fpu/softfloat-specialize.h

   1
   2 /*============================================================================
   3
   4 This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
   5 Arithmetic Package, Release 2b.
   6
   7 Written by John R. Hauser.  This work was made possible in part by the
   8 International Computer Science Institute, located at Suite 600, 1947 Center
   9 Street, Berkeley, California 94704.  Funding was partially provided by the
  10 National Science Foundation under grant MIP-9311980.  The original version
  11 of this code was written as part of a project to build a fixed-point vector
  12 processor in collaboration with the University of California at Berkeley,
  13 overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
  14 is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
  15 arithmetic/SoftFloat.html'.
  16
  17 THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort has
  18 been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
  19 RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
  20 AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
  21 COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
  22 EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
  23 INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
  24 OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
  25
  26 Derivative works are acceptable, even for commercial purposes, so long as
  27 (1) the source code for the derivative work includes prominent notice that
  28 the work is derivative, and (2) the source code includes prominent notice with
  29 these four paragraphs for those parts of this code that are retained.
  30
  31 =============================================================================*/
  32
  33 /*----------------------------------------------------------------------------
  34 | Underflow tininess-detection mode, statically initialized to default value.
  35 | (The declaration in `softfloat.h' must match the `int8' type here.)
  36 *----------------------------------------------------------------------------*/
  37 int8 float_detect_tininess = float_tininess_after_rounding;
  38
  39 /*----------------------------------------------------------------------------
  40 | Raises the exceptions specified by `flags'.  Floating-point traps can be
  41 | defined here if desired.  It is currently not possible for such a trap
  42 | to substitute a result value.  If traps are not implemented, this routine
  43 | should be simply `float_exception_flags |= flags;'.
  44 *----------------------------------------------------------------------------*/
  45
  46 void float_raise( int8 flags STATUS_PARAM )
  47 {
  48
  49     STATUS(float_exception_flags) |= flags;
  50
  51 }
  52
  53 /*----------------------------------------------------------------------------
  54 | Internal canonical NaN format.
  55 *----------------------------------------------------------------------------*/
  56 typedef struct {
  57     flag sign;
  58     bits64 high, low;
  59 } commonNaNT;
  60
  61 /*----------------------------------------------------------------------------
  62 | The pattern for a default generated single-precision NaN.
  63 *----------------------------------------------------------------------------*/
  64 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
  65 #define float32_default_nan 0xFF800000
  66 #else
  67 #define float32_default_nan 0xFFC00000
  68 #endif
  69
  70 /*----------------------------------------------------------------------------
  71 | Returns 1 if the single-precision floating-point value `a' is a NaN;
  72 | otherwise returns 0.
  73 *----------------------------------------------------------------------------*/
  74
  75 int float32_is_nan( float32 a )
  76 {
  77 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
  78     return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
  79 #else
  80     return ( 0xFF800000 <= (bits32) ( a<<1 ) );
  81 #endif
  82 }
  83
  84 /*----------------------------------------------------------------------------
  85 | Returns 1 if the single-precision floating-point value `a' is a signaling
  86 | NaN; otherwise returns 0.
  87 *----------------------------------------------------------------------------*/
  88
  89 int float32_is_signaling_nan( float32 a )
  90 {
  91 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
  92     return ( 0xFF800000 <= (bits32) ( a<<1 ) );
  93 #else
  94     return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
  95 #endif
  96 }
  97
  98 /*----------------------------------------------------------------------------
  99 | Returns the result of converting the single-precision floating-point NaN
 100 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 101 | exception is raised.
 102 *----------------------------------------------------------------------------*/
 103
 104 static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM )
 105 {
 106     commonNaNT z;
 107
 108     if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR );
 109     z.sign = a>>31;
 110     z.low = 0;
 111     z.high = ( (bits64) a )<<41;
 112     return z;
 113
 114 }
 115
 116 /*----------------------------------------------------------------------------
 117 | Returns the result of converting the canonical NaN `a' to the single-
 118 | precision floating-point format.
 119 *----------------------------------------------------------------------------*/
 120
 121 static float32 commonNaNToFloat32( commonNaNT a )
 122 {
 123
 124     return ( ( (bits32) a.sign )<<31 ) | 0x7FC00000 | ( a.high>>41 );
 125
 126 }
 127
 128 /*----------------------------------------------------------------------------
 129 | Takes two single-precision floating-point values `a' and `b', one of which
 130 | is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
 131 | signaling NaN, the invalid exception is raised.
 132 *----------------------------------------------------------------------------*/
 133
 134 static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM)
 135 {
 136     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 137
 138     aIsNaN = float32_is_nan( a );
 139     aIsSignalingNaN = float32_is_signaling_nan( a );
 140     bIsNaN = float32_is_nan( b );
 141     bIsSignalingNaN = float32_is_signaling_nan( b );
 142 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
 143     a &= ~0x00400000;
 144     b &= ~0x00400000;
 145 #else
 146     a |= 0x00400000;
 147     b |= 0x00400000;
 148 #endif
 149     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 150     if ( aIsSignalingNaN ) {
 151         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 152         return bIsNaN ? b : a;
 153     }
 154     else if ( aIsNaN ) {
 155         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 156  returnLargerSignificand:
 157         if ( (bits32) ( a<<1 ) < (bits32) ( b<<1 ) ) return b;
 158         if ( (bits32) ( b<<1 ) < (bits32) ( a<<1 ) ) return a;
 159         return ( a < b ) ? a : b;
 160     }
 161     else {
 162         return b;
 163     }
 164
 165 }
 166
 167 /*----------------------------------------------------------------------------
 168 | The pattern for a default generated double-precision NaN.
 169 *----------------------------------------------------------------------------*/
 170 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
 171 #define float64_default_nan LIT64( 0xFFF0000000000000 )
 172 #else
 173 #define float64_default_nan LIT64( 0xFFF8000000000000 )
 174 #endif
 175
 176 /*----------------------------------------------------------------------------
 177 | Returns 1 if the double-precision floating-point value `a' is a NaN;
 178 | otherwise returns 0.
 179 *----------------------------------------------------------------------------*/
 180
 181 int float64_is_nan( float64 a )
 182 {
 183 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
 184     return
 185            ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
 186         && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
 187 #else
 188     return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) );
 189 #endif
 190 }
 191
 192 /*----------------------------------------------------------------------------
 193 | Returns 1 if the double-precision floating-point value `a' is a signaling
 194 | NaN; otherwise returns 0.
 195 *----------------------------------------------------------------------------*/
 196
 197 int float64_is_signaling_nan( float64 a )
 198 {
 199 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
 200     return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) );
 201 #else
 202     return
 203            ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
 204         && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
 205 #endif
 206 }
 207
 208 /*----------------------------------------------------------------------------
 209 | Returns the result of converting the double-precision floating-point NaN
 210 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 211 | exception is raised.
 212 *----------------------------------------------------------------------------*/
 213
 214 static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM)
 215 {
 216     commonNaNT z;
 217
 218     if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
 219     z.sign = a>>63;
 220     z.low = 0;
 221     z.high = a<<12;
 222     return z;
 223
 224 }
 225
 226 /*----------------------------------------------------------------------------
 227 | Returns the result of converting the canonical NaN `a' to the double-
 228 | precision floating-point format.
 229 *----------------------------------------------------------------------------*/
 230
 231 static float64 commonNaNToFloat64( commonNaNT a )
 232 {
 233
 234     return
 235           ( ( (bits64) a.sign )<<63 )
 236         | LIT64( 0x7FF8000000000000 )
 237         | ( a.high>>12 );
 238
 239 }
 240
 241 /*----------------------------------------------------------------------------
 242 | Takes two double-precision floating-point values `a' and `b', one of which
 243 | is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
 244 | signaling NaN, the invalid exception is raised.
 245 *----------------------------------------------------------------------------*/
 246
 247 static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM)
 248 {
 249     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 250
 251     aIsNaN = float64_is_nan( a );
 252     aIsSignalingNaN = float64_is_signaling_nan( a );
 253     bIsNaN = float64_is_nan( b );
 254     bIsSignalingNaN = float64_is_signaling_nan( b );
 255 #if defined(TARGET_MIPS) || defined(TARGET_HPPA)
 256     a &= ~LIT64( 0x0008000000000000 );
 257     b &= ~LIT64( 0x0008000000000000 );
 258 #else
 259     a |= LIT64( 0x0008000000000000 );
 260     b |= LIT64( 0x0008000000000000 );
 261 #endif
 262     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 263     if ( aIsSignalingNaN ) {
 264         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 265         return bIsNaN ? b : a;
 266     }
 267     else if ( aIsNaN ) {
 268         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 269  returnLargerSignificand:
 270         if ( (bits64) ( a<<1 ) < (bits64) ( b<<1 ) ) return b;
 271         if ( (bits64) ( b<<1 ) < (bits64) ( a<<1 ) ) return a;
 272         return ( a < b ) ? a : b;
 273     }
 274     else {
 275         return b;
 276     }
 277
 278 }
 279
 280 #ifdef FLOATX80
 281
 282 /*----------------------------------------------------------------------------
 283 | The pattern for a default generated extended double-precision NaN.  The
 284 | `high' and `low' values hold the most- and least-significant bits,
 285 | respectively.
 286 *----------------------------------------------------------------------------*/
 287 #define floatx80_default_nan_high 0xFFFF
 288 #define floatx80_default_nan_low  LIT64( 0xC000000000000000 )
 289
 290 /*----------------------------------------------------------------------------
 291 | Returns 1 if the extended double-precision floating-point value `a' is a
 292 | NaN; otherwise returns 0.
 293 *----------------------------------------------------------------------------*/
 294
 295 int floatx80_is_nan( floatx80 a )
 296 {
 297
 298     return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
 299
 300 }
 301
 302 /*----------------------------------------------------------------------------
 303 | Returns 1 if the extended double-precision floating-point value `a' is a
 304 | signaling NaN; otherwise returns 0.
 305 *----------------------------------------------------------------------------*/
 306
 307 int floatx80_is_signaling_nan( floatx80 a )
 308 {
 309     bits64 aLow;
 310
 311     aLow = a.low & ~ LIT64( 0x4000000000000000 );
 312     return
 313            ( ( a.high & 0x7FFF ) == 0x7FFF )
 314         && (bits64) ( aLow<<1 )
 315         && ( a.low == aLow );
 316
 317 }
 318
 319 /*----------------------------------------------------------------------------
 320 | Returns the result of converting the extended double-precision floating-
 321 | point NaN `a' to the canonical NaN format.  If `a' is a signaling NaN, the
 322 | invalid exception is raised.
 323 *----------------------------------------------------------------------------*/
 324
 325 static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM)
 326 {
 327     commonNaNT z;
 328
 329     if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
 330     z.sign = a.high>>15;
 331     z.low = 0;
 332     z.high = a.low<<1;
 333     return z;
 334
 335 }
 336
 337 /*----------------------------------------------------------------------------
 338 | Returns the result of converting the canonical NaN `a' to the extended
 339 | double-precision floating-point format.
 340 *----------------------------------------------------------------------------*/
 341
 342 static floatx80 commonNaNToFloatx80( commonNaNT a )
 343 {
 344     floatx80 z;
 345
 346     z.low = LIT64( 0xC000000000000000 ) | ( a.high>>1 );
 347     z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF;
 348     return z;
 349
 350 }
 351
 352 /*----------------------------------------------------------------------------
 353 | Takes two extended double-precision floating-point values `a' and `b', one
 354 | of which is a NaN, and returns the appropriate NaN result.  If either `a' or
 355 | `b' is a signaling NaN, the invalid exception is raised.
 356 *----------------------------------------------------------------------------*/
 357
 358 static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM)
 359 {
 360     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 361
 362     aIsNaN = floatx80_is_nan( a );
 363     aIsSignalingNaN = floatx80_is_signaling_nan( a );
 364     bIsNaN = floatx80_is_nan( b );
 365     bIsSignalingNaN = floatx80_is_signaling_nan( b );
 366     a.low |= LIT64( 0xC000000000000000 );
 367     b.low |= LIT64( 0xC000000000000000 );
 368     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 369     if ( aIsSignalingNaN ) {
 370         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 371         return bIsNaN ? b : a;
 372     }
 373     else if ( aIsNaN ) {
 374         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 375  returnLargerSignificand:
 376         if ( a.low < b.low ) return b;
 377         if ( b.low < a.low ) return a;
 378         return ( a.high < b.high ) ? a : b;
 379     }
 380     else {
 381         return b;
 382     }
 383
 384 }
 385
 386 #endif
 387
 388 #ifdef FLOAT128
 389
 390 /*----------------------------------------------------------------------------
 391 | The pattern for a default generated quadruple-precision NaN.  The `high' and
 392 | `low' values hold the most- and least-significant bits, respectively.
 393 *----------------------------------------------------------------------------*/
 394 #define float128_default_nan_high LIT64( 0xFFFF800000000000 )
 395 #define float128_default_nan_low  LIT64( 0x0000000000000000 )
 396
 397 /*----------------------------------------------------------------------------
 398 | Returns 1 if the quadruple-precision floating-point value `a' is a NaN;
 399 | otherwise returns 0.
 400 *----------------------------------------------------------------------------*/
 401
 402 int float128_is_nan( float128 a )
 403 {
 404
 405     return
 406            ( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
 407         && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
 408
 409 }
 410
 411 /*----------------------------------------------------------------------------
 412 | Returns 1 if the quadruple-precision floating-point value `a' is a
 413 | signaling NaN; otherwise returns 0.
 414 *----------------------------------------------------------------------------*/
 415
 416 int float128_is_signaling_nan( float128 a )
 417 {
 418
 419     return
 420            ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
 421         && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
 422
 423 }
 424
 425 /*----------------------------------------------------------------------------
 426 | Returns the result of converting the quadruple-precision floating-point NaN
 427 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 428 | exception is raised.
 429 *----------------------------------------------------------------------------*/
 430
 431 static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM)
 432 {
 433     commonNaNT z;
 434
 435     if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
 436     z.sign = a.high>>63;
 437     shortShift128Left( a.high, a.low, 16, &z.high, &z.low );
 438     return z;
 439
 440 }
 441
 442 /*----------------------------------------------------------------------------
 443 | Returns the result of converting the canonical NaN `a' to the quadruple-
 444 | precision floating-point format.
 445 *----------------------------------------------------------------------------*/
 446
 447 static float128 commonNaNToFloat128( commonNaNT a )
 448 {
 449     float128 z;
 450
 451     shift128Right( a.high, a.low, 16, &z.high, &z.low );
 452     z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF800000000000 );
 453     return z;
 454
 455 }
 456
 457 /*----------------------------------------------------------------------------
 458 | Takes two quadruple-precision floating-point values `a' and `b', one of
 459 | which is a NaN, and returns the appropriate NaN result.  If either `a' or
 460 | `b' is a signaling NaN, the invalid exception is raised.
 461 *----------------------------------------------------------------------------*/
 462
 463 static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM)
 464 {
 465     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 466
 467     aIsNaN = float128_is_nan( a );
 468     aIsSignalingNaN = float128_is_signaling_nan( a );
 469     bIsNaN = float128_is_nan( b );
 470     bIsSignalingNaN = float128_is_signaling_nan( b );
 471     a.high |= LIT64( 0x0000800000000000 );
 472     b.high |= LIT64( 0x0000800000000000 );
 473     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 474     if ( aIsSignalingNaN ) {
 475         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 476         return bIsNaN ? b : a;
 477     }
 478     else if ( aIsNaN ) {
 479         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 480  returnLargerSignificand:
 481         if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b;
 482         if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a;
 483         return ( a.high < b.high ) ? a : b;
 484     }
 485     else {
 486         return b;
 487     }
 488
 489 }
 490
 491 #endif
 492