xref: /qemu/include/fpu/softfloat.h (revision 513823e7521a09ed7ad1e32e6454bac3b2cbf52d)
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 header file 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 #ifndef SOFTFLOAT_H
83 #define SOFTFLOAT_H
84 
85 /*----------------------------------------------------------------------------
86 | Software IEC/IEEE floating-point ordering relations
87 *----------------------------------------------------------------------------*/
88 
89 typedef enum {
90     float_relation_less      = -1,
91     float_relation_equal     =  0,
92     float_relation_greater   =  1,
93     float_relation_unordered =  2
94 } FloatRelation;
95 
96 #include "fpu/softfloat-types.h"
97 #include "fpu/softfloat-helpers.h"
98 #include "qemu/int128.h"
99 
100 /*----------------------------------------------------------------------------
101 | Routine to raise any or all of the software IEC/IEEE floating-point
102 | exception flags.
103 *----------------------------------------------------------------------------*/
104 static inline void float_raise(uint16_t flags, float_status *status)
105 {
106     status->float_exception_flags |= flags;
107 }
108 
109 /*----------------------------------------------------------------------------
110 | If `a' is denormal and we are in flush-to-zero mode then set the
111 | input-denormal exception and return zero. Otherwise just return the value.
112 *----------------------------------------------------------------------------*/
113 float16 float16_squash_input_denormal(float16 a, float_status *status);
114 float32 float32_squash_input_denormal(float32 a, float_status *status);
115 float64 float64_squash_input_denormal(float64 a, float_status *status);
116 bfloat16 bfloat16_squash_input_denormal(bfloat16 a, float_status *status);
117 
118 /*----------------------------------------------------------------------------
119 | Options to indicate which negations to perform in float*_muladd()
120 | Using these differs from negating an input or output before calling
121 | the muladd function in that this means that a NaN doesn't have its
122 | sign bit inverted before it is propagated.
123 |
124 | With float_muladd_suppress_add_product_zero, if A or B is zero
125 | such that the product is a true zero, then return C without addition.
126 | This preserves the sign of C when C is +/- 0.  Used for Hexagon.
127 *----------------------------------------------------------------------------*/
128 enum {
129     float_muladd_negate_c = 1,
130     float_muladd_negate_product = 2,
131     float_muladd_negate_result = 4,
132     float_muladd_suppress_add_product_zero = 8,
133 };
134 
135 /*----------------------------------------------------------------------------
136 | Software IEC/IEEE integer-to-floating-point conversion routines.
137 *----------------------------------------------------------------------------*/
138 
139 float16 int16_to_float16_scalbn(int16_t a, int, float_status *status);
140 float16 int32_to_float16_scalbn(int32_t a, int, float_status *status);
141 float16 int64_to_float16_scalbn(int64_t a, int, float_status *status);
142 float16 uint16_to_float16_scalbn(uint16_t a, int, float_status *status);
143 float16 uint32_to_float16_scalbn(uint32_t a, int, float_status *status);
144 float16 uint64_to_float16_scalbn(uint64_t a, int, float_status *status);
145 
146 float16 int8_to_float16(int8_t a, float_status *status);
147 float16 int16_to_float16(int16_t a, float_status *status);
148 float16 int32_to_float16(int32_t a, float_status *status);
149 float16 int64_to_float16(int64_t a, float_status *status);
150 float16 uint8_to_float16(uint8_t a, float_status *status);
151 float16 uint16_to_float16(uint16_t a, float_status *status);
152 float16 uint32_to_float16(uint32_t a, float_status *status);
153 float16 uint64_to_float16(uint64_t a, float_status *status);
154 
155 float32 int16_to_float32_scalbn(int16_t, int, float_status *status);
156 float32 int32_to_float32_scalbn(int32_t, int, float_status *status);
157 float32 int64_to_float32_scalbn(int64_t, int, float_status *status);
158 float32 uint16_to_float32_scalbn(uint16_t, int, float_status *status);
159 float32 uint32_to_float32_scalbn(uint32_t, int, float_status *status);
160 float32 uint64_to_float32_scalbn(uint64_t, int, float_status *status);
161 
162 float32 int16_to_float32(int16_t, float_status *status);
163 float32 int32_to_float32(int32_t, float_status *status);
164 float32 int64_to_float32(int64_t, float_status *status);
165 float32 uint16_to_float32(uint16_t, float_status *status);
166 float32 uint32_to_float32(uint32_t, float_status *status);
167 float32 uint64_to_float32(uint64_t, float_status *status);
168 
169 float64 int16_to_float64_scalbn(int16_t, int, float_status *status);
170 float64 int32_to_float64_scalbn(int32_t, int, float_status *status);
171 float64 int64_to_float64_scalbn(int64_t, int, float_status *status);
172 float64 uint16_to_float64_scalbn(uint16_t, int, float_status *status);
173 float64 uint32_to_float64_scalbn(uint32_t, int, float_status *status);
174 float64 uint64_to_float64_scalbn(uint64_t, int, float_status *status);
175 
176 float64 int16_to_float64(int16_t, float_status *status);
177 float64 int32_to_float64(int32_t, float_status *status);
178 float64 int64_to_float64(int64_t, float_status *status);
179 float64 uint16_to_float64(uint16_t, float_status *status);
180 float64 uint32_to_float64(uint32_t, float_status *status);
181 float64 uint64_to_float64(uint64_t, float_status *status);
182 
183 floatx80 int32_to_floatx80(int32_t, float_status *status);
184 floatx80 int64_to_floatx80(int64_t, float_status *status);
185 
186 float128 int32_to_float128(int32_t, float_status *status);
187 float128 int64_to_float128(int64_t, float_status *status);
188 float128 int128_to_float128(Int128, float_status *status);
189 float128 uint64_to_float128(uint64_t, float_status *status);
190 float128 uint128_to_float128(Int128, float_status *status);
191 
192 /*----------------------------------------------------------------------------
193 | Software half-precision conversion routines.
194 *----------------------------------------------------------------------------*/
195 
196 float16 float32_to_float16(float32, bool ieee, float_status *status);
197 float32 float16_to_float32(float16, bool ieee, float_status *status);
198 float16 float64_to_float16(float64 a, bool ieee, float_status *status);
199 float64 float16_to_float64(float16 a, bool ieee, float_status *status);
200 
201 int8_t  float16_to_int8_scalbn(float16, FloatRoundMode, int,
202                                float_status *status);
203 int16_t float16_to_int16_scalbn(float16, FloatRoundMode, int, float_status *);
204 int32_t float16_to_int32_scalbn(float16, FloatRoundMode, int, float_status *);
205 int64_t float16_to_int64_scalbn(float16, FloatRoundMode, int, float_status *);
206 
207 int8_t  float16_to_int8(float16, float_status *status);
208 int16_t float16_to_int16(float16, float_status *status);
209 int32_t float16_to_int32(float16, float_status *status);
210 int64_t float16_to_int64(float16, float_status *status);
211 
212 int16_t float16_to_int16_round_to_zero(float16, float_status *status);
213 int32_t float16_to_int32_round_to_zero(float16, float_status *status);
214 int64_t float16_to_int64_round_to_zero(float16, float_status *status);
215 
216 uint8_t float16_to_uint8_scalbn(float16 a, FloatRoundMode,
217                                 int, float_status *status);
218 uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode,
219                                   int, float_status *status);
220 uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode,
221                                   int, float_status *status);
222 uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode,
223                                   int, float_status *status);
224 
225 uint8_t  float16_to_uint8(float16 a, float_status *status);
226 uint16_t float16_to_uint16(float16 a, float_status *status);
227 uint32_t float16_to_uint32(float16 a, float_status *status);
228 uint64_t float16_to_uint64(float16 a, float_status *status);
229 
230 uint16_t float16_to_uint16_round_to_zero(float16 a, float_status *status);
231 uint32_t float16_to_uint32_round_to_zero(float16 a, float_status *status);
232 uint64_t float16_to_uint64_round_to_zero(float16 a, float_status *status);
233 
234 /*----------------------------------------------------------------------------
235 | Software half-precision operations.
236 *----------------------------------------------------------------------------*/
237 
238 float16 float16_round_to_int(float16, float_status *status);
239 float16 float16_add(float16, float16, float_status *status);
240 float16 float16_sub(float16, float16, float_status *status);
241 float16 float16_mul(float16, float16, float_status *status);
242 float16 float16_muladd(float16, float16, float16, int, float_status *status);
243 float16 float16_muladd_scalbn(float16, float16, float16,
244                               int, int, float_status *status);
245 float16 float16_div(float16, float16, float_status *status);
246 float16 float16_scalbn(float16, int, float_status *status);
247 float16 float16_min(float16, float16, float_status *status);
248 float16 float16_max(float16, float16, float_status *status);
249 float16 float16_minnum(float16, float16, float_status *status);
250 float16 float16_maxnum(float16, float16, float_status *status);
251 float16 float16_minnummag(float16, float16, float_status *status);
252 float16 float16_maxnummag(float16, float16, float_status *status);
253 float16 float16_minimum_number(float16, float16, float_status *status);
254 float16 float16_maximum_number(float16, float16, float_status *status);
255 float16 float16_sqrt(float16, float_status *status);
256 FloatRelation float16_compare(float16, float16, float_status *status);
257 FloatRelation float16_compare_quiet(float16, float16, float_status *status);
258 
259 bool float16_is_quiet_nan(float16, float_status *status);
260 bool float16_is_signaling_nan(float16, float_status *status);
261 float16 float16_silence_nan(float16, float_status *status);
262 
263 static inline bool float16_is_any_nan(float16 a)
264 {
265     return ((float16_val(a) & ~0x8000) > 0x7c00);
266 }
267 
268 static inline bool float16_is_neg(float16 a)
269 {
270     return float16_val(a) >> 15;
271 }
272 
273 static inline bool float16_is_infinity(float16 a)
274 {
275     return (float16_val(a) & 0x7fff) == 0x7c00;
276 }
277 
278 static inline bool float16_is_zero(float16 a)
279 {
280     return (float16_val(a) & 0x7fff) == 0;
281 }
282 
283 static inline bool float16_is_zero_or_denormal(float16 a)
284 {
285     return (float16_val(a) & 0x7c00) == 0;
286 }
287 
288 static inline bool float16_is_normal(float16 a)
289 {
290     return (((float16_val(a) >> 10) + 1) & 0x1f) >= 2;
291 }
292 
293 static inline float16 float16_abs(float16 a)
294 {
295     /* Note that abs does *not* handle NaN specially, nor does
296      * it flush denormal inputs to zero.
297      */
298     return make_float16(float16_val(a) & 0x7fff);
299 }
300 
301 static inline float16 float16_chs(float16 a)
302 {
303     /* Note that chs does *not* handle NaN specially, nor does
304      * it flush denormal inputs to zero.
305      */
306     return make_float16(float16_val(a) ^ 0x8000);
307 }
308 
309 static inline float16 float16_set_sign(float16 a, int sign)
310 {
311     return make_float16((float16_val(a) & 0x7fff) | (sign << 15));
312 }
313 
314 static inline bool float16_eq(float16 a, float16 b, float_status *s)
315 {
316     return float16_compare(a, b, s) == float_relation_equal;
317 }
318 
319 static inline bool float16_le(float16 a, float16 b, float_status *s)
320 {
321     return float16_compare(a, b, s) <= float_relation_equal;
322 }
323 
324 static inline bool float16_lt(float16 a, float16 b, float_status *s)
325 {
326     return float16_compare(a, b, s) < float_relation_equal;
327 }
328 
329 static inline bool float16_unordered(float16 a, float16 b, float_status *s)
330 {
331     return float16_compare(a, b, s) == float_relation_unordered;
332 }
333 
334 static inline bool float16_eq_quiet(float16 a, float16 b, float_status *s)
335 {
336     return float16_compare_quiet(a, b, s) == float_relation_equal;
337 }
338 
339 static inline bool float16_le_quiet(float16 a, float16 b, float_status *s)
340 {
341     return float16_compare_quiet(a, b, s) <= float_relation_equal;
342 }
343 
344 static inline bool float16_lt_quiet(float16 a, float16 b, float_status *s)
345 {
346     return float16_compare_quiet(a, b, s) < float_relation_equal;
347 }
348 
349 static inline bool float16_unordered_quiet(float16 a, float16 b,
350                                            float_status *s)
351 {
352     return float16_compare_quiet(a, b, s) == float_relation_unordered;
353 }
354 
355 #define float16_zero make_float16(0)
356 #define float16_half make_float16(0x3800)
357 #define float16_one make_float16(0x3c00)
358 #define float16_one_point_five make_float16(0x3e00)
359 #define float16_two make_float16(0x4000)
360 #define float16_three make_float16(0x4200)
361 #define float16_infinity make_float16(0x7c00)
362 
363 /*----------------------------------------------------------------------------
364 | Software bfloat16 conversion routines.
365 *----------------------------------------------------------------------------*/
366 
367 bfloat16 bfloat16_round_to_int(bfloat16, float_status *status);
368 bfloat16 float32_to_bfloat16(float32, float_status *status);
369 float32 bfloat16_to_float32(bfloat16, float_status *status);
370 bfloat16 float64_to_bfloat16(float64 a, float_status *status);
371 float64 bfloat16_to_float64(bfloat16 a, float_status *status);
372 
373 int8_t bfloat16_to_int8_scalbn(bfloat16, FloatRoundMode,
374                                int, float_status *status);
375 int16_t bfloat16_to_int16_scalbn(bfloat16, FloatRoundMode,
376                                  int, float_status *status);
377 int32_t bfloat16_to_int32_scalbn(bfloat16, FloatRoundMode,
378                                  int, float_status *status);
379 int64_t bfloat16_to_int64_scalbn(bfloat16, FloatRoundMode,
380                                  int, float_status *status);
381 
382 int8_t bfloat16_to_int8(bfloat16, float_status *status);
383 int16_t bfloat16_to_int16(bfloat16, float_status *status);
384 int32_t bfloat16_to_int32(bfloat16, float_status *status);
385 int64_t bfloat16_to_int64(bfloat16, float_status *status);
386 
387 int8_t bfloat16_to_int8_round_to_zero(bfloat16, float_status *status);
388 int16_t bfloat16_to_int16_round_to_zero(bfloat16, float_status *status);
389 int32_t bfloat16_to_int32_round_to_zero(bfloat16, float_status *status);
390 int64_t bfloat16_to_int64_round_to_zero(bfloat16, float_status *status);
391 
392 uint8_t bfloat16_to_uint8_scalbn(bfloat16 a, FloatRoundMode,
393                                  int, float_status *status);
394 uint16_t bfloat16_to_uint16_scalbn(bfloat16 a, FloatRoundMode,
395                                    int, float_status *status);
396 uint32_t bfloat16_to_uint32_scalbn(bfloat16 a, FloatRoundMode,
397                                    int, float_status *status);
398 uint64_t bfloat16_to_uint64_scalbn(bfloat16 a, FloatRoundMode,
399                                    int, float_status *status);
400 
401 uint8_t bfloat16_to_uint8(bfloat16 a, float_status *status);
402 uint16_t bfloat16_to_uint16(bfloat16 a, float_status *status);
403 uint32_t bfloat16_to_uint32(bfloat16 a, float_status *status);
404 uint64_t bfloat16_to_uint64(bfloat16 a, float_status *status);
405 
406 uint8_t bfloat16_to_uint8_round_to_zero(bfloat16 a, float_status *status);
407 uint16_t bfloat16_to_uint16_round_to_zero(bfloat16 a, float_status *status);
408 uint32_t bfloat16_to_uint32_round_to_zero(bfloat16 a, float_status *status);
409 uint64_t bfloat16_to_uint64_round_to_zero(bfloat16 a, float_status *status);
410 
411 bfloat16 int8_to_bfloat16_scalbn(int8_t a, int, float_status *status);
412 bfloat16 int16_to_bfloat16_scalbn(int16_t a, int, float_status *status);
413 bfloat16 int32_to_bfloat16_scalbn(int32_t a, int, float_status *status);
414 bfloat16 int64_to_bfloat16_scalbn(int64_t a, int, float_status *status);
415 bfloat16 uint8_to_bfloat16_scalbn(uint8_t a, int, float_status *status);
416 bfloat16 uint16_to_bfloat16_scalbn(uint16_t a, int, float_status *status);
417 bfloat16 uint32_to_bfloat16_scalbn(uint32_t a, int, float_status *status);
418 bfloat16 uint64_to_bfloat16_scalbn(uint64_t a, int, float_status *status);
419 
420 bfloat16 int8_to_bfloat16(int8_t a, float_status *status);
421 bfloat16 int16_to_bfloat16(int16_t a, float_status *status);
422 bfloat16 int32_to_bfloat16(int32_t a, float_status *status);
423 bfloat16 int64_to_bfloat16(int64_t a, float_status *status);
424 bfloat16 uint8_to_bfloat16(uint8_t a, float_status *status);
425 bfloat16 uint16_to_bfloat16(uint16_t a, float_status *status);
426 bfloat16 uint32_to_bfloat16(uint32_t a, float_status *status);
427 bfloat16 uint64_to_bfloat16(uint64_t a, float_status *status);
428 
429 /*----------------------------------------------------------------------------
430 | Software bfloat16 operations.
431 *----------------------------------------------------------------------------*/
432 
433 bfloat16 bfloat16_add(bfloat16, bfloat16, float_status *status);
434 bfloat16 bfloat16_sub(bfloat16, bfloat16, float_status *status);
435 bfloat16 bfloat16_mul(bfloat16, bfloat16, float_status *status);
436 bfloat16 bfloat16_div(bfloat16, bfloat16, float_status *status);
437 bfloat16 bfloat16_muladd(bfloat16, bfloat16, bfloat16, int,
438                          float_status *status);
439 float16 bfloat16_scalbn(bfloat16, int, float_status *status);
440 bfloat16 bfloat16_min(bfloat16, bfloat16, float_status *status);
441 bfloat16 bfloat16_max(bfloat16, bfloat16, float_status *status);
442 bfloat16 bfloat16_minnum(bfloat16, bfloat16, float_status *status);
443 bfloat16 bfloat16_maxnum(bfloat16, bfloat16, float_status *status);
444 bfloat16 bfloat16_minnummag(bfloat16, bfloat16, float_status *status);
445 bfloat16 bfloat16_maxnummag(bfloat16, bfloat16, float_status *status);
446 bfloat16 bfloat16_minimum_number(bfloat16, bfloat16, float_status *status);
447 bfloat16 bfloat16_maximum_number(bfloat16, bfloat16, float_status *status);
448 bfloat16 bfloat16_sqrt(bfloat16, float_status *status);
449 FloatRelation bfloat16_compare(bfloat16, bfloat16, float_status *status);
450 FloatRelation bfloat16_compare_quiet(bfloat16, bfloat16, float_status *status);
451 
452 bool bfloat16_is_quiet_nan(bfloat16, float_status *status);
453 bool bfloat16_is_signaling_nan(bfloat16, float_status *status);
454 bfloat16 bfloat16_silence_nan(bfloat16, float_status *status);
455 bfloat16 bfloat16_default_nan(float_status *status);
456 
457 static inline bool bfloat16_is_any_nan(bfloat16 a)
458 {
459     return ((a & ~0x8000) > 0x7F80);
460 }
461 
462 static inline bool bfloat16_is_neg(bfloat16 a)
463 {
464     return a >> 15;
465 }
466 
467 static inline bool bfloat16_is_infinity(bfloat16 a)
468 {
469     return (a & 0x7fff) == 0x7F80;
470 }
471 
472 static inline bool bfloat16_is_zero(bfloat16 a)
473 {
474     return (a & 0x7fff) == 0;
475 }
476 
477 static inline bool bfloat16_is_zero_or_denormal(bfloat16 a)
478 {
479     return (a & 0x7F80) == 0;
480 }
481 
482 static inline bool bfloat16_is_normal(bfloat16 a)
483 {
484     return (((a >> 7) + 1) & 0xff) >= 2;
485 }
486 
487 static inline bfloat16 bfloat16_abs(bfloat16 a)
488 {
489     /* Note that abs does *not* handle NaN specially, nor does
490      * it flush denormal inputs to zero.
491      */
492     return a & 0x7fff;
493 }
494 
495 static inline bfloat16 bfloat16_chs(bfloat16 a)
496 {
497     /* Note that chs does *not* handle NaN specially, nor does
498      * it flush denormal inputs to zero.
499      */
500     return a ^ 0x8000;
501 }
502 
503 static inline bfloat16 bfloat16_set_sign(bfloat16 a, int sign)
504 {
505     return (a & 0x7fff) | (sign << 15);
506 }
507 
508 static inline bool bfloat16_eq(bfloat16 a, bfloat16 b, float_status *s)
509 {
510     return bfloat16_compare(a, b, s) == float_relation_equal;
511 }
512 
513 static inline bool bfloat16_le(bfloat16 a, bfloat16 b, float_status *s)
514 {
515     return bfloat16_compare(a, b, s) <= float_relation_equal;
516 }
517 
518 static inline bool bfloat16_lt(bfloat16 a, bfloat16 b, float_status *s)
519 {
520     return bfloat16_compare(a, b, s) < float_relation_equal;
521 }
522 
523 static inline bool bfloat16_unordered(bfloat16 a, bfloat16 b, float_status *s)
524 {
525     return bfloat16_compare(a, b, s) == float_relation_unordered;
526 }
527 
528 static inline bool bfloat16_eq_quiet(bfloat16 a, bfloat16 b, float_status *s)
529 {
530     return bfloat16_compare_quiet(a, b, s) == float_relation_equal;
531 }
532 
533 static inline bool bfloat16_le_quiet(bfloat16 a, bfloat16 b, float_status *s)
534 {
535     return bfloat16_compare_quiet(a, b, s) <= float_relation_equal;
536 }
537 
538 static inline bool bfloat16_lt_quiet(bfloat16 a, bfloat16 b, float_status *s)
539 {
540     return bfloat16_compare_quiet(a, b, s) < float_relation_equal;
541 }
542 
543 static inline bool bfloat16_unordered_quiet(bfloat16 a, bfloat16 b,
544                                            float_status *s)
545 {
546     return bfloat16_compare_quiet(a, b, s) == float_relation_unordered;
547 }
548 
549 #define bfloat16_zero 0
550 #define bfloat16_half 0x3f00
551 #define bfloat16_one 0x3f80
552 #define bfloat16_one_point_five 0x3fc0
553 #define bfloat16_two 0x4000
554 #define bfloat16_three 0x4040
555 #define bfloat16_infinity 0x7f80
556 
557 /*----------------------------------------------------------------------------
558 | The pattern for a default generated half-precision NaN.
559 *----------------------------------------------------------------------------*/
560 float16 float16_default_nan(float_status *status);
561 
562 /*----------------------------------------------------------------------------
563 | Software IEC/IEEE single-precision conversion routines.
564 *----------------------------------------------------------------------------*/
565 
566 int16_t float32_to_int16_scalbn(float32, FloatRoundMode, int, float_status *);
567 int32_t float32_to_int32_scalbn(float32, FloatRoundMode, int, float_status *);
568 int64_t float32_to_int64_scalbn(float32, FloatRoundMode, int, float_status *);
569 
570 int16_t float32_to_int16(float32, float_status *status);
571 int32_t float32_to_int32(float32, float_status *status);
572 int64_t float32_to_int64(float32, float_status *status);
573 
574 int16_t float32_to_int16_round_to_zero(float32, float_status *status);
575 int32_t float32_to_int32_round_to_zero(float32, float_status *status);
576 int64_t float32_to_int64_round_to_zero(float32, float_status *status);
577 
578 uint16_t float32_to_uint16_scalbn(float32, FloatRoundMode, int, float_status *);
579 uint32_t float32_to_uint32_scalbn(float32, FloatRoundMode, int, float_status *);
580 uint64_t float32_to_uint64_scalbn(float32, FloatRoundMode, int, float_status *);
581 
582 uint16_t float32_to_uint16(float32, float_status *status);
583 uint32_t float32_to_uint32(float32, float_status *status);
584 uint64_t float32_to_uint64(float32, float_status *status);
585 
586 uint16_t float32_to_uint16_round_to_zero(float32, float_status *status);
587 uint32_t float32_to_uint32_round_to_zero(float32, float_status *status);
588 uint64_t float32_to_uint64_round_to_zero(float32, float_status *status);
589 
590 float64 float32_to_float64(float32, float_status *status);
591 floatx80 float32_to_floatx80(float32, float_status *status);
592 float128 float32_to_float128(float32, float_status *status);
593 
594 /*----------------------------------------------------------------------------
595 | Software IEC/IEEE single-precision operations.
596 *----------------------------------------------------------------------------*/
597 float32 float32_round_to_int(float32, float_status *status);
598 float32 float32_add(float32, float32, float_status *status);
599 float32 float32_sub(float32, float32, float_status *status);
600 float32 float32_mul(float32, float32, float_status *status);
601 float32 float32_div(float32, float32, float_status *status);
602 float32 float32_rem(float32, float32, float_status *status);
603 float32 float32_muladd(float32, float32, float32, int, float_status *status);
604 float32 float32_muladd_scalbn(float32, float32, float32,
605                               int, int, float_status *status);
606 float32 float32_sqrt(float32, float_status *status);
607 float32 float32_exp2(float32, float_status *status);
608 float32 float32_log2(float32, float_status *status);
609 FloatRelation float32_compare(float32, float32, float_status *status);
610 FloatRelation float32_compare_quiet(float32, float32, float_status *status);
611 float32 float32_min(float32, float32, float_status *status);
612 float32 float32_max(float32, float32, float_status *status);
613 float32 float32_minnum(float32, float32, float_status *status);
614 float32 float32_maxnum(float32, float32, float_status *status);
615 float32 float32_minnummag(float32, float32, float_status *status);
616 float32 float32_maxnummag(float32, float32, float_status *status);
617 float32 float32_minimum_number(float32, float32, float_status *status);
618 float32 float32_maximum_number(float32, float32, float_status *status);
619 bool float32_is_quiet_nan(float32, float_status *status);
620 bool float32_is_signaling_nan(float32, float_status *status);
621 float32 float32_silence_nan(float32, float_status *status);
622 float32 float32_scalbn(float32, int, float_status *status);
623 
624 static inline float32 float32_abs(float32 a)
625 {
626     /* Note that abs does *not* handle NaN specially, nor does
627      * it flush denormal inputs to zero.
628      */
629     return make_float32(float32_val(a) & 0x7fffffff);
630 }
631 
632 static inline float32 float32_chs(float32 a)
633 {
634     /* Note that chs does *not* handle NaN specially, nor does
635      * it flush denormal inputs to zero.
636      */
637     return make_float32(float32_val(a) ^ 0x80000000);
638 }
639 
640 static inline bool float32_is_infinity(float32 a)
641 {
642     return (float32_val(a) & 0x7fffffff) == 0x7f800000;
643 }
644 
645 static inline bool float32_is_neg(float32 a)
646 {
647     return float32_val(a) >> 31;
648 }
649 
650 static inline bool float32_is_zero(float32 a)
651 {
652     return (float32_val(a) & 0x7fffffff) == 0;
653 }
654 
655 static inline bool float32_is_any_nan(float32 a)
656 {
657     return ((float32_val(a) & ~(1 << 31)) > 0x7f800000UL);
658 }
659 
660 static inline bool float32_is_zero_or_denormal(float32 a)
661 {
662     return (float32_val(a) & 0x7f800000) == 0;
663 }
664 
665 static inline bool float32_is_normal(float32 a)
666 {
667     return (((float32_val(a) >> 23) + 1) & 0xff) >= 2;
668 }
669 
670 static inline bool float32_is_denormal(float32 a)
671 {
672     return float32_is_zero_or_denormal(a) && !float32_is_zero(a);
673 }
674 
675 static inline bool float32_is_zero_or_normal(float32 a)
676 {
677     return float32_is_normal(a) || float32_is_zero(a);
678 }
679 
680 static inline float32 float32_set_sign(float32 a, int sign)
681 {
682     return make_float32((float32_val(a) & 0x7fffffff) | (sign << 31));
683 }
684 
685 static inline bool float32_eq(float32 a, float32 b, float_status *s)
686 {
687     return float32_compare(a, b, s) == float_relation_equal;
688 }
689 
690 static inline bool float32_le(float32 a, float32 b, float_status *s)
691 {
692     return float32_compare(a, b, s) <= float_relation_equal;
693 }
694 
695 static inline bool float32_lt(float32 a, float32 b, float_status *s)
696 {
697     return float32_compare(a, b, s) < float_relation_equal;
698 }
699 
700 static inline bool float32_unordered(float32 a, float32 b, float_status *s)
701 {
702     return float32_compare(a, b, s) == float_relation_unordered;
703 }
704 
705 static inline bool float32_eq_quiet(float32 a, float32 b, float_status *s)
706 {
707     return float32_compare_quiet(a, b, s) == float_relation_equal;
708 }
709 
710 static inline bool float32_le_quiet(float32 a, float32 b, float_status *s)
711 {
712     return float32_compare_quiet(a, b, s) <= float_relation_equal;
713 }
714 
715 static inline bool float32_lt_quiet(float32 a, float32 b, float_status *s)
716 {
717     return float32_compare_quiet(a, b, s) < float_relation_equal;
718 }
719 
720 static inline bool float32_unordered_quiet(float32 a, float32 b,
721                                            float_status *s)
722 {
723     return float32_compare_quiet(a, b, s) == float_relation_unordered;
724 }
725 
726 #define float32_zero make_float32(0)
727 #define float32_half make_float32(0x3f000000)
728 #define float32_one make_float32(0x3f800000)
729 #define float32_one_point_five make_float32(0x3fc00000)
730 #define float32_two make_float32(0x40000000)
731 #define float32_three make_float32(0x40400000)
732 #define float32_infinity make_float32(0x7f800000)
733 
734 /*----------------------------------------------------------------------------
735 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
736 | single-precision floating-point value, returning the result.  After being
737 | shifted into the proper positions, the three fields are simply added
738 | together to form the result.  This means that any integer portion of `zSig'
739 | will be added into the exponent.  Since a properly normalized significand
740 | will have an integer portion equal to 1, the `zExp' input should be 1 less
741 | than the desired result exponent whenever `zSig' is a complete, normalized
742 | significand.
743 *----------------------------------------------------------------------------*/
744 
745 static inline float32 packFloat32(bool zSign, int zExp, uint32_t zSig)
746 {
747     return make_float32(
748           (((uint32_t)zSign) << 31) + (((uint32_t)zExp) << 23) + zSig);
749 }
750 
751 /*----------------------------------------------------------------------------
752 | The pattern for a default generated single-precision NaN.
753 *----------------------------------------------------------------------------*/
754 float32 float32_default_nan(float_status *status);
755 
756 /*----------------------------------------------------------------------------
757 | Software IEC/IEEE double-precision conversion routines.
758 *----------------------------------------------------------------------------*/
759 
760 int16_t float64_to_int16_scalbn(float64, FloatRoundMode, int, float_status *);
761 int32_t float64_to_int32_scalbn(float64, FloatRoundMode, int, float_status *);
762 int64_t float64_to_int64_scalbn(float64, FloatRoundMode, int, float_status *);
763 
764 int16_t float64_to_int16(float64, float_status *status);
765 int32_t float64_to_int32(float64, float_status *status);
766 int64_t float64_to_int64(float64, float_status *status);
767 
768 int16_t float64_to_int16_round_to_zero(float64, float_status *status);
769 int32_t float64_to_int32_round_to_zero(float64, float_status *status);
770 int64_t float64_to_int64_round_to_zero(float64, float_status *status);
771 
772 int32_t float64_to_int32_modulo(float64, FloatRoundMode, float_status *status);
773 int64_t float64_to_int64_modulo(float64, FloatRoundMode, float_status *status);
774 
775 uint16_t float64_to_uint16_scalbn(float64, FloatRoundMode, int, float_status *);
776 uint32_t float64_to_uint32_scalbn(float64, FloatRoundMode, int, float_status *);
777 uint64_t float64_to_uint64_scalbn(float64, FloatRoundMode, int, float_status *);
778 
779 uint16_t float64_to_uint16(float64, float_status *status);
780 uint32_t float64_to_uint32(float64, float_status *status);
781 uint64_t float64_to_uint64(float64, float_status *status);
782 
783 uint16_t float64_to_uint16_round_to_zero(float64, float_status *status);
784 uint32_t float64_to_uint32_round_to_zero(float64, float_status *status);
785 uint64_t float64_to_uint64_round_to_zero(float64, float_status *status);
786 
787 float32 float64_to_float32(float64, float_status *status);
788 floatx80 float64_to_floatx80(float64, float_status *status);
789 float128 float64_to_float128(float64, float_status *status);
790 
791 /*----------------------------------------------------------------------------
792 | Software IEC/IEEE double-precision operations.
793 *----------------------------------------------------------------------------*/
794 float64 float64_round_to_int(float64, float_status *status);
795 float64 float64_add(float64, float64, float_status *status);
796 float64 float64_sub(float64, float64, float_status *status);
797 float64 float64_mul(float64, float64, float_status *status);
798 float64 float64_div(float64, float64, float_status *status);
799 float64 float64_rem(float64, float64, float_status *status);
800 float64 float64_muladd(float64, float64, float64, int, float_status *status);
801 float64 float64_muladd_scalbn(float64, float64, float64,
802                               int, int, float_status *status);
803 float64 float64_sqrt(float64, float_status *status);
804 float64 float64_log2(float64, float_status *status);
805 FloatRelation float64_compare(float64, float64, float_status *status);
806 FloatRelation float64_compare_quiet(float64, float64, float_status *status);
807 float64 float64_min(float64, float64, float_status *status);
808 float64 float64_max(float64, float64, float_status *status);
809 float64 float64_minnum(float64, float64, float_status *status);
810 float64 float64_maxnum(float64, float64, float_status *status);
811 float64 float64_minnummag(float64, float64, float_status *status);
812 float64 float64_maxnummag(float64, float64, float_status *status);
813 float64 float64_minimum_number(float64, float64, float_status *status);
814 float64 float64_maximum_number(float64, float64, float_status *status);
815 bool float64_is_quiet_nan(float64 a, float_status *status);
816 bool float64_is_signaling_nan(float64, float_status *status);
817 float64 float64_silence_nan(float64, float_status *status);
818 float64 float64_scalbn(float64, int, float_status *status);
819 
820 static inline float64 float64_abs(float64 a)
821 {
822     /* Note that abs does *not* handle NaN specially, nor does
823      * it flush denormal inputs to zero.
824      */
825     return make_float64(float64_val(a) & 0x7fffffffffffffffLL);
826 }
827 
828 static inline float64 float64_chs(float64 a)
829 {
830     /* Note that chs does *not* handle NaN specially, nor does
831      * it flush denormal inputs to zero.
832      */
833     return make_float64(float64_val(a) ^ 0x8000000000000000LL);
834 }
835 
836 static inline bool float64_is_infinity(float64 a)
837 {
838     return (float64_val(a) & 0x7fffffffffffffffLL ) == 0x7ff0000000000000LL;
839 }
840 
841 static inline bool float64_is_neg(float64 a)
842 {
843     return float64_val(a) >> 63;
844 }
845 
846 static inline bool float64_is_zero(float64 a)
847 {
848     return (float64_val(a) & 0x7fffffffffffffffLL) == 0;
849 }
850 
851 static inline bool float64_is_any_nan(float64 a)
852 {
853     return ((float64_val(a) & ~(1ULL << 63)) > 0x7ff0000000000000ULL);
854 }
855 
856 static inline bool float64_is_zero_or_denormal(float64 a)
857 {
858     return (float64_val(a) & 0x7ff0000000000000LL) == 0;
859 }
860 
861 static inline bool float64_is_normal(float64 a)
862 {
863     return (((float64_val(a) >> 52) + 1) & 0x7ff) >= 2;
864 }
865 
866 static inline bool float64_is_denormal(float64 a)
867 {
868     return float64_is_zero_or_denormal(a) && !float64_is_zero(a);
869 }
870 
871 static inline bool float64_is_zero_or_normal(float64 a)
872 {
873     return float64_is_normal(a) || float64_is_zero(a);
874 }
875 
876 static inline float64 float64_set_sign(float64 a, int sign)
877 {
878     return make_float64((float64_val(a) & 0x7fffffffffffffffULL)
879                         | ((int64_t)sign << 63));
880 }
881 
882 static inline bool float64_eq(float64 a, float64 b, float_status *s)
883 {
884     return float64_compare(a, b, s) == float_relation_equal;
885 }
886 
887 static inline bool float64_le(float64 a, float64 b, float_status *s)
888 {
889     return float64_compare(a, b, s) <= float_relation_equal;
890 }
891 
892 static inline bool float64_lt(float64 a, float64 b, float_status *s)
893 {
894     return float64_compare(a, b, s) < float_relation_equal;
895 }
896 
897 static inline bool float64_unordered(float64 a, float64 b, float_status *s)
898 {
899     return float64_compare(a, b, s) == float_relation_unordered;
900 }
901 
902 static inline bool float64_eq_quiet(float64 a, float64 b, float_status *s)
903 {
904     return float64_compare_quiet(a, b, s) == float_relation_equal;
905 }
906 
907 static inline bool float64_le_quiet(float64 a, float64 b, float_status *s)
908 {
909     return float64_compare_quiet(a, b, s) <= float_relation_equal;
910 }
911 
912 static inline bool float64_lt_quiet(float64 a, float64 b, float_status *s)
913 {
914     return float64_compare_quiet(a, b, s) < float_relation_equal;
915 }
916 
917 static inline bool float64_unordered_quiet(float64 a, float64 b,
918                                            float_status *s)
919 {
920     return float64_compare_quiet(a, b, s) == float_relation_unordered;
921 }
922 
923 #define float64_zero make_float64(0)
924 #define float64_half make_float64(0x3fe0000000000000LL)
925 #define float64_one make_float64(0x3ff0000000000000LL)
926 #define float64_one_point_five make_float64(0x3FF8000000000000ULL)
927 #define float64_two make_float64(0x4000000000000000ULL)
928 #define float64_three make_float64(0x4008000000000000ULL)
929 #define float64_ln2 make_float64(0x3fe62e42fefa39efLL)
930 #define float64_infinity make_float64(0x7ff0000000000000LL)
931 
932 /*----------------------------------------------------------------------------
933 | The pattern for a default generated double-precision NaN.
934 *----------------------------------------------------------------------------*/
935 float64 float64_default_nan(float_status *status);
936 
937 /*----------------------------------------------------------------------------
938 | Software IEC/IEEE double-precision operations, rounding to single precision,
939 | returning a result in double precision, with only one rounding step.
940 *----------------------------------------------------------------------------*/
941 
942 float64 float64r32_add(float64, float64, float_status *status);
943 float64 float64r32_sub(float64, float64, float_status *status);
944 float64 float64r32_mul(float64, float64, float_status *status);
945 float64 float64r32_div(float64, float64, float_status *status);
946 float64 float64r32_muladd(float64, float64, float64, int, float_status *status);
947 float64 float64r32_sqrt(float64, float_status *status);
948 
949 /*----------------------------------------------------------------------------
950 | Software IEC/IEEE extended double-precision conversion routines.
951 *----------------------------------------------------------------------------*/
952 int32_t floatx80_to_int32(floatx80, float_status *status);
953 int32_t floatx80_to_int32_round_to_zero(floatx80, float_status *status);
954 int64_t floatx80_to_int64(floatx80, float_status *status);
955 int64_t floatx80_to_int64_round_to_zero(floatx80, float_status *status);
956 float32 floatx80_to_float32(floatx80, float_status *status);
957 float64 floatx80_to_float64(floatx80, float_status *status);
958 float128 floatx80_to_float128(floatx80, float_status *status);
959 
960 /*----------------------------------------------------------------------------
961 | The pattern for an extended double-precision inf.
962 *----------------------------------------------------------------------------*/
963 extern const floatx80 floatx80_infinity;
964 
965 /*----------------------------------------------------------------------------
966 | Software IEC/IEEE extended double-precision operations.
967 *----------------------------------------------------------------------------*/
968 floatx80 floatx80_round(floatx80 a, float_status *status);
969 floatx80 floatx80_round_to_int(floatx80, float_status *status);
970 floatx80 floatx80_add(floatx80, floatx80, float_status *status);
971 floatx80 floatx80_sub(floatx80, floatx80, float_status *status);
972 floatx80 floatx80_mul(floatx80, floatx80, float_status *status);
973 floatx80 floatx80_div(floatx80, floatx80, float_status *status);
974 floatx80 floatx80_modrem(floatx80, floatx80, bool, uint64_t *,
975                          float_status *status);
976 floatx80 floatx80_mod(floatx80, floatx80, float_status *status);
977 floatx80 floatx80_rem(floatx80, floatx80, float_status *status);
978 floatx80 floatx80_sqrt(floatx80, float_status *status);
979 FloatRelation floatx80_compare(floatx80, floatx80, float_status *status);
980 FloatRelation floatx80_compare_quiet(floatx80, floatx80, float_status *status);
981 int floatx80_is_quiet_nan(floatx80, float_status *status);
982 int floatx80_is_signaling_nan(floatx80, float_status *status);
983 floatx80 floatx80_silence_nan(floatx80, float_status *status);
984 floatx80 floatx80_scalbn(floatx80, int, float_status *status);
985 
986 static inline floatx80 floatx80_abs(floatx80 a)
987 {
988     a.high &= 0x7fff;
989     return a;
990 }
991 
992 static inline floatx80 floatx80_chs(floatx80 a)
993 {
994     a.high ^= 0x8000;
995     return a;
996 }
997 
998 static inline bool floatx80_is_infinity(floatx80 a)
999 {
1000 #if defined(TARGET_M68K)
1001     return (a.high & 0x7fff) == floatx80_infinity.high && !(a.low << 1);
1002 #else
1003     return (a.high & 0x7fff) == floatx80_infinity.high &&
1004                        a.low == floatx80_infinity.low;
1005 #endif
1006 }
1007 
1008 static inline bool floatx80_is_neg(floatx80 a)
1009 {
1010     return a.high >> 15;
1011 }
1012 
1013 static inline bool floatx80_is_zero(floatx80 a)
1014 {
1015     return (a.high & 0x7fff) == 0 && a.low == 0;
1016 }
1017 
1018 static inline bool floatx80_is_zero_or_denormal(floatx80 a)
1019 {
1020     return (a.high & 0x7fff) == 0;
1021 }
1022 
1023 static inline bool floatx80_is_any_nan(floatx80 a)
1024 {
1025     return ((a.high & 0x7fff) == 0x7fff) && (a.low<<1);
1026 }
1027 
1028 static inline bool floatx80_eq(floatx80 a, floatx80 b, float_status *s)
1029 {
1030     return floatx80_compare(a, b, s) == float_relation_equal;
1031 }
1032 
1033 static inline bool floatx80_le(floatx80 a, floatx80 b, float_status *s)
1034 {
1035     return floatx80_compare(a, b, s) <= float_relation_equal;
1036 }
1037 
1038 static inline bool floatx80_lt(floatx80 a, floatx80 b, float_status *s)
1039 {
1040     return floatx80_compare(a, b, s) < float_relation_equal;
1041 }
1042 
1043 static inline bool floatx80_unordered(floatx80 a, floatx80 b, float_status *s)
1044 {
1045     return floatx80_compare(a, b, s) == float_relation_unordered;
1046 }
1047 
1048 static inline bool floatx80_eq_quiet(floatx80 a, floatx80 b, float_status *s)
1049 {
1050     return floatx80_compare_quiet(a, b, s) == float_relation_equal;
1051 }
1052 
1053 static inline bool floatx80_le_quiet(floatx80 a, floatx80 b, float_status *s)
1054 {
1055     return floatx80_compare_quiet(a, b, s) <= float_relation_equal;
1056 }
1057 
1058 static inline bool floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *s)
1059 {
1060     return floatx80_compare_quiet(a, b, s) < float_relation_equal;
1061 }
1062 
1063 static inline bool floatx80_unordered_quiet(floatx80 a, floatx80 b,
1064                                            float_status *s)
1065 {
1066     return floatx80_compare_quiet(a, b, s) == float_relation_unordered;
1067 }
1068 
1069 /*----------------------------------------------------------------------------
1070 | Return whether the given value is an invalid floatx80 encoding.
1071 | Invalid floatx80 encodings arise when the integer bit is not set, but
1072 | the exponent is not zero. The only times the integer bit is permitted to
1073 | be zero is in subnormal numbers and the value zero.
1074 | This includes what the Intel software developer's manual calls pseudo-NaNs,
1075 | pseudo-infinities and un-normal numbers. It does not include
1076 | pseudo-denormals, which must still be correctly handled as inputs even
1077 | if they are never generated as outputs.
1078 *----------------------------------------------------------------------------*/
1079 static inline bool floatx80_invalid_encoding(floatx80 a)
1080 {
1081 #if defined(TARGET_M68K)
1082     /*-------------------------------------------------------------------------
1083     | With m68k, the explicit integer bit can be zero in the case of:
1084     | - zeros                (exp == 0, mantissa == 0)
1085     | - denormalized numbers (exp == 0, mantissa != 0)
1086     | - unnormalized numbers (exp != 0, exp < 0x7FFF)
1087     | - infinities           (exp == 0x7FFF, mantissa == 0)
1088     | - not-a-numbers        (exp == 0x7FFF, mantissa != 0)
1089     |
1090     | For infinities and NaNs, the explicit integer bit can be either one or
1091     | zero.
1092     |
1093     | The IEEE 754 standard does not define a zero integer bit. Such a number
1094     | is an unnormalized number. Hardware does not directly support
1095     | denormalized and unnormalized numbers, but implicitly supports them by
1096     | trapping them as unimplemented data types, allowing efficient conversion
1097     | in software.
1098     |
1099     | See "M68000 FAMILY PROGRAMMER’S REFERENCE MANUAL",
1100     |     "1.6 FLOATING-POINT DATA TYPES"
1101     *------------------------------------------------------------------------*/
1102     return false;
1103 #else
1104     return (a.low & (1ULL << 63)) == 0 && (a.high & 0x7FFF) != 0;
1105 #endif
1106 }
1107 
1108 #define floatx80_zero make_floatx80(0x0000, 0x0000000000000000LL)
1109 #define floatx80_zero_init make_floatx80_init(0x0000, 0x0000000000000000LL)
1110 #define floatx80_one make_floatx80(0x3fff, 0x8000000000000000LL)
1111 #define floatx80_ln2 make_floatx80(0x3ffe, 0xb17217f7d1cf79acLL)
1112 #define floatx80_pi make_floatx80(0x4000, 0xc90fdaa22168c235LL)
1113 #define floatx80_half make_floatx80(0x3ffe, 0x8000000000000000LL)
1114 
1115 /*----------------------------------------------------------------------------
1116 | Returns the fraction bits of the extended double-precision floating-point
1117 | value `a'.
1118 *----------------------------------------------------------------------------*/
1119 
1120 static inline uint64_t extractFloatx80Frac(floatx80 a)
1121 {
1122     return a.low;
1123 }
1124 
1125 /*----------------------------------------------------------------------------
1126 | Returns the exponent bits of the extended double-precision floating-point
1127 | value `a'.
1128 *----------------------------------------------------------------------------*/
1129 
1130 static inline int32_t extractFloatx80Exp(floatx80 a)
1131 {
1132     return a.high & 0x7FFF;
1133 }
1134 
1135 /*----------------------------------------------------------------------------
1136 | Returns the sign bit of the extended double-precision floating-point value
1137 | `a'.
1138 *----------------------------------------------------------------------------*/
1139 
1140 static inline bool extractFloatx80Sign(floatx80 a)
1141 {
1142     return a.high >> 15;
1143 }
1144 
1145 /*----------------------------------------------------------------------------
1146 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
1147 | extended double-precision floating-point value, returning the result.
1148 *----------------------------------------------------------------------------*/
1149 
1150 static inline floatx80 packFloatx80(bool zSign, int32_t zExp, uint64_t zSig)
1151 {
1152     floatx80 z;
1153 
1154     z.low = zSig;
1155     z.high = (((uint16_t)zSign) << 15) + zExp;
1156     return z;
1157 }
1158 
1159 /*----------------------------------------------------------------------------
1160 | Normalizes the subnormal extended double-precision floating-point value
1161 | represented by the denormalized significand `aSig'.  The normalized exponent
1162 | and significand are stored at the locations pointed to by `zExpPtr' and
1163 | `zSigPtr', respectively.
1164 *----------------------------------------------------------------------------*/
1165 
1166 void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr,
1167                                 uint64_t *zSigPtr);
1168 
1169 /*----------------------------------------------------------------------------
1170 | Takes two extended double-precision floating-point values `a' and `b', one
1171 | of which is a NaN, and returns the appropriate NaN result.  If either `a' or
1172 | `b' is a signaling NaN, the invalid exception is raised.
1173 *----------------------------------------------------------------------------*/
1174 
1175 floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status);
1176 
1177 /*----------------------------------------------------------------------------
1178 | Takes an abstract floating-point value having sign `zSign', exponent `zExp',
1179 | and extended significand formed by the concatenation of `zSig0' and `zSig1',
1180 | and returns the proper extended double-precision floating-point value
1181 | corresponding to the abstract input.  Ordinarily, the abstract value is
1182 | rounded and packed into the extended double-precision format, with the
1183 | inexact exception raised if the abstract input cannot be represented
1184 | exactly.  However, if the abstract value is too large, the overflow and
1185 | inexact exceptions are raised and an infinity or maximal finite value is
1186 | returned.  If the abstract value is too small, the input value is rounded to
1187 | a subnormal number, and the underflow and inexact exceptions are raised if
1188 | the abstract input cannot be represented exactly as a subnormal extended
1189 | double-precision floating-point number.
1190 |     If `roundingPrecision' is 32 or 64, the result is rounded to the same
1191 | number of bits as single or double precision, respectively.  Otherwise, the
1192 | result is rounded to the full precision of the extended double-precision
1193 | format.
1194 |     The input significand must be normalized or smaller.  If the input
1195 | significand is not normalized, `zExp' must be 0; in that case, the result
1196 | returned is a subnormal number, and it must not require rounding.  The
1197 | handling of underflow and overflow follows the IEC/IEEE Standard for Binary
1198 | Floating-Point Arithmetic.
1199 *----------------------------------------------------------------------------*/
1200 
1201 floatx80 roundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, bool zSign,
1202                               int32_t zExp, uint64_t zSig0, uint64_t zSig1,
1203                               float_status *status);
1204 
1205 /*----------------------------------------------------------------------------
1206 | Takes an abstract floating-point value having sign `zSign', exponent
1207 | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
1208 | and returns the proper extended double-precision floating-point value
1209 | corresponding to the abstract input.  This routine is just like
1210 | `roundAndPackFloatx80' except that the input significand does not have to be
1211 | normalized.
1212 *----------------------------------------------------------------------------*/
1213 
1214 floatx80 normalizeRoundAndPackFloatx80(FloatX80RoundPrec roundingPrecision,
1215                                        bool zSign, int32_t zExp,
1216                                        uint64_t zSig0, uint64_t zSig1,
1217                                        float_status *status);
1218 
1219 /*----------------------------------------------------------------------------
1220 | The pattern for a default generated extended double-precision NaN.
1221 *----------------------------------------------------------------------------*/
1222 floatx80 floatx80_default_nan(float_status *status);
1223 
1224 /*----------------------------------------------------------------------------
1225 | Software IEC/IEEE quadruple-precision conversion routines.
1226 *----------------------------------------------------------------------------*/
1227 int32_t float128_to_int32(float128, float_status *status);
1228 int32_t float128_to_int32_round_to_zero(float128, float_status *status);
1229 int64_t float128_to_int64(float128, float_status *status);
1230 Int128 float128_to_int128(float128, float_status *status);
1231 int64_t float128_to_int64_round_to_zero(float128, float_status *status);
1232 Int128 float128_to_int128_round_to_zero(float128, float_status *status);
1233 uint64_t float128_to_uint64(float128, float_status *status);
1234 Int128 float128_to_uint128(float128, float_status *status);
1235 uint64_t float128_to_uint64_round_to_zero(float128, float_status *status);
1236 Int128 float128_to_uint128_round_to_zero(float128, float_status *status);
1237 uint32_t float128_to_uint32(float128, float_status *status);
1238 uint32_t float128_to_uint32_round_to_zero(float128, float_status *status);
1239 float32 float128_to_float32(float128, float_status *status);
1240 float64 float128_to_float64(float128, float_status *status);
1241 floatx80 float128_to_floatx80(float128, float_status *status);
1242 
1243 /*----------------------------------------------------------------------------
1244 | Software IEC/IEEE quadruple-precision operations.
1245 *----------------------------------------------------------------------------*/
1246 float128 float128_round_to_int(float128, float_status *status);
1247 float128 float128_add(float128, float128, float_status *status);
1248 float128 float128_sub(float128, float128, float_status *status);
1249 float128 float128_mul(float128, float128, float_status *status);
1250 float128 float128_muladd(float128, float128, float128, int,
1251                          float_status *status);
1252 float128 float128_div(float128, float128, float_status *status);
1253 float128 float128_rem(float128, float128, float_status *status);
1254 float128 float128_sqrt(float128, float_status *status);
1255 FloatRelation float128_compare(float128, float128, float_status *status);
1256 FloatRelation float128_compare_quiet(float128, float128, float_status *status);
1257 float128 float128_min(float128, float128, float_status *status);
1258 float128 float128_max(float128, float128, float_status *status);
1259 float128 float128_minnum(float128, float128, float_status *status);
1260 float128 float128_maxnum(float128, float128, float_status *status);
1261 float128 float128_minnummag(float128, float128, float_status *status);
1262 float128 float128_maxnummag(float128, float128, float_status *status);
1263 float128 float128_minimum_number(float128, float128, float_status *status);
1264 float128 float128_maximum_number(float128, float128, float_status *status);
1265 bool float128_is_quiet_nan(float128, float_status *status);
1266 bool float128_is_signaling_nan(float128, float_status *status);
1267 float128 float128_silence_nan(float128, float_status *status);
1268 float128 float128_scalbn(float128, int, float_status *status);
1269 
1270 static inline float128 float128_abs(float128 a)
1271 {
1272     a.high &= 0x7fffffffffffffffLL;
1273     return a;
1274 }
1275 
1276 static inline float128 float128_chs(float128 a)
1277 {
1278     a.high ^= 0x8000000000000000LL;
1279     return a;
1280 }
1281 
1282 static inline bool float128_is_infinity(float128 a)
1283 {
1284     return (a.high & 0x7fffffffffffffffLL) == 0x7fff000000000000LL && a.low == 0;
1285 }
1286 
1287 static inline bool float128_is_neg(float128 a)
1288 {
1289     return a.high >> 63;
1290 }
1291 
1292 static inline bool float128_is_zero(float128 a)
1293 {
1294     return (a.high & 0x7fffffffffffffffLL) == 0 && a.low == 0;
1295 }
1296 
1297 static inline bool float128_is_zero_or_denormal(float128 a)
1298 {
1299     return (a.high & 0x7fff000000000000LL) == 0;
1300 }
1301 
1302 static inline bool float128_is_normal(float128 a)
1303 {
1304     return (((a.high >> 48) + 1) & 0x7fff) >= 2;
1305 }
1306 
1307 static inline bool float128_is_denormal(float128 a)
1308 {
1309     return float128_is_zero_or_denormal(a) && !float128_is_zero(a);
1310 }
1311 
1312 static inline bool float128_is_any_nan(float128 a)
1313 {
1314     return ((a.high >> 48) & 0x7fff) == 0x7fff &&
1315         ((a.low != 0) || ((a.high & 0xffffffffffffLL) != 0));
1316 }
1317 
1318 static inline bool float128_eq(float128 a, float128 b, float_status *s)
1319 {
1320     return float128_compare(a, b, s) == float_relation_equal;
1321 }
1322 
1323 static inline bool float128_le(float128 a, float128 b, float_status *s)
1324 {
1325     return float128_compare(a, b, s) <= float_relation_equal;
1326 }
1327 
1328 static inline bool float128_lt(float128 a, float128 b, float_status *s)
1329 {
1330     return float128_compare(a, b, s) < float_relation_equal;
1331 }
1332 
1333 static inline bool float128_unordered(float128 a, float128 b, float_status *s)
1334 {
1335     return float128_compare(a, b, s) == float_relation_unordered;
1336 }
1337 
1338 static inline bool float128_eq_quiet(float128 a, float128 b, float_status *s)
1339 {
1340     return float128_compare_quiet(a, b, s) == float_relation_equal;
1341 }
1342 
1343 static inline bool float128_le_quiet(float128 a, float128 b, float_status *s)
1344 {
1345     return float128_compare_quiet(a, b, s) <= float_relation_equal;
1346 }
1347 
1348 static inline bool float128_lt_quiet(float128 a, float128 b, float_status *s)
1349 {
1350     return float128_compare_quiet(a, b, s) < float_relation_equal;
1351 }
1352 
1353 static inline bool float128_unordered_quiet(float128 a, float128 b,
1354                                            float_status *s)
1355 {
1356     return float128_compare_quiet(a, b, s) == float_relation_unordered;
1357 }
1358 
1359 #define float128_zero make_float128(0, 0)
1360 
1361 /*----------------------------------------------------------------------------
1362 | The pattern for a default generated quadruple-precision NaN.
1363 *----------------------------------------------------------------------------*/
1364 float128 float128_default_nan(float_status *status);
1365 
1366 #endif /* SOFTFLOAT_H */
1367