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 uint64_to_float128(uint64_t, float_status *status); 187 float128 uint128_to_float128(Int128, float_status *status); 188 189 /*---------------------------------------------------------------------------- 190 | Software half-precision conversion routines. 191 *----------------------------------------------------------------------------*/ 192 193 float16 float32_to_float16(float32, bool ieee, float_status *status); 194 float32 float16_to_float32(float16, bool ieee, float_status *status); 195 float16 float64_to_float16(float64 a, bool ieee, float_status *status); 196 float64 float16_to_float64(float16 a, bool ieee, float_status *status); 197 198 int8_t float16_to_int8_scalbn(float16, FloatRoundMode, int, 199 float_status *status); 200 int16_t float16_to_int16_scalbn(float16, FloatRoundMode, int, float_status *); 201 int32_t float16_to_int32_scalbn(float16, FloatRoundMode, int, float_status *); 202 int64_t float16_to_int64_scalbn(float16, FloatRoundMode, int, float_status *); 203 204 int8_t float16_to_int8(float16, float_status *status); 205 int16_t float16_to_int16(float16, float_status *status); 206 int32_t float16_to_int32(float16, float_status *status); 207 int64_t float16_to_int64(float16, float_status *status); 208 209 int16_t float16_to_int16_round_to_zero(float16, float_status *status); 210 int32_t float16_to_int32_round_to_zero(float16, float_status *status); 211 int64_t float16_to_int64_round_to_zero(float16, float_status *status); 212 213 uint8_t float16_to_uint8_scalbn(float16 a, FloatRoundMode, 214 int, float_status *status); 215 uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode, 216 int, float_status *status); 217 uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode, 218 int, float_status *status); 219 uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode, 220 int, float_status *status); 221 222 uint8_t float16_to_uint8(float16 a, float_status *status); 223 uint16_t float16_to_uint16(float16 a, float_status *status); 224 uint32_t float16_to_uint32(float16 a, float_status *status); 225 uint64_t float16_to_uint64(float16 a, float_status *status); 226 227 uint16_t float16_to_uint16_round_to_zero(float16 a, float_status *status); 228 uint32_t float16_to_uint32_round_to_zero(float16 a, float_status *status); 229 uint64_t float16_to_uint64_round_to_zero(float16 a, float_status *status); 230 231 /*---------------------------------------------------------------------------- 232 | Software half-precision operations. 233 *----------------------------------------------------------------------------*/ 234 235 float16 float16_round_to_int(float16, float_status *status); 236 float16 float16_add(float16, float16, float_status *status); 237 float16 float16_sub(float16, float16, float_status *status); 238 float16 float16_mul(float16, float16, float_status *status); 239 float16 float16_muladd(float16, float16, float16, int, float_status *status); 240 float16 float16_div(float16, float16, float_status *status); 241 float16 float16_scalbn(float16, int, float_status *status); 242 float16 float16_min(float16, float16, float_status *status); 243 float16 float16_max(float16, float16, float_status *status); 244 float16 float16_minnum(float16, float16, float_status *status); 245 float16 float16_maxnum(float16, float16, float_status *status); 246 float16 float16_minnummag(float16, float16, float_status *status); 247 float16 float16_maxnummag(float16, float16, float_status *status); 248 float16 float16_minimum_number(float16, float16, float_status *status); 249 float16 float16_maximum_number(float16, float16, float_status *status); 250 float16 float16_sqrt(float16, float_status *status); 251 FloatRelation float16_compare(float16, float16, float_status *status); 252 FloatRelation float16_compare_quiet(float16, float16, float_status *status); 253 254 bool float16_is_quiet_nan(float16, float_status *status); 255 bool float16_is_signaling_nan(float16, float_status *status); 256 float16 float16_silence_nan(float16, float_status *status); 257 258 static inline bool float16_is_any_nan(float16 a) 259 { 260 return ((float16_val(a) & ~0x8000) > 0x7c00); 261 } 262 263 static inline bool float16_is_neg(float16 a) 264 { 265 return float16_val(a) >> 15; 266 } 267 268 static inline bool float16_is_infinity(float16 a) 269 { 270 return (float16_val(a) & 0x7fff) == 0x7c00; 271 } 272 273 static inline bool float16_is_zero(float16 a) 274 { 275 return (float16_val(a) & 0x7fff) == 0; 276 } 277 278 static inline bool float16_is_zero_or_denormal(float16 a) 279 { 280 return (float16_val(a) & 0x7c00) == 0; 281 } 282 283 static inline bool float16_is_normal(float16 a) 284 { 285 return (((float16_val(a) >> 10) + 1) & 0x1f) >= 2; 286 } 287 288 static inline float16 float16_abs(float16 a) 289 { 290 /* Note that abs does *not* handle NaN specially, nor does 291 * it flush denormal inputs to zero. 292 */ 293 return make_float16(float16_val(a) & 0x7fff); 294 } 295 296 static inline float16 float16_chs(float16 a) 297 { 298 /* Note that chs does *not* handle NaN specially, nor does 299 * it flush denormal inputs to zero. 300 */ 301 return make_float16(float16_val(a) ^ 0x8000); 302 } 303 304 static inline float16 float16_set_sign(float16 a, int sign) 305 { 306 return make_float16((float16_val(a) & 0x7fff) | (sign << 15)); 307 } 308 309 static inline bool float16_eq(float16 a, float16 b, float_status *s) 310 { 311 return float16_compare(a, b, s) == float_relation_equal; 312 } 313 314 static inline bool float16_le(float16 a, float16 b, float_status *s) 315 { 316 return float16_compare(a, b, s) <= float_relation_equal; 317 } 318 319 static inline bool float16_lt(float16 a, float16 b, float_status *s) 320 { 321 return float16_compare(a, b, s) < float_relation_equal; 322 } 323 324 static inline bool float16_unordered(float16 a, float16 b, float_status *s) 325 { 326 return float16_compare(a, b, s) == float_relation_unordered; 327 } 328 329 static inline bool float16_eq_quiet(float16 a, float16 b, float_status *s) 330 { 331 return float16_compare_quiet(a, b, s) == float_relation_equal; 332 } 333 334 static inline bool float16_le_quiet(float16 a, float16 b, float_status *s) 335 { 336 return float16_compare_quiet(a, b, s) <= float_relation_equal; 337 } 338 339 static inline bool float16_lt_quiet(float16 a, float16 b, float_status *s) 340 { 341 return float16_compare_quiet(a, b, s) < float_relation_equal; 342 } 343 344 static inline bool float16_unordered_quiet(float16 a, float16 b, 345 float_status *s) 346 { 347 return float16_compare_quiet(a, b, s) == float_relation_unordered; 348 } 349 350 #define float16_zero make_float16(0) 351 #define float16_half make_float16(0x3800) 352 #define float16_one make_float16(0x3c00) 353 #define float16_one_point_five make_float16(0x3e00) 354 #define float16_two make_float16(0x4000) 355 #define float16_three make_float16(0x4200) 356 #define float16_infinity make_float16(0x7c00) 357 358 /*---------------------------------------------------------------------------- 359 | Software bfloat16 conversion routines. 360 *----------------------------------------------------------------------------*/ 361 362 bfloat16 bfloat16_round_to_int(bfloat16, float_status *status); 363 bfloat16 float32_to_bfloat16(float32, float_status *status); 364 float32 bfloat16_to_float32(bfloat16, float_status *status); 365 bfloat16 float64_to_bfloat16(float64 a, float_status *status); 366 float64 bfloat16_to_float64(bfloat16 a, float_status *status); 367 368 int16_t bfloat16_to_int16_scalbn(bfloat16, FloatRoundMode, 369 int, float_status *status); 370 int32_t bfloat16_to_int32_scalbn(bfloat16, FloatRoundMode, 371 int, float_status *status); 372 int64_t bfloat16_to_int64_scalbn(bfloat16, FloatRoundMode, 373 int, float_status *status); 374 375 int16_t bfloat16_to_int16(bfloat16, float_status *status); 376 int32_t bfloat16_to_int32(bfloat16, float_status *status); 377 int64_t bfloat16_to_int64(bfloat16, float_status *status); 378 379 int16_t bfloat16_to_int16_round_to_zero(bfloat16, float_status *status); 380 int32_t bfloat16_to_int32_round_to_zero(bfloat16, float_status *status); 381 int64_t bfloat16_to_int64_round_to_zero(bfloat16, float_status *status); 382 383 uint16_t bfloat16_to_uint16_scalbn(bfloat16 a, FloatRoundMode, 384 int, float_status *status); 385 uint32_t bfloat16_to_uint32_scalbn(bfloat16 a, FloatRoundMode, 386 int, float_status *status); 387 uint64_t bfloat16_to_uint64_scalbn(bfloat16 a, FloatRoundMode, 388 int, float_status *status); 389 390 uint16_t bfloat16_to_uint16(bfloat16 a, float_status *status); 391 uint32_t bfloat16_to_uint32(bfloat16 a, float_status *status); 392 uint64_t bfloat16_to_uint64(bfloat16 a, float_status *status); 393 394 uint16_t bfloat16_to_uint16_round_to_zero(bfloat16 a, float_status *status); 395 uint32_t bfloat16_to_uint32_round_to_zero(bfloat16 a, float_status *status); 396 uint64_t bfloat16_to_uint64_round_to_zero(bfloat16 a, float_status *status); 397 398 bfloat16 int16_to_bfloat16_scalbn(int16_t a, int, float_status *status); 399 bfloat16 int32_to_bfloat16_scalbn(int32_t a, int, float_status *status); 400 bfloat16 int64_to_bfloat16_scalbn(int64_t a, int, float_status *status); 401 bfloat16 uint16_to_bfloat16_scalbn(uint16_t a, int, float_status *status); 402 bfloat16 uint32_to_bfloat16_scalbn(uint32_t a, int, float_status *status); 403 bfloat16 uint64_to_bfloat16_scalbn(uint64_t a, int, float_status *status); 404 405 bfloat16 int16_to_bfloat16(int16_t a, float_status *status); 406 bfloat16 int32_to_bfloat16(int32_t a, float_status *status); 407 bfloat16 int64_to_bfloat16(int64_t a, float_status *status); 408 bfloat16 uint16_to_bfloat16(uint16_t a, float_status *status); 409 bfloat16 uint32_to_bfloat16(uint32_t a, float_status *status); 410 bfloat16 uint64_to_bfloat16(uint64_t a, float_status *status); 411 412 /*---------------------------------------------------------------------------- 413 | Software bfloat16 operations. 414 *----------------------------------------------------------------------------*/ 415 416 bfloat16 bfloat16_add(bfloat16, bfloat16, float_status *status); 417 bfloat16 bfloat16_sub(bfloat16, bfloat16, float_status *status); 418 bfloat16 bfloat16_mul(bfloat16, bfloat16, float_status *status); 419 bfloat16 bfloat16_div(bfloat16, bfloat16, float_status *status); 420 bfloat16 bfloat16_muladd(bfloat16, bfloat16, bfloat16, int, 421 float_status *status); 422 float16 bfloat16_scalbn(bfloat16, int, float_status *status); 423 bfloat16 bfloat16_min(bfloat16, bfloat16, float_status *status); 424 bfloat16 bfloat16_max(bfloat16, bfloat16, float_status *status); 425 bfloat16 bfloat16_minnum(bfloat16, bfloat16, float_status *status); 426 bfloat16 bfloat16_maxnum(bfloat16, bfloat16, float_status *status); 427 bfloat16 bfloat16_minnummag(bfloat16, bfloat16, float_status *status); 428 bfloat16 bfloat16_maxnummag(bfloat16, bfloat16, float_status *status); 429 bfloat16 bfloat16_minimum_number(bfloat16, bfloat16, float_status *status); 430 bfloat16 bfloat16_maximum_number(bfloat16, bfloat16, float_status *status); 431 bfloat16 bfloat16_sqrt(bfloat16, float_status *status); 432 FloatRelation bfloat16_compare(bfloat16, bfloat16, float_status *status); 433 FloatRelation bfloat16_compare_quiet(bfloat16, bfloat16, float_status *status); 434 435 bool bfloat16_is_quiet_nan(bfloat16, float_status *status); 436 bool bfloat16_is_signaling_nan(bfloat16, float_status *status); 437 bfloat16 bfloat16_silence_nan(bfloat16, float_status *status); 438 bfloat16 bfloat16_default_nan(float_status *status); 439 440 static inline bool bfloat16_is_any_nan(bfloat16 a) 441 { 442 return ((a & ~0x8000) > 0x7F80); 443 } 444 445 static inline bool bfloat16_is_neg(bfloat16 a) 446 { 447 return a >> 15; 448 } 449 450 static inline bool bfloat16_is_infinity(bfloat16 a) 451 { 452 return (a & 0x7fff) == 0x7F80; 453 } 454 455 static inline bool bfloat16_is_zero(bfloat16 a) 456 { 457 return (a & 0x7fff) == 0; 458 } 459 460 static inline bool bfloat16_is_zero_or_denormal(bfloat16 a) 461 { 462 return (a & 0x7F80) == 0; 463 } 464 465 static inline bool bfloat16_is_normal(bfloat16 a) 466 { 467 return (((a >> 7) + 1) & 0xff) >= 2; 468 } 469 470 static inline bfloat16 bfloat16_abs(bfloat16 a) 471 { 472 /* Note that abs does *not* handle NaN specially, nor does 473 * it flush denormal inputs to zero. 474 */ 475 return a & 0x7fff; 476 } 477 478 static inline bfloat16 bfloat16_chs(bfloat16 a) 479 { 480 /* Note that chs does *not* handle NaN specially, nor does 481 * it flush denormal inputs to zero. 482 */ 483 return a ^ 0x8000; 484 } 485 486 static inline bfloat16 bfloat16_set_sign(bfloat16 a, int sign) 487 { 488 return (a & 0x7fff) | (sign << 15); 489 } 490 491 static inline bool bfloat16_eq(bfloat16 a, bfloat16 b, float_status *s) 492 { 493 return bfloat16_compare(a, b, s) == float_relation_equal; 494 } 495 496 static inline bool bfloat16_le(bfloat16 a, bfloat16 b, float_status *s) 497 { 498 return bfloat16_compare(a, b, s) <= float_relation_equal; 499 } 500 501 static inline bool bfloat16_lt(bfloat16 a, bfloat16 b, float_status *s) 502 { 503 return bfloat16_compare(a, b, s) < float_relation_equal; 504 } 505 506 static inline bool bfloat16_unordered(bfloat16 a, bfloat16 b, float_status *s) 507 { 508 return bfloat16_compare(a, b, s) == float_relation_unordered; 509 } 510 511 static inline bool bfloat16_eq_quiet(bfloat16 a, bfloat16 b, float_status *s) 512 { 513 return bfloat16_compare_quiet(a, b, s) == float_relation_equal; 514 } 515 516 static inline bool bfloat16_le_quiet(bfloat16 a, bfloat16 b, float_status *s) 517 { 518 return bfloat16_compare_quiet(a, b, s) <= float_relation_equal; 519 } 520 521 static inline bool bfloat16_lt_quiet(bfloat16 a, bfloat16 b, float_status *s) 522 { 523 return bfloat16_compare_quiet(a, b, s) < float_relation_equal; 524 } 525 526 static inline bool bfloat16_unordered_quiet(bfloat16 a, bfloat16 b, 527 float_status *s) 528 { 529 return bfloat16_compare_quiet(a, b, s) == float_relation_unordered; 530 } 531 532 #define bfloat16_zero 0 533 #define bfloat16_half 0x3f00 534 #define bfloat16_one 0x3f80 535 #define bfloat16_one_point_five 0x3fc0 536 #define bfloat16_two 0x4000 537 #define bfloat16_three 0x4040 538 #define bfloat16_infinity 0x7f80 539 540 /*---------------------------------------------------------------------------- 541 | The pattern for a default generated half-precision NaN. 542 *----------------------------------------------------------------------------*/ 543 float16 float16_default_nan(float_status *status); 544 545 /*---------------------------------------------------------------------------- 546 | Software IEC/IEEE single-precision conversion routines. 547 *----------------------------------------------------------------------------*/ 548 549 int16_t float32_to_int16_scalbn(float32, FloatRoundMode, int, float_status *); 550 int32_t float32_to_int32_scalbn(float32, FloatRoundMode, int, float_status *); 551 int64_t float32_to_int64_scalbn(float32, FloatRoundMode, int, float_status *); 552 553 int16_t float32_to_int16(float32, float_status *status); 554 int32_t float32_to_int32(float32, float_status *status); 555 int64_t float32_to_int64(float32, float_status *status); 556 557 int16_t float32_to_int16_round_to_zero(float32, float_status *status); 558 int32_t float32_to_int32_round_to_zero(float32, float_status *status); 559 int64_t float32_to_int64_round_to_zero(float32, float_status *status); 560 561 uint16_t float32_to_uint16_scalbn(float32, FloatRoundMode, int, float_status *); 562 uint32_t float32_to_uint32_scalbn(float32, FloatRoundMode, int, float_status *); 563 uint64_t float32_to_uint64_scalbn(float32, FloatRoundMode, int, float_status *); 564 565 uint16_t float32_to_uint16(float32, float_status *status); 566 uint32_t float32_to_uint32(float32, float_status *status); 567 uint64_t float32_to_uint64(float32, float_status *status); 568 569 uint16_t float32_to_uint16_round_to_zero(float32, float_status *status); 570 uint32_t float32_to_uint32_round_to_zero(float32, float_status *status); 571 uint64_t float32_to_uint64_round_to_zero(float32, float_status *status); 572 573 float64 float32_to_float64(float32, float_status *status); 574 floatx80 float32_to_floatx80(float32, float_status *status); 575 float128 float32_to_float128(float32, float_status *status); 576 577 /*---------------------------------------------------------------------------- 578 | Software IEC/IEEE single-precision operations. 579 *----------------------------------------------------------------------------*/ 580 float32 float32_round_to_int(float32, float_status *status); 581 float32 float32_add(float32, float32, float_status *status); 582 float32 float32_sub(float32, float32, float_status *status); 583 float32 float32_mul(float32, float32, float_status *status); 584 float32 float32_div(float32, float32, float_status *status); 585 float32 float32_rem(float32, float32, float_status *status); 586 float32 float32_muladd(float32, float32, float32, int, float_status *status); 587 float32 float32_sqrt(float32, float_status *status); 588 float32 float32_exp2(float32, float_status *status); 589 float32 float32_log2(float32, float_status *status); 590 FloatRelation float32_compare(float32, float32, float_status *status); 591 FloatRelation float32_compare_quiet(float32, float32, float_status *status); 592 float32 float32_min(float32, float32, float_status *status); 593 float32 float32_max(float32, float32, float_status *status); 594 float32 float32_minnum(float32, float32, float_status *status); 595 float32 float32_maxnum(float32, float32, float_status *status); 596 float32 float32_minnummag(float32, float32, float_status *status); 597 float32 float32_maxnummag(float32, float32, float_status *status); 598 float32 float32_minimum_number(float32, float32, float_status *status); 599 float32 float32_maximum_number(float32, float32, float_status *status); 600 bool float32_is_quiet_nan(float32, float_status *status); 601 bool float32_is_signaling_nan(float32, float_status *status); 602 float32 float32_silence_nan(float32, float_status *status); 603 float32 float32_scalbn(float32, int, float_status *status); 604 605 static inline float32 float32_abs(float32 a) 606 { 607 /* Note that abs does *not* handle NaN specially, nor does 608 * it flush denormal inputs to zero. 609 */ 610 return make_float32(float32_val(a) & 0x7fffffff); 611 } 612 613 static inline float32 float32_chs(float32 a) 614 { 615 /* Note that chs does *not* handle NaN specially, nor does 616 * it flush denormal inputs to zero. 617 */ 618 return make_float32(float32_val(a) ^ 0x80000000); 619 } 620 621 static inline bool float32_is_infinity(float32 a) 622 { 623 return (float32_val(a) & 0x7fffffff) == 0x7f800000; 624 } 625 626 static inline bool float32_is_neg(float32 a) 627 { 628 return float32_val(a) >> 31; 629 } 630 631 static inline bool float32_is_zero(float32 a) 632 { 633 return (float32_val(a) & 0x7fffffff) == 0; 634 } 635 636 static inline bool float32_is_any_nan(float32 a) 637 { 638 return ((float32_val(a) & ~(1 << 31)) > 0x7f800000UL); 639 } 640 641 static inline bool float32_is_zero_or_denormal(float32 a) 642 { 643 return (float32_val(a) & 0x7f800000) == 0; 644 } 645 646 static inline bool float32_is_normal(float32 a) 647 { 648 return (((float32_val(a) >> 23) + 1) & 0xff) >= 2; 649 } 650 651 static inline bool float32_is_denormal(float32 a) 652 { 653 return float32_is_zero_or_denormal(a) && !float32_is_zero(a); 654 } 655 656 static inline bool float32_is_zero_or_normal(float32 a) 657 { 658 return float32_is_normal(a) || float32_is_zero(a); 659 } 660 661 static inline float32 float32_set_sign(float32 a, int sign) 662 { 663 return make_float32((float32_val(a) & 0x7fffffff) | (sign << 31)); 664 } 665 666 static inline bool float32_eq(float32 a, float32 b, float_status *s) 667 { 668 return float32_compare(a, b, s) == float_relation_equal; 669 } 670 671 static inline bool float32_le(float32 a, float32 b, float_status *s) 672 { 673 return float32_compare(a, b, s) <= float_relation_equal; 674 } 675 676 static inline bool float32_lt(float32 a, float32 b, float_status *s) 677 { 678 return float32_compare(a, b, s) < float_relation_equal; 679 } 680 681 static inline bool float32_unordered(float32 a, float32 b, float_status *s) 682 { 683 return float32_compare(a, b, s) == float_relation_unordered; 684 } 685 686 static inline bool float32_eq_quiet(float32 a, float32 b, float_status *s) 687 { 688 return float32_compare_quiet(a, b, s) == float_relation_equal; 689 } 690 691 static inline bool float32_le_quiet(float32 a, float32 b, float_status *s) 692 { 693 return float32_compare_quiet(a, b, s) <= float_relation_equal; 694 } 695 696 static inline bool float32_lt_quiet(float32 a, float32 b, float_status *s) 697 { 698 return float32_compare_quiet(a, b, s) < float_relation_equal; 699 } 700 701 static inline bool float32_unordered_quiet(float32 a, float32 b, 702 float_status *s) 703 { 704 return float32_compare_quiet(a, b, s) == float_relation_unordered; 705 } 706 707 #define float32_zero make_float32(0) 708 #define float32_half make_float32(0x3f000000) 709 #define float32_one make_float32(0x3f800000) 710 #define float32_one_point_five make_float32(0x3fc00000) 711 #define float32_two make_float32(0x40000000) 712 #define float32_three make_float32(0x40400000) 713 #define float32_infinity make_float32(0x7f800000) 714 715 /*---------------------------------------------------------------------------- 716 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a 717 | single-precision floating-point value, returning the result. After being 718 | shifted into the proper positions, the three fields are simply added 719 | together to form the result. This means that any integer portion of `zSig' 720 | will be added into the exponent. Since a properly normalized significand 721 | will have an integer portion equal to 1, the `zExp' input should be 1 less 722 | than the desired result exponent whenever `zSig' is a complete, normalized 723 | significand. 724 *----------------------------------------------------------------------------*/ 725 726 static inline float32 packFloat32(bool zSign, int zExp, uint32_t zSig) 727 { 728 return make_float32( 729 (((uint32_t)zSign) << 31) + (((uint32_t)zExp) << 23) + zSig); 730 } 731 732 /*---------------------------------------------------------------------------- 733 | The pattern for a default generated single-precision NaN. 734 *----------------------------------------------------------------------------*/ 735 float32 float32_default_nan(float_status *status); 736 737 /*---------------------------------------------------------------------------- 738 | Software IEC/IEEE double-precision conversion routines. 739 *----------------------------------------------------------------------------*/ 740 741 int16_t float64_to_int16_scalbn(float64, FloatRoundMode, int, float_status *); 742 int32_t float64_to_int32_scalbn(float64, FloatRoundMode, int, float_status *); 743 int64_t float64_to_int64_scalbn(float64, FloatRoundMode, int, float_status *); 744 745 int16_t float64_to_int16(float64, float_status *status); 746 int32_t float64_to_int32(float64, float_status *status); 747 int64_t float64_to_int64(float64, float_status *status); 748 749 int16_t float64_to_int16_round_to_zero(float64, float_status *status); 750 int32_t float64_to_int32_round_to_zero(float64, float_status *status); 751 int64_t float64_to_int64_round_to_zero(float64, float_status *status); 752 753 uint16_t float64_to_uint16_scalbn(float64, FloatRoundMode, int, float_status *); 754 uint32_t float64_to_uint32_scalbn(float64, FloatRoundMode, int, float_status *); 755 uint64_t float64_to_uint64_scalbn(float64, FloatRoundMode, int, float_status *); 756 757 uint16_t float64_to_uint16(float64, float_status *status); 758 uint32_t float64_to_uint32(float64, float_status *status); 759 uint64_t float64_to_uint64(float64, float_status *status); 760 761 uint16_t float64_to_uint16_round_to_zero(float64, float_status *status); 762 uint32_t float64_to_uint32_round_to_zero(float64, float_status *status); 763 uint64_t float64_to_uint64_round_to_zero(float64, float_status *status); 764 765 float32 float64_to_float32(float64, float_status *status); 766 floatx80 float64_to_floatx80(float64, float_status *status); 767 float128 float64_to_float128(float64, float_status *status); 768 769 /*---------------------------------------------------------------------------- 770 | Software IEC/IEEE double-precision operations. 771 *----------------------------------------------------------------------------*/ 772 float64 float64_round_to_int(float64, float_status *status); 773 float64 float64_add(float64, float64, float_status *status); 774 float64 float64_sub(float64, float64, float_status *status); 775 float64 float64_mul(float64, float64, float_status *status); 776 float64 float64_div(float64, float64, float_status *status); 777 float64 float64_rem(float64, float64, float_status *status); 778 float64 float64_muladd(float64, float64, float64, int, float_status *status); 779 float64 float64_sqrt(float64, float_status *status); 780 float64 float64_log2(float64, float_status *status); 781 FloatRelation float64_compare(float64, float64, float_status *status); 782 FloatRelation float64_compare_quiet(float64, float64, float_status *status); 783 float64 float64_min(float64, float64, float_status *status); 784 float64 float64_max(float64, float64, float_status *status); 785 float64 float64_minnum(float64, float64, float_status *status); 786 float64 float64_maxnum(float64, float64, float_status *status); 787 float64 float64_minnummag(float64, float64, float_status *status); 788 float64 float64_maxnummag(float64, float64, float_status *status); 789 float64 float64_minimum_number(float64, float64, float_status *status); 790 float64 float64_maximum_number(float64, float64, float_status *status); 791 bool float64_is_quiet_nan(float64 a, float_status *status); 792 bool float64_is_signaling_nan(float64, float_status *status); 793 float64 float64_silence_nan(float64, float_status *status); 794 float64 float64_scalbn(float64, int, float_status *status); 795 796 static inline float64 float64_abs(float64 a) 797 { 798 /* Note that abs does *not* handle NaN specially, nor does 799 * it flush denormal inputs to zero. 800 */ 801 return make_float64(float64_val(a) & 0x7fffffffffffffffLL); 802 } 803 804 static inline float64 float64_chs(float64 a) 805 { 806 /* Note that chs does *not* handle NaN specially, nor does 807 * it flush denormal inputs to zero. 808 */ 809 return make_float64(float64_val(a) ^ 0x8000000000000000LL); 810 } 811 812 static inline bool float64_is_infinity(float64 a) 813 { 814 return (float64_val(a) & 0x7fffffffffffffffLL ) == 0x7ff0000000000000LL; 815 } 816 817 static inline bool float64_is_neg(float64 a) 818 { 819 return float64_val(a) >> 63; 820 } 821 822 static inline bool float64_is_zero(float64 a) 823 { 824 return (float64_val(a) & 0x7fffffffffffffffLL) == 0; 825 } 826 827 static inline bool float64_is_any_nan(float64 a) 828 { 829 return ((float64_val(a) & ~(1ULL << 63)) > 0x7ff0000000000000ULL); 830 } 831 832 static inline bool float64_is_zero_or_denormal(float64 a) 833 { 834 return (float64_val(a) & 0x7ff0000000000000LL) == 0; 835 } 836 837 static inline bool float64_is_normal(float64 a) 838 { 839 return (((float64_val(a) >> 52) + 1) & 0x7ff) >= 2; 840 } 841 842 static inline bool float64_is_denormal(float64 a) 843 { 844 return float64_is_zero_or_denormal(a) && !float64_is_zero(a); 845 } 846 847 static inline bool float64_is_zero_or_normal(float64 a) 848 { 849 return float64_is_normal(a) || float64_is_zero(a); 850 } 851 852 static inline float64 float64_set_sign(float64 a, int sign) 853 { 854 return make_float64((float64_val(a) & 0x7fffffffffffffffULL) 855 | ((int64_t)sign << 63)); 856 } 857 858 static inline bool float64_eq(float64 a, float64 b, float_status *s) 859 { 860 return float64_compare(a, b, s) == float_relation_equal; 861 } 862 863 static inline bool float64_le(float64 a, float64 b, float_status *s) 864 { 865 return float64_compare(a, b, s) <= float_relation_equal; 866 } 867 868 static inline bool float64_lt(float64 a, float64 b, float_status *s) 869 { 870 return float64_compare(a, b, s) < float_relation_equal; 871 } 872 873 static inline bool float64_unordered(float64 a, float64 b, float_status *s) 874 { 875 return float64_compare(a, b, s) == float_relation_unordered; 876 } 877 878 static inline bool float64_eq_quiet(float64 a, float64 b, float_status *s) 879 { 880 return float64_compare_quiet(a, b, s) == float_relation_equal; 881 } 882 883 static inline bool float64_le_quiet(float64 a, float64 b, float_status *s) 884 { 885 return float64_compare_quiet(a, b, s) <= float_relation_equal; 886 } 887 888 static inline bool float64_lt_quiet(float64 a, float64 b, float_status *s) 889 { 890 return float64_compare_quiet(a, b, s) < float_relation_equal; 891 } 892 893 static inline bool float64_unordered_quiet(float64 a, float64 b, 894 float_status *s) 895 { 896 return float64_compare_quiet(a, b, s) == float_relation_unordered; 897 } 898 899 #define float64_zero make_float64(0) 900 #define float64_half make_float64(0x3fe0000000000000LL) 901 #define float64_one make_float64(0x3ff0000000000000LL) 902 #define float64_one_point_five make_float64(0x3FF8000000000000ULL) 903 #define float64_two make_float64(0x4000000000000000ULL) 904 #define float64_three make_float64(0x4008000000000000ULL) 905 #define float64_ln2 make_float64(0x3fe62e42fefa39efLL) 906 #define float64_infinity make_float64(0x7ff0000000000000LL) 907 908 /*---------------------------------------------------------------------------- 909 | The pattern for a default generated double-precision NaN. 910 *----------------------------------------------------------------------------*/ 911 float64 float64_default_nan(float_status *status); 912 913 /*---------------------------------------------------------------------------- 914 | Software IEC/IEEE double-precision operations, rounding to single precision, 915 | returning a result in double precision, with only one rounding step. 916 *----------------------------------------------------------------------------*/ 917 918 float64 float64r32_add(float64, float64, float_status *status); 919 float64 float64r32_sub(float64, float64, float_status *status); 920 float64 float64r32_mul(float64, float64, float_status *status); 921 float64 float64r32_div(float64, float64, float_status *status); 922 float64 float64r32_muladd(float64, float64, float64, int, float_status *status); 923 float64 float64r32_sqrt(float64, float_status *status); 924 925 /*---------------------------------------------------------------------------- 926 | Software IEC/IEEE extended double-precision conversion routines. 927 *----------------------------------------------------------------------------*/ 928 int32_t floatx80_to_int32(floatx80, float_status *status); 929 int32_t floatx80_to_int32_round_to_zero(floatx80, float_status *status); 930 int64_t floatx80_to_int64(floatx80, float_status *status); 931 int64_t floatx80_to_int64_round_to_zero(floatx80, float_status *status); 932 float32 floatx80_to_float32(floatx80, float_status *status); 933 float64 floatx80_to_float64(floatx80, float_status *status); 934 float128 floatx80_to_float128(floatx80, float_status *status); 935 936 /*---------------------------------------------------------------------------- 937 | The pattern for an extended double-precision inf. 938 *----------------------------------------------------------------------------*/ 939 extern const floatx80 floatx80_infinity; 940 941 /*---------------------------------------------------------------------------- 942 | Software IEC/IEEE extended double-precision operations. 943 *----------------------------------------------------------------------------*/ 944 floatx80 floatx80_round(floatx80 a, float_status *status); 945 floatx80 floatx80_round_to_int(floatx80, float_status *status); 946 floatx80 floatx80_add(floatx80, floatx80, float_status *status); 947 floatx80 floatx80_sub(floatx80, floatx80, float_status *status); 948 floatx80 floatx80_mul(floatx80, floatx80, float_status *status); 949 floatx80 floatx80_div(floatx80, floatx80, float_status *status); 950 floatx80 floatx80_modrem(floatx80, floatx80, bool, uint64_t *, 951 float_status *status); 952 floatx80 floatx80_mod(floatx80, floatx80, float_status *status); 953 floatx80 floatx80_rem(floatx80, floatx80, float_status *status); 954 floatx80 floatx80_sqrt(floatx80, float_status *status); 955 FloatRelation floatx80_compare(floatx80, floatx80, float_status *status); 956 FloatRelation floatx80_compare_quiet(floatx80, floatx80, float_status *status); 957 int floatx80_is_quiet_nan(floatx80, float_status *status); 958 int floatx80_is_signaling_nan(floatx80, float_status *status); 959 floatx80 floatx80_silence_nan(floatx80, float_status *status); 960 floatx80 floatx80_scalbn(floatx80, int, float_status *status); 961 962 static inline floatx80 floatx80_abs(floatx80 a) 963 { 964 a.high &= 0x7fff; 965 return a; 966 } 967 968 static inline floatx80 floatx80_chs(floatx80 a) 969 { 970 a.high ^= 0x8000; 971 return a; 972 } 973 974 static inline bool floatx80_is_infinity(floatx80 a) 975 { 976 #if defined(TARGET_M68K) 977 return (a.high & 0x7fff) == floatx80_infinity.high && !(a.low << 1); 978 #else 979 return (a.high & 0x7fff) == floatx80_infinity.high && 980 a.low == floatx80_infinity.low; 981 #endif 982 } 983 984 static inline bool floatx80_is_neg(floatx80 a) 985 { 986 return a.high >> 15; 987 } 988 989 static inline bool floatx80_is_zero(floatx80 a) 990 { 991 return (a.high & 0x7fff) == 0 && a.low == 0; 992 } 993 994 static inline bool floatx80_is_zero_or_denormal(floatx80 a) 995 { 996 return (a.high & 0x7fff) == 0; 997 } 998 999 static inline bool floatx80_is_any_nan(floatx80 a) 1000 { 1001 return ((a.high & 0x7fff) == 0x7fff) && (a.low<<1); 1002 } 1003 1004 static inline bool floatx80_eq(floatx80 a, floatx80 b, float_status *s) 1005 { 1006 return floatx80_compare(a, b, s) == float_relation_equal; 1007 } 1008 1009 static inline bool floatx80_le(floatx80 a, floatx80 b, float_status *s) 1010 { 1011 return floatx80_compare(a, b, s) <= float_relation_equal; 1012 } 1013 1014 static inline bool floatx80_lt(floatx80 a, floatx80 b, float_status *s) 1015 { 1016 return floatx80_compare(a, b, s) < float_relation_equal; 1017 } 1018 1019 static inline bool floatx80_unordered(floatx80 a, floatx80 b, float_status *s) 1020 { 1021 return floatx80_compare(a, b, s) == float_relation_unordered; 1022 } 1023 1024 static inline bool floatx80_eq_quiet(floatx80 a, floatx80 b, float_status *s) 1025 { 1026 return floatx80_compare_quiet(a, b, s) == float_relation_equal; 1027 } 1028 1029 static inline bool floatx80_le_quiet(floatx80 a, floatx80 b, float_status *s) 1030 { 1031 return floatx80_compare_quiet(a, b, s) <= float_relation_equal; 1032 } 1033 1034 static inline bool floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *s) 1035 { 1036 return floatx80_compare_quiet(a, b, s) < float_relation_equal; 1037 } 1038 1039 static inline bool floatx80_unordered_quiet(floatx80 a, floatx80 b, 1040 float_status *s) 1041 { 1042 return floatx80_compare_quiet(a, b, s) == float_relation_unordered; 1043 } 1044 1045 /*---------------------------------------------------------------------------- 1046 | Return whether the given value is an invalid floatx80 encoding. 1047 | Invalid floatx80 encodings arise when the integer bit is not set, but 1048 | the exponent is not zero. The only times the integer bit is permitted to 1049 | be zero is in subnormal numbers and the value zero. 1050 | This includes what the Intel software developer's manual calls pseudo-NaNs, 1051 | pseudo-infinities and un-normal numbers. It does not include 1052 | pseudo-denormals, which must still be correctly handled as inputs even 1053 | if they are never generated as outputs. 1054 *----------------------------------------------------------------------------*/ 1055 static inline bool floatx80_invalid_encoding(floatx80 a) 1056 { 1057 #if defined(TARGET_M68K) 1058 /*------------------------------------------------------------------------- 1059 | With m68k, the explicit integer bit can be zero in the case of: 1060 | - zeros (exp == 0, mantissa == 0) 1061 | - denormalized numbers (exp == 0, mantissa != 0) 1062 | - unnormalized numbers (exp != 0, exp < 0x7FFF) 1063 | - infinities (exp == 0x7FFF, mantissa == 0) 1064 | - not-a-numbers (exp == 0x7FFF, mantissa != 0) 1065 | 1066 | For infinities and NaNs, the explicit integer bit can be either one or 1067 | zero. 1068 | 1069 | The IEEE 754 standard does not define a zero integer bit. Such a number 1070 | is an unnormalized number. Hardware does not directly support 1071 | denormalized and unnormalized numbers, but implicitly supports them by 1072 | trapping them as unimplemented data types, allowing efficient conversion 1073 | in software. 1074 | 1075 | See "M68000 FAMILY PROGRAMMER’S REFERENCE MANUAL", 1076 | "1.6 FLOATING-POINT DATA TYPES" 1077 *------------------------------------------------------------------------*/ 1078 return false; 1079 #else 1080 return (a.low & (1ULL << 63)) == 0 && (a.high & 0x7FFF) != 0; 1081 #endif 1082 } 1083 1084 #define floatx80_zero make_floatx80(0x0000, 0x0000000000000000LL) 1085 #define floatx80_zero_init make_floatx80_init(0x0000, 0x0000000000000000LL) 1086 #define floatx80_one make_floatx80(0x3fff, 0x8000000000000000LL) 1087 #define floatx80_ln2 make_floatx80(0x3ffe, 0xb17217f7d1cf79acLL) 1088 #define floatx80_pi make_floatx80(0x4000, 0xc90fdaa22168c235LL) 1089 #define floatx80_half make_floatx80(0x3ffe, 0x8000000000000000LL) 1090 1091 /*---------------------------------------------------------------------------- 1092 | Returns the fraction bits of the extended double-precision floating-point 1093 | value `a'. 1094 *----------------------------------------------------------------------------*/ 1095 1096 static inline uint64_t extractFloatx80Frac(floatx80 a) 1097 { 1098 return a.low; 1099 } 1100 1101 /*---------------------------------------------------------------------------- 1102 | Returns the exponent bits of the extended double-precision floating-point 1103 | value `a'. 1104 *----------------------------------------------------------------------------*/ 1105 1106 static inline int32_t extractFloatx80Exp(floatx80 a) 1107 { 1108 return a.high & 0x7FFF; 1109 } 1110 1111 /*---------------------------------------------------------------------------- 1112 | Returns the sign bit of the extended double-precision floating-point value 1113 | `a'. 1114 *----------------------------------------------------------------------------*/ 1115 1116 static inline bool extractFloatx80Sign(floatx80 a) 1117 { 1118 return a.high >> 15; 1119 } 1120 1121 /*---------------------------------------------------------------------------- 1122 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an 1123 | extended double-precision floating-point value, returning the result. 1124 *----------------------------------------------------------------------------*/ 1125 1126 static inline floatx80 packFloatx80(bool zSign, int32_t zExp, uint64_t zSig) 1127 { 1128 floatx80 z; 1129 1130 z.low = zSig; 1131 z.high = (((uint16_t)zSign) << 15) + zExp; 1132 return z; 1133 } 1134 1135 /*---------------------------------------------------------------------------- 1136 | Normalizes the subnormal extended double-precision floating-point value 1137 | represented by the denormalized significand `aSig'. The normalized exponent 1138 | and significand are stored at the locations pointed to by `zExpPtr' and 1139 | `zSigPtr', respectively. 1140 *----------------------------------------------------------------------------*/ 1141 1142 void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr, 1143 uint64_t *zSigPtr); 1144 1145 /*---------------------------------------------------------------------------- 1146 | Takes two extended double-precision floating-point values `a' and `b', one 1147 | of which is a NaN, and returns the appropriate NaN result. If either `a' or 1148 | `b' is a signaling NaN, the invalid exception is raised. 1149 *----------------------------------------------------------------------------*/ 1150 1151 floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status); 1152 1153 /*---------------------------------------------------------------------------- 1154 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 1155 | and extended significand formed by the concatenation of `zSig0' and `zSig1', 1156 | and returns the proper extended double-precision floating-point value 1157 | corresponding to the abstract input. Ordinarily, the abstract value is 1158 | rounded and packed into the extended double-precision format, with the 1159 | inexact exception raised if the abstract input cannot be represented 1160 | exactly. However, if the abstract value is too large, the overflow and 1161 | inexact exceptions are raised and an infinity or maximal finite value is 1162 | returned. If the abstract value is too small, the input value is rounded to 1163 | a subnormal number, and the underflow and inexact exceptions are raised if 1164 | the abstract input cannot be represented exactly as a subnormal extended 1165 | double-precision floating-point number. 1166 | If `roundingPrecision' is 32 or 64, the result is rounded to the same 1167 | number of bits as single or double precision, respectively. Otherwise, the 1168 | result is rounded to the full precision of the extended double-precision 1169 | format. 1170 | The input significand must be normalized or smaller. If the input 1171 | significand is not normalized, `zExp' must be 0; in that case, the result 1172 | returned is a subnormal number, and it must not require rounding. The 1173 | handling of underflow and overflow follows the IEC/IEEE Standard for Binary 1174 | Floating-Point Arithmetic. 1175 *----------------------------------------------------------------------------*/ 1176 1177 floatx80 roundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, bool zSign, 1178 int32_t zExp, uint64_t zSig0, uint64_t zSig1, 1179 float_status *status); 1180 1181 /*---------------------------------------------------------------------------- 1182 | Takes an abstract floating-point value having sign `zSign', exponent 1183 | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', 1184 | and returns the proper extended double-precision floating-point value 1185 | corresponding to the abstract input. This routine is just like 1186 | `roundAndPackFloatx80' except that the input significand does not have to be 1187 | normalized. 1188 *----------------------------------------------------------------------------*/ 1189 1190 floatx80 normalizeRoundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, 1191 bool zSign, int32_t zExp, 1192 uint64_t zSig0, uint64_t zSig1, 1193 float_status *status); 1194 1195 /*---------------------------------------------------------------------------- 1196 | The pattern for a default generated extended double-precision NaN. 1197 *----------------------------------------------------------------------------*/ 1198 floatx80 floatx80_default_nan(float_status *status); 1199 1200 /*---------------------------------------------------------------------------- 1201 | Software IEC/IEEE quadruple-precision conversion routines. 1202 *----------------------------------------------------------------------------*/ 1203 int32_t float128_to_int32(float128, float_status *status); 1204 int32_t float128_to_int32_round_to_zero(float128, float_status *status); 1205 int64_t float128_to_int64(float128, float_status *status); 1206 int64_t float128_to_int64_round_to_zero(float128, float_status *status); 1207 uint64_t float128_to_uint64(float128, float_status *status); 1208 uint64_t float128_to_uint64_round_to_zero(float128, float_status *status); 1209 uint32_t float128_to_uint32(float128, float_status *status); 1210 uint32_t float128_to_uint32_round_to_zero(float128, float_status *status); 1211 float32 float128_to_float32(float128, float_status *status); 1212 float64 float128_to_float64(float128, float_status *status); 1213 floatx80 float128_to_floatx80(float128, float_status *status); 1214 1215 /*---------------------------------------------------------------------------- 1216 | Software IEC/IEEE quadruple-precision operations. 1217 *----------------------------------------------------------------------------*/ 1218 float128 float128_round_to_int(float128, float_status *status); 1219 float128 float128_add(float128, float128, float_status *status); 1220 float128 float128_sub(float128, float128, float_status *status); 1221 float128 float128_mul(float128, float128, float_status *status); 1222 float128 float128_muladd(float128, float128, float128, int, 1223 float_status *status); 1224 float128 float128_div(float128, float128, float_status *status); 1225 float128 float128_rem(float128, float128, float_status *status); 1226 float128 float128_sqrt(float128, float_status *status); 1227 FloatRelation float128_compare(float128, float128, float_status *status); 1228 FloatRelation float128_compare_quiet(float128, float128, float_status *status); 1229 float128 float128_min(float128, float128, float_status *status); 1230 float128 float128_max(float128, float128, float_status *status); 1231 float128 float128_minnum(float128, float128, float_status *status); 1232 float128 float128_maxnum(float128, float128, float_status *status); 1233 float128 float128_minnummag(float128, float128, float_status *status); 1234 float128 float128_maxnummag(float128, float128, float_status *status); 1235 float128 float128_minimum_number(float128, float128, float_status *status); 1236 float128 float128_maximum_number(float128, float128, float_status *status); 1237 bool float128_is_quiet_nan(float128, float_status *status); 1238 bool float128_is_signaling_nan(float128, float_status *status); 1239 float128 float128_silence_nan(float128, float_status *status); 1240 float128 float128_scalbn(float128, int, float_status *status); 1241 1242 static inline float128 float128_abs(float128 a) 1243 { 1244 a.high &= 0x7fffffffffffffffLL; 1245 return a; 1246 } 1247 1248 static inline float128 float128_chs(float128 a) 1249 { 1250 a.high ^= 0x8000000000000000LL; 1251 return a; 1252 } 1253 1254 static inline bool float128_is_infinity(float128 a) 1255 { 1256 return (a.high & 0x7fffffffffffffffLL) == 0x7fff000000000000LL && a.low == 0; 1257 } 1258 1259 static inline bool float128_is_neg(float128 a) 1260 { 1261 return a.high >> 63; 1262 } 1263 1264 static inline bool float128_is_zero(float128 a) 1265 { 1266 return (a.high & 0x7fffffffffffffffLL) == 0 && a.low == 0; 1267 } 1268 1269 static inline bool float128_is_zero_or_denormal(float128 a) 1270 { 1271 return (a.high & 0x7fff000000000000LL) == 0; 1272 } 1273 1274 static inline bool float128_is_normal(float128 a) 1275 { 1276 return (((a.high >> 48) + 1) & 0x7fff) >= 2; 1277 } 1278 1279 static inline bool float128_is_denormal(float128 a) 1280 { 1281 return float128_is_zero_or_denormal(a) && !float128_is_zero(a); 1282 } 1283 1284 static inline bool float128_is_any_nan(float128 a) 1285 { 1286 return ((a.high >> 48) & 0x7fff) == 0x7fff && 1287 ((a.low != 0) || ((a.high & 0xffffffffffffLL) != 0)); 1288 } 1289 1290 static inline bool float128_eq(float128 a, float128 b, float_status *s) 1291 { 1292 return float128_compare(a, b, s) == float_relation_equal; 1293 } 1294 1295 static inline bool float128_le(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_lt(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_unordered(float128 a, float128 b, float_status *s) 1306 { 1307 return float128_compare(a, b, s) == float_relation_unordered; 1308 } 1309 1310 static inline bool float128_eq_quiet(float128 a, float128 b, float_status *s) 1311 { 1312 return float128_compare_quiet(a, b, s) == float_relation_equal; 1313 } 1314 1315 static inline bool float128_le_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_lt_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_unordered_quiet(float128 a, float128 b, 1326 float_status *s) 1327 { 1328 return float128_compare_quiet(a, b, s) == float_relation_unordered; 1329 } 1330 1331 #define float128_zero make_float128(0, 0) 1332 1333 /*---------------------------------------------------------------------------- 1334 | The pattern for a default generated quadruple-precision NaN. 1335 *----------------------------------------------------------------------------*/ 1336 float128 float128_default_nan(float_status *status); 1337 1338 #endif /* SOFTFLOAT_H */ 1339