } | |
| 1656 | } else if (ind <= 21) { // if 3 <= ind <= 21 | |
| 1657 | if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0 | |
| 1658 | && highf2star.w[0] > | |
| 1659 | onehalf128[ind]) | |
| 1660 | || (highf2star.w[1] == 0x0 | |
| 1661 | && highf2star.w[0] == onehalf128[ind] | |
| 1662 | && (R256.w[1] || R256.w[0]))) { | |
| 1663 | // f2* > 1/2 and the result may be exact | |
| 1664 | // Calculate f2* - 1/2 | |
| 1665 | tmp64A = highf2star.w[0] - onehalf128[ind]; | |
| 1666 | tmp64B = highf2star.w[1]; | |
| 1667 | if (tmp64A > highf2star.w[0]) | |
| 1668 | tmp64B--; | |
| 1669 | if (tmp64B || tmp64A | |
| 1670 | || R256.w[1] > ten2mk128trunc[ind].w[1] | |
| 1671 | || (R256.w[1] == ten2mk128trunc[ind].w[1] | |
| 1672 | && R256.w[0] > ten2mk128trunc[ind].w[0])) { | |
| 1673 | // set the inexact flag | |
| 1674 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1675 | // this rounding is applied to C2 only! | |
| 1676 | // x_sign != y_sign | |
| 1677 | is_inexact_gt_midpoint = 1; | |
| 1678 | } // else the result is exact | |
| 1679 | } else { // the result is inexact; f2* <= 1/2 | |
| 1680 | // set the inexact flag | |
| 1681 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1682 | // this rounding is applied to C2 only! | |
| 1683 | // x_sign != y_sign | |
| 1684 | is_inexact_lt_midpoint = 1; | |
| 1685 | } | |
| 1686 | } else { // if 22 <= ind <= 33 | |
| 1687 | if (highf2star.w[1] > onehalf128[ind] | |
| 1688 | || (highf2star.w[1] == onehalf128[ind] | |
| 1689 | && (highf2star.w[0] || R256.w[1] | |
| 1690 | || R256.w[0]))) { | |
| 1691 | // f2* > 1/2 and the result may be exact | |
| 1692 | // Calculate f2* - 1/2 | |
| 1693 | // tmp64A = highf2star.w[0]; | |
| 1694 | tmp64B = highf2star.w[1] - onehalf128[ind]; | |
| 1695 | if (tmp64B || highf2star.w[0] | |
| 1696 | || R256.w[1] > ten2mk128trunc[ind].w[1] | |
| 1697 | || (R256.w[1] == ten2mk128trunc[ind].w[1] | |
| 1698 | && R256.w[0] > ten2mk128trunc[ind].w[0])) { | |
| 1699 | // set the inexact flag | |
| 1700 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1701 | // this rounding is applied to C2 only! | |
| 1702 | // x_sign != y_sign | |
| 1703 | is_inexact_gt_midpoint = 1; | |
| 1704 | } // else the result is exact | |
| 1705 | } else { // the result is inexact; f2* <= 1/2 | |
| 1706 | // set the inexact flag | |
| 1707 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1708 | // this rounding is applied to C2 only! | |
| 1709 | // x_sign != y_sign | |
| 1710 | is_inexact_lt_midpoint = 1; | |
| 1711 | } | |
| 1712 | } | |
| 1713 | // check for midpoints after determining inexactness | |
| 1714 | if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0) | |
| 1715 | && (highf2star.w[0] == 0) | |
| 1716 | && (R256.w[1] < ten2mk128trunc[ind].w[1] | |
| 1717 | || (R256.w[1] == ten2mk128trunc[ind].w[1] | |
| 1718 | && R256.w[0] <= ten2mk128trunc[ind].w[0]))) { | |
| 1719 | // the result is a midpoint | |
| 1720 | if ((tmp64 + R256.w[2]) & 0x01) { // MP in [EVEN, ODD] | |
| 1721 | // if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0 | |
| 1722 | R256.w[2]--; | |
| 1723 | if (R256.w[2] == 0xffffffffffffffffull) | |
| 1724 | R256.w[3]--; | |
| 1725 | // this rounding is applied to C2 only! | |
| 1726 | // x_sign != y_sign | |
| 1727 | is_midpoint_lt_even = 1; | |
| 1728 | is_inexact_lt_midpoint = 0; | |
| 1729 | is_inexact_gt_midpoint = 0; | |
| 1730 | } else { | |
| 1731 | // else MP in [ODD, EVEN] | |
| 1732 | // this rounding is applied to C2 only! | |
| 1733 | // x_sign != y_sign | |
| 1734 | is_midpoint_gt_even = 1; | |
| 1735 | is_inexact_lt_midpoint = 0; | |
| 1736 | is_inexact_gt_midpoint = 0; | |
| 1737 | } | |
| 1738 | } | |
| 1739 | } else { // if (ind == -1) only when x1 = 0 | |
| 1740 | R256.w[2] = C2_lo; | |
| 1741 | R256.w[3] = C2_hi; | |
| 1742 | is_midpoint_lt_even = 0; | |
| 1743 | is_midpoint_gt_even = 0; | |
| 1744 | is_inexact_lt_midpoint = 0; | |
| 1745 | is_inexact_gt_midpoint = 0; | |
| 1746 | } | |
| 1747 | // and now subtract C1 * 10^(e1-e2-x1) - (C2 * 10^(-x1))rnd,P34 | |
| 1748 | // because x_sign != y_sign this last operation is exact | |
| 1749 | C1.w[0] = C1.w[0] - R256.w[2]; | |
| 1750 | C1.w[1] = C1.w[1] - R256.w[3]; | |
| 1751 | if (C1.w[0] > tmp64) | |
| 1752 | C1.w[1]--; // borrow | |
| 1753 | if (C1.w[1] >= 0x8000000000000000ull) { // negative coefficient! | |
| 1754 | C1.w[0] = ~C1.w[0]; | |
| 1755 | C1.w[0]++; | |
| 1756 | C1.w[1] = ~C1.w[1]; | |
| 1757 | if (C1.w[0] == 0x0) | |
| 1758 | C1.w[1]++; | |
| 1759 | tmp_sign = y_sign; // the result will have the sign of y | |
| 1760 | } else { | |
| 1761 | tmp_sign = x_sign; | |
| 1762 | } | |
| 1763 | // the difference has exactly P34 digits | |
| 1764 | x_sign = tmp_sign; | |
| 1765 | if (x1 >= 1) | |
| 1766 | y_exp = y_exp + ((UINT64) x1 << 49); | |
| 1767 | C1_hi = C1.w[1]; | |
| 1768 | C1_lo = C1.w[0]; | |
| 1769 | // general correction from RN to RA, RM, RP, RZ; result uses y_exp | |
| 1770 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 1771 | if ((!x_sign | |
| 1772 | && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) | |
| 1773 | || | |
| 1774 | ((rnd_mode == ROUNDING_TIES_AWAY | |
| 1775 | || rnd_mode == ROUNDING_UP) | |
| 1776 | && is_midpoint_gt_even))) || (x_sign | |
| 1777 | && | |
| 1778 | ((rnd_mode == | |
| 1779 | ROUNDING_DOWN | |
| 1780 | && | |
| 1781 | is_inexact_lt_midpoint) | |
| 1782 | || | |
| 1783 | ((rnd_mode == | |
| 1784 | ROUNDING_TIES_AWAY | |
| 1785 | || rnd_mode == | |
| 1786 | ROUNDING_DOWN) | |
| 1787 | && | |
| 1788 | is_midpoint_gt_even)))) | |
| 1789 | { | |
| 1790 | // C1 = C1 + 1 | |
| 1791 | C1_lo = C1_lo + 1; | |
| 1792 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 1793 | C1_hi = C1_hi + 1; | |
| 1794 | } | |
| 1795 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 1796 | && C1_lo == 0x378d8e6400000000ull) { | |
| 1797 | // C1 = 10^34 => rounding overflow | |
| 1798 | C1_hi = 0x0000314dc6448d93ull; | |
| 1799 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 1800 | y_exp = y_exp + EXP_P1; | |
| 1801 | } | |
| 1802 | } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) | |
| 1803 | && | |
| 1804 | ((x_sign | |
| 1805 | && (rnd_mode == ROUNDING_UP | |
| 1806 | || rnd_mode == ROUNDING_TO_ZERO)) | |
| 1807 | || (!x_sign | |
| 1808 | && (rnd_mode == ROUNDING_DOWN | |
| 1809 | || rnd_mode == ROUNDING_TO_ZERO)))) { | |
| 1810 | // C1 = C1 - 1 | |
| 1811 | C1_lo = C1_lo - 1; | |
| 1812 | if (C1_lo == 0xffffffffffffffffull) | |
| 1813 | C1_hi--; | |
| 1814 | // check if we crossed into the lower decade | |
| 1815 | if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 | |
| 1816 | C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 | |
| 1817 | C1_lo = 0x378d8e63ffffffffull; | |
| 1818 | y_exp = y_exp - EXP_P1; | |
| 1819 | // no underflow, because delta + q2 >= P34 + 1 | |
| 1820 | } | |
| 1821 | } else { | |
| 1822 | ; // exact, the result is already correct | |
| 1823 | } | |
| 1824 | } | |
| 1825 | // assemble the result | |
| 1826 | res.w[1] = x_sign | y_exp | C1_hi; | |
| 1827 | res.w[0] = C1_lo; | |
| 1828 | } | |
| 1829 | } // end delta = P34 | |
| 1830 | } else { // if (|delta| <= P34 - 1) | |
| 1831 | if (delta >= 0) { // if (0 <= delta <= P34 - 1) | |
| 1832 | if (delta <= P34 - 1 - q2) { | |
| 1833 | // calculate C' directly; the result is exact | |
| 1834 | // in this case 1<=q1<=P34-1, 1<=q2<=P34-1 and 0 <= e1-e2 <= P34-2 | |
| 1835 | // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the | |
| 1836 | // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, | |
| 1837 | // but their product fits with certainty in 128 bits (actually in 113) | |
| 1838 | scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) | |
| 1839 | ||
| 1840 | if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does | |
| 1841 | __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); | |
| 1842 | C1_hi = C1.w[1]; | |
| 1843 | C1_lo = C1.w[0]; | |
| 1844 | } else if (scale >= 1) { | |
| 1845 | // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits | |
| 1846 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1847 | __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); | |
| 1848 | } else { // q1 >= 20 | |
| 1849 | C1.w[1] = C1_hi; | |
| 1850 | C1.w[0] = C1_lo; | |
| 1851 | __mul_128x64_to_128 (C1, ten2k64[scale], C1); | |
| 1852 | } | |
| 1853 | C1_hi = C1.w[1]; | |
| 1854 | C1_lo = C1.w[0]; | |
| 1855 | } else { // if (scale == 0) C1 is unchanged | |
| 1856 | C1.w[0] = C1_lo; // C1.w[1] = C1_hi; | |
| 1857 | } | |
| 1858 | // now add C2 | |
| 1859 | if (x_sign == y_sign) { | |
| 1860 | // the result cannot overflow | |
| 1861 | C1_lo = C1_lo + C2_lo; | |
| 1862 | C1_hi = C1_hi + C2_hi; | |
| 1863 | if (C1_lo < C1.w[0]) | |
| 1864 | C1_hi++; | |
| 1865 | } else { // if x_sign != y_sign | |
| 1866 | C1_lo = C1_lo - C2_lo; | |
| 1867 | C1_hi = C1_hi - C2_hi; | |
| 1868 | if (C1_lo > C1.w[0]) | |
| 1869 | C1_hi--; | |
| 1870 | // the result can be zero, but it cannot overflow | |
| 1871 | if (C1_lo == 0 && C1_hi == 0) { | |
| 1872 | // assemble the result | |
| 1873 | if (x_exp < y_exp) | |
| 1874 | res.w[1] = x_exp; | |
| 1875 | else | |
| 1876 | res.w[1] = y_exp; | |
| 1877 | res.w[0] = 0; | |
| 1878 | if (rnd_mode == ROUNDING_DOWN) { | |
| 1879 | res.w[1] |= 0x8000000000000000ull; | |
| 1880 | } | |
| 1881 | BID_SWAP128 (res); | |
| 1882 | BID_RETURN (res); | |
| 1883 | } | |
| 1884 | if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! | |
| 1885 | C1_lo = ~C1_lo; | |
| 1886 | C1_lo++; | |
| 1887 | C1_hi = ~C1_hi; | |
| 1888 | if (C1_lo == 0x0) | |
| 1889 | C1_hi++; | |
| 1890 | x_sign = y_sign; // the result will have the sign of y | |
| 1891 | } | |
| 1892 | } | |
| 1893 | // assemble the result | |
| 1894 | res.w[1] = x_sign | y_exp | C1_hi; | |
| 1895 | res.w[0] = C1_lo; | |
| 1896 | } else if (delta == P34 - q2) { | |
| 1897 | // calculate C' directly; the result may be inexact if it requires | |
| 1898 | // P34+1 decimal digits; in this case the 'cutoff' point for addition | |
| 1899 | // is at the position of the lsb of C2, so 0 <= e1-e2 <= P34-1 | |
| 1900 | // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the | |
| 1901 | // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, | |
| 1902 | // but their product fits with certainty in 128 bits (actually in 113) | |
| 1903 | scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) | |
| 1904 | if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does | |
| 1905 | __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); | |
| 1906 | } else if (scale >= 1) { | |
| 1907 | // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits | |
| 1908 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 1909 | __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); | |
| 1910 | } else { // q1 >= 20 | |
| 1911 | C1.w[1] = C1_hi; | |
| 1912 | C1.w[0] = C1_lo; | |
| 1913 | __mul_128x64_to_128 (C1, ten2k64[scale], C1); | |
| 1914 | } | |
| 1915 | } else { // if (scale == 0) C1 is unchanged | |
| 1916 | C1.w[1] = C1_hi; | |
| 1917 | C1.w[0] = C1_lo; // only the low part is necessary | |
| 1918 | } | |
| 1919 | C1_hi = C1.w[1]; | |
| 1920 | C1_lo = C1.w[0]; | |
| 1921 | // now add C2 | |
| 1922 | if (x_sign == y_sign) { | |
| 1923 | // the result can overflow! | |
| 1924 | C1_lo = C1_lo + C2_lo; | |
| 1925 | C1_hi = C1_hi + C2_hi; | |
| 1926 | if (C1_lo < C1.w[0]) | |
| 1927 | C1_hi++; | |
| 1928 | // test for overflow, possible only when C1 >= 10^34 | |
| 1929 | if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) { // C1 >= 10^34 | |
| 1930 | // in this case q = P34 + 1 and x = q - P34 = 1, so multiply | |
| 1931 | // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 | |
| 1932 | // decimal digits | |
| 1933 | // Calculate C'' = C' + 1/2 * 10^x | |
| 1934 | if (C1_lo >= 0xfffffffffffffffbull) { // low half add has carry | |
| 1935 | C1_lo = C1_lo + 5; | |
| 1936 | C1_hi = C1_hi + 1; | |
| 1937 | } else { | |
| 1938 | C1_lo = C1_lo + 5; | |
| 1939 | } | |
| 1940 | // the approximation of 10^(-1) was rounded up to 118 bits | |
| 1941 | // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129 | |
| 1942 | // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128 | |
| 1943 | C1.w[1] = C1_hi; | |
| 1944 | C1.w[0] = C1_lo; // C'' | |
| 1945 | ten2m1.w[1] = 0x1999999999999999ull; | |
| 1946 | ten2m1.w[0] = 0x9999999999999a00ull; | |
| 1947 | __mul_128x128_to_256 (P256, C1, ten2m1); // P256 = C*, f* | |
| 1948 | // C* is actually floor(C*) in this case | |
| 1949 | // the top Ex = 128 bits of 10^(-1) are | |
| 1950 | // T* = 0x00199999999999999999999999999999 | |
| 1951 | // if (0 < f* < 10^(-x)) then | |
| 1952 | // if floor(C*) is even then C = floor(C*) - logical right | |
| 1953 | // shift; C has p decimal digits, correct by Prop. 1) | |
| 1954 | // else if floor(C*) is odd C = floor(C*) - 1 (logical right | |
| 1955 | // shift; C has p decimal digits, correct by Pr. 1) | |
| 1956 | // else | |
| 1957 | // C = floor(C*) (logical right shift; C has p decimal digits, | |
| 1958 | // correct by Property 1) | |
| 1959 | // n = C * 10^(e2+x) | |
| 1960 | if ((P256.w[1] || P256.w[0]) | |
| 1961 | && (P256.w[1] < 0x1999999999999999ull | |
| 1962 | || (P256.w[1] == 0x1999999999999999ull | |
| 1963 | && P256.w[0] <= 0x9999999999999999ull))) { | |
| 1964 | // the result is a midpoint | |
| 1965 | if (P256.w[2] & 0x01) { | |
| 1966 | is_midpoint_gt_even = 1; | |
| 1967 | // if floor(C*) is odd C = floor(C*) - 1; the result is not 0 | |
| 1968 | P256.w[2]--; | |
| 1969 | if (P256.w[2] == 0xffffffffffffffffull) | |
| 1970 | P256.w[3]--; | |
| 1971 | } else { | |
| 1972 | is_midpoint_lt_even = 1; | |
| 1973 | } | |
| 1974 | } | |
| 1975 | // n = Cstar * 10^(e2+1) | |
| 1976 | y_exp = y_exp + EXP_P1; | |
| 1977 | // C* != 10^P because C* has P34 digits | |
| 1978 | // check for overflow | |
| 1979 | if (y_exp == EXP_MAX_P1 | |
| 1980 | && (rnd_mode == ROUNDING_TO_NEAREST | |
| 1981 | || rnd_mode == ROUNDING_TIES_AWAY)) { | |
| 1982 | // overflow for RN | |
| 1983 | res.w[1] = x_sign | 0x7800000000000000ull; // +/-inf | |
| 1984 | res.w[0] = 0x0ull; | |
| 1985 | // set the inexact flag | |
| 1986 | *pfpsf |= INEXACT_EXCEPTION; | |
| 1987 | // set the overflow flag | |
| 1988 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 1989 | BID_SWAP128 (res); | |
| 1990 | BID_RETURN (res); | |
| 1991 | } | |
| 1992 | // if (0 < f* - 1/2 < 10^(-x)) then | |
| 1993 | // the result of the addition is exact | |
| 1994 | // else | |
| 1995 | // the result of the addition is inexact | |
| 1996 | if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) { // the result may be exact | |
| 1997 | tmp64 = P256.w[1] - 0x8000000000000000ull; // f* - 1/2 | |
| 1998 | if ((tmp64 > 0x1999999999999999ull | |
| 1999 | || (tmp64 == 0x1999999999999999ull | |
| 2000 | && P256.w[0] >= 0x9999999999999999ull))) { | |
| 2001 | // set the inexact flag | |
| 2002 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2003 | is_inexact = 1; | |
| 2004 | } // else the result is exact | |
| 2005 | } else { // the result is inexact | |
| 2006 | // set the inexact flag | |
| 2007 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2008 | is_inexact = 1; | |
| 2009 | } | |
| 2010 | C1_hi = P256.w[3]; | |
| 2011 | C1_lo = P256.w[2]; | |
| 2012 | if (!is_midpoint_gt_even && !is_midpoint_lt_even) { | |
| 2013 | is_inexact_lt_midpoint = is_inexact | |
| 2014 | && (P256.w[1] & 0x8000000000000000ull); | |
| 2015 | is_inexact_gt_midpoint = is_inexact | |
| 2016 | && !(P256.w[1] & 0x8000000000000000ull); | |
| 2017 | } | |
| 2018 | // general correction from RN to RA, RM, RP, RZ; | |
| 2019 | // result uses y_exp | |
| 2020 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 2021 | if ((!x_sign | |
| 2022 | && | |
| 2023 | ((rnd_mode == ROUNDING_UP | |
| 2024 | && is_inexact_lt_midpoint) | |
| 2025 | || | |
| 2026 | ((rnd_mode == ROUNDING_TIES_AWAY | |
| 2027 | || rnd_mode == ROUNDING_UP) | |
| 2028 | && is_midpoint_gt_even))) || (x_sign | |
| 2029 | && | |
| 2030 | ((rnd_mode == | |
| 2031 | ROUNDING_DOWN | |
| 2032 | && | |
| 2033 | is_inexact_lt_midpoint) | |
| 2034 | || | |
| 2035 | ((rnd_mode == | |
| 2036 | ROUNDING_TIES_AWAY | |
| 2037 | || rnd_mode == | |
| 2038 | ROUNDING_DOWN) | |
| 2039 | && | |
| 2040 | is_midpoint_gt_even)))) | |
| 2041 | { | |
| 2042 | // C1 = C1 + 1 | |
| 2043 | C1_lo = C1_lo + 1; | |
| 2044 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 2045 | C1_hi = C1_hi + 1; | |
| 2046 | } | |
| 2047 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 2048 | && C1_lo == 0x378d8e6400000000ull) { | |
| 2049 | // C1 = 10^34 => rounding overflow | |
| 2050 | C1_hi = 0x0000314dc6448d93ull; | |
| 2051 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 2052 | y_exp = y_exp + EXP_P1; | |
| 2053 | } | |
| 2054 | } else | |
| 2055 | if ((is_midpoint_lt_even || is_inexact_gt_midpoint) | |
| 2056 | && | |
| 2057 | ((x_sign | |
| 2058 | && (rnd_mode == ROUNDING_UP | |
| 2059 | || rnd_mode == ROUNDING_TO_ZERO)) | |
| 2060 | || (!x_sign | |
| 2061 | && (rnd_mode == ROUNDING_DOWN | |
| 2062 | || rnd_mode == ROUNDING_TO_ZERO)))) { | |
| 2063 | // C1 = C1 - 1 | |
| 2064 | C1_lo = C1_lo - 1; | |
| 2065 | if (C1_lo == 0xffffffffffffffffull) | |
| 2066 | C1_hi--; | |
| 2067 | // check if we crossed into the lower decade | |
| 2068 | if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 | |
| 2069 | C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 | |
| 2070 | C1_lo = 0x378d8e63ffffffffull; | |
| 2071 | y_exp = y_exp - EXP_P1; | |
| 2072 | // no underflow, because delta + q2 >= P34 + 1 | |
| 2073 | } | |
| 2074 | } else { | |
| 2075 | ; // exact, the result is already correct | |
| 2076 | } | |
| 2077 | // in all cases check for overflow (RN and RA solved already) | |
| 2078 | if (y_exp == EXP_MAX_P1) { // overflow | |
| 2079 | if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 | |
| 2080 | (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 | |
| 2081 | C1_hi = 0x7800000000000000ull; // +inf | |
| 2082 | C1_lo = 0x0ull; | |
| 2083 | } else { // RM and res > 0, RP and res < 0, or RZ | |
| 2084 | C1_hi = 0x5fffed09bead87c0ull; | |
| 2085 | C1_lo = 0x378d8e63ffffffffull; | |
| 2086 | } | |
| 2087 | y_exp = 0; // x_sign is preserved | |
| 2088 | // set the inexact flag (in case the exact addition was exact) | |
| 2089 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2090 | // set the overflow flag | |
| 2091 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 2092 | } | |
| 2093 | } | |
| 2094 | } // else if (C1 < 10^34) then C1 is the coeff.; the result is exact | |
| 2095 | } else { // if x_sign != y_sign the result is exact | |
| 2096 | C1_lo = C1_lo - C2_lo; | |
| 2097 | C1_hi = C1_hi - C2_hi; | |
| 2098 | if (C1_lo > C1.w[0]) | |
| 2099 | C1_hi--; | |
| 2100 | // the result can be zero, but it cannot overflow | |
| 2101 | if (C1_lo == 0 && C1_hi == 0) { | |
| 2102 | // assemble the result | |
| 2103 | if (x_exp < y_exp) | |
| 2104 | res.w[1] = x_exp; | |
| 2105 | else | |
| 2106 | res.w[1] = y_exp; | |
| 2107 | res.w[0] = 0; | |
| 2108 | if (rnd_mode == ROUNDING_DOWN) { | |
| 2109 | res.w[1] |= 0x8000000000000000ull; | |
| 2110 | } | |
| 2111 | BID_SWAP128 (res); | |
| 2112 | BID_RETURN (res); | |
| 2113 | } | |
| 2114 | if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! | |
| 2115 | C1_lo = ~C1_lo; | |
| 2116 | C1_lo++; | |
| 2117 | C1_hi = ~C1_hi; | |
| 2118 | if (C1_lo == 0x0) | |
| 2119 | C1_hi++; | |
| 2120 | x_sign = y_sign; // the result will have the sign of y | |
| 2121 | } | |
| 2122 | } | |
| 2123 | // assemble the result | |
| 2124 | res.w[1] = x_sign | y_exp | C1_hi; | |
| 2125 | res.w[0] = C1_lo; | |
| 2126 | } else { // if (delta >= P34 + 1 - q2) | |
| 2127 | // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34 | |
| 2128 | // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 | |
| 2129 | // where x1 = q1 + e1 - e2 - P34, 1 <= x1 <= P34 - 1 | |
| 2130 | // In most cases C' will have P34 digits, and n = C' * 10^(e2+x1) | |
| 2131 | // If the result has P34+1 digits, redo the steps above with x1+1 | |
| 2132 | // If the result has P34-1 digits or less, redo the steps above with | |
| 2133 | // x1-1 but only if initially x1 >= 1 | |
| 2134 | // NOTE: these two steps can be improved, e.g we could guess if | |
| 2135 | // P34+1 or P34-1 digits will be obtained by adding/subtracting just | |
| 2136 | // the top 64 bits of the two operands | |
| 2137 | // The result cannot be zero, but it can overflow | |
| 2138 | x1 = delta + q2 - P34; // 1 <= x1 <= P34-1 | |
| 2139 | roundC2: | |
| 2140 | // Calculate C1 * 10^(e1-e2-x1) where 0 <= e1-e2-x1 <= P34 - 1 | |
| 2141 | // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1 | |
| 2142 | scale = delta - q1 + q2 - x1; // scale = e1 - e2 - x1 = P34 - q1 | |
| 2143 | // either C1 or 10^(e1-e2-x1) may not fit is 64 bits, | |
| 2144 | // but their product fits with certainty in 128 bits (actually in 113) | |
| 2145 | if (scale >= 20) { //10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does | |
| 2146 | __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); | |
| 2147 | } else if (scale >= 1) { | |
| 2148 | // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits | |
| 2149 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 2150 | __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); | |
| 2151 | } else { // q1 >= 20 | |
| 2152 | C1.w[1] = C1_hi; | |
| 2153 | C1.w[0] = C1_lo; | |
| 2154 | __mul_128x64_to_128 (C1, ten2k64[scale], C1); | |
| 2155 | } | |
| 2156 | } else { // if (scale == 0) C1 is unchanged | |
| 2157 | C1.w[1] = C1_hi; | |
| 2158 | C1.w[0] = C1_lo; | |
| 2159 | } | |
| 2160 | tmp64 = C1.w[0]; // C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1) | |
| 2161 | ||
| 2162 | // now round C2 to q2-x1 decimal digits, where 1<=x1<=q2-1<=P34-1 | |
| 2163 | // (but if we got here a second time after x1 = x1 - 1, then | |
| 2164 | // x1 >= 0; note that for x1 = 0 C2 is unchanged) | |
| 2165 | // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1) | |
| 2166 | ind = x1 - 1; // 0 <= ind <= q2-2<=P34-2=32; but note that if x1 = 0 | |
| 2167 | // during a second pass, then ind = -1 | |
| 2168 | if (ind >= 0) { // if (x1 >= 1) | |
| 2169 | C2.w[0] = C2_lo; | |
| 2170 | C2.w[1] = C2_hi; | |
| 2171 | if (ind <= 18) { | |
| 2172 | C2.w[0] = C2.w[0] + midpoint64[ind]; | |
| 2173 | if (C2.w[0] < C2_lo) | |
| 2174 | C2.w[1]++; | |
| 2175 | } else { // 19 <= ind <= 32 | |
| 2176 | C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0]; | |
| 2177 | C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1]; | |
| 2178 | if (C2.w[0] < C2_lo) | |
| 2179 | C2.w[1]++; | |
| 2180 | } | |
| 2181 | // the approximation of 10^(-x1) was rounded up to 118 bits | |
| 2182 | __mul_128x128_to_256 (R256, C2, ten2mk128[ind]); // R256 = C2*, f2* | |
| 2183 | // calculate C2* and f2* | |
| 2184 | // C2* is actually floor(C2*) in this case | |
| 2185 | // C2* and f2* need shifting and masking, as shown by | |
| 2186 | // shiftright128[] and maskhigh128[] | |
| 2187 | // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g. | |
| 2188 | // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 | |
| 2189 | // if (0 < f2* < 10^(-x1)) then | |
| 2190 | // if floor(C1+C2*) is even then C2* = floor(C2*) - logical right | |
| 2191 | // shift; C2* has p decimal digits, correct by Prop. 1) | |
| 2192 | // else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right | |
| 2193 | // shift; C2* has p decimal digits, correct by Pr. 1) | |
| 2194 | // else | |
| 2195 | // C2* = floor(C2*) (logical right shift; C has p decimal digits, | |
| 2196 | // correct by Property 1) | |
| 2197 | // n = C2* * 10^(e2+x1) | |
| 2198 | ||
| 2199 | if (ind <= 2) { | |
| 2200 | highf2star.w[1] = 0x0; | |
| 2201 | highf2star.w[0] = 0x0; // low f2* ok | |
| 2202 | } else if (ind <= 21) { | |
| 2203 | highf2star.w[1] = 0x0; | |
| 2204 | highf2star.w[0] = R256.w[2] & maskhigh128[ind]; // low f2* ok | |
| 2205 | } else { | |
| 2206 | highf2star.w[1] = R256.w[3] & maskhigh128[ind]; | |
| 2207 | highf2star.w[0] = R256.w[2]; // low f2* is ok | |
| 2208 | } | |
| 2209 | // shift right C2* by Ex-128 = shiftright128[ind] | |
| 2210 | if (ind >= 3) { | |
| 2211 | shift = shiftright128[ind]; | |
| 2212 | if (shift < 64) { // 3 <= shift <= 63 | |
| 2213 | R256.w[2] = | |
| 2214 | (R256.w[2] >> shift) | (R256.w[3] << (64 - shift)); | |
| 2215 | R256.w[3] = (R256.w[3] >> shift); | |
| 2216 | } else { // 66 <= shift <= 102 | |
| 2217 | R256.w[2] = (R256.w[3] >> (shift - 64)); | |
| 2218 | R256.w[3] = 0x0ULL; | |
| 2219 | } | |
| 2220 | } | |
| 2221 | if (second_pass) { | |
| 2222 | is_inexact_lt_midpoint = 0; | |
| 2223 | is_inexact_gt_midpoint = 0; | |
| 2224 | is_midpoint_lt_even = 0; | |
| 2225 | is_midpoint_gt_even = 0; | |
| 2226 | } | |
| 2227 | // determine inexactness of the rounding of C2* (this may be | |
| 2228 | // followed by a second rounding only if we get P34+1 | |
| 2229 | // decimal digits) | |
| 2230 | // if (0 < f2* - 1/2 < 10^(-x1)) then | |
| 2231 | // the result is exact | |
| 2232 | // else (if f2* - 1/2 > T* then) | |
| 2233 | // the result of is inexact | |
| 2234 | if (ind <= 2) { | |
| 2235 | if (R256.w[1] > 0x8000000000000000ull || | |
| 2236 | (R256.w[1] == 0x8000000000000000ull | |
| 2237 | && R256.w[0] > 0x0ull)) { | |
| 2238 | // f2* > 1/2 and the result may be exact | |
| 2239 | tmp64A = R256.w[1] - 0x8000000000000000ull; // f* - 1/2 | |
| 2240 | if ((tmp64A > ten2mk128trunc[ind].w[1] | |
| 2241 | || (tmp64A == ten2mk128trunc[ind].w[1] | |
| 2242 | && R256.w[0] >= ten2mk128trunc[ind].w[0]))) { | |
| 2243 | // set the inexact flag | |
| 2244 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2245 | tmp_inexact = 1; // may be set again during a second pass | |
| 2246 | // this rounding is applied to C2 only! | |
| 2247 | if (x_sign == y_sign) | |
| 2248 | is_inexact_lt_midpoint = 1; | |
| 2249 | else // if (x_sign != y_sign) | |
| 2250 | is_inexact_gt_midpoint = 1; | |
| 2251 | } // else the result is exact | |
| 2252 | // rounding down, unless a midpoint in [ODD, EVEN] | |
| 2253 | } else { // the result is inexact; f2* <= 1/2 | |
| 2254 | // set the inexact flag | |
| 2255 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2256 | tmp_inexact = 1; // just in case we will round a second time | |
| 2257 | // rounding up, unless a midpoint in [EVEN, ODD] | |
| 2258 | // this rounding is applied to C2 only! | |
| 2259 | if (x_sign == y_sign) | |
| 2260 | is_inexact_gt_midpoint = 1; | |
| 2261 | else // if (x_sign != y_sign) | |
| 2262 | is_inexact_lt_midpoint = 1; | |
| 2263 | } | |
| 2264 | } else if (ind <= 21) { // if 3 <= ind <= 21 | |
| 2265 | if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0 | |
| 2266 | && highf2star.w[0] > | |
| 2267 | onehalf128[ind]) | |
| 2268 | || (highf2star.w[1] == 0x0 | |
| 2269 | && highf2star.w[0] == onehalf128[ind] | |
| 2270 | && (R256.w[1] || R256.w[0]))) { | |
| 2271 | // f2* > 1/2 and the result may be exact | |
| 2272 | // Calculate f2* - 1/2 | |
| 2273 | tmp64A = highf2star.w[0] - onehalf128[ind]; | |
| 2274 | tmp64B = highf2star.w[1]; | |
| 2275 | if (tmp64A > highf2star.w[0]) | |
| 2276 | tmp64B--; | |
| 2277 | if (tmp64B || tmp64A | |
| 2278 | || R256.w[1] > ten2mk128trunc[ind].w[1] | |
| 2279 | || (R256.w[1] == ten2mk128trunc[ind].w[1] | |
| 2280 | && R256.w[0] > ten2mk128trunc[ind].w[0])) { | |
| 2281 | // set the inexact flag | |
| 2282 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2283 | tmp_inexact = 1; // may be set again during a second pass | |
| 2284 | // this rounding is applied to C2 only! | |
| 2285 | if (x_sign == y_sign) | |
| 2286 | is_inexact_lt_midpoint = 1; | |
| 2287 | else // if (x_sign != y_sign) | |
| 2288 | is_inexact_gt_midpoint = 1; | |
| 2289 | } // else the result is exact | |
| 2290 | } else { // the result is inexact; f2* <= 1/2 | |
| 2291 | // set the inexact flag | |
| 2292 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2293 | tmp_inexact = 1; // may be set again during a second pass | |
| 2294 | // rounding up, unless a midpoint in [EVEN, ODD] | |
| 2295 | // this rounding is applied to C2 only! | |
| 2296 | if (x_sign == y_sign) | |
| 2297 | is_inexact_gt_midpoint = 1; | |
| 2298 | else // if (x_sign != y_sign) | |
| 2299 | is_inexact_lt_midpoint = 1; | |
| 2300 | } | |
| 2301 | } else { // if 22 <= ind <= 33 | |
| 2302 | if (highf2star.w[1] > onehalf128[ind] | |
| 2303 | || (highf2star.w[1] == onehalf128[ind] | |
| 2304 | && (highf2star.w[0] || R256.w[1] | |
| 2305 | || R256.w[0]))) { | |
| 2306 | // f2* > 1/2 and the result may be exact | |
| 2307 | // Calculate f2* - 1/2 | |
| 2308 | // tmp64A = highf2star.w[0]; | |
| 2309 | tmp64B = highf2star.w[1] - onehalf128[ind]; | |
| 2310 | if (tmp64B || highf2star.w[0] | |
| 2311 | || R256.w[1] > ten2mk128trunc[ind].w[1] | |
| 2312 | || (R256.w[1] == ten2mk128trunc[ind].w[1] | |
| 2313 | && R256.w[0] > ten2mk128trunc[ind].w[0])) { | |
| 2314 | // set the inexact flag | |
| 2315 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2316 | tmp_inexact = 1; // may be set again during a second pass | |
| 2317 | // this rounding is applied to C2 only! | |
| 2318 | if (x_sign == y_sign) | |
| 2319 | is_inexact_lt_midpoint = 1; | |
| 2320 | else // if (x_sign != y_sign) | |
| 2321 | is_inexact_gt_midpoint = 1; | |
| 2322 | } // else the result is exact | |
| 2323 | } else { // the result is inexact; f2* <= 1/2 | |
| 2324 | // set the inexact flag | |
| 2325 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2326 | tmp_inexact = 1; // may be set again during a second pass | |
| 2327 | // rounding up, unless a midpoint in [EVEN, ODD] | |
| 2328 | // this rounding is applied to C2 only! | |
| 2329 | if (x_sign == y_sign) | |
| 2330 | is_inexact_gt_midpoint = 1; | |
| 2331 | else // if (x_sign != y_sign) | |
| 2332 | is_inexact_lt_midpoint = 1; | |
| 2333 | } | |
| 2334 | } | |
| 2335 | // check for midpoints | |
| 2336 | if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0) | |
| 2337 | && (highf2star.w[0] == 0) | |
| 2338 | && (R256.w[1] < ten2mk128trunc[ind].w[1] | |
| 2339 | || (R256.w[1] == ten2mk128trunc[ind].w[1] | |
| 2340 | && R256.w[0] <= ten2mk128trunc[ind].w[0]))) { | |
| 2341 | // the result is a midpoint | |
| 2342 | if ((tmp64 + R256.w[2]) & 0x01) { // MP in [EVEN, ODD] | |
| 2343 | // if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0 | |
| 2344 | R256.w[2]--; | |
| 2345 | if (R256.w[2] == 0xffffffffffffffffull) | |
| 2346 | R256.w[3]--; | |
| 2347 | // this rounding is applied to C2 only! | |
| 2348 | if (x_sign == y_sign) | |
| 2349 | is_midpoint_gt_even = 1; | |
| 2350 | else // if (x_sign != y_sign) | |
| 2351 | is_midpoint_lt_even = 1; | |
| 2352 | is_inexact_lt_midpoint = 0; | |
| 2353 | is_inexact_gt_midpoint = 0; | |
| 2354 | } else { | |
| 2355 | // else MP in [ODD, EVEN] | |
| 2356 | // this rounding is applied to C2 only! | |
| 2357 | if (x_sign == y_sign) | |
| 2358 | is_midpoint_lt_even = 1; | |
| 2359 | else // if (x_sign != y_sign) | |
| 2360 | is_midpoint_gt_even = 1; | |
| 2361 | is_inexact_lt_midpoint = 0; | |
| 2362 | is_inexact_gt_midpoint = 0; | |
| 2363 | } | |
| 2364 | } | |
| 2365 | // end if (ind >= 0) | |
| 2366 | } else { // if (ind == -1); only during a 2nd pass, and when x1 = 0 | |
| 2367 | R256.w[2] = C2_lo; | |
| 2368 | R256.w[3] = C2_hi; | |
| 2369 | tmp_inexact = 0; | |
| 2370 | // to correct a possible setting to 1 from 1st pass | |
| 2371 | if (second_pass) { | |
| 2372 | is_midpoint_lt_even = 0; | |
| 2373 | is_midpoint_gt_even = 0; | |
| 2374 | is_inexact_lt_midpoint = 0; | |
| 2375 | is_inexact_gt_midpoint = 0; | |
| 2376 | } | |
| 2377 | } | |
| 2378 | // and now add/subtract C1 * 10^(e1-e2-x1) +/- (C2 * 10^(-x1))rnd,P34 | |
| 2379 | if (x_sign == y_sign) { // addition; could overflow | |
| 2380 | // no second pass is possible this way (only for x_sign != y_sign) | |
| 2381 | C1.w[0] = C1.w[0] + R256.w[2]; | |
| 2382 | C1.w[1] = C1.w[1] + R256.w[3]; | |
| 2383 | if (C1.w[0] < tmp64) | |
| 2384 | C1.w[1]++; // carry | |
| 2385 | // if the sum has P34+1 digits, i.e. C1>=10^34 redo the calculation | |
| 2386 | // with x1=x1+1 | |
| 2387 | if (C1.w[1] > 0x0001ed09bead87c0ull || (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] >= 0x378d8e6400000000ull)) { // C1 >= 10^34 | |
| 2388 | // chop off one more digit from the sum, but make sure there is | |
| 2389 | // no double-rounding error (see table - double rounding logic) | |
| 2390 | // now round C1 from P34+1 to P34 decimal digits | |
| 2391 | // C1' = C1 + 1/2 * 10 = C1 + 5 | |
| 2392 | if (C1.w[0] >= 0xfffffffffffffffbull) { // low half add has carry | |
| 2393 | C1.w[0] = C1.w[0] + 5; | |
| 2394 | C1.w[1] = C1.w[1] + 1; | |
| 2395 | } else { | |
| 2396 | C1.w[0] = C1.w[0] + 5; | |
| 2397 | } | |
| 2398 | // the approximation of 10^(-1) was rounded up to 118 bits | |
| 2399 | __mul_128x128_to_256 (Q256, C1, ten2mk128[0]); // Q256 = C1*, f1* | |
| 2400 | // C1* is actually floor(C1*) in this case | |
| 2401 | // the top 128 bits of 10^(-1) are | |
| 2402 | // T* = ten2mk128trunc[0]=0x19999999999999999999999999999999 | |
| 2403 | // if (0 < f1* < 10^(-1)) then | |
| 2404 | // if floor(C1*) is even then C1* = floor(C1*) - logical right | |
| 2405 | // shift; C1* has p decimal digits, correct by Prop. 1) | |
| 2406 | // else if floor(C1*) is odd C1* = floor(C1*) - 1 (logical right | |
| 2407 | // shift; C1* has p decimal digits, correct by Pr. 1) | |
| 2408 | // else | |
| 2409 | // C1* = floor(C1*) (logical right shift; C has p decimal digits | |
| 2410 | // correct by Property 1) | |
| 2411 | // n = C1* * 10^(e2+x1+1) | |
| 2412 | if ((Q256.w[1] || Q256.w[0]) | |
| 2413 | && (Q256.w[1] < ten2mk128trunc[0].w[1] | |
| 2414 | || (Q256.w[1] == ten2mk128trunc[0].w[1] | |
| 2415 | && Q256.w[0] <= ten2mk128trunc[0].w[0]))) { | |
| 2416 | // the result is a midpoint | |
| 2417 | if (is_inexact_lt_midpoint) { // for the 1st rounding | |
| 2418 | is_inexact_gt_midpoint = 1; | |
| 2419 | is_inexact_lt_midpoint = 0; | |
| 2420 | is_midpoint_gt_even = 0; | |
| 2421 | is_midpoint_lt_even = 0; | |
| 2422 | } else if (is_inexact_gt_midpoint) { // for the 1st rounding | |
| 2423 | Q256.w[2]--; | |
| 2424 | if (Q256.w[2] == 0xffffffffffffffffull) | |
| 2425 | Q256.w[3]--; | |
| 2426 | is_inexact_gt_midpoint = 0; | |
| 2427 | is_inexact_lt_midpoint = 1; | |
| 2428 | is_midpoint_gt_even = 0; | |
| 2429 | is_midpoint_lt_even = 0; | |
| 2430 | } else if (is_midpoint_gt_even) { // for the 1st rounding | |
| 2431 | // Note: cannot have is_midpoint_lt_even | |
| 2432 | is_inexact_gt_midpoint = 0; | |
| 2433 | is_inexact_lt_midpoint = 1; | |
| 2434 | is_midpoint_gt_even = 0; | |
| 2435 | is_midpoint_lt_even = 0; | |
| 2436 | } else { // the first rounding must have been exact | |
| 2437 | if (Q256.w[2] & 0x01) { // MP in [EVEN, ODD] | |
| 2438 | // the truncated result is correct | |
| 2439 | Q256.w[2]--; | |
| 2440 | if (Q256.w[2] == 0xffffffffffffffffull) | |
| 2441 | Q256.w[3]--; | |
| 2442 | is_inexact_gt_midpoint = 0; | |
| 2443 | is_inexact_lt_midpoint = 0; | |
| 2444 | is_midpoint_gt_even = 1; | |
| 2445 | is_midpoint_lt_even = 0; | |
| 2446 | } else { // MP in [ODD, EVEN] | |
| 2447 | is_inexact_gt_midpoint = 0; | |
| 2448 | is_inexact_lt_midpoint = 0; | |
| 2449 | is_midpoint_gt_even = 0; | |
| 2450 | is_midpoint_lt_even = 1; | |
| 2451 | } | |
| 2452 | } | |
| 2453 | tmp_inexact = 1; // in all cases | |
| 2454 | } else { // the result is not a midpoint | |
| 2455 | // determine inexactness of the rounding of C1 (the sum C1+C2*) | |
| 2456 | // if (0 < f1* - 1/2 < 10^(-1)) then | |
| 2457 | // the result is exact | |
| 2458 | // else (if f1* - 1/2 > T* then) | |
| 2459 | // the result of is inexact | |
| 2460 | // ind = 0 | |
| 2461 | if (Q256.w[1] > 0x8000000000000000ull | |
| 2462 | || (Q256.w[1] == 0x8000000000000000ull | |
| 2463 | && Q256.w[0] > 0x0ull)) { | |
| 2464 | // f1* > 1/2 and the result may be exact | |
| 2465 | Q256.w[1] = Q256.w[1] - 0x8000000000000000ull; // f1* - 1/2 | |
| 2466 | if ((Q256.w[1] > ten2mk128trunc[0].w[1] | |
| 2467 | || (Q256.w[1] == ten2mk128trunc[0].w[1] | |
| 2468 | && Q256.w[0] > ten2mk128trunc[0].w[0]))) { | |
| 2469 | is_inexact_gt_midpoint = 0; | |
| 2470 | is_inexact_lt_midpoint = 1; | |
| 2471 | is_midpoint_gt_even = 0; | |
| 2472 | is_midpoint_lt_even = 0; | |
| 2473 | // set the inexact flag | |
| 2474 | tmp_inexact = 1; | |
| 2475 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2476 | } else { // else the result is exact for the 2nd rounding | |
| 2477 | if (tmp_inexact) { // if the previous rounding was inexact | |
| 2478 | if (is_midpoint_lt_even) { | |
| 2479 | is_inexact_gt_midpoint = 1; | |
| 2480 | is_midpoint_lt_even = 0; | |
| 2481 | } else if (is_midpoint_gt_even) { | |
| 2482 | is_inexact_lt_midpoint = 1; | |
| 2483 | is_midpoint_gt_even = 0; | |
| 2484 | } else { | |
| 2485 | ; // no change | |
| 2486 | } | |
| 2487 | } | |
| 2488 | } | |
| 2489 | // rounding down, unless a midpoint in [ODD, EVEN] | |
| 2490 | } else { // the result is inexact; f1* <= 1/2 | |
| 2491 | is_inexact_gt_midpoint = 1; | |
| 2492 | is_inexact_lt_midpoint = 0; | |
| 2493 | is_midpoint_gt_even = 0; | |
| 2494 | is_midpoint_lt_even = 0; | |
| 2495 | // set the inexact flag | |
| 2496 | tmp_inexact = 1; | |
| 2497 | // *pfpsf |= INEXACT_EXCEPTION; | |
| 2498 | } | |
| 2499 | } // end 'the result is not a midpoint' | |
| 2500 | // n = C1 * 10^(e2+x1) | |
| 2501 | C1.w[1] = Q256.w[3]; | |
| 2502 | C1.w[0] = Q256.w[2]; | |
| 2503 | y_exp = y_exp + ((UINT64) (x1 + 1) << 49); | |
| 2504 | } else { // C1 < 10^34 | |
| 2505 | // C1.w[1] and C1.w[0] already set | |
| 2506 | // n = C1 * 10^(e2+x1) | |
| 2507 | y_exp = y_exp + ((UINT64) x1 << 49); | |
| 2508 | } | |
| 2509 | // check for overflow | |
| 2510 | if (y_exp == EXP_MAX_P1 | |
| 2511 | && (rnd_mode == ROUNDING_TO_NEAREST | |
| 2512 | || rnd_mode == ROUNDING_TIES_AWAY)) { | |
| 2513 | res.w[1] = 0x7800000000000000ull | x_sign; // +/-inf | |
| 2514 | res.w[0] = 0x0ull; | |
| 2515 | // set the inexact flag | |
| 2516 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2517 | // set the overflow flag | |
| 2518 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 2519 | BID_SWAP128 (res); | |
| 2520 | BID_RETURN (res); | |
| 2521 | } // else no overflow | |
| 2522 | } else { // if x_sign != y_sign the result of this subtract. is exact | |
| 2523 | C1.w[0] = C1.w[0] - R256.w[2]; | |
| 2524 | C1.w[1] = C1.w[1] - R256.w[3]; | |
| 2525 | if (C1.w[0] > tmp64) | |
| 2526 | C1.w[1]--; // borrow | |
| 2527 | if (C1.w[1] >= 0x8000000000000000ull) { // negative coefficient! | |
| 2528 | C1.w[0] = ~C1.w[0]; | |
| 2529 | C1.w[0]++; | |
| 2530 | C1.w[1] = ~C1.w[1]; | |
| 2531 | if (C1.w[0] == 0x0) | |
| 2532 | C1.w[1]++; | |
| 2533 | tmp_sign = y_sign; | |
| 2534 | // the result will have the sign of y if last rnd | |
| 2535 | } else { | |
| 2536 | tmp_sign = x_sign; | |
| 2537 | } | |
| 2538 | // if the difference has P34-1 digits or less, i.e. C1 < 10^33 then | |
| 2539 | // redo the calculation with x1=x1-1; | |
| 2540 | // redo the calculation also if C1 = 10^33 and | |
| 2541 | // (is_inexact_gt_midpoint or is_midpoint_lt_even); | |
| 2542 | // (the last part should have really been | |
| 2543 | // (is_inexact_lt_midpoint or is_midpoint_gt_even) from | |
| 2544 | // the rounding of C2, but the position flags have been reversed) | |
| 2545 | // 10^33 = 0x0000314dc6448d93 0x38c15b0a00000000 | |
| 2546 | if ((C1.w[1] < 0x0000314dc6448d93ull || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] < 0x38c15b0a00000000ull)) || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b0a00000000ull && (is_inexact_gt_midpoint || is_midpoint_lt_even))) { // C1=10^33 | |
| 2547 | x1 = x1 - 1; // x1 >= 0 | |
| 2548 | if (x1 >= 0) { | |
| 2549 | // clear position flags and tmp_inexact | |
| 2550 | is_midpoint_lt_even = 0; | |
| 2551 | is_midpoint_gt_even = 0; | |
| 2552 | is_inexact_lt_midpoint = 0; | |
| 2553 | is_inexact_gt_midpoint = 0; | |
| 2554 | tmp_inexact = 0; | |
| 2555 | second_pass = 1; | |
| 2556 | goto roundC2; // else result has less than P34 digits | |
| 2557 | } | |
| 2558 | } | |
| 2559 | // if the coefficient of the result is 10^34 it means that this | |
| 2560 | // must be the second pass, and we are done | |
| 2561 | if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34 | |
| 2562 | C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33 | |
| 2563 | C1.w[0] = 0x38c15b0a00000000ull; | |
| 2564 | y_exp = y_exp + ((UINT64) 1 << 49); | |
| 2565 | } | |
| 2566 | x_sign = tmp_sign; | |
| 2567 | if (x1 >= 1) | |
| 2568 | y_exp = y_exp + ((UINT64) x1 << 49); | |
| 2569 | // x1 = -1 is possible at the end of a second pass when the | |
| 2570 | // first pass started with x1 = 1 | |
| 2571 | } | |
| 2572 | C1_hi = C1.w[1]; | |
| 2573 | C1_lo = C1.w[0]; | |
| 2574 | // general correction from RN to RA, RM, RP, RZ; result uses y_exp | |
| 2575 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 2576 | if ((!x_sign | |
| 2577 | && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) | |
| 2578 | || | |
| 2579 | ((rnd_mode == ROUNDING_TIES_AWAY | |
| 2580 | || rnd_mode == ROUNDING_UP) | |
| 2581 | && is_midpoint_gt_even))) || (x_sign | |
| 2582 | && | |
| 2583 | ((rnd_mode == | |
| 2584 | ROUNDING_DOWN | |
| 2585 | && | |
| 2586 | is_inexact_lt_midpoint) | |
| 2587 | || | |
| 2588 | ((rnd_mode == | |
| 2589 | ROUNDING_TIES_AWAY | |
| 2590 | || rnd_mode == | |
| 2591 | ROUNDING_DOWN) | |
| 2592 | && | |
| 2593 | is_midpoint_gt_even)))) | |
| 2594 | { | |
| 2595 | // C1 = C1 + 1 | |
| 2596 | C1_lo = C1_lo + 1; | |
| 2597 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 2598 | C1_hi = C1_hi + 1; | |
| 2599 | } | |
| 2600 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 2601 | && C1_lo == 0x378d8e6400000000ull) { | |
| 2602 | // C1 = 10^34 => rounding overflow | |
| 2603 | C1_hi = 0x0000314dc6448d93ull; | |
| 2604 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 2605 | y_exp = y_exp + EXP_P1; | |
| 2606 | } | |
| 2607 | } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) | |
| 2608 | && | |
| 2609 | ((x_sign | |
| 2610 | && (rnd_mode == ROUNDING_UP | |
| 2611 | || rnd_mode == ROUNDING_TO_ZERO)) | |
| 2612 | || (!x_sign | |
| 2613 | && (rnd_mode == ROUNDING_DOWN | |
| 2614 | || rnd_mode == ROUNDING_TO_ZERO)))) { | |
| 2615 | // C1 = C1 - 1 | |
| 2616 | C1_lo = C1_lo - 1; | |
| 2617 | if (C1_lo == 0xffffffffffffffffull) | |
| 2618 | C1_hi--; | |
| 2619 | // check if we crossed into the lower decade | |
| 2620 | if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 | |
| 2621 | C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 | |
| 2622 | C1_lo = 0x378d8e63ffffffffull; | |
| 2623 | y_exp = y_exp - EXP_P1; | |
| 2624 | // no underflow, because delta + q2 >= P34 + 1 | |
| 2625 | } | |
| 2626 | } else { | |
| 2627 | ; // exact, the result is already correct | |
| 2628 | } | |
| 2629 | // in all cases check for overflow (RN and RA solved already) | |
| 2630 | if (y_exp == EXP_MAX_P1) { // overflow | |
| 2631 | if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 | |
| 2632 | (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 | |
| 2633 | C1_hi = 0x7800000000000000ull; // +inf | |
| 2634 | C1_lo = 0x0ull; | |
| 2635 | } else { // RM and res > 0, RP and res < 0, or RZ | |
| 2636 | C1_hi = 0x5fffed09bead87c0ull; | |
| 2637 | C1_lo = 0x378d8e63ffffffffull; | |
| 2638 | } | |
| 2639 | y_exp = 0; // x_sign is preserved | |
| 2640 | // set the inexact flag (in case the exact addition was exact) | |
| 2641 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2642 | // set the overflow flag | |
| 2643 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 2644 | } | |
| 2645 | } | |
| 2646 | // assemble the result | |
| 2647 | res.w[1] = x_sign | y_exp | C1_hi; | |
| 2648 | res.w[0] = C1_lo; | |
| 2649 | if (tmp_inexact) | |
| 2650 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2651 | } | |
| 2652 | } else { // if (-P34 + 1 <= delta <= -1) <=> 1 <= -delta <= P34 - 1 | |
| 2653 | // NOTE: the following, up to "} else { // if x_sign != y_sign | |
| 2654 | // the result is exact" is identical to "else if (delta == P34 - q2) {" | |
| 2655 | // from above; also, the code is not symmetric: a+b and b+a may take | |
| 2656 | // different paths (need to unify eventually!) | |
| 2657 | // calculate C' = C2 + C1 * 10^(e1-e2) directly; the result may be | |
| 2658 | // inexact if it requires P34 + 1 decimal digits; in either case the | |
| 2659 | // 'cutoff' point for addition is at the position of the lsb of C2 | |
| 2660 | // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the | |
| 2661 | // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, | |
| 2662 | // but their product fits with certainty in 128 bits (actually in 113) | |
| 2663 | // Note that 0 <= e1 - e2 <= P34 - 2 | |
| 2664 | // -P34 + 1 <= delta <= -1 <=> -P34 + 1 <= delta <= -1 <=> | |
| 2665 | // -P34 + 1 <= q1 + e1 - q2 - e2 <= -1 <=> | |
| 2666 | // q2 - q1 - P34 + 1 <= e1 - e2 <= q2 - q1 - 1 <=> | |
| 2667 | // 1 - P34 - P34 + 1 <= e1-e2 <= P34 - 1 - 1 => 0 <= e1-e2 <= P34 - 2 | |
| 2668 | scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) | |
| 2669 | if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does | |
| 2670 | __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); | |
| 2671 | } else if (scale >= 1) { | |
| 2672 | // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits | |
| 2673 | if (q1 <= 19) { // C1 fits in 64 bits | |
| 2674 | __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); | |
| 2675 | } else { // q1 >= 20 | |
| 2676 | C1.w[1] = C1_hi; | |
| 2677 | C1.w[0] = C1_lo; | |
| 2678 | __mul_128x64_to_128 (C1, ten2k64[scale], C1); | |
| 2679 | } | |
| 2680 | } else { // if (scale == 0) C1 is unchanged | |
| 2681 | C1.w[1] = C1_hi; | |
| 2682 | C1.w[0] = C1_lo; // only the low part is necessary | |
| 2683 | } | |
| 2684 | C1_hi = C1.w[1]; | |
| 2685 | C1_lo = C1.w[0]; | |
| 2686 | // now add C2 | |
| 2687 | if (x_sign == y_sign) { | |
| 2688 | // the result can overflow! | |
| 2689 | C1_lo = C1_lo + C2_lo; | |
| 2690 | C1_hi = C1_hi + C2_hi; | |
| 2691 | if (C1_lo < C1.w[0]) | |
| 2692 | C1_hi++; | |
| 2693 | // test for overflow, possible only when C1 >= 10^34 | |
| 2694 | if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) { // C1 >= 10^34 | |
| 2695 | // in this case q = P34 + 1 and x = q - P34 = 1, so multiply | |
| 2696 | // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 | |
| 2697 | // decimal digits | |
| 2698 | // Calculate C'' = C' + 1/2 * 10^x | |
| 2699 | if (C1_lo >= 0xfffffffffffffffbull) { // low half add has carry | |
| 2700 | C1_lo = C1_lo + 5; | |
| 2701 | C1_hi = C1_hi + 1; | |
| 2702 | } else { | |
| 2703 | C1_lo = C1_lo + 5; | |
| 2704 | } | |
| 2705 | // the approximation of 10^(-1) was rounded up to 118 bits | |
| 2706 | // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129 | |
| 2707 | // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128 | |
| 2708 | C1.w[1] = C1_hi; | |
| 2709 | C1.w[0] = C1_lo; // C'' | |
| 2710 | ten2m1.w[1] = 0x1999999999999999ull; | |
| 2711 | ten2m1.w[0] = 0x9999999999999a00ull; | |
| 2712 | __mul_128x128_to_256 (P256, C1, ten2m1); // P256 = C*, f* | |
| 2713 | // C* is actually floor(C*) in this case | |
| 2714 | // the top Ex = 128 bits of 10^(-1) are | |
| 2715 | // T* = 0x00199999999999999999999999999999 | |
| 2716 | // if (0 < f* < 10^(-x)) then | |
| 2717 | // if floor(C*) is even then C = floor(C*) - logical right | |
| 2718 | // shift; C has p decimal digits, correct by Prop. 1) | |
| 2719 | // else if floor(C*) is odd C = floor(C*) - 1 (logical right | |
| 2720 | // shift; C has p decimal digits, correct by Pr. 1) | |
| 2721 | // else | |
| 2722 | // C = floor(C*) (logical right shift; C has p decimal digits, | |
| 2723 | // correct by Property 1) | |
| 2724 | // n = C * 10^(e2+x) | |
| 2725 | if ((P256.w[1] || P256.w[0]) | |
| 2726 | && (P256.w[1] < 0x1999999999999999ull | |
| 2727 | || (P256.w[1] == 0x1999999999999999ull | |
| 2728 | && P256.w[0] <= 0x9999999999999999ull))) { | |
| 2729 | // the result is a midpoint | |
| 2730 | if (P256.w[2] & 0x01) { | |
| 2731 | is_midpoint_gt_even = 1; | |
| 2732 | // if floor(C*) is odd C = floor(C*) - 1; the result is not 0 | |
| 2733 | P256.w[2]--; | |
| 2734 | if (P256.w[2] == 0xffffffffffffffffull) | |
| 2735 | P256.w[3]--; | |
| 2736 | } else { | |
| 2737 | is_midpoint_lt_even = 1; | |
| 2738 | } | |
| 2739 | } | |
| 2740 | // n = Cstar * 10^(e2+1) | |
| 2741 | y_exp = y_exp + EXP_P1; | |
| 2742 | // C* != 10^P34 because C* has P34 digits | |
| 2743 | // check for overflow | |
| 2744 | if (y_exp == EXP_MAX_P1 | |
| 2745 | && (rnd_mode == ROUNDING_TO_NEAREST | |
| 2746 | || rnd_mode == ROUNDING_TIES_AWAY)) { | |
| 2747 | // overflow for RN | |
| 2748 | res.w[1] = x_sign | 0x7800000000000000ull; // +/-inf | |
| 2749 | res.w[0] = 0x0ull; | |
| 2750 | // set the inexact flag | |
| 2751 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2752 | // set the overflow flag | |
| 2753 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 2754 | BID_SWAP128 (res); | |
| 2755 | BID_RETURN (res); | |
| 2756 | } | |
| 2757 | // if (0 < f* - 1/2 < 10^(-x)) then | |
| 2758 | // the result of the addition is exact | |
| 2759 | // else | |
| 2760 | // the result of the addition is inexact | |
| 2761 | if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) { // the result may be exact | |
| 2762 | tmp64 = P256.w[1] - 0x8000000000000000ull; // f* - 1/2 | |
| 2763 | if ((tmp64 > 0x1999999999999999ull | |
| 2764 | || (tmp64 == 0x1999999999999999ull | |
| 2765 | && P256.w[0] >= 0x9999999999999999ull))) { | |
| 2766 | // set the inexact flag | |
| 2767 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2768 | is_inexact = 1; | |
| 2769 | } // else the result is exact | |
| 2770 | } else { // the result is inexact | |
| 2771 | // set the inexact flag | |
| 2772 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2773 | is_inexact = 1; | |
| 2774 | } | |
| 2775 | C1_hi = P256.w[3]; | |
| 2776 | C1_lo = P256.w[2]; | |
| 2777 | if (!is_midpoint_gt_even && !is_midpoint_lt_even) { | |
| 2778 | is_inexact_lt_midpoint = is_inexact | |
| 2779 | && (P256.w[1] & 0x8000000000000000ull); | |
| 2780 | is_inexact_gt_midpoint = is_inexact | |
| 2781 | && !(P256.w[1] & 0x8000000000000000ull); | |
| 2782 | } | |
| 2783 | // general correction from RN to RA, RM, RP, RZ; result uses y_exp | |
| 2784 | if (rnd_mode != ROUNDING_TO_NEAREST) { | |
| 2785 | if ((!x_sign | |
| 2786 | && ((rnd_mode == ROUNDING_UP | |
| 2787 | && is_inexact_lt_midpoint) | |
| 2788 | || ((rnd_mode == ROUNDING_TIES_AWAY | |
| 2789 | || rnd_mode == ROUNDING_UP) | |
| 2790 | && is_midpoint_gt_even))) || (x_sign | |
| 2791 | && | |
| 2792 | ((rnd_mode == | |
| 2793 | ROUNDING_DOWN | |
| 2794 | && | |
| 2795 | is_inexact_lt_midpoint) | |
| 2796 | || | |
| 2797 | ((rnd_mode == | |
| 2798 | ROUNDING_TIES_AWAY | |
| 2799 | || rnd_mode | |
| 2800 | == | |
| 2801 | ROUNDING_DOWN) | |
| 2802 | && | |
| 2803 | is_midpoint_gt_even)))) | |
| 2804 | { | |
| 2805 | // C1 = C1 + 1 | |
| 2806 | C1_lo = C1_lo + 1; | |
| 2807 | if (C1_lo == 0) { // rounding overflow in the low 64 bits | |
| 2808 | C1_hi = C1_hi + 1; | |
| 2809 | } | |
| 2810 | if (C1_hi == 0x0001ed09bead87c0ull | |
| 2811 | && C1_lo == 0x378d8e6400000000ull) { | |
| 2812 | // C1 = 10^34 => rounding overflow | |
| 2813 | C1_hi = 0x0000314dc6448d93ull; | |
| 2814 | C1_lo = 0x38c15b0a00000000ull; // 10^33 | |
| 2815 | y_exp = y_exp + EXP_P1; | |
| 2816 | } | |
| 2817 | } else | |
| 2818 | if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && | |
| 2819 | ((x_sign && (rnd_mode == ROUNDING_UP || | |
| 2820 | rnd_mode == ROUNDING_TO_ZERO)) || | |
| 2821 | (!x_sign && (rnd_mode == ROUNDING_DOWN || | |
| 2822 | rnd_mode == ROUNDING_TO_ZERO)))) { | |
| 2823 | // C1 = C1 - 1 | |
| 2824 | C1_lo = C1_lo - 1; | |
| 2825 | if (C1_lo == 0xffffffffffffffffull) | |
| 2826 | C1_hi--; | |
| 2827 | // check if we crossed into the lower decade | |
| 2828 | if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 | |
| 2829 | C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 | |
| 2830 | C1_lo = 0x378d8e63ffffffffull; | |
| 2831 | y_exp = y_exp - EXP_P1; | |
| 2832 | // no underflow, because delta + q2 >= P34 + 1 | |
| 2833 | } | |
| 2834 | } else { | |
| 2835 | ; // exact, the result is already correct | |
| 2836 | } | |
| 2837 | // in all cases check for overflow (RN and RA solved already) | |
| 2838 | if (y_exp == EXP_MAX_P1) { // overflow | |
| 2839 | if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 | |
| 2840 | (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 | |
| 2841 | C1_hi = 0x7800000000000000ull; // +inf | |
| 2842 | C1_lo = 0x0ull; | |
| 2843 | } else { // RM and res > 0, RP and res < 0, or RZ | |
| 2844 | C1_hi = 0x5fffed09bead87c0ull; | |
| 2845 | C1_lo = 0x378d8e63ffffffffull; | |
| 2846 | } | |
| 2847 | y_exp = 0; // x_sign is preserved | |
| 2848 | // set the inexact flag (in case the exact addition was exact) | |
| 2849 | *pfpsf |= INEXACT_EXCEPTION; | |
| 2850 | // set the overflow flag | |
| 2851 | *pfpsf |= OVERFLOW_EXCEPTION; | |
| 2852 | } | |
| 2853 | } | |
| 2854 | } // else if (C1 < 10^34) then C1 is the coeff.; the result is exact | |
| 2855 | // assemble the result | |
| 2856 | res.w[1] = x_sign | y_exp | C1_hi; | |
| 2857 | res.w[0] = C1_lo; | |
| 2858 | } else { // if x_sign != y_sign the result is exact | |
| 2859 | C1_lo = C2_lo - C1_lo; | |
| 2860 | C1_hi = C2_hi - C1_hi; | |
| 2861 | if (C1_lo > C2_lo) | |
| 2862 | C1_hi--; | |
| 2863 | if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! | |
| 2864 | C1_lo = ~C1_lo; | |
| 2865 | C1_lo++; | |
| 2866 | C1_hi = ~C1_hi; | |
| 2867 | if (C1_lo == 0x0) | |
| 2868 | C1_hi++; | |
| 2869 | x_sign = y_sign; // the result will have the sign of y | |
| 2870 | } | |
| 2871 | // the result can be zero, but it cannot overflow | |
| 2872 | if (C1_lo == 0 && C1_hi == 0) { | |
| 2873 | // assemble the result | |
| 2874 | if (x_exp < y_exp) | |
| 2875 | res.w[1] = x_exp; | |
| 2876 | else | |
| 2877 | res.w[1] = y_exp; | |
| 2878 | res.w[0] = 0; | |
| 2879 | if (rnd_mode == ROUNDING_DOWN) { | |
| 2880 | res.w[1] |= 0x8000000000000000ull; | |
| 2881 | } | |
| 2882 | BID_SWAP128 (res); | |
| 2883 | BID_RETURN (res); | |
| 2884 | } | |
| 2885 | // assemble the result | |
| 2886 | res.w[1] = y_sign | y_exp | C1_hi; | |
| 2887 | res.w[0] = C1_lo; | |
| 2888 | } | |
| 200359e8 L |
2889 | } |
| 2890 | } | |
| b2a00c89 | 2891 | BID_SWAP128 (res); |
| 200359e8 L |
2892 | BID_RETURN (res) |
| 2893 | } | |
| 2894 | } | |
| 2895 | ||
| b2a00c89 L |
2896 | |
| 2897 | ||
| 2898 | // bid128_sub stands for bid128qq_sub | |
| 2899 | ||
| 200359e8 L |
2900 | /***************************************************************************** |
| 2901 | * BID128 sub | |
| 2902 | ****************************************************************************/ | |
| 2903 | ||
| 2904 | #if DECIMAL_CALL_BY_REFERENCE | |
| 2905 | void | |
| b2a00c89 L |
2906 | bid128_sub (UINT128 * pres, UINT128 * px, UINT128 * py |
| 2907 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 2908 | _EXC_INFO_PARAM) { | |
| 200359e8 L |
2909 | UINT128 x = *px, y = *py; |
| 2910 | #if !DECIMAL_GLOBAL_ROUNDING | |
| 2911 | unsigned int rnd_mode = *prnd_mode; | |
| 2912 | #endif | |
| 2913 | #else | |
| 2914 | UINT128 | |
| b2a00c89 L |
2915 | bid128_sub (UINT128 x, UINT128 y |
| 2916 | _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM | |
| 2917 | _EXC_INFO_PARAM) { | |
| 200359e8 L |
2918 | #endif |
| 2919 | ||
| 2920 | UINT128 res; | |
| 2921 | UINT64 y_sign; | |
| 2922 | ||
| b2a00c89 | 2923 | if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) { // y is not NAN |
| 200359e8 | 2924 | // change its sign |
| b2a00c89 | 2925 | y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| 200359e8 | 2926 | if (y_sign) |
| b2a00c89 | 2927 | y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull; |
| 200359e8 | 2928 | else |
| b2a00c89 | 2929 | y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull; |
| 200359e8 L |
2930 | } |
| 2931 | #if DECIMAL_CALL_BY_REFERENCE | |
| b2a00c89 L |
2932 | bid128_add (&res, &x, &y |
| 2933 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 2934 | _EXC_INFO_ARG); | |
| 200359e8 | 2935 | #else |
| b2a00c89 L |
2936 | res = bid128_add (x, y |
| 2937 | _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG | |
| 2938 | _EXC_INFO_ARG); | |
| 200359e8 L |
2939 | #endif |
| 2940 | BID_RETURN (res); | |
| 2941 | } |