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1 | /* | |
2 | * QEMU float support | |
3 | * | |
4 | * Derived from SoftFloat. | |
5 | */ | |
6 | ||
7 | /*============================================================================ | |
8 | ||
9 | This C source fragment is part of the SoftFloat IEC/IEEE Floating-point | |
10 | Arithmetic Package, Release 2b. | |
11 | ||
12 | Written by John R. Hauser. This work was made possible in part by the | |
13 | International Computer Science Institute, located at Suite 600, 1947 Center | |
14 | Street, Berkeley, California 94704. Funding was partially provided by the | |
15 | National Science Foundation under grant MIP-9311980. The original version | |
16 | of this code was written as part of a project to build a fixed-point vector | |
17 | processor in collaboration with the University of California at Berkeley, | |
18 | overseen by Profs. Nelson Morgan and John Wawrzynek. More information | |
19 | is available through the Web page `http://www.cs.berkeley.edu/~jhauser/ | |
20 | arithmetic/SoftFloat.html'. | |
21 | ||
22 | THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has | |
23 | been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES | |
24 | RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS | |
25 | AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES, | |
26 | COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE | |
27 | EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE | |
28 | INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR | |
29 | OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. | |
30 | ||
31 | Derivative works are acceptable, even for commercial purposes, so long as | |
32 | (1) the source code for the derivative work includes prominent notice that | |
33 | the work is derivative, and (2) the source code includes prominent notice with | |
34 | these four paragraphs for those parts of this code that are retained. | |
35 | ||
36 | =============================================================================*/ | |
37 | ||
38 | /*---------------------------------------------------------------------------- | |
39 | | Raises the exceptions specified by `flags'. Floating-point traps can be | |
40 | | defined here if desired. It is currently not possible for such a trap | |
41 | | to substitute a result value. If traps are not implemented, this routine | |
42 | | should be simply `float_exception_flags |= flags;'. | |
43 | *----------------------------------------------------------------------------*/ | |
44 | ||
45 | void float_raise( int8 flags STATUS_PARAM ) | |
46 | { | |
47 | STATUS(float_exception_flags) |= flags; | |
48 | } | |
49 | ||
50 | /*---------------------------------------------------------------------------- | |
51 | | Internal canonical NaN format. | |
52 | *----------------------------------------------------------------------------*/ | |
53 | typedef struct { | |
54 | flag sign; | |
55 | uint64_t high, low; | |
56 | } commonNaNT; | |
57 | ||
58 | /*---------------------------------------------------------------------------- | |
59 | | Returns 1 if the half-precision floating-point value `a' is a quiet | |
60 | | NaN; otherwise returns 0. | |
61 | *----------------------------------------------------------------------------*/ | |
62 | ||
63 | int float16_is_quiet_nan(float16 a_) | |
64 | { | |
65 | uint16_t a = float16_val(a_); | |
66 | #if SNAN_BIT_IS_ONE | |
67 | return (((a >> 9) & 0x3F) == 0x3E) && (a & 0x1FF); | |
68 | #else | |
69 | return ((a & ~0x8000) >= 0x7c80); | |
70 | #endif | |
71 | } | |
72 | ||
73 | /*---------------------------------------------------------------------------- | |
74 | | Returns 1 if the half-precision floating-point value `a' is a signaling | |
75 | | NaN; otherwise returns 0. | |
76 | *----------------------------------------------------------------------------*/ | |
77 | ||
78 | int float16_is_signaling_nan(float16 a_) | |
79 | { | |
80 | uint16_t a = float16_val(a_); | |
81 | #if SNAN_BIT_IS_ONE | |
82 | return ((a & ~0x8000) >= 0x7c80); | |
83 | #else | |
84 | return (((a >> 9) & 0x3F) == 0x3E) && (a & 0x1FF); | |
85 | #endif | |
86 | } | |
87 | ||
88 | /*---------------------------------------------------------------------------- | |
89 | | Returns a quiet NaN if the half-precision floating point value `a' is a | |
90 | | signaling NaN; otherwise returns `a'. | |
91 | *----------------------------------------------------------------------------*/ | |
92 | float16 float16_maybe_silence_nan(float16 a_) | |
93 | { | |
94 | if (float16_is_signaling_nan(a_)) { | |
95 | #if SNAN_BIT_IS_ONE | |
96 | # if defined(TARGET_MIPS) || defined(TARGET_SH4) || defined(TARGET_UNICORE32) | |
97 | return float16_default_nan; | |
98 | # else | |
99 | # error Rules for silencing a signaling NaN are target-specific | |
100 | # endif | |
101 | #else | |
102 | uint16_t a = float16_val(a_); | |
103 | a |= (1 << 9); | |
104 | return make_float16(a); | |
105 | #endif | |
106 | } | |
107 | return a_; | |
108 | } | |
109 | ||
110 | /*---------------------------------------------------------------------------- | |
111 | | Returns the result of converting the half-precision floating-point NaN | |
112 | | `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid | |
113 | | exception is raised. | |
114 | *----------------------------------------------------------------------------*/ | |
115 | ||
116 | static commonNaNT float16ToCommonNaN( float16 a STATUS_PARAM ) | |
117 | { | |
118 | commonNaNT z; | |
119 | ||
120 | if ( float16_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR ); | |
121 | z.sign = float16_val(a) >> 15; | |
122 | z.low = 0; | |
123 | z.high = ((uint64_t) float16_val(a))<<54; | |
124 | return z; | |
125 | } | |
126 | ||
127 | /*---------------------------------------------------------------------------- | |
128 | | Returns the result of converting the canonical NaN `a' to the half- | |
129 | | precision floating-point format. | |
130 | *----------------------------------------------------------------------------*/ | |
131 | ||
132 | static float16 commonNaNToFloat16(commonNaNT a STATUS_PARAM) | |
133 | { | |
134 | uint16_t mantissa = a.high>>54; | |
135 | ||
136 | if (STATUS(default_nan_mode)) { | |
137 | return float16_default_nan; | |
138 | } | |
139 | ||
140 | if (mantissa) { | |
141 | return make_float16(((((uint16_t) a.sign) << 15) | |
142 | | (0x1F << 10) | mantissa)); | |
143 | } else { | |
144 | return float16_default_nan; | |
145 | } | |
146 | } | |
147 | ||
148 | /*---------------------------------------------------------------------------- | |
149 | | Returns 1 if the single-precision floating-point value `a' is a quiet | |
150 | | NaN; otherwise returns 0. | |
151 | *----------------------------------------------------------------------------*/ | |
152 | ||
153 | int float32_is_quiet_nan( float32 a_ ) | |
154 | { | |
155 | uint32_t a = float32_val(a_); | |
156 | #if SNAN_BIT_IS_ONE | |
157 | return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF ); | |
158 | #else | |
159 | return ( 0xFF800000 <= (uint32_t) ( a<<1 ) ); | |
160 | #endif | |
161 | } | |
162 | ||
163 | /*---------------------------------------------------------------------------- | |
164 | | Returns 1 if the single-precision floating-point value `a' is a signaling | |
165 | | NaN; otherwise returns 0. | |
166 | *----------------------------------------------------------------------------*/ | |
167 | ||
168 | int float32_is_signaling_nan( float32 a_ ) | |
169 | { | |
170 | uint32_t a = float32_val(a_); | |
171 | #if SNAN_BIT_IS_ONE | |
172 | return ( 0xFF800000 <= (uint32_t) ( a<<1 ) ); | |
173 | #else | |
174 | return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF ); | |
175 | #endif | |
176 | } | |
177 | ||
178 | /*---------------------------------------------------------------------------- | |
179 | | Returns a quiet NaN if the single-precision floating point value `a' is a | |
180 | | signaling NaN; otherwise returns `a'. | |
181 | *----------------------------------------------------------------------------*/ | |
182 | ||
183 | float32 float32_maybe_silence_nan( float32 a_ ) | |
184 | { | |
185 | if (float32_is_signaling_nan(a_)) { | |
186 | #if SNAN_BIT_IS_ONE | |
187 | # if defined(TARGET_MIPS) || defined(TARGET_SH4) || defined(TARGET_UNICORE32) | |
188 | return float32_default_nan; | |
189 | # else | |
190 | # error Rules for silencing a signaling NaN are target-specific | |
191 | # endif | |
192 | #else | |
193 | uint32_t a = float32_val(a_); | |
194 | a |= (1 << 22); | |
195 | return make_float32(a); | |
196 | #endif | |
197 | } | |
198 | return a_; | |
199 | } | |
200 | ||
201 | /*---------------------------------------------------------------------------- | |
202 | | Returns the result of converting the single-precision floating-point NaN | |
203 | | `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid | |
204 | | exception is raised. | |
205 | *----------------------------------------------------------------------------*/ | |
206 | ||
207 | static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM ) | |
208 | { | |
209 | commonNaNT z; | |
210 | ||
211 | if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR ); | |
212 | z.sign = float32_val(a)>>31; | |
213 | z.low = 0; | |
214 | z.high = ( (uint64_t) float32_val(a) )<<41; | |
215 | return z; | |
216 | } | |
217 | ||
218 | /*---------------------------------------------------------------------------- | |
219 | | Returns the result of converting the canonical NaN `a' to the single- | |
220 | | precision floating-point format. | |
221 | *----------------------------------------------------------------------------*/ | |
222 | ||
223 | static float32 commonNaNToFloat32( commonNaNT a STATUS_PARAM) | |
224 | { | |
225 | uint32_t mantissa = a.high>>41; | |
226 | ||
227 | if ( STATUS(default_nan_mode) ) { | |
228 | return float32_default_nan; | |
229 | } | |
230 | ||
231 | if ( mantissa ) | |
232 | return make_float32( | |
233 | ( ( (uint32_t) a.sign )<<31 ) | 0x7F800000 | ( a.high>>41 ) ); | |
234 | else | |
235 | return float32_default_nan; | |
236 | } | |
237 | ||
238 | /*---------------------------------------------------------------------------- | |
239 | | Select which NaN to propagate for a two-input operation. | |
240 | | IEEE754 doesn't specify all the details of this, so the | |
241 | | algorithm is target-specific. | |
242 | | The routine is passed various bits of information about the | |
243 | | two NaNs and should return 0 to select NaN a and 1 for NaN b. | |
244 | | Note that signalling NaNs are always squashed to quiet NaNs | |
245 | | by the caller, by calling floatXX_maybe_silence_nan() before | |
246 | | returning them. | |
247 | | | |
248 | | aIsLargerSignificand is only valid if both a and b are NaNs | |
249 | | of some kind, and is true if a has the larger significand, | |
250 | | or if both a and b have the same significand but a is | |
251 | | positive but b is negative. It is only needed for the x87 | |
252 | | tie-break rule. | |
253 | *----------------------------------------------------------------------------*/ | |
254 | ||
255 | #if defined(TARGET_ARM) | |
256 | static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN, | |
257 | flag aIsLargerSignificand) | |
258 | { | |
259 | /* ARM mandated NaN propagation rules: take the first of: | |
260 | * 1. A if it is signaling | |
261 | * 2. B if it is signaling | |
262 | * 3. A (quiet) | |
263 | * 4. B (quiet) | |
264 | * A signaling NaN is always quietened before returning it. | |
265 | */ | |
266 | if (aIsSNaN) { | |
267 | return 0; | |
268 | } else if (bIsSNaN) { | |
269 | return 1; | |
270 | } else if (aIsQNaN) { | |
271 | return 0; | |
272 | } else { | |
273 | return 1; | |
274 | } | |
275 | } | |
276 | #elif defined(TARGET_MIPS) | |
277 | static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN, | |
278 | flag aIsLargerSignificand) | |
279 | { | |
280 | /* According to MIPS specifications, if one of the two operands is | |
281 | * a sNaN, a new qNaN has to be generated. This is done in | |
282 | * floatXX_maybe_silence_nan(). For qNaN inputs the specifications | |
283 | * says: "When possible, this QNaN result is one of the operand QNaN | |
284 | * values." In practice it seems that most implementations choose | |
285 | * the first operand if both operands are qNaN. In short this gives | |
286 | * the following rules: | |
287 | * 1. A if it is signaling | |
288 | * 2. B if it is signaling | |
289 | * 3. A (quiet) | |
290 | * 4. B (quiet) | |
291 | * A signaling NaN is always silenced before returning it. | |
292 | */ | |
293 | if (aIsSNaN) { | |
294 | return 0; | |
295 | } else if (bIsSNaN) { | |
296 | return 1; | |
297 | } else if (aIsQNaN) { | |
298 | return 0; | |
299 | } else { | |
300 | return 1; | |
301 | } | |
302 | } | |
303 | #elif defined(TARGET_PPC) | |
304 | static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN, | |
305 | flag aIsLargerSignificand) | |
306 | { | |
307 | /* PowerPC propagation rules: | |
308 | * 1. A if it sNaN or qNaN | |
309 | * 2. B if it sNaN or qNaN | |
310 | * A signaling NaN is always silenced before returning it. | |
311 | */ | |
312 | if (aIsSNaN || aIsQNaN) { | |
313 | return 0; | |
314 | } else { | |
315 | return 1; | |
316 | } | |
317 | } | |
318 | #else | |
319 | static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN, | |
320 | flag aIsLargerSignificand) | |
321 | { | |
322 | /* This implements x87 NaN propagation rules: | |
323 | * SNaN + QNaN => return the QNaN | |
324 | * two SNaNs => return the one with the larger significand, silenced | |
325 | * two QNaNs => return the one with the larger significand | |
326 | * SNaN and a non-NaN => return the SNaN, silenced | |
327 | * QNaN and a non-NaN => return the QNaN | |
328 | * | |
329 | * If we get down to comparing significands and they are the same, | |
330 | * return the NaN with the positive sign bit (if any). | |
331 | */ | |
332 | if (aIsSNaN) { | |
333 | if (bIsSNaN) { | |
334 | return aIsLargerSignificand ? 0 : 1; | |
335 | } | |
336 | return bIsQNaN ? 1 : 0; | |
337 | } | |
338 | else if (aIsQNaN) { | |
339 | if (bIsSNaN || !bIsQNaN) | |
340 | return 0; | |
341 | else { | |
342 | return aIsLargerSignificand ? 0 : 1; | |
343 | } | |
344 | } else { | |
345 | return 1; | |
346 | } | |
347 | } | |
348 | #endif | |
349 | ||
350 | /*---------------------------------------------------------------------------- | |
351 | | Takes two single-precision floating-point values `a' and `b', one of which | |
352 | | is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a | |
353 | | signaling NaN, the invalid exception is raised. | |
354 | *----------------------------------------------------------------------------*/ | |
355 | ||
356 | static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM) | |
357 | { | |
358 | flag aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN; | |
359 | flag aIsLargerSignificand; | |
360 | uint32_t av, bv; | |
361 | ||
362 | aIsQuietNaN = float32_is_quiet_nan( a ); | |
363 | aIsSignalingNaN = float32_is_signaling_nan( a ); | |
364 | bIsQuietNaN = float32_is_quiet_nan( b ); | |
365 | bIsSignalingNaN = float32_is_signaling_nan( b ); | |
366 | av = float32_val(a); | |
367 | bv = float32_val(b); | |
368 | ||
369 | if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); | |
370 | ||
371 | if ( STATUS(default_nan_mode) ) | |
372 | return float32_default_nan; | |
373 | ||
374 | if ((uint32_t)(av<<1) < (uint32_t)(bv<<1)) { | |
375 | aIsLargerSignificand = 0; | |
376 | } else if ((uint32_t)(bv<<1) < (uint32_t)(av<<1)) { | |
377 | aIsLargerSignificand = 1; | |
378 | } else { | |
379 | aIsLargerSignificand = (av < bv) ? 1 : 0; | |
380 | } | |
381 | ||
382 | if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN, | |
383 | aIsLargerSignificand)) { | |
384 | return float32_maybe_silence_nan(b); | |
385 | } else { | |
386 | return float32_maybe_silence_nan(a); | |
387 | } | |
388 | } | |
389 | ||
390 | /*---------------------------------------------------------------------------- | |
391 | | Returns 1 if the double-precision floating-point value `a' is a quiet | |
392 | | NaN; otherwise returns 0. | |
393 | *----------------------------------------------------------------------------*/ | |
394 | ||
395 | int float64_is_quiet_nan( float64 a_ ) | |
396 | { | |
397 | uint64_t a = float64_val(a_); | |
398 | #if SNAN_BIT_IS_ONE | |
399 | return | |
400 | ( ( ( a>>51 ) & 0xFFF ) == 0xFFE ) | |
401 | && ( a & LIT64( 0x0007FFFFFFFFFFFF ) ); | |
402 | #else | |
403 | return ( LIT64( 0xFFF0000000000000 ) <= (uint64_t) ( a<<1 ) ); | |
404 | #endif | |
405 | } | |
406 | ||
407 | /*---------------------------------------------------------------------------- | |
408 | | Returns 1 if the double-precision floating-point value `a' is a signaling | |
409 | | NaN; otherwise returns 0. | |
410 | *----------------------------------------------------------------------------*/ | |
411 | ||
412 | int float64_is_signaling_nan( float64 a_ ) | |
413 | { | |
414 | uint64_t a = float64_val(a_); | |
415 | #if SNAN_BIT_IS_ONE | |
416 | return ( LIT64( 0xFFF0000000000000 ) <= (uint64_t) ( a<<1 ) ); | |
417 | #else | |
418 | return | |
419 | ( ( ( a>>51 ) & 0xFFF ) == 0xFFE ) | |
420 | && ( a & LIT64( 0x0007FFFFFFFFFFFF ) ); | |
421 | #endif | |
422 | } | |
423 | ||
424 | /*---------------------------------------------------------------------------- | |
425 | | Returns a quiet NaN if the double-precision floating point value `a' is a | |
426 | | signaling NaN; otherwise returns `a'. | |
427 | *----------------------------------------------------------------------------*/ | |
428 | ||
429 | float64 float64_maybe_silence_nan( float64 a_ ) | |
430 | { | |
431 | if (float64_is_signaling_nan(a_)) { | |
432 | #if SNAN_BIT_IS_ONE | |
433 | # if defined(TARGET_MIPS) || defined(TARGET_SH4) || defined(TARGET_UNICORE32) | |
434 | return float64_default_nan; | |
435 | # else | |
436 | # error Rules for silencing a signaling NaN are target-specific | |
437 | # endif | |
438 | #else | |
439 | uint64_t a = float64_val(a_); | |
440 | a |= LIT64( 0x0008000000000000 ); | |
441 | return make_float64(a); | |
442 | #endif | |
443 | } | |
444 | return a_; | |
445 | } | |
446 | ||
447 | /*---------------------------------------------------------------------------- | |
448 | | Returns the result of converting the double-precision floating-point NaN | |
449 | | `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid | |
450 | | exception is raised. | |
451 | *----------------------------------------------------------------------------*/ | |
452 | ||
453 | static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM) | |
454 | { | |
455 | commonNaNT z; | |
456 | ||
457 | if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR); | |
458 | z.sign = float64_val(a)>>63; | |
459 | z.low = 0; | |
460 | z.high = float64_val(a)<<12; | |
461 | return z; | |
462 | } | |
463 | ||
464 | /*---------------------------------------------------------------------------- | |
465 | | Returns the result of converting the canonical NaN `a' to the double- | |
466 | | precision floating-point format. | |
467 | *----------------------------------------------------------------------------*/ | |
468 | ||
469 | static float64 commonNaNToFloat64( commonNaNT a STATUS_PARAM) | |
470 | { | |
471 | uint64_t mantissa = a.high>>12; | |
472 | ||
473 | if ( STATUS(default_nan_mode) ) { | |
474 | return float64_default_nan; | |
475 | } | |
476 | ||
477 | if ( mantissa ) | |
478 | return make_float64( | |
479 | ( ( (uint64_t) a.sign )<<63 ) | |
480 | | LIT64( 0x7FF0000000000000 ) | |
481 | | ( a.high>>12 )); | |
482 | else | |
483 | return float64_default_nan; | |
484 | } | |
485 | ||
486 | /*---------------------------------------------------------------------------- | |
487 | | Takes two double-precision floating-point values `a' and `b', one of which | |
488 | | is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a | |
489 | | signaling NaN, the invalid exception is raised. | |
490 | *----------------------------------------------------------------------------*/ | |
491 | ||
492 | static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM) | |
493 | { | |
494 | flag aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN; | |
495 | flag aIsLargerSignificand; | |
496 | uint64_t av, bv; | |
497 | ||
498 | aIsQuietNaN = float64_is_quiet_nan( a ); | |
499 | aIsSignalingNaN = float64_is_signaling_nan( a ); | |
500 | bIsQuietNaN = float64_is_quiet_nan( b ); | |
501 | bIsSignalingNaN = float64_is_signaling_nan( b ); | |
502 | av = float64_val(a); | |
503 | bv = float64_val(b); | |
504 | ||
505 | if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); | |
506 | ||
507 | if ( STATUS(default_nan_mode) ) | |
508 | return float64_default_nan; | |
509 | ||
510 | if ((uint64_t)(av<<1) < (uint64_t)(bv<<1)) { | |
511 | aIsLargerSignificand = 0; | |
512 | } else if ((uint64_t)(bv<<1) < (uint64_t)(av<<1)) { | |
513 | aIsLargerSignificand = 1; | |
514 | } else { | |
515 | aIsLargerSignificand = (av < bv) ? 1 : 0; | |
516 | } | |
517 | ||
518 | if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN, | |
519 | aIsLargerSignificand)) { | |
520 | return float64_maybe_silence_nan(b); | |
521 | } else { | |
522 | return float64_maybe_silence_nan(a); | |
523 | } | |
524 | } | |
525 | ||
526 | #ifdef FLOATX80 | |
527 | ||
528 | /*---------------------------------------------------------------------------- | |
529 | | Returns 1 if the extended double-precision floating-point value `a' is a | |
530 | | quiet NaN; otherwise returns 0. This slightly differs from the same | |
531 | | function for other types as floatx80 has an explicit bit. | |
532 | *----------------------------------------------------------------------------*/ | |
533 | ||
534 | int floatx80_is_quiet_nan( floatx80 a ) | |
535 | { | |
536 | #if SNAN_BIT_IS_ONE | |
537 | uint64_t aLow; | |
538 | ||
539 | aLow = a.low & ~ LIT64( 0x4000000000000000 ); | |
540 | return | |
541 | ( ( a.high & 0x7FFF ) == 0x7FFF ) | |
542 | && (uint64_t) ( aLow<<1 ) | |
543 | && ( a.low == aLow ); | |
544 | #else | |
545 | return ( ( a.high & 0x7FFF ) == 0x7FFF ) | |
546 | && (LIT64( 0x8000000000000000 ) <= ((uint64_t) ( a.low<<1 ))); | |
547 | #endif | |
548 | } | |
549 | ||
550 | /*---------------------------------------------------------------------------- | |
551 | | Returns 1 if the extended double-precision floating-point value `a' is a | |
552 | | signaling NaN; otherwise returns 0. This slightly differs from the same | |
553 | | function for other types as floatx80 has an explicit bit. | |
554 | *----------------------------------------------------------------------------*/ | |
555 | ||
556 | int floatx80_is_signaling_nan( floatx80 a ) | |
557 | { | |
558 | #if SNAN_BIT_IS_ONE | |
559 | return ( ( a.high & 0x7FFF ) == 0x7FFF ) | |
560 | && (LIT64( 0x8000000000000000 ) <= ((uint64_t) ( a.low<<1 ))); | |
561 | #else | |
562 | uint64_t aLow; | |
563 | ||
564 | aLow = a.low & ~ LIT64( 0x4000000000000000 ); | |
565 | return | |
566 | ( ( a.high & 0x7FFF ) == 0x7FFF ) | |
567 | && (uint64_t) ( aLow<<1 ) | |
568 | && ( a.low == aLow ); | |
569 | #endif | |
570 | } | |
571 | ||
572 | /*---------------------------------------------------------------------------- | |
573 | | Returns a quiet NaN if the extended double-precision floating point value | |
574 | | `a' is a signaling NaN; otherwise returns `a'. | |
575 | *----------------------------------------------------------------------------*/ | |
576 | ||
577 | floatx80 floatx80_maybe_silence_nan( floatx80 a ) | |
578 | { | |
579 | if (floatx80_is_signaling_nan(a)) { | |
580 | #if SNAN_BIT_IS_ONE | |
581 | # if defined(TARGET_MIPS) || defined(TARGET_SH4) || defined(TARGET_UNICORE32) | |
582 | a.low = floatx80_default_nan_low; | |
583 | a.high = floatx80_default_nan_high; | |
584 | # else | |
585 | # error Rules for silencing a signaling NaN are target-specific | |
586 | # endif | |
587 | #else | |
588 | a.low |= LIT64( 0xC000000000000000 ); | |
589 | return a; | |
590 | #endif | |
591 | } | |
592 | return a; | |
593 | } | |
594 | ||
595 | /*---------------------------------------------------------------------------- | |
596 | | Returns the result of converting the extended double-precision floating- | |
597 | | point NaN `a' to the canonical NaN format. If `a' is a signaling NaN, the | |
598 | | invalid exception is raised. | |
599 | *----------------------------------------------------------------------------*/ | |
600 | ||
601 | static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM) | |
602 | { | |
603 | commonNaNT z; | |
604 | ||
605 | if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR); | |
606 | if ( a.low >> 63 ) { | |
607 | z.sign = a.high >> 15; | |
608 | z.low = 0; | |
609 | z.high = a.low << 1; | |
610 | } else { | |
611 | z.sign = floatx80_default_nan_high >> 15; | |
612 | z.low = 0; | |
613 | z.high = floatx80_default_nan_low << 1; | |
614 | } | |
615 | return z; | |
616 | } | |
617 | ||
618 | /*---------------------------------------------------------------------------- | |
619 | | Returns the result of converting the canonical NaN `a' to the extended | |
620 | | double-precision floating-point format. | |
621 | *----------------------------------------------------------------------------*/ | |
622 | ||
623 | static floatx80 commonNaNToFloatx80( commonNaNT a STATUS_PARAM) | |
624 | { | |
625 | floatx80 z; | |
626 | ||
627 | if ( STATUS(default_nan_mode) ) { | |
628 | z.low = floatx80_default_nan_low; | |
629 | z.high = floatx80_default_nan_high; | |
630 | return z; | |
631 | } | |
632 | ||
633 | if (a.high >> 1) { | |
634 | z.low = LIT64( 0x8000000000000000 ) | a.high >> 1; | |
635 | z.high = ( ( (uint16_t) a.sign )<<15 ) | 0x7FFF; | |
636 | } else { | |
637 | z.low = floatx80_default_nan_low; | |
638 | z.high = floatx80_default_nan_high; | |
639 | } | |
640 | ||
641 | return z; | |
642 | } | |
643 | ||
644 | /*---------------------------------------------------------------------------- | |
645 | | Takes two extended double-precision floating-point values `a' and `b', one | |
646 | | of which is a NaN, and returns the appropriate NaN result. If either `a' or | |
647 | | `b' is a signaling NaN, the invalid exception is raised. | |
648 | *----------------------------------------------------------------------------*/ | |
649 | ||
650 | static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM) | |
651 | { | |
652 | flag aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN; | |
653 | flag aIsLargerSignificand; | |
654 | ||
655 | aIsQuietNaN = floatx80_is_quiet_nan( a ); | |
656 | aIsSignalingNaN = floatx80_is_signaling_nan( a ); | |
657 | bIsQuietNaN = floatx80_is_quiet_nan( b ); | |
658 | bIsSignalingNaN = floatx80_is_signaling_nan( b ); | |
659 | ||
660 | if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); | |
661 | ||
662 | if ( STATUS(default_nan_mode) ) { | |
663 | a.low = floatx80_default_nan_low; | |
664 | a.high = floatx80_default_nan_high; | |
665 | return a; | |
666 | } | |
667 | ||
668 | if (a.low < b.low) { | |
669 | aIsLargerSignificand = 0; | |
670 | } else if (b.low < a.low) { | |
671 | aIsLargerSignificand = 1; | |
672 | } else { | |
673 | aIsLargerSignificand = (a.high < b.high) ? 1 : 0; | |
674 | } | |
675 | ||
676 | if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN, | |
677 | aIsLargerSignificand)) { | |
678 | return floatx80_maybe_silence_nan(b); | |
679 | } else { | |
680 | return floatx80_maybe_silence_nan(a); | |
681 | } | |
682 | } | |
683 | ||
684 | #endif | |
685 | ||
686 | #ifdef FLOAT128 | |
687 | ||
688 | /*---------------------------------------------------------------------------- | |
689 | | Returns 1 if the quadruple-precision floating-point value `a' is a quiet | |
690 | | NaN; otherwise returns 0. | |
691 | *----------------------------------------------------------------------------*/ | |
692 | ||
693 | int float128_is_quiet_nan( float128 a ) | |
694 | { | |
695 | #if SNAN_BIT_IS_ONE | |
696 | return | |
697 | ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE ) | |
698 | && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) ); | |
699 | #else | |
700 | return | |
701 | ( LIT64( 0xFFFE000000000000 ) <= (uint64_t) ( a.high<<1 ) ) | |
702 | && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) ); | |
703 | #endif | |
704 | } | |
705 | ||
706 | /*---------------------------------------------------------------------------- | |
707 | | Returns 1 if the quadruple-precision floating-point value `a' is a | |
708 | | signaling NaN; otherwise returns 0. | |
709 | *----------------------------------------------------------------------------*/ | |
710 | ||
711 | int float128_is_signaling_nan( float128 a ) | |
712 | { | |
713 | #if SNAN_BIT_IS_ONE | |
714 | return | |
715 | ( LIT64( 0xFFFE000000000000 ) <= (uint64_t) ( a.high<<1 ) ) | |
716 | && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) ); | |
717 | #else | |
718 | return | |
719 | ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE ) | |
720 | && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) ); | |
721 | #endif | |
722 | } | |
723 | ||
724 | /*---------------------------------------------------------------------------- | |
725 | | Returns a quiet NaN if the quadruple-precision floating point value `a' is | |
726 | | a signaling NaN; otherwise returns `a'. | |
727 | *----------------------------------------------------------------------------*/ | |
728 | ||
729 | float128 float128_maybe_silence_nan( float128 a ) | |
730 | { | |
731 | if (float128_is_signaling_nan(a)) { | |
732 | #if SNAN_BIT_IS_ONE | |
733 | # if defined(TARGET_MIPS) || defined(TARGET_SH4) || defined(TARGET_UNICORE32) | |
734 | a.low = float128_default_nan_low; | |
735 | a.high = float128_default_nan_high; | |
736 | # else | |
737 | # error Rules for silencing a signaling NaN are target-specific | |
738 | # endif | |
739 | #else | |
740 | a.high |= LIT64( 0x0000800000000000 ); | |
741 | return a; | |
742 | #endif | |
743 | } | |
744 | return a; | |
745 | } | |
746 | ||
747 | /*---------------------------------------------------------------------------- | |
748 | | Returns the result of converting the quadruple-precision floating-point NaN | |
749 | | `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid | |
750 | | exception is raised. | |
751 | *----------------------------------------------------------------------------*/ | |
752 | ||
753 | static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM) | |
754 | { | |
755 | commonNaNT z; | |
756 | ||
757 | if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR); | |
758 | z.sign = a.high>>63; | |
759 | shortShift128Left( a.high, a.low, 16, &z.high, &z.low ); | |
760 | return z; | |
761 | } | |
762 | ||
763 | /*---------------------------------------------------------------------------- | |
764 | | Returns the result of converting the canonical NaN `a' to the quadruple- | |
765 | | precision floating-point format. | |
766 | *----------------------------------------------------------------------------*/ | |
767 | ||
768 | static float128 commonNaNToFloat128( commonNaNT a STATUS_PARAM) | |
769 | { | |
770 | float128 z; | |
771 | ||
772 | if ( STATUS(default_nan_mode) ) { | |
773 | z.low = float128_default_nan_low; | |
774 | z.high = float128_default_nan_high; | |
775 | return z; | |
776 | } | |
777 | ||
778 | shift128Right( a.high, a.low, 16, &z.high, &z.low ); | |
779 | z.high |= ( ( (uint64_t) a.sign )<<63 ) | LIT64( 0x7FFF000000000000 ); | |
780 | return z; | |
781 | } | |
782 | ||
783 | /*---------------------------------------------------------------------------- | |
784 | | Takes two quadruple-precision floating-point values `a' and `b', one of | |
785 | | which is a NaN, and returns the appropriate NaN result. If either `a' or | |
786 | | `b' is a signaling NaN, the invalid exception is raised. | |
787 | *----------------------------------------------------------------------------*/ | |
788 | ||
789 | static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM) | |
790 | { | |
791 | flag aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN; | |
792 | flag aIsLargerSignificand; | |
793 | ||
794 | aIsQuietNaN = float128_is_quiet_nan( a ); | |
795 | aIsSignalingNaN = float128_is_signaling_nan( a ); | |
796 | bIsQuietNaN = float128_is_quiet_nan( b ); | |
797 | bIsSignalingNaN = float128_is_signaling_nan( b ); | |
798 | ||
799 | if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); | |
800 | ||
801 | if ( STATUS(default_nan_mode) ) { | |
802 | a.low = float128_default_nan_low; | |
803 | a.high = float128_default_nan_high; | |
804 | return a; | |
805 | } | |
806 | ||
807 | if (lt128(a.high<<1, a.low, b.high<<1, b.low)) { | |
808 | aIsLargerSignificand = 0; | |
809 | } else if (lt128(b.high<<1, b.low, a.high<<1, a.low)) { | |
810 | aIsLargerSignificand = 1; | |
811 | } else { | |
812 | aIsLargerSignificand = (a.high < b.high) ? 1 : 0; | |
813 | } | |
814 | ||
815 | if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN, | |
816 | aIsLargerSignificand)) { | |
817 | return float128_maybe_silence_nan(b); | |
818 | } else { | |
819 | return float128_maybe_silence_nan(a); | |
820 | } | |
821 | } | |
822 | ||
823 | #endif |