| File: | root/firefox-clang/js/src/xsum/xsum.cpp |
| Warning: | line 549, column 5 Value stored to 'exp' is never read |
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| 1 | /* FUNCTIONS FOR EXACT SUMMATION. */ |
| 2 | |
| 3 | /* Copyright 2015, 2018, 2021, 2024 Radford M. Neal |
| 4 | |
| 5 | Permission is hereby granted, free of charge, to any person obtaining |
| 6 | a copy of this software and associated documentation files (the |
| 7 | "Software"), to deal in the Software without restriction, including |
| 8 | without limitation the rights to use, copy, modify, merge, publish, |
| 9 | distribute, sublicense, and/or sell copies of the Software, and to |
| 10 | permit persons to whom the Software is furnished to do so, subject to |
| 11 | the following conditions: |
| 12 | |
| 13 | The above copyright notice and this permission notice shall be |
| 14 | included in all copies or substantial portions of the Software. |
| 15 | |
| 16 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
| 17 | EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF |
| 18 | MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND |
| 19 | NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE |
| 20 | LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION |
| 21 | OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION |
| 22 | WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
| 23 | */ |
| 24 | |
| 25 | #include <stdio.h> |
| 26 | #include <string.h> |
| 27 | #include <math.h> |
| 28 | #include "xsum.h" |
| 29 | |
| 30 | /* ---------------------- IMPLEMENTATION ASSUMPTIONS ----------------------- */ |
| 31 | |
| 32 | /* This code makes the following assumptions: |
| 33 | |
| 34 | o The 'double' type is a IEEE-754 standard 64-bit floating-point value. |
| 35 | |
| 36 | o The 'int64_t' and 'uint64_t' types exist, for 64-bit signed and |
| 37 | unsigned integers. |
| 38 | |
| 39 | o The 'endianness' of 'double' and 64-bit integers is consistent |
| 40 | between these types - that is, looking at the bits of a 'double' |
| 41 | value as an 64-bit integer will have the expected result. |
| 42 | |
| 43 | o Right shifts of a signed operand produce the results expected for |
| 44 | a two's complement representation. |
| 45 | |
| 46 | o Rounding should be done in the "round to nearest, ties to even" mode. |
| 47 | */ |
| 48 | |
| 49 | /* --------------------------- CONFIGURATION ------------------------------- */ |
| 50 | |
| 51 | /* IMPLEMENTATION OPTIONS. Can be set to either 0 or 1, whichever seems |
| 52 | to be fastest. */ |
| 53 | |
| 54 | #define USE_SIMD1 1 /* Use SIMD intrinsics (SSE2/AVX) if available? */ |
| 55 | |
| 56 | #define USE_MEMSET_SMALL1 \ |
| 57 | 1 /* Use memset rather than a loop (for small mem)? \ |
| 58 | */ |
| 59 | #define USE_MEMSET_LARGE1 \ |
| 60 | 1 /* Use memset rather than a loop (for large mem)? \ |
| 61 | */ |
| 62 | #define USE_USED_LARGE1 1 /* Use the used flags in a large accumulator? */ |
| 63 | |
| 64 | #define OPT_SMALL0 0 /* Class of manual optimization for operations on */ |
| 65 | /* small accumulator: 0 (none), 1, 2, 3 (SIMD) */ |
| 66 | #define OPT_CARRY1 1 /* Use manually optimized carry propagation? */ |
| 67 | |
| 68 | #define OPT_LARGE_SUM1 1 /* Should manually optimized routines be used for */ |
| 69 | #define OPT_LARGE_SQNORM1 1 /* operations using the large accumulator? */ |
| 70 | #define OPT_LARGE_DOT1 1 |
| 71 | |
| 72 | #define OPT_SIMPLE_SUM1 1 /* Should manually optimized routines be used for */ |
| 73 | #define OPT_SIMPLE_SQNORM1 1 /* operations done with simple FP arithmetic? */ |
| 74 | #define OPT_SIMPLE_DOT1 1 |
| 75 | |
| 76 | #define OPT_KAHAN_SUM0 0 /* Use manually optimized routine for Kahan sum? */ |
| 77 | |
| 78 | #define INLINE_SMALL1 1 /* Inline more of the small accumulator routines? */ |
| 79 | /* (Not currently used) */ |
| 80 | #define INLINE_LARGE1 1 /* Inline more of the large accumulator routines? */ |
| 81 | |
| 82 | /* INCLUDE INTEL INTRINSICS IF USED AND AVAILABLE. */ |
| 83 | |
| 84 | #if USE_SIMD1 && __SSE2__1 |
| 85 | # include <immintrin.h> |
| 86 | #endif |
| 87 | |
| 88 | /* COPY A 64-BIT QUANTITY - DOUBLE TO 64-BIT INT OR VICE VERSA. The |
| 89 | arguments are destination and source variables (not values). */ |
| 90 | |
| 91 | #define COPY64(dst, src)memcpy(&(dst), &(src), sizeof(double)) memcpy(&(dst), &(src), sizeof(double)) |
| 92 | |
| 93 | /* OPTIONAL INCLUSION OF PBINARY MODULE. Used for debug output. */ |
| 94 | |
| 95 | #ifdef PBINARY |
| 96 | # include "pbinary.h" |
| 97 | #else |
| 98 | # define pbinary_int64(x, y)0 0 |
| 99 | # define pbinary_double(x)0 0 |
| 100 | #endif |
| 101 | |
| 102 | /* SET UP DEBUG FLAG. It's a variable if debuging is enabled, and a |
| 103 | constant if disabled (so that no code will be generated then). */ |
| 104 | |
| 105 | int xsum_debug = 0; |
| 106 | |
| 107 | #ifndef DEBUG1 |
| 108 | # define xsum_debug 0 |
| 109 | #endif |
| 110 | |
| 111 | /* SET UP INLINE / NOINLINE MACROS. */ |
| 112 | |
| 113 | #if __GNUC__4 |
| 114 | # define INLINEinline __attribute__((always_inline)) inline __attribute__((always_inline)) |
| 115 | # define NOINLINE__attribute__((noinline)) __attribute__((noinline)) |
| 116 | #else |
| 117 | # define INLINEinline __attribute__((always_inline)) inline |
| 118 | # define NOINLINE__attribute__((noinline)) |
| 119 | #endif |
| 120 | |
| 121 | /* ------------------------ INTERNAL ROUTINES ------------------------------- */ |
| 122 | |
| 123 | /* ADD AN INF OR NAN TO A SMALL ACCUMULATOR. This only changes the flags, |
| 124 | not the chunks in the accumulator, which retains the sum of the finite |
| 125 | terms (which is perhaps sometimes useful to access, though no function |
| 126 | to do so is defined at present). A NaN with larger payload (seen as a |
| 127 | 52-bit unsigned integer) takes precedence, with the sign of the NaN always |
| 128 | being positive. This ensures that the order of summing NaN values doesn't |
| 129 | matter. */ |
| 130 | |
| 131 | static NOINLINE__attribute__((noinline)) void xsum_small_add_inf_nan(xsum_small_accumulator* sacc, |
| 132 | xsum_int ivalue) { |
| 133 | xsum_int mantissa; |
| 134 | double fltv; |
| 135 | |
| 136 | mantissa = ivalue & XSUM_MANTISSA_MASK(((xsum_int)1 << 52) - 1); |
| 137 | |
| 138 | if (mantissa == 0) /* Inf */ |
| 139 | { |
| 140 | if (sacc->Inf == 0) { /* no previous Inf */ |
| 141 | sacc->Inf = ivalue; |
| 142 | } else if (sacc->Inf != ivalue) { /* previous Inf was opposite sign */ |
| 143 | COPY64(fltv, ivalue)memcpy(&(fltv), &(ivalue), sizeof(double)); |
| 144 | fltv = fltv - fltv; /* result will be a NaN */ |
| 145 | COPY64(sacc->Inf, fltv)memcpy(&(sacc->Inf), &(fltv), sizeof(double)); |
| 146 | } |
| 147 | } else /* NaN */ |
| 148 | { /* Choose the NaN with the bigger payload and clear its sign. Using <= |
| 149 | ensures that we will choose the first NaN over the previous zero. */ |
| 150 | if ((sacc->NaN & XSUM_MANTISSA_MASK(((xsum_int)1 << 52) - 1)) <= mantissa) { |
| 151 | sacc->NaN = ivalue & ~XSUM_SIGN_MASK((xsum_uint)1 << (52 + 11)); |
| 152 | } |
| 153 | } |
| 154 | } |
| 155 | |
| 156 | /* PROPAGATE CARRIES TO NEXT CHUNK IN A SMALL ACCUMULATOR. Needs to |
| 157 | be called often enough that accumulated carries don't overflow out |
| 158 | the top, as indicated by sacc->adds_until_propagate. Returns the |
| 159 | index of the uppermost non-zero chunk (0 if number is zero). |
| 160 | |
| 161 | After carry propagation, the uppermost non-zero chunk will indicate |
| 162 | the sign of the number, and will not be -1 (all 1s). It will be in |
| 163 | the range -2^XSUM_LOW_MANTISSA_BITS to 2^XSUM_LOW_MANTISSA_BITS - 1. |
| 164 | Lower chunks will be non-negative, and in the range from 0 up to |
| 165 | 2^XSUM_LOW_MANTISSA_BITS - 1. */ |
| 166 | |
| 167 | static NOINLINE__attribute__((noinline)) int xsum_carry_propagate(xsum_small_accumulator* sacc) { |
| 168 | int i, u, uix; |
| 169 | |
| 170 | if (xsum_debug) printf("\nCARRY PROPAGATING IN SMALL ACCUMULATOR\n"); |
| 171 | |
| 172 | /* Set u to the index of the uppermost non-zero (for now) chunk, or |
| 173 | return with value 0 if there is none. */ |
| 174 | |
| 175 | #if OPT_CARRY1 |
| 176 | |
| 177 | { |
| 178 | u = XSUM_SCHUNKS((1 << (11 - 5)) + 3) - 1; |
| 179 | switch (XSUM_SCHUNKS((1 << (11 - 5)) + 3) & 0x3) /* get u to be a multiple of 4 minus one */ |
| 180 | { |
| 181 | case 3: |
| 182 | if (sacc->chunk[u] != 0) { |
| 183 | goto found2; |
| 184 | } |
| 185 | u -= 1; /* XSUM_SCHUNKS is a */ |
| 186 | case 2: |
| 187 | if (sacc->chunk[u] != 0) /* constant, so the */ |
| 188 | { |
| 189 | goto found2; /* compiler will do */ |
| 190 | } /* simple code here */ |
| 191 | u -= 1; |
| 192 | case 1: |
| 193 | if (sacc->chunk[u] != 0) { |
| 194 | goto found2; |
| 195 | } |
| 196 | u -= 1; |
| 197 | case 0:; |
| 198 | } |
| 199 | |
| 200 | do /* here, u should be a multiple of 4 minus one, and at least 3 */ |
| 201 | { |
| 202 | # if USE_SIMD1 && __AVX__ |
| 203 | { |
| 204 | __m256i ch; |
| 205 | ch = _mm256_loadu_si256((__m256i*)(sacc->chunk + u - 3)); |
| 206 | if (!_mm256_testz_si256(ch, ch)) { |
| 207 | goto found; |
| 208 | } |
| 209 | u -= 4; |
| 210 | if (u < 0) /* never actually happens, because value of XSUM_SCHUNKS */ |
| 211 | { |
| 212 | break; /* is such that u < 0 occurs at end of do loop instead */ |
| 213 | } |
| 214 | ch = _mm256_loadu_si256((__m256i*)(sacc->chunk + u - 3)); |
| 215 | if (!_mm256_testz_si256(ch, ch)) { |
| 216 | goto found; |
| 217 | } |
| 218 | u -= 4; |
| 219 | } |
| 220 | # else |
| 221 | { |
| 222 | if (sacc->chunk[u] | sacc->chunk[u - 1] | sacc->chunk[u - 2] | |
| 223 | sacc->chunk[u - 3]) { |
| 224 | goto found; |
| 225 | } |
| 226 | u -= 4; |
| 227 | } |
| 228 | # endif |
| 229 | |
| 230 | } while (u >= 0); |
| 231 | |
| 232 | if (xsum_debug) printf("number is zero (1)\n"); |
| 233 | uix = 0; |
| 234 | goto done; |
| 235 | |
| 236 | found: |
| 237 | if (sacc->chunk[u] != 0) { |
| 238 | goto found2; |
| 239 | } |
| 240 | u -= 1; |
| 241 | if (sacc->chunk[u] != 0) { |
| 242 | goto found2; |
| 243 | } |
| 244 | u -= 1; |
| 245 | if (sacc->chunk[u] != 0) { |
| 246 | goto found2; |
| 247 | } |
| 248 | u -= 1; |
| 249 | |
| 250 | found2:; |
| 251 | } |
| 252 | |
| 253 | #else /* Non-optimized search for uppermost non-zero chunk */ |
| 254 | |
| 255 | { |
| 256 | for (u = XSUM_SCHUNKS((1 << (11 - 5)) + 3) - 1; sacc->chunk[u] == 0; u--) { |
| 257 | if (u == 0) { |
| 258 | if (xsum_debug) printf("number is zero (1)\n"); |
| 259 | uix = 0; |
| 260 | goto done; |
| 261 | } |
| 262 | } |
| 263 | } |
| 264 | |
| 265 | #endif |
| 266 | |
| 267 | /* At this point, sacc->chunk[u] must be non-zero */ |
| 268 | |
| 269 | if (xsum_debug) printf("u: %d, sacc->chunk[u]: %ld", u, sacc->chunk[u]); |
| 270 | |
| 271 | /* Carry propagate, starting at the low-order chunks. Note that the |
| 272 | loop limit of u may be increased inside the loop. */ |
| 273 | |
| 274 | i = 0; /* set to the index of the next non-zero chunck, from bottom */ |
| 275 | |
| 276 | #if OPT_CARRY1 |
| 277 | { |
| 278 | /* Quickly skip over unused low-order chunks. Done here at the start |
| 279 | on the theory that there are often many unused low-order chunks, |
| 280 | justifying some overhead to begin, but later stretches of unused |
| 281 | chunks may not be as large. */ |
| 282 | |
| 283 | int e = u - 3; /* go only to 3 before so won't access beyond chunk array */ |
| 284 | |
| 285 | do { |
| 286 | # if USE_SIMD1 && __AVX__ |
| 287 | { |
| 288 | __m256i ch; |
| 289 | ch = _mm256_loadu_si256((__m256i*)(sacc->chunk + i)); |
| 290 | if (!_mm256_testz_si256(ch, ch)) { |
| 291 | break; |
| 292 | } |
| 293 | i += 4; |
| 294 | if (i >= e) { |
| 295 | break; |
| 296 | } |
| 297 | ch = _mm256_loadu_si256((__m256i*)(sacc->chunk + i)); |
| 298 | if (!_mm256_testz_si256(ch, ch)) { |
| 299 | break; |
| 300 | } |
| 301 | } |
| 302 | # else |
| 303 | { |
| 304 | if (sacc->chunk[i] | sacc->chunk[i + 1] | sacc->chunk[i + 2] | |
| 305 | sacc->chunk[i + 3]) { |
| 306 | break; |
| 307 | } |
| 308 | } |
| 309 | # endif |
| 310 | |
| 311 | i += 4; |
| 312 | |
| 313 | } while (i <= e); |
| 314 | } |
| 315 | #endif |
| 316 | |
| 317 | uix = -1; /* indicates that a non-zero chunk has not been found yet */ |
| 318 | |
| 319 | do { |
| 320 | xsum_schunk c; /* Set to the chunk at index i (next non-zero one) */ |
| 321 | xsum_schunk clow; /* Low-order bits of c */ |
| 322 | xsum_schunk chigh; /* High-order bits of c */ |
| 323 | |
| 324 | /* Find the next non-zero chunk, setting i to its index, or break out |
| 325 | of loop if there is none. Note that the chunk at index u is not |
| 326 | necessarily non-zero - it was initially, but u or the chunk at u |
| 327 | may have changed. */ |
| 328 | |
| 329 | #if OPT_CARRY1 |
| 330 | { |
| 331 | c = sacc->chunk[i]; |
| 332 | if (c != 0) { |
| 333 | goto nonzero; |
| 334 | } |
| 335 | i += 1; |
| 336 | if (i > u) { |
| 337 | break; /* reaching here is only possible when u == i initially, */ |
| 338 | } /* with the last add to a chunk having changed it to 0 */ |
| 339 | |
| 340 | for (;;) { |
| 341 | c = sacc->chunk[i]; |
| 342 | if (c != 0) { |
| 343 | goto nonzero; |
| 344 | } |
| 345 | i += 1; |
| 346 | c = sacc->chunk[i]; |
| 347 | if (c != 0) { |
| 348 | goto nonzero; |
| 349 | } |
| 350 | i += 1; |
| 351 | c = sacc->chunk[i]; |
| 352 | if (c != 0) { |
| 353 | goto nonzero; |
| 354 | } |
| 355 | i += 1; |
| 356 | c = sacc->chunk[i]; |
| 357 | if (c != 0) { |
| 358 | goto nonzero; |
| 359 | } |
| 360 | i += 1; |
| 361 | } |
| 362 | } |
| 363 | #else |
| 364 | { |
| 365 | do { |
| 366 | c = sacc->chunk[i]; |
| 367 | if (c != 0) { |
| 368 | goto nonzero; |
| 369 | } |
| 370 | i += 1; |
| 371 | } while (i <= u); |
| 372 | |
| 373 | break; |
| 374 | } |
| 375 | #endif |
| 376 | |
| 377 | /* Propagate possible carry from this chunk to next chunk up. */ |
| 378 | |
| 379 | nonzero: |
| 380 | chigh = c >> XSUM_LOW_MANTISSA_BITS(1 << 5); |
| 381 | if (chigh == 0) { |
| 382 | uix = i; |
| 383 | i += 1; |
| 384 | continue; /* no need to change this chunk */ |
| 385 | } |
| 386 | |
| 387 | if (u == i) { |
| 388 | if (chigh == -1) { |
| 389 | uix = i; |
| 390 | break; /* don't propagate -1 into the region of all zeros above */ |
| 391 | } |
| 392 | u = i + 1; /* we will change chunk[u+1], so we'll need to look at it */ |
| 393 | } |
| 394 | |
| 395 | clow = c & XSUM_LOW_MANTISSA_MASK(((xsum_int)1 << (1 << 5)) - 1); |
| 396 | if (clow != 0) { |
| 397 | uix = i; |
| 398 | } |
| 399 | |
| 400 | /* We now change chunk[i] and add to chunk[i+1]. Note that i+1 should be |
| 401 | in range (no bigger than XSUM_CHUNKS-1) if summing memory, since |
| 402 | the number of chunks is big enough to hold any sum, and we do not |
| 403 | store redundant chunks with values 0 or -1 above previously non-zero |
| 404 | chunks. But other add operations might cause overflow, in which |
| 405 | case we produce a NaN with all 1s as payload. (We can't reliably produce |
| 406 | an Inf of the right sign.) */ |
| 407 | |
| 408 | sacc->chunk[i] = clow; |
| 409 | if (i + 1 >= XSUM_SCHUNKS((1 << (11 - 5)) + 3)) { |
| 410 | xsum_small_add_inf_nan( |
| 411 | sacc, |
| 412 | ((xsum_int)XSUM_EXP_MASK((1 << 11) - 1) << XSUM_MANTISSA_BITS52) | XSUM_MANTISSA_MASK(((xsum_int)1 << 52) - 1)); |
| 413 | u = i; |
| 414 | } else { |
| 415 | sacc->chunk[i + 1] += |
| 416 | chigh; /* note: this could make this chunk be zero */ |
| 417 | } |
| 418 | |
| 419 | i += 1; |
| 420 | |
| 421 | } while (i <= u); |
| 422 | |
| 423 | if (xsum_debug) printf(" uix: %d new u: %d\n", uix, u); |
| 424 | |
| 425 | /* Check again for the number being zero, since carry propagation might |
| 426 | have created zero from something that initially looked non-zero. */ |
| 427 | |
| 428 | if (uix < 0) { |
| 429 | if (xsum_debug) printf("number is zero (2)\n"); |
| 430 | uix = 0; |
| 431 | goto done; |
| 432 | } |
| 433 | |
| 434 | /* While the uppermost chunk is negative, with value -1, combine it with |
| 435 | the chunk below (if there is one) to produce the same number but with |
| 436 | one fewer non-zero chunks. */ |
| 437 | |
| 438 | while (sacc->chunk[uix] == -1 && |
| 439 | uix > 0) { /* Left shift of a negative number is undefined according to |
| 440 | the standard, so do a multiply - it's all presumably |
| 441 | constant-folded by the compiler.*/ |
| 442 | sacc->chunk[uix - 1] += |
| 443 | ((xsum_schunk)-1) * (((xsum_schunk)1) << XSUM_LOW_MANTISSA_BITS(1 << 5)); |
| 444 | sacc->chunk[uix] = 0; |
| 445 | uix -= 1; |
| 446 | } |
| 447 | |
| 448 | /* We can now add one less than the total allowed terms before the |
| 449 | next carry propagate. */ |
| 450 | |
| 451 | done: |
| 452 | sacc->adds_until_propagate = XSUM_SMALL_CARRY_TERMS((1 << ((64 - 1) - 52)) - 1) - 1; |
| 453 | |
| 454 | /* Return index of uppermost non-zero chunk. */ |
| 455 | |
| 456 | return uix; |
| 457 | } |
| 458 | |
| 459 | /* ------------------------ EXTERNAL ROUTINES ------------------------------- */ |
| 460 | |
| 461 | /* INITIALIZE A SMALL ACCUMULATOR TO ZERO. */ |
| 462 | |
| 463 | void xsum_small_init(xsum_small_accumulator* sacc) { |
| 464 | sacc->adds_until_propagate = XSUM_SMALL_CARRY_TERMS((1 << ((64 - 1) - 52)) - 1); |
| 465 | sacc->Inf = sacc->NaN = 0; |
| 466 | #if USE_MEMSET_SMALL1 |
| 467 | { memset(sacc->chunk, 0, XSUM_SCHUNKS((1 << (11 - 5)) + 3) * sizeof(xsum_schunk)); } |
| 468 | #elif USE_SIMD1 && __AVX__ && XSUM_SCHUNKS((1 << (11 - 5)) + 3) == 67 |
| 469 | { |
| 470 | xsum_schunk* ch = sacc->chunk; |
| 471 | __m256i z = _mm256_setzero_si256(); |
| 472 | _mm256_storeu_si256((__m256i*)(ch + 0), z); |
| 473 | _mm256_storeu_si256((__m256i*)(ch + 4), z); |
| 474 | _mm256_storeu_si256((__m256i*)(ch + 8), z); |
| 475 | _mm256_storeu_si256((__m256i*)(ch + 12), z); |
| 476 | _mm256_storeu_si256((__m256i*)(ch + 16), z); |
| 477 | _mm256_storeu_si256((__m256i*)(ch + 20), z); |
| 478 | _mm256_storeu_si256((__m256i*)(ch + 24), z); |
| 479 | _mm256_storeu_si256((__m256i*)(ch + 28), z); |
| 480 | _mm256_storeu_si256((__m256i*)(ch + 32), z); |
| 481 | _mm256_storeu_si256((__m256i*)(ch + 36), z); |
| 482 | _mm256_storeu_si256((__m256i*)(ch + 40), z); |
| 483 | _mm256_storeu_si256((__m256i*)(ch + 44), z); |
| 484 | _mm256_storeu_si256((__m256i*)(ch + 48), z); |
| 485 | _mm256_storeu_si256((__m256i*)(ch + 52), z); |
| 486 | _mm256_storeu_si256((__m256i*)(ch + 56), z); |
| 487 | _mm256_storeu_si256((__m256i*)(ch + 60), z); |
| 488 | _mm_storeu_si128((__m128i*)(ch + 64), _mm256_castsi256_si128(z)); |
| 489 | _mm_storeu_si64(ch + 66, _mm256_castsi256_si128(z)); |
| 490 | } |
| 491 | #else |
| 492 | { |
| 493 | xsum_schunk* p; |
| 494 | int n; |
| 495 | p = sacc->chunk; |
| 496 | n = XSUM_SCHUNKS((1 << (11 - 5)) + 3); |
| 497 | do { |
| 498 | *p++ = 0; |
| 499 | n -= 1; |
| 500 | } while (n > 0); |
| 501 | } |
| 502 | #endif |
| 503 | } |
| 504 | |
| 505 | /* ADD ONE NUMBER TO A SMALL ACCUMULATOR ASSUMING NO CARRY PROPAGATION REQ'D. |
| 506 | This function is declared INLINE regardless of the setting of INLINE_SMALL |
| 507 | and for good performance it must be inlined by the compiler (otherwise the |
| 508 | procedure call overhead will result in substantial inefficiency). */ |
| 509 | |
| 510 | static INLINEinline __attribute__((always_inline)) void xsum_add1_no_carry(xsum_small_accumulator* sacc, |
| 511 | xsum_flt value) { |
| 512 | xsum_int ivalue; |
| 513 | xsum_int mantissa; |
| 514 | xsum_expint exp, low_exp, high_exp; |
| 515 | xsum_schunk* chunk_ptr; |
| 516 | |
| 517 | if (xsum_debug) { |
| 518 | printf("ADD1 %+.17le\n ", (double)value); |
| 519 | pbinary_double((double)value)0; |
| 520 | printf("\n"); |
| 521 | } |
| 522 | |
| 523 | /* Extract exponent and mantissa. Split exponent into high and low parts. */ |
| 524 | |
| 525 | COPY64(ivalue, value)memcpy(&(ivalue), &(value), sizeof(double)); |
| 526 | |
| 527 | exp = (ivalue >> XSUM_MANTISSA_BITS52) & XSUM_EXP_MASK((1 << 11) - 1); |
| 528 | mantissa = ivalue & XSUM_MANTISSA_MASK(((xsum_int)1 << 52) - 1); |
| 529 | high_exp = exp >> XSUM_LOW_EXP_BITS5; |
| 530 | low_exp = exp & XSUM_LOW_EXP_MASK((1 << 5) - 1); |
| 531 | |
| 532 | if (xsum_debug) { |
| 533 | printf(" high exp: "); |
| 534 | pbinary_int64(high_exp, XSUM_HIGH_EXP_BITS)0; |
| 535 | printf(" low exp: "); |
| 536 | pbinary_int64(low_exp, XSUM_LOW_EXP_BITS)0; |
| 537 | printf("\n"); |
| 538 | } |
| 539 | |
| 540 | /* Categorize number as normal, denormalized, or Inf/NaN according to |
| 541 | the value of the exponent field. */ |
| 542 | |
| 543 | if (exp == 0) /* zero or denormalized */ |
| 544 | { /* If it's a zero (positive or negative), we do nothing. */ |
| 545 | if (mantissa == 0) { |
| 546 | return; |
| 547 | } |
| 548 | /* Denormalized mantissa has no implicit 1, but exponent is 1 not 0. */ |
| 549 | exp = low_exp = 1; |
Value stored to 'exp' is never read | |
| 550 | } else if (exp == XSUM_EXP_MASK((1 << 11) - 1)) /* Inf or NaN */ |
| 551 | { /* Just update flags in accumulator structure. */ |
| 552 | xsum_small_add_inf_nan(sacc, ivalue); |
| 553 | return; |
| 554 | } else /* normalized */ |
| 555 | { /* OR in implicit 1 bit at top of mantissa */ |
| 556 | mantissa |= (xsum_int)1 << XSUM_MANTISSA_BITS52; |
| 557 | } |
| 558 | |
| 559 | if (xsum_debug) { |
| 560 | printf(" mantissa: "); |
| 561 | pbinary_int64(mantissa, XSUM_MANTISSA_BITS + 1)0; |
| 562 | printf("\n"); |
| 563 | } |
| 564 | |
| 565 | /* Use high part of exponent as index of chunk, and low part of |
| 566 | exponent to give position within chunk. Fetch the two chunks |
| 567 | that will be modified. */ |
| 568 | |
| 569 | chunk_ptr = sacc->chunk + high_exp; |
| 570 | |
| 571 | /* Separate mantissa into two parts, after shifting, and add to (or |
| 572 | subtract from) this chunk and the next higher chunk (which always |
| 573 | exists since there are three extra ones at the top). |
| 574 | |
| 575 | Note that low_mantissa will have at most XSUM_LOW_MANTISSA_BITS bits, |
| 576 | while high_mantissa will have at most XSUM_MANTISSA_BITS bits, since |
| 577 | even though the high mantissa includes the extra implicit 1 bit, it will |
| 578 | also be shifted right by at least one bit. */ |
| 579 | |
| 580 | xsum_int split_mantissa[2]; |
| 581 | split_mantissa[0] = ((xsum_uint)mantissa << low_exp) & XSUM_LOW_MANTISSA_MASK(((xsum_int)1 << (1 << 5)) - 1); |
| 582 | split_mantissa[1] = mantissa >> (XSUM_LOW_MANTISSA_BITS(1 << 5) - low_exp); |
| 583 | |
| 584 | /* Add to, or subtract from, the two affected chunks. */ |
| 585 | |
| 586 | #if OPT_SMALL0 == 1 |
| 587 | { |
| 588 | xsum_int ivalue_sign = ivalue < 0 ? -1 : 1; |
| 589 | chunk_ptr[0] += ivalue_sign * split_mantissa[0]; |
| 590 | chunk_ptr[1] += ivalue_sign * split_mantissa[1]; |
| 591 | } |
| 592 | #elif OPT_SMALL0 == 2 |
| 593 | { |
| 594 | xsum_int ivalue_neg = |
| 595 | ivalue >> (XSUM_SCHUNK_BITS64 - 1); /* all 0s if +ve, all 1s if -ve */ |
| 596 | chunk_ptr[0] += (split_mantissa[0] ^ ivalue_neg) + (ivalue_neg & 1); |
| 597 | chunk_ptr[1] += (split_mantissa[1] ^ ivalue_neg) + (ivalue_neg & 1); |
| 598 | } |
| 599 | #elif OPT_SMALL0 == 3 && USE_SIMD1 && __SSE2__1 |
| 600 | { |
| 601 | xsum_int ivalue_neg = |
| 602 | ivalue >> (XSUM_SCHUNK_BITS64 - 1); /* all 0s if +ve, all 1s if -ve */ |
| 603 | _mm_storeu_si128( |
| 604 | (__m128i*)chunk_ptr, |
| 605 | _mm_add_epi64( |
| 606 | _mm_loadu_si128((__m128i*)chunk_ptr), |
| 607 | _mm_add_epi64( |
| 608 | _mm_set1_epi64((__m64)(ivalue_neg & 1)), |
| 609 | _mm_xor_si128(_mm_set1_epi64((__m64)ivalue_neg), |
| 610 | _mm_loadu_si128((__m128i*)split_mantissa))))); |
| 611 | } |
| 612 | #else |
| 613 | { |
| 614 | if (ivalue < 0) { |
| 615 | chunk_ptr[0] -= split_mantissa[0]; |
| 616 | chunk_ptr[1] -= split_mantissa[1]; |
| 617 | } else { |
| 618 | chunk_ptr[0] += split_mantissa[0]; |
| 619 | chunk_ptr[1] += split_mantissa[1]; |
| 620 | } |
| 621 | } |
| 622 | #endif |
| 623 | |
| 624 | if (xsum_debug) { |
| 625 | if (ivalue < 0) { |
| 626 | printf(" -high man: "); |
| 627 | pbinary_int64(-split_mantissa[1], XSUM_MANTISSA_BITS)0; |
| 628 | printf("\n -low man: "); |
| 629 | pbinary_int64(-split_mantissa[0], XSUM_LOW_MANTISSA_BITS)0; |
| 630 | printf("\n"); |
| 631 | } else { |
| 632 | printf(" high man: "); |
| 633 | pbinary_int64(split_mantissa[1], XSUM_MANTISSA_BITS)0; |
| 634 | printf("\n low man: "); |
| 635 | pbinary_int64(split_mantissa[0], XSUM_LOW_MANTISSA_BITS)0; |
| 636 | printf("\n"); |
| 637 | } |
| 638 | } |
| 639 | } |
| 640 | |
| 641 | /* ADD ONE DOUBLE TO A SMALL ACCUMULATOR. This is equivalent to, but |
| 642 | somewhat faster than, calling xsum_small_addv with a vector of one |
| 643 | value. */ |
| 644 | |
| 645 | void xsum_small_add1(xsum_small_accumulator* sacc, xsum_flt value) { |
| 646 | if (sacc->adds_until_propagate == 0) { |
| 647 | (void)xsum_carry_propagate(sacc); |
| 648 | } |
| 649 | |
| 650 | xsum_add1_no_carry(sacc, value); |
| 651 | |
| 652 | sacc->adds_until_propagate -= 1; |
| 653 | } |
| 654 | |
| 655 | /* RETURN THE RESULT OF ROUNDING A SMALL ACCUMULATOR. The rounding mode |
| 656 | is to nearest, with ties to even. The small accumulator may be modified |
| 657 | by this operation (by carry propagation being done), but the value it |
| 658 | represents should not change. */ |
| 659 | |
| 660 | xsum_flt xsum_small_round(xsum_small_accumulator* sacc) { |
| 661 | xsum_int ivalue; |
| 662 | xsum_schunk lower; |
| 663 | int i, j, e, more; |
| 664 | xsum_int intv; |
| 665 | double fltv; |
| 666 | |
| 667 | if (xsum_debug) printf("\nROUNDING SMALL ACCUMULATOR\n"); |
| 668 | |
| 669 | /* See if we have a NaN from one of the numbers being a NaN, in |
| 670 | which case we return the NaN with largest payload, or an infinite |
| 671 | result (+Inf, -Inf, or a NaN if both +Inf and -Inf occurred). |
| 672 | Note that we do NOT return NaN if we have both an infinite number |
| 673 | and a sum of other numbers that overflows with opposite sign, |
| 674 | since there is no real ambiguity regarding the sign in such a case. */ |
| 675 | |
| 676 | if (sacc->NaN != 0) { |
| 677 | COPY64(fltv, sacc->NaN)memcpy(&(fltv), &(sacc->NaN), sizeof(double)); |
| 678 | return fltv; |
| 679 | } |
| 680 | |
| 681 | if (sacc->Inf != 0) { |
| 682 | COPY64(fltv, sacc->Inf)memcpy(&(fltv), &(sacc->Inf), sizeof(double)); |
| 683 | return fltv; |
| 684 | } |
| 685 | |
| 686 | /* If none of the numbers summed were infinite or NaN, we proceed to |
| 687 | propagate carries, as a preliminary to finding the magnitude of |
| 688 | the sum. This also ensures that the sign of the result can be |
| 689 | determined from the uppermost non-zero chunk. |
| 690 | |
| 691 | We also find the index, i, of this uppermost non-zero chunk, as |
| 692 | the value returned by xsum_carry_propagate, and set ivalue to |
| 693 | sacc->chunk[i]. Note that ivalue will not be 0 or -1, unless |
| 694 | i is 0 (the lowest chunk), in which case it will be handled by |
| 695 | the code for denormalized numbers. */ |
| 696 | |
| 697 | i = xsum_carry_propagate(sacc); |
| 698 | |
| 699 | if (xsum_debug) xsum_small_display(sacc); |
| 700 | |
| 701 | ivalue = sacc->chunk[i]; |
| 702 | |
| 703 | /* Handle a possible denormalized number, including zero. */ |
| 704 | |
| 705 | if (i <= 1) { |
| 706 | /* Check for zero value, in which case we can return immediately. */ |
| 707 | |
| 708 | if (ivalue == 0) { |
| 709 | return 0.0; |
| 710 | } |
| 711 | |
| 712 | /* Check if it is actually a denormalized number. It always is if only |
| 713 | the lowest chunk is non-zero. If the highest non-zero chunk is the |
| 714 | next-to-lowest, we check the magnitude of the absolute value. |
| 715 | Note that the real exponent is 1 (not 0), so we need to shift right |
| 716 | by 1 here. */ |
| 717 | |
| 718 | if (i == 0) { |
| 719 | intv = ivalue >= 0 ? ivalue : -ivalue; |
| 720 | intv >>= 1; |
| 721 | if (ivalue < 0) { |
| 722 | intv |= XSUM_SIGN_MASK((xsum_uint)1 << (52 + 11)); |
| 723 | } |
| 724 | if (xsum_debug) { |
| 725 | printf("denormalized with i==0: intv %016llx\n", (long long)intv); |
| 726 | } |
| 727 | COPY64(fltv, intv)memcpy(&(fltv), &(intv), sizeof(double)); |
| 728 | return fltv; |
| 729 | } else { /* Note: Left shift of -ve number is undefined, so do a multiply |
| 730 | instead, which is probably optimized to a shift. */ |
| 731 | intv = ivalue * ((xsum_int)1 << (XSUM_LOW_MANTISSA_BITS(1 << 5) - 1)) + |
| 732 | (sacc->chunk[0] >> 1); |
| 733 | if (intv < 0) { |
| 734 | if (intv > -((xsum_int)1 << XSUM_MANTISSA_BITS52)) { |
| 735 | intv = (-intv) | XSUM_SIGN_MASK((xsum_uint)1 << (52 + 11)); |
| 736 | if (xsum_debug) { |
| 737 | printf("denormalized with i==1: intv %016llx\n", (long long)intv); |
| 738 | } |
| 739 | COPY64(fltv, intv)memcpy(&(fltv), &(intv), sizeof(double)); |
| 740 | return fltv; |
| 741 | } |
| 742 | } else /* non-negative */ |
| 743 | { |
| 744 | if ((xsum_uint)intv < (xsum_uint)1 << XSUM_MANTISSA_BITS52) { |
| 745 | if (xsum_debug) { |
| 746 | printf("denormalized with i==1: intv %016llx\n", (long long)intv); |
| 747 | } |
| 748 | COPY64(fltv, intv)memcpy(&(fltv), &(intv), sizeof(double)); |
| 749 | return fltv; |
| 750 | } |
| 751 | } |
| 752 | /* otherwise, it's not actually denormalized, so fall through to below */ |
| 753 | } |
| 754 | } |
| 755 | |
| 756 | /* Find the location of the uppermost 1 bit in the absolute value of |
| 757 | the upper chunk by converting it (as a signed integer) to a |
| 758 | floating point value, and looking at the exponent. Then set |
| 759 | 'more' to the number of bits from the lower chunk (and maybe the |
| 760 | next lower) that are needed to fill out the mantissa of the |
| 761 | result (including the top implicit 1 bit), plus two extra bits to |
| 762 | help decide on rounding. For negative numbers, it may turn out |
| 763 | later that we need another bit, because negating a negative value |
| 764 | may carry out of the top here, but not carry out of the top once |
| 765 | more bits are shifted into the bottom later on. */ |
| 766 | |
| 767 | fltv = (xsum_flt)ivalue; /* finds position of topmost 1 bit of |ivalue| */ |
| 768 | COPY64(intv, fltv)memcpy(&(intv), &(fltv), sizeof(double)); |
| 769 | e = (intv >> XSUM_MANTISSA_BITS52) & XSUM_EXP_MASK((1 << 11) - 1); /* e-bias is in 0..32 */ |
| 770 | more = 2 + XSUM_MANTISSA_BITS52 + XSUM_EXP_BIAS((1 << (11 - 1)) - 1) - e; |
| 771 | |
| 772 | if (xsum_debug) { |
| 773 | printf("e: %d, more: %d, ivalue: %016llx\n", e, more, |
| 774 | (long long)ivalue); |
| 775 | } |
| 776 | |
| 777 | /* Change 'ivalue' to put in 'more' bits from lower chunks into the bottom. |
| 778 | Also set 'j' to the index of the lowest chunk from which these bits came, |
| 779 | and 'lower' to the remaining bits of that chunk not now in 'ivalue'. |
| 780 | Note that 'lower' initially has at least one bit in it, which we can |
| 781 | later move into 'ivalue' if it turns out that one more bit is needed. */ |
| 782 | |
| 783 | ivalue *= (xsum_int)1 << more; /* multiply, since << of negative undefined */ |
| 784 | if (xsum_debug) { |
| 785 | printf("after ivalue <<= more, ivalue: %016llx\n", |
| 786 | (long long)ivalue); |
| 787 | } |
| 788 | j = i - 1; |
| 789 | lower = sacc->chunk[j]; /* must exist, since denormalized if i==0 */ |
| 790 | if (more >= XSUM_LOW_MANTISSA_BITS(1 << 5)) { |
| 791 | more -= XSUM_LOW_MANTISSA_BITS(1 << 5); |
| 792 | ivalue += lower << more; |
| 793 | if (xsum_debug) { |
| 794 | printf("after ivalue += lower << more, ivalue: %016llx\n", |
| 795 | (long long)ivalue); |
| 796 | } |
| 797 | j -= 1; |
| 798 | lower = j < 0 ? 0 : sacc->chunk[j]; |
| 799 | } |
| 800 | ivalue += lower >> (XSUM_LOW_MANTISSA_BITS(1 << 5) - more); |
| 801 | lower &= ((xsum_schunk)1 << (XSUM_LOW_MANTISSA_BITS(1 << 5) - more)) - 1; |
| 802 | |
| 803 | if (xsum_debug) { |
| 804 | printf("after final add to ivalue, ivalue: %016llx\n", |
| 805 | (long long)ivalue); |
| 806 | printf("j: %d, e: %d, |ivalue|: %016llx, lower: %016llx (a)\n", j, e, |
| 807 | (long long)(ivalue < 0 ? -ivalue : ivalue), (long long)lower); |
| 808 | printf(" mask of low 55 bits: 007fffffffffffff, mask: %016llx\n", |
| 809 | (long long)((xsum_schunk)1 << (XSUM_LOW_MANTISSA_BITS(1 << 5) - more)) - 1); |
| 810 | } |
| 811 | |
| 812 | /* Decide on rounding, with separate code for positive and negative values. |
| 813 | |
| 814 | At this point, 'ivalue' has the signed mantissa bits, plus two extra |
| 815 | bits, with 'e' recording the exponent position for these within their |
| 816 | top chunk. For positive 'ivalue', the bits in 'lower' and chunks |
| 817 | below 'j' add to the absolute value; for negative 'ivalue' they |
| 818 | subtract. |
| 819 | |
| 820 | After setting 'ivalue' to the tentative unsigned mantissa |
| 821 | (shifted left 2), and 'intv' to have the correct sign, this |
| 822 | code goes to done_rounding if it finds that just discarding lower |
| 823 | order bits is correct, and to round_away_from_zero if instead the |
| 824 | magnitude should be increased by one in the lowest mantissa bit. */ |
| 825 | |
| 826 | if (ivalue >= 0) /* number is positive, lower bits are added to magnitude */ |
| 827 | { |
| 828 | intv = 0; /* positive sign */ |
| 829 | |
| 830 | if ((ivalue & 2) == 0) /* extra bits are 0x */ |
| 831 | { |
| 832 | if (xsum_debug) { |
| 833 | printf("+, no adjustment, since remainder adds <1/2\n"); |
| 834 | } |
| 835 | goto done_rounding; |
| 836 | } |
| 837 | |
| 838 | if ((ivalue & 1) != 0) /* extra bits are 11 */ |
| 839 | { |
| 840 | if (xsum_debug) { |
| 841 | printf("+, round away from 0, since remainder adds >1/2\n"); |
| 842 | } |
| 843 | goto round_away_from_zero; |
| 844 | } |
| 845 | |
| 846 | if ((ivalue & 4) != 0) /* low bit is 1 (odd), extra bits are 10 */ |
| 847 | { |
| 848 | if (xsum_debug) { |
| 849 | printf("+odd, round away from 0, since remainder adds >=1/2\n"); |
| 850 | } |
| 851 | goto round_away_from_zero; |
| 852 | } |
| 853 | |
| 854 | if (lower == 0) /* see if any lower bits are non-zero */ |
| 855 | { |
| 856 | while (j > 0) { |
| 857 | j -= 1; |
| 858 | if (sacc->chunk[j] != 0) { |
| 859 | lower = 1; |
| 860 | break; |
| 861 | } |
| 862 | } |
| 863 | } |
| 864 | |
| 865 | if (lower != 0) /* low bit 0 (even), extra bits 10, non-zero lower bits */ |
| 866 | { |
| 867 | if (xsum_debug) { |
| 868 | printf("+even, round away from 0, since remainder adds >1/2\n"); |
| 869 | } |
| 870 | goto round_away_from_zero; |
| 871 | } else /* low bit 0 (even), extra bits 10, all lower bits 0 */ |
| 872 | { |
| 873 | if (xsum_debug) { |
| 874 | printf("+even, no adjustment, since reaminder adds exactly 1/2\n"); |
| 875 | } |
| 876 | goto done_rounding; |
| 877 | } |
| 878 | } |
| 879 | |
| 880 | else /* number is negative, lower bits are subtracted from magnitude */ |
| 881 | { |
| 882 | /* Check for a negative 'ivalue' that when negated doesn't contain a full |
| 883 | mantissa's worth of bits, plus one to help rounding. If so, move one |
| 884 | more bit into 'ivalue' from 'lower' (and remove it from 'lower'). |
| 885 | This happens when the negation of the upper part of 'ivalue' has the |
| 886 | form 10000... but the negation of the full 'ivalue' is not 10000... */ |
| 887 | |
| 888 | if (((-ivalue) & ((xsum_int)1 << (XSUM_MANTISSA_BITS52 + 2))) == 0) { |
| 889 | int pos = (xsum_schunk)1 << (XSUM_LOW_MANTISSA_BITS(1 << 5) - 1 - more); |
| 890 | ivalue *= 2; /* note that left shift undefined if ivalue is negative */ |
| 891 | if (lower & pos) { |
| 892 | ivalue += 1; |
| 893 | lower &= ~pos; |
| 894 | } |
| 895 | e -= 1; |
| 896 | if (xsum_debug) { |
| 897 | printf("j: %d, e: %d, |ivalue|: %016llx, lower: %016llx (b)\n", j, e, |
| 898 | (long long)(ivalue < 0 ? -ivalue : ivalue), (long long)lower); |
| 899 | } |
| 900 | } |
| 901 | |
| 902 | intv = XSUM_SIGN_MASK((xsum_uint)1 << (52 + 11)); /* negative sign */ |
| 903 | ivalue = -ivalue; /* ivalue now contains the absolute value */ |
| 904 | |
| 905 | if ((ivalue & 3) == 3) /* extra bits are 11 */ |
| 906 | { |
| 907 | if (xsum_debug) { |
| 908 | printf("-, round away from 0, since remainder adds >1/2\n"); |
| 909 | } |
| 910 | goto round_away_from_zero; |
| 911 | } |
| 912 | |
| 913 | if ((ivalue & 3) <= 1) /* extra bits are 00 or 01 */ |
| 914 | { |
| 915 | if (xsum_debug) { |
| 916 | printf( |
| 917 | "-, no adjustment, since remainder adds <=1/4 or subtracts <1/4\n"); |
| 918 | } |
| 919 | goto done_rounding; |
| 920 | } |
| 921 | |
| 922 | if ((ivalue & 4) == 0) /* low bit is 0 (even), extra bits are 10 */ |
| 923 | { |
| 924 | if (xsum_debug) { |
| 925 | printf("-even, no adjustment, since remainder adds <=1/2\n"); |
| 926 | } |
| 927 | goto done_rounding; |
| 928 | } |
| 929 | |
| 930 | if (lower == 0) /* see if any lower bits are non-zero */ |
| 931 | { |
| 932 | while (j > 0) { |
| 933 | j -= 1; |
| 934 | if (sacc->chunk[j] != 0) { |
| 935 | lower = 1; |
| 936 | break; |
| 937 | } |
| 938 | } |
| 939 | } |
| 940 | |
| 941 | if (lower != 0) /* low bit 1 (odd), extra bits 10, non-zero lower bits */ |
| 942 | { |
| 943 | if (xsum_debug) { |
| 944 | printf("-odd, no adjustment, since remainder adds <1/2\n"); |
| 945 | } |
| 946 | goto done_rounding; |
| 947 | } else /* low bit 1 (odd), extra bits are 10, lower bits are all 0 */ |
| 948 | { |
| 949 | if (xsum_debug) { |
| 950 | printf("-odd, round away from 0, since remainder adds exactly 1/2\n"); |
| 951 | } |
| 952 | goto round_away_from_zero; |
| 953 | } |
| 954 | } |
| 955 | |
| 956 | round_away_from_zero: |
| 957 | |
| 958 | /* Round away from zero, then check for carry having propagated out the |
| 959 | top, and shift if so. */ |
| 960 | |
| 961 | ivalue += 4; /* add 1 to low-order mantissa bit */ |
| 962 | if (ivalue & ((xsum_int)1 << (XSUM_MANTISSA_BITS52 + 3))) { |
| 963 | ivalue >>= 1; |
| 964 | e += 1; |
| 965 | } |
| 966 | |
| 967 | done_rounding:; |
| 968 | |
| 969 | /* Get rid of the bottom 2 bits that were used to decide on rounding. */ |
| 970 | |
| 971 | ivalue >>= 2; |
| 972 | |
| 973 | /* Adjust to the true exponent, accounting for where this chunk is. */ |
| 974 | |
| 975 | e += (i << XSUM_LOW_EXP_BITS5) - XSUM_EXP_BIAS((1 << (11 - 1)) - 1) - XSUM_MANTISSA_BITS52; |
| 976 | |
| 977 | /* If exponent has overflowed, change to plus or minus Inf and return. */ |
| 978 | |
| 979 | if (e >= XSUM_EXP_MASK((1 << 11) - 1)) { |
| 980 | intv |= (xsum_int)XSUM_EXP_MASK((1 << 11) - 1) << XSUM_MANTISSA_BITS52; |
| 981 | COPY64(fltv, intv)memcpy(&(fltv), &(intv), sizeof(double)); |
| 982 | if (xsum_debug) { |
| 983 | printf("Final rounded result: %.17le (overflowed)\n ", fltv); |
| 984 | pbinary_double(fltv)0; |
| 985 | printf("\n"); |
| 986 | } |
| 987 | return fltv; |
| 988 | } |
| 989 | |
| 990 | /* Put exponent and mantissa into intv, which already has the sign, |
| 991 | then copy into fltv. */ |
| 992 | |
| 993 | intv += (xsum_int)e << XSUM_MANTISSA_BITS52; |
| 994 | intv += ivalue & XSUM_MANTISSA_MASK(((xsum_int)1 << 52) - 1); /* mask out the implicit 1 bit */ |
| 995 | COPY64(fltv, intv)memcpy(&(fltv), &(intv), sizeof(double)); |
| 996 | |
| 997 | if (xsum_debug) { |
| 998 | printf("Final rounded result: %.17le\n ", fltv); |
| 999 | pbinary_double(fltv)0; |
| 1000 | printf("\n"); |
| 1001 | if ((ivalue >> XSUM_MANTISSA_BITS52) != 1) abort(); |
| 1002 | } |
| 1003 | |
| 1004 | return fltv; |
| 1005 | } |
| 1006 | |
| 1007 | /* ------------------------- DEBUGGING ROUTINES ----------------------------- */ |
| 1008 | |
| 1009 | /* DISPLAY A SMALL ACCUMULATOR. */ |
| 1010 | |
| 1011 | void xsum_small_display(xsum_small_accumulator* sacc) { |
| 1012 | int i, dots; |
| 1013 | printf("Small accumulator:"); |
| 1014 | if (sacc->Inf) { |
| 1015 | printf(" %cInf", sacc->Inf > 0 ? '+' : '-'); |
| 1016 | if ((sacc->Inf & ((xsum_uint)XSUM_EXP_MASK((1 << 11) - 1) << XSUM_MANTISSA_BITS52)) != |
| 1017 | ((xsum_uint)XSUM_EXP_MASK((1 << 11) - 1) << XSUM_MANTISSA_BITS52)) { |
| 1018 | printf(" BUT WRONG CONTENTS: %llx", (long long)sacc->Inf); |
| 1019 | } |
| 1020 | } |
| 1021 | if (sacc->NaN) { |
| 1022 | printf(" NaN (%llx)", (long long)sacc->NaN); |
| 1023 | } |
| 1024 | printf("\n"); |
| 1025 | dots = 0; |
| 1026 | for (i = XSUM_SCHUNKS((1 << (11 - 5)) + 3) - 1; i >= 0; i--) { |
| 1027 | if (sacc->chunk[i] == 0) { |
| 1028 | if (!dots) printf(" ...\n"); |
| 1029 | dots = 1; |
| 1030 | } else { |
| 1031 | printf( |
| 1032 | "%5d %5d ", i, |
| 1033 | (int)((i << XSUM_LOW_EXP_BITS5) - XSUM_EXP_BIAS((1 << (11 - 1)) - 1) - XSUM_MANTISSA_BITS52)); |
| 1034 | pbinary_int64((int64_t)sacc->chunk[i] >> 32, XSUM_SCHUNK_BITS - 32)0; |
| 1035 | printf(" "); |
| 1036 | pbinary_int64((int64_t)sacc->chunk[i] & 0xffffffff, 32)0; |
| 1037 | printf("\n"); |
| 1038 | dots = 0; |
| 1039 | } |
| 1040 | } |
| 1041 | printf("\n"); |
| 1042 | } |