1 /*============================================================================
3 This C header file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
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'.
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.
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.
30 =============================================================================*/
35 #if defined(CONFIG_SOLARIS) && defined(CONFIG_NEEDS_LIBSUNMATH)
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 *----------------------------------------------------------------------------*/
51 typedef uint8_t uint8
;
57 typedef unsigned int uint32
;
58 typedef signed int int32
;
59 typedef uint64_t uint64
;
60 typedef int64_t int64
;
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
;
77 #define LIT64( a ) a##LL
78 #define INLINE static inline
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 */
92 /* native float support */
93 #if (defined(__i386__) || defined(__x86_64__)) && !defined(CONFIG_BSD)
96 #endif /* !CONFIG_SOFTFLOAT */
98 #define STATUS_PARAM , float_status *status
99 #define STATUS(field) status->field
100 #define STATUS_VAR , status
102 /*----------------------------------------------------------------------------
103 | Software IEC/IEEE floating-point ordering relations
104 *----------------------------------------------------------------------------*/
106 float_relation_less
= -1,
107 float_relation_equal
= 0,
108 float_relation_greater
= 1,
109 float_relation_unordered
= 2
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
125 #define float16_val(x) (((float16)(x)).v)
126 #define make_float16(x) __extension__ ({ float16 f16_val = {x}; f16_val; })
127 #define const_float16(x) { x }
131 /* The cast ensures an error if the wrong type is passed. */
132 #define float32_val(x) (((float32)(x)).v)
133 #define make_float32(x) __extension__ ({ float32 f32_val = {x}; f32_val; })
134 #define const_float32(x) { x }
138 #define float64_val(x) (((float64)(x)).v)
139 #define make_float64(x) __extension__ ({ float64 f64_val = {x}; f64_val; })
140 #define const_float64(x) { x }
142 typedef uint16_t float16
;
143 typedef uint32_t float32
;
144 typedef uint64_t float64
;
145 #define float16_val(x) (x)
146 #define float32_val(x) (x)
147 #define float64_val(x) (x)
148 #define make_float16(x) (x)
149 #define make_float32(x) (x)
150 #define make_float64(x) (x)
151 #define const_float16(x) (x)
152 #define const_float32(x) (x)
153 #define const_float64(x) (x)
163 #ifdef HOST_WORDS_BIGENDIAN
171 /*----------------------------------------------------------------------------
172 | Software IEC/IEEE floating-point underflow tininess-detection mode.
173 *----------------------------------------------------------------------------*/
175 float_tininess_after_rounding
= 0,
176 float_tininess_before_rounding
= 1
179 /*----------------------------------------------------------------------------
180 | Software IEC/IEEE floating-point rounding mode.
181 *----------------------------------------------------------------------------*/
183 float_round_nearest_even
= 0,
184 float_round_down
= 1,
186 float_round_to_zero
= 3
189 /*----------------------------------------------------------------------------
190 | Software IEC/IEEE floating-point exception flags.
191 *----------------------------------------------------------------------------*/
193 float_flag_invalid
= 1,
194 float_flag_divbyzero
= 4,
195 float_flag_overflow
= 8,
196 float_flag_underflow
= 16,
197 float_flag_inexact
= 32,
198 float_flag_input_denormal
= 64
201 typedef struct float_status
{
202 signed char float_detect_tininess
;
203 signed char float_rounding_mode
;
204 signed char float_exception_flags
;
206 signed char floatx80_rounding_precision
;
208 /* should denormalised results go to zero and set the inexact flag? */
210 /* should denormalised inputs go to zero and set the input_denormal flag? */
211 flag flush_inputs_to_zero
;
212 flag default_nan_mode
;
215 void set_float_rounding_mode(int val STATUS_PARAM
);
216 void set_float_exception_flags(int val STATUS_PARAM
);
217 INLINE
void set_flush_to_zero(flag val STATUS_PARAM
)
219 STATUS(flush_to_zero
) = val
;
221 INLINE
void set_flush_inputs_to_zero(flag val STATUS_PARAM
)
223 STATUS(flush_inputs_to_zero
) = val
;
225 INLINE
void set_default_nan_mode(flag val STATUS_PARAM
)
227 STATUS(default_nan_mode
) = val
;
229 INLINE
int get_float_exception_flags(float_status
*status
)
231 return STATUS(float_exception_flags
);
234 void set_floatx80_rounding_precision(int val STATUS_PARAM
);
237 /*----------------------------------------------------------------------------
238 | Routine to raise any or all of the software IEC/IEEE floating-point
240 *----------------------------------------------------------------------------*/
241 void float_raise( int8 flags STATUS_PARAM
);
243 /*----------------------------------------------------------------------------
244 | Software IEC/IEEE integer-to-floating-point conversion routines.
245 *----------------------------------------------------------------------------*/
246 float32
int32_to_float32( int STATUS_PARAM
);
247 float64
int32_to_float64( int STATUS_PARAM
);
248 float32
uint32_to_float32( unsigned int STATUS_PARAM
);
249 float64
uint32_to_float64( unsigned int STATUS_PARAM
);
251 floatx80
int32_to_floatx80( int STATUS_PARAM
);
254 float128
int32_to_float128( int STATUS_PARAM
);
256 float32
int64_to_float32( int64_t STATUS_PARAM
);
257 float32
uint64_to_float32( uint64_t STATUS_PARAM
);
258 float64
int64_to_float64( int64_t STATUS_PARAM
);
259 float64
uint64_to_float64( uint64_t STATUS_PARAM
);
261 floatx80
int64_to_floatx80( int64_t STATUS_PARAM
);
264 float128
int64_to_float128( int64_t STATUS_PARAM
);
267 /*----------------------------------------------------------------------------
268 | Software half-precision conversion routines.
269 *----------------------------------------------------------------------------*/
270 float16
float32_to_float16( float32
, flag STATUS_PARAM
);
271 float32
float16_to_float32( float16
, flag STATUS_PARAM
);
273 /*----------------------------------------------------------------------------
274 | Software half-precision operations.
275 *----------------------------------------------------------------------------*/
276 int float16_is_quiet_nan( float16
);
277 int float16_is_signaling_nan( float16
);
278 float16
float16_maybe_silence_nan( float16
);
280 /*----------------------------------------------------------------------------
281 | Software IEC/IEEE single-precision conversion routines.
282 *----------------------------------------------------------------------------*/
283 int float32_to_int16_round_to_zero( float32 STATUS_PARAM
);
284 unsigned int float32_to_uint16_round_to_zero( float32 STATUS_PARAM
);
285 int float32_to_int32( float32 STATUS_PARAM
);
286 int float32_to_int32_round_to_zero( float32 STATUS_PARAM
);
287 unsigned int float32_to_uint32( float32 STATUS_PARAM
);
288 unsigned int float32_to_uint32_round_to_zero( float32 STATUS_PARAM
);
289 int64_t float32_to_int64( float32 STATUS_PARAM
);
290 int64_t float32_to_int64_round_to_zero( float32 STATUS_PARAM
);
291 float64
float32_to_float64( float32 STATUS_PARAM
);
293 floatx80
float32_to_floatx80( float32 STATUS_PARAM
);
296 float128
float32_to_float128( float32 STATUS_PARAM
);
299 /*----------------------------------------------------------------------------
300 | Software IEC/IEEE single-precision operations.
301 *----------------------------------------------------------------------------*/
302 float32
float32_round_to_int( float32 STATUS_PARAM
);
303 float32
float32_add( float32
, float32 STATUS_PARAM
);
304 float32
float32_sub( float32
, float32 STATUS_PARAM
);
305 float32
float32_mul( float32
, float32 STATUS_PARAM
);
306 float32
float32_div( float32
, float32 STATUS_PARAM
);
307 float32
float32_rem( float32
, float32 STATUS_PARAM
);
308 float32
float32_sqrt( float32 STATUS_PARAM
);
309 float32
float32_exp2( float32 STATUS_PARAM
);
310 float32
float32_log2( float32 STATUS_PARAM
);
311 int float32_eq( float32
, float32 STATUS_PARAM
);
312 int float32_le( float32
, float32 STATUS_PARAM
);
313 int float32_lt( float32
, float32 STATUS_PARAM
);
314 int float32_eq_signaling( float32
, float32 STATUS_PARAM
);
315 int float32_le_quiet( float32
, float32 STATUS_PARAM
);
316 int float32_lt_quiet( float32
, float32 STATUS_PARAM
);
317 int float32_compare( float32
, float32 STATUS_PARAM
);
318 int float32_compare_quiet( float32
, float32 STATUS_PARAM
);
319 int float32_is_quiet_nan( float32
);
320 int float32_is_signaling_nan( float32
);
321 float32
float32_maybe_silence_nan( float32
);
322 float32
float32_scalbn( float32
, int STATUS_PARAM
);
324 INLINE float32
float32_abs(float32 a
)
326 /* Note that abs does *not* handle NaN specially, nor does
327 * it flush denormal inputs to zero.
329 return make_float32(float32_val(a
) & 0x7fffffff);
332 INLINE float32
float32_chs(float32 a
)
334 /* Note that chs does *not* handle NaN specially, nor does
335 * it flush denormal inputs to zero.
337 return make_float32(float32_val(a
) ^ 0x80000000);
340 INLINE
int float32_is_infinity(float32 a
)
342 return (float32_val(a
) & 0x7fffffff) == 0x7f800000;
345 INLINE
int float32_is_neg(float32 a
)
347 return float32_val(a
) >> 31;
350 INLINE
int float32_is_zero(float32 a
)
352 return (float32_val(a
) & 0x7fffffff) == 0;
355 INLINE
int float32_is_any_nan(float32 a
)
357 return ((float32_val(a
) & ~(1 << 31)) > 0x7f800000UL
);
360 INLINE
int float32_is_zero_or_denormal(float32 a
)
362 return (float32_val(a
) & 0x7f800000) == 0;
365 #define float32_zero make_float32(0)
366 #define float32_one make_float32(0x3f800000)
367 #define float32_ln2 make_float32(0x3f317218)
369 /*----------------------------------------------------------------------------
370 | Software IEC/IEEE double-precision conversion routines.
371 *----------------------------------------------------------------------------*/
372 int float64_to_int16_round_to_zero( float64 STATUS_PARAM
);
373 unsigned int float64_to_uint16_round_to_zero( float64 STATUS_PARAM
);
374 int float64_to_int32( float64 STATUS_PARAM
);
375 int float64_to_int32_round_to_zero( float64 STATUS_PARAM
);
376 unsigned int float64_to_uint32( float64 STATUS_PARAM
);
377 unsigned int float64_to_uint32_round_to_zero( float64 STATUS_PARAM
);
378 int64_t float64_to_int64( float64 STATUS_PARAM
);
379 int64_t float64_to_int64_round_to_zero( float64 STATUS_PARAM
);
380 uint64_t float64_to_uint64 (float64 a STATUS_PARAM
);
381 uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM
);
382 float32
float64_to_float32( float64 STATUS_PARAM
);
384 floatx80
float64_to_floatx80( float64 STATUS_PARAM
);
387 float128
float64_to_float128( float64 STATUS_PARAM
);
390 /*----------------------------------------------------------------------------
391 | Software IEC/IEEE double-precision operations.
392 *----------------------------------------------------------------------------*/
393 float64
float64_round_to_int( float64 STATUS_PARAM
);
394 float64
float64_trunc_to_int( float64 STATUS_PARAM
);
395 float64
float64_add( float64
, float64 STATUS_PARAM
);
396 float64
float64_sub( float64
, float64 STATUS_PARAM
);
397 float64
float64_mul( float64
, float64 STATUS_PARAM
);
398 float64
float64_div( float64
, float64 STATUS_PARAM
);
399 float64
float64_rem( float64
, float64 STATUS_PARAM
);
400 float64
float64_sqrt( float64 STATUS_PARAM
);
401 float64
float64_log2( float64 STATUS_PARAM
);
402 int float64_eq( float64
, float64 STATUS_PARAM
);
403 int float64_le( float64
, float64 STATUS_PARAM
);
404 int float64_lt( float64
, float64 STATUS_PARAM
);
405 int float64_eq_signaling( float64
, float64 STATUS_PARAM
);
406 int float64_le_quiet( float64
, float64 STATUS_PARAM
);
407 int float64_lt_quiet( float64
, float64 STATUS_PARAM
);
408 int float64_compare( float64
, float64 STATUS_PARAM
);
409 int float64_compare_quiet( float64
, float64 STATUS_PARAM
);
410 int float64_is_quiet_nan( float64 a
);
411 int float64_is_signaling_nan( float64
);
412 float64
float64_maybe_silence_nan( float64
);
413 float64
float64_scalbn( float64
, int STATUS_PARAM
);
415 INLINE float64
float64_abs(float64 a
)
417 /* Note that abs does *not* handle NaN specially, nor does
418 * it flush denormal inputs to zero.
420 return make_float64(float64_val(a
) & 0x7fffffffffffffffLL
);
423 INLINE float64
float64_chs(float64 a
)
425 /* Note that chs does *not* handle NaN specially, nor does
426 * it flush denormal inputs to zero.
428 return make_float64(float64_val(a
) ^ 0x8000000000000000LL
);
431 INLINE
int float64_is_infinity(float64 a
)
433 return (float64_val(a
) & 0x7fffffffffffffffLL
) == 0x7ff0000000000000LL
;
436 INLINE
int float64_is_neg(float64 a
)
438 return float64_val(a
) >> 63;
441 INLINE
int float64_is_zero(float64 a
)
443 return (float64_val(a
) & 0x7fffffffffffffffLL
) == 0;
446 INLINE
int float64_is_any_nan(float64 a
)
448 return ((float64_val(a
) & ~(1ULL << 63)) > 0x7ff0000000000000ULL
);
451 #define float64_zero make_float64(0)
452 #define float64_one make_float64(0x3ff0000000000000LL)
453 #define float64_ln2 make_float64(0x3fe62e42fefa39efLL)
457 /*----------------------------------------------------------------------------
458 | Software IEC/IEEE extended double-precision conversion routines.
459 *----------------------------------------------------------------------------*/
460 int floatx80_to_int32( floatx80 STATUS_PARAM
);
461 int floatx80_to_int32_round_to_zero( floatx80 STATUS_PARAM
);
462 int64_t floatx80_to_int64( floatx80 STATUS_PARAM
);
463 int64_t floatx80_to_int64_round_to_zero( floatx80 STATUS_PARAM
);
464 float32
floatx80_to_float32( floatx80 STATUS_PARAM
);
465 float64
floatx80_to_float64( floatx80 STATUS_PARAM
);
467 float128
floatx80_to_float128( floatx80 STATUS_PARAM
);
470 /*----------------------------------------------------------------------------
471 | Software IEC/IEEE extended double-precision operations.
472 *----------------------------------------------------------------------------*/
473 floatx80
floatx80_round_to_int( floatx80 STATUS_PARAM
);
474 floatx80
floatx80_add( floatx80
, floatx80 STATUS_PARAM
);
475 floatx80
floatx80_sub( floatx80
, floatx80 STATUS_PARAM
);
476 floatx80
floatx80_mul( floatx80
, floatx80 STATUS_PARAM
);
477 floatx80
floatx80_div( floatx80
, floatx80 STATUS_PARAM
);
478 floatx80
floatx80_rem( floatx80
, floatx80 STATUS_PARAM
);
479 floatx80
floatx80_sqrt( floatx80 STATUS_PARAM
);
480 int floatx80_eq( floatx80
, floatx80 STATUS_PARAM
);
481 int floatx80_le( floatx80
, floatx80 STATUS_PARAM
);
482 int floatx80_lt( floatx80
, floatx80 STATUS_PARAM
);
483 int floatx80_eq_signaling( floatx80
, floatx80 STATUS_PARAM
);
484 int floatx80_le_quiet( floatx80
, floatx80 STATUS_PARAM
);
485 int floatx80_lt_quiet( floatx80
, floatx80 STATUS_PARAM
);
486 int floatx80_is_quiet_nan( floatx80
);
487 int floatx80_is_signaling_nan( floatx80
);
488 floatx80
floatx80_maybe_silence_nan( floatx80
);
489 floatx80
floatx80_scalbn( floatx80
, int STATUS_PARAM
);
491 INLINE floatx80
floatx80_abs(floatx80 a
)
497 INLINE floatx80
floatx80_chs(floatx80 a
)
503 INLINE
int floatx80_is_infinity(floatx80 a
)
505 return (a
.high
& 0x7fff) == 0x7fff && a
.low
== 0;
508 INLINE
int floatx80_is_neg(floatx80 a
)
513 INLINE
int floatx80_is_zero(floatx80 a
)
515 return (a
.high
& 0x7fff) == 0 && a
.low
== 0;
518 INLINE
int floatx80_is_any_nan(floatx80 a
)
520 return ((a
.high
& 0x7fff) == 0x7fff) && (a
.low
<<1);
527 /*----------------------------------------------------------------------------
528 | Software IEC/IEEE quadruple-precision conversion routines.
529 *----------------------------------------------------------------------------*/
530 int float128_to_int32( float128 STATUS_PARAM
);
531 int float128_to_int32_round_to_zero( float128 STATUS_PARAM
);
532 int64_t float128_to_int64( float128 STATUS_PARAM
);
533 int64_t float128_to_int64_round_to_zero( float128 STATUS_PARAM
);
534 float32
float128_to_float32( float128 STATUS_PARAM
);
535 float64
float128_to_float64( float128 STATUS_PARAM
);
537 floatx80
float128_to_floatx80( float128 STATUS_PARAM
);
540 /*----------------------------------------------------------------------------
541 | Software IEC/IEEE quadruple-precision operations.
542 *----------------------------------------------------------------------------*/
543 float128
float128_round_to_int( float128 STATUS_PARAM
);
544 float128
float128_add( float128
, float128 STATUS_PARAM
);
545 float128
float128_sub( float128
, float128 STATUS_PARAM
);
546 float128
float128_mul( float128
, float128 STATUS_PARAM
);
547 float128
float128_div( float128
, float128 STATUS_PARAM
);
548 float128
float128_rem( float128
, float128 STATUS_PARAM
);
549 float128
float128_sqrt( float128 STATUS_PARAM
);
550 int float128_eq( float128
, float128 STATUS_PARAM
);
551 int float128_le( float128
, float128 STATUS_PARAM
);
552 int float128_lt( float128
, float128 STATUS_PARAM
);
553 int float128_eq_signaling( float128
, float128 STATUS_PARAM
);
554 int float128_le_quiet( float128
, float128 STATUS_PARAM
);
555 int float128_lt_quiet( float128
, float128 STATUS_PARAM
);
556 int float128_compare( float128
, float128 STATUS_PARAM
);
557 int float128_compare_quiet( float128
, float128 STATUS_PARAM
);
558 int float128_is_quiet_nan( float128
);
559 int float128_is_signaling_nan( float128
);
560 float128
float128_maybe_silence_nan( float128
);
561 float128
float128_scalbn( float128
, int STATUS_PARAM
);
563 INLINE float128
float128_abs(float128 a
)
565 a
.high
&= 0x7fffffffffffffffLL
;
569 INLINE float128
float128_chs(float128 a
)
571 a
.high
^= 0x8000000000000000LL
;
575 INLINE
int float128_is_infinity(float128 a
)
577 return (a
.high
& 0x7fffffffffffffffLL
) == 0x7fff000000000000LL
&& a
.low
== 0;
580 INLINE
int float128_is_neg(float128 a
)
585 INLINE
int float128_is_zero(float128 a
)
587 return (a
.high
& 0x7fffffffffffffffLL
) == 0 && a
.low
== 0;
590 INLINE
int float128_is_any_nan(float128 a
)
592 return ((a
.high
>> 48) & 0x7fff) == 0x7fff &&
593 ((a
.low
!= 0) || ((a
.high
& 0xffffffffffffLL
) != 0));
598 #else /* CONFIG_SOFTFLOAT */
600 #include "softfloat-native.h"
602 #endif /* !CONFIG_SOFTFLOAT */
604 #endif /* !SOFTFLOAT_H */