1 /* 2 * QEMU float support 3 * 4 * The code in this source file is derived from release 2a of the SoftFloat 5 * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and 6 * some later contributions) are provided under that license, as detailed below. 7 * It has subsequently been modified by contributors to the QEMU Project, 8 * so some portions are provided under: 9 * the SoftFloat-2a license 10 * the BSD license 11 * GPL-v2-or-later 12 * 13 * Any future contributions to this file after December 1st 2014 will be 14 * taken to be licensed under the Softfloat-2a license unless specifically 15 * indicated otherwise. 16 */ 17 18 /* 19 =============================================================================== 20 This C header file is part of the SoftFloat IEC/IEEE Floating-point 21 Arithmetic Package, Release 2a. 22 23 Written by John R. Hauser. This work was made possible in part by the 24 International Computer Science Institute, located at Suite 600, 1947 Center 25 Street, Berkeley, California 94704. Funding was partially provided by the 26 National Science Foundation under grant MIP-9311980. The original version 27 of this code was written as part of a project to build a fixed-point vector 28 processor in collaboration with the University of California at Berkeley, 29 overseen by Profs. Nelson Morgan and John Wawrzynek. More information 30 is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/ 31 arithmetic/SoftFloat.html'. 32 33 THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort 34 has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT 35 TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO 36 PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY 37 AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. 38 39 Derivative works are acceptable, even for commercial purposes, so long as 40 (1) they include prominent notice that the work is derivative, and (2) they 41 include prominent notice akin to these four paragraphs for those parts of 42 this code that are retained. 43 44 =============================================================================== 45 */ 46 47 /* BSD licensing: 48 * Copyright (c) 2006, Fabrice Bellard 49 * All rights reserved. 50 * 51 * Redistribution and use in source and binary forms, with or without 52 * modification, are permitted provided that the following conditions are met: 53 * 54 * 1. Redistributions of source code must retain the above copyright notice, 55 * this list of conditions and the following disclaimer. 56 * 57 * 2. Redistributions in binary form must reproduce the above copyright notice, 58 * this list of conditions and the following disclaimer in the documentation 59 * and/or other materials provided with the distribution. 60 * 61 * 3. Neither the name of the copyright holder nor the names of its contributors 62 * may be used to endorse or promote products derived from this software without 63 * specific prior written permission. 64 * 65 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 66 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 67 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 68 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE 69 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 70 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 71 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 72 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 73 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 74 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF 75 * THE POSSIBILITY OF SUCH DAMAGE. 76 */ 77 78 /* Portions of this work are licensed under the terms of the GNU GPL, 79 * version 2 or later. See the COPYING file in the top-level directory. 80 */ 81 82 #ifndef SOFTFLOAT_H 83 #define SOFTFLOAT_H 84 85 /*---------------------------------------------------------------------------- 86 | Software IEC/IEEE floating-point ordering relations 87 *----------------------------------------------------------------------------*/ 88 89 typedef enum { 90 float_relation_less = -1, 91 float_relation_equal = 0, 92 float_relation_greater = 1, 93 float_relation_unordered = 2 94 } FloatRelation; 95 96 #include "fpu/softfloat-types.h" 97 #include "fpu/softfloat-helpers.h" 98 #include "qemu/int128.h" 99 100 /*---------------------------------------------------------------------------- 101 | Routine to raise any or all of the software IEC/IEEE floating-point 102 | exception flags. 103 *----------------------------------------------------------------------------*/ 104 static inline void float_raise(uint16_t flags, float_status *status) 105 { 106 status->float_exception_flags |= flags; 107 } 108 109 /*---------------------------------------------------------------------------- 110 | If `a' is denormal and we are in flush-to-zero mode then set the 111 | input-denormal exception and return zero. Otherwise just return the value. 112 *----------------------------------------------------------------------------*/ 113 float16 float16_squash_input_denormal(float16 a, float_status *status); 114 float32 float32_squash_input_denormal(float32 a, float_status *status); 115 float64 float64_squash_input_denormal(float64 a, float_status *status); 116 bfloat16 bfloat16_squash_input_denormal(bfloat16 a, float_status *status); 117 118 /*---------------------------------------------------------------------------- 119 | Options to indicate which negations to perform in float*_muladd() 120 | Using these differs from negating an input or output before calling 121 | the muladd function in that this means that a NaN doesn't have its 122 | sign bit inverted before it is propagated. 123 | We also support halving the result before rounding, as a special 124 | case to support the ARM fused-sqrt-step instruction FRSQRTS. 125 *----------------------------------------------------------------------------*/ 126 enum { 127 float_muladd_negate_c = 1, 128 float_muladd_negate_product = 2, 129 float_muladd_negate_result = 4, 130 float_muladd_halve_result = 8, 131 }; 132 133 /*---------------------------------------------------------------------------- 134 | Software IEC/IEEE integer-to-floating-point conversion routines. 135 *----------------------------------------------------------------------------*/ 136 137 float16 int16_to_float16_scalbn(int16_t a, int, float_status *status); 138 float16 int32_to_float16_scalbn(int32_t a, int, float_status *status); 139 float16 int64_to_float16_scalbn(int64_t a, int, float_status *status); 140 float16 uint16_to_float16_scalbn(uint16_t a, int, float_status *status); 141 float16 uint32_to_float16_scalbn(uint32_t a, int, float_status *status); 142 float16 uint64_to_float16_scalbn(uint64_t a, int, float_status *status); 143 144 float16 int8_to_float16(int8_t a, float_status *status); 145 float16 int16_to_float16(int16_t a, float_status *status); 146 float16 int32_to_float16(int32_t a, float_status *status); 147 float16 int64_to_float16(int64_t a, float_status *status); 148 float16 uint8_to_float16(uint8_t a, float_status *status); 149 float16 uint16_to_float16(uint16_t a, float_status *status); 150 float16 uint32_to_float16(uint32_t a, float_status *status); 151 float16 uint64_to_float16(uint64_t a, float_status *status); 152 153 float32 int16_to_float32_scalbn(int16_t, int, float_status *status); 154 float32 int32_to_float32_scalbn(int32_t, int, float_status *status); 155 float32 int64_to_float32_scalbn(int64_t, int, float_status *status); 156 float32 uint16_to_float32_scalbn(uint16_t, int, float_status *status); 157 float32 uint32_to_float32_scalbn(uint32_t, int, float_status *status); 158 float32 uint64_to_float32_scalbn(uint64_t, int, float_status *status); 159 160 float32 int16_to_float32(int16_t, float_status *status); 161 float32 int32_to_float32(int32_t, float_status *status); 162 float32 int64_to_float32(int64_t, float_status *status); 163 float32 uint16_to_float32(uint16_t, float_status *status); 164 float32 uint32_to_float32(uint32_t, float_status *status); 165 float32 uint64_to_float32(uint64_t, float_status *status); 166 167 float64 int16_to_float64_scalbn(int16_t, int, float_status *status); 168 float64 int32_to_float64_scalbn(int32_t, int, float_status *status); 169 float64 int64_to_float64_scalbn(int64_t, int, float_status *status); 170 float64 uint16_to_float64_scalbn(uint16_t, int, float_status *status); 171 float64 uint32_to_float64_scalbn(uint32_t, int, float_status *status); 172 float64 uint64_to_float64_scalbn(uint64_t, int, float_status *status); 173 174 float64 int16_to_float64(int16_t, float_status *status); 175 float64 int32_to_float64(int32_t, float_status *status); 176 float64 int64_to_float64(int64_t, float_status *status); 177 float64 uint16_to_float64(uint16_t, float_status *status); 178 float64 uint32_to_float64(uint32_t, float_status *status); 179 float64 uint64_to_float64(uint64_t, float_status *status); 180 181 floatx80 int32_to_floatx80(int32_t, float_status *status); 182 floatx80 int64_to_floatx80(int64_t, float_status *status); 183 184 float128 int32_to_float128(int32_t, float_status *status); 185 float128 int64_to_float128(int64_t, float_status *status); 186 float128 int128_to_float128(Int128, float_status *status); 187 float128 uint64_to_float128(uint64_t, float_status *status); 188 float128 uint128_to_float128(Int128, float_status *status); 189 190 /*---------------------------------------------------------------------------- 191 | Software half-precision conversion routines. 192 *----------------------------------------------------------------------------*/ 193 194 float16 float32_to_float16(float32, bool ieee, float_status *status); 195 float32 float16_to_float32(float16, bool ieee, float_status *status); 196 float16 float64_to_float16(float64 a, bool ieee, float_status *status); 197 float64 float16_to_float64(float16 a, bool ieee, float_status *status); 198 199 int8_t float16_to_int8_scalbn(float16, FloatRoundMode, int, 200 float_status *status); 201 int16_t float16_to_int16_scalbn(float16, FloatRoundMode, int, float_status *); 202 int32_t float16_to_int32_scalbn(float16, FloatRoundMode, int, float_status *); 203 int64_t float16_to_int64_scalbn(float16, FloatRoundMode, int, float_status *); 204 205 int8_t float16_to_int8(float16, float_status *status); 206 int16_t float16_to_int16(float16, float_status *status); 207 int32_t float16_to_int32(float16, float_status *status); 208 int64_t float16_to_int64(float16, float_status *status); 209 210 int16_t float16_to_int16_round_to_zero(float16, float_status *status); 211 int32_t float16_to_int32_round_to_zero(float16, float_status *status); 212 int64_t float16_to_int64_round_to_zero(float16, float_status *status); 213 214 uint8_t float16_to_uint8_scalbn(float16 a, FloatRoundMode, 215 int, float_status *status); 216 uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode, 217 int, float_status *status); 218 uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode, 219 int, float_status *status); 220 uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode, 221 int, float_status *status); 222 223 uint8_t float16_to_uint8(float16 a, float_status *status); 224 uint16_t float16_to_uint16(float16 a, float_status *status); 225 uint32_t float16_to_uint32(float16 a, float_status *status); 226 uint64_t float16_to_uint64(float16 a, float_status *status); 227 228 uint16_t float16_to_uint16_round_to_zero(float16 a, float_status *status); 229 uint32_t float16_to_uint32_round_to_zero(float16 a, float_status *status); 230 uint64_t float16_to_uint64_round_to_zero(float16 a, float_status *status); 231 232 /*---------------------------------------------------------------------------- 233 | Software half-precision operations. 234 *----------------------------------------------------------------------------*/ 235 236 float16 float16_round_to_int(float16, float_status *status); 237 float16 float16_add(float16, float16, float_status *status); 238 float16 float16_sub(float16, float16, float_status *status); 239 float16 float16_mul(float16, float16, float_status *status); 240 float16 float16_muladd(float16, float16, float16, int, float_status *status); 241 float16 float16_div(float16, float16, float_status *status); 242 float16 float16_scalbn(float16, int, float_status *status); 243 float16 float16_min(float16, float16, float_status *status); 244 float16 float16_max(float16, float16, float_status *status); 245 float16 float16_minnum(float16, float16, float_status *status); 246 float16 float16_maxnum(float16, float16, float_status *status); 247 float16 float16_minnummag(float16, float16, float_status *status); 248 float16 float16_maxnummag(float16, float16, float_status *status); 249 float16 float16_minimum_number(float16, float16, float_status *status); 250 float16 float16_maximum_number(float16, float16, float_status *status); 251 float16 float16_sqrt(float16, float_status *status); 252 FloatRelation float16_compare(float16, float16, float_status *status); 253 FloatRelation float16_compare_quiet(float16, float16, float_status *status); 254 255 bool float16_is_quiet_nan(float16, float_status *status); 256 bool float16_is_signaling_nan(float16, float_status *status); 257 float16 float16_silence_nan(float16, float_status *status); 258 259 static inline bool float16_is_any_nan(float16 a) 260 { 261 return ((float16_val(a) & ~0x8000) > 0x7c00); 262 } 263 264 static inline bool float16_is_neg(float16 a) 265 { 266 return float16_val(a) >> 15; 267 } 268 269 static inline bool float16_is_infinity(float16 a) 270 { 271 return (float16_val(a) & 0x7fff) == 0x7c00; 272 } 273 274 static inline bool float16_is_zero(float16 a) 275 { 276 return (float16_val(a) & 0x7fff) == 0; 277 } 278 279 static inline bool float16_is_zero_or_denormal(float16 a) 280 { 281 return (float16_val(a) & 0x7c00) == 0; 282 } 283 284 static inline bool float16_is_normal(float16 a) 285 { 286 return (((float16_val(a) >> 10) + 1) & 0x1f) >= 2; 287 } 288 289 static inline float16 float16_abs(float16 a) 290 { 291 /* Note that abs does *not* handle NaN specially, nor does 292 * it flush denormal inputs to zero. 293 */ 294 return make_float16(float16_val(a) & 0x7fff); 295 } 296 297 static inline float16 float16_chs(float16 a) 298 { 299 /* Note that chs does *not* handle NaN specially, nor does 300 * it flush denormal inputs to zero. 301 */ 302 return make_float16(float16_val(a) ^ 0x8000); 303 } 304 305 static inline float16 float16_set_sign(float16 a, int sign) 306 { 307 return make_float16((float16_val(a) & 0x7fff) | (sign << 15)); 308 } 309 310 static inline bool float16_eq(float16 a, float16 b, float_status *s) 311 { 312 return float16_compare(a, b, s) == float_relation_equal; 313 } 314 315 static inline bool float16_le(float16 a, float16 b, float_status *s) 316 { 317 return float16_compare(a, b, s) <= float_relation_equal; 318 } 319 320 static inline bool float16_lt(float16 a, float16 b, float_status *s) 321 { 322 return float16_compare(a, b, s) < float_relation_equal; 323 } 324 325 static inline bool float16_unordered(float16 a, float16 b, float_status *s) 326 { 327 return float16_compare(a, b, s) == float_relation_unordered; 328 } 329 330 static inline bool float16_eq_quiet(float16 a, float16 b, float_status *s) 331 { 332 return float16_compare_quiet(a, b, s) == float_relation_equal; 333 } 334 335 static inline bool float16_le_quiet(float16 a, float16 b, float_status *s) 336 { 337 return float16_compare_quiet(a, b, s) <= float_relation_equal; 338 } 339 340 static inline bool float16_lt_quiet(float16 a, float16 b, float_status *s) 341 { 342 return float16_compare_quiet(a, b, s) < float_relation_equal; 343 } 344 345 static inline bool float16_unordered_quiet(float16 a, float16 b, 346 float_status *s) 347 { 348 return float16_compare_quiet(a, b, s) == float_relation_unordered; 349 } 350 351 #define float16_zero make_float16(0) 352 #define float16_half make_float16(0x3800) 353 #define float16_one make_float16(0x3c00) 354 #define float16_one_point_five make_float16(0x3e00) 355 #define float16_two make_float16(0x4000) 356 #define float16_three make_float16(0x4200) 357 #define float16_infinity make_float16(0x7c00) 358 359 /*---------------------------------------------------------------------------- 360 | Software bfloat16 conversion routines. 361 *----------------------------------------------------------------------------*/ 362 363 bfloat16 bfloat16_round_to_int(bfloat16, float_status *status); 364 bfloat16 float32_to_bfloat16(float32, float_status *status); 365 float32 bfloat16_to_float32(bfloat16, float_status *status); 366 bfloat16 float64_to_bfloat16(float64 a, float_status *status); 367 float64 bfloat16_to_float64(bfloat16 a, float_status *status); 368 369 int16_t bfloat16_to_int16_scalbn(bfloat16, FloatRoundMode, 370 int, float_status *status); 371 int32_t bfloat16_to_int32_scalbn(bfloat16, FloatRoundMode, 372 int, float_status *status); 373 int64_t bfloat16_to_int64_scalbn(bfloat16, FloatRoundMode, 374 int, float_status *status); 375 376 int16_t bfloat16_to_int16(bfloat16, float_status *status); 377 int32_t bfloat16_to_int32(bfloat16, float_status *status); 378 int64_t bfloat16_to_int64(bfloat16, float_status *status); 379 380 int16_t bfloat16_to_int16_round_to_zero(bfloat16, float_status *status); 381 int32_t bfloat16_to_int32_round_to_zero(bfloat16, float_status *status); 382 int64_t bfloat16_to_int64_round_to_zero(bfloat16, float_status *status); 383 384 uint16_t bfloat16_to_uint16_scalbn(bfloat16 a, FloatRoundMode, 385 int, float_status *status); 386 uint32_t bfloat16_to_uint32_scalbn(bfloat16 a, FloatRoundMode, 387 int, float_status *status); 388 uint64_t bfloat16_to_uint64_scalbn(bfloat16 a, FloatRoundMode, 389 int, float_status *status); 390 391 uint16_t bfloat16_to_uint16(bfloat16 a, float_status *status); 392 uint32_t bfloat16_to_uint32(bfloat16 a, float_status *status); 393 uint64_t bfloat16_to_uint64(bfloat16 a, float_status *status); 394 395 uint16_t bfloat16_to_uint16_round_to_zero(bfloat16 a, float_status *status); 396 uint32_t bfloat16_to_uint32_round_to_zero(bfloat16 a, float_status *status); 397 uint64_t bfloat16_to_uint64_round_to_zero(bfloat16 a, float_status *status); 398 399 bfloat16 int16_to_bfloat16_scalbn(int16_t a, int, float_status *status); 400 bfloat16 int32_to_bfloat16_scalbn(int32_t a, int, float_status *status); 401 bfloat16 int64_to_bfloat16_scalbn(int64_t a, int, float_status *status); 402 bfloat16 uint16_to_bfloat16_scalbn(uint16_t a, int, float_status *status); 403 bfloat16 uint32_to_bfloat16_scalbn(uint32_t a, int, float_status *status); 404 bfloat16 uint64_to_bfloat16_scalbn(uint64_t a, int, float_status *status); 405 406 bfloat16 int16_to_bfloat16(int16_t a, float_status *status); 407 bfloat16 int32_to_bfloat16(int32_t a, float_status *status); 408 bfloat16 int64_to_bfloat16(int64_t a, float_status *status); 409 bfloat16 uint16_to_bfloat16(uint16_t a, float_status *status); 410 bfloat16 uint32_to_bfloat16(uint32_t a, float_status *status); 411 bfloat16 uint64_to_bfloat16(uint64_t a, float_status *status); 412 413 /*---------------------------------------------------------------------------- 414 | Software bfloat16 operations. 415 *----------------------------------------------------------------------------*/ 416 417 bfloat16 bfloat16_add(bfloat16, bfloat16, float_status *status); 418 bfloat16 bfloat16_sub(bfloat16, bfloat16, float_status *status); 419 bfloat16 bfloat16_mul(bfloat16, bfloat16, float_status *status); 420 bfloat16 bfloat16_div(bfloat16, bfloat16, float_status *status); 421 bfloat16 bfloat16_muladd(bfloat16, bfloat16, bfloat16, int, 422 float_status *status); 423 float16 bfloat16_scalbn(bfloat16, int, float_status *status); 424 bfloat16 bfloat16_min(bfloat16, bfloat16, float_status *status); 425 bfloat16 bfloat16_max(bfloat16, bfloat16, float_status *status); 426 bfloat16 bfloat16_minnum(bfloat16, bfloat16, float_status *status); 427 bfloat16 bfloat16_maxnum(bfloat16, bfloat16, float_status *status); 428 bfloat16 bfloat16_minnummag(bfloat16, bfloat16, float_status *status); 429 bfloat16 bfloat16_maxnummag(bfloat16, bfloat16, float_status *status); 430 bfloat16 bfloat16_minimum_number(bfloat16, bfloat16, float_status *status); 431 bfloat16 bfloat16_maximum_number(bfloat16, bfloat16, float_status *status); 432 bfloat16 bfloat16_sqrt(bfloat16, float_status *status); 433 FloatRelation bfloat16_compare(bfloat16, bfloat16, float_status *status); 434 FloatRelation bfloat16_compare_quiet(bfloat16, bfloat16, float_status *status); 435 436 bool bfloat16_is_quiet_nan(bfloat16, float_status *status); 437 bool bfloat16_is_signaling_nan(bfloat16, float_status *status); 438 bfloat16 bfloat16_silence_nan(bfloat16, float_status *status); 439 bfloat16 bfloat16_default_nan(float_status *status); 440 441 static inline bool bfloat16_is_any_nan(bfloat16 a) 442 { 443 return ((a & ~0x8000) > 0x7F80); 444 } 445 446 static inline bool bfloat16_is_neg(bfloat16 a) 447 { 448 return a >> 15; 449 } 450 451 static inline bool bfloat16_is_infinity(bfloat16 a) 452 { 453 return (a & 0x7fff) == 0x7F80; 454 } 455 456 static inline bool bfloat16_is_zero(bfloat16 a) 457 { 458 return (a & 0x7fff) == 0; 459 } 460 461 static inline bool bfloat16_is_zero_or_denormal(bfloat16 a) 462 { 463 return (a & 0x7F80) == 0; 464 } 465 466 static inline bool bfloat16_is_normal(bfloat16 a) 467 { 468 return (((a >> 7) + 1) & 0xff) >= 2; 469 } 470 471 static inline bfloat16 bfloat16_abs(bfloat16 a) 472 { 473 /* Note that abs does *not* handle NaN specially, nor does 474 * it flush denormal inputs to zero. 475 */ 476 return a & 0x7fff; 477 } 478 479 static inline bfloat16 bfloat16_chs(bfloat16 a) 480 { 481 /* Note that chs does *not* handle NaN specially, nor does 482 * it flush denormal inputs to zero. 483 */ 484 return a ^ 0x8000; 485 } 486 487 static inline bfloat16 bfloat16_set_sign(bfloat16 a, int sign) 488 { 489 return (a & 0x7fff) | (sign << 15); 490 } 491 492 static inline bool bfloat16_eq(bfloat16 a, bfloat16 b, float_status *s) 493 { 494 return bfloat16_compare(a, b, s) == float_relation_equal; 495 } 496 497 static inline bool bfloat16_le(bfloat16 a, bfloat16 b, float_status *s) 498 { 499 return bfloat16_compare(a, b, s) <= float_relation_equal; 500 } 501 502 static inline bool bfloat16_lt(bfloat16 a, bfloat16 b, float_status *s) 503 { 504 return bfloat16_compare(a, b, s) < float_relation_equal; 505 } 506 507 static inline bool bfloat16_unordered(bfloat16 a, bfloat16 b, float_status *s) 508 { 509 return bfloat16_compare(a, b, s) == float_relation_unordered; 510 } 511 512 static inline bool bfloat16_eq_quiet(bfloat16 a, bfloat16 b, float_status *s) 513 { 514 return bfloat16_compare_quiet(a, b, s) == float_relation_equal; 515 } 516 517 static inline bool bfloat16_le_quiet(bfloat16 a, bfloat16 b, float_status *s) 518 { 519 return bfloat16_compare_quiet(a, b, s) <= float_relation_equal; 520 } 521 522 static inline bool bfloat16_lt_quiet(bfloat16 a, bfloat16 b, float_status *s) 523 { 524 return bfloat16_compare_quiet(a, b, s) < float_relation_equal; 525 } 526 527 static inline bool bfloat16_unordered_quiet(bfloat16 a, bfloat16 b, 528 float_status *s) 529 { 530 return bfloat16_compare_quiet(a, b, s) == float_relation_unordered; 531 } 532 533 #define bfloat16_zero 0 534 #define bfloat16_half 0x3f00 535 #define bfloat16_one 0x3f80 536 #define bfloat16_one_point_five 0x3fc0 537 #define bfloat16_two 0x4000 538 #define bfloat16_three 0x4040 539 #define bfloat16_infinity 0x7f80 540 541 /*---------------------------------------------------------------------------- 542 | The pattern for a default generated half-precision NaN. 543 *----------------------------------------------------------------------------*/ 544 float16 float16_default_nan(float_status *status); 545 546 /*---------------------------------------------------------------------------- 547 | Software IEC/IEEE single-precision conversion routines. 548 *----------------------------------------------------------------------------*/ 549 550 int16_t float32_to_int16_scalbn(float32, FloatRoundMode, int, float_status *); 551 int32_t float32_to_int32_scalbn(float32, FloatRoundMode, int, float_status *); 552 int64_t float32_to_int64_scalbn(float32, FloatRoundMode, int, float_status *); 553 554 int16_t float32_to_int16(float32, float_status *status); 555 int32_t float32_to_int32(float32, float_status *status); 556 int64_t float32_to_int64(float32, float_status *status); 557 558 int16_t float32_to_int16_round_to_zero(float32, float_status *status); 559 int32_t float32_to_int32_round_to_zero(float32, float_status *status); 560 int64_t float32_to_int64_round_to_zero(float32, float_status *status); 561 562 uint16_t float32_to_uint16_scalbn(float32, FloatRoundMode, int, float_status *); 563 uint32_t float32_to_uint32_scalbn(float32, FloatRoundMode, int, float_status *); 564 uint64_t float32_to_uint64_scalbn(float32, FloatRoundMode, int, float_status *); 565 566 uint16_t float32_to_uint16(float32, float_status *status); 567 uint32_t float32_to_uint32(float32, float_status *status); 568 uint64_t float32_to_uint64(float32, float_status *status); 569 570 uint16_t float32_to_uint16_round_to_zero(float32, float_status *status); 571 uint32_t float32_to_uint32_round_to_zero(float32, float_status *status); 572 uint64_t float32_to_uint64_round_to_zero(float32, float_status *status); 573 574 float64 float32_to_float64(float32, float_status *status); 575 floatx80 float32_to_floatx80(float32, float_status *status); 576 float128 float32_to_float128(float32, float_status *status); 577 578 /*---------------------------------------------------------------------------- 579 | Software IEC/IEEE single-precision operations. 580 *----------------------------------------------------------------------------*/ 581 float32 float32_round_to_int(float32, float_status *status); 582 float32 float32_add(float32, float32, float_status *status); 583 float32 float32_sub(float32, float32, float_status *status); 584 float32 float32_mul(float32, float32, float_status *status); 585 float32 float32_div(float32, float32, float_status *status); 586 float32 float32_rem(float32, float32, float_status *status); 587 float32 float32_muladd(float32, float32, float32, int, float_status *status); 588 float32 float32_sqrt(float32, float_status *status); 589 float32 float32_exp2(float32, float_status *status); 590 float32 float32_log2(float32, float_status *status); 591 FloatRelation float32_compare(float32, float32, float_status *status); 592 FloatRelation float32_compare_quiet(float32, float32, float_status *status); 593 float32 float32_min(float32, float32, float_status *status); 594 float32 float32_max(float32, float32, float_status *status); 595 float32 float32_minnum(float32, float32, float_status *status); 596 float32 float32_maxnum(float32, float32, float_status *status); 597 float32 float32_minnummag(float32, float32, float_status *status); 598 float32 float32_maxnummag(float32, float32, float_status *status); 599 float32 float32_minimum_number(float32, float32, float_status *status); 600 float32 float32_maximum_number(float32, float32, float_status *status); 601 bool float32_is_quiet_nan(float32, float_status *status); 602 bool float32_is_signaling_nan(float32, float_status *status); 603 float32 float32_silence_nan(float32, float_status *status); 604 float32 float32_scalbn(float32, int, float_status *status); 605 606 static inline float32 float32_abs(float32 a) 607 { 608 /* Note that abs does *not* handle NaN specially, nor does 609 * it flush denormal inputs to zero. 610 */ 611 return make_float32(float32_val(a) & 0x7fffffff); 612 } 613 614 static inline float32 float32_chs(float32 a) 615 { 616 /* Note that chs does *not* handle NaN specially, nor does 617 * it flush denormal inputs to zero. 618 */ 619 return make_float32(float32_val(a) ^ 0x80000000); 620 } 621 622 static inline bool float32_is_infinity(float32 a) 623 { 624 return (float32_val(a) & 0x7fffffff) == 0x7f800000; 625 } 626 627 static inline bool float32_is_neg(float32 a) 628 { 629 return float32_val(a) >> 31; 630 } 631 632 static inline bool float32_is_zero(float32 a) 633 { 634 return (float32_val(a) & 0x7fffffff) == 0; 635 } 636 637 static inline bool float32_is_any_nan(float32 a) 638 { 639 return ((float32_val(a) & ~(1 << 31)) > 0x7f800000UL); 640 } 641 642 static inline bool float32_is_zero_or_denormal(float32 a) 643 { 644 return (float32_val(a) & 0x7f800000) == 0; 645 } 646 647 static inline bool float32_is_normal(float32 a) 648 { 649 return (((float32_val(a) >> 23) + 1) & 0xff) >= 2; 650 } 651 652 static inline bool float32_is_denormal(float32 a) 653 { 654 return float32_is_zero_or_denormal(a) && !float32_is_zero(a); 655 } 656 657 static inline bool float32_is_zero_or_normal(float32 a) 658 { 659 return float32_is_normal(a) || float32_is_zero(a); 660 } 661 662 static inline float32 float32_set_sign(float32 a, int sign) 663 { 664 return make_float32((float32_val(a) & 0x7fffffff) | (sign << 31)); 665 } 666 667 static inline bool float32_eq(float32 a, float32 b, float_status *s) 668 { 669 return float32_compare(a, b, s) == float_relation_equal; 670 } 671 672 static inline bool float32_le(float32 a, float32 b, float_status *s) 673 { 674 return float32_compare(a, b, s) <= float_relation_equal; 675 } 676 677 static inline bool float32_lt(float32 a, float32 b, float_status *s) 678 { 679 return float32_compare(a, b, s) < float_relation_equal; 680 } 681 682 static inline bool float32_unordered(float32 a, float32 b, float_status *s) 683 { 684 return float32_compare(a, b, s) == float_relation_unordered; 685 } 686 687 static inline bool float32_eq_quiet(float32 a, float32 b, float_status *s) 688 { 689 return float32_compare_quiet(a, b, s) == float_relation_equal; 690 } 691 692 static inline bool float32_le_quiet(float32 a, float32 b, float_status *s) 693 { 694 return float32_compare_quiet(a, b, s) <= float_relation_equal; 695 } 696 697 static inline bool float32_lt_quiet(float32 a, float32 b, float_status *s) 698 { 699 return float32_compare_quiet(a, b, s) < float_relation_equal; 700 } 701 702 static inline bool float32_unordered_quiet(float32 a, float32 b, 703 float_status *s) 704 { 705 return float32_compare_quiet(a, b, s) == float_relation_unordered; 706 } 707 708 #define float32_zero make_float32(0) 709 #define float32_half make_float32(0x3f000000) 710 #define float32_one make_float32(0x3f800000) 711 #define float32_one_point_five make_float32(0x3fc00000) 712 #define float32_two make_float32(0x40000000) 713 #define float32_three make_float32(0x40400000) 714 #define float32_infinity make_float32(0x7f800000) 715 716 /*---------------------------------------------------------------------------- 717 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a 718 | single-precision floating-point value, returning the result. After being 719 | shifted into the proper positions, the three fields are simply added 720 | together to form the result. This means that any integer portion of `zSig' 721 | will be added into the exponent. Since a properly normalized significand 722 | will have an integer portion equal to 1, the `zExp' input should be 1 less 723 | than the desired result exponent whenever `zSig' is a complete, normalized 724 | significand. 725 *----------------------------------------------------------------------------*/ 726 727 static inline float32 packFloat32(bool zSign, int zExp, uint32_t zSig) 728 { 729 return make_float32( 730 (((uint32_t)zSign) << 31) + (((uint32_t)zExp) << 23) + zSig); 731 } 732 733 /*---------------------------------------------------------------------------- 734 | The pattern for a default generated single-precision NaN. 735 *----------------------------------------------------------------------------*/ 736 float32 float32_default_nan(float_status *status); 737 738 /*---------------------------------------------------------------------------- 739 | Software IEC/IEEE double-precision conversion routines. 740 *----------------------------------------------------------------------------*/ 741 742 int16_t float64_to_int16_scalbn(float64, FloatRoundMode, int, float_status *); 743 int32_t float64_to_int32_scalbn(float64, FloatRoundMode, int, float_status *); 744 int64_t float64_to_int64_scalbn(float64, FloatRoundMode, int, float_status *); 745 746 int16_t float64_to_int16(float64, float_status *status); 747 int32_t float64_to_int32(float64, float_status *status); 748 int64_t float64_to_int64(float64, float_status *status); 749 750 int16_t float64_to_int16_round_to_zero(float64, float_status *status); 751 int32_t float64_to_int32_round_to_zero(float64, float_status *status); 752 int64_t float64_to_int64_round_to_zero(float64, float_status *status); 753 754 uint16_t float64_to_uint16_scalbn(float64, FloatRoundMode, int, float_status *); 755 uint32_t float64_to_uint32_scalbn(float64, FloatRoundMode, int, float_status *); 756 uint64_t float64_to_uint64_scalbn(float64, FloatRoundMode, int, float_status *); 757 758 uint16_t float64_to_uint16(float64, float_status *status); 759 uint32_t float64_to_uint32(float64, float_status *status); 760 uint64_t float64_to_uint64(float64, float_status *status); 761 762 uint16_t float64_to_uint16_round_to_zero(float64, float_status *status); 763 uint32_t float64_to_uint32_round_to_zero(float64, float_status *status); 764 uint64_t float64_to_uint64_round_to_zero(float64, float_status *status); 765 766 float32 float64_to_float32(float64, float_status *status); 767 floatx80 float64_to_floatx80(float64, float_status *status); 768 float128 float64_to_float128(float64, float_status *status); 769 770 /*---------------------------------------------------------------------------- 771 | Software IEC/IEEE double-precision operations. 772 *----------------------------------------------------------------------------*/ 773 float64 float64_round_to_int(float64, float_status *status); 774 float64 float64_add(float64, float64, float_status *status); 775 float64 float64_sub(float64, float64, float_status *status); 776 float64 float64_mul(float64, float64, float_status *status); 777 float64 float64_div(float64, float64, float_status *status); 778 float64 float64_rem(float64, float64, float_status *status); 779 float64 float64_muladd(float64, float64, float64, int, float_status *status); 780 float64 float64_sqrt(float64, float_status *status); 781 float64 float64_log2(float64, float_status *status); 782 FloatRelation float64_compare(float64, float64, float_status *status); 783 FloatRelation float64_compare_quiet(float64, float64, float_status *status); 784 float64 float64_min(float64, float64, float_status *status); 785 float64 float64_max(float64, float64, float_status *status); 786 float64 float64_minnum(float64, float64, float_status *status); 787 float64 float64_maxnum(float64, float64, float_status *status); 788 float64 float64_minnummag(float64, float64, float_status *status); 789 float64 float64_maxnummag(float64, float64, float_status *status); 790 float64 float64_minimum_number(float64, float64, float_status *status); 791 float64 float64_maximum_number(float64, float64, float_status *status); 792 bool float64_is_quiet_nan(float64 a, float_status *status); 793 bool float64_is_signaling_nan(float64, float_status *status); 794 float64 float64_silence_nan(float64, float_status *status); 795 float64 float64_scalbn(float64, int, float_status *status); 796 797 static inline float64 float64_abs(float64 a) 798 { 799 /* Note that abs does *not* handle NaN specially, nor does 800 * it flush denormal inputs to zero. 801 */ 802 return make_float64(float64_val(a) & 0x7fffffffffffffffLL); 803 } 804 805 static inline float64 float64_chs(float64 a) 806 { 807 /* Note that chs does *not* handle NaN specially, nor does 808 * it flush denormal inputs to zero. 809 */ 810 return make_float64(float64_val(a) ^ 0x8000000000000000LL); 811 } 812 813 static inline bool float64_is_infinity(float64 a) 814 { 815 return (float64_val(a) & 0x7fffffffffffffffLL ) == 0x7ff0000000000000LL; 816 } 817 818 static inline bool float64_is_neg(float64 a) 819 { 820 return float64_val(a) >> 63; 821 } 822 823 static inline bool float64_is_zero(float64 a) 824 { 825 return (float64_val(a) & 0x7fffffffffffffffLL) == 0; 826 } 827 828 static inline bool float64_is_any_nan(float64 a) 829 { 830 return ((float64_val(a) & ~(1ULL << 63)) > 0x7ff0000000000000ULL); 831 } 832 833 static inline bool float64_is_zero_or_denormal(float64 a) 834 { 835 return (float64_val(a) & 0x7ff0000000000000LL) == 0; 836 } 837 838 static inline bool float64_is_normal(float64 a) 839 { 840 return (((float64_val(a) >> 52) + 1) & 0x7ff) >= 2; 841 } 842 843 static inline bool float64_is_denormal(float64 a) 844 { 845 return float64_is_zero_or_denormal(a) && !float64_is_zero(a); 846 } 847 848 static inline bool float64_is_zero_or_normal(float64 a) 849 { 850 return float64_is_normal(a) || float64_is_zero(a); 851 } 852 853 static inline float64 float64_set_sign(float64 a, int sign) 854 { 855 return make_float64((float64_val(a) & 0x7fffffffffffffffULL) 856 | ((int64_t)sign << 63)); 857 } 858 859 static inline bool float64_eq(float64 a, float64 b, float_status *s) 860 { 861 return float64_compare(a, b, s) == float_relation_equal; 862 } 863 864 static inline bool float64_le(float64 a, float64 b, float_status *s) 865 { 866 return float64_compare(a, b, s) <= float_relation_equal; 867 } 868 869 static inline bool float64_lt(float64 a, float64 b, float_status *s) 870 { 871 return float64_compare(a, b, s) < float_relation_equal; 872 } 873 874 static inline bool float64_unordered(float64 a, float64 b, float_status *s) 875 { 876 return float64_compare(a, b, s) == float_relation_unordered; 877 } 878 879 static inline bool float64_eq_quiet(float64 a, float64 b, float_status *s) 880 { 881 return float64_compare_quiet(a, b, s) == float_relation_equal; 882 } 883 884 static inline bool float64_le_quiet(float64 a, float64 b, float_status *s) 885 { 886 return float64_compare_quiet(a, b, s) <= float_relation_equal; 887 } 888 889 static inline bool float64_lt_quiet(float64 a, float64 b, float_status *s) 890 { 891 return float64_compare_quiet(a, b, s) < float_relation_equal; 892 } 893 894 static inline bool float64_unordered_quiet(float64 a, float64 b, 895 float_status *s) 896 { 897 return float64_compare_quiet(a, b, s) == float_relation_unordered; 898 } 899 900 #define float64_zero make_float64(0) 901 #define float64_half make_float64(0x3fe0000000000000LL) 902 #define float64_one make_float64(0x3ff0000000000000LL) 903 #define float64_one_point_five make_float64(0x3FF8000000000000ULL) 904 #define float64_two make_float64(0x4000000000000000ULL) 905 #define float64_three make_float64(0x4008000000000000ULL) 906 #define float64_ln2 make_float64(0x3fe62e42fefa39efLL) 907 #define float64_infinity make_float64(0x7ff0000000000000LL) 908 909 /*---------------------------------------------------------------------------- 910 | The pattern for a default generated double-precision NaN. 911 *----------------------------------------------------------------------------*/ 912 float64 float64_default_nan(float_status *status); 913 914 /*---------------------------------------------------------------------------- 915 | Software IEC/IEEE double-precision operations, rounding to single precision, 916 | returning a result in double precision, with only one rounding step. 917 *----------------------------------------------------------------------------*/ 918 919 float64 float64r32_add(float64, float64, float_status *status); 920 float64 float64r32_sub(float64, float64, float_status *status); 921 float64 float64r32_mul(float64, float64, float_status *status); 922 float64 float64r32_div(float64, float64, float_status *status); 923 float64 float64r32_muladd(float64, float64, float64, int, float_status *status); 924 float64 float64r32_sqrt(float64, float_status *status); 925 926 /*---------------------------------------------------------------------------- 927 | Software IEC/IEEE extended double-precision conversion routines. 928 *----------------------------------------------------------------------------*/ 929 int32_t floatx80_to_int32(floatx80, float_status *status); 930 int32_t floatx80_to_int32_round_to_zero(floatx80, float_status *status); 931 int64_t floatx80_to_int64(floatx80, float_status *status); 932 int64_t floatx80_to_int64_round_to_zero(floatx80, float_status *status); 933 float32 floatx80_to_float32(floatx80, float_status *status); 934 float64 floatx80_to_float64(floatx80, float_status *status); 935 float128 floatx80_to_float128(floatx80, float_status *status); 936 937 /*---------------------------------------------------------------------------- 938 | The pattern for an extended double-precision inf. 939 *----------------------------------------------------------------------------*/ 940 extern const floatx80 floatx80_infinity; 941 942 /*---------------------------------------------------------------------------- 943 | Software IEC/IEEE extended double-precision operations. 944 *----------------------------------------------------------------------------*/ 945 floatx80 floatx80_round(floatx80 a, float_status *status); 946 floatx80 floatx80_round_to_int(floatx80, float_status *status); 947 floatx80 floatx80_add(floatx80, floatx80, float_status *status); 948 floatx80 floatx80_sub(floatx80, floatx80, float_status *status); 949 floatx80 floatx80_mul(floatx80, floatx80, float_status *status); 950 floatx80 floatx80_div(floatx80, floatx80, float_status *status); 951 floatx80 floatx80_modrem(floatx80, floatx80, bool, uint64_t *, 952 float_status *status); 953 floatx80 floatx80_mod(floatx80, floatx80, float_status *status); 954 floatx80 floatx80_rem(floatx80, floatx80, float_status *status); 955 floatx80 floatx80_sqrt(floatx80, float_status *status); 956 FloatRelation floatx80_compare(floatx80, floatx80, float_status *status); 957 FloatRelation floatx80_compare_quiet(floatx80, floatx80, float_status *status); 958 int floatx80_is_quiet_nan(floatx80, float_status *status); 959 int floatx80_is_signaling_nan(floatx80, float_status *status); 960 floatx80 floatx80_silence_nan(floatx80, float_status *status); 961 floatx80 floatx80_scalbn(floatx80, int, float_status *status); 962 963 static inline floatx80 floatx80_abs(floatx80 a) 964 { 965 a.high &= 0x7fff; 966 return a; 967 } 968 969 static inline floatx80 floatx80_chs(floatx80 a) 970 { 971 a.high ^= 0x8000; 972 return a; 973 } 974 975 static inline bool floatx80_is_infinity(floatx80 a) 976 { 977 #if defined(TARGET_M68K) 978 return (a.high & 0x7fff) == floatx80_infinity.high && !(a.low << 1); 979 #else 980 return (a.high & 0x7fff) == floatx80_infinity.high && 981 a.low == floatx80_infinity.low; 982 #endif 983 } 984 985 static inline bool floatx80_is_neg(floatx80 a) 986 { 987 return a.high >> 15; 988 } 989 990 static inline bool floatx80_is_zero(floatx80 a) 991 { 992 return (a.high & 0x7fff) == 0 && a.low == 0; 993 } 994 995 static inline bool floatx80_is_zero_or_denormal(floatx80 a) 996 { 997 return (a.high & 0x7fff) == 0; 998 } 999 1000 static inline bool floatx80_is_any_nan(floatx80 a) 1001 { 1002 return ((a.high & 0x7fff) == 0x7fff) && (a.low<<1); 1003 } 1004 1005 static inline bool floatx80_eq(floatx80 a, floatx80 b, float_status *s) 1006 { 1007 return floatx80_compare(a, b, s) == float_relation_equal; 1008 } 1009 1010 static inline bool floatx80_le(floatx80 a, floatx80 b, float_status *s) 1011 { 1012 return floatx80_compare(a, b, s) <= float_relation_equal; 1013 } 1014 1015 static inline bool floatx80_lt(floatx80 a, floatx80 b, float_status *s) 1016 { 1017 return floatx80_compare(a, b, s) < float_relation_equal; 1018 } 1019 1020 static inline bool floatx80_unordered(floatx80 a, floatx80 b, float_status *s) 1021 { 1022 return floatx80_compare(a, b, s) == float_relation_unordered; 1023 } 1024 1025 static inline bool floatx80_eq_quiet(floatx80 a, floatx80 b, float_status *s) 1026 { 1027 return floatx80_compare_quiet(a, b, s) == float_relation_equal; 1028 } 1029 1030 static inline bool floatx80_le_quiet(floatx80 a, floatx80 b, float_status *s) 1031 { 1032 return floatx80_compare_quiet(a, b, s) <= float_relation_equal; 1033 } 1034 1035 static inline bool floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *s) 1036 { 1037 return floatx80_compare_quiet(a, b, s) < float_relation_equal; 1038 } 1039 1040 static inline bool floatx80_unordered_quiet(floatx80 a, floatx80 b, 1041 float_status *s) 1042 { 1043 return floatx80_compare_quiet(a, b, s) == float_relation_unordered; 1044 } 1045 1046 /*---------------------------------------------------------------------------- 1047 | Return whether the given value is an invalid floatx80 encoding. 1048 | Invalid floatx80 encodings arise when the integer bit is not set, but 1049 | the exponent is not zero. The only times the integer bit is permitted to 1050 | be zero is in subnormal numbers and the value zero. 1051 | This includes what the Intel software developer's manual calls pseudo-NaNs, 1052 | pseudo-infinities and un-normal numbers. It does not include 1053 | pseudo-denormals, which must still be correctly handled as inputs even 1054 | if they are never generated as outputs. 1055 *----------------------------------------------------------------------------*/ 1056 static inline bool floatx80_invalid_encoding(floatx80 a) 1057 { 1058 #if defined(TARGET_M68K) 1059 /*------------------------------------------------------------------------- 1060 | With m68k, the explicit integer bit can be zero in the case of: 1061 | - zeros (exp == 0, mantissa == 0) 1062 | - denormalized numbers (exp == 0, mantissa != 0) 1063 | - unnormalized numbers (exp != 0, exp < 0x7FFF) 1064 | - infinities (exp == 0x7FFF, mantissa == 0) 1065 | - not-a-numbers (exp == 0x7FFF, mantissa != 0) 1066 | 1067 | For infinities and NaNs, the explicit integer bit can be either one or 1068 | zero. 1069 | 1070 | The IEEE 754 standard does not define a zero integer bit. Such a number 1071 | is an unnormalized number. Hardware does not directly support 1072 | denormalized and unnormalized numbers, but implicitly supports them by 1073 | trapping them as unimplemented data types, allowing efficient conversion 1074 | in software. 1075 | 1076 | See "M68000 FAMILY PROGRAMMER’S REFERENCE MANUAL", 1077 | "1.6 FLOATING-POINT DATA TYPES" 1078 *------------------------------------------------------------------------*/ 1079 return false; 1080 #else 1081 return (a.low & (1ULL << 63)) == 0 && (a.high & 0x7FFF) != 0; 1082 #endif 1083 } 1084 1085 #define floatx80_zero make_floatx80(0x0000, 0x0000000000000000LL) 1086 #define floatx80_zero_init make_floatx80_init(0x0000, 0x0000000000000000LL) 1087 #define floatx80_one make_floatx80(0x3fff, 0x8000000000000000LL) 1088 #define floatx80_ln2 make_floatx80(0x3ffe, 0xb17217f7d1cf79acLL) 1089 #define floatx80_pi make_floatx80(0x4000, 0xc90fdaa22168c235LL) 1090 #define floatx80_half make_floatx80(0x3ffe, 0x8000000000000000LL) 1091 1092 /*---------------------------------------------------------------------------- 1093 | Returns the fraction bits of the extended double-precision floating-point 1094 | value `a'. 1095 *----------------------------------------------------------------------------*/ 1096 1097 static inline uint64_t extractFloatx80Frac(floatx80 a) 1098 { 1099 return a.low; 1100 } 1101 1102 /*---------------------------------------------------------------------------- 1103 | Returns the exponent bits of the extended double-precision floating-point 1104 | value `a'. 1105 *----------------------------------------------------------------------------*/ 1106 1107 static inline int32_t extractFloatx80Exp(floatx80 a) 1108 { 1109 return a.high & 0x7FFF; 1110 } 1111 1112 /*---------------------------------------------------------------------------- 1113 | Returns the sign bit of the extended double-precision floating-point value 1114 | `a'. 1115 *----------------------------------------------------------------------------*/ 1116 1117 static inline bool extractFloatx80Sign(floatx80 a) 1118 { 1119 return a.high >> 15; 1120 } 1121 1122 /*---------------------------------------------------------------------------- 1123 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an 1124 | extended double-precision floating-point value, returning the result. 1125 *----------------------------------------------------------------------------*/ 1126 1127 static inline floatx80 packFloatx80(bool zSign, int32_t zExp, uint64_t zSig) 1128 { 1129 floatx80 z; 1130 1131 z.low = zSig; 1132 z.high = (((uint16_t)zSign) << 15) + zExp; 1133 return z; 1134 } 1135 1136 /*---------------------------------------------------------------------------- 1137 | Normalizes the subnormal extended double-precision floating-point value 1138 | represented by the denormalized significand `aSig'. The normalized exponent 1139 | and significand are stored at the locations pointed to by `zExpPtr' and 1140 | `zSigPtr', respectively. 1141 *----------------------------------------------------------------------------*/ 1142 1143 void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr, 1144 uint64_t *zSigPtr); 1145 1146 /*---------------------------------------------------------------------------- 1147 | Takes two extended double-precision floating-point values `a' and `b', one 1148 | of which is a NaN, and returns the appropriate NaN result. If either `a' or 1149 | `b' is a signaling NaN, the invalid exception is raised. 1150 *----------------------------------------------------------------------------*/ 1151 1152 floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status); 1153 1154 /*---------------------------------------------------------------------------- 1155 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 1156 | and extended significand formed by the concatenation of `zSig0' and `zSig1', 1157 | and returns the proper extended double-precision floating-point value 1158 | corresponding to the abstract input. Ordinarily, the abstract value is 1159 | rounded and packed into the extended double-precision format, with the 1160 | inexact exception raised if the abstract input cannot be represented 1161 | exactly. However, if the abstract value is too large, the overflow and 1162 | inexact exceptions are raised and an infinity or maximal finite value is 1163 | returned. If the abstract value is too small, the input value is rounded to 1164 | a subnormal number, and the underflow and inexact exceptions are raised if 1165 | the abstract input cannot be represented exactly as a subnormal extended 1166 | double-precision floating-point number. 1167 | If `roundingPrecision' is 32 or 64, the result is rounded to the same 1168 | number of bits as single or double precision, respectively. Otherwise, the 1169 | result is rounded to the full precision of the extended double-precision 1170 | format. 1171 | The input significand must be normalized or smaller. If the input 1172 | significand is not normalized, `zExp' must be 0; in that case, the result 1173 | returned is a subnormal number, and it must not require rounding. The 1174 | handling of underflow and overflow follows the IEC/IEEE Standard for Binary 1175 | Floating-Point Arithmetic. 1176 *----------------------------------------------------------------------------*/ 1177 1178 floatx80 roundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, bool zSign, 1179 int32_t zExp, uint64_t zSig0, uint64_t zSig1, 1180 float_status *status); 1181 1182 /*---------------------------------------------------------------------------- 1183 | Takes an abstract floating-point value having sign `zSign', exponent 1184 | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', 1185 | and returns the proper extended double-precision floating-point value 1186 | corresponding to the abstract input. This routine is just like 1187 | `roundAndPackFloatx80' except that the input significand does not have to be 1188 | normalized. 1189 *----------------------------------------------------------------------------*/ 1190 1191 floatx80 normalizeRoundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, 1192 bool zSign, int32_t zExp, 1193 uint64_t zSig0, uint64_t zSig1, 1194 float_status *status); 1195 1196 /*---------------------------------------------------------------------------- 1197 | The pattern for a default generated extended double-precision NaN. 1198 *----------------------------------------------------------------------------*/ 1199 floatx80 floatx80_default_nan(float_status *status); 1200 1201 /*---------------------------------------------------------------------------- 1202 | Software IEC/IEEE quadruple-precision conversion routines. 1203 *----------------------------------------------------------------------------*/ 1204 int32_t float128_to_int32(float128, float_status *status); 1205 int32_t float128_to_int32_round_to_zero(float128, float_status *status); 1206 int64_t float128_to_int64(float128, float_status *status); 1207 Int128 float128_to_int128(float128, float_status *status); 1208 int64_t float128_to_int64_round_to_zero(float128, float_status *status); 1209 Int128 float128_to_int128_round_to_zero(float128, float_status *status); 1210 uint64_t float128_to_uint64(float128, float_status *status); 1211 Int128 float128_to_uint128(float128, float_status *status); 1212 uint64_t float128_to_uint64_round_to_zero(float128, float_status *status); 1213 Int128 float128_to_uint128_round_to_zero(float128, float_status *status); 1214 uint32_t float128_to_uint32(float128, float_status *status); 1215 uint32_t float128_to_uint32_round_to_zero(float128, float_status *status); 1216 float32 float128_to_float32(float128, float_status *status); 1217 float64 float128_to_float64(float128, float_status *status); 1218 floatx80 float128_to_floatx80(float128, float_status *status); 1219 1220 /*---------------------------------------------------------------------------- 1221 | Software IEC/IEEE quadruple-precision operations. 1222 *----------------------------------------------------------------------------*/ 1223 float128 float128_round_to_int(float128, float_status *status); 1224 float128 float128_add(float128, float128, float_status *status); 1225 float128 float128_sub(float128, float128, float_status *status); 1226 float128 float128_mul(float128, float128, float_status *status); 1227 float128 float128_muladd(float128, float128, float128, int, 1228 float_status *status); 1229 float128 float128_div(float128, float128, float_status *status); 1230 float128 float128_rem(float128, float128, float_status *status); 1231 float128 float128_sqrt(float128, float_status *status); 1232 FloatRelation float128_compare(float128, float128, float_status *status); 1233 FloatRelation float128_compare_quiet(float128, float128, float_status *status); 1234 float128 float128_min(float128, float128, float_status *status); 1235 float128 float128_max(float128, float128, float_status *status); 1236 float128 float128_minnum(float128, float128, float_status *status); 1237 float128 float128_maxnum(float128, float128, float_status *status); 1238 float128 float128_minnummag(float128, float128, float_status *status); 1239 float128 float128_maxnummag(float128, float128, float_status *status); 1240 float128 float128_minimum_number(float128, float128, float_status *status); 1241 float128 float128_maximum_number(float128, float128, float_status *status); 1242 bool float128_is_quiet_nan(float128, float_status *status); 1243 bool float128_is_signaling_nan(float128, float_status *status); 1244 float128 float128_silence_nan(float128, float_status *status); 1245 float128 float128_scalbn(float128, int, float_status *status); 1246 1247 static inline float128 float128_abs(float128 a) 1248 { 1249 a.high &= 0x7fffffffffffffffLL; 1250 return a; 1251 } 1252 1253 static inline float128 float128_chs(float128 a) 1254 { 1255 a.high ^= 0x8000000000000000LL; 1256 return a; 1257 } 1258 1259 static inline bool float128_is_infinity(float128 a) 1260 { 1261 return (a.high & 0x7fffffffffffffffLL) == 0x7fff000000000000LL && a.low == 0; 1262 } 1263 1264 static inline bool float128_is_neg(float128 a) 1265 { 1266 return a.high >> 63; 1267 } 1268 1269 static inline bool float128_is_zero(float128 a) 1270 { 1271 return (a.high & 0x7fffffffffffffffLL) == 0 && a.low == 0; 1272 } 1273 1274 static inline bool float128_is_zero_or_denormal(float128 a) 1275 { 1276 return (a.high & 0x7fff000000000000LL) == 0; 1277 } 1278 1279 static inline bool float128_is_normal(float128 a) 1280 { 1281 return (((a.high >> 48) + 1) & 0x7fff) >= 2; 1282 } 1283 1284 static inline bool float128_is_denormal(float128 a) 1285 { 1286 return float128_is_zero_or_denormal(a) && !float128_is_zero(a); 1287 } 1288 1289 static inline bool float128_is_any_nan(float128 a) 1290 { 1291 return ((a.high >> 48) & 0x7fff) == 0x7fff && 1292 ((a.low != 0) || ((a.high & 0xffffffffffffLL) != 0)); 1293 } 1294 1295 static inline bool float128_eq(float128 a, float128 b, float_status *s) 1296 { 1297 return float128_compare(a, b, s) == float_relation_equal; 1298 } 1299 1300 static inline bool float128_le(float128 a, float128 b, float_status *s) 1301 { 1302 return float128_compare(a, b, s) <= float_relation_equal; 1303 } 1304 1305 static inline bool float128_lt(float128 a, float128 b, float_status *s) 1306 { 1307 return float128_compare(a, b, s) < float_relation_equal; 1308 } 1309 1310 static inline bool float128_unordered(float128 a, float128 b, float_status *s) 1311 { 1312 return float128_compare(a, b, s) == float_relation_unordered; 1313 } 1314 1315 static inline bool float128_eq_quiet(float128 a, float128 b, float_status *s) 1316 { 1317 return float128_compare_quiet(a, b, s) == float_relation_equal; 1318 } 1319 1320 static inline bool float128_le_quiet(float128 a, float128 b, float_status *s) 1321 { 1322 return float128_compare_quiet(a, b, s) <= float_relation_equal; 1323 } 1324 1325 static inline bool float128_lt_quiet(float128 a, float128 b, float_status *s) 1326 { 1327 return float128_compare_quiet(a, b, s) < float_relation_equal; 1328 } 1329 1330 static inline bool float128_unordered_quiet(float128 a, float128 b, 1331 float_status *s) 1332 { 1333 return float128_compare_quiet(a, b, s) == float_relation_unordered; 1334 } 1335 1336 #define float128_zero make_float128(0, 0) 1337 1338 /*---------------------------------------------------------------------------- 1339 | The pattern for a default generated quadruple-precision NaN. 1340 *----------------------------------------------------------------------------*/ 1341 float128 float128_default_nan(float_status *status); 1342 1343 #endif /* SOFTFLOAT_H */ 1344