fpu/softfloat.h

   1 /*============================================================================
   2
   3 This C header file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
   4 Package, Release 2b.
   5
   6 Written by John R. Hauser.  This work was made possible in part by the
   7 International Computer Science Institute, located at Suite 600, 1947 Center
   8 Street, Berkeley, California 94704.  Funding was partially provided by the
   9 National Science Foundation under grant MIP-9311980.  The original version
  10 of this code was written as part of a project to build a fixed-point vector
  11 processor in collaboration with the University of California at Berkeley,
  12 overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
  13 is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
  14 arithmetic/SoftFloat.html'.
  15
  16 THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort has
  17 been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
  18 RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
  19 AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
  20 COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
  21 EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
  22 INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
  23 OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
  24
  25 Derivative works are acceptable, even for commercial purposes, so long as
  26 (1) the source code for the derivative work includes prominent notice that
  27 the work is derivative, and (2) the source code includes prominent notice with
  28 these four paragraphs for those parts of this code that are retained.
  29
  30 =============================================================================*/
  31
  32 #ifndef SOFTFLOAT_H
  33 #define SOFTFLOAT_H
  34
  35 #if defined(CONFIG_SOLARIS) && defined(CONFIG_NEEDS_LIBSUNMATH)
  36 #include <sunmath.h>
  37 #endif
  38
  39 #include <inttypes.h>
  40 #include "config.h"
  41
  42 /*----------------------------------------------------------------------------
  43 | Each of the following `typedef's defines the most convenient type that holds
  44 | integers of at least as many bits as specified.  For example, `uint8' should
  45 | be the most convenient type that can hold unsigned integers of as many as
  46 | 8 bits.  The `flag' type must be able to hold either a 0 or 1.  For most
  47 | implementations of C, `flag', `uint8', and `int8' should all be `typedef'ed
  48 | to the same as `int'.
  49 *----------------------------------------------------------------------------*/
  50 typedef uint8_t flag;
  51 typedef uint8_t uint8;
  52 typedef int8_t int8;
  53 #ifndef _AIX
  54 typedef int uint16;
  55 typedef int int16;
  56 #endif
  57 typedef unsigned int uint32;
  58 typedef signed int int32;
  59 typedef uint64_t uint64;
  60 typedef int64_t int64;
  61
  62 /*----------------------------------------------------------------------------
  63 | Each of the following `typedef's defines a type that holds integers
  64 | of _exactly_ the number of bits specified.  For instance, for most
  65 | implementation of C, `bits16' and `sbits16' should be `typedef'ed to
  66 | `unsigned short int' and `signed short int' (or `short int'), respectively.
  67 *----------------------------------------------------------------------------*/
  68 typedef uint8_t bits8;
  69 typedef int8_t sbits8;
  70 typedef uint16_t bits16;
  71 typedef int16_t sbits16;
  72 typedef uint32_t bits32;
  73 typedef int32_t sbits32;
  74 typedef uint64_t bits64;
  75 typedef int64_t sbits64;
  76
  77 #define LIT64( a ) a##LL
  78 #define INLINE static inline
  79
  80 /*----------------------------------------------------------------------------
  81 | The macro `FLOATX80' must be defined to enable the extended double-precision
  82 | floating-point format `floatx80'.  If this macro is not defined, the
  83 | `floatx80' type will not be defined, and none of the functions that either
  84 | input or output the `floatx80' type will be defined.  The same applies to
  85 | the `FLOAT128' macro and the quadruple-precision format `float128'.
  86 *----------------------------------------------------------------------------*/
  87 #ifdef CONFIG_SOFTFLOAT
  88 /* bit exact soft float support */
  89 #define FLOATX80
  90 #define FLOAT128
  91 #else
  92 /* native float support */
  93 #if (defined(__i386__) || defined(__x86_64__)) && !defined(CONFIG_BSD)
  94 #define FLOATX80
  95 #endif
  96 #endif /* !CONFIG_SOFTFLOAT */
  97
  98 #define STATUS_PARAM , float_status *status
  99 #define STATUS(field) status->field
 100 #define STATUS_VAR , status
 101
 102 /*----------------------------------------------------------------------------
 103 | Software IEC/IEEE floating-point ordering relations
 104 *----------------------------------------------------------------------------*/
 105 enum {
 106     float_relation_less      = -1,
 107     float_relation_equal     =  0,
 108     float_relation_greater   =  1,
 109     float_relation_unordered =  2
 110 };
 111
 112 #ifdef CONFIG_SOFTFLOAT
 113 /*----------------------------------------------------------------------------
 114 | Software IEC/IEEE floating-point types.
 115 *----------------------------------------------------------------------------*/
 116 /* Use structures for soft-float types.  This prevents accidentally mixing
 117    them with native int/float types.  A sufficiently clever compiler and
 118    sane ABI should be able to see though these structs.  However
 119    x86/gcc 3.x seems to struggle a bit, so leave them disabled by default.  */
 120 //#define USE_SOFTFLOAT_STRUCT_TYPES
 121 #ifdef USE_SOFTFLOAT_STRUCT_TYPES
 122 typedef struct {
 123     uint32_t v;
 124 } float32;
 125 /* The cast ensures an error if the wrong type is passed.  */
 126 #define float32_val(x) (((float32)(x)).v)
 127 #define make_float32(x) __extension__ ({ float32 f32_val = {x}; f32_val; })
 128 typedef struct {
 129     uint64_t v;
 130 } float64;
 131 #define float64_val(x) (((float64)(x)).v)
 132 #define make_float64(x) __extension__ ({ float64 f64_val = {x}; f64_val; })
 133 #else
 134 typedef uint32_t float32;
 135 typedef uint64_t float64;
 136 #define float32_val(x) (x)
 137 #define float64_val(x) (x)
 138 #define make_float32(x) (x)
 139 #define make_float64(x) (x)
 140 #endif
 141 #ifdef FLOATX80
 142 typedef struct {
 143     uint64_t low;
 144     uint16_t high;
 145 } floatx80;
 146 #endif
 147 #ifdef FLOAT128
 148 typedef struct {
 149 #ifdef HOST_WORDS_BIGENDIAN
 150     uint64_t high, low;
 151 #else
 152     uint64_t low, high;
 153 #endif
 154 } float128;
 155 #endif
 156
 157 /*----------------------------------------------------------------------------
 158 | Software IEC/IEEE floating-point underflow tininess-detection mode.
 159 *----------------------------------------------------------------------------*/
 160 enum {
 161     float_tininess_after_rounding  = 0,
 162     float_tininess_before_rounding = 1
 163 };
 164
 165 /*----------------------------------------------------------------------------
 166 | Software IEC/IEEE floating-point rounding mode.
 167 *----------------------------------------------------------------------------*/
 168 enum {
 169     float_round_nearest_even = 0,
 170     float_round_down         = 1,
 171     float_round_up           = 2,
 172     float_round_to_zero      = 3
 173 };
 174
 175 /*----------------------------------------------------------------------------
 176 | Software IEC/IEEE floating-point exception flags.
 177 *----------------------------------------------------------------------------*/
 178 enum {
 179     float_flag_invalid   =  1,
 180     float_flag_divbyzero =  4,
 181     float_flag_overflow  =  8,
 182     float_flag_underflow = 16,
 183     float_flag_inexact   = 32
 184 };
 185
 186 typedef struct float_status {
 187     signed char float_detect_tininess;
 188     signed char float_rounding_mode;
 189     signed char float_exception_flags;
 190 #ifdef FLOATX80
 191     signed char floatx80_rounding_precision;
 192 #endif
 193     flag flush_to_zero;
 194     flag default_nan_mode;
 195 } float_status;
 196
 197 void set_float_rounding_mode(int val STATUS_PARAM);
 198 void set_float_exception_flags(int val STATUS_PARAM);
 199 INLINE void set_flush_to_zero(flag val STATUS_PARAM)
 200 {
 201     STATUS(flush_to_zero) = val;
 202 }
 203 INLINE void set_default_nan_mode(flag val STATUS_PARAM)
 204 {
 205     STATUS(default_nan_mode) = val;
 206 }
 207 INLINE int get_float_exception_flags(float_status *status)
 208 {
 209     return STATUS(float_exception_flags);
 210 }
 211 #ifdef FLOATX80
 212 void set_floatx80_rounding_precision(int val STATUS_PARAM);
 213 #endif
 214
 215 /*----------------------------------------------------------------------------
 216 | Routine to raise any or all of the software IEC/IEEE floating-point
 217 | exception flags.
 218 *----------------------------------------------------------------------------*/
 219 void float_raise( int8 flags STATUS_PARAM);
 220
 221 /*----------------------------------------------------------------------------
 222 | Software IEC/IEEE integer-to-floating-point conversion routines.
 223 *----------------------------------------------------------------------------*/
 224 float32 int32_to_float32( int STATUS_PARAM );
 225 float64 int32_to_float64( int STATUS_PARAM );
 226 float32 uint32_to_float32( unsigned int STATUS_PARAM );
 227 float64 uint32_to_float64( unsigned int STATUS_PARAM );
 228 #ifdef FLOATX80
 229 floatx80 int32_to_floatx80( int STATUS_PARAM );
 230 #endif
 231 #ifdef FLOAT128
 232 float128 int32_to_float128( int STATUS_PARAM );
 233 #endif
 234 float32 int64_to_float32( int64_t STATUS_PARAM );
 235 float32 uint64_to_float32( uint64_t STATUS_PARAM );
 236 float64 int64_to_float64( int64_t STATUS_PARAM );
 237 float64 uint64_to_float64( uint64_t STATUS_PARAM );
 238 #ifdef FLOATX80
 239 floatx80 int64_to_floatx80( int64_t STATUS_PARAM );
 240 #endif
 241 #ifdef FLOAT128
 242 float128 int64_to_float128( int64_t STATUS_PARAM );
 243 #endif
 244
 245 /*----------------------------------------------------------------------------
 246 | Software half-precision conversion routines.
 247 *----------------------------------------------------------------------------*/
 248 bits16 float32_to_float16( float32, flag STATUS_PARAM );
 249 float32 float16_to_float32( bits16, flag STATUS_PARAM );
 250
 251 /*----------------------------------------------------------------------------
 252 | Software IEC/IEEE single-precision conversion routines.
 253 *----------------------------------------------------------------------------*/
 254 int float32_to_int32( float32 STATUS_PARAM );
 255 int float32_to_int32_round_to_zero( float32 STATUS_PARAM );
 256 unsigned int float32_to_uint32( float32 STATUS_PARAM );
 257 unsigned int float32_to_uint32_round_to_zero( float32 STATUS_PARAM );
 258 int64_t float32_to_int64( float32 STATUS_PARAM );
 259 int64_t float32_to_int64_round_to_zero( float32 STATUS_PARAM );
 260 float64 float32_to_float64( float32 STATUS_PARAM );
 261 #ifdef FLOATX80
 262 floatx80 float32_to_floatx80( float32 STATUS_PARAM );
 263 #endif
 264 #ifdef FLOAT128
 265 float128 float32_to_float128( float32 STATUS_PARAM );
 266 #endif
 267
 268 /*----------------------------------------------------------------------------
 269 | Software IEC/IEEE single-precision operations.
 270 *----------------------------------------------------------------------------*/
 271 float32 float32_round_to_int( float32 STATUS_PARAM );
 272 float32 float32_add( float32, float32 STATUS_PARAM );
 273 float32 float32_sub( float32, float32 STATUS_PARAM );
 274 float32 float32_mul( float32, float32 STATUS_PARAM );
 275 float32 float32_div( float32, float32 STATUS_PARAM );
 276 float32 float32_rem( float32, float32 STATUS_PARAM );
 277 float32 float32_sqrt( float32 STATUS_PARAM );
 278 float32 float32_log2( float32 STATUS_PARAM );
 279 int float32_eq( float32, float32 STATUS_PARAM );
 280 int float32_le( float32, float32 STATUS_PARAM );
 281 int float32_lt( float32, float32 STATUS_PARAM );
 282 int float32_eq_signaling( float32, float32 STATUS_PARAM );
 283 int float32_le_quiet( float32, float32 STATUS_PARAM );
 284 int float32_lt_quiet( float32, float32 STATUS_PARAM );
 285 int float32_compare( float32, float32 STATUS_PARAM );
 286 int float32_compare_quiet( float32, float32 STATUS_PARAM );
 287 int float32_is_nan( float32 );
 288 int float32_is_signaling_nan( float32 );
 289 float32 float32_scalbn( float32, int STATUS_PARAM );
 290
 291 INLINE float32 float32_abs(float32 a)
 292 {
 293     return make_float32(float32_val(a) & 0x7fffffff);
 294 }
 295
 296 INLINE float32 float32_chs(float32 a)
 297 {
 298     return make_float32(float32_val(a) ^ 0x80000000);
 299 }
 300
 301 INLINE int float32_is_infinity(float32 a)
 302 {
 303     return (float32_val(a) & 0x7fffffff) == 0x7f800000;
 304 }
 305
 306 INLINE int float32_is_neg(float32 a)
 307 {
 308     return float32_val(a) >> 31;
 309 }
 310
 311 INLINE int float32_is_zero(float32 a)
 312 {
 313     return (float32_val(a) & 0x7fffffff) == 0;
 314 }
 315
 316 #define float32_zero make_float32(0)
 317 #define float32_one make_float32(0x3f800000)
 318
 319 /*----------------------------------------------------------------------------
 320 | Software IEC/IEEE double-precision conversion routines.
 321 *----------------------------------------------------------------------------*/
 322 int float64_to_int32( float64 STATUS_PARAM );
 323 int float64_to_int32_round_to_zero( float64 STATUS_PARAM );
 324 unsigned int float64_to_uint32( float64 STATUS_PARAM );
 325 unsigned int float64_to_uint32_round_to_zero( float64 STATUS_PARAM );
 326 int64_t float64_to_int64( float64 STATUS_PARAM );
 327 int64_t float64_to_int64_round_to_zero( float64 STATUS_PARAM );
 328 uint64_t float64_to_uint64 (float64 a STATUS_PARAM);
 329 uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM);
 330 float32 float64_to_float32( float64 STATUS_PARAM );
 331 #ifdef FLOATX80
 332 floatx80 float64_to_floatx80( float64 STATUS_PARAM );
 333 #endif
 334 #ifdef FLOAT128
 335 float128 float64_to_float128( float64 STATUS_PARAM );
 336 #endif
 337
 338 /*----------------------------------------------------------------------------
 339 | Software IEC/IEEE double-precision operations.
 340 *----------------------------------------------------------------------------*/
 341 float64 float64_round_to_int( float64 STATUS_PARAM );
 342 float64 float64_trunc_to_int( float64 STATUS_PARAM );
 343 float64 float64_add( float64, float64 STATUS_PARAM );
 344 float64 float64_sub( float64, float64 STATUS_PARAM );
 345 float64 float64_mul( float64, float64 STATUS_PARAM );
 346 float64 float64_div( float64, float64 STATUS_PARAM );
 347 float64 float64_rem( float64, float64 STATUS_PARAM );
 348 float64 float64_sqrt( float64 STATUS_PARAM );
 349 float64 float64_log2( float64 STATUS_PARAM );
 350 int float64_eq( float64, float64 STATUS_PARAM );
 351 int float64_le( float64, float64 STATUS_PARAM );
 352 int float64_lt( float64, float64 STATUS_PARAM );
 353 int float64_eq_signaling( float64, float64 STATUS_PARAM );
 354 int float64_le_quiet( float64, float64 STATUS_PARAM );
 355 int float64_lt_quiet( float64, float64 STATUS_PARAM );
 356 int float64_compare( float64, float64 STATUS_PARAM );
 357 int float64_compare_quiet( float64, float64 STATUS_PARAM );
 358 int float64_is_nan( float64 a );
 359 int float64_is_signaling_nan( float64 );
 360 float64 float64_scalbn( float64, int STATUS_PARAM );
 361
 362 INLINE float64 float64_abs(float64 a)
 363 {
 364     return make_float64(float64_val(a) & 0x7fffffffffffffffLL);
 365 }
 366
 367 INLINE float64 float64_chs(float64 a)
 368 {
 369     return make_float64(float64_val(a) ^ 0x8000000000000000LL);
 370 }
 371
 372 INLINE int float64_is_infinity(float64 a)
 373 {
 374     return (float64_val(a) & 0x7fffffffffffffffLL ) == 0x7ff0000000000000LL;
 375 }
 376
 377 INLINE int float64_is_neg(float64 a)
 378 {
 379     return float64_val(a) >> 63;
 380 }
 381
 382 INLINE int float64_is_zero(float64 a)
 383 {
 384     return (float64_val(a) & 0x7fffffffffffffffLL) == 0;
 385 }
 386
 387 #define float64_zero make_float64(0)
 388 #define float64_one make_float64(0x3ff0000000000000LL)
 389
 390 #ifdef FLOATX80
 391
 392 /*----------------------------------------------------------------------------
 393 | Software IEC/IEEE extended double-precision conversion routines.
 394 *----------------------------------------------------------------------------*/
 395 int floatx80_to_int32( floatx80 STATUS_PARAM );
 396 int floatx80_to_int32_round_to_zero( floatx80 STATUS_PARAM );
 397 int64_t floatx80_to_int64( floatx80 STATUS_PARAM );
 398 int64_t floatx80_to_int64_round_to_zero( floatx80 STATUS_PARAM );
 399 float32 floatx80_to_float32( floatx80 STATUS_PARAM );
 400 float64 floatx80_to_float64( floatx80 STATUS_PARAM );
 401 #ifdef FLOAT128
 402 float128 floatx80_to_float128( floatx80 STATUS_PARAM );
 403 #endif
 404
 405 /*----------------------------------------------------------------------------
 406 | Software IEC/IEEE extended double-precision operations.
 407 *----------------------------------------------------------------------------*/
 408 floatx80 floatx80_round_to_int( floatx80 STATUS_PARAM );
 409 floatx80 floatx80_add( floatx80, floatx80 STATUS_PARAM );
 410 floatx80 floatx80_sub( floatx80, floatx80 STATUS_PARAM );
 411 floatx80 floatx80_mul( floatx80, floatx80 STATUS_PARAM );
 412 floatx80 floatx80_div( floatx80, floatx80 STATUS_PARAM );
 413 floatx80 floatx80_rem( floatx80, floatx80 STATUS_PARAM );
 414 floatx80 floatx80_sqrt( floatx80 STATUS_PARAM );
 415 int floatx80_eq( floatx80, floatx80 STATUS_PARAM );
 416 int floatx80_le( floatx80, floatx80 STATUS_PARAM );
 417 int floatx80_lt( floatx80, floatx80 STATUS_PARAM );
 418 int floatx80_eq_signaling( floatx80, floatx80 STATUS_PARAM );
 419 int floatx80_le_quiet( floatx80, floatx80 STATUS_PARAM );
 420 int floatx80_lt_quiet( floatx80, floatx80 STATUS_PARAM );
 421 int floatx80_is_nan( floatx80 );
 422 int floatx80_is_signaling_nan( floatx80 );
 423 floatx80 floatx80_scalbn( floatx80, int STATUS_PARAM );
 424
 425 INLINE floatx80 floatx80_abs(floatx80 a)
 426 {
 427     a.high &= 0x7fff;
 428     return a;
 429 }
 430
 431 INLINE floatx80 floatx80_chs(floatx80 a)
 432 {
 433     a.high ^= 0x8000;
 434     return a;
 435 }
 436
 437 INLINE int floatx80_is_infinity(floatx80 a)
 438 {
 439     return (a.high & 0x7fff) == 0x7fff && a.low == 0;
 440 }
 441
 442 INLINE int floatx80_is_neg(floatx80 a)
 443 {
 444     return a.high >> 15;
 445 }
 446
 447 INLINE int floatx80_is_zero(floatx80 a)
 448 {
 449     return (a.high & 0x7fff) == 0 && a.low == 0;
 450 }
 451
 452 #endif
 453
 454 #ifdef FLOAT128
 455
 456 /*----------------------------------------------------------------------------
 457 | Software IEC/IEEE quadruple-precision conversion routines.
 458 *----------------------------------------------------------------------------*/
 459 int float128_to_int32( float128 STATUS_PARAM );
 460 int float128_to_int32_round_to_zero( float128 STATUS_PARAM );
 461 int64_t float128_to_int64( float128 STATUS_PARAM );
 462 int64_t float128_to_int64_round_to_zero( float128 STATUS_PARAM );
 463 float32 float128_to_float32( float128 STATUS_PARAM );
 464 float64 float128_to_float64( float128 STATUS_PARAM );
 465 #ifdef FLOATX80
 466 floatx80 float128_to_floatx80( float128 STATUS_PARAM );
 467 #endif
 468
 469 /*----------------------------------------------------------------------------
 470 | Software IEC/IEEE quadruple-precision operations.
 471 *----------------------------------------------------------------------------*/
 472 float128 float128_round_to_int( float128 STATUS_PARAM );
 473 float128 float128_add( float128, float128 STATUS_PARAM );
 474 float128 float128_sub( float128, float128 STATUS_PARAM );
 475 float128 float128_mul( float128, float128 STATUS_PARAM );
 476 float128 float128_div( float128, float128 STATUS_PARAM );
 477 float128 float128_rem( float128, float128 STATUS_PARAM );
 478 float128 float128_sqrt( float128 STATUS_PARAM );
 479 int float128_eq( float128, float128 STATUS_PARAM );
 480 int float128_le( float128, float128 STATUS_PARAM );
 481 int float128_lt( float128, float128 STATUS_PARAM );
 482 int float128_eq_signaling( float128, float128 STATUS_PARAM );
 483 int float128_le_quiet( float128, float128 STATUS_PARAM );
 484 int float128_lt_quiet( float128, float128 STATUS_PARAM );
 485 int float128_compare( float128, float128 STATUS_PARAM );
 486 int float128_compare_quiet( float128, float128 STATUS_PARAM );
 487 int float128_is_nan( float128 );
 488 int float128_is_signaling_nan( float128 );
 489 float128 float128_scalbn( float128, int STATUS_PARAM );
 490
 491 INLINE float128 float128_abs(float128 a)
 492 {
 493     a.high &= 0x7fffffffffffffffLL;
 494     return a;
 495 }
 496
 497 INLINE float128 float128_chs(float128 a)
 498 {
 499     a.high ^= 0x8000000000000000LL;
 500     return a;
 501 }
 502
 503 INLINE int float128_is_infinity(float128 a)
 504 {
 505     return (a.high & 0x7fffffffffffffffLL) == 0x7fff000000000000LL && a.low == 0;
 506 }
 507
 508 INLINE int float128_is_neg(float128 a)
 509 {
 510     return a.high >> 63;
 511 }
 512
 513 INLINE int float128_is_zero(float128 a)
 514 {
 515     return (a.high & 0x7fffffffffffffffLL) == 0 && a.low == 0;
 516 }
 517
 518 #endif
 519
 520 #else /* CONFIG_SOFTFLOAT */
 521
 522 #include "softfloat-native.h"
 523
 524 #endif /* !CONFIG_SOFTFLOAT */
 525
 526 #endif /* !SOFTFLOAT_H */