fpu/softfloat-specialize.inc.c

   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 source fragment 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 /* Define for architectures which deviate from IEEE in not supporting
  83  * signaling NaNs (so all NaNs are treated as quiet).
  84  */
  85 #if defined(TARGET_XTENSA)
  86 #define NO_SIGNALING_NANS 1
  87 #endif
  88
  89 /* Define how the architecture discriminates signaling NaNs.
  90  * This done with the most significant bit of the fraction.
  91  * In IEEE 754-1985 this was implementation defined, but in IEEE 754-2008
  92  * the msb must be zero.  MIPS is (so far) unique in supporting both the
  93  * 2008 revision and backward compatibility with their original choice.
  94  * Thus for MIPS we must make the choice at runtime.
  95  */
  96 static inline bool snan_bit_is_one(float_status *status)
  97 {
  98 #if defined(TARGET_MIPS)
  99     return status->snan_bit_is_one;
 100 #elif defined(TARGET_HPPA) || defined(TARGET_UNICORE32) || defined(TARGET_SH4)
 101     return 1;
 102 #else
 103     return 0;
 104 #endif
 105 }
 106
 107 /*----------------------------------------------------------------------------
 108 | For the deconstructed floating-point with fraction FRAC, return true
 109 | if the fraction represents a signalling NaN; otherwise false.
 110 *----------------------------------------------------------------------------*/
 111
 112 static bool parts_is_snan_frac(uint64_t frac, float_status *status)
 113 {
 114 #ifdef NO_SIGNALING_NANS
 115     return false;
 116 #else
 117     bool msb = extract64(frac, DECOMPOSED_BINARY_POINT - 1, 1);
 118     return msb == snan_bit_is_one(status);
 119 #endif
 120 }
 121
 122 /*----------------------------------------------------------------------------
 123 | The pattern for a default generated deconstructed floating-point NaN.
 124 *----------------------------------------------------------------------------*/
 125
 126 static FloatParts parts_default_nan(float_status *status)
 127 {
 128     bool sign = 0;
 129     uint64_t frac;
 130
 131 #if defined(TARGET_SPARC) || defined(TARGET_M68K)
 132     /* !snan_bit_is_one, set all bits */
 133     frac = (1ULL << DECOMPOSED_BINARY_POINT) - 1;
 134 #elif defined(TARGET_I386) || defined(TARGET_X86_64) \
 135     || defined(TARGET_MICROBLAZE)
 136     /* !snan_bit_is_one, set sign and msb */
 137     frac = 1ULL << (DECOMPOSED_BINARY_POINT - 1);
 138     sign = 1;
 139 #elif defined(TARGET_HPPA)
 140     /* snan_bit_is_one, set msb-1.  */
 141     frac = 1ULL << (DECOMPOSED_BINARY_POINT - 2);
 142 #else
 143     /* This case is true for Alpha, ARM, MIPS, OpenRISC, PPC, RISC-V,
 144      * S390, SH4, TriCore, and Xtensa.  I cannot find documentation
 145      * for Unicore32; the choice from the original commit is unchanged.
 146      * Our other supported targets, CRIS, LM32, Moxie, Nios2, and Tile,
 147      * do not have floating-point.
 148      */
 149     if (snan_bit_is_one(status)) {
 150         /* set all bits other than msb */
 151         frac = (1ULL << (DECOMPOSED_BINARY_POINT - 1)) - 1;
 152     } else {
 153         /* set msb */
 154         frac = 1ULL << (DECOMPOSED_BINARY_POINT - 1);
 155     }
 156 #endif
 157
 158     return (FloatParts) {
 159         .cls = float_class_qnan,
 160         .sign = sign,
 161         .exp = INT_MAX,
 162         .frac = frac
 163     };
 164 }
 165
 166 /*----------------------------------------------------------------------------
 167 | Returns a quiet NaN from a signalling NaN for the deconstructed
 168 | floating-point parts.
 169 *----------------------------------------------------------------------------*/
 170
 171 static FloatParts parts_silence_nan(FloatParts a, float_status *status)
 172 {
 173 #ifdef NO_SIGNALING_NANS
 174     g_assert_not_reached();
 175 #elif defined(TARGET_HPPA)
 176     a.frac &= ~(1ULL << (DECOMPOSED_BINARY_POINT - 1));
 177     a.frac |= 1ULL << (DECOMPOSED_BINARY_POINT - 2);
 178 #else
 179     if (snan_bit_is_one(status)) {
 180         return parts_default_nan(status);
 181     } else {
 182         a.frac |= 1ULL << (DECOMPOSED_BINARY_POINT - 1);
 183     }
 184 #endif
 185     a.cls = float_class_qnan;
 186     return a;
 187 }
 188
 189 /*----------------------------------------------------------------------------
 190 | The pattern for a default generated extended double-precision NaN.
 191 *----------------------------------------------------------------------------*/
 192 floatx80 floatx80_default_nan(float_status *status)
 193 {
 194     floatx80 r;
 195
 196     /* None of the targets that have snan_bit_is_one use floatx80.  */
 197     assert(!snan_bit_is_one(status));
 198 #if defined(TARGET_M68K)
 199     r.low = UINT64_C(0xFFFFFFFFFFFFFFFF);
 200     r.high = 0x7FFF;
 201 #else
 202     /* X86 */
 203     r.low = UINT64_C(0xC000000000000000);
 204     r.high = 0xFFFF;
 205 #endif
 206     return r;
 207 }
 208
 209 /*----------------------------------------------------------------------------
 210 | The pattern for a default generated extended double-precision inf.
 211 *----------------------------------------------------------------------------*/
 212
 213 #define floatx80_infinity_high 0x7FFF
 214 #if defined(TARGET_M68K)
 215 #define floatx80_infinity_low  UINT64_C(0x0000000000000000)
 216 #else
 217 #define floatx80_infinity_low  UINT64_C(0x8000000000000000)
 218 #endif
 219
 220 const floatx80 floatx80_infinity
 221     = make_floatx80_init(floatx80_infinity_high, floatx80_infinity_low);
 222
 223 /*----------------------------------------------------------------------------
 224 | Raises the exceptions specified by `flags'.  Floating-point traps can be
 225 | defined here if desired.  It is currently not possible for such a trap
 226 | to substitute a result value.  If traps are not implemented, this routine
 227 | should be simply `float_exception_flags |= flags;'.
 228 *----------------------------------------------------------------------------*/
 229
 230 void float_raise(uint8_t flags, float_status *status)
 231 {
 232     status->float_exception_flags |= flags;
 233 }
 234
 235 /*----------------------------------------------------------------------------
 236 | Internal canonical NaN format.
 237 *----------------------------------------------------------------------------*/
 238 typedef struct {
 239     bool sign;
 240     uint64_t high, low;
 241 } commonNaNT;
 242
 243 /*----------------------------------------------------------------------------
 244 | Returns 1 if the half-precision floating-point value `a' is a quiet
 245 | NaN; otherwise returns 0.
 246 *----------------------------------------------------------------------------*/
 247
 248 bool float16_is_quiet_nan(float16 a_, float_status *status)
 249 {
 250 #ifdef NO_SIGNALING_NANS
 251     return float16_is_any_nan(a_);
 252 #else
 253     uint16_t a = float16_val(a_);
 254     if (snan_bit_is_one(status)) {
 255         return (((a >> 9) & 0x3F) == 0x3E) && (a & 0x1FF);
 256     } else {
 257         return ((a & ~0x8000) >= 0x7C80);
 258     }
 259 #endif
 260 }
 261
 262 /*----------------------------------------------------------------------------
 263 | Returns 1 if the half-precision floating-point value `a' is a signaling
 264 | NaN; otherwise returns 0.
 265 *----------------------------------------------------------------------------*/
 266
 267 bool float16_is_signaling_nan(float16 a_, float_status *status)
 268 {
 269 #ifdef NO_SIGNALING_NANS
 270     return 0;
 271 #else
 272     uint16_t a = float16_val(a_);
 273     if (snan_bit_is_one(status)) {
 274         return ((a & ~0x8000) >= 0x7C80);
 275     } else {
 276         return (((a >> 9) & 0x3F) == 0x3E) && (a & 0x1FF);
 277     }
 278 #endif
 279 }
 280
 281 /*----------------------------------------------------------------------------
 282 | Returns 1 if the single-precision floating-point value `a' is a quiet
 283 | NaN; otherwise returns 0.
 284 *----------------------------------------------------------------------------*/
 285
 286 bool float32_is_quiet_nan(float32 a_, float_status *status)
 287 {
 288 #ifdef NO_SIGNALING_NANS
 289     return float32_is_any_nan(a_);
 290 #else
 291     uint32_t a = float32_val(a_);
 292     if (snan_bit_is_one(status)) {
 293         return (((a >> 22) & 0x1FF) == 0x1FE) && (a & 0x003FFFFF);
 294     } else {
 295         return ((uint32_t)(a << 1) >= 0xFF800000);
 296     }
 297 #endif
 298 }
 299
 300 /*----------------------------------------------------------------------------
 301 | Returns 1 if the single-precision floating-point value `a' is a signaling
 302 | NaN; otherwise returns 0.
 303 *----------------------------------------------------------------------------*/
 304
 305 bool float32_is_signaling_nan(float32 a_, float_status *status)
 306 {
 307 #ifdef NO_SIGNALING_NANS
 308     return 0;
 309 #else
 310     uint32_t a = float32_val(a_);
 311     if (snan_bit_is_one(status)) {
 312         return ((uint32_t)(a << 1) >= 0xFF800000);
 313     } else {
 314         return (((a >> 22) & 0x1FF) == 0x1FE) && (a & 0x003FFFFF);
 315     }
 316 #endif
 317 }
 318
 319 /*----------------------------------------------------------------------------
 320 | Returns the result of converting the single-precision floating-point NaN
 321 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 322 | exception is raised.
 323 *----------------------------------------------------------------------------*/
 324
 325 static commonNaNT float32ToCommonNaN(float32 a, float_status *status)
 326 {
 327     commonNaNT z;
 328
 329     if (float32_is_signaling_nan(a, status)) {
 330         float_raise(float_flag_invalid, status);
 331     }
 332     z.sign = float32_val(a) >> 31;
 333     z.low = 0;
 334     z.high = ((uint64_t)float32_val(a)) << 41;
 335     return z;
 336 }
 337
 338 /*----------------------------------------------------------------------------
 339 | Returns the result of converting the canonical NaN `a' to the single-
 340 | precision floating-point format.
 341 *----------------------------------------------------------------------------*/
 342
 343 static float32 commonNaNToFloat32(commonNaNT a, float_status *status)
 344 {
 345     uint32_t mantissa = a.high >> 41;
 346
 347     if (status->default_nan_mode) {
 348         return float32_default_nan(status);
 349     }
 350
 351     if (mantissa) {
 352         return make_float32(
 353             (((uint32_t)a.sign) << 31) | 0x7F800000 | (a.high >> 41));
 354     } else {
 355         return float32_default_nan(status);
 356     }
 357 }
 358
 359 /*----------------------------------------------------------------------------
 360 | Select which NaN to propagate for a two-input operation.
 361 | IEEE754 doesn't specify all the details of this, so the
 362 | algorithm is target-specific.
 363 | The routine is passed various bits of information about the
 364 | two NaNs and should return 0 to select NaN a and 1 for NaN b.
 365 | Note that signalling NaNs are always squashed to quiet NaNs
 366 | by the caller, by calling floatXX_silence_nan() before
 367 | returning them.
 368 |
 369 | aIsLargerSignificand is only valid if both a and b are NaNs
 370 | of some kind, and is true if a has the larger significand,
 371 | or if both a and b have the same significand but a is
 372 | positive but b is negative. It is only needed for the x87
 373 | tie-break rule.
 374 *----------------------------------------------------------------------------*/
 375
 376 static int pickNaN(FloatClass a_cls, FloatClass b_cls,
 377                    bool aIsLargerSignificand)
 378 {
 379 #if defined(TARGET_ARM) || defined(TARGET_MIPS) || defined(TARGET_HPPA)
 380     /* ARM mandated NaN propagation rules (see FPProcessNaNs()), take
 381      * the first of:
 382      *  1. A if it is signaling
 383      *  2. B if it is signaling
 384      *  3. A (quiet)
 385      *  4. B (quiet)
 386      * A signaling NaN is always quietened before returning it.
 387      */
 388     /* According to MIPS specifications, if one of the two operands is
 389      * a sNaN, a new qNaN has to be generated. This is done in
 390      * floatXX_silence_nan(). For qNaN inputs the specifications
 391      * says: "When possible, this QNaN result is one of the operand QNaN
 392      * values." In practice it seems that most implementations choose
 393      * the first operand if both operands are qNaN. In short this gives
 394      * the following rules:
 395      *  1. A if it is signaling
 396      *  2. B if it is signaling
 397      *  3. A (quiet)
 398      *  4. B (quiet)
 399      * A signaling NaN is always silenced before returning it.
 400      */
 401     if (is_snan(a_cls)) {
 402         return 0;
 403     } else if (is_snan(b_cls)) {
 404         return 1;
 405     } else if (is_qnan(a_cls)) {
 406         return 0;
 407     } else {
 408         return 1;
 409     }
 410 #elif defined(TARGET_PPC) || defined(TARGET_XTENSA) || defined(TARGET_M68K)
 411     /* PowerPC propagation rules:
 412      *  1. A if it sNaN or qNaN
 413      *  2. B if it sNaN or qNaN
 414      * A signaling NaN is always silenced before returning it.
 415      */
 416     /* M68000 FAMILY PROGRAMMER'S REFERENCE MANUAL
 417      * 3.4 FLOATING-POINT INSTRUCTION DETAILS
 418      * If either operand, but not both operands, of an operation is a
 419      * nonsignaling NaN, then that NaN is returned as the result. If both
 420      * operands are nonsignaling NaNs, then the destination operand
 421      * nonsignaling NaN is returned as the result.
 422      * If either operand to an operation is a signaling NaN (SNaN), then the
 423      * SNaN bit is set in the FPSR EXC byte. If the SNaN exception enable bit
 424      * is set in the FPCR ENABLE byte, then the exception is taken and the
 425      * destination is not modified. If the SNaN exception enable bit is not
 426      * set, setting the SNaN bit in the operand to a one converts the SNaN to
 427      * a nonsignaling NaN. The operation then continues as described in the
 428      * preceding paragraph for nonsignaling NaNs.
 429      */
 430     if (is_nan(a_cls)) {
 431         return 0;
 432     } else {
 433         return 1;
 434     }
 435 #else
 436     /* This implements x87 NaN propagation rules:
 437      * SNaN + QNaN => return the QNaN
 438      * two SNaNs => return the one with the larger significand, silenced
 439      * two QNaNs => return the one with the larger significand
 440      * SNaN and a non-NaN => return the SNaN, silenced
 441      * QNaN and a non-NaN => return the QNaN
 442      *
 443      * If we get down to comparing significands and they are the same,
 444      * return the NaN with the positive sign bit (if any).
 445      */
 446     if (is_snan(a_cls)) {
 447         if (is_snan(b_cls)) {
 448             return aIsLargerSignificand ? 0 : 1;
 449         }
 450         return is_qnan(b_cls) ? 1 : 0;
 451     } else if (is_qnan(a_cls)) {
 452         if (is_snan(b_cls) || !is_qnan(b_cls)) {
 453             return 0;
 454         } else {
 455             return aIsLargerSignificand ? 0 : 1;
 456         }
 457     } else {
 458         return 1;
 459     }
 460 #endif
 461 }
 462
 463 /*----------------------------------------------------------------------------
 464 | Select which NaN to propagate for a three-input operation.
 465 | For the moment we assume that no CPU needs the 'larger significand'
 466 | information.
 467 | Return values : 0 : a; 1 : b; 2 : c; 3 : default-NaN
 468 *----------------------------------------------------------------------------*/
 469 static int pickNaNMulAdd(FloatClass a_cls, FloatClass b_cls, FloatClass c_cls,
 470                          bool infzero, float_status *status)
 471 {
 472 #if defined(TARGET_ARM)
 473     /* For ARM, the (inf,zero,qnan) case sets InvalidOp and returns
 474      * the default NaN
 475      */
 476     if (infzero && is_qnan(c_cls)) {
 477         float_raise(float_flag_invalid, status);
 478         return 3;
 479     }
 480
 481     /* This looks different from the ARM ARM pseudocode, because the ARM ARM
 482      * puts the operands to a fused mac operation (a*b)+c in the order c,a,b.
 483      */
 484     if (is_snan(c_cls)) {
 485         return 2;
 486     } else if (is_snan(a_cls)) {
 487         return 0;
 488     } else if (is_snan(b_cls)) {
 489         return 1;
 490     } else if (is_qnan(c_cls)) {
 491         return 2;
 492     } else if (is_qnan(a_cls)) {
 493         return 0;
 494     } else {
 495         return 1;
 496     }
 497 #elif defined(TARGET_MIPS)
 498     if (snan_bit_is_one(status)) {
 499         /*
 500          * For MIPS systems that conform to IEEE754-1985, the (inf,zero,nan)
 501          * case sets InvalidOp and returns the default NaN
 502          */
 503         if (infzero) {
 504             float_raise(float_flag_invalid, status);
 505             return 3;
 506         }
 507         /* Prefer sNaN over qNaN, in the a, b, c order. */
 508         if (is_snan(a_cls)) {
 509             return 0;
 510         } else if (is_snan(b_cls)) {
 511             return 1;
 512         } else if (is_snan(c_cls)) {
 513             return 2;
 514         } else if (is_qnan(a_cls)) {
 515             return 0;
 516         } else if (is_qnan(b_cls)) {
 517             return 1;
 518         } else {
 519             return 2;
 520         }
 521     } else {
 522         /*
 523          * For MIPS systems that conform to IEEE754-2008, the (inf,zero,nan)
 524          * case sets InvalidOp and returns the input value 'c'
 525          */
 526         if (infzero) {
 527             float_raise(float_flag_invalid, status);
 528             return 2;
 529         }
 530         /* Prefer sNaN over qNaN, in the c, a, b order. */
 531         if (is_snan(c_cls)) {
 532             return 2;
 533         } else if (is_snan(a_cls)) {
 534             return 0;
 535         } else if (is_snan(b_cls)) {
 536             return 1;
 537         } else if (is_qnan(c_cls)) {
 538             return 2;
 539         } else if (is_qnan(a_cls)) {
 540             return 0;
 541         } else {
 542             return 1;
 543         }
 544     }
 545 #elif defined(TARGET_PPC)
 546     /* For PPC, the (inf,zero,qnan) case sets InvalidOp, but we prefer
 547      * to return an input NaN if we have one (ie c) rather than generating
 548      * a default NaN
 549      */
 550     if (infzero) {
 551         float_raise(float_flag_invalid, status);
 552         return 2;
 553     }
 554
 555     /* If fRA is a NaN return it; otherwise if fRB is a NaN return it;
 556      * otherwise return fRC. Note that muladd on PPC is (fRA * fRC) + frB
 557      */
 558     if (is_nan(a_cls)) {
 559         return 0;
 560     } else if (is_nan(c_cls)) {
 561         return 2;
 562     } else {
 563         return 1;
 564     }
 565 #else
 566     /* A default implementation: prefer a to b to c.
 567      * This is unlikely to actually match any real implementation.
 568      */
 569     if (is_nan(a_cls)) {
 570         return 0;
 571     } else if (is_nan(b_cls)) {
 572         return 1;
 573     } else {
 574         return 2;
 575     }
 576 #endif
 577 }
 578
 579 /*----------------------------------------------------------------------------
 580 | Takes two single-precision floating-point values `a' and `b', one of which
 581 | is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
 582 | signaling NaN, the invalid exception is raised.
 583 *----------------------------------------------------------------------------*/
 584
 585 static float32 propagateFloat32NaN(float32 a, float32 b, float_status *status)
 586 {
 587     bool aIsLargerSignificand;
 588     uint32_t av, bv;
 589     FloatClass a_cls, b_cls;
 590
 591     /* This is not complete, but is good enough for pickNaN.  */
 592     a_cls = (!float32_is_any_nan(a)
 593              ? float_class_normal
 594              : float32_is_signaling_nan(a, status)
 595              ? float_class_snan
 596              : float_class_qnan);
 597     b_cls = (!float32_is_any_nan(b)
 598              ? float_class_normal
 599              : float32_is_signaling_nan(b, status)
 600              ? float_class_snan
 601              : float_class_qnan);
 602
 603     av = float32_val(a);
 604     bv = float32_val(b);
 605
 606     if (is_snan(a_cls) || is_snan(b_cls)) {
 607         float_raise(float_flag_invalid, status);
 608     }
 609
 610     if (status->default_nan_mode) {
 611         return float32_default_nan(status);
 612     }
 613
 614     if ((uint32_t)(av << 1) < (uint32_t)(bv << 1)) {
 615         aIsLargerSignificand = 0;
 616     } else if ((uint32_t)(bv << 1) < (uint32_t)(av << 1)) {
 617         aIsLargerSignificand = 1;
 618     } else {
 619         aIsLargerSignificand = (av < bv) ? 1 : 0;
 620     }
 621
 622     if (pickNaN(a_cls, b_cls, aIsLargerSignificand)) {
 623         if (is_snan(b_cls)) {
 624             return float32_silence_nan(b, status);
 625         }
 626         return b;
 627     } else {
 628         if (is_snan(a_cls)) {
 629             return float32_silence_nan(a, status);
 630         }
 631         return a;
 632     }
 633 }
 634
 635 /*----------------------------------------------------------------------------
 636 | Returns 1 if the double-precision floating-point value `a' is a quiet
 637 | NaN; otherwise returns 0.
 638 *----------------------------------------------------------------------------*/
 639
 640 bool float64_is_quiet_nan(float64 a_, float_status *status)
 641 {
 642 #ifdef NO_SIGNALING_NANS
 643     return float64_is_any_nan(a_);
 644 #else
 645     uint64_t a = float64_val(a_);
 646     if (snan_bit_is_one(status)) {
 647         return (((a >> 51) & 0xFFF) == 0xFFE)
 648             && (a & 0x0007FFFFFFFFFFFFULL);
 649     } else {
 650         return ((a << 1) >= 0xFFF0000000000000ULL);
 651     }
 652 #endif
 653 }
 654
 655 /*----------------------------------------------------------------------------
 656 | Returns 1 if the double-precision floating-point value `a' is a signaling
 657 | NaN; otherwise returns 0.
 658 *----------------------------------------------------------------------------*/
 659
 660 bool float64_is_signaling_nan(float64 a_, float_status *status)
 661 {
 662 #ifdef NO_SIGNALING_NANS
 663     return 0;
 664 #else
 665     uint64_t a = float64_val(a_);
 666     if (snan_bit_is_one(status)) {
 667         return ((a << 1) >= 0xFFF0000000000000ULL);
 668     } else {
 669         return (((a >> 51) & 0xFFF) == 0xFFE)
 670             && (a & UINT64_C(0x0007FFFFFFFFFFFF));
 671     }
 672 #endif
 673 }
 674
 675 /*----------------------------------------------------------------------------
 676 | Returns the result of converting the double-precision floating-point NaN
 677 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 678 | exception is raised.
 679 *----------------------------------------------------------------------------*/
 680
 681 static commonNaNT float64ToCommonNaN(float64 a, float_status *status)
 682 {
 683     commonNaNT z;
 684
 685     if (float64_is_signaling_nan(a, status)) {
 686         float_raise(float_flag_invalid, status);
 687     }
 688     z.sign = float64_val(a) >> 63;
 689     z.low = 0;
 690     z.high = float64_val(a) << 12;
 691     return z;
 692 }
 693
 694 /*----------------------------------------------------------------------------
 695 | Returns the result of converting the canonical NaN `a' to the double-
 696 | precision floating-point format.
 697 *----------------------------------------------------------------------------*/
 698
 699 static float64 commonNaNToFloat64(commonNaNT a, float_status *status)
 700 {
 701     uint64_t mantissa = a.high >> 12;
 702
 703     if (status->default_nan_mode) {
 704         return float64_default_nan(status);
 705     }
 706
 707     if (mantissa) {
 708         return make_float64(
 709               (((uint64_t) a.sign) << 63)
 710             | UINT64_C(0x7FF0000000000000)
 711             | (a.high >> 12));
 712     } else {
 713         return float64_default_nan(status);
 714     }
 715 }
 716
 717 /*----------------------------------------------------------------------------
 718 | Takes two double-precision floating-point values `a' and `b', one of which
 719 | is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
 720 | signaling NaN, the invalid exception is raised.
 721 *----------------------------------------------------------------------------*/
 722
 723 static float64 propagateFloat64NaN(float64 a, float64 b, float_status *status)
 724 {
 725     bool aIsLargerSignificand;
 726     uint64_t av, bv;
 727     FloatClass a_cls, b_cls;
 728
 729     /* This is not complete, but is good enough for pickNaN.  */
 730     a_cls = (!float64_is_any_nan(a)
 731              ? float_class_normal
 732              : float64_is_signaling_nan(a, status)
 733              ? float_class_snan
 734              : float_class_qnan);
 735     b_cls = (!float64_is_any_nan(b)
 736              ? float_class_normal
 737              : float64_is_signaling_nan(b, status)
 738              ? float_class_snan
 739              : float_class_qnan);
 740
 741     av = float64_val(a);
 742     bv = float64_val(b);
 743
 744     if (is_snan(a_cls) || is_snan(b_cls)) {
 745         float_raise(float_flag_invalid, status);
 746     }
 747
 748     if (status->default_nan_mode) {
 749         return float64_default_nan(status);
 750     }
 751
 752     if ((uint64_t)(av << 1) < (uint64_t)(bv << 1)) {
 753         aIsLargerSignificand = 0;
 754     } else if ((uint64_t)(bv << 1) < (uint64_t)(av << 1)) {
 755         aIsLargerSignificand = 1;
 756     } else {
 757         aIsLargerSignificand = (av < bv) ? 1 : 0;
 758     }
 759
 760     if (pickNaN(a_cls, b_cls, aIsLargerSignificand)) {
 761         if (is_snan(b_cls)) {
 762             return float64_silence_nan(b, status);
 763         }
 764         return b;
 765     } else {
 766         if (is_snan(a_cls)) {
 767             return float64_silence_nan(a, status);
 768         }
 769         return a;
 770     }
 771 }
 772
 773 /*----------------------------------------------------------------------------
 774 | Returns 1 if the extended double-precision floating-point value `a' is a
 775 | quiet NaN; otherwise returns 0. This slightly differs from the same
 776 | function for other types as floatx80 has an explicit bit.
 777 *----------------------------------------------------------------------------*/
 778
 779 int floatx80_is_quiet_nan(floatx80 a, float_status *status)
 780 {
 781 #ifdef NO_SIGNALING_NANS
 782     return floatx80_is_any_nan(a);
 783 #else
 784     if (snan_bit_is_one(status)) {
 785         uint64_t aLow;
 786
 787         aLow = a.low & ~0x4000000000000000ULL;
 788         return ((a.high & 0x7FFF) == 0x7FFF)
 789             && (aLow << 1)
 790             && (a.low == aLow);
 791     } else {
 792         return ((a.high & 0x7FFF) == 0x7FFF)
 793             && (UINT64_C(0x8000000000000000) <= ((uint64_t)(a.low << 1)));
 794     }
 795 #endif
 796 }
 797
 798 /*----------------------------------------------------------------------------
 799 | Returns 1 if the extended double-precision floating-point value `a' is a
 800 | signaling NaN; otherwise returns 0. This slightly differs from the same
 801 | function for other types as floatx80 has an explicit bit.
 802 *----------------------------------------------------------------------------*/
 803
 804 int floatx80_is_signaling_nan(floatx80 a, float_status *status)
 805 {
 806 #ifdef NO_SIGNALING_NANS
 807     return 0;
 808 #else
 809     if (snan_bit_is_one(status)) {
 810         return ((a.high & 0x7FFF) == 0x7FFF)
 811             && ((a.low << 1) >= 0x8000000000000000ULL);
 812     } else {
 813         uint64_t aLow;
 814
 815         aLow = a.low & ~UINT64_C(0x4000000000000000);
 816         return ((a.high & 0x7FFF) == 0x7FFF)
 817             && (uint64_t)(aLow << 1)
 818             && (a.low == aLow);
 819     }
 820 #endif
 821 }
 822
 823 /*----------------------------------------------------------------------------
 824 | Returns a quiet NaN from a signalling NaN for the extended double-precision
 825 | floating point value `a'.
 826 *----------------------------------------------------------------------------*/
 827
 828 floatx80 floatx80_silence_nan(floatx80 a, float_status *status)
 829 {
 830     /* None of the targets that have snan_bit_is_one use floatx80.  */
 831     assert(!snan_bit_is_one(status));
 832     a.low |= UINT64_C(0xC000000000000000);
 833     return a;
 834 }
 835
 836 /*----------------------------------------------------------------------------
 837 | Returns the result of converting the extended double-precision floating-
 838 | point NaN `a' to the canonical NaN format.  If `a' is a signaling NaN, the
 839 | invalid exception is raised.
 840 *----------------------------------------------------------------------------*/
 841
 842 static commonNaNT floatx80ToCommonNaN(floatx80 a, float_status *status)
 843 {
 844     floatx80 dflt;
 845     commonNaNT z;
 846
 847     if (floatx80_is_signaling_nan(a, status)) {
 848         float_raise(float_flag_invalid, status);
 849     }
 850     if (a.low >> 63) {
 851         z.sign = a.high >> 15;
 852         z.low = 0;
 853         z.high = a.low << 1;
 854     } else {
 855         dflt = floatx80_default_nan(status);
 856         z.sign = dflt.high >> 15;
 857         z.low = 0;
 858         z.high = dflt.low << 1;
 859     }
 860     return z;
 861 }
 862
 863 /*----------------------------------------------------------------------------
 864 | Returns the result of converting the canonical NaN `a' to the extended
 865 | double-precision floating-point format.
 866 *----------------------------------------------------------------------------*/
 867
 868 static floatx80 commonNaNToFloatx80(commonNaNT a, float_status *status)
 869 {
 870     floatx80 z;
 871
 872     if (status->default_nan_mode) {
 873         return floatx80_default_nan(status);
 874     }
 875
 876     if (a.high >> 1) {
 877         z.low = UINT64_C(0x8000000000000000) | a.high >> 1;
 878         z.high = (((uint16_t)a.sign) << 15) | 0x7FFF;
 879     } else {
 880         z = floatx80_default_nan(status);
 881     }
 882     return z;
 883 }
 884
 885 /*----------------------------------------------------------------------------
 886 | Takes two extended double-precision floating-point values `a' and `b', one
 887 | of which is a NaN, and returns the appropriate NaN result.  If either `a' or
 888 | `b' is a signaling NaN, the invalid exception is raised.
 889 *----------------------------------------------------------------------------*/
 890
 891 floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status)
 892 {
 893     bool aIsLargerSignificand;
 894     FloatClass a_cls, b_cls;
 895
 896     /* This is not complete, but is good enough for pickNaN.  */
 897     a_cls = (!floatx80_is_any_nan(a)
 898              ? float_class_normal
 899              : floatx80_is_signaling_nan(a, status)
 900              ? float_class_snan
 901              : float_class_qnan);
 902     b_cls = (!floatx80_is_any_nan(b)
 903              ? float_class_normal
 904              : floatx80_is_signaling_nan(b, status)
 905              ? float_class_snan
 906              : float_class_qnan);
 907
 908     if (is_snan(a_cls) || is_snan(b_cls)) {
 909         float_raise(float_flag_invalid, status);
 910     }
 911
 912     if (status->default_nan_mode) {
 913         return floatx80_default_nan(status);
 914     }
 915
 916     if (a.low < b.low) {
 917         aIsLargerSignificand = 0;
 918     } else if (b.low < a.low) {
 919         aIsLargerSignificand = 1;
 920     } else {
 921         aIsLargerSignificand = (a.high < b.high) ? 1 : 0;
 922     }
 923
 924     if (pickNaN(a_cls, b_cls, aIsLargerSignificand)) {
 925         if (is_snan(b_cls)) {
 926             return floatx80_silence_nan(b, status);
 927         }
 928         return b;
 929     } else {
 930         if (is_snan(a_cls)) {
 931             return floatx80_silence_nan(a, status);
 932         }
 933         return a;
 934     }
 935 }
 936
 937 /*----------------------------------------------------------------------------
 938 | Returns 1 if the quadruple-precision floating-point value `a' is a quiet
 939 | NaN; otherwise returns 0.
 940 *----------------------------------------------------------------------------*/
 941
 942 bool float128_is_quiet_nan(float128 a, float_status *status)
 943 {
 944 #ifdef NO_SIGNALING_NANS
 945     return float128_is_any_nan(a);
 946 #else
 947     if (snan_bit_is_one(status)) {
 948         return (((a.high >> 47) & 0xFFFF) == 0xFFFE)
 949             && (a.low || (a.high & 0x00007FFFFFFFFFFFULL));
 950     } else {
 951         return ((a.high << 1) >= 0xFFFF000000000000ULL)
 952             && (a.low || (a.high & 0x0000FFFFFFFFFFFFULL));
 953     }
 954 #endif
 955 }
 956
 957 /*----------------------------------------------------------------------------
 958 | Returns 1 if the quadruple-precision floating-point value `a' is a
 959 | signaling NaN; otherwise returns 0.
 960 *----------------------------------------------------------------------------*/
 961
 962 bool float128_is_signaling_nan(float128 a, float_status *status)
 963 {
 964 #ifdef NO_SIGNALING_NANS
 965     return 0;
 966 #else
 967     if (snan_bit_is_one(status)) {
 968         return ((a.high << 1) >= 0xFFFF000000000000ULL)
 969             && (a.low || (a.high & 0x0000FFFFFFFFFFFFULL));
 970     } else {
 971         return (((a.high >> 47) & 0xFFFF) == 0xFFFE)
 972             && (a.low || (a.high & UINT64_C(0x00007FFFFFFFFFFF)));
 973     }
 974 #endif
 975 }
 976
 977 /*----------------------------------------------------------------------------
 978 | Returns a quiet NaN from a signalling NaN for the quadruple-precision
 979 | floating point value `a'.
 980 *----------------------------------------------------------------------------*/
 981
 982 float128 float128_silence_nan(float128 a, float_status *status)
 983 {
 984 #ifdef NO_SIGNALING_NANS
 985     g_assert_not_reached();
 986 #else
 987     if (snan_bit_is_one(status)) {
 988         return float128_default_nan(status);
 989     } else {
 990         a.high |= UINT64_C(0x0000800000000000);
 991         return a;
 992     }
 993 #endif
 994 }
 995
 996 /*----------------------------------------------------------------------------
 997 | Returns the result of converting the quadruple-precision floating-point NaN
 998 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 999 | exception is raised.
1000 *----------------------------------------------------------------------------*/
1001
1002 static commonNaNT float128ToCommonNaN(float128 a, float_status *status)
1003 {
1004     commonNaNT z;
1005
1006     if (float128_is_signaling_nan(a, status)) {
1007         float_raise(float_flag_invalid, status);
1008     }
1009     z.sign = a.high >> 63;
1010     shortShift128Left(a.high, a.low, 16, &z.high, &z.low);
1011     return z;
1012 }
1013
1014 /*----------------------------------------------------------------------------
1015 | Returns the result of converting the canonical NaN `a' to the quadruple-
1016 | precision floating-point format.
1017 *----------------------------------------------------------------------------*/
1018
1019 static float128 commonNaNToFloat128(commonNaNT a, float_status *status)
1020 {
1021     float128 z;
1022
1023     if (status->default_nan_mode) {
1024         return float128_default_nan(status);
1025     }
1026
1027     shift128Right(a.high, a.low, 16, &z.high, &z.low);
1028     z.high |= (((uint64_t)a.sign) << 63) | UINT64_C(0x7FFF000000000000);
1029     return z;
1030 }
1031
1032 /*----------------------------------------------------------------------------
1033 | Takes two quadruple-precision floating-point values `a' and `b', one of
1034 | which is a NaN, and returns the appropriate NaN result.  If either `a' or
1035 | `b' is a signaling NaN, the invalid exception is raised.
1036 *----------------------------------------------------------------------------*/
1037
1038 static float128 propagateFloat128NaN(float128 a, float128 b,
1039                                      float_status *status)
1040 {
1041     bool aIsLargerSignificand;
1042     FloatClass a_cls, b_cls;
1043
1044     /* This is not complete, but is good enough for pickNaN.  */
1045     a_cls = (!float128_is_any_nan(a)
1046              ? float_class_normal
1047              : float128_is_signaling_nan(a, status)
1048              ? float_class_snan
1049              : float_class_qnan);
1050     b_cls = (!float128_is_any_nan(b)
1051              ? float_class_normal
1052              : float128_is_signaling_nan(b, status)
1053              ? float_class_snan
1054              : float_class_qnan);
1055
1056     if (is_snan(a_cls) || is_snan(b_cls)) {
1057         float_raise(float_flag_invalid, status);
1058     }
1059
1060     if (status->default_nan_mode) {
1061         return float128_default_nan(status);
1062     }
1063
1064     if (lt128(a.high << 1, a.low, b.high << 1, b.low)) {
1065         aIsLargerSignificand = 0;
1066     } else if (lt128(b.high << 1, b.low, a.high << 1, a.low)) {
1067         aIsLargerSignificand = 1;
1068     } else {
1069         aIsLargerSignificand = (a.high < b.high) ? 1 : 0;
1070     }
1071
1072     if (pickNaN(a_cls, b_cls, aIsLargerSignificand)) {
1073         if (is_snan(b_cls)) {
1074             return float128_silence_nan(b, status);
1075         }
1076         return b;
1077     } else {
1078         if (is_snan(a_cls)) {
1079             return float128_silence_nan(a, status);
1080         }
1081         return a;
1082     }
1083 }