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 #define float32_default_nan 0xFFC00000
  65
  66 /*----------------------------------------------------------------------------
  67 | Returns 1 if the single-precision floating-point value `a' is a NaN;
  68 | otherwise returns 0.
  69 *----------------------------------------------------------------------------*/
  70
  71 flag float32_is_nan( float32 a )
  72 {
  73
  74     return ( 0xFF000000 < (bits32) ( a<<1 ) );
  75
  76 }
  77
  78 /*----------------------------------------------------------------------------
  79 | Returns 1 if the single-precision floating-point value `a' is a signaling
  80 | NaN; otherwise returns 0.
  81 *----------------------------------------------------------------------------*/
  82
  83 flag float32_is_signaling_nan( float32 a )
  84 {
  85
  86     return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
  87
  88 }
  89
  90 /*----------------------------------------------------------------------------
  91 | Returns the result of converting the single-precision floating-point NaN
  92 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
  93 | exception is raised.
  94 *----------------------------------------------------------------------------*/
  95
  96 static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM )
  97 {
  98     commonNaNT z;
  99
 100     if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR );
 101     z.sign = a>>31;
 102     z.low = 0;
 103     z.high = ( (bits64) a )<<41;
 104     return z;
 105
 106 }
 107
 108 /*----------------------------------------------------------------------------
 109 | Returns the result of converting the canonical NaN `a' to the single-
 110 | precision floating-point format.
 111 *----------------------------------------------------------------------------*/
 112
 113 static float32 commonNaNToFloat32( commonNaNT a )
 114 {
 115
 116     return ( ( (bits32) a.sign )<<31 ) | 0x7FC00000 | ( a.high>>41 );
 117
 118 }
 119
 120 /*----------------------------------------------------------------------------
 121 | Takes two single-precision floating-point values `a' and `b', one of which
 122 | is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
 123 | signaling NaN, the invalid exception is raised.
 124 *----------------------------------------------------------------------------*/
 125
 126 static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM)
 127 {
 128     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 129
 130     aIsNaN = float32_is_nan( a );
 131     aIsSignalingNaN = float32_is_signaling_nan( a );
 132     bIsNaN = float32_is_nan( b );
 133     bIsSignalingNaN = float32_is_signaling_nan( b );
 134     a |= 0x00400000;
 135     b |= 0x00400000;
 136     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 137     if ( aIsSignalingNaN ) {
 138         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 139         return bIsNaN ? b : a;
 140     }
 141     else if ( aIsNaN ) {
 142         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 143  returnLargerSignificand:
 144         if ( (bits32) ( a<<1 ) < (bits32) ( b<<1 ) ) return b;
 145         if ( (bits32) ( b<<1 ) < (bits32) ( a<<1 ) ) return a;
 146         return ( a < b ) ? a : b;
 147     }
 148     else {
 149         return b;
 150     }
 151
 152 }
 153
 154 /*----------------------------------------------------------------------------
 155 | The pattern for a default generated double-precision NaN.
 156 *----------------------------------------------------------------------------*/
 157 #define float64_default_nan LIT64( 0xFFF8000000000000 )
 158
 159 /*----------------------------------------------------------------------------
 160 | Returns 1 if the double-precision floating-point value `a' is a NaN;
 161 | otherwise returns 0.
 162 *----------------------------------------------------------------------------*/
 163
 164 flag float64_is_nan( float64 a )
 165 {
 166
 167     return ( LIT64( 0xFFE0000000000000 ) < (bits64) ( a<<1 ) );
 168
 169 }
 170
 171 /*----------------------------------------------------------------------------
 172 | Returns 1 if the double-precision floating-point value `a' is a signaling
 173 | NaN; otherwise returns 0.
 174 *----------------------------------------------------------------------------*/
 175
 176 flag float64_is_signaling_nan( float64 a )
 177 {
 178
 179     return
 180            ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
 181         && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
 182
 183 }
 184
 185 /*----------------------------------------------------------------------------
 186 | Returns the result of converting the double-precision floating-point NaN
 187 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 188 | exception is raised.
 189 *----------------------------------------------------------------------------*/
 190
 191 static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM)
 192 {
 193     commonNaNT z;
 194
 195     if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
 196     z.sign = a>>63;
 197     z.low = 0;
 198     z.high = a<<12;
 199     return z;
 200
 201 }
 202
 203 /*----------------------------------------------------------------------------
 204 | Returns the result of converting the canonical NaN `a' to the double-
 205 | precision floating-point format.
 206 *----------------------------------------------------------------------------*/
 207
 208 static float64 commonNaNToFloat64( commonNaNT a )
 209 {
 210
 211     return
 212           ( ( (bits64) a.sign )<<63 )
 213         | LIT64( 0x7FF8000000000000 )
 214         | ( a.high>>12 );
 215
 216 }
 217
 218 /*----------------------------------------------------------------------------
 219 | Takes two double-precision floating-point values `a' and `b', one of which
 220 | is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
 221 | signaling NaN, the invalid exception is raised.
 222 *----------------------------------------------------------------------------*/
 223
 224 static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM)
 225 {
 226     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 227
 228     aIsNaN = float64_is_nan( a );
 229     aIsSignalingNaN = float64_is_signaling_nan( a );
 230     bIsNaN = float64_is_nan( b );
 231     bIsSignalingNaN = float64_is_signaling_nan( b );
 232     a |= LIT64( 0x0008000000000000 );
 233     b |= LIT64( 0x0008000000000000 );
 234     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 235     if ( aIsSignalingNaN ) {
 236         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 237         return bIsNaN ? b : a;
 238     }
 239     else if ( aIsNaN ) {
 240         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 241  returnLargerSignificand:
 242         if ( (bits64) ( a<<1 ) < (bits64) ( b<<1 ) ) return b;
 243         if ( (bits64) ( b<<1 ) < (bits64) ( a<<1 ) ) return a;
 244         return ( a < b ) ? a : b;
 245     }
 246     else {
 247         return b;
 248     }
 249
 250 }
 251
 252 #ifdef FLOATX80
 253
 254 /*----------------------------------------------------------------------------
 255 | The pattern for a default generated extended double-precision NaN.  The
 256 | `high' and `low' values hold the most- and least-significant bits,
 257 | respectively.
 258 *----------------------------------------------------------------------------*/
 259 #define floatx80_default_nan_high 0xFFFF
 260 #define floatx80_default_nan_low  LIT64( 0xC000000000000000 )
 261
 262 /*----------------------------------------------------------------------------
 263 | Returns 1 if the extended double-precision floating-point value `a' is a
 264 | NaN; otherwise returns 0.
 265 *----------------------------------------------------------------------------*/
 266
 267 flag floatx80_is_nan( floatx80 a )
 268 {
 269
 270     return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
 271
 272 }
 273
 274 /*----------------------------------------------------------------------------
 275 | Returns 1 if the extended double-precision floating-point value `a' is a
 276 | signaling NaN; otherwise returns 0.
 277 *----------------------------------------------------------------------------*/
 278
 279 flag floatx80_is_signaling_nan( floatx80 a )
 280 {
 281     bits64 aLow;
 282
 283     aLow = a.low & ~ LIT64( 0x4000000000000000 );
 284     return
 285            ( ( a.high & 0x7FFF ) == 0x7FFF )
 286         && (bits64) ( aLow<<1 )
 287         && ( a.low == aLow );
 288
 289 }
 290
 291 /*----------------------------------------------------------------------------
 292 | Returns the result of converting the extended double-precision floating-
 293 | point NaN `a' to the canonical NaN format.  If `a' is a signaling NaN, the
 294 | invalid exception is raised.
 295 *----------------------------------------------------------------------------*/
 296
 297 static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM)
 298 {
 299     commonNaNT z;
 300
 301     if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
 302     z.sign = a.high>>15;
 303     z.low = 0;
 304     z.high = a.low<<1;
 305     return z;
 306
 307 }
 308
 309 /*----------------------------------------------------------------------------
 310 | Returns the result of converting the canonical NaN `a' to the extended
 311 | double-precision floating-point format.
 312 *----------------------------------------------------------------------------*/
 313
 314 static floatx80 commonNaNToFloatx80( commonNaNT a )
 315 {
 316     floatx80 z;
 317
 318     z.low = LIT64( 0xC000000000000000 ) | ( a.high>>1 );
 319     z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF;
 320     return z;
 321
 322 }
 323
 324 /*----------------------------------------------------------------------------
 325 | Takes two extended double-precision floating-point values `a' and `b', one
 326 | of which is a NaN, and returns the appropriate NaN result.  If either `a' or
 327 | `b' is a signaling NaN, the invalid exception is raised.
 328 *----------------------------------------------------------------------------*/
 329
 330 static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM)
 331 {
 332     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 333
 334     aIsNaN = floatx80_is_nan( a );
 335     aIsSignalingNaN = floatx80_is_signaling_nan( a );
 336     bIsNaN = floatx80_is_nan( b );
 337     bIsSignalingNaN = floatx80_is_signaling_nan( b );
 338     a.low |= LIT64( 0xC000000000000000 );
 339     b.low |= LIT64( 0xC000000000000000 );
 340     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 341     if ( aIsSignalingNaN ) {
 342         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 343         return bIsNaN ? b : a;
 344     }
 345     else if ( aIsNaN ) {
 346         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 347  returnLargerSignificand:
 348         if ( a.low < b.low ) return b;
 349         if ( b.low < a.low ) return a;
 350         return ( a.high < b.high ) ? a : b;
 351     }
 352     else {
 353         return b;
 354     }
 355
 356 }
 357
 358 #endif
 359
 360 #ifdef FLOAT128
 361
 362 /*----------------------------------------------------------------------------
 363 | The pattern for a default generated quadruple-precision NaN.  The `high' and
 364 | `low' values hold the most- and least-significant bits, respectively.
 365 *----------------------------------------------------------------------------*/
 366 #define float128_default_nan_high LIT64( 0xFFFF800000000000 )
 367 #define float128_default_nan_low  LIT64( 0x0000000000000000 )
 368
 369 /*----------------------------------------------------------------------------
 370 | Returns 1 if the quadruple-precision floating-point value `a' is a NaN;
 371 | otherwise returns 0.
 372 *----------------------------------------------------------------------------*/
 373
 374 flag float128_is_nan( float128 a )
 375 {
 376
 377     return
 378            ( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
 379         && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
 380
 381 }
 382
 383 /*----------------------------------------------------------------------------
 384 | Returns 1 if the quadruple-precision floating-point value `a' is a
 385 | signaling NaN; otherwise returns 0.
 386 *----------------------------------------------------------------------------*/
 387
 388 flag float128_is_signaling_nan( float128 a )
 389 {
 390
 391     return
 392            ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
 393         && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
 394
 395 }
 396
 397 /*----------------------------------------------------------------------------
 398 | Returns the result of converting the quadruple-precision floating-point NaN
 399 | `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
 400 | exception is raised.
 401 *----------------------------------------------------------------------------*/
 402
 403 static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM)
 404 {
 405     commonNaNT z;
 406
 407     if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
 408     z.sign = a.high>>63;
 409     shortShift128Left( a.high, a.low, 16, &z.high, &z.low );
 410     return z;
 411
 412 }
 413
 414 /*----------------------------------------------------------------------------
 415 | Returns the result of converting the canonical NaN `a' to the quadruple-
 416 | precision floating-point format.
 417 *----------------------------------------------------------------------------*/
 418
 419 static float128 commonNaNToFloat128( commonNaNT a )
 420 {
 421     float128 z;
 422
 423     shift128Right( a.high, a.low, 16, &z.high, &z.low );
 424     z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF800000000000 );
 425     return z;
 426
 427 }
 428
 429 /*----------------------------------------------------------------------------
 430 | Takes two quadruple-precision floating-point values `a' and `b', one of
 431 | which is a NaN, and returns the appropriate NaN result.  If either `a' or
 432 | `b' is a signaling NaN, the invalid exception is raised.
 433 *----------------------------------------------------------------------------*/
 434
 435 static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM)
 436 {
 437     flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
 438
 439     aIsNaN = float128_is_nan( a );
 440     aIsSignalingNaN = float128_is_signaling_nan( a );
 441     bIsNaN = float128_is_nan( b );
 442     bIsSignalingNaN = float128_is_signaling_nan( b );
 443     a.high |= LIT64( 0x0000800000000000 );
 444     b.high |= LIT64( 0x0000800000000000 );
 445     if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
 446     if ( aIsSignalingNaN ) {
 447         if ( bIsSignalingNaN ) goto returnLargerSignificand;
 448         return bIsNaN ? b : a;
 449     }
 450     else if ( aIsNaN ) {
 451         if ( bIsSignalingNaN | ! bIsNaN ) return a;
 452  returnLargerSignificand:
 453         if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b;
 454         if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a;
 455         return ( a.high < b.high ) ? a : b;
 456     }
 457     else {
 458         return b;
 459     }
 460
 461 }
 462
 463 #endif
 464