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Commit | Line | Data |
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8d725fac AF |
1 | /* |
2 | * QEMU float support | |
3 | * | |
4 | * Derived from SoftFloat. | |
5 | */ | |
158142c2 FB |
6 | |
7 | /*============================================================================ | |
8 | ||
9 | This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic | |
10 | 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 | #include "softfloat.h" | |
39 | ||
40 | /*---------------------------------------------------------------------------- | |
41 | | Primitive arithmetic functions, including multi-word arithmetic, and | |
42 | | division and square root approximations. (Can be specialized to target if | |
43 | | desired.) | |
44 | *----------------------------------------------------------------------------*/ | |
45 | #include "softfloat-macros.h" | |
46 | ||
47 | /*---------------------------------------------------------------------------- | |
48 | | Functions and definitions to determine: (1) whether tininess for underflow | |
49 | | is detected before or after rounding by default, (2) what (if anything) | |
50 | | happens when exceptions are raised, (3) how signaling NaNs are distinguished | |
51 | | from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs | |
52 | | are propagated from function inputs to output. These details are target- | |
53 | | specific. | |
54 | *----------------------------------------------------------------------------*/ | |
55 | #include "softfloat-specialize.h" | |
56 | ||
57 | void set_float_rounding_mode(int val STATUS_PARAM) | |
58 | { | |
59 | STATUS(float_rounding_mode) = val; | |
60 | } | |
61 | ||
1d6bda35 FB |
62 | void set_float_exception_flags(int val STATUS_PARAM) |
63 | { | |
64 | STATUS(float_exception_flags) = val; | |
65 | } | |
66 | ||
158142c2 FB |
67 | #ifdef FLOATX80 |
68 | void set_floatx80_rounding_precision(int val STATUS_PARAM) | |
69 | { | |
70 | STATUS(floatx80_rounding_precision) = val; | |
71 | } | |
72 | #endif | |
73 | ||
bb4d4bb3 PM |
74 | /*---------------------------------------------------------------------------- |
75 | | Returns the fraction bits of the half-precision floating-point value `a'. | |
76 | *----------------------------------------------------------------------------*/ | |
77 | ||
78 | INLINE uint32_t extractFloat16Frac(float16 a) | |
79 | { | |
80 | return float16_val(a) & 0x3ff; | |
81 | } | |
82 | ||
83 | /*---------------------------------------------------------------------------- | |
84 | | Returns the exponent bits of the half-precision floating-point value `a'. | |
85 | *----------------------------------------------------------------------------*/ | |
86 | ||
87 | INLINE int16 extractFloat16Exp(float16 a) | |
88 | { | |
89 | return (float16_val(a) >> 10) & 0x1f; | |
90 | } | |
91 | ||
92 | /*---------------------------------------------------------------------------- | |
93 | | Returns the sign bit of the single-precision floating-point value `a'. | |
94 | *----------------------------------------------------------------------------*/ | |
95 | ||
96 | INLINE flag extractFloat16Sign(float16 a) | |
97 | { | |
98 | return float16_val(a)>>15; | |
99 | } | |
100 | ||
158142c2 FB |
101 | /*---------------------------------------------------------------------------- |
102 | | Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 | |
103 | | and 7, and returns the properly rounded 32-bit integer corresponding to the | |
104 | | input. If `zSign' is 1, the input is negated before being converted to an | |
105 | | integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input | |
106 | | is simply rounded to an integer, with the inexact exception raised if the | |
107 | | input cannot be represented exactly as an integer. However, if the fixed- | |
108 | | point input is too large, the invalid exception is raised and the largest | |
109 | | positive or negative integer is returned. | |
110 | *----------------------------------------------------------------------------*/ | |
111 | ||
bb98fe42 | 112 | static int32 roundAndPackInt32( flag zSign, uint64_t absZ STATUS_PARAM) |
158142c2 FB |
113 | { |
114 | int8 roundingMode; | |
115 | flag roundNearestEven; | |
116 | int8 roundIncrement, roundBits; | |
117 | int32 z; | |
118 | ||
119 | roundingMode = STATUS(float_rounding_mode); | |
120 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
121 | roundIncrement = 0x40; | |
122 | if ( ! roundNearestEven ) { | |
123 | if ( roundingMode == float_round_to_zero ) { | |
124 | roundIncrement = 0; | |
125 | } | |
126 | else { | |
127 | roundIncrement = 0x7F; | |
128 | if ( zSign ) { | |
129 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
130 | } | |
131 | else { | |
132 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
133 | } | |
134 | } | |
135 | } | |
136 | roundBits = absZ & 0x7F; | |
137 | absZ = ( absZ + roundIncrement )>>7; | |
138 | absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); | |
139 | z = absZ; | |
140 | if ( zSign ) z = - z; | |
141 | if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) { | |
142 | float_raise( float_flag_invalid STATUS_VAR); | |
bb98fe42 | 143 | return zSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
158142c2 FB |
144 | } |
145 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
146 | return z; | |
147 | ||
148 | } | |
149 | ||
150 | /*---------------------------------------------------------------------------- | |
151 | | Takes the 128-bit fixed-point value formed by concatenating `absZ0' and | |
152 | | `absZ1', with binary point between bits 63 and 64 (between the input words), | |
153 | | and returns the properly rounded 64-bit integer corresponding to the input. | |
154 | | If `zSign' is 1, the input is negated before being converted to an integer. | |
155 | | Ordinarily, the fixed-point input is simply rounded to an integer, with | |
156 | | the inexact exception raised if the input cannot be represented exactly as | |
157 | | an integer. However, if the fixed-point input is too large, the invalid | |
158 | | exception is raised and the largest positive or negative integer is | |
159 | | returned. | |
160 | *----------------------------------------------------------------------------*/ | |
161 | ||
bb98fe42 | 162 | static int64 roundAndPackInt64( flag zSign, uint64_t absZ0, uint64_t absZ1 STATUS_PARAM) |
158142c2 FB |
163 | { |
164 | int8 roundingMode; | |
165 | flag roundNearestEven, increment; | |
166 | int64 z; | |
167 | ||
168 | roundingMode = STATUS(float_rounding_mode); | |
169 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
bb98fe42 | 170 | increment = ( (int64_t) absZ1 < 0 ); |
158142c2 FB |
171 | if ( ! roundNearestEven ) { |
172 | if ( roundingMode == float_round_to_zero ) { | |
173 | increment = 0; | |
174 | } | |
175 | else { | |
176 | if ( zSign ) { | |
177 | increment = ( roundingMode == float_round_down ) && absZ1; | |
178 | } | |
179 | else { | |
180 | increment = ( roundingMode == float_round_up ) && absZ1; | |
181 | } | |
182 | } | |
183 | } | |
184 | if ( increment ) { | |
185 | ++absZ0; | |
186 | if ( absZ0 == 0 ) goto overflow; | |
bb98fe42 | 187 | absZ0 &= ~ ( ( (uint64_t) ( absZ1<<1 ) == 0 ) & roundNearestEven ); |
158142c2 FB |
188 | } |
189 | z = absZ0; | |
190 | if ( zSign ) z = - z; | |
191 | if ( z && ( ( z < 0 ) ^ zSign ) ) { | |
192 | overflow: | |
193 | float_raise( float_flag_invalid STATUS_VAR); | |
194 | return | |
bb98fe42 | 195 | zSign ? (int64_t) LIT64( 0x8000000000000000 ) |
158142c2 FB |
196 | : LIT64( 0x7FFFFFFFFFFFFFFF ); |
197 | } | |
198 | if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
199 | return z; | |
200 | ||
201 | } | |
202 | ||
203 | /*---------------------------------------------------------------------------- | |
204 | | Returns the fraction bits of the single-precision floating-point value `a'. | |
205 | *----------------------------------------------------------------------------*/ | |
206 | ||
bb98fe42 | 207 | INLINE uint32_t extractFloat32Frac( float32 a ) |
158142c2 FB |
208 | { |
209 | ||
f090c9d4 | 210 | return float32_val(a) & 0x007FFFFF; |
158142c2 FB |
211 | |
212 | } | |
213 | ||
214 | /*---------------------------------------------------------------------------- | |
215 | | Returns the exponent bits of the single-precision floating-point value `a'. | |
216 | *----------------------------------------------------------------------------*/ | |
217 | ||
218 | INLINE int16 extractFloat32Exp( float32 a ) | |
219 | { | |
220 | ||
f090c9d4 | 221 | return ( float32_val(a)>>23 ) & 0xFF; |
158142c2 FB |
222 | |
223 | } | |
224 | ||
225 | /*---------------------------------------------------------------------------- | |
226 | | Returns the sign bit of the single-precision floating-point value `a'. | |
227 | *----------------------------------------------------------------------------*/ | |
228 | ||
229 | INLINE flag extractFloat32Sign( float32 a ) | |
230 | { | |
231 | ||
f090c9d4 | 232 | return float32_val(a)>>31; |
158142c2 FB |
233 | |
234 | } | |
235 | ||
37d18660 PM |
236 | /*---------------------------------------------------------------------------- |
237 | | If `a' is denormal and we are in flush-to-zero mode then set the | |
238 | | input-denormal exception and return zero. Otherwise just return the value. | |
239 | *----------------------------------------------------------------------------*/ | |
240 | static float32 float32_squash_input_denormal(float32 a STATUS_PARAM) | |
241 | { | |
242 | if (STATUS(flush_inputs_to_zero)) { | |
243 | if (extractFloat32Exp(a) == 0 && extractFloat32Frac(a) != 0) { | |
244 | float_raise(float_flag_input_denormal STATUS_VAR); | |
245 | return make_float32(float32_val(a) & 0x80000000); | |
246 | } | |
247 | } | |
248 | return a; | |
249 | } | |
250 | ||
158142c2 FB |
251 | /*---------------------------------------------------------------------------- |
252 | | Normalizes the subnormal single-precision floating-point value represented | |
253 | | by the denormalized significand `aSig'. The normalized exponent and | |
254 | | significand are stored at the locations pointed to by `zExpPtr' and | |
255 | | `zSigPtr', respectively. | |
256 | *----------------------------------------------------------------------------*/ | |
257 | ||
258 | static void | |
bb98fe42 | 259 | normalizeFloat32Subnormal( uint32_t aSig, int16 *zExpPtr, uint32_t *zSigPtr ) |
158142c2 FB |
260 | { |
261 | int8 shiftCount; | |
262 | ||
263 | shiftCount = countLeadingZeros32( aSig ) - 8; | |
264 | *zSigPtr = aSig<<shiftCount; | |
265 | *zExpPtr = 1 - shiftCount; | |
266 | ||
267 | } | |
268 | ||
269 | /*---------------------------------------------------------------------------- | |
270 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
271 | | single-precision floating-point value, returning the result. After being | |
272 | | shifted into the proper positions, the three fields are simply added | |
273 | | together to form the result. This means that any integer portion of `zSig' | |
274 | | will be added into the exponent. Since a properly normalized significand | |
275 | | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
276 | | than the desired result exponent whenever `zSig' is a complete, normalized | |
277 | | significand. | |
278 | *----------------------------------------------------------------------------*/ | |
279 | ||
bb98fe42 | 280 | INLINE float32 packFloat32( flag zSign, int16 zExp, uint32_t zSig ) |
158142c2 FB |
281 | { |
282 | ||
f090c9d4 | 283 | return make_float32( |
bb98fe42 | 284 | ( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) zExp )<<23 ) + zSig); |
158142c2 FB |
285 | |
286 | } | |
287 | ||
288 | /*---------------------------------------------------------------------------- | |
289 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
290 | | and significand `zSig', and returns the proper single-precision floating- | |
291 | | point value corresponding to the abstract input. Ordinarily, the abstract | |
292 | | value is simply rounded and packed into the single-precision format, with | |
293 | | the inexact exception raised if the abstract input cannot be represented | |
294 | | exactly. However, if the abstract value is too large, the overflow and | |
295 | | inexact exceptions are raised and an infinity or maximal finite value is | |
296 | | returned. If the abstract value is too small, the input value is rounded to | |
297 | | a subnormal number, and the underflow and inexact exceptions are raised if | |
298 | | the abstract input cannot be represented exactly as a subnormal single- | |
299 | | precision floating-point number. | |
300 | | The input significand `zSig' has its binary point between bits 30 | |
301 | | and 29, which is 7 bits to the left of the usual location. This shifted | |
302 | | significand must be normalized or smaller. If `zSig' is not normalized, | |
303 | | `zExp' must be 0; in that case, the result returned is a subnormal number, | |
304 | | and it must not require rounding. In the usual case that `zSig' is | |
305 | | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. | |
306 | | The handling of underflow and overflow follows the IEC/IEEE Standard for | |
307 | | Binary Floating-Point Arithmetic. | |
308 | *----------------------------------------------------------------------------*/ | |
309 | ||
bb98fe42 | 310 | static float32 roundAndPackFloat32( flag zSign, int16 zExp, uint32_t zSig STATUS_PARAM) |
158142c2 FB |
311 | { |
312 | int8 roundingMode; | |
313 | flag roundNearestEven; | |
314 | int8 roundIncrement, roundBits; | |
315 | flag isTiny; | |
316 | ||
317 | roundingMode = STATUS(float_rounding_mode); | |
318 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
319 | roundIncrement = 0x40; | |
320 | if ( ! roundNearestEven ) { | |
321 | if ( roundingMode == float_round_to_zero ) { | |
322 | roundIncrement = 0; | |
323 | } | |
324 | else { | |
325 | roundIncrement = 0x7F; | |
326 | if ( zSign ) { | |
327 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
328 | } | |
329 | else { | |
330 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
331 | } | |
332 | } | |
333 | } | |
334 | roundBits = zSig & 0x7F; | |
bb98fe42 | 335 | if ( 0xFD <= (uint16_t) zExp ) { |
158142c2 FB |
336 | if ( ( 0xFD < zExp ) |
337 | || ( ( zExp == 0xFD ) | |
bb98fe42 | 338 | && ( (int32_t) ( zSig + roundIncrement ) < 0 ) ) |
158142c2 FB |
339 | ) { |
340 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
f090c9d4 | 341 | return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 )); |
158142c2 FB |
342 | } |
343 | if ( zExp < 0 ) { | |
fe76d976 | 344 | if ( STATUS(flush_to_zero) ) return packFloat32( zSign, 0, 0 ); |
158142c2 FB |
345 | isTiny = |
346 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
347 | || ( zExp < -1 ) | |
348 | || ( zSig + roundIncrement < 0x80000000 ); | |
349 | shift32RightJamming( zSig, - zExp, &zSig ); | |
350 | zExp = 0; | |
351 | roundBits = zSig & 0x7F; | |
352 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); | |
353 | } | |
354 | } | |
355 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
356 | zSig = ( zSig + roundIncrement )>>7; | |
357 | zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); | |
358 | if ( zSig == 0 ) zExp = 0; | |
359 | return packFloat32( zSign, zExp, zSig ); | |
360 | ||
361 | } | |
362 | ||
363 | /*---------------------------------------------------------------------------- | |
364 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
365 | | and significand `zSig', and returns the proper single-precision floating- | |
366 | | point value corresponding to the abstract input. This routine is just like | |
367 | | `roundAndPackFloat32' except that `zSig' does not have to be normalized. | |
368 | | Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' | |
369 | | floating-point exponent. | |
370 | *----------------------------------------------------------------------------*/ | |
371 | ||
372 | static float32 | |
bb98fe42 | 373 | normalizeRoundAndPackFloat32( flag zSign, int16 zExp, uint32_t zSig STATUS_PARAM) |
158142c2 FB |
374 | { |
375 | int8 shiftCount; | |
376 | ||
377 | shiftCount = countLeadingZeros32( zSig ) - 1; | |
378 | return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); | |
379 | ||
380 | } | |
381 | ||
382 | /*---------------------------------------------------------------------------- | |
383 | | Returns the fraction bits of the double-precision floating-point value `a'. | |
384 | *----------------------------------------------------------------------------*/ | |
385 | ||
bb98fe42 | 386 | INLINE uint64_t extractFloat64Frac( float64 a ) |
158142c2 FB |
387 | { |
388 | ||
f090c9d4 | 389 | return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF ); |
158142c2 FB |
390 | |
391 | } | |
392 | ||
393 | /*---------------------------------------------------------------------------- | |
394 | | Returns the exponent bits of the double-precision floating-point value `a'. | |
395 | *----------------------------------------------------------------------------*/ | |
396 | ||
397 | INLINE int16 extractFloat64Exp( float64 a ) | |
398 | { | |
399 | ||
f090c9d4 | 400 | return ( float64_val(a)>>52 ) & 0x7FF; |
158142c2 FB |
401 | |
402 | } | |
403 | ||
404 | /*---------------------------------------------------------------------------- | |
405 | | Returns the sign bit of the double-precision floating-point value `a'. | |
406 | *----------------------------------------------------------------------------*/ | |
407 | ||
408 | INLINE flag extractFloat64Sign( float64 a ) | |
409 | { | |
410 | ||
f090c9d4 | 411 | return float64_val(a)>>63; |
158142c2 FB |
412 | |
413 | } | |
414 | ||
37d18660 PM |
415 | /*---------------------------------------------------------------------------- |
416 | | If `a' is denormal and we are in flush-to-zero mode then set the | |
417 | | input-denormal exception and return zero. Otherwise just return the value. | |
418 | *----------------------------------------------------------------------------*/ | |
419 | static float64 float64_squash_input_denormal(float64 a STATUS_PARAM) | |
420 | { | |
421 | if (STATUS(flush_inputs_to_zero)) { | |
422 | if (extractFloat64Exp(a) == 0 && extractFloat64Frac(a) != 0) { | |
423 | float_raise(float_flag_input_denormal STATUS_VAR); | |
424 | return make_float64(float64_val(a) & (1ULL << 63)); | |
425 | } | |
426 | } | |
427 | return a; | |
428 | } | |
429 | ||
158142c2 FB |
430 | /*---------------------------------------------------------------------------- |
431 | | Normalizes the subnormal double-precision floating-point value represented | |
432 | | by the denormalized significand `aSig'. The normalized exponent and | |
433 | | significand are stored at the locations pointed to by `zExpPtr' and | |
434 | | `zSigPtr', respectively. | |
435 | *----------------------------------------------------------------------------*/ | |
436 | ||
437 | static void | |
bb98fe42 | 438 | normalizeFloat64Subnormal( uint64_t aSig, int16 *zExpPtr, uint64_t *zSigPtr ) |
158142c2 FB |
439 | { |
440 | int8 shiftCount; | |
441 | ||
442 | shiftCount = countLeadingZeros64( aSig ) - 11; | |
443 | *zSigPtr = aSig<<shiftCount; | |
444 | *zExpPtr = 1 - shiftCount; | |
445 | ||
446 | } | |
447 | ||
448 | /*---------------------------------------------------------------------------- | |
449 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
450 | | double-precision floating-point value, returning the result. After being | |
451 | | shifted into the proper positions, the three fields are simply added | |
452 | | together to form the result. This means that any integer portion of `zSig' | |
453 | | will be added into the exponent. Since a properly normalized significand | |
454 | | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
455 | | than the desired result exponent whenever `zSig' is a complete, normalized | |
456 | | significand. | |
457 | *----------------------------------------------------------------------------*/ | |
458 | ||
bb98fe42 | 459 | INLINE float64 packFloat64( flag zSign, int16 zExp, uint64_t zSig ) |
158142c2 FB |
460 | { |
461 | ||
f090c9d4 | 462 | return make_float64( |
bb98fe42 | 463 | ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig); |
158142c2 FB |
464 | |
465 | } | |
466 | ||
467 | /*---------------------------------------------------------------------------- | |
468 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
469 | | and significand `zSig', and returns the proper double-precision floating- | |
470 | | point value corresponding to the abstract input. Ordinarily, the abstract | |
471 | | value is simply rounded and packed into the double-precision format, with | |
472 | | the inexact exception raised if the abstract input cannot be represented | |
473 | | exactly. However, if the abstract value is too large, the overflow and | |
474 | | inexact exceptions are raised and an infinity or maximal finite value is | |
475 | | returned. If the abstract value is too small, the input value is rounded | |
476 | | to a subnormal number, and the underflow and inexact exceptions are raised | |
477 | | if the abstract input cannot be represented exactly as a subnormal double- | |
478 | | precision floating-point number. | |
479 | | The input significand `zSig' has its binary point between bits 62 | |
480 | | and 61, which is 10 bits to the left of the usual location. This shifted | |
481 | | significand must be normalized or smaller. If `zSig' is not normalized, | |
482 | | `zExp' must be 0; in that case, the result returned is a subnormal number, | |
483 | | and it must not require rounding. In the usual case that `zSig' is | |
484 | | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. | |
485 | | The handling of underflow and overflow follows the IEC/IEEE Standard for | |
486 | | Binary Floating-Point Arithmetic. | |
487 | *----------------------------------------------------------------------------*/ | |
488 | ||
bb98fe42 | 489 | static float64 roundAndPackFloat64( flag zSign, int16 zExp, uint64_t zSig STATUS_PARAM) |
158142c2 FB |
490 | { |
491 | int8 roundingMode; | |
492 | flag roundNearestEven; | |
493 | int16 roundIncrement, roundBits; | |
494 | flag isTiny; | |
495 | ||
496 | roundingMode = STATUS(float_rounding_mode); | |
497 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
498 | roundIncrement = 0x200; | |
499 | if ( ! roundNearestEven ) { | |
500 | if ( roundingMode == float_round_to_zero ) { | |
501 | roundIncrement = 0; | |
502 | } | |
503 | else { | |
504 | roundIncrement = 0x3FF; | |
505 | if ( zSign ) { | |
506 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
507 | } | |
508 | else { | |
509 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
510 | } | |
511 | } | |
512 | } | |
513 | roundBits = zSig & 0x3FF; | |
bb98fe42 | 514 | if ( 0x7FD <= (uint16_t) zExp ) { |
158142c2 FB |
515 | if ( ( 0x7FD < zExp ) |
516 | || ( ( zExp == 0x7FD ) | |
bb98fe42 | 517 | && ( (int64_t) ( zSig + roundIncrement ) < 0 ) ) |
158142c2 FB |
518 | ) { |
519 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
f090c9d4 | 520 | return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 )); |
158142c2 FB |
521 | } |
522 | if ( zExp < 0 ) { | |
fe76d976 | 523 | if ( STATUS(flush_to_zero) ) return packFloat64( zSign, 0, 0 ); |
158142c2 FB |
524 | isTiny = |
525 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
526 | || ( zExp < -1 ) | |
527 | || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) ); | |
528 | shift64RightJamming( zSig, - zExp, &zSig ); | |
529 | zExp = 0; | |
530 | roundBits = zSig & 0x3FF; | |
531 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); | |
532 | } | |
533 | } | |
534 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
535 | zSig = ( zSig + roundIncrement )>>10; | |
536 | zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); | |
537 | if ( zSig == 0 ) zExp = 0; | |
538 | return packFloat64( zSign, zExp, zSig ); | |
539 | ||
540 | } | |
541 | ||
542 | /*---------------------------------------------------------------------------- | |
543 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
544 | | and significand `zSig', and returns the proper double-precision floating- | |
545 | | point value corresponding to the abstract input. This routine is just like | |
546 | | `roundAndPackFloat64' except that `zSig' does not have to be normalized. | |
547 | | Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' | |
548 | | floating-point exponent. | |
549 | *----------------------------------------------------------------------------*/ | |
550 | ||
551 | static float64 | |
bb98fe42 | 552 | normalizeRoundAndPackFloat64( flag zSign, int16 zExp, uint64_t zSig STATUS_PARAM) |
158142c2 FB |
553 | { |
554 | int8 shiftCount; | |
555 | ||
556 | shiftCount = countLeadingZeros64( zSig ) - 1; | |
557 | return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); | |
558 | ||
559 | } | |
560 | ||
561 | #ifdef FLOATX80 | |
562 | ||
563 | /*---------------------------------------------------------------------------- | |
564 | | Returns the fraction bits of the extended double-precision floating-point | |
565 | | value `a'. | |
566 | *----------------------------------------------------------------------------*/ | |
567 | ||
bb98fe42 | 568 | INLINE uint64_t extractFloatx80Frac( floatx80 a ) |
158142c2 FB |
569 | { |
570 | ||
571 | return a.low; | |
572 | ||
573 | } | |
574 | ||
575 | /*---------------------------------------------------------------------------- | |
576 | | Returns the exponent bits of the extended double-precision floating-point | |
577 | | value `a'. | |
578 | *----------------------------------------------------------------------------*/ | |
579 | ||
580 | INLINE int32 extractFloatx80Exp( floatx80 a ) | |
581 | { | |
582 | ||
583 | return a.high & 0x7FFF; | |
584 | ||
585 | } | |
586 | ||
587 | /*---------------------------------------------------------------------------- | |
588 | | Returns the sign bit of the extended double-precision floating-point value | |
589 | | `a'. | |
590 | *----------------------------------------------------------------------------*/ | |
591 | ||
592 | INLINE flag extractFloatx80Sign( floatx80 a ) | |
593 | { | |
594 | ||
595 | return a.high>>15; | |
596 | ||
597 | } | |
598 | ||
599 | /*---------------------------------------------------------------------------- | |
600 | | Normalizes the subnormal extended double-precision floating-point value | |
601 | | represented by the denormalized significand `aSig'. The normalized exponent | |
602 | | and significand are stored at the locations pointed to by `zExpPtr' and | |
603 | | `zSigPtr', respectively. | |
604 | *----------------------------------------------------------------------------*/ | |
605 | ||
606 | static void | |
bb98fe42 | 607 | normalizeFloatx80Subnormal( uint64_t aSig, int32 *zExpPtr, uint64_t *zSigPtr ) |
158142c2 FB |
608 | { |
609 | int8 shiftCount; | |
610 | ||
611 | shiftCount = countLeadingZeros64( aSig ); | |
612 | *zSigPtr = aSig<<shiftCount; | |
613 | *zExpPtr = 1 - shiftCount; | |
614 | ||
615 | } | |
616 | ||
617 | /*---------------------------------------------------------------------------- | |
618 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an | |
619 | | extended double-precision floating-point value, returning the result. | |
620 | *----------------------------------------------------------------------------*/ | |
621 | ||
bb98fe42 | 622 | INLINE floatx80 packFloatx80( flag zSign, int32 zExp, uint64_t zSig ) |
158142c2 FB |
623 | { |
624 | floatx80 z; | |
625 | ||
626 | z.low = zSig; | |
bb98fe42 | 627 | z.high = ( ( (uint16_t) zSign )<<15 ) + zExp; |
158142c2 FB |
628 | return z; |
629 | ||
630 | } | |
631 | ||
632 | /*---------------------------------------------------------------------------- | |
633 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
634 | | and extended significand formed by the concatenation of `zSig0' and `zSig1', | |
635 | | and returns the proper extended double-precision floating-point value | |
636 | | corresponding to the abstract input. Ordinarily, the abstract value is | |
637 | | rounded and packed into the extended double-precision format, with the | |
638 | | inexact exception raised if the abstract input cannot be represented | |
639 | | exactly. However, if the abstract value is too large, the overflow and | |
640 | | inexact exceptions are raised and an infinity or maximal finite value is | |
641 | | returned. If the abstract value is too small, the input value is rounded to | |
642 | | a subnormal number, and the underflow and inexact exceptions are raised if | |
643 | | the abstract input cannot be represented exactly as a subnormal extended | |
644 | | double-precision floating-point number. | |
645 | | If `roundingPrecision' is 32 or 64, the result is rounded to the same | |
646 | | number of bits as single or double precision, respectively. Otherwise, the | |
647 | | result is rounded to the full precision of the extended double-precision | |
648 | | format. | |
649 | | The input significand must be normalized or smaller. If the input | |
650 | | significand is not normalized, `zExp' must be 0; in that case, the result | |
651 | | returned is a subnormal number, and it must not require rounding. The | |
652 | | handling of underflow and overflow follows the IEC/IEEE Standard for Binary | |
653 | | Floating-Point Arithmetic. | |
654 | *----------------------------------------------------------------------------*/ | |
655 | ||
656 | static floatx80 | |
657 | roundAndPackFloatx80( | |
bb98fe42 | 658 | int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 |
158142c2 FB |
659 | STATUS_PARAM) |
660 | { | |
661 | int8 roundingMode; | |
662 | flag roundNearestEven, increment, isTiny; | |
663 | int64 roundIncrement, roundMask, roundBits; | |
664 | ||
665 | roundingMode = STATUS(float_rounding_mode); | |
666 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
667 | if ( roundingPrecision == 80 ) goto precision80; | |
668 | if ( roundingPrecision == 64 ) { | |
669 | roundIncrement = LIT64( 0x0000000000000400 ); | |
670 | roundMask = LIT64( 0x00000000000007FF ); | |
671 | } | |
672 | else if ( roundingPrecision == 32 ) { | |
673 | roundIncrement = LIT64( 0x0000008000000000 ); | |
674 | roundMask = LIT64( 0x000000FFFFFFFFFF ); | |
675 | } | |
676 | else { | |
677 | goto precision80; | |
678 | } | |
679 | zSig0 |= ( zSig1 != 0 ); | |
680 | if ( ! roundNearestEven ) { | |
681 | if ( roundingMode == float_round_to_zero ) { | |
682 | roundIncrement = 0; | |
683 | } | |
684 | else { | |
685 | roundIncrement = roundMask; | |
686 | if ( zSign ) { | |
687 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
688 | } | |
689 | else { | |
690 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
691 | } | |
692 | } | |
693 | } | |
694 | roundBits = zSig0 & roundMask; | |
bb98fe42 | 695 | if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { |
158142c2 FB |
696 | if ( ( 0x7FFE < zExp ) |
697 | || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) ) | |
698 | ) { | |
699 | goto overflow; | |
700 | } | |
701 | if ( zExp <= 0 ) { | |
fe76d976 | 702 | if ( STATUS(flush_to_zero) ) return packFloatx80( zSign, 0, 0 ); |
158142c2 FB |
703 | isTiny = |
704 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
705 | || ( zExp < 0 ) | |
706 | || ( zSig0 <= zSig0 + roundIncrement ); | |
707 | shift64RightJamming( zSig0, 1 - zExp, &zSig0 ); | |
708 | zExp = 0; | |
709 | roundBits = zSig0 & roundMask; | |
710 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); | |
711 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
712 | zSig0 += roundIncrement; | |
bb98fe42 | 713 | if ( (int64_t) zSig0 < 0 ) zExp = 1; |
158142c2 FB |
714 | roundIncrement = roundMask + 1; |
715 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { | |
716 | roundMask |= roundIncrement; | |
717 | } | |
718 | zSig0 &= ~ roundMask; | |
719 | return packFloatx80( zSign, zExp, zSig0 ); | |
720 | } | |
721 | } | |
722 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
723 | zSig0 += roundIncrement; | |
724 | if ( zSig0 < roundIncrement ) { | |
725 | ++zExp; | |
726 | zSig0 = LIT64( 0x8000000000000000 ); | |
727 | } | |
728 | roundIncrement = roundMask + 1; | |
729 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { | |
730 | roundMask |= roundIncrement; | |
731 | } | |
732 | zSig0 &= ~ roundMask; | |
733 | if ( zSig0 == 0 ) zExp = 0; | |
734 | return packFloatx80( zSign, zExp, zSig0 ); | |
735 | precision80: | |
bb98fe42 | 736 | increment = ( (int64_t) zSig1 < 0 ); |
158142c2 FB |
737 | if ( ! roundNearestEven ) { |
738 | if ( roundingMode == float_round_to_zero ) { | |
739 | increment = 0; | |
740 | } | |
741 | else { | |
742 | if ( zSign ) { | |
743 | increment = ( roundingMode == float_round_down ) && zSig1; | |
744 | } | |
745 | else { | |
746 | increment = ( roundingMode == float_round_up ) && zSig1; | |
747 | } | |
748 | } | |
749 | } | |
bb98fe42 | 750 | if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { |
158142c2 FB |
751 | if ( ( 0x7FFE < zExp ) |
752 | || ( ( zExp == 0x7FFE ) | |
753 | && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) ) | |
754 | && increment | |
755 | ) | |
756 | ) { | |
757 | roundMask = 0; | |
758 | overflow: | |
759 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
760 | if ( ( roundingMode == float_round_to_zero ) | |
761 | || ( zSign && ( roundingMode == float_round_up ) ) | |
762 | || ( ! zSign && ( roundingMode == float_round_down ) ) | |
763 | ) { | |
764 | return packFloatx80( zSign, 0x7FFE, ~ roundMask ); | |
765 | } | |
766 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
767 | } | |
768 | if ( zExp <= 0 ) { | |
769 | isTiny = | |
770 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
771 | || ( zExp < 0 ) | |
772 | || ! increment | |
773 | || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) ); | |
774 | shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 ); | |
775 | zExp = 0; | |
776 | if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR); | |
777 | if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
778 | if ( roundNearestEven ) { | |
bb98fe42 | 779 | increment = ( (int64_t) zSig1 < 0 ); |
158142c2 FB |
780 | } |
781 | else { | |
782 | if ( zSign ) { | |
783 | increment = ( roundingMode == float_round_down ) && zSig1; | |
784 | } | |
785 | else { | |
786 | increment = ( roundingMode == float_round_up ) && zSig1; | |
787 | } | |
788 | } | |
789 | if ( increment ) { | |
790 | ++zSig0; | |
791 | zSig0 &= | |
bb98fe42 AF |
792 | ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
793 | if ( (int64_t) zSig0 < 0 ) zExp = 1; | |
158142c2 FB |
794 | } |
795 | return packFloatx80( zSign, zExp, zSig0 ); | |
796 | } | |
797 | } | |
798 | if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
799 | if ( increment ) { | |
800 | ++zSig0; | |
801 | if ( zSig0 == 0 ) { | |
802 | ++zExp; | |
803 | zSig0 = LIT64( 0x8000000000000000 ); | |
804 | } | |
805 | else { | |
bb98fe42 | 806 | zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
158142c2 FB |
807 | } |
808 | } | |
809 | else { | |
810 | if ( zSig0 == 0 ) zExp = 0; | |
811 | } | |
812 | return packFloatx80( zSign, zExp, zSig0 ); | |
813 | ||
814 | } | |
815 | ||
816 | /*---------------------------------------------------------------------------- | |
817 | | Takes an abstract floating-point value having sign `zSign', exponent | |
818 | | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', | |
819 | | and returns the proper extended double-precision floating-point value | |
820 | | corresponding to the abstract input. This routine is just like | |
821 | | `roundAndPackFloatx80' except that the input significand does not have to be | |
822 | | normalized. | |
823 | *----------------------------------------------------------------------------*/ | |
824 | ||
825 | static floatx80 | |
826 | normalizeRoundAndPackFloatx80( | |
bb98fe42 | 827 | int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 |
158142c2 FB |
828 | STATUS_PARAM) |
829 | { | |
830 | int8 shiftCount; | |
831 | ||
832 | if ( zSig0 == 0 ) { | |
833 | zSig0 = zSig1; | |
834 | zSig1 = 0; | |
835 | zExp -= 64; | |
836 | } | |
837 | shiftCount = countLeadingZeros64( zSig0 ); | |
838 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
839 | zExp -= shiftCount; | |
840 | return | |
841 | roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); | |
842 | ||
843 | } | |
844 | ||
845 | #endif | |
846 | ||
847 | #ifdef FLOAT128 | |
848 | ||
849 | /*---------------------------------------------------------------------------- | |
850 | | Returns the least-significant 64 fraction bits of the quadruple-precision | |
851 | | floating-point value `a'. | |
852 | *----------------------------------------------------------------------------*/ | |
853 | ||
bb98fe42 | 854 | INLINE uint64_t extractFloat128Frac1( float128 a ) |
158142c2 FB |
855 | { |
856 | ||
857 | return a.low; | |
858 | ||
859 | } | |
860 | ||
861 | /*---------------------------------------------------------------------------- | |
862 | | Returns the most-significant 48 fraction bits of the quadruple-precision | |
863 | | floating-point value `a'. | |
864 | *----------------------------------------------------------------------------*/ | |
865 | ||
bb98fe42 | 866 | INLINE uint64_t extractFloat128Frac0( float128 a ) |
158142c2 FB |
867 | { |
868 | ||
869 | return a.high & LIT64( 0x0000FFFFFFFFFFFF ); | |
870 | ||
871 | } | |
872 | ||
873 | /*---------------------------------------------------------------------------- | |
874 | | Returns the exponent bits of the quadruple-precision floating-point value | |
875 | | `a'. | |
876 | *----------------------------------------------------------------------------*/ | |
877 | ||
878 | INLINE int32 extractFloat128Exp( float128 a ) | |
879 | { | |
880 | ||
881 | return ( a.high>>48 ) & 0x7FFF; | |
882 | ||
883 | } | |
884 | ||
885 | /*---------------------------------------------------------------------------- | |
886 | | Returns the sign bit of the quadruple-precision floating-point value `a'. | |
887 | *----------------------------------------------------------------------------*/ | |
888 | ||
889 | INLINE flag extractFloat128Sign( float128 a ) | |
890 | { | |
891 | ||
892 | return a.high>>63; | |
893 | ||
894 | } | |
895 | ||
896 | /*---------------------------------------------------------------------------- | |
897 | | Normalizes the subnormal quadruple-precision floating-point value | |
898 | | represented by the denormalized significand formed by the concatenation of | |
899 | | `aSig0' and `aSig1'. The normalized exponent is stored at the location | |
900 | | pointed to by `zExpPtr'. The most significant 49 bits of the normalized | |
901 | | significand are stored at the location pointed to by `zSig0Ptr', and the | |
902 | | least significant 64 bits of the normalized significand are stored at the | |
903 | | location pointed to by `zSig1Ptr'. | |
904 | *----------------------------------------------------------------------------*/ | |
905 | ||
906 | static void | |
907 | normalizeFloat128Subnormal( | |
bb98fe42 AF |
908 | uint64_t aSig0, |
909 | uint64_t aSig1, | |
158142c2 | 910 | int32 *zExpPtr, |
bb98fe42 AF |
911 | uint64_t *zSig0Ptr, |
912 | uint64_t *zSig1Ptr | |
158142c2 FB |
913 | ) |
914 | { | |
915 | int8 shiftCount; | |
916 | ||
917 | if ( aSig0 == 0 ) { | |
918 | shiftCount = countLeadingZeros64( aSig1 ) - 15; | |
919 | if ( shiftCount < 0 ) { | |
920 | *zSig0Ptr = aSig1>>( - shiftCount ); | |
921 | *zSig1Ptr = aSig1<<( shiftCount & 63 ); | |
922 | } | |
923 | else { | |
924 | *zSig0Ptr = aSig1<<shiftCount; | |
925 | *zSig1Ptr = 0; | |
926 | } | |
927 | *zExpPtr = - shiftCount - 63; | |
928 | } | |
929 | else { | |
930 | shiftCount = countLeadingZeros64( aSig0 ) - 15; | |
931 | shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); | |
932 | *zExpPtr = 1 - shiftCount; | |
933 | } | |
934 | ||
935 | } | |
936 | ||
937 | /*---------------------------------------------------------------------------- | |
938 | | Packs the sign `zSign', the exponent `zExp', and the significand formed | |
939 | | by the concatenation of `zSig0' and `zSig1' into a quadruple-precision | |
940 | | floating-point value, returning the result. After being shifted into the | |
941 | | proper positions, the three fields `zSign', `zExp', and `zSig0' are simply | |
942 | | added together to form the most significant 32 bits of the result. This | |
943 | | means that any integer portion of `zSig0' will be added into the exponent. | |
944 | | Since a properly normalized significand will have an integer portion equal | |
945 | | to 1, the `zExp' input should be 1 less than the desired result exponent | |
946 | | whenever `zSig0' and `zSig1' concatenated form a complete, normalized | |
947 | | significand. | |
948 | *----------------------------------------------------------------------------*/ | |
949 | ||
950 | INLINE float128 | |
bb98fe42 | 951 | packFloat128( flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 ) |
158142c2 FB |
952 | { |
953 | float128 z; | |
954 | ||
955 | z.low = zSig1; | |
bb98fe42 | 956 | z.high = ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<48 ) + zSig0; |
158142c2 FB |
957 | return z; |
958 | ||
959 | } | |
960 | ||
961 | /*---------------------------------------------------------------------------- | |
962 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
963 | | and extended significand formed by the concatenation of `zSig0', `zSig1', | |
964 | | and `zSig2', and returns the proper quadruple-precision floating-point value | |
965 | | corresponding to the abstract input. Ordinarily, the abstract value is | |
966 | | simply rounded and packed into the quadruple-precision format, with the | |
967 | | inexact exception raised if the abstract input cannot be represented | |
968 | | exactly. However, if the abstract value is too large, the overflow and | |
969 | | inexact exceptions are raised and an infinity or maximal finite value is | |
970 | | returned. If the abstract value is too small, the input value is rounded to | |
971 | | a subnormal number, and the underflow and inexact exceptions are raised if | |
972 | | the abstract input cannot be represented exactly as a subnormal quadruple- | |
973 | | precision floating-point number. | |
974 | | The input significand must be normalized or smaller. If the input | |
975 | | significand is not normalized, `zExp' must be 0; in that case, the result | |
976 | | returned is a subnormal number, and it must not require rounding. In the | |
977 | | usual case that the input significand is normalized, `zExp' must be 1 less | |
978 | | than the ``true'' floating-point exponent. The handling of underflow and | |
979 | | overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
980 | *----------------------------------------------------------------------------*/ | |
981 | ||
982 | static float128 | |
983 | roundAndPackFloat128( | |
bb98fe42 | 984 | flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1, uint64_t zSig2 STATUS_PARAM) |
158142c2 FB |
985 | { |
986 | int8 roundingMode; | |
987 | flag roundNearestEven, increment, isTiny; | |
988 | ||
989 | roundingMode = STATUS(float_rounding_mode); | |
990 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
bb98fe42 | 991 | increment = ( (int64_t) zSig2 < 0 ); |
158142c2 FB |
992 | if ( ! roundNearestEven ) { |
993 | if ( roundingMode == float_round_to_zero ) { | |
994 | increment = 0; | |
995 | } | |
996 | else { | |
997 | if ( zSign ) { | |
998 | increment = ( roundingMode == float_round_down ) && zSig2; | |
999 | } | |
1000 | else { | |
1001 | increment = ( roundingMode == float_round_up ) && zSig2; | |
1002 | } | |
1003 | } | |
1004 | } | |
bb98fe42 | 1005 | if ( 0x7FFD <= (uint32_t) zExp ) { |
158142c2 FB |
1006 | if ( ( 0x7FFD < zExp ) |
1007 | || ( ( zExp == 0x7FFD ) | |
1008 | && eq128( | |
1009 | LIT64( 0x0001FFFFFFFFFFFF ), | |
1010 | LIT64( 0xFFFFFFFFFFFFFFFF ), | |
1011 | zSig0, | |
1012 | zSig1 | |
1013 | ) | |
1014 | && increment | |
1015 | ) | |
1016 | ) { | |
1017 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
1018 | if ( ( roundingMode == float_round_to_zero ) | |
1019 | || ( zSign && ( roundingMode == float_round_up ) ) | |
1020 | || ( ! zSign && ( roundingMode == float_round_down ) ) | |
1021 | ) { | |
1022 | return | |
1023 | packFloat128( | |
1024 | zSign, | |
1025 | 0x7FFE, | |
1026 | LIT64( 0x0000FFFFFFFFFFFF ), | |
1027 | LIT64( 0xFFFFFFFFFFFFFFFF ) | |
1028 | ); | |
1029 | } | |
1030 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
1031 | } | |
1032 | if ( zExp < 0 ) { | |
fe76d976 | 1033 | if ( STATUS(flush_to_zero) ) return packFloat128( zSign, 0, 0, 0 ); |
158142c2 FB |
1034 | isTiny = |
1035 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
1036 | || ( zExp < -1 ) | |
1037 | || ! increment | |
1038 | || lt128( | |
1039 | zSig0, | |
1040 | zSig1, | |
1041 | LIT64( 0x0001FFFFFFFFFFFF ), | |
1042 | LIT64( 0xFFFFFFFFFFFFFFFF ) | |
1043 | ); | |
1044 | shift128ExtraRightJamming( | |
1045 | zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); | |
1046 | zExp = 0; | |
1047 | if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR); | |
1048 | if ( roundNearestEven ) { | |
bb98fe42 | 1049 | increment = ( (int64_t) zSig2 < 0 ); |
158142c2 FB |
1050 | } |
1051 | else { | |
1052 | if ( zSign ) { | |
1053 | increment = ( roundingMode == float_round_down ) && zSig2; | |
1054 | } | |
1055 | else { | |
1056 | increment = ( roundingMode == float_round_up ) && zSig2; | |
1057 | } | |
1058 | } | |
1059 | } | |
1060 | } | |
1061 | if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
1062 | if ( increment ) { | |
1063 | add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); | |
1064 | zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven ); | |
1065 | } | |
1066 | else { | |
1067 | if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; | |
1068 | } | |
1069 | return packFloat128( zSign, zExp, zSig0, zSig1 ); | |
1070 | ||
1071 | } | |
1072 | ||
1073 | /*---------------------------------------------------------------------------- | |
1074 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
1075 | | and significand formed by the concatenation of `zSig0' and `zSig1', and | |
1076 | | returns the proper quadruple-precision floating-point value corresponding | |
1077 | | to the abstract input. This routine is just like `roundAndPackFloat128' | |
1078 | | except that the input significand has fewer bits and does not have to be | |
1079 | | normalized. In all cases, `zExp' must be 1 less than the ``true'' floating- | |
1080 | | point exponent. | |
1081 | *----------------------------------------------------------------------------*/ | |
1082 | ||
1083 | static float128 | |
1084 | normalizeRoundAndPackFloat128( | |
bb98fe42 | 1085 | flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 STATUS_PARAM) |
158142c2 FB |
1086 | { |
1087 | int8 shiftCount; | |
bb98fe42 | 1088 | uint64_t zSig2; |
158142c2 FB |
1089 | |
1090 | if ( zSig0 == 0 ) { | |
1091 | zSig0 = zSig1; | |
1092 | zSig1 = 0; | |
1093 | zExp -= 64; | |
1094 | } | |
1095 | shiftCount = countLeadingZeros64( zSig0 ) - 15; | |
1096 | if ( 0 <= shiftCount ) { | |
1097 | zSig2 = 0; | |
1098 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
1099 | } | |
1100 | else { | |
1101 | shift128ExtraRightJamming( | |
1102 | zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 ); | |
1103 | } | |
1104 | zExp -= shiftCount; | |
1105 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR); | |
1106 | ||
1107 | } | |
1108 | ||
1109 | #endif | |
1110 | ||
1111 | /*---------------------------------------------------------------------------- | |
1112 | | Returns the result of converting the 32-bit two's complement integer `a' | |
1113 | | to the single-precision floating-point format. The conversion is performed | |
1114 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1115 | *----------------------------------------------------------------------------*/ | |
1116 | ||
1117 | float32 int32_to_float32( int32 a STATUS_PARAM ) | |
1118 | { | |
1119 | flag zSign; | |
1120 | ||
f090c9d4 | 1121 | if ( a == 0 ) return float32_zero; |
bb98fe42 | 1122 | if ( a == (int32_t) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); |
158142c2 FB |
1123 | zSign = ( a < 0 ); |
1124 | return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); | |
1125 | ||
1126 | } | |
1127 | ||
1128 | /*---------------------------------------------------------------------------- | |
1129 | | Returns the result of converting the 32-bit two's complement integer `a' | |
1130 | | to the double-precision floating-point format. The conversion is performed | |
1131 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1132 | *----------------------------------------------------------------------------*/ | |
1133 | ||
1134 | float64 int32_to_float64( int32 a STATUS_PARAM ) | |
1135 | { | |
1136 | flag zSign; | |
1137 | uint32 absA; | |
1138 | int8 shiftCount; | |
bb98fe42 | 1139 | uint64_t zSig; |
158142c2 | 1140 | |
f090c9d4 | 1141 | if ( a == 0 ) return float64_zero; |
158142c2 FB |
1142 | zSign = ( a < 0 ); |
1143 | absA = zSign ? - a : a; | |
1144 | shiftCount = countLeadingZeros32( absA ) + 21; | |
1145 | zSig = absA; | |
1146 | return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); | |
1147 | ||
1148 | } | |
1149 | ||
1150 | #ifdef FLOATX80 | |
1151 | ||
1152 | /*---------------------------------------------------------------------------- | |
1153 | | Returns the result of converting the 32-bit two's complement integer `a' | |
1154 | | to the extended double-precision floating-point format. The conversion | |
1155 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1156 | | Arithmetic. | |
1157 | *----------------------------------------------------------------------------*/ | |
1158 | ||
1159 | floatx80 int32_to_floatx80( int32 a STATUS_PARAM ) | |
1160 | { | |
1161 | flag zSign; | |
1162 | uint32 absA; | |
1163 | int8 shiftCount; | |
bb98fe42 | 1164 | uint64_t zSig; |
158142c2 FB |
1165 | |
1166 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); | |
1167 | zSign = ( a < 0 ); | |
1168 | absA = zSign ? - a : a; | |
1169 | shiftCount = countLeadingZeros32( absA ) + 32; | |
1170 | zSig = absA; | |
1171 | return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); | |
1172 | ||
1173 | } | |
1174 | ||
1175 | #endif | |
1176 | ||
1177 | #ifdef FLOAT128 | |
1178 | ||
1179 | /*---------------------------------------------------------------------------- | |
1180 | | Returns the result of converting the 32-bit two's complement integer `a' to | |
1181 | | the quadruple-precision floating-point format. The conversion is performed | |
1182 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1183 | *----------------------------------------------------------------------------*/ | |
1184 | ||
1185 | float128 int32_to_float128( int32 a STATUS_PARAM ) | |
1186 | { | |
1187 | flag zSign; | |
1188 | uint32 absA; | |
1189 | int8 shiftCount; | |
bb98fe42 | 1190 | uint64_t zSig0; |
158142c2 FB |
1191 | |
1192 | if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); | |
1193 | zSign = ( a < 0 ); | |
1194 | absA = zSign ? - a : a; | |
1195 | shiftCount = countLeadingZeros32( absA ) + 17; | |
1196 | zSig0 = absA; | |
1197 | return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); | |
1198 | ||
1199 | } | |
1200 | ||
1201 | #endif | |
1202 | ||
1203 | /*---------------------------------------------------------------------------- | |
1204 | | Returns the result of converting the 64-bit two's complement integer `a' | |
1205 | | to the single-precision floating-point format. The conversion is performed | |
1206 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1207 | *----------------------------------------------------------------------------*/ | |
1208 | ||
1209 | float32 int64_to_float32( int64 a STATUS_PARAM ) | |
1210 | { | |
1211 | flag zSign; | |
1212 | uint64 absA; | |
1213 | int8 shiftCount; | |
1214 | ||
f090c9d4 | 1215 | if ( a == 0 ) return float32_zero; |
158142c2 FB |
1216 | zSign = ( a < 0 ); |
1217 | absA = zSign ? - a : a; | |
1218 | shiftCount = countLeadingZeros64( absA ) - 40; | |
1219 | if ( 0 <= shiftCount ) { | |
1220 | return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); | |
1221 | } | |
1222 | else { | |
1223 | shiftCount += 7; | |
1224 | if ( shiftCount < 0 ) { | |
1225 | shift64RightJamming( absA, - shiftCount, &absA ); | |
1226 | } | |
1227 | else { | |
1228 | absA <<= shiftCount; | |
1229 | } | |
1230 | return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); | |
1231 | } | |
1232 | ||
1233 | } | |
1234 | ||
3430b0be | 1235 | float32 uint64_to_float32( uint64 a STATUS_PARAM ) |
75d62a58 JM |
1236 | { |
1237 | int8 shiftCount; | |
1238 | ||
f090c9d4 | 1239 | if ( a == 0 ) return float32_zero; |
75d62a58 JM |
1240 | shiftCount = countLeadingZeros64( a ) - 40; |
1241 | if ( 0 <= shiftCount ) { | |
1242 | return packFloat32( 1 > 0, 0x95 - shiftCount, a<<shiftCount ); | |
1243 | } | |
1244 | else { | |
1245 | shiftCount += 7; | |
1246 | if ( shiftCount < 0 ) { | |
1247 | shift64RightJamming( a, - shiftCount, &a ); | |
1248 | } | |
1249 | else { | |
1250 | a <<= shiftCount; | |
1251 | } | |
1252 | return roundAndPackFloat32( 1 > 0, 0x9C - shiftCount, a STATUS_VAR ); | |
1253 | } | |
1254 | } | |
1255 | ||
158142c2 FB |
1256 | /*---------------------------------------------------------------------------- |
1257 | | Returns the result of converting the 64-bit two's complement integer `a' | |
1258 | | to the double-precision floating-point format. The conversion is performed | |
1259 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1260 | *----------------------------------------------------------------------------*/ | |
1261 | ||
1262 | float64 int64_to_float64( int64 a STATUS_PARAM ) | |
1263 | { | |
1264 | flag zSign; | |
1265 | ||
f090c9d4 | 1266 | if ( a == 0 ) return float64_zero; |
bb98fe42 | 1267 | if ( a == (int64_t) LIT64( 0x8000000000000000 ) ) { |
158142c2 FB |
1268 | return packFloat64( 1, 0x43E, 0 ); |
1269 | } | |
1270 | zSign = ( a < 0 ); | |
1271 | return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); | |
1272 | ||
1273 | } | |
1274 | ||
75d62a58 JM |
1275 | float64 uint64_to_float64( uint64 a STATUS_PARAM ) |
1276 | { | |
f090c9d4 | 1277 | if ( a == 0 ) return float64_zero; |
75d62a58 JM |
1278 | return normalizeRoundAndPackFloat64( 0, 0x43C, a STATUS_VAR ); |
1279 | ||
1280 | } | |
1281 | ||
158142c2 FB |
1282 | #ifdef FLOATX80 |
1283 | ||
1284 | /*---------------------------------------------------------------------------- | |
1285 | | Returns the result of converting the 64-bit two's complement integer `a' | |
1286 | | to the extended double-precision floating-point format. The conversion | |
1287 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1288 | | Arithmetic. | |
1289 | *----------------------------------------------------------------------------*/ | |
1290 | ||
1291 | floatx80 int64_to_floatx80( int64 a STATUS_PARAM ) | |
1292 | { | |
1293 | flag zSign; | |
1294 | uint64 absA; | |
1295 | int8 shiftCount; | |
1296 | ||
1297 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); | |
1298 | zSign = ( a < 0 ); | |
1299 | absA = zSign ? - a : a; | |
1300 | shiftCount = countLeadingZeros64( absA ); | |
1301 | return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); | |
1302 | ||
1303 | } | |
1304 | ||
1305 | #endif | |
1306 | ||
1307 | #ifdef FLOAT128 | |
1308 | ||
1309 | /*---------------------------------------------------------------------------- | |
1310 | | Returns the result of converting the 64-bit two's complement integer `a' to | |
1311 | | the quadruple-precision floating-point format. The conversion is performed | |
1312 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1313 | *----------------------------------------------------------------------------*/ | |
1314 | ||
1315 | float128 int64_to_float128( int64 a STATUS_PARAM ) | |
1316 | { | |
1317 | flag zSign; | |
1318 | uint64 absA; | |
1319 | int8 shiftCount; | |
1320 | int32 zExp; | |
bb98fe42 | 1321 | uint64_t zSig0, zSig1; |
158142c2 FB |
1322 | |
1323 | if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); | |
1324 | zSign = ( a < 0 ); | |
1325 | absA = zSign ? - a : a; | |
1326 | shiftCount = countLeadingZeros64( absA ) + 49; | |
1327 | zExp = 0x406E - shiftCount; | |
1328 | if ( 64 <= shiftCount ) { | |
1329 | zSig1 = 0; | |
1330 | zSig0 = absA; | |
1331 | shiftCount -= 64; | |
1332 | } | |
1333 | else { | |
1334 | zSig1 = absA; | |
1335 | zSig0 = 0; | |
1336 | } | |
1337 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
1338 | return packFloat128( zSign, zExp, zSig0, zSig1 ); | |
1339 | ||
1340 | } | |
1341 | ||
1342 | #endif | |
1343 | ||
1344 | /*---------------------------------------------------------------------------- | |
1345 | | Returns the result of converting the single-precision floating-point value | |
1346 | | `a' to the 32-bit two's complement integer format. The conversion is | |
1347 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1348 | | Arithmetic---which means in particular that the conversion is rounded | |
1349 | | according to the current rounding mode. If `a' is a NaN, the largest | |
1350 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
1351 | | largest integer with the same sign as `a' is returned. | |
1352 | *----------------------------------------------------------------------------*/ | |
1353 | ||
1354 | int32 float32_to_int32( float32 a STATUS_PARAM ) | |
1355 | { | |
1356 | flag aSign; | |
1357 | int16 aExp, shiftCount; | |
bb98fe42 AF |
1358 | uint32_t aSig; |
1359 | uint64_t aSig64; | |
158142c2 | 1360 | |
37d18660 | 1361 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1362 | aSig = extractFloat32Frac( a ); |
1363 | aExp = extractFloat32Exp( a ); | |
1364 | aSign = extractFloat32Sign( a ); | |
1365 | if ( ( aExp == 0xFF ) && aSig ) aSign = 0; | |
1366 | if ( aExp ) aSig |= 0x00800000; | |
1367 | shiftCount = 0xAF - aExp; | |
1368 | aSig64 = aSig; | |
1369 | aSig64 <<= 32; | |
1370 | if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); | |
1371 | return roundAndPackInt32( aSign, aSig64 STATUS_VAR ); | |
1372 | ||
1373 | } | |
1374 | ||
1375 | /*---------------------------------------------------------------------------- | |
1376 | | Returns the result of converting the single-precision floating-point value | |
1377 | | `a' to the 32-bit two's complement integer format. The conversion is | |
1378 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1379 | | Arithmetic, except that the conversion is always rounded toward zero. | |
1380 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
1381 | | the conversion overflows, the largest integer with the same sign as `a' is | |
1382 | | returned. | |
1383 | *----------------------------------------------------------------------------*/ | |
1384 | ||
1385 | int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) | |
1386 | { | |
1387 | flag aSign; | |
1388 | int16 aExp, shiftCount; | |
bb98fe42 | 1389 | uint32_t aSig; |
158142c2 | 1390 | int32 z; |
37d18660 | 1391 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1392 | |
1393 | aSig = extractFloat32Frac( a ); | |
1394 | aExp = extractFloat32Exp( a ); | |
1395 | aSign = extractFloat32Sign( a ); | |
1396 | shiftCount = aExp - 0x9E; | |
1397 | if ( 0 <= shiftCount ) { | |
f090c9d4 | 1398 | if ( float32_val(a) != 0xCF000000 ) { |
158142c2 FB |
1399 | float_raise( float_flag_invalid STATUS_VAR); |
1400 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; | |
1401 | } | |
bb98fe42 | 1402 | return (int32_t) 0x80000000; |
158142c2 FB |
1403 | } |
1404 | else if ( aExp <= 0x7E ) { | |
1405 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
1406 | return 0; | |
1407 | } | |
1408 | aSig = ( aSig | 0x00800000 )<<8; | |
1409 | z = aSig>>( - shiftCount ); | |
bb98fe42 | 1410 | if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { |
158142c2 FB |
1411 | STATUS(float_exception_flags) |= float_flag_inexact; |
1412 | } | |
1413 | if ( aSign ) z = - z; | |
1414 | return z; | |
1415 | ||
1416 | } | |
1417 | ||
cbcef455 PM |
1418 | /*---------------------------------------------------------------------------- |
1419 | | Returns the result of converting the single-precision floating-point value | |
1420 | | `a' to the 16-bit two's complement integer format. The conversion is | |
1421 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1422 | | Arithmetic, except that the conversion is always rounded toward zero. | |
1423 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
1424 | | the conversion overflows, the largest integer with the same sign as `a' is | |
1425 | | returned. | |
1426 | *----------------------------------------------------------------------------*/ | |
1427 | ||
1428 | int16 float32_to_int16_round_to_zero( float32 a STATUS_PARAM ) | |
1429 | { | |
1430 | flag aSign; | |
1431 | int16 aExp, shiftCount; | |
bb98fe42 | 1432 | uint32_t aSig; |
cbcef455 PM |
1433 | int32 z; |
1434 | ||
1435 | aSig = extractFloat32Frac( a ); | |
1436 | aExp = extractFloat32Exp( a ); | |
1437 | aSign = extractFloat32Sign( a ); | |
1438 | shiftCount = aExp - 0x8E; | |
1439 | if ( 0 <= shiftCount ) { | |
1440 | if ( float32_val(a) != 0xC7000000 ) { | |
1441 | float_raise( float_flag_invalid STATUS_VAR); | |
1442 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { | |
1443 | return 0x7FFF; | |
1444 | } | |
1445 | } | |
bb98fe42 | 1446 | return (int32_t) 0xffff8000; |
cbcef455 PM |
1447 | } |
1448 | else if ( aExp <= 0x7E ) { | |
1449 | if ( aExp | aSig ) { | |
1450 | STATUS(float_exception_flags) |= float_flag_inexact; | |
1451 | } | |
1452 | return 0; | |
1453 | } | |
1454 | shiftCount -= 0x10; | |
1455 | aSig = ( aSig | 0x00800000 )<<8; | |
1456 | z = aSig>>( - shiftCount ); | |
bb98fe42 | 1457 | if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { |
cbcef455 PM |
1458 | STATUS(float_exception_flags) |= float_flag_inexact; |
1459 | } | |
1460 | if ( aSign ) { | |
1461 | z = - z; | |
1462 | } | |
1463 | return z; | |
1464 | ||
1465 | } | |
1466 | ||
158142c2 FB |
1467 | /*---------------------------------------------------------------------------- |
1468 | | Returns the result of converting the single-precision floating-point value | |
1469 | | `a' to the 64-bit two's complement integer format. The conversion is | |
1470 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1471 | | Arithmetic---which means in particular that the conversion is rounded | |
1472 | | according to the current rounding mode. If `a' is a NaN, the largest | |
1473 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
1474 | | largest integer with the same sign as `a' is returned. | |
1475 | *----------------------------------------------------------------------------*/ | |
1476 | ||
1477 | int64 float32_to_int64( float32 a STATUS_PARAM ) | |
1478 | { | |
1479 | flag aSign; | |
1480 | int16 aExp, shiftCount; | |
bb98fe42 AF |
1481 | uint32_t aSig; |
1482 | uint64_t aSig64, aSigExtra; | |
37d18660 | 1483 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1484 | |
1485 | aSig = extractFloat32Frac( a ); | |
1486 | aExp = extractFloat32Exp( a ); | |
1487 | aSign = extractFloat32Sign( a ); | |
1488 | shiftCount = 0xBE - aExp; | |
1489 | if ( shiftCount < 0 ) { | |
1490 | float_raise( float_flag_invalid STATUS_VAR); | |
1491 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { | |
1492 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
1493 | } | |
bb98fe42 | 1494 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
1495 | } |
1496 | if ( aExp ) aSig |= 0x00800000; | |
1497 | aSig64 = aSig; | |
1498 | aSig64 <<= 40; | |
1499 | shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra ); | |
1500 | return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR ); | |
1501 | ||
1502 | } | |
1503 | ||
1504 | /*---------------------------------------------------------------------------- | |
1505 | | Returns the result of converting the single-precision floating-point value | |
1506 | | `a' to the 64-bit two's complement integer format. The conversion is | |
1507 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1508 | | Arithmetic, except that the conversion is always rounded toward zero. If | |
1509 | | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
1510 | | conversion overflows, the largest integer with the same sign as `a' is | |
1511 | | returned. | |
1512 | *----------------------------------------------------------------------------*/ | |
1513 | ||
1514 | int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) | |
1515 | { | |
1516 | flag aSign; | |
1517 | int16 aExp, shiftCount; | |
bb98fe42 AF |
1518 | uint32_t aSig; |
1519 | uint64_t aSig64; | |
158142c2 | 1520 | int64 z; |
37d18660 | 1521 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1522 | |
1523 | aSig = extractFloat32Frac( a ); | |
1524 | aExp = extractFloat32Exp( a ); | |
1525 | aSign = extractFloat32Sign( a ); | |
1526 | shiftCount = aExp - 0xBE; | |
1527 | if ( 0 <= shiftCount ) { | |
f090c9d4 | 1528 | if ( float32_val(a) != 0xDF000000 ) { |
158142c2 FB |
1529 | float_raise( float_flag_invalid STATUS_VAR); |
1530 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { | |
1531 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
1532 | } | |
1533 | } | |
bb98fe42 | 1534 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
1535 | } |
1536 | else if ( aExp <= 0x7E ) { | |
1537 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
1538 | return 0; | |
1539 | } | |
1540 | aSig64 = aSig | 0x00800000; | |
1541 | aSig64 <<= 40; | |
1542 | z = aSig64>>( - shiftCount ); | |
bb98fe42 | 1543 | if ( (uint64_t) ( aSig64<<( shiftCount & 63 ) ) ) { |
158142c2 FB |
1544 | STATUS(float_exception_flags) |= float_flag_inexact; |
1545 | } | |
1546 | if ( aSign ) z = - z; | |
1547 | return z; | |
1548 | ||
1549 | } | |
1550 | ||
1551 | /*---------------------------------------------------------------------------- | |
1552 | | Returns the result of converting the single-precision floating-point value | |
1553 | | `a' to the double-precision floating-point format. The conversion is | |
1554 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1555 | | Arithmetic. | |
1556 | *----------------------------------------------------------------------------*/ | |
1557 | ||
1558 | float64 float32_to_float64( float32 a STATUS_PARAM ) | |
1559 | { | |
1560 | flag aSign; | |
1561 | int16 aExp; | |
bb98fe42 | 1562 | uint32_t aSig; |
37d18660 | 1563 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1564 | |
1565 | aSig = extractFloat32Frac( a ); | |
1566 | aExp = extractFloat32Exp( a ); | |
1567 | aSign = extractFloat32Sign( a ); | |
1568 | if ( aExp == 0xFF ) { | |
bcd4d9af | 1569 | if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
1570 | return packFloat64( aSign, 0x7FF, 0 ); |
1571 | } | |
1572 | if ( aExp == 0 ) { | |
1573 | if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); | |
1574 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1575 | --aExp; | |
1576 | } | |
bb98fe42 | 1577 | return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 ); |
158142c2 FB |
1578 | |
1579 | } | |
1580 | ||
1581 | #ifdef FLOATX80 | |
1582 | ||
1583 | /*---------------------------------------------------------------------------- | |
1584 | | Returns the result of converting the single-precision floating-point value | |
1585 | | `a' to the extended double-precision floating-point format. The conversion | |
1586 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1587 | | Arithmetic. | |
1588 | *----------------------------------------------------------------------------*/ | |
1589 | ||
1590 | floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) | |
1591 | { | |
1592 | flag aSign; | |
1593 | int16 aExp; | |
bb98fe42 | 1594 | uint32_t aSig; |
158142c2 | 1595 | |
37d18660 | 1596 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1597 | aSig = extractFloat32Frac( a ); |
1598 | aExp = extractFloat32Exp( a ); | |
1599 | aSign = extractFloat32Sign( a ); | |
1600 | if ( aExp == 0xFF ) { | |
bcd4d9af | 1601 | if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
1602 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
1603 | } | |
1604 | if ( aExp == 0 ) { | |
1605 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); | |
1606 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1607 | } | |
1608 | aSig |= 0x00800000; | |
bb98fe42 | 1609 | return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 ); |
158142c2 FB |
1610 | |
1611 | } | |
1612 | ||
1613 | #endif | |
1614 | ||
1615 | #ifdef FLOAT128 | |
1616 | ||
1617 | /*---------------------------------------------------------------------------- | |
1618 | | Returns the result of converting the single-precision floating-point value | |
1619 | | `a' to the double-precision floating-point format. The conversion is | |
1620 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1621 | | Arithmetic. | |
1622 | *----------------------------------------------------------------------------*/ | |
1623 | ||
1624 | float128 float32_to_float128( float32 a STATUS_PARAM ) | |
1625 | { | |
1626 | flag aSign; | |
1627 | int16 aExp; | |
bb98fe42 | 1628 | uint32_t aSig; |
158142c2 | 1629 | |
37d18660 | 1630 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1631 | aSig = extractFloat32Frac( a ); |
1632 | aExp = extractFloat32Exp( a ); | |
1633 | aSign = extractFloat32Sign( a ); | |
1634 | if ( aExp == 0xFF ) { | |
bcd4d9af | 1635 | if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
1636 | return packFloat128( aSign, 0x7FFF, 0, 0 ); |
1637 | } | |
1638 | if ( aExp == 0 ) { | |
1639 | if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); | |
1640 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1641 | --aExp; | |
1642 | } | |
bb98fe42 | 1643 | return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 ); |
158142c2 FB |
1644 | |
1645 | } | |
1646 | ||
1647 | #endif | |
1648 | ||
1649 | /*---------------------------------------------------------------------------- | |
1650 | | Rounds the single-precision floating-point value `a' to an integer, and | |
1651 | | returns the result as a single-precision floating-point value. The | |
1652 | | operation is performed according to the IEC/IEEE Standard for Binary | |
1653 | | Floating-Point Arithmetic. | |
1654 | *----------------------------------------------------------------------------*/ | |
1655 | ||
1656 | float32 float32_round_to_int( float32 a STATUS_PARAM) | |
1657 | { | |
1658 | flag aSign; | |
1659 | int16 aExp; | |
bb98fe42 | 1660 | uint32_t lastBitMask, roundBitsMask; |
158142c2 | 1661 | int8 roundingMode; |
bb98fe42 | 1662 | uint32_t z; |
37d18660 | 1663 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
1664 | |
1665 | aExp = extractFloat32Exp( a ); | |
1666 | if ( 0x96 <= aExp ) { | |
1667 | if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { | |
1668 | return propagateFloat32NaN( a, a STATUS_VAR ); | |
1669 | } | |
1670 | return a; | |
1671 | } | |
1672 | if ( aExp <= 0x7E ) { | |
bb98fe42 | 1673 | if ( (uint32_t) ( float32_val(a)<<1 ) == 0 ) return a; |
158142c2 FB |
1674 | STATUS(float_exception_flags) |= float_flag_inexact; |
1675 | aSign = extractFloat32Sign( a ); | |
1676 | switch ( STATUS(float_rounding_mode) ) { | |
1677 | case float_round_nearest_even: | |
1678 | if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { | |
1679 | return packFloat32( aSign, 0x7F, 0 ); | |
1680 | } | |
1681 | break; | |
1682 | case float_round_down: | |
f090c9d4 | 1683 | return make_float32(aSign ? 0xBF800000 : 0); |
158142c2 | 1684 | case float_round_up: |
f090c9d4 | 1685 | return make_float32(aSign ? 0x80000000 : 0x3F800000); |
158142c2 FB |
1686 | } |
1687 | return packFloat32( aSign, 0, 0 ); | |
1688 | } | |
1689 | lastBitMask = 1; | |
1690 | lastBitMask <<= 0x96 - aExp; | |
1691 | roundBitsMask = lastBitMask - 1; | |
f090c9d4 | 1692 | z = float32_val(a); |
158142c2 FB |
1693 | roundingMode = STATUS(float_rounding_mode); |
1694 | if ( roundingMode == float_round_nearest_even ) { | |
1695 | z += lastBitMask>>1; | |
1696 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; | |
1697 | } | |
1698 | else if ( roundingMode != float_round_to_zero ) { | |
f090c9d4 | 1699 | if ( extractFloat32Sign( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) { |
158142c2 FB |
1700 | z += roundBitsMask; |
1701 | } | |
1702 | } | |
1703 | z &= ~ roundBitsMask; | |
f090c9d4 PB |
1704 | if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact; |
1705 | return make_float32(z); | |
158142c2 FB |
1706 | |
1707 | } | |
1708 | ||
1709 | /*---------------------------------------------------------------------------- | |
1710 | | Returns the result of adding the absolute values of the single-precision | |
1711 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated | |
1712 | | before being returned. `zSign' is ignored if the result is a NaN. | |
1713 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
1714 | | Floating-Point Arithmetic. | |
1715 | *----------------------------------------------------------------------------*/ | |
1716 | ||
1717 | static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) | |
1718 | { | |
1719 | int16 aExp, bExp, zExp; | |
bb98fe42 | 1720 | uint32_t aSig, bSig, zSig; |
158142c2 FB |
1721 | int16 expDiff; |
1722 | ||
1723 | aSig = extractFloat32Frac( a ); | |
1724 | aExp = extractFloat32Exp( a ); | |
1725 | bSig = extractFloat32Frac( b ); | |
1726 | bExp = extractFloat32Exp( b ); | |
1727 | expDiff = aExp - bExp; | |
1728 | aSig <<= 6; | |
1729 | bSig <<= 6; | |
1730 | if ( 0 < expDiff ) { | |
1731 | if ( aExp == 0xFF ) { | |
1732 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1733 | return a; | |
1734 | } | |
1735 | if ( bExp == 0 ) { | |
1736 | --expDiff; | |
1737 | } | |
1738 | else { | |
1739 | bSig |= 0x20000000; | |
1740 | } | |
1741 | shift32RightJamming( bSig, expDiff, &bSig ); | |
1742 | zExp = aExp; | |
1743 | } | |
1744 | else if ( expDiff < 0 ) { | |
1745 | if ( bExp == 0xFF ) { | |
1746 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1747 | return packFloat32( zSign, 0xFF, 0 ); | |
1748 | } | |
1749 | if ( aExp == 0 ) { | |
1750 | ++expDiff; | |
1751 | } | |
1752 | else { | |
1753 | aSig |= 0x20000000; | |
1754 | } | |
1755 | shift32RightJamming( aSig, - expDiff, &aSig ); | |
1756 | zExp = bExp; | |
1757 | } | |
1758 | else { | |
1759 | if ( aExp == 0xFF ) { | |
1760 | if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1761 | return a; | |
1762 | } | |
fe76d976 PB |
1763 | if ( aExp == 0 ) { |
1764 | if ( STATUS(flush_to_zero) ) return packFloat32( zSign, 0, 0 ); | |
1765 | return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); | |
1766 | } | |
158142c2 FB |
1767 | zSig = 0x40000000 + aSig + bSig; |
1768 | zExp = aExp; | |
1769 | goto roundAndPack; | |
1770 | } | |
1771 | aSig |= 0x20000000; | |
1772 | zSig = ( aSig + bSig )<<1; | |
1773 | --zExp; | |
bb98fe42 | 1774 | if ( (int32_t) zSig < 0 ) { |
158142c2 FB |
1775 | zSig = aSig + bSig; |
1776 | ++zExp; | |
1777 | } | |
1778 | roundAndPack: | |
1779 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1780 | ||
1781 | } | |
1782 | ||
1783 | /*---------------------------------------------------------------------------- | |
1784 | | Returns the result of subtracting the absolute values of the single- | |
1785 | | precision floating-point values `a' and `b'. If `zSign' is 1, the | |
1786 | | difference is negated before being returned. `zSign' is ignored if the | |
1787 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
1788 | | Standard for Binary Floating-Point Arithmetic. | |
1789 | *----------------------------------------------------------------------------*/ | |
1790 | ||
1791 | static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) | |
1792 | { | |
1793 | int16 aExp, bExp, zExp; | |
bb98fe42 | 1794 | uint32_t aSig, bSig, zSig; |
158142c2 FB |
1795 | int16 expDiff; |
1796 | ||
1797 | aSig = extractFloat32Frac( a ); | |
1798 | aExp = extractFloat32Exp( a ); | |
1799 | bSig = extractFloat32Frac( b ); | |
1800 | bExp = extractFloat32Exp( b ); | |
1801 | expDiff = aExp - bExp; | |
1802 | aSig <<= 7; | |
1803 | bSig <<= 7; | |
1804 | if ( 0 < expDiff ) goto aExpBigger; | |
1805 | if ( expDiff < 0 ) goto bExpBigger; | |
1806 | if ( aExp == 0xFF ) { | |
1807 | if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1808 | float_raise( float_flag_invalid STATUS_VAR); | |
1809 | return float32_default_nan; | |
1810 | } | |
1811 | if ( aExp == 0 ) { | |
1812 | aExp = 1; | |
1813 | bExp = 1; | |
1814 | } | |
1815 | if ( bSig < aSig ) goto aBigger; | |
1816 | if ( aSig < bSig ) goto bBigger; | |
1817 | return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); | |
1818 | bExpBigger: | |
1819 | if ( bExp == 0xFF ) { | |
1820 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1821 | return packFloat32( zSign ^ 1, 0xFF, 0 ); | |
1822 | } | |
1823 | if ( aExp == 0 ) { | |
1824 | ++expDiff; | |
1825 | } | |
1826 | else { | |
1827 | aSig |= 0x40000000; | |
1828 | } | |
1829 | shift32RightJamming( aSig, - expDiff, &aSig ); | |
1830 | bSig |= 0x40000000; | |
1831 | bBigger: | |
1832 | zSig = bSig - aSig; | |
1833 | zExp = bExp; | |
1834 | zSign ^= 1; | |
1835 | goto normalizeRoundAndPack; | |
1836 | aExpBigger: | |
1837 | if ( aExp == 0xFF ) { | |
1838 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1839 | return a; | |
1840 | } | |
1841 | if ( bExp == 0 ) { | |
1842 | --expDiff; | |
1843 | } | |
1844 | else { | |
1845 | bSig |= 0x40000000; | |
1846 | } | |
1847 | shift32RightJamming( bSig, expDiff, &bSig ); | |
1848 | aSig |= 0x40000000; | |
1849 | aBigger: | |
1850 | zSig = aSig - bSig; | |
1851 | zExp = aExp; | |
1852 | normalizeRoundAndPack: | |
1853 | --zExp; | |
1854 | return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1855 | ||
1856 | } | |
1857 | ||
1858 | /*---------------------------------------------------------------------------- | |
1859 | | Returns the result of adding the single-precision floating-point values `a' | |
1860 | | and `b'. The operation is performed according to the IEC/IEEE Standard for | |
1861 | | Binary Floating-Point Arithmetic. | |
1862 | *----------------------------------------------------------------------------*/ | |
1863 | ||
1864 | float32 float32_add( float32 a, float32 b STATUS_PARAM ) | |
1865 | { | |
1866 | flag aSign, bSign; | |
37d18660 PM |
1867 | a = float32_squash_input_denormal(a STATUS_VAR); |
1868 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
1869 | |
1870 | aSign = extractFloat32Sign( a ); | |
1871 | bSign = extractFloat32Sign( b ); | |
1872 | if ( aSign == bSign ) { | |
1873 | return addFloat32Sigs( a, b, aSign STATUS_VAR); | |
1874 | } | |
1875 | else { | |
1876 | return subFloat32Sigs( a, b, aSign STATUS_VAR ); | |
1877 | } | |
1878 | ||
1879 | } | |
1880 | ||
1881 | /*---------------------------------------------------------------------------- | |
1882 | | Returns the result of subtracting the single-precision floating-point values | |
1883 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
1884 | | for Binary Floating-Point Arithmetic. | |
1885 | *----------------------------------------------------------------------------*/ | |
1886 | ||
1887 | float32 float32_sub( float32 a, float32 b STATUS_PARAM ) | |
1888 | { | |
1889 | flag aSign, bSign; | |
37d18660 PM |
1890 | a = float32_squash_input_denormal(a STATUS_VAR); |
1891 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
1892 | |
1893 | aSign = extractFloat32Sign( a ); | |
1894 | bSign = extractFloat32Sign( b ); | |
1895 | if ( aSign == bSign ) { | |
1896 | return subFloat32Sigs( a, b, aSign STATUS_VAR ); | |
1897 | } | |
1898 | else { | |
1899 | return addFloat32Sigs( a, b, aSign STATUS_VAR ); | |
1900 | } | |
1901 | ||
1902 | } | |
1903 | ||
1904 | /*---------------------------------------------------------------------------- | |
1905 | | Returns the result of multiplying the single-precision floating-point values | |
1906 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
1907 | | for Binary Floating-Point Arithmetic. | |
1908 | *----------------------------------------------------------------------------*/ | |
1909 | ||
1910 | float32 float32_mul( float32 a, float32 b STATUS_PARAM ) | |
1911 | { | |
1912 | flag aSign, bSign, zSign; | |
1913 | int16 aExp, bExp, zExp; | |
bb98fe42 AF |
1914 | uint32_t aSig, bSig; |
1915 | uint64_t zSig64; | |
1916 | uint32_t zSig; | |
158142c2 | 1917 | |
37d18660 PM |
1918 | a = float32_squash_input_denormal(a STATUS_VAR); |
1919 | b = float32_squash_input_denormal(b STATUS_VAR); | |
1920 | ||
158142c2 FB |
1921 | aSig = extractFloat32Frac( a ); |
1922 | aExp = extractFloat32Exp( a ); | |
1923 | aSign = extractFloat32Sign( a ); | |
1924 | bSig = extractFloat32Frac( b ); | |
1925 | bExp = extractFloat32Exp( b ); | |
1926 | bSign = extractFloat32Sign( b ); | |
1927 | zSign = aSign ^ bSign; | |
1928 | if ( aExp == 0xFF ) { | |
1929 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { | |
1930 | return propagateFloat32NaN( a, b STATUS_VAR ); | |
1931 | } | |
1932 | if ( ( bExp | bSig ) == 0 ) { | |
1933 | float_raise( float_flag_invalid STATUS_VAR); | |
1934 | return float32_default_nan; | |
1935 | } | |
1936 | return packFloat32( zSign, 0xFF, 0 ); | |
1937 | } | |
1938 | if ( bExp == 0xFF ) { | |
1939 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1940 | if ( ( aExp | aSig ) == 0 ) { | |
1941 | float_raise( float_flag_invalid STATUS_VAR); | |
1942 | return float32_default_nan; | |
1943 | } | |
1944 | return packFloat32( zSign, 0xFF, 0 ); | |
1945 | } | |
1946 | if ( aExp == 0 ) { | |
1947 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1948 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1949 | } | |
1950 | if ( bExp == 0 ) { | |
1951 | if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1952 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1953 | } | |
1954 | zExp = aExp + bExp - 0x7F; | |
1955 | aSig = ( aSig | 0x00800000 )<<7; | |
1956 | bSig = ( bSig | 0x00800000 )<<8; | |
bb98fe42 | 1957 | shift64RightJamming( ( (uint64_t) aSig ) * bSig, 32, &zSig64 ); |
158142c2 | 1958 | zSig = zSig64; |
bb98fe42 | 1959 | if ( 0 <= (int32_t) ( zSig<<1 ) ) { |
158142c2 FB |
1960 | zSig <<= 1; |
1961 | --zExp; | |
1962 | } | |
1963 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1964 | ||
1965 | } | |
1966 | ||
1967 | /*---------------------------------------------------------------------------- | |
1968 | | Returns the result of dividing the single-precision floating-point value `a' | |
1969 | | by the corresponding value `b'. The operation is performed according to the | |
1970 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1971 | *----------------------------------------------------------------------------*/ | |
1972 | ||
1973 | float32 float32_div( float32 a, float32 b STATUS_PARAM ) | |
1974 | { | |
1975 | flag aSign, bSign, zSign; | |
1976 | int16 aExp, bExp, zExp; | |
bb98fe42 | 1977 | uint32_t aSig, bSig, zSig; |
37d18660 PM |
1978 | a = float32_squash_input_denormal(a STATUS_VAR); |
1979 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
1980 | |
1981 | aSig = extractFloat32Frac( a ); | |
1982 | aExp = extractFloat32Exp( a ); | |
1983 | aSign = extractFloat32Sign( a ); | |
1984 | bSig = extractFloat32Frac( b ); | |
1985 | bExp = extractFloat32Exp( b ); | |
1986 | bSign = extractFloat32Sign( b ); | |
1987 | zSign = aSign ^ bSign; | |
1988 | if ( aExp == 0xFF ) { | |
1989 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1990 | if ( bExp == 0xFF ) { | |
1991 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1992 | float_raise( float_flag_invalid STATUS_VAR); | |
1993 | return float32_default_nan; | |
1994 | } | |
1995 | return packFloat32( zSign, 0xFF, 0 ); | |
1996 | } | |
1997 | if ( bExp == 0xFF ) { | |
1998 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1999 | return packFloat32( zSign, 0, 0 ); | |
2000 | } | |
2001 | if ( bExp == 0 ) { | |
2002 | if ( bSig == 0 ) { | |
2003 | if ( ( aExp | aSig ) == 0 ) { | |
2004 | float_raise( float_flag_invalid STATUS_VAR); | |
2005 | return float32_default_nan; | |
2006 | } | |
2007 | float_raise( float_flag_divbyzero STATUS_VAR); | |
2008 | return packFloat32( zSign, 0xFF, 0 ); | |
2009 | } | |
2010 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
2011 | } | |
2012 | if ( aExp == 0 ) { | |
2013 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
2014 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
2015 | } | |
2016 | zExp = aExp - bExp + 0x7D; | |
2017 | aSig = ( aSig | 0x00800000 )<<7; | |
2018 | bSig = ( bSig | 0x00800000 )<<8; | |
2019 | if ( bSig <= ( aSig + aSig ) ) { | |
2020 | aSig >>= 1; | |
2021 | ++zExp; | |
2022 | } | |
bb98fe42 | 2023 | zSig = ( ( (uint64_t) aSig )<<32 ) / bSig; |
158142c2 | 2024 | if ( ( zSig & 0x3F ) == 0 ) { |
bb98fe42 | 2025 | zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 ); |
158142c2 FB |
2026 | } |
2027 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
2028 | ||
2029 | } | |
2030 | ||
2031 | /*---------------------------------------------------------------------------- | |
2032 | | Returns the remainder of the single-precision floating-point value `a' | |
2033 | | with respect to the corresponding value `b'. The operation is performed | |
2034 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2035 | *----------------------------------------------------------------------------*/ | |
2036 | ||
2037 | float32 float32_rem( float32 a, float32 b STATUS_PARAM ) | |
2038 | { | |
ed086f3d | 2039 | flag aSign, zSign; |
158142c2 | 2040 | int16 aExp, bExp, expDiff; |
bb98fe42 AF |
2041 | uint32_t aSig, bSig; |
2042 | uint32_t q; | |
2043 | uint64_t aSig64, bSig64, q64; | |
2044 | uint32_t alternateASig; | |
2045 | int32_t sigMean; | |
37d18660 PM |
2046 | a = float32_squash_input_denormal(a STATUS_VAR); |
2047 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2048 | |
2049 | aSig = extractFloat32Frac( a ); | |
2050 | aExp = extractFloat32Exp( a ); | |
2051 | aSign = extractFloat32Sign( a ); | |
2052 | bSig = extractFloat32Frac( b ); | |
2053 | bExp = extractFloat32Exp( b ); | |
158142c2 FB |
2054 | if ( aExp == 0xFF ) { |
2055 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { | |
2056 | return propagateFloat32NaN( a, b STATUS_VAR ); | |
2057 | } | |
2058 | float_raise( float_flag_invalid STATUS_VAR); | |
2059 | return float32_default_nan; | |
2060 | } | |
2061 | if ( bExp == 0xFF ) { | |
2062 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
2063 | return a; | |
2064 | } | |
2065 | if ( bExp == 0 ) { | |
2066 | if ( bSig == 0 ) { | |
2067 | float_raise( float_flag_invalid STATUS_VAR); | |
2068 | return float32_default_nan; | |
2069 | } | |
2070 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
2071 | } | |
2072 | if ( aExp == 0 ) { | |
2073 | if ( aSig == 0 ) return a; | |
2074 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
2075 | } | |
2076 | expDiff = aExp - bExp; | |
2077 | aSig |= 0x00800000; | |
2078 | bSig |= 0x00800000; | |
2079 | if ( expDiff < 32 ) { | |
2080 | aSig <<= 8; | |
2081 | bSig <<= 8; | |
2082 | if ( expDiff < 0 ) { | |
2083 | if ( expDiff < -1 ) return a; | |
2084 | aSig >>= 1; | |
2085 | } | |
2086 | q = ( bSig <= aSig ); | |
2087 | if ( q ) aSig -= bSig; | |
2088 | if ( 0 < expDiff ) { | |
bb98fe42 | 2089 | q = ( ( (uint64_t) aSig )<<32 ) / bSig; |
158142c2 FB |
2090 | q >>= 32 - expDiff; |
2091 | bSig >>= 2; | |
2092 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; | |
2093 | } | |
2094 | else { | |
2095 | aSig >>= 2; | |
2096 | bSig >>= 2; | |
2097 | } | |
2098 | } | |
2099 | else { | |
2100 | if ( bSig <= aSig ) aSig -= bSig; | |
bb98fe42 AF |
2101 | aSig64 = ( (uint64_t) aSig )<<40; |
2102 | bSig64 = ( (uint64_t) bSig )<<40; | |
158142c2 FB |
2103 | expDiff -= 64; |
2104 | while ( 0 < expDiff ) { | |
2105 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); | |
2106 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; | |
2107 | aSig64 = - ( ( bSig * q64 )<<38 ); | |
2108 | expDiff -= 62; | |
2109 | } | |
2110 | expDiff += 64; | |
2111 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); | |
2112 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; | |
2113 | q = q64>>( 64 - expDiff ); | |
2114 | bSig <<= 6; | |
2115 | aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; | |
2116 | } | |
2117 | do { | |
2118 | alternateASig = aSig; | |
2119 | ++q; | |
2120 | aSig -= bSig; | |
bb98fe42 | 2121 | } while ( 0 <= (int32_t) aSig ); |
158142c2 FB |
2122 | sigMean = aSig + alternateASig; |
2123 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { | |
2124 | aSig = alternateASig; | |
2125 | } | |
bb98fe42 | 2126 | zSign = ( (int32_t) aSig < 0 ); |
158142c2 FB |
2127 | if ( zSign ) aSig = - aSig; |
2128 | return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR ); | |
2129 | ||
2130 | } | |
2131 | ||
2132 | /*---------------------------------------------------------------------------- | |
2133 | | Returns the square root of the single-precision floating-point value `a'. | |
2134 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
2135 | | Floating-Point Arithmetic. | |
2136 | *----------------------------------------------------------------------------*/ | |
2137 | ||
2138 | float32 float32_sqrt( float32 a STATUS_PARAM ) | |
2139 | { | |
2140 | flag aSign; | |
2141 | int16 aExp, zExp; | |
bb98fe42 AF |
2142 | uint32_t aSig, zSig; |
2143 | uint64_t rem, term; | |
37d18660 | 2144 | a = float32_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2145 | |
2146 | aSig = extractFloat32Frac( a ); | |
2147 | aExp = extractFloat32Exp( a ); | |
2148 | aSign = extractFloat32Sign( a ); | |
2149 | if ( aExp == 0xFF ) { | |
f090c9d4 | 2150 | if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
158142c2 FB |
2151 | if ( ! aSign ) return a; |
2152 | float_raise( float_flag_invalid STATUS_VAR); | |
2153 | return float32_default_nan; | |
2154 | } | |
2155 | if ( aSign ) { | |
2156 | if ( ( aExp | aSig ) == 0 ) return a; | |
2157 | float_raise( float_flag_invalid STATUS_VAR); | |
2158 | return float32_default_nan; | |
2159 | } | |
2160 | if ( aExp == 0 ) { | |
f090c9d4 | 2161 | if ( aSig == 0 ) return float32_zero; |
158142c2 FB |
2162 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2163 | } | |
2164 | zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; | |
2165 | aSig = ( aSig | 0x00800000 )<<8; | |
2166 | zSig = estimateSqrt32( aExp, aSig ) + 2; | |
2167 | if ( ( zSig & 0x7F ) <= 5 ) { | |
2168 | if ( zSig < 2 ) { | |
2169 | zSig = 0x7FFFFFFF; | |
2170 | goto roundAndPack; | |
2171 | } | |
2172 | aSig >>= aExp & 1; | |
bb98fe42 AF |
2173 | term = ( (uint64_t) zSig ) * zSig; |
2174 | rem = ( ( (uint64_t) aSig )<<32 ) - term; | |
2175 | while ( (int64_t) rem < 0 ) { | |
158142c2 | 2176 | --zSig; |
bb98fe42 | 2177 | rem += ( ( (uint64_t) zSig )<<1 ) | 1; |
158142c2 FB |
2178 | } |
2179 | zSig |= ( rem != 0 ); | |
2180 | } | |
2181 | shift32RightJamming( zSig, 1, &zSig ); | |
2182 | roundAndPack: | |
2183 | return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); | |
2184 | ||
2185 | } | |
2186 | ||
8229c991 AJ |
2187 | /*---------------------------------------------------------------------------- |
2188 | | Returns the binary exponential of the single-precision floating-point value | |
2189 | | `a'. The operation is performed according to the IEC/IEEE Standard for | |
2190 | | Binary Floating-Point Arithmetic. | |
2191 | | | |
2192 | | Uses the following identities: | |
2193 | | | |
2194 | | 1. ------------------------------------------------------------------------- | |
2195 | | x x*ln(2) | |
2196 | | 2 = e | |
2197 | | | |
2198 | | 2. ------------------------------------------------------------------------- | |
2199 | | 2 3 4 5 n | |
2200 | | x x x x x x x | |
2201 | | e = 1 + --- + --- + --- + --- + --- + ... + --- + ... | |
2202 | | 1! 2! 3! 4! 5! n! | |
2203 | *----------------------------------------------------------------------------*/ | |
2204 | ||
2205 | static const float64 float32_exp2_coefficients[15] = | |
2206 | { | |
d5138cf4 PM |
2207 | const_float64( 0x3ff0000000000000ll ), /* 1 */ |
2208 | const_float64( 0x3fe0000000000000ll ), /* 2 */ | |
2209 | const_float64( 0x3fc5555555555555ll ), /* 3 */ | |
2210 | const_float64( 0x3fa5555555555555ll ), /* 4 */ | |
2211 | const_float64( 0x3f81111111111111ll ), /* 5 */ | |
2212 | const_float64( 0x3f56c16c16c16c17ll ), /* 6 */ | |
2213 | const_float64( 0x3f2a01a01a01a01all ), /* 7 */ | |
2214 | const_float64( 0x3efa01a01a01a01all ), /* 8 */ | |
2215 | const_float64( 0x3ec71de3a556c734ll ), /* 9 */ | |
2216 | const_float64( 0x3e927e4fb7789f5cll ), /* 10 */ | |
2217 | const_float64( 0x3e5ae64567f544e4ll ), /* 11 */ | |
2218 | const_float64( 0x3e21eed8eff8d898ll ), /* 12 */ | |
2219 | const_float64( 0x3de6124613a86d09ll ), /* 13 */ | |
2220 | const_float64( 0x3da93974a8c07c9dll ), /* 14 */ | |
2221 | const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */ | |
8229c991 AJ |
2222 | }; |
2223 | ||
2224 | float32 float32_exp2( float32 a STATUS_PARAM ) | |
2225 | { | |
2226 | flag aSign; | |
2227 | int16 aExp; | |
bb98fe42 | 2228 | uint32_t aSig; |
8229c991 AJ |
2229 | float64 r, x, xn; |
2230 | int i; | |
37d18660 | 2231 | a = float32_squash_input_denormal(a STATUS_VAR); |
8229c991 AJ |
2232 | |
2233 | aSig = extractFloat32Frac( a ); | |
2234 | aExp = extractFloat32Exp( a ); | |
2235 | aSign = extractFloat32Sign( a ); | |
2236 | ||
2237 | if ( aExp == 0xFF) { | |
2238 | if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); | |
2239 | return (aSign) ? float32_zero : a; | |
2240 | } | |
2241 | if (aExp == 0) { | |
2242 | if (aSig == 0) return float32_one; | |
2243 | } | |
2244 | ||
2245 | float_raise( float_flag_inexact STATUS_VAR); | |
2246 | ||
2247 | /* ******************************* */ | |
2248 | /* using float64 for approximation */ | |
2249 | /* ******************************* */ | |
2250 | x = float32_to_float64(a STATUS_VAR); | |
2251 | x = float64_mul(x, float64_ln2 STATUS_VAR); | |
2252 | ||
2253 | xn = x; | |
2254 | r = float64_one; | |
2255 | for (i = 0 ; i < 15 ; i++) { | |
2256 | float64 f; | |
2257 | ||
2258 | f = float64_mul(xn, float32_exp2_coefficients[i] STATUS_VAR); | |
2259 | r = float64_add(r, f STATUS_VAR); | |
2260 | ||
2261 | xn = float64_mul(xn, x STATUS_VAR); | |
2262 | } | |
2263 | ||
2264 | return float64_to_float32(r, status); | |
2265 | } | |
2266 | ||
374dfc33 AJ |
2267 | /*---------------------------------------------------------------------------- |
2268 | | Returns the binary log of the single-precision floating-point value `a'. | |
2269 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
2270 | | Floating-Point Arithmetic. | |
2271 | *----------------------------------------------------------------------------*/ | |
2272 | float32 float32_log2( float32 a STATUS_PARAM ) | |
2273 | { | |
2274 | flag aSign, zSign; | |
2275 | int16 aExp; | |
bb98fe42 | 2276 | uint32_t aSig, zSig, i; |
374dfc33 | 2277 | |
37d18660 | 2278 | a = float32_squash_input_denormal(a STATUS_VAR); |
374dfc33 AJ |
2279 | aSig = extractFloat32Frac( a ); |
2280 | aExp = extractFloat32Exp( a ); | |
2281 | aSign = extractFloat32Sign( a ); | |
2282 | ||
2283 | if ( aExp == 0 ) { | |
2284 | if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 ); | |
2285 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
2286 | } | |
2287 | if ( aSign ) { | |
2288 | float_raise( float_flag_invalid STATUS_VAR); | |
2289 | return float32_default_nan; | |
2290 | } | |
2291 | if ( aExp == 0xFF ) { | |
2292 | if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); | |
2293 | return a; | |
2294 | } | |
2295 | ||
2296 | aExp -= 0x7F; | |
2297 | aSig |= 0x00800000; | |
2298 | zSign = aExp < 0; | |
2299 | zSig = aExp << 23; | |
2300 | ||
2301 | for (i = 1 << 22; i > 0; i >>= 1) { | |
bb98fe42 | 2302 | aSig = ( (uint64_t)aSig * aSig ) >> 23; |
374dfc33 AJ |
2303 | if ( aSig & 0x01000000 ) { |
2304 | aSig >>= 1; | |
2305 | zSig |= i; | |
2306 | } | |
2307 | } | |
2308 | ||
2309 | if ( zSign ) | |
2310 | zSig = -zSig; | |
2311 | ||
2312 | return normalizeRoundAndPackFloat32( zSign, 0x85, zSig STATUS_VAR ); | |
2313 | } | |
2314 | ||
158142c2 FB |
2315 | /*---------------------------------------------------------------------------- |
2316 | | Returns 1 if the single-precision floating-point value `a' is equal to | |
2317 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
2318 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2319 | *----------------------------------------------------------------------------*/ | |
2320 | ||
750afe93 | 2321 | int float32_eq( float32 a, float32 b STATUS_PARAM ) |
158142c2 | 2322 | { |
37d18660 PM |
2323 | a = float32_squash_input_denormal(a STATUS_VAR); |
2324 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2325 | |
2326 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2327 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2328 | ) { | |
2329 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
2330 | float_raise( float_flag_invalid STATUS_VAR); | |
2331 | } | |
2332 | return 0; | |
2333 | } | |
f090c9d4 | 2334 | return ( float32_val(a) == float32_val(b) ) || |
bb98fe42 | 2335 | ( (uint32_t) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 ); |
158142c2 FB |
2336 | |
2337 | } | |
2338 | ||
2339 | /*---------------------------------------------------------------------------- | |
2340 | | Returns 1 if the single-precision floating-point value `a' is less than | |
2341 | | or equal to the corresponding value `b', and 0 otherwise. The comparison | |
2342 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2343 | | Arithmetic. | |
2344 | *----------------------------------------------------------------------------*/ | |
2345 | ||
750afe93 | 2346 | int float32_le( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2347 | { |
2348 | flag aSign, bSign; | |
bb98fe42 | 2349 | uint32_t av, bv; |
37d18660 PM |
2350 | a = float32_squash_input_denormal(a STATUS_VAR); |
2351 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2352 | |
2353 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2354 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2355 | ) { | |
2356 | float_raise( float_flag_invalid STATUS_VAR); | |
2357 | return 0; | |
2358 | } | |
2359 | aSign = extractFloat32Sign( a ); | |
2360 | bSign = extractFloat32Sign( b ); | |
f090c9d4 PB |
2361 | av = float32_val(a); |
2362 | bv = float32_val(b); | |
bb98fe42 | 2363 | if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
f090c9d4 | 2364 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
158142c2 FB |
2365 | |
2366 | } | |
2367 | ||
2368 | /*---------------------------------------------------------------------------- | |
2369 | | Returns 1 if the single-precision floating-point value `a' is less than | |
2370 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
2371 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2372 | *----------------------------------------------------------------------------*/ | |
2373 | ||
750afe93 | 2374 | int float32_lt( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2375 | { |
2376 | flag aSign, bSign; | |
bb98fe42 | 2377 | uint32_t av, bv; |
37d18660 PM |
2378 | a = float32_squash_input_denormal(a STATUS_VAR); |
2379 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2380 | |
2381 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2382 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2383 | ) { | |
2384 | float_raise( float_flag_invalid STATUS_VAR); | |
2385 | return 0; | |
2386 | } | |
2387 | aSign = extractFloat32Sign( a ); | |
2388 | bSign = extractFloat32Sign( b ); | |
f090c9d4 PB |
2389 | av = float32_val(a); |
2390 | bv = float32_val(b); | |
bb98fe42 | 2391 | if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); |
f090c9d4 | 2392 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
158142c2 FB |
2393 | |
2394 | } | |
2395 | ||
2396 | /*---------------------------------------------------------------------------- | |
2397 | | Returns 1 if the single-precision floating-point value `a' is equal to | |
2398 | | the corresponding value `b', and 0 otherwise. The invalid exception is | |
2399 | | raised if either operand is a NaN. Otherwise, the comparison is performed | |
2400 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2401 | *----------------------------------------------------------------------------*/ | |
2402 | ||
750afe93 | 2403 | int float32_eq_signaling( float32 a, float32 b STATUS_PARAM ) |
158142c2 | 2404 | { |
bb98fe42 | 2405 | uint32_t av, bv; |
37d18660 PM |
2406 | a = float32_squash_input_denormal(a STATUS_VAR); |
2407 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2408 | |
2409 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2410 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2411 | ) { | |
2412 | float_raise( float_flag_invalid STATUS_VAR); | |
2413 | return 0; | |
2414 | } | |
f090c9d4 PB |
2415 | av = float32_val(a); |
2416 | bv = float32_val(b); | |
bb98fe42 | 2417 | return ( av == bv ) || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
158142c2 FB |
2418 | |
2419 | } | |
2420 | ||
2421 | /*---------------------------------------------------------------------------- | |
2422 | | Returns 1 if the single-precision floating-point value `a' is less than or | |
2423 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
2424 | | cause an exception. Otherwise, the comparison is performed according to the | |
2425 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2426 | *----------------------------------------------------------------------------*/ | |
2427 | ||
750afe93 | 2428 | int float32_le_quiet( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2429 | { |
2430 | flag aSign, bSign; | |
bb98fe42 | 2431 | uint32_t av, bv; |
37d18660 PM |
2432 | a = float32_squash_input_denormal(a STATUS_VAR); |
2433 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2434 | |
2435 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2436 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2437 | ) { | |
2438 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
2439 | float_raise( float_flag_invalid STATUS_VAR); | |
2440 | } | |
2441 | return 0; | |
2442 | } | |
2443 | aSign = extractFloat32Sign( a ); | |
2444 | bSign = extractFloat32Sign( b ); | |
f090c9d4 PB |
2445 | av = float32_val(a); |
2446 | bv = float32_val(b); | |
bb98fe42 | 2447 | if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
f090c9d4 | 2448 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
158142c2 FB |
2449 | |
2450 | } | |
2451 | ||
2452 | /*---------------------------------------------------------------------------- | |
2453 | | Returns 1 if the single-precision floating-point value `a' is less than | |
2454 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
2455 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
2456 | | Standard for Binary Floating-Point Arithmetic. | |
2457 | *----------------------------------------------------------------------------*/ | |
2458 | ||
750afe93 | 2459 | int float32_lt_quiet( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2460 | { |
2461 | flag aSign, bSign; | |
bb98fe42 | 2462 | uint32_t av, bv; |
37d18660 PM |
2463 | a = float32_squash_input_denormal(a STATUS_VAR); |
2464 | b = float32_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
2465 | |
2466 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2467 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2468 | ) { | |
2469 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
2470 | float_raise( float_flag_invalid STATUS_VAR); | |
2471 | } | |
2472 | return 0; | |
2473 | } | |
2474 | aSign = extractFloat32Sign( a ); | |
2475 | bSign = extractFloat32Sign( b ); | |
f090c9d4 PB |
2476 | av = float32_val(a); |
2477 | bv = float32_val(b); | |
bb98fe42 | 2478 | if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); |
f090c9d4 | 2479 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
158142c2 FB |
2480 | |
2481 | } | |
2482 | ||
2483 | /*---------------------------------------------------------------------------- | |
2484 | | Returns the result of converting the double-precision floating-point value | |
2485 | | `a' to the 32-bit two's complement integer format. The conversion is | |
2486 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2487 | | Arithmetic---which means in particular that the conversion is rounded | |
2488 | | according to the current rounding mode. If `a' is a NaN, the largest | |
2489 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
2490 | | largest integer with the same sign as `a' is returned. | |
2491 | *----------------------------------------------------------------------------*/ | |
2492 | ||
2493 | int32 float64_to_int32( float64 a STATUS_PARAM ) | |
2494 | { | |
2495 | flag aSign; | |
2496 | int16 aExp, shiftCount; | |
bb98fe42 | 2497 | uint64_t aSig; |
37d18660 | 2498 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2499 | |
2500 | aSig = extractFloat64Frac( a ); | |
2501 | aExp = extractFloat64Exp( a ); | |
2502 | aSign = extractFloat64Sign( a ); | |
2503 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
2504 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
2505 | shiftCount = 0x42C - aExp; | |
2506 | if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); | |
2507 | return roundAndPackInt32( aSign, aSig STATUS_VAR ); | |
2508 | ||
2509 | } | |
2510 | ||
2511 | /*---------------------------------------------------------------------------- | |
2512 | | Returns the result of converting the double-precision floating-point value | |
2513 | | `a' to the 32-bit two's complement integer format. The conversion is | |
2514 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2515 | | Arithmetic, except that the conversion is always rounded toward zero. | |
2516 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
2517 | | the conversion overflows, the largest integer with the same sign as `a' is | |
2518 | | returned. | |
2519 | *----------------------------------------------------------------------------*/ | |
2520 | ||
2521 | int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) | |
2522 | { | |
2523 | flag aSign; | |
2524 | int16 aExp, shiftCount; | |
bb98fe42 | 2525 | uint64_t aSig, savedASig; |
158142c2 | 2526 | int32 z; |
37d18660 | 2527 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2528 | |
2529 | aSig = extractFloat64Frac( a ); | |
2530 | aExp = extractFloat64Exp( a ); | |
2531 | aSign = extractFloat64Sign( a ); | |
2532 | if ( 0x41E < aExp ) { | |
2533 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
2534 | goto invalid; | |
2535 | } | |
2536 | else if ( aExp < 0x3FF ) { | |
2537 | if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
2538 | return 0; | |
2539 | } | |
2540 | aSig |= LIT64( 0x0010000000000000 ); | |
2541 | shiftCount = 0x433 - aExp; | |
2542 | savedASig = aSig; | |
2543 | aSig >>= shiftCount; | |
2544 | z = aSig; | |
2545 | if ( aSign ) z = - z; | |
2546 | if ( ( z < 0 ) ^ aSign ) { | |
2547 | invalid: | |
2548 | float_raise( float_flag_invalid STATUS_VAR); | |
bb98fe42 | 2549 | return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
158142c2 FB |
2550 | } |
2551 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
2552 | STATUS(float_exception_flags) |= float_flag_inexact; | |
2553 | } | |
2554 | return z; | |
2555 | ||
2556 | } | |
2557 | ||
cbcef455 PM |
2558 | /*---------------------------------------------------------------------------- |
2559 | | Returns the result of converting the double-precision floating-point value | |
2560 | | `a' to the 16-bit two's complement integer format. The conversion is | |
2561 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2562 | | Arithmetic, except that the conversion is always rounded toward zero. | |
2563 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
2564 | | the conversion overflows, the largest integer with the same sign as `a' is | |
2565 | | returned. | |
2566 | *----------------------------------------------------------------------------*/ | |
2567 | ||
2568 | int16 float64_to_int16_round_to_zero( float64 a STATUS_PARAM ) | |
2569 | { | |
2570 | flag aSign; | |
2571 | int16 aExp, shiftCount; | |
bb98fe42 | 2572 | uint64_t aSig, savedASig; |
cbcef455 PM |
2573 | int32 z; |
2574 | ||
2575 | aSig = extractFloat64Frac( a ); | |
2576 | aExp = extractFloat64Exp( a ); | |
2577 | aSign = extractFloat64Sign( a ); | |
2578 | if ( 0x40E < aExp ) { | |
2579 | if ( ( aExp == 0x7FF ) && aSig ) { | |
2580 | aSign = 0; | |
2581 | } | |
2582 | goto invalid; | |
2583 | } | |
2584 | else if ( aExp < 0x3FF ) { | |
2585 | if ( aExp || aSig ) { | |
2586 | STATUS(float_exception_flags) |= float_flag_inexact; | |
2587 | } | |
2588 | return 0; | |
2589 | } | |
2590 | aSig |= LIT64( 0x0010000000000000 ); | |
2591 | shiftCount = 0x433 - aExp; | |
2592 | savedASig = aSig; | |
2593 | aSig >>= shiftCount; | |
2594 | z = aSig; | |
2595 | if ( aSign ) { | |
2596 | z = - z; | |
2597 | } | |
2598 | if ( ( (int16_t)z < 0 ) ^ aSign ) { | |
2599 | invalid: | |
2600 | float_raise( float_flag_invalid STATUS_VAR); | |
bb98fe42 | 2601 | return aSign ? (int32_t) 0xffff8000 : 0x7FFF; |
cbcef455 PM |
2602 | } |
2603 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
2604 | STATUS(float_exception_flags) |= float_flag_inexact; | |
2605 | } | |
2606 | return z; | |
2607 | } | |
2608 | ||
158142c2 FB |
2609 | /*---------------------------------------------------------------------------- |
2610 | | Returns the result of converting the double-precision floating-point value | |
2611 | | `a' to the 64-bit two's complement integer format. The conversion is | |
2612 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2613 | | Arithmetic---which means in particular that the conversion is rounded | |
2614 | | according to the current rounding mode. If `a' is a NaN, the largest | |
2615 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
2616 | | largest integer with the same sign as `a' is returned. | |
2617 | *----------------------------------------------------------------------------*/ | |
2618 | ||
2619 | int64 float64_to_int64( float64 a STATUS_PARAM ) | |
2620 | { | |
2621 | flag aSign; | |
2622 | int16 aExp, shiftCount; | |
bb98fe42 | 2623 | uint64_t aSig, aSigExtra; |
37d18660 | 2624 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2625 | |
2626 | aSig = extractFloat64Frac( a ); | |
2627 | aExp = extractFloat64Exp( a ); | |
2628 | aSign = extractFloat64Sign( a ); | |
2629 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
2630 | shiftCount = 0x433 - aExp; | |
2631 | if ( shiftCount <= 0 ) { | |
2632 | if ( 0x43E < aExp ) { | |
2633 | float_raise( float_flag_invalid STATUS_VAR); | |
2634 | if ( ! aSign | |
2635 | || ( ( aExp == 0x7FF ) | |
2636 | && ( aSig != LIT64( 0x0010000000000000 ) ) ) | |
2637 | ) { | |
2638 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
2639 | } | |
bb98fe42 | 2640 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
2641 | } |
2642 | aSigExtra = 0; | |
2643 | aSig <<= - shiftCount; | |
2644 | } | |
2645 | else { | |
2646 | shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); | |
2647 | } | |
2648 | return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); | |
2649 | ||
2650 | } | |
2651 | ||
2652 | /*---------------------------------------------------------------------------- | |
2653 | | Returns the result of converting the double-precision floating-point value | |
2654 | | `a' to the 64-bit two's complement integer format. The conversion is | |
2655 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2656 | | Arithmetic, except that the conversion is always rounded toward zero. | |
2657 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
2658 | | the conversion overflows, the largest integer with the same sign as `a' is | |
2659 | | returned. | |
2660 | *----------------------------------------------------------------------------*/ | |
2661 | ||
2662 | int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) | |
2663 | { | |
2664 | flag aSign; | |
2665 | int16 aExp, shiftCount; | |
bb98fe42 | 2666 | uint64_t aSig; |
158142c2 | 2667 | int64 z; |
37d18660 | 2668 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2669 | |
2670 | aSig = extractFloat64Frac( a ); | |
2671 | aExp = extractFloat64Exp( a ); | |
2672 | aSign = extractFloat64Sign( a ); | |
2673 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
2674 | shiftCount = aExp - 0x433; | |
2675 | if ( 0 <= shiftCount ) { | |
2676 | if ( 0x43E <= aExp ) { | |
f090c9d4 | 2677 | if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) { |
158142c2 FB |
2678 | float_raise( float_flag_invalid STATUS_VAR); |
2679 | if ( ! aSign | |
2680 | || ( ( aExp == 0x7FF ) | |
2681 | && ( aSig != LIT64( 0x0010000000000000 ) ) ) | |
2682 | ) { | |
2683 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
2684 | } | |
2685 | } | |
bb98fe42 | 2686 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
2687 | } |
2688 | z = aSig<<shiftCount; | |
2689 | } | |
2690 | else { | |
2691 | if ( aExp < 0x3FE ) { | |
2692 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
2693 | return 0; | |
2694 | } | |
2695 | z = aSig>>( - shiftCount ); | |
bb98fe42 | 2696 | if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { |
158142c2 FB |
2697 | STATUS(float_exception_flags) |= float_flag_inexact; |
2698 | } | |
2699 | } | |
2700 | if ( aSign ) z = - z; | |
2701 | return z; | |
2702 | ||
2703 | } | |
2704 | ||
2705 | /*---------------------------------------------------------------------------- | |
2706 | | Returns the result of converting the double-precision floating-point value | |
2707 | | `a' to the single-precision floating-point format. The conversion is | |
2708 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2709 | | Arithmetic. | |
2710 | *----------------------------------------------------------------------------*/ | |
2711 | ||
2712 | float32 float64_to_float32( float64 a STATUS_PARAM ) | |
2713 | { | |
2714 | flag aSign; | |
2715 | int16 aExp; | |
bb98fe42 AF |
2716 | uint64_t aSig; |
2717 | uint32_t zSig; | |
37d18660 | 2718 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2719 | |
2720 | aSig = extractFloat64Frac( a ); | |
2721 | aExp = extractFloat64Exp( a ); | |
2722 | aSign = extractFloat64Sign( a ); | |
2723 | if ( aExp == 0x7FF ) { | |
bcd4d9af | 2724 | if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
2725 | return packFloat32( aSign, 0xFF, 0 ); |
2726 | } | |
2727 | shift64RightJamming( aSig, 22, &aSig ); | |
2728 | zSig = aSig; | |
2729 | if ( aExp || zSig ) { | |
2730 | zSig |= 0x40000000; | |
2731 | aExp -= 0x381; | |
2732 | } | |
2733 | return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); | |
2734 | ||
2735 | } | |
2736 | ||
60011498 PB |
2737 | |
2738 | /*---------------------------------------------------------------------------- | |
2739 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
2740 | | half-precision floating-point value, returning the result. After being | |
2741 | | shifted into the proper positions, the three fields are simply added | |
2742 | | together to form the result. This means that any integer portion of `zSig' | |
2743 | | will be added into the exponent. Since a properly normalized significand | |
2744 | | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
2745 | | than the desired result exponent whenever `zSig' is a complete, normalized | |
2746 | | significand. | |
2747 | *----------------------------------------------------------------------------*/ | |
bb98fe42 | 2748 | static float16 packFloat16(flag zSign, int16 zExp, uint16_t zSig) |
60011498 | 2749 | { |
bb4d4bb3 | 2750 | return make_float16( |
bb98fe42 | 2751 | (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig); |
60011498 PB |
2752 | } |
2753 | ||
2754 | /* Half precision floats come in two formats: standard IEEE and "ARM" format. | |
2755 | The latter gains extra exponent range by omitting the NaN/Inf encodings. */ | |
bb4d4bb3 PM |
2756 | |
2757 | float32 float16_to_float32(float16 a, flag ieee STATUS_PARAM) | |
60011498 PB |
2758 | { |
2759 | flag aSign; | |
2760 | int16 aExp; | |
bb98fe42 | 2761 | uint32_t aSig; |
60011498 | 2762 | |
bb4d4bb3 PM |
2763 | aSign = extractFloat16Sign(a); |
2764 | aExp = extractFloat16Exp(a); | |
2765 | aSig = extractFloat16Frac(a); | |
60011498 PB |
2766 | |
2767 | if (aExp == 0x1f && ieee) { | |
2768 | if (aSig) { | |
f591e1be | 2769 | return commonNaNToFloat32(float16ToCommonNaN(a STATUS_VAR) STATUS_VAR); |
60011498 PB |
2770 | } |
2771 | return packFloat32(aSign, 0xff, aSig << 13); | |
2772 | } | |
2773 | if (aExp == 0) { | |
2774 | int8 shiftCount; | |
2775 | ||
2776 | if (aSig == 0) { | |
2777 | return packFloat32(aSign, 0, 0); | |
2778 | } | |
2779 | ||
2780 | shiftCount = countLeadingZeros32( aSig ) - 21; | |
2781 | aSig = aSig << shiftCount; | |
2782 | aExp = -shiftCount; | |
2783 | } | |
2784 | return packFloat32( aSign, aExp + 0x70, aSig << 13); | |
2785 | } | |
2786 | ||
bb4d4bb3 | 2787 | float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM) |
60011498 PB |
2788 | { |
2789 | flag aSign; | |
2790 | int16 aExp; | |
bb98fe42 AF |
2791 | uint32_t aSig; |
2792 | uint32_t mask; | |
2793 | uint32_t increment; | |
60011498 | 2794 | int8 roundingMode; |
37d18660 | 2795 | a = float32_squash_input_denormal(a STATUS_VAR); |
60011498 PB |
2796 | |
2797 | aSig = extractFloat32Frac( a ); | |
2798 | aExp = extractFloat32Exp( a ); | |
2799 | aSign = extractFloat32Sign( a ); | |
2800 | if ( aExp == 0xFF ) { | |
2801 | if (aSig) { | |
600e30d2 PM |
2802 | /* Input is a NaN */ |
2803 | float16 r = commonNaNToFloat16( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); | |
2804 | if (!ieee) { | |
2805 | return packFloat16(aSign, 0, 0); | |
2806 | } | |
2807 | return r; | |
60011498 | 2808 | } |
600e30d2 PM |
2809 | /* Infinity */ |
2810 | if (!ieee) { | |
2811 | float_raise(float_flag_invalid STATUS_VAR); | |
2812 | return packFloat16(aSign, 0x1f, 0x3ff); | |
2813 | } | |
2814 | return packFloat16(aSign, 0x1f, 0); | |
60011498 | 2815 | } |
600e30d2 | 2816 | if (aExp == 0 && aSig == 0) { |
60011498 PB |
2817 | return packFloat16(aSign, 0, 0); |
2818 | } | |
2819 | /* Decimal point between bits 22 and 23. */ | |
2820 | aSig |= 0x00800000; | |
2821 | aExp -= 0x7f; | |
2822 | if (aExp < -14) { | |
600e30d2 PM |
2823 | mask = 0x00ffffff; |
2824 | if (aExp >= -24) { | |
2825 | mask >>= 25 + aExp; | |
60011498 PB |
2826 | } |
2827 | } else { | |
2828 | mask = 0x00001fff; | |
2829 | } | |
2830 | if (aSig & mask) { | |
2831 | float_raise( float_flag_underflow STATUS_VAR ); | |
2832 | roundingMode = STATUS(float_rounding_mode); | |
2833 | switch (roundingMode) { | |
2834 | case float_round_nearest_even: | |
2835 | increment = (mask + 1) >> 1; | |
2836 | if ((aSig & mask) == increment) { | |
2837 | increment = aSig & (increment << 1); | |
2838 | } | |
2839 | break; | |
2840 | case float_round_up: | |
2841 | increment = aSign ? 0 : mask; | |
2842 | break; | |
2843 | case float_round_down: | |
2844 | increment = aSign ? mask : 0; | |
2845 | break; | |
2846 | default: /* round_to_zero */ | |
2847 | increment = 0; | |
2848 | break; | |
2849 | } | |
2850 | aSig += increment; | |
2851 | if (aSig >= 0x01000000) { | |
2852 | aSig >>= 1; | |
2853 | aExp++; | |
2854 | } | |
2855 | } else if (aExp < -14 | |
2856 | && STATUS(float_detect_tininess) == float_tininess_before_rounding) { | |
2857 | float_raise( float_flag_underflow STATUS_VAR); | |
2858 | } | |
2859 | ||
2860 | if (ieee) { | |
2861 | if (aExp > 15) { | |
2862 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
2863 | return packFloat16(aSign, 0x1f, 0); | |
2864 | } | |
2865 | } else { | |
2866 | if (aExp > 16) { | |
600e30d2 | 2867 | float_raise(float_flag_invalid | float_flag_inexact STATUS_VAR); |
60011498 PB |
2868 | return packFloat16(aSign, 0x1f, 0x3ff); |
2869 | } | |
2870 | } | |
2871 | if (aExp < -24) { | |
2872 | return packFloat16(aSign, 0, 0); | |
2873 | } | |
2874 | if (aExp < -14) { | |
2875 | aSig >>= -14 - aExp; | |
2876 | aExp = -14; | |
2877 | } | |
2878 | return packFloat16(aSign, aExp + 14, aSig >> 13); | |
2879 | } | |
2880 | ||
158142c2 FB |
2881 | #ifdef FLOATX80 |
2882 | ||
2883 | /*---------------------------------------------------------------------------- | |
2884 | | Returns the result of converting the double-precision floating-point value | |
2885 | | `a' to the extended double-precision floating-point format. The conversion | |
2886 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2887 | | Arithmetic. | |
2888 | *----------------------------------------------------------------------------*/ | |
2889 | ||
2890 | floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) | |
2891 | { | |
2892 | flag aSign; | |
2893 | int16 aExp; | |
bb98fe42 | 2894 | uint64_t aSig; |
158142c2 | 2895 | |
37d18660 | 2896 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2897 | aSig = extractFloat64Frac( a ); |
2898 | aExp = extractFloat64Exp( a ); | |
2899 | aSign = extractFloat64Sign( a ); | |
2900 | if ( aExp == 0x7FF ) { | |
bcd4d9af | 2901 | if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
2902 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
2903 | } | |
2904 | if ( aExp == 0 ) { | |
2905 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); | |
2906 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2907 | } | |
2908 | return | |
2909 | packFloatx80( | |
2910 | aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); | |
2911 | ||
2912 | } | |
2913 | ||
2914 | #endif | |
2915 | ||
2916 | #ifdef FLOAT128 | |
2917 | ||
2918 | /*---------------------------------------------------------------------------- | |
2919 | | Returns the result of converting the double-precision floating-point value | |
2920 | | `a' to the quadruple-precision floating-point format. The conversion is | |
2921 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2922 | | Arithmetic. | |
2923 | *----------------------------------------------------------------------------*/ | |
2924 | ||
2925 | float128 float64_to_float128( float64 a STATUS_PARAM ) | |
2926 | { | |
2927 | flag aSign; | |
2928 | int16 aExp; | |
bb98fe42 | 2929 | uint64_t aSig, zSig0, zSig1; |
158142c2 | 2930 | |
37d18660 | 2931 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2932 | aSig = extractFloat64Frac( a ); |
2933 | aExp = extractFloat64Exp( a ); | |
2934 | aSign = extractFloat64Sign( a ); | |
2935 | if ( aExp == 0x7FF ) { | |
bcd4d9af | 2936 | if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
2937 | return packFloat128( aSign, 0x7FFF, 0, 0 ); |
2938 | } | |
2939 | if ( aExp == 0 ) { | |
2940 | if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); | |
2941 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2942 | --aExp; | |
2943 | } | |
2944 | shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); | |
2945 | return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); | |
2946 | ||
2947 | } | |
2948 | ||
2949 | #endif | |
2950 | ||
2951 | /*---------------------------------------------------------------------------- | |
2952 | | Rounds the double-precision floating-point value `a' to an integer, and | |
2953 | | returns the result as a double-precision floating-point value. The | |
2954 | | operation is performed according to the IEC/IEEE Standard for Binary | |
2955 | | Floating-Point Arithmetic. | |
2956 | *----------------------------------------------------------------------------*/ | |
2957 | ||
2958 | float64 float64_round_to_int( float64 a STATUS_PARAM ) | |
2959 | { | |
2960 | flag aSign; | |
2961 | int16 aExp; | |
bb98fe42 | 2962 | uint64_t lastBitMask, roundBitsMask; |
158142c2 | 2963 | int8 roundingMode; |
bb98fe42 | 2964 | uint64_t z; |
37d18660 | 2965 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
2966 | |
2967 | aExp = extractFloat64Exp( a ); | |
2968 | if ( 0x433 <= aExp ) { | |
2969 | if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { | |
2970 | return propagateFloat64NaN( a, a STATUS_VAR ); | |
2971 | } | |
2972 | return a; | |
2973 | } | |
2974 | if ( aExp < 0x3FF ) { | |
bb98fe42 | 2975 | if ( (uint64_t) ( float64_val(a)<<1 ) == 0 ) return a; |
158142c2 FB |
2976 | STATUS(float_exception_flags) |= float_flag_inexact; |
2977 | aSign = extractFloat64Sign( a ); | |
2978 | switch ( STATUS(float_rounding_mode) ) { | |
2979 | case float_round_nearest_even: | |
2980 | if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { | |
2981 | return packFloat64( aSign, 0x3FF, 0 ); | |
2982 | } | |
2983 | break; | |
2984 | case float_round_down: | |
f090c9d4 | 2985 | return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0); |
158142c2 | 2986 | case float_round_up: |
f090c9d4 PB |
2987 | return make_float64( |
2988 | aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 )); | |
158142c2 FB |
2989 | } |
2990 | return packFloat64( aSign, 0, 0 ); | |
2991 | } | |
2992 | lastBitMask = 1; | |
2993 | lastBitMask <<= 0x433 - aExp; | |
2994 | roundBitsMask = lastBitMask - 1; | |
f090c9d4 | 2995 | z = float64_val(a); |
158142c2 FB |
2996 | roundingMode = STATUS(float_rounding_mode); |
2997 | if ( roundingMode == float_round_nearest_even ) { | |
2998 | z += lastBitMask>>1; | |
2999 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; | |
3000 | } | |
3001 | else if ( roundingMode != float_round_to_zero ) { | |
f090c9d4 | 3002 | if ( extractFloat64Sign( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) { |
158142c2 FB |
3003 | z += roundBitsMask; |
3004 | } | |
3005 | } | |
3006 | z &= ~ roundBitsMask; | |
f090c9d4 PB |
3007 | if ( z != float64_val(a) ) |
3008 | STATUS(float_exception_flags) |= float_flag_inexact; | |
3009 | return make_float64(z); | |
158142c2 FB |
3010 | |
3011 | } | |
3012 | ||
e6e5906b PB |
3013 | float64 float64_trunc_to_int( float64 a STATUS_PARAM) |
3014 | { | |
3015 | int oldmode; | |
3016 | float64 res; | |
3017 | oldmode = STATUS(float_rounding_mode); | |
3018 | STATUS(float_rounding_mode) = float_round_to_zero; | |
3019 | res = float64_round_to_int(a STATUS_VAR); | |
3020 | STATUS(float_rounding_mode) = oldmode; | |
3021 | return res; | |
3022 | } | |
3023 | ||
158142c2 FB |
3024 | /*---------------------------------------------------------------------------- |
3025 | | Returns the result of adding the absolute values of the double-precision | |
3026 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated | |
3027 | | before being returned. `zSign' is ignored if the result is a NaN. | |
3028 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
3029 | | Floating-Point Arithmetic. | |
3030 | *----------------------------------------------------------------------------*/ | |
3031 | ||
3032 | static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) | |
3033 | { | |
3034 | int16 aExp, bExp, zExp; | |
bb98fe42 | 3035 | uint64_t aSig, bSig, zSig; |
158142c2 FB |
3036 | int16 expDiff; |
3037 | ||
3038 | aSig = extractFloat64Frac( a ); | |
3039 | aExp = extractFloat64Exp( a ); | |
3040 | bSig = extractFloat64Frac( b ); | |
3041 | bExp = extractFloat64Exp( b ); | |
3042 | expDiff = aExp - bExp; | |
3043 | aSig <<= 9; | |
3044 | bSig <<= 9; | |
3045 | if ( 0 < expDiff ) { | |
3046 | if ( aExp == 0x7FF ) { | |
3047 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3048 | return a; | |
3049 | } | |
3050 | if ( bExp == 0 ) { | |
3051 | --expDiff; | |
3052 | } | |
3053 | else { | |
3054 | bSig |= LIT64( 0x2000000000000000 ); | |
3055 | } | |
3056 | shift64RightJamming( bSig, expDiff, &bSig ); | |
3057 | zExp = aExp; | |
3058 | } | |
3059 | else if ( expDiff < 0 ) { | |
3060 | if ( bExp == 0x7FF ) { | |
3061 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3062 | return packFloat64( zSign, 0x7FF, 0 ); | |
3063 | } | |
3064 | if ( aExp == 0 ) { | |
3065 | ++expDiff; | |
3066 | } | |
3067 | else { | |
3068 | aSig |= LIT64( 0x2000000000000000 ); | |
3069 | } | |
3070 | shift64RightJamming( aSig, - expDiff, &aSig ); | |
3071 | zExp = bExp; | |
3072 | } | |
3073 | else { | |
3074 | if ( aExp == 0x7FF ) { | |
3075 | if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3076 | return a; | |
3077 | } | |
fe76d976 PB |
3078 | if ( aExp == 0 ) { |
3079 | if ( STATUS(flush_to_zero) ) return packFloat64( zSign, 0, 0 ); | |
3080 | return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); | |
3081 | } | |
158142c2 FB |
3082 | zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; |
3083 | zExp = aExp; | |
3084 | goto roundAndPack; | |
3085 | } | |
3086 | aSig |= LIT64( 0x2000000000000000 ); | |
3087 | zSig = ( aSig + bSig )<<1; | |
3088 | --zExp; | |
bb98fe42 | 3089 | if ( (int64_t) zSig < 0 ) { |
158142c2 FB |
3090 | zSig = aSig + bSig; |
3091 | ++zExp; | |
3092 | } | |
3093 | roundAndPack: | |
3094 | return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); | |
3095 | ||
3096 | } | |
3097 | ||
3098 | /*---------------------------------------------------------------------------- | |
3099 | | Returns the result of subtracting the absolute values of the double- | |
3100 | | precision floating-point values `a' and `b'. If `zSign' is 1, the | |
3101 | | difference is negated before being returned. `zSign' is ignored if the | |
3102 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
3103 | | Standard for Binary Floating-Point Arithmetic. | |
3104 | *----------------------------------------------------------------------------*/ | |
3105 | ||
3106 | static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) | |
3107 | { | |
3108 | int16 aExp, bExp, zExp; | |
bb98fe42 | 3109 | uint64_t aSig, bSig, zSig; |
158142c2 FB |
3110 | int16 expDiff; |
3111 | ||
3112 | aSig = extractFloat64Frac( a ); | |
3113 | aExp = extractFloat64Exp( a ); | |
3114 | bSig = extractFloat64Frac( b ); | |
3115 | bExp = extractFloat64Exp( b ); | |
3116 | expDiff = aExp - bExp; | |
3117 | aSig <<= 10; | |
3118 | bSig <<= 10; | |
3119 | if ( 0 < expDiff ) goto aExpBigger; | |
3120 | if ( expDiff < 0 ) goto bExpBigger; | |
3121 | if ( aExp == 0x7FF ) { | |
3122 | if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3123 | float_raise( float_flag_invalid STATUS_VAR); | |
3124 | return float64_default_nan; | |
3125 | } | |
3126 | if ( aExp == 0 ) { | |
3127 | aExp = 1; | |
3128 | bExp = 1; | |
3129 | } | |
3130 | if ( bSig < aSig ) goto aBigger; | |
3131 | if ( aSig < bSig ) goto bBigger; | |
3132 | return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); | |
3133 | bExpBigger: | |
3134 | if ( bExp == 0x7FF ) { | |
3135 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3136 | return packFloat64( zSign ^ 1, 0x7FF, 0 ); | |
3137 | } | |
3138 | if ( aExp == 0 ) { | |
3139 | ++expDiff; | |
3140 | } | |
3141 | else { | |
3142 | aSig |= LIT64( 0x4000000000000000 ); | |
3143 | } | |
3144 | shift64RightJamming( aSig, - expDiff, &aSig ); | |
3145 | bSig |= LIT64( 0x4000000000000000 ); | |
3146 | bBigger: | |
3147 | zSig = bSig - aSig; | |
3148 | zExp = bExp; | |
3149 | zSign ^= 1; | |
3150 | goto normalizeRoundAndPack; | |
3151 | aExpBigger: | |
3152 | if ( aExp == 0x7FF ) { | |
3153 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3154 | return a; | |
3155 | } | |
3156 | if ( bExp == 0 ) { | |
3157 | --expDiff; | |
3158 | } | |
3159 | else { | |
3160 | bSig |= LIT64( 0x4000000000000000 ); | |
3161 | } | |
3162 | shift64RightJamming( bSig, expDiff, &bSig ); | |
3163 | aSig |= LIT64( 0x4000000000000000 ); | |
3164 | aBigger: | |
3165 | zSig = aSig - bSig; | |
3166 | zExp = aExp; | |
3167 | normalizeRoundAndPack: | |
3168 | --zExp; | |
3169 | return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); | |
3170 | ||
3171 | } | |
3172 | ||
3173 | /*---------------------------------------------------------------------------- | |
3174 | | Returns the result of adding the double-precision floating-point values `a' | |
3175 | | and `b'. The operation is performed according to the IEC/IEEE Standard for | |
3176 | | Binary Floating-Point Arithmetic. | |
3177 | *----------------------------------------------------------------------------*/ | |
3178 | ||
3179 | float64 float64_add( float64 a, float64 b STATUS_PARAM ) | |
3180 | { | |
3181 | flag aSign, bSign; | |
37d18660 PM |
3182 | a = float64_squash_input_denormal(a STATUS_VAR); |
3183 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3184 | |
3185 | aSign = extractFloat64Sign( a ); | |
3186 | bSign = extractFloat64Sign( b ); | |
3187 | if ( aSign == bSign ) { | |
3188 | return addFloat64Sigs( a, b, aSign STATUS_VAR ); | |
3189 | } | |
3190 | else { | |
3191 | return subFloat64Sigs( a, b, aSign STATUS_VAR ); | |
3192 | } | |
3193 | ||
3194 | } | |
3195 | ||
3196 | /*---------------------------------------------------------------------------- | |
3197 | | Returns the result of subtracting the double-precision floating-point values | |
3198 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
3199 | | for Binary Floating-Point Arithmetic. | |
3200 | *----------------------------------------------------------------------------*/ | |
3201 | ||
3202 | float64 float64_sub( float64 a, float64 b STATUS_PARAM ) | |
3203 | { | |
3204 | flag aSign, bSign; | |
37d18660 PM |
3205 | a = float64_squash_input_denormal(a STATUS_VAR); |
3206 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3207 | |
3208 | aSign = extractFloat64Sign( a ); | |
3209 | bSign = extractFloat64Sign( b ); | |
3210 | if ( aSign == bSign ) { | |
3211 | return subFloat64Sigs( a, b, aSign STATUS_VAR ); | |
3212 | } | |
3213 | else { | |
3214 | return addFloat64Sigs( a, b, aSign STATUS_VAR ); | |
3215 | } | |
3216 | ||
3217 | } | |
3218 | ||
3219 | /*---------------------------------------------------------------------------- | |
3220 | | Returns the result of multiplying the double-precision floating-point values | |
3221 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
3222 | | for Binary Floating-Point Arithmetic. | |
3223 | *----------------------------------------------------------------------------*/ | |
3224 | ||
3225 | float64 float64_mul( float64 a, float64 b STATUS_PARAM ) | |
3226 | { | |
3227 | flag aSign, bSign, zSign; | |
3228 | int16 aExp, bExp, zExp; | |
bb98fe42 | 3229 | uint64_t aSig, bSig, zSig0, zSig1; |
158142c2 | 3230 | |
37d18660 PM |
3231 | a = float64_squash_input_denormal(a STATUS_VAR); |
3232 | b = float64_squash_input_denormal(b STATUS_VAR); | |
3233 | ||
158142c2 FB |
3234 | aSig = extractFloat64Frac( a ); |
3235 | aExp = extractFloat64Exp( a ); | |
3236 | aSign = extractFloat64Sign( a ); | |
3237 | bSig = extractFloat64Frac( b ); | |
3238 | bExp = extractFloat64Exp( b ); | |
3239 | bSign = extractFloat64Sign( b ); | |
3240 | zSign = aSign ^ bSign; | |
3241 | if ( aExp == 0x7FF ) { | |
3242 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { | |
3243 | return propagateFloat64NaN( a, b STATUS_VAR ); | |
3244 | } | |
3245 | if ( ( bExp | bSig ) == 0 ) { | |
3246 | float_raise( float_flag_invalid STATUS_VAR); | |
3247 | return float64_default_nan; | |
3248 | } | |
3249 | return packFloat64( zSign, 0x7FF, 0 ); | |
3250 | } | |
3251 | if ( bExp == 0x7FF ) { | |
3252 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3253 | if ( ( aExp | aSig ) == 0 ) { | |
3254 | float_raise( float_flag_invalid STATUS_VAR); | |
3255 | return float64_default_nan; | |
3256 | } | |
3257 | return packFloat64( zSign, 0x7FF, 0 ); | |
3258 | } | |
3259 | if ( aExp == 0 ) { | |
3260 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
3261 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
3262 | } | |
3263 | if ( bExp == 0 ) { | |
3264 | if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
3265 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
3266 | } | |
3267 | zExp = aExp + bExp - 0x3FF; | |
3268 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; | |
3269 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
3270 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); | |
3271 | zSig0 |= ( zSig1 != 0 ); | |
bb98fe42 | 3272 | if ( 0 <= (int64_t) ( zSig0<<1 ) ) { |
158142c2 FB |
3273 | zSig0 <<= 1; |
3274 | --zExp; | |
3275 | } | |
3276 | return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR ); | |
3277 | ||
3278 | } | |
3279 | ||
3280 | /*---------------------------------------------------------------------------- | |
3281 | | Returns the result of dividing the double-precision floating-point value `a' | |
3282 | | by the corresponding value `b'. The operation is performed according to | |
3283 | | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3284 | *----------------------------------------------------------------------------*/ | |
3285 | ||
3286 | float64 float64_div( float64 a, float64 b STATUS_PARAM ) | |
3287 | { | |
3288 | flag aSign, bSign, zSign; | |
3289 | int16 aExp, bExp, zExp; | |
bb98fe42 AF |
3290 | uint64_t aSig, bSig, zSig; |
3291 | uint64_t rem0, rem1; | |
3292 | uint64_t term0, term1; | |
37d18660 PM |
3293 | a = float64_squash_input_denormal(a STATUS_VAR); |
3294 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3295 | |
3296 | aSig = extractFloat64Frac( a ); | |
3297 | aExp = extractFloat64Exp( a ); | |
3298 | aSign = extractFloat64Sign( a ); | |
3299 | bSig = extractFloat64Frac( b ); | |
3300 | bExp = extractFloat64Exp( b ); | |
3301 | bSign = extractFloat64Sign( b ); | |
3302 | zSign = aSign ^ bSign; | |
3303 | if ( aExp == 0x7FF ) { | |
3304 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3305 | if ( bExp == 0x7FF ) { | |
3306 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3307 | float_raise( float_flag_invalid STATUS_VAR); | |
3308 | return float64_default_nan; | |
3309 | } | |
3310 | return packFloat64( zSign, 0x7FF, 0 ); | |
3311 | } | |
3312 | if ( bExp == 0x7FF ) { | |
3313 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3314 | return packFloat64( zSign, 0, 0 ); | |
3315 | } | |
3316 | if ( bExp == 0 ) { | |
3317 | if ( bSig == 0 ) { | |
3318 | if ( ( aExp | aSig ) == 0 ) { | |
3319 | float_raise( float_flag_invalid STATUS_VAR); | |
3320 | return float64_default_nan; | |
3321 | } | |
3322 | float_raise( float_flag_divbyzero STATUS_VAR); | |
3323 | return packFloat64( zSign, 0x7FF, 0 ); | |
3324 | } | |
3325 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
3326 | } | |
3327 | if ( aExp == 0 ) { | |
3328 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
3329 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
3330 | } | |
3331 | zExp = aExp - bExp + 0x3FD; | |
3332 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; | |
3333 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
3334 | if ( bSig <= ( aSig + aSig ) ) { | |
3335 | aSig >>= 1; | |
3336 | ++zExp; | |
3337 | } | |
3338 | zSig = estimateDiv128To64( aSig, 0, bSig ); | |
3339 | if ( ( zSig & 0x1FF ) <= 2 ) { | |
3340 | mul64To128( bSig, zSig, &term0, &term1 ); | |
3341 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); | |
bb98fe42 | 3342 | while ( (int64_t) rem0 < 0 ) { |
158142c2 FB |
3343 | --zSig; |
3344 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); | |
3345 | } | |
3346 | zSig |= ( rem1 != 0 ); | |
3347 | } | |
3348 | return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); | |
3349 | ||
3350 | } | |
3351 | ||
3352 | /*---------------------------------------------------------------------------- | |
3353 | | Returns the remainder of the double-precision floating-point value `a' | |
3354 | | with respect to the corresponding value `b'. The operation is performed | |
3355 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3356 | *----------------------------------------------------------------------------*/ | |
3357 | ||
3358 | float64 float64_rem( float64 a, float64 b STATUS_PARAM ) | |
3359 | { | |
ed086f3d | 3360 | flag aSign, zSign; |
158142c2 | 3361 | int16 aExp, bExp, expDiff; |
bb98fe42 AF |
3362 | uint64_t aSig, bSig; |
3363 | uint64_t q, alternateASig; | |
3364 | int64_t sigMean; | |
158142c2 | 3365 | |
37d18660 PM |
3366 | a = float64_squash_input_denormal(a STATUS_VAR); |
3367 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3368 | aSig = extractFloat64Frac( a ); |
3369 | aExp = extractFloat64Exp( a ); | |
3370 | aSign = extractFloat64Sign( a ); | |
3371 | bSig = extractFloat64Frac( b ); | |
3372 | bExp = extractFloat64Exp( b ); | |
158142c2 FB |
3373 | if ( aExp == 0x7FF ) { |
3374 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { | |
3375 | return propagateFloat64NaN( a, b STATUS_VAR ); | |
3376 | } | |
3377 | float_raise( float_flag_invalid STATUS_VAR); | |
3378 | return float64_default_nan; | |
3379 | } | |
3380 | if ( bExp == 0x7FF ) { | |
3381 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
3382 | return a; | |
3383 | } | |
3384 | if ( bExp == 0 ) { | |
3385 | if ( bSig == 0 ) { | |
3386 | float_raise( float_flag_invalid STATUS_VAR); | |
3387 | return float64_default_nan; | |
3388 | } | |
3389 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
3390 | } | |
3391 | if ( aExp == 0 ) { | |
3392 | if ( aSig == 0 ) return a; | |
3393 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
3394 | } | |
3395 | expDiff = aExp - bExp; | |
3396 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; | |
3397 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
3398 | if ( expDiff < 0 ) { | |
3399 | if ( expDiff < -1 ) return a; | |
3400 | aSig >>= 1; | |
3401 | } | |
3402 | q = ( bSig <= aSig ); | |
3403 | if ( q ) aSig -= bSig; | |
3404 | expDiff -= 64; | |
3405 | while ( 0 < expDiff ) { | |
3406 | q = estimateDiv128To64( aSig, 0, bSig ); | |
3407 | q = ( 2 < q ) ? q - 2 : 0; | |
3408 | aSig = - ( ( bSig>>2 ) * q ); | |
3409 | expDiff -= 62; | |
3410 | } | |
3411 | expDiff += 64; | |
3412 | if ( 0 < expDiff ) { | |
3413 | q = estimateDiv128To64( aSig, 0, bSig ); | |
3414 | q = ( 2 < q ) ? q - 2 : 0; | |
3415 | q >>= 64 - expDiff; | |
3416 | bSig >>= 2; | |
3417 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; | |
3418 | } | |
3419 | else { | |
3420 | aSig >>= 2; | |
3421 | bSig >>= 2; | |
3422 | } | |
3423 | do { | |
3424 | alternateASig = aSig; | |
3425 | ++q; | |
3426 | aSig -= bSig; | |
bb98fe42 | 3427 | } while ( 0 <= (int64_t) aSig ); |
158142c2 FB |
3428 | sigMean = aSig + alternateASig; |
3429 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { | |
3430 | aSig = alternateASig; | |
3431 | } | |
bb98fe42 | 3432 | zSign = ( (int64_t) aSig < 0 ); |
158142c2 FB |
3433 | if ( zSign ) aSig = - aSig; |
3434 | return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR ); | |
3435 | ||
3436 | } | |
3437 | ||
3438 | /*---------------------------------------------------------------------------- | |
3439 | | Returns the square root of the double-precision floating-point value `a'. | |
3440 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
3441 | | Floating-Point Arithmetic. | |
3442 | *----------------------------------------------------------------------------*/ | |
3443 | ||
3444 | float64 float64_sqrt( float64 a STATUS_PARAM ) | |
3445 | { | |
3446 | flag aSign; | |
3447 | int16 aExp, zExp; | |
bb98fe42 AF |
3448 | uint64_t aSig, zSig, doubleZSig; |
3449 | uint64_t rem0, rem1, term0, term1; | |
37d18660 | 3450 | a = float64_squash_input_denormal(a STATUS_VAR); |
158142c2 FB |
3451 | |
3452 | aSig = extractFloat64Frac( a ); | |
3453 | aExp = extractFloat64Exp( a ); | |
3454 | aSign = extractFloat64Sign( a ); | |
3455 | if ( aExp == 0x7FF ) { | |
3456 | if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); | |
3457 | if ( ! aSign ) return a; | |
3458 | float_raise( float_flag_invalid STATUS_VAR); | |
3459 | return float64_default_nan; | |
3460 | } | |
3461 | if ( aSign ) { | |
3462 | if ( ( aExp | aSig ) == 0 ) return a; | |
3463 | float_raise( float_flag_invalid STATUS_VAR); | |
3464 | return float64_default_nan; | |
3465 | } | |
3466 | if ( aExp == 0 ) { | |
f090c9d4 | 3467 | if ( aSig == 0 ) return float64_zero; |
158142c2 FB |
3468 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3469 | } | |
3470 | zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; | |
3471 | aSig |= LIT64( 0x0010000000000000 ); | |
3472 | zSig = estimateSqrt32( aExp, aSig>>21 ); | |
3473 | aSig <<= 9 - ( aExp & 1 ); | |
3474 | zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); | |
3475 | if ( ( zSig & 0x1FF ) <= 5 ) { | |
3476 | doubleZSig = zSig<<1; | |
3477 | mul64To128( zSig, zSig, &term0, &term1 ); | |
3478 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); | |
bb98fe42 | 3479 | while ( (int64_t) rem0 < 0 ) { |
158142c2 FB |
3480 | --zSig; |
3481 | doubleZSig -= 2; | |
3482 | add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); | |
3483 | } | |
3484 | zSig |= ( ( rem0 | rem1 ) != 0 ); | |
3485 | } | |
3486 | return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); | |
3487 | ||
3488 | } | |
3489 | ||
374dfc33 AJ |
3490 | /*---------------------------------------------------------------------------- |
3491 | | Returns the binary log of the double-precision floating-point value `a'. | |
3492 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
3493 | | Floating-Point Arithmetic. | |
3494 | *----------------------------------------------------------------------------*/ | |
3495 | float64 float64_log2( float64 a STATUS_PARAM ) | |
3496 | { | |
3497 | flag aSign, zSign; | |
3498 | int16 aExp; | |
bb98fe42 | 3499 | uint64_t aSig, aSig0, aSig1, zSig, i; |
37d18660 | 3500 | a = float64_squash_input_denormal(a STATUS_VAR); |
374dfc33 AJ |
3501 | |
3502 | aSig = extractFloat64Frac( a ); | |
3503 | aExp = extractFloat64Exp( a ); | |
3504 | aSign = extractFloat64Sign( a ); | |
3505 | ||
3506 | if ( aExp == 0 ) { | |
3507 | if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 ); | |
3508 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
3509 | } | |
3510 | if ( aSign ) { | |
3511 | float_raise( float_flag_invalid STATUS_VAR); | |
3512 | return float64_default_nan; | |
3513 | } | |
3514 | if ( aExp == 0x7FF ) { | |
3515 | if ( aSig ) return propagateFloat64NaN( a, float64_zero STATUS_VAR ); | |
3516 | return a; | |
3517 | } | |
3518 | ||
3519 | aExp -= 0x3FF; | |
3520 | aSig |= LIT64( 0x0010000000000000 ); | |
3521 | zSign = aExp < 0; | |
bb98fe42 | 3522 | zSig = (uint64_t)aExp << 52; |
374dfc33 AJ |
3523 | for (i = 1LL << 51; i > 0; i >>= 1) { |
3524 | mul64To128( aSig, aSig, &aSig0, &aSig1 ); | |
3525 | aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 ); | |
3526 | if ( aSig & LIT64( 0x0020000000000000 ) ) { | |
3527 | aSig >>= 1; | |
3528 | zSig |= i; | |
3529 | } | |
3530 | } | |
3531 | ||
3532 | if ( zSign ) | |
3533 | zSig = -zSig; | |
3534 | return normalizeRoundAndPackFloat64( zSign, 0x408, zSig STATUS_VAR ); | |
3535 | } | |
3536 | ||
158142c2 FB |
3537 | /*---------------------------------------------------------------------------- |
3538 | | Returns 1 if the double-precision floating-point value `a' is equal to the | |
3539 | | corresponding value `b', and 0 otherwise. The comparison is performed | |
3540 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3541 | *----------------------------------------------------------------------------*/ | |
3542 | ||
750afe93 | 3543 | int float64_eq( float64 a, float64 b STATUS_PARAM ) |
158142c2 | 3544 | { |
bb98fe42 | 3545 | uint64_t av, bv; |
37d18660 PM |
3546 | a = float64_squash_input_denormal(a STATUS_VAR); |
3547 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3548 | |
3549 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3550 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3551 | ) { | |
3552 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
3553 | float_raise( float_flag_invalid STATUS_VAR); | |
3554 | } | |
3555 | return 0; | |
3556 | } | |
f090c9d4 | 3557 | av = float64_val(a); |
a1b91bb4 | 3558 | bv = float64_val(b); |
bb98fe42 | 3559 | return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
158142c2 FB |
3560 | |
3561 | } | |
3562 | ||
3563 | /*---------------------------------------------------------------------------- | |
3564 | | Returns 1 if the double-precision floating-point value `a' is less than or | |
3565 | | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
3566 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
3567 | | Arithmetic. | |
3568 | *----------------------------------------------------------------------------*/ | |
3569 | ||
750afe93 | 3570 | int float64_le( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3571 | { |
3572 | flag aSign, bSign; | |
bb98fe42 | 3573 | uint64_t av, bv; |
37d18660 PM |
3574 | a = float64_squash_input_denormal(a STATUS_VAR); |
3575 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3576 | |
3577 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3578 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3579 | ) { | |
3580 | float_raise( float_flag_invalid STATUS_VAR); | |
3581 | return 0; | |
3582 | } | |
3583 | aSign = extractFloat64Sign( a ); | |
3584 | bSign = extractFloat64Sign( b ); | |
f090c9d4 | 3585 | av = float64_val(a); |
a1b91bb4 | 3586 | bv = float64_val(b); |
bb98fe42 | 3587 | if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
f090c9d4 | 3588 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
158142c2 FB |
3589 | |
3590 | } | |
3591 | ||
3592 | /*---------------------------------------------------------------------------- | |
3593 | | Returns 1 if the double-precision floating-point value `a' is less than | |
3594 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
3595 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3596 | *----------------------------------------------------------------------------*/ | |
3597 | ||
750afe93 | 3598 | int float64_lt( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3599 | { |
3600 | flag aSign, bSign; | |
bb98fe42 | 3601 | uint64_t av, bv; |
158142c2 | 3602 | |
37d18660 PM |
3603 | a = float64_squash_input_denormal(a STATUS_VAR); |
3604 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3605 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3606 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3607 | ) { | |
3608 | float_raise( float_flag_invalid STATUS_VAR); | |
3609 | return 0; | |
3610 | } | |
3611 | aSign = extractFloat64Sign( a ); | |
3612 | bSign = extractFloat64Sign( b ); | |
f090c9d4 | 3613 | av = float64_val(a); |
a1b91bb4 | 3614 | bv = float64_val(b); |
bb98fe42 | 3615 | if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); |
f090c9d4 | 3616 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
158142c2 FB |
3617 | |
3618 | } | |
3619 | ||
3620 | /*---------------------------------------------------------------------------- | |
3621 | | Returns 1 if the double-precision floating-point value `a' is equal to the | |
3622 | | corresponding value `b', and 0 otherwise. The invalid exception is raised | |
3623 | | if either operand is a NaN. Otherwise, the comparison is performed | |
3624 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3625 | *----------------------------------------------------------------------------*/ | |
3626 | ||
750afe93 | 3627 | int float64_eq_signaling( float64 a, float64 b STATUS_PARAM ) |
158142c2 | 3628 | { |
bb98fe42 | 3629 | uint64_t av, bv; |
37d18660 PM |
3630 | a = float64_squash_input_denormal(a STATUS_VAR); |
3631 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3632 | |
3633 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3634 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3635 | ) { | |
3636 | float_raise( float_flag_invalid STATUS_VAR); | |
3637 | return 0; | |
3638 | } | |
f090c9d4 | 3639 | av = float64_val(a); |
a1b91bb4 | 3640 | bv = float64_val(b); |
bb98fe42 | 3641 | return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
158142c2 FB |
3642 | |
3643 | } | |
3644 | ||
3645 | /*---------------------------------------------------------------------------- | |
3646 | | Returns 1 if the double-precision floating-point value `a' is less than or | |
3647 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
3648 | | cause an exception. Otherwise, the comparison is performed according to the | |
3649 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3650 | *----------------------------------------------------------------------------*/ | |
3651 | ||
750afe93 | 3652 | int float64_le_quiet( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3653 | { |
3654 | flag aSign, bSign; | |
bb98fe42 | 3655 | uint64_t av, bv; |
37d18660 PM |
3656 | a = float64_squash_input_denormal(a STATUS_VAR); |
3657 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3658 | |
3659 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3660 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3661 | ) { | |
3662 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
3663 | float_raise( float_flag_invalid STATUS_VAR); | |
3664 | } | |
3665 | return 0; | |
3666 | } | |
3667 | aSign = extractFloat64Sign( a ); | |
3668 | bSign = extractFloat64Sign( b ); | |
f090c9d4 | 3669 | av = float64_val(a); |
a1b91bb4 | 3670 | bv = float64_val(b); |
bb98fe42 | 3671 | if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
f090c9d4 | 3672 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
158142c2 FB |
3673 | |
3674 | } | |
3675 | ||
3676 | /*---------------------------------------------------------------------------- | |
3677 | | Returns 1 if the double-precision floating-point value `a' is less than | |
3678 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
3679 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
3680 | | Standard for Binary Floating-Point Arithmetic. | |
3681 | *----------------------------------------------------------------------------*/ | |
3682 | ||
750afe93 | 3683 | int float64_lt_quiet( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3684 | { |
3685 | flag aSign, bSign; | |
bb98fe42 | 3686 | uint64_t av, bv; |
37d18660 PM |
3687 | a = float64_squash_input_denormal(a STATUS_VAR); |
3688 | b = float64_squash_input_denormal(b STATUS_VAR); | |
158142c2 FB |
3689 | |
3690 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3691 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3692 | ) { | |
3693 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
3694 | float_raise( float_flag_invalid STATUS_VAR); | |
3695 | } | |
3696 | return 0; | |
3697 | } | |
3698 | aSign = extractFloat64Sign( a ); | |
3699 | bSign = extractFloat64Sign( b ); | |
f090c9d4 | 3700 | av = float64_val(a); |
a1b91bb4 | 3701 | bv = float64_val(b); |
bb98fe42 | 3702 | if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); |
f090c9d4 | 3703 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
158142c2 FB |
3704 | |
3705 | } | |
3706 | ||
3707 | #ifdef FLOATX80 | |
3708 | ||
3709 | /*---------------------------------------------------------------------------- | |
3710 | | Returns the result of converting the extended double-precision floating- | |
3711 | | point value `a' to the 32-bit two's complement integer format. The | |
3712 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3713 | | Floating-Point Arithmetic---which means in particular that the conversion | |
3714 | | is rounded according to the current rounding mode. If `a' is a NaN, the | |
3715 | | largest positive integer is returned. Otherwise, if the conversion | |
3716 | | overflows, the largest integer with the same sign as `a' is returned. | |
3717 | *----------------------------------------------------------------------------*/ | |
3718 | ||
3719 | int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) | |
3720 | { | |
3721 | flag aSign; | |
3722 | int32 aExp, shiftCount; | |
bb98fe42 | 3723 | uint64_t aSig; |
158142c2 FB |
3724 | |
3725 | aSig = extractFloatx80Frac( a ); | |
3726 | aExp = extractFloatx80Exp( a ); | |
3727 | aSign = extractFloatx80Sign( a ); | |
bb98fe42 | 3728 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; |
158142c2 FB |
3729 | shiftCount = 0x4037 - aExp; |
3730 | if ( shiftCount <= 0 ) shiftCount = 1; | |
3731 | shift64RightJamming( aSig, shiftCount, &aSig ); | |
3732 | return roundAndPackInt32( aSign, aSig STATUS_VAR ); | |
3733 | ||
3734 | } | |
3735 | ||
3736 | /*---------------------------------------------------------------------------- | |
3737 | | Returns the result of converting the extended double-precision floating- | |
3738 | | point value `a' to the 32-bit two's complement integer format. The | |
3739 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3740 | | Floating-Point Arithmetic, except that the conversion is always rounded | |
3741 | | toward zero. If `a' is a NaN, the largest positive integer is returned. | |
3742 | | Otherwise, if the conversion overflows, the largest integer with the same | |
3743 | | sign as `a' is returned. | |
3744 | *----------------------------------------------------------------------------*/ | |
3745 | ||
3746 | int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) | |
3747 | { | |
3748 | flag aSign; | |
3749 | int32 aExp, shiftCount; | |
bb98fe42 | 3750 | uint64_t aSig, savedASig; |
158142c2 FB |
3751 | int32 z; |
3752 | ||
3753 | aSig = extractFloatx80Frac( a ); | |
3754 | aExp = extractFloatx80Exp( a ); | |
3755 | aSign = extractFloatx80Sign( a ); | |
3756 | if ( 0x401E < aExp ) { | |
bb98fe42 | 3757 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; |
158142c2 FB |
3758 | goto invalid; |
3759 | } | |
3760 | else if ( aExp < 0x3FFF ) { | |
3761 | if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
3762 | return 0; | |
3763 | } | |
3764 | shiftCount = 0x403E - aExp; | |
3765 | savedASig = aSig; | |
3766 | aSig >>= shiftCount; | |
3767 | z = aSig; | |
3768 | if ( aSign ) z = - z; | |
3769 | if ( ( z < 0 ) ^ aSign ) { | |
3770 | invalid: | |
3771 | float_raise( float_flag_invalid STATUS_VAR); | |
bb98fe42 | 3772 | return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
158142c2 FB |
3773 | } |
3774 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
3775 | STATUS(float_exception_flags) |= float_flag_inexact; | |
3776 | } | |
3777 | return z; | |
3778 | ||
3779 | } | |
3780 | ||
3781 | /*---------------------------------------------------------------------------- | |
3782 | | Returns the result of converting the extended double-precision floating- | |
3783 | | point value `a' to the 64-bit two's complement integer format. The | |
3784 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3785 | | Floating-Point Arithmetic---which means in particular that the conversion | |
3786 | | is rounded according to the current rounding mode. If `a' is a NaN, | |
3787 | | the largest positive integer is returned. Otherwise, if the conversion | |
3788 | | overflows, the largest integer with the same sign as `a' is returned. | |
3789 | *----------------------------------------------------------------------------*/ | |
3790 | ||
3791 | int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) | |
3792 | { | |
3793 | flag aSign; | |
3794 | int32 aExp, shiftCount; | |
bb98fe42 | 3795 | uint64_t aSig, aSigExtra; |
158142c2 FB |
3796 | |
3797 | aSig = extractFloatx80Frac( a ); | |
3798 | aExp = extractFloatx80Exp( a ); | |
3799 | aSign = extractFloatx80Sign( a ); | |
3800 | shiftCount = 0x403E - aExp; | |
3801 | if ( shiftCount <= 0 ) { | |
3802 | if ( shiftCount ) { | |
3803 | float_raise( float_flag_invalid STATUS_VAR); | |
3804 | if ( ! aSign | |
3805 | || ( ( aExp == 0x7FFF ) | |
3806 | && ( aSig != LIT64( 0x8000000000000000 ) ) ) | |
3807 | ) { | |
3808 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
3809 | } | |
bb98fe42 | 3810 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
3811 | } |
3812 | aSigExtra = 0; | |
3813 | } | |
3814 | else { | |
3815 | shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); | |
3816 | } | |
3817 | return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); | |
3818 | ||
3819 | } | |
3820 | ||
3821 | /*---------------------------------------------------------------------------- | |
3822 | | Returns the result of converting the extended double-precision floating- | |
3823 | | point value `a' to the 64-bit two's complement integer format. The | |
3824 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3825 | | Floating-Point Arithmetic, except that the conversion is always rounded | |
3826 | | toward zero. If `a' is a NaN, the largest positive integer is returned. | |
3827 | | Otherwise, if the conversion overflows, the largest integer with the same | |
3828 | | sign as `a' is returned. | |
3829 | *----------------------------------------------------------------------------*/ | |
3830 | ||
3831 | int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) | |
3832 | { | |
3833 | flag aSign; | |
3834 | int32 aExp, shiftCount; | |
bb98fe42 | 3835 | uint64_t aSig; |
158142c2 FB |
3836 | int64 z; |
3837 | ||
3838 | aSig = extractFloatx80Frac( a ); | |
3839 | aExp = extractFloatx80Exp( a ); | |
3840 | aSign = extractFloatx80Sign( a ); | |
3841 | shiftCount = aExp - 0x403E; | |
3842 | if ( 0 <= shiftCount ) { | |
3843 | aSig &= LIT64( 0x7FFFFFFFFFFFFFFF ); | |
3844 | if ( ( a.high != 0xC03E ) || aSig ) { | |
3845 | float_raise( float_flag_invalid STATUS_VAR); | |
3846 | if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { | |
3847 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
3848 | } | |
3849 | } | |
bb98fe42 | 3850 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
3851 | } |
3852 | else if ( aExp < 0x3FFF ) { | |
3853 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
3854 | return 0; | |
3855 | } | |
3856 | z = aSig>>( - shiftCount ); | |
bb98fe42 | 3857 | if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { |
158142c2 FB |
3858 | STATUS(float_exception_flags) |= float_flag_inexact; |
3859 | } | |
3860 | if ( aSign ) z = - z; | |
3861 | return z; | |
3862 | ||
3863 | } | |
3864 | ||
3865 | /*---------------------------------------------------------------------------- | |
3866 | | Returns the result of converting the extended double-precision floating- | |
3867 | | point value `a' to the single-precision floating-point format. The | |
3868 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3869 | | Floating-Point Arithmetic. | |
3870 | *----------------------------------------------------------------------------*/ | |
3871 | ||
3872 | float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) | |
3873 | { | |
3874 | flag aSign; | |
3875 | int32 aExp; | |
bb98fe42 | 3876 | uint64_t aSig; |
158142c2 FB |
3877 | |
3878 | aSig = extractFloatx80Frac( a ); | |
3879 | aExp = extractFloatx80Exp( a ); | |
3880 | aSign = extractFloatx80Sign( a ); | |
3881 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 3882 | if ( (uint64_t) ( aSig<<1 ) ) { |
bcd4d9af | 3883 | return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
3884 | } |
3885 | return packFloat32( aSign, 0xFF, 0 ); | |
3886 | } | |
3887 | shift64RightJamming( aSig, 33, &aSig ); | |
3888 | if ( aExp || aSig ) aExp -= 0x3F81; | |
3889 | return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); | |
3890 | ||
3891 | } | |
3892 | ||
3893 | /*---------------------------------------------------------------------------- | |
3894 | | Returns the result of converting the extended double-precision floating- | |
3895 | | point value `a' to the double-precision floating-point format. The | |
3896 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3897 | | Floating-Point Arithmetic. | |
3898 | *----------------------------------------------------------------------------*/ | |
3899 | ||
3900 | float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) | |
3901 | { | |
3902 | flag aSign; | |
3903 | int32 aExp; | |
bb98fe42 | 3904 | uint64_t aSig, zSig; |
158142c2 FB |
3905 | |
3906 | aSig = extractFloatx80Frac( a ); | |
3907 | aExp = extractFloatx80Exp( a ); | |
3908 | aSign = extractFloatx80Sign( a ); | |
3909 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 3910 | if ( (uint64_t) ( aSig<<1 ) ) { |
bcd4d9af | 3911 | return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
3912 | } |
3913 | return packFloat64( aSign, 0x7FF, 0 ); | |
3914 | } | |
3915 | shift64RightJamming( aSig, 1, &zSig ); | |
3916 | if ( aExp || aSig ) aExp -= 0x3C01; | |
3917 | return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR ); | |
3918 | ||
3919 | } | |
3920 | ||
3921 | #ifdef FLOAT128 | |
3922 | ||
3923 | /*---------------------------------------------------------------------------- | |
3924 | | Returns the result of converting the extended double-precision floating- | |
3925 | | point value `a' to the quadruple-precision floating-point format. The | |
3926 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3927 | | Floating-Point Arithmetic. | |
3928 | *----------------------------------------------------------------------------*/ | |
3929 | ||
3930 | float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) | |
3931 | { | |
3932 | flag aSign; | |
3933 | int16 aExp; | |
bb98fe42 | 3934 | uint64_t aSig, zSig0, zSig1; |
158142c2 FB |
3935 | |
3936 | aSig = extractFloatx80Frac( a ); | |
3937 | aExp = extractFloatx80Exp( a ); | |
3938 | aSign = extractFloatx80Sign( a ); | |
bb98fe42 | 3939 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) { |
bcd4d9af | 3940 | return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
3941 | } |
3942 | shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); | |
3943 | return packFloat128( aSign, aExp, zSig0, zSig1 ); | |
3944 | ||
3945 | } | |
3946 | ||
3947 | #endif | |
3948 | ||
3949 | /*---------------------------------------------------------------------------- | |
3950 | | Rounds the extended double-precision floating-point value `a' to an integer, | |
3951 | | and returns the result as an extended quadruple-precision floating-point | |
3952 | | value. The operation is performed according to the IEC/IEEE Standard for | |
3953 | | Binary Floating-Point Arithmetic. | |
3954 | *----------------------------------------------------------------------------*/ | |
3955 | ||
3956 | floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) | |
3957 | { | |
3958 | flag aSign; | |
3959 | int32 aExp; | |
bb98fe42 | 3960 | uint64_t lastBitMask, roundBitsMask; |
158142c2 FB |
3961 | int8 roundingMode; |
3962 | floatx80 z; | |
3963 | ||
3964 | aExp = extractFloatx80Exp( a ); | |
3965 | if ( 0x403E <= aExp ) { | |
bb98fe42 | 3966 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) { |
158142c2 FB |
3967 | return propagateFloatx80NaN( a, a STATUS_VAR ); |
3968 | } | |
3969 | return a; | |
3970 | } | |
3971 | if ( aExp < 0x3FFF ) { | |
3972 | if ( ( aExp == 0 ) | |
bb98fe42 | 3973 | && ( (uint64_t) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { |
158142c2 FB |
3974 | return a; |
3975 | } | |
3976 | STATUS(float_exception_flags) |= float_flag_inexact; | |
3977 | aSign = extractFloatx80Sign( a ); | |
3978 | switch ( STATUS(float_rounding_mode) ) { | |
3979 | case float_round_nearest_even: | |
bb98fe42 | 3980 | if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) |
158142c2 FB |
3981 | ) { |
3982 | return | |
3983 | packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); | |
3984 | } | |
3985 | break; | |
3986 | case float_round_down: | |
3987 | return | |
3988 | aSign ? | |
3989 | packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) | |
3990 | : packFloatx80( 0, 0, 0 ); | |
3991 | case float_round_up: | |
3992 | return | |
3993 | aSign ? packFloatx80( 1, 0, 0 ) | |
3994 | : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); | |
3995 | } | |
3996 | return packFloatx80( aSign, 0, 0 ); | |
3997 | } | |
3998 | lastBitMask = 1; | |
3999 | lastBitMask <<= 0x403E - aExp; | |
4000 | roundBitsMask = lastBitMask - 1; | |
4001 | z = a; | |
4002 | roundingMode = STATUS(float_rounding_mode); | |
4003 | if ( roundingMode == float_round_nearest_even ) { | |
4004 | z.low += lastBitMask>>1; | |
4005 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; | |
4006 | } | |
4007 | else if ( roundingMode != float_round_to_zero ) { | |
4008 | if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
4009 | z.low += roundBitsMask; | |
4010 | } | |
4011 | } | |
4012 | z.low &= ~ roundBitsMask; | |
4013 | if ( z.low == 0 ) { | |
4014 | ++z.high; | |
4015 | z.low = LIT64( 0x8000000000000000 ); | |
4016 | } | |
4017 | if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact; | |
4018 | return z; | |
4019 | ||
4020 | } | |
4021 | ||
4022 | /*---------------------------------------------------------------------------- | |
4023 | | Returns the result of adding the absolute values of the extended double- | |
4024 | | precision floating-point values `a' and `b'. If `zSign' is 1, the sum is | |
4025 | | negated before being returned. `zSign' is ignored if the result is a NaN. | |
4026 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
4027 | | Floating-Point Arithmetic. | |
4028 | *----------------------------------------------------------------------------*/ | |
4029 | ||
4030 | static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM) | |
4031 | { | |
4032 | int32 aExp, bExp, zExp; | |
bb98fe42 | 4033 | uint64_t aSig, bSig, zSig0, zSig1; |
158142c2 FB |
4034 | int32 expDiff; |
4035 | ||
4036 | aSig = extractFloatx80Frac( a ); | |
4037 | aExp = extractFloatx80Exp( a ); | |
4038 | bSig = extractFloatx80Frac( b ); | |
4039 | bExp = extractFloatx80Exp( b ); | |
4040 | expDiff = aExp - bExp; | |
4041 | if ( 0 < expDiff ) { | |
4042 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 4043 | if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4044 | return a; |
4045 | } | |
4046 | if ( bExp == 0 ) --expDiff; | |
4047 | shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); | |
4048 | zExp = aExp; | |
4049 | } | |
4050 | else if ( expDiff < 0 ) { | |
4051 | if ( bExp == 0x7FFF ) { | |
bb98fe42 | 4052 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4053 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4054 | } | |
4055 | if ( aExp == 0 ) ++expDiff; | |
4056 | shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); | |
4057 | zExp = bExp; | |
4058 | } | |
4059 | else { | |
4060 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 4061 | if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { |
158142c2 FB |
4062 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
4063 | } | |
4064 | return a; | |
4065 | } | |
4066 | zSig1 = 0; | |
4067 | zSig0 = aSig + bSig; | |
4068 | if ( aExp == 0 ) { | |
4069 | normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); | |
4070 | goto roundAndPack; | |
4071 | } | |
4072 | zExp = aExp; | |
4073 | goto shiftRight1; | |
4074 | } | |
4075 | zSig0 = aSig + bSig; | |
bb98fe42 | 4076 | if ( (int64_t) zSig0 < 0 ) goto roundAndPack; |
158142c2 FB |
4077 | shiftRight1: |
4078 | shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); | |
4079 | zSig0 |= LIT64( 0x8000000000000000 ); | |
4080 | ++zExp; | |
4081 | roundAndPack: | |
4082 | return | |
4083 | roundAndPackFloatx80( | |
4084 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
4085 | ||
4086 | } | |
4087 | ||
4088 | /*---------------------------------------------------------------------------- | |
4089 | | Returns the result of subtracting the absolute values of the extended | |
4090 | | double-precision floating-point values `a' and `b'. If `zSign' is 1, the | |
4091 | | difference is negated before being returned. `zSign' is ignored if the | |
4092 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
4093 | | Standard for Binary Floating-Point Arithmetic. | |
4094 | *----------------------------------------------------------------------------*/ | |
4095 | ||
4096 | static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM ) | |
4097 | { | |
4098 | int32 aExp, bExp, zExp; | |
bb98fe42 | 4099 | uint64_t aSig, bSig, zSig0, zSig1; |
158142c2 FB |
4100 | int32 expDiff; |
4101 | floatx80 z; | |
4102 | ||
4103 | aSig = extractFloatx80Frac( a ); | |
4104 | aExp = extractFloatx80Exp( a ); | |
4105 | bSig = extractFloatx80Frac( b ); | |
4106 | bExp = extractFloatx80Exp( b ); | |
4107 | expDiff = aExp - bExp; | |
4108 | if ( 0 < expDiff ) goto aExpBigger; | |
4109 | if ( expDiff < 0 ) goto bExpBigger; | |
4110 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 4111 | if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { |
158142c2 FB |
4112 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
4113 | } | |
4114 | float_raise( float_flag_invalid STATUS_VAR); | |
4115 | z.low = floatx80_default_nan_low; | |
4116 | z.high = floatx80_default_nan_high; | |
4117 | return z; | |
4118 | } | |
4119 | if ( aExp == 0 ) { | |
4120 | aExp = 1; | |
4121 | bExp = 1; | |
4122 | } | |
4123 | zSig1 = 0; | |
4124 | if ( bSig < aSig ) goto aBigger; | |
4125 | if ( aSig < bSig ) goto bBigger; | |
4126 | return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); | |
4127 | bExpBigger: | |
4128 | if ( bExp == 0x7FFF ) { | |
bb98fe42 | 4129 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4130 | return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4131 | } | |
4132 | if ( aExp == 0 ) ++expDiff; | |
4133 | shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); | |
4134 | bBigger: | |
4135 | sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); | |
4136 | zExp = bExp; | |
4137 | zSign ^= 1; | |
4138 | goto normalizeRoundAndPack; | |
4139 | aExpBigger: | |
4140 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 4141 | if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4142 | return a; |
4143 | } | |
4144 | if ( bExp == 0 ) --expDiff; | |
4145 | shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); | |
4146 | aBigger: | |
4147 | sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); | |
4148 | zExp = aExp; | |
4149 | normalizeRoundAndPack: | |
4150 | return | |
4151 | normalizeRoundAndPackFloatx80( | |
4152 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
4153 | ||
4154 | } | |
4155 | ||
4156 | /*---------------------------------------------------------------------------- | |
4157 | | Returns the result of adding the extended double-precision floating-point | |
4158 | | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
4159 | | Standard for Binary Floating-Point Arithmetic. | |
4160 | *----------------------------------------------------------------------------*/ | |
4161 | ||
4162 | floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) | |
4163 | { | |
4164 | flag aSign, bSign; | |
4165 | ||
4166 | aSign = extractFloatx80Sign( a ); | |
4167 | bSign = extractFloatx80Sign( b ); | |
4168 | if ( aSign == bSign ) { | |
4169 | return addFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
4170 | } | |
4171 | else { | |
4172 | return subFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
4173 | } | |
4174 | ||
4175 | } | |
4176 | ||
4177 | /*---------------------------------------------------------------------------- | |
4178 | | Returns the result of subtracting the extended double-precision floating- | |
4179 | | point values `a' and `b'. The operation is performed according to the | |
4180 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4181 | *----------------------------------------------------------------------------*/ | |
4182 | ||
4183 | floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) | |
4184 | { | |
4185 | flag aSign, bSign; | |
4186 | ||
4187 | aSign = extractFloatx80Sign( a ); | |
4188 | bSign = extractFloatx80Sign( b ); | |
4189 | if ( aSign == bSign ) { | |
4190 | return subFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
4191 | } | |
4192 | else { | |
4193 | return addFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
4194 | } | |
4195 | ||
4196 | } | |
4197 | ||
4198 | /*---------------------------------------------------------------------------- | |
4199 | | Returns the result of multiplying the extended double-precision floating- | |
4200 | | point values `a' and `b'. The operation is performed according to the | |
4201 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4202 | *----------------------------------------------------------------------------*/ | |
4203 | ||
4204 | floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) | |
4205 | { | |
4206 | flag aSign, bSign, zSign; | |
4207 | int32 aExp, bExp, zExp; | |
bb98fe42 | 4208 | uint64_t aSig, bSig, zSig0, zSig1; |
158142c2 FB |
4209 | floatx80 z; |
4210 | ||
4211 | aSig = extractFloatx80Frac( a ); | |
4212 | aExp = extractFloatx80Exp( a ); | |
4213 | aSign = extractFloatx80Sign( a ); | |
4214 | bSig = extractFloatx80Frac( b ); | |
4215 | bExp = extractFloatx80Exp( b ); | |
4216 | bSign = extractFloatx80Sign( b ); | |
4217 | zSign = aSign ^ bSign; | |
4218 | if ( aExp == 0x7FFF ) { | |
bb98fe42 AF |
4219 | if ( (uint64_t) ( aSig<<1 ) |
4220 | || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { | |
158142c2 FB |
4221 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
4222 | } | |
4223 | if ( ( bExp | bSig ) == 0 ) goto invalid; | |
4224 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
4225 | } | |
4226 | if ( bExp == 0x7FFF ) { | |
bb98fe42 | 4227 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4228 | if ( ( aExp | aSig ) == 0 ) { |
4229 | invalid: | |
4230 | float_raise( float_flag_invalid STATUS_VAR); | |
4231 | z.low = floatx80_default_nan_low; | |
4232 | z.high = floatx80_default_nan_high; | |
4233 | return z; | |
4234 | } | |
4235 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
4236 | } | |
4237 | if ( aExp == 0 ) { | |
4238 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
4239 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); | |
4240 | } | |
4241 | if ( bExp == 0 ) { | |
4242 | if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
4243 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
4244 | } | |
4245 | zExp = aExp + bExp - 0x3FFE; | |
4246 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); | |
bb98fe42 | 4247 | if ( 0 < (int64_t) zSig0 ) { |
158142c2 FB |
4248 | shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); |
4249 | --zExp; | |
4250 | } | |
4251 | return | |
4252 | roundAndPackFloatx80( | |
4253 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
4254 | ||
4255 | } | |
4256 | ||
4257 | /*---------------------------------------------------------------------------- | |
4258 | | Returns the result of dividing the extended double-precision floating-point | |
4259 | | value `a' by the corresponding value `b'. The operation is performed | |
4260 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4261 | *----------------------------------------------------------------------------*/ | |
4262 | ||
4263 | floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) | |
4264 | { | |
4265 | flag aSign, bSign, zSign; | |
4266 | int32 aExp, bExp, zExp; | |
bb98fe42 AF |
4267 | uint64_t aSig, bSig, zSig0, zSig1; |
4268 | uint64_t rem0, rem1, rem2, term0, term1, term2; | |
158142c2 FB |
4269 | floatx80 z; |
4270 | ||
4271 | aSig = extractFloatx80Frac( a ); | |
4272 | aExp = extractFloatx80Exp( a ); | |
4273 | aSign = extractFloatx80Sign( a ); | |
4274 | bSig = extractFloatx80Frac( b ); | |
4275 | bExp = extractFloatx80Exp( b ); | |
4276 | bSign = extractFloatx80Sign( b ); | |
4277 | zSign = aSign ^ bSign; | |
4278 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 4279 | if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 | 4280 | if ( bExp == 0x7FFF ) { |
bb98fe42 | 4281 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4282 | goto invalid; |
4283 | } | |
4284 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
4285 | } | |
4286 | if ( bExp == 0x7FFF ) { | |
bb98fe42 | 4287 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4288 | return packFloatx80( zSign, 0, 0 ); |
4289 | } | |
4290 | if ( bExp == 0 ) { | |
4291 | if ( bSig == 0 ) { | |
4292 | if ( ( aExp | aSig ) == 0 ) { | |
4293 | invalid: | |
4294 | float_raise( float_flag_invalid STATUS_VAR); | |
4295 | z.low = floatx80_default_nan_low; | |
4296 | z.high = floatx80_default_nan_high; | |
4297 | return z; | |
4298 | } | |
4299 | float_raise( float_flag_divbyzero STATUS_VAR); | |
4300 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
4301 | } | |
4302 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
4303 | } | |
4304 | if ( aExp == 0 ) { | |
4305 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
4306 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); | |
4307 | } | |
4308 | zExp = aExp - bExp + 0x3FFE; | |
4309 | rem1 = 0; | |
4310 | if ( bSig <= aSig ) { | |
4311 | shift128Right( aSig, 0, 1, &aSig, &rem1 ); | |
4312 | ++zExp; | |
4313 | } | |
4314 | zSig0 = estimateDiv128To64( aSig, rem1, bSig ); | |
4315 | mul64To128( bSig, zSig0, &term0, &term1 ); | |
4316 | sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); | |
bb98fe42 | 4317 | while ( (int64_t) rem0 < 0 ) { |
158142c2 FB |
4318 | --zSig0; |
4319 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); | |
4320 | } | |
4321 | zSig1 = estimateDiv128To64( rem1, 0, bSig ); | |
bb98fe42 | 4322 | if ( (uint64_t) ( zSig1<<1 ) <= 8 ) { |
158142c2 FB |
4323 | mul64To128( bSig, zSig1, &term1, &term2 ); |
4324 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
bb98fe42 | 4325 | while ( (int64_t) rem1 < 0 ) { |
158142c2 FB |
4326 | --zSig1; |
4327 | add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); | |
4328 | } | |
4329 | zSig1 |= ( ( rem1 | rem2 ) != 0 ); | |
4330 | } | |
4331 | return | |
4332 | roundAndPackFloatx80( | |
4333 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
4334 | ||
4335 | } | |
4336 | ||
4337 | /*---------------------------------------------------------------------------- | |
4338 | | Returns the remainder of the extended double-precision floating-point value | |
4339 | | `a' with respect to the corresponding value `b'. The operation is performed | |
4340 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4341 | *----------------------------------------------------------------------------*/ | |
4342 | ||
4343 | floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) | |
4344 | { | |
ed086f3d | 4345 | flag aSign, zSign; |
158142c2 | 4346 | int32 aExp, bExp, expDiff; |
bb98fe42 AF |
4347 | uint64_t aSig0, aSig1, bSig; |
4348 | uint64_t q, term0, term1, alternateASig0, alternateASig1; | |
158142c2 FB |
4349 | floatx80 z; |
4350 | ||
4351 | aSig0 = extractFloatx80Frac( a ); | |
4352 | aExp = extractFloatx80Exp( a ); | |
4353 | aSign = extractFloatx80Sign( a ); | |
4354 | bSig = extractFloatx80Frac( b ); | |
4355 | bExp = extractFloatx80Exp( b ); | |
158142c2 | 4356 | if ( aExp == 0x7FFF ) { |
bb98fe42 AF |
4357 | if ( (uint64_t) ( aSig0<<1 ) |
4358 | || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { | |
158142c2 FB |
4359 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
4360 | } | |
4361 | goto invalid; | |
4362 | } | |
4363 | if ( bExp == 0x7FFF ) { | |
bb98fe42 | 4364 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
158142c2 FB |
4365 | return a; |
4366 | } | |
4367 | if ( bExp == 0 ) { | |
4368 | if ( bSig == 0 ) { | |
4369 | invalid: | |
4370 | float_raise( float_flag_invalid STATUS_VAR); | |
4371 | z.low = floatx80_default_nan_low; | |
4372 | z.high = floatx80_default_nan_high; | |
4373 | return z; | |
4374 | } | |
4375 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
4376 | } | |
4377 | if ( aExp == 0 ) { | |
bb98fe42 | 4378 | if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a; |
158142c2 FB |
4379 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
4380 | } | |
4381 | bSig |= LIT64( 0x8000000000000000 ); | |
4382 | zSign = aSign; | |
4383 | expDiff = aExp - bExp; | |
4384 | aSig1 = 0; | |
4385 | if ( expDiff < 0 ) { | |
4386 | if ( expDiff < -1 ) return a; | |
4387 | shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); | |
4388 | expDiff = 0; | |
4389 | } | |
4390 | q = ( bSig <= aSig0 ); | |
4391 | if ( q ) aSig0 -= bSig; | |
4392 | expDiff -= 64; | |
4393 | while ( 0 < expDiff ) { | |
4394 | q = estimateDiv128To64( aSig0, aSig1, bSig ); | |
4395 | q = ( 2 < q ) ? q - 2 : 0; | |
4396 | mul64To128( bSig, q, &term0, &term1 ); | |
4397 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
4398 | shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); | |
4399 | expDiff -= 62; | |
4400 | } | |
4401 | expDiff += 64; | |
4402 | if ( 0 < expDiff ) { | |
4403 | q = estimateDiv128To64( aSig0, aSig1, bSig ); | |
4404 | q = ( 2 < q ) ? q - 2 : 0; | |
4405 | q >>= 64 - expDiff; | |
4406 | mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); | |
4407 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
4408 | shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); | |
4409 | while ( le128( term0, term1, aSig0, aSig1 ) ) { | |
4410 | ++q; | |
4411 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
4412 | } | |
4413 | } | |
4414 | else { | |
4415 | term1 = 0; | |
4416 | term0 = bSig; | |
4417 | } | |
4418 | sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); | |
4419 | if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) | |
4420 | || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) | |
4421 | && ( q & 1 ) ) | |
4422 | ) { | |
4423 | aSig0 = alternateASig0; | |
4424 | aSig1 = alternateASig1; | |
4425 | zSign = ! zSign; | |
4426 | } | |
4427 | return | |
4428 | normalizeRoundAndPackFloatx80( | |
4429 | 80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR ); | |
4430 | ||
4431 | } | |
4432 | ||
4433 | /*---------------------------------------------------------------------------- | |
4434 | | Returns the square root of the extended double-precision floating-point | |
4435 | | value `a'. The operation is performed according to the IEC/IEEE Standard | |
4436 | | for Binary Floating-Point Arithmetic. | |
4437 | *----------------------------------------------------------------------------*/ | |
4438 | ||
4439 | floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) | |
4440 | { | |
4441 | flag aSign; | |
4442 | int32 aExp, zExp; | |
bb98fe42 AF |
4443 | uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0; |
4444 | uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
158142c2 FB |
4445 | floatx80 z; |
4446 | ||
4447 | aSig0 = extractFloatx80Frac( a ); | |
4448 | aExp = extractFloatx80Exp( a ); | |
4449 | aSign = extractFloatx80Sign( a ); | |
4450 | if ( aExp == 0x7FFF ) { | |
bb98fe42 | 4451 | if ( (uint64_t) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); |
158142c2 FB |
4452 | if ( ! aSign ) return a; |
4453 | goto invalid; | |
4454 | } | |
4455 | if ( aSign ) { | |
4456 | if ( ( aExp | aSig0 ) == 0 ) return a; | |
4457 | invalid: | |
4458 | float_raise( float_flag_invalid STATUS_VAR); | |
4459 | z.low = floatx80_default_nan_low; | |
4460 | z.high = floatx80_default_nan_high; | |
4461 | return z; | |
4462 | } | |
4463 | if ( aExp == 0 ) { | |
4464 | if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); | |
4465 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); | |
4466 | } | |
4467 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; | |
4468 | zSig0 = estimateSqrt32( aExp, aSig0>>32 ); | |
4469 | shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); | |
4470 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); | |
4471 | doubleZSig0 = zSig0<<1; | |
4472 | mul64To128( zSig0, zSig0, &term0, &term1 ); | |
4473 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); | |
bb98fe42 | 4474 | while ( (int64_t) rem0 < 0 ) { |
158142c2 FB |
4475 | --zSig0; |
4476 | doubleZSig0 -= 2; | |
4477 | add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); | |
4478 | } | |
4479 | zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); | |
4480 | if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { | |
4481 | if ( zSig1 == 0 ) zSig1 = 1; | |
4482 | mul64To128( doubleZSig0, zSig1, &term1, &term2 ); | |
4483 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
4484 | mul64To128( zSig1, zSig1, &term2, &term3 ); | |
4485 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
bb98fe42 | 4486 | while ( (int64_t) rem1 < 0 ) { |
158142c2 FB |
4487 | --zSig1; |
4488 | shortShift128Left( 0, zSig1, 1, &term2, &term3 ); | |
4489 | term3 |= 1; | |
4490 | term2 |= doubleZSig0; | |
4491 | add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
4492 | } | |
4493 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
4494 | } | |
4495 | shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); | |
4496 | zSig0 |= doubleZSig0; | |
4497 | return | |
4498 | roundAndPackFloatx80( | |
4499 | STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR ); | |
4500 | ||
4501 | } | |
4502 | ||
4503 | /*---------------------------------------------------------------------------- | |
4504 | | Returns 1 if the extended double-precision floating-point value `a' is | |
4505 | | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
4506 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4507 | | Arithmetic. | |
4508 | *----------------------------------------------------------------------------*/ | |
4509 | ||
750afe93 | 4510 | int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4511 | { |
4512 | ||
4513 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
bb98fe42 | 4514 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
158142c2 | 4515 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
bb98fe42 | 4516 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
158142c2 FB |
4517 | ) { |
4518 | if ( floatx80_is_signaling_nan( a ) | |
4519 | || floatx80_is_signaling_nan( b ) ) { | |
4520 | float_raise( float_flag_invalid STATUS_VAR); | |
4521 | } | |
4522 | return 0; | |
4523 | } | |
4524 | return | |
4525 | ( a.low == b.low ) | |
4526 | && ( ( a.high == b.high ) | |
4527 | || ( ( a.low == 0 ) | |
bb98fe42 | 4528 | && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
158142c2 FB |
4529 | ); |
4530 | ||
4531 | } | |
4532 | ||
4533 | /*---------------------------------------------------------------------------- | |
4534 | | Returns 1 if the extended double-precision floating-point value `a' is | |
4535 | | less than or equal to the corresponding value `b', and 0 otherwise. The | |
4536 | | comparison is performed according to the IEC/IEEE Standard for Binary | |
4537 | | Floating-Point Arithmetic. | |
4538 | *----------------------------------------------------------------------------*/ | |
4539 | ||
750afe93 | 4540 | int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4541 | { |
4542 | flag aSign, bSign; | |
4543 | ||
4544 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
bb98fe42 | 4545 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
158142c2 | 4546 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
bb98fe42 | 4547 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
158142c2 FB |
4548 | ) { |
4549 | float_raise( float_flag_invalid STATUS_VAR); | |
4550 | return 0; | |
4551 | } | |
4552 | aSign = extractFloatx80Sign( a ); | |
4553 | bSign = extractFloatx80Sign( b ); | |
4554 | if ( aSign != bSign ) { | |
4555 | return | |
4556 | aSign | |
bb98fe42 | 4557 | || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
4558 | == 0 ); |
4559 | } | |
4560 | return | |
4561 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
4562 | : le128( a.high, a.low, b.high, b.low ); | |
4563 | ||
4564 | } | |
4565 | ||
4566 | /*---------------------------------------------------------------------------- | |
4567 | | Returns 1 if the extended double-precision floating-point value `a' is | |
4568 | | less than the corresponding value `b', and 0 otherwise. The comparison | |
4569 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4570 | | Arithmetic. | |
4571 | *----------------------------------------------------------------------------*/ | |
4572 | ||
750afe93 | 4573 | int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4574 | { |
4575 | flag aSign, bSign; | |
4576 | ||
4577 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
bb98fe42 | 4578 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
158142c2 | 4579 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
bb98fe42 | 4580 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
158142c2 FB |
4581 | ) { |
4582 | float_raise( float_flag_invalid STATUS_VAR); | |
4583 | return 0; | |
4584 | } | |
4585 | aSign = extractFloatx80Sign( a ); | |
4586 | bSign = extractFloatx80Sign( b ); | |
4587 | if ( aSign != bSign ) { | |
4588 | return | |
4589 | aSign | |
bb98fe42 | 4590 | && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
4591 | != 0 ); |
4592 | } | |
4593 | return | |
4594 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
4595 | : lt128( a.high, a.low, b.high, b.low ); | |
4596 | ||
4597 | } | |
4598 | ||
4599 | /*---------------------------------------------------------------------------- | |
4600 | | Returns 1 if the extended double-precision floating-point value `a' is equal | |
4601 | | to the corresponding value `b', and 0 otherwise. The invalid exception is | |
4602 | | raised if either operand is a NaN. Otherwise, the comparison is performed | |
4603 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4604 | *----------------------------------------------------------------------------*/ | |
4605 | ||
750afe93 | 4606 | int floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4607 | { |
4608 | ||
4609 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
bb98fe42 | 4610 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
158142c2 | 4611 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
bb98fe42 | 4612 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
158142c2 FB |
4613 | ) { |
4614 | float_raise( float_flag_invalid STATUS_VAR); | |
4615 | return 0; | |
4616 | } | |
4617 | return | |
4618 | ( a.low == b.low ) | |
4619 | && ( ( a.high == b.high ) | |
4620 | || ( ( a.low == 0 ) | |
bb98fe42 | 4621 | && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
158142c2 FB |
4622 | ); |
4623 | ||
4624 | } | |
4625 | ||
4626 | /*---------------------------------------------------------------------------- | |
4627 | | Returns 1 if the extended double-precision floating-point value `a' is less | |
4628 | | than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs | |
4629 | | do not cause an exception. Otherwise, the comparison is performed according | |
4630 | | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4631 | *----------------------------------------------------------------------------*/ | |
4632 | ||
750afe93 | 4633 | int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4634 | { |
4635 | flag aSign, bSign; | |
4636 | ||
4637 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
bb98fe42 | 4638 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
158142c2 | 4639 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
bb98fe42 | 4640 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
158142c2 FB |
4641 | ) { |
4642 | if ( floatx80_is_signaling_nan( a ) | |
4643 | || floatx80_is_signaling_nan( b ) ) { | |
4644 | float_raise( float_flag_invalid STATUS_VAR); | |
4645 | } | |
4646 | return 0; | |
4647 | } | |
4648 | aSign = extractFloatx80Sign( a ); | |
4649 | bSign = extractFloatx80Sign( b ); | |
4650 | if ( aSign != bSign ) { | |
4651 | return | |
4652 | aSign | |
bb98fe42 | 4653 | || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
4654 | == 0 ); |
4655 | } | |
4656 | return | |
4657 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
4658 | : le128( a.high, a.low, b.high, b.low ); | |
4659 | ||
4660 | } | |
4661 | ||
4662 | /*---------------------------------------------------------------------------- | |
4663 | | Returns 1 if the extended double-precision floating-point value `a' is less | |
4664 | | than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause | |
4665 | | an exception. Otherwise, the comparison is performed according to the | |
4666 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4667 | *----------------------------------------------------------------------------*/ | |
4668 | ||
750afe93 | 4669 | int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4670 | { |
4671 | flag aSign, bSign; | |
4672 | ||
4673 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
bb98fe42 | 4674 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
158142c2 | 4675 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
bb98fe42 | 4676 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
158142c2 FB |
4677 | ) { |
4678 | if ( floatx80_is_signaling_nan( a ) | |
4679 | || floatx80_is_signaling_nan( b ) ) { | |
4680 | float_raise( float_flag_invalid STATUS_VAR); | |
4681 | } | |
4682 | return 0; | |
4683 | } | |
4684 | aSign = extractFloatx80Sign( a ); | |
4685 | bSign = extractFloatx80Sign( b ); | |
4686 | if ( aSign != bSign ) { | |
4687 | return | |
4688 | aSign | |
bb98fe42 | 4689 | && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
4690 | != 0 ); |
4691 | } | |
4692 | return | |
4693 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
4694 | : lt128( a.high, a.low, b.high, b.low ); | |
4695 | ||
4696 | } | |
4697 | ||
4698 | #endif | |
4699 | ||
4700 | #ifdef FLOAT128 | |
4701 | ||
4702 | /*---------------------------------------------------------------------------- | |
4703 | | Returns the result of converting the quadruple-precision floating-point | |
4704 | | value `a' to the 32-bit two's complement integer format. The conversion | |
4705 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4706 | | Arithmetic---which means in particular that the conversion is rounded | |
4707 | | according to the current rounding mode. If `a' is a NaN, the largest | |
4708 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
4709 | | largest integer with the same sign as `a' is returned. | |
4710 | *----------------------------------------------------------------------------*/ | |
4711 | ||
4712 | int32 float128_to_int32( float128 a STATUS_PARAM ) | |
4713 | { | |
4714 | flag aSign; | |
4715 | int32 aExp, shiftCount; | |
bb98fe42 | 4716 | uint64_t aSig0, aSig1; |
158142c2 FB |
4717 | |
4718 | aSig1 = extractFloat128Frac1( a ); | |
4719 | aSig0 = extractFloat128Frac0( a ); | |
4720 | aExp = extractFloat128Exp( a ); | |
4721 | aSign = extractFloat128Sign( a ); | |
4722 | if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; | |
4723 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); | |
4724 | aSig0 |= ( aSig1 != 0 ); | |
4725 | shiftCount = 0x4028 - aExp; | |
4726 | if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); | |
4727 | return roundAndPackInt32( aSign, aSig0 STATUS_VAR ); | |
4728 | ||
4729 | } | |
4730 | ||
4731 | /*---------------------------------------------------------------------------- | |
4732 | | Returns the result of converting the quadruple-precision floating-point | |
4733 | | value `a' to the 32-bit two's complement integer format. The conversion | |
4734 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4735 | | Arithmetic, except that the conversion is always rounded toward zero. If | |
4736 | | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
4737 | | conversion overflows, the largest integer with the same sign as `a' is | |
4738 | | returned. | |
4739 | *----------------------------------------------------------------------------*/ | |
4740 | ||
4741 | int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) | |
4742 | { | |
4743 | flag aSign; | |
4744 | int32 aExp, shiftCount; | |
bb98fe42 | 4745 | uint64_t aSig0, aSig1, savedASig; |
158142c2 FB |
4746 | int32 z; |
4747 | ||
4748 | aSig1 = extractFloat128Frac1( a ); | |
4749 | aSig0 = extractFloat128Frac0( a ); | |
4750 | aExp = extractFloat128Exp( a ); | |
4751 | aSign = extractFloat128Sign( a ); | |
4752 | aSig0 |= ( aSig1 != 0 ); | |
4753 | if ( 0x401E < aExp ) { | |
4754 | if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; | |
4755 | goto invalid; | |
4756 | } | |
4757 | else if ( aExp < 0x3FFF ) { | |
4758 | if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
4759 | return 0; | |
4760 | } | |
4761 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4762 | shiftCount = 0x402F - aExp; | |
4763 | savedASig = aSig0; | |
4764 | aSig0 >>= shiftCount; | |
4765 | z = aSig0; | |
4766 | if ( aSign ) z = - z; | |
4767 | if ( ( z < 0 ) ^ aSign ) { | |
4768 | invalid: | |
4769 | float_raise( float_flag_invalid STATUS_VAR); | |
bb98fe42 | 4770 | return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
158142c2 FB |
4771 | } |
4772 | if ( ( aSig0<<shiftCount ) != savedASig ) { | |
4773 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4774 | } | |
4775 | return z; | |
4776 | ||
4777 | } | |
4778 | ||
4779 | /*---------------------------------------------------------------------------- | |
4780 | | Returns the result of converting the quadruple-precision floating-point | |
4781 | | value `a' to the 64-bit two's complement integer format. The conversion | |
4782 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4783 | | Arithmetic---which means in particular that the conversion is rounded | |
4784 | | according to the current rounding mode. If `a' is a NaN, the largest | |
4785 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
4786 | | largest integer with the same sign as `a' is returned. | |
4787 | *----------------------------------------------------------------------------*/ | |
4788 | ||
4789 | int64 float128_to_int64( float128 a STATUS_PARAM ) | |
4790 | { | |
4791 | flag aSign; | |
4792 | int32 aExp, shiftCount; | |
bb98fe42 | 4793 | uint64_t aSig0, aSig1; |
158142c2 FB |
4794 | |
4795 | aSig1 = extractFloat128Frac1( a ); | |
4796 | aSig0 = extractFloat128Frac0( a ); | |
4797 | aExp = extractFloat128Exp( a ); | |
4798 | aSign = extractFloat128Sign( a ); | |
4799 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); | |
4800 | shiftCount = 0x402F - aExp; | |
4801 | if ( shiftCount <= 0 ) { | |
4802 | if ( 0x403E < aExp ) { | |
4803 | float_raise( float_flag_invalid STATUS_VAR); | |
4804 | if ( ! aSign | |
4805 | || ( ( aExp == 0x7FFF ) | |
4806 | && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) | |
4807 | ) | |
4808 | ) { | |
4809 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
4810 | } | |
bb98fe42 | 4811 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
4812 | } |
4813 | shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); | |
4814 | } | |
4815 | else { | |
4816 | shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); | |
4817 | } | |
4818 | return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR ); | |
4819 | ||
4820 | } | |
4821 | ||
4822 | /*---------------------------------------------------------------------------- | |
4823 | | Returns the result of converting the quadruple-precision floating-point | |
4824 | | value `a' to the 64-bit two's complement integer format. The conversion | |
4825 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4826 | | Arithmetic, except that the conversion is always rounded toward zero. | |
4827 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
4828 | | the conversion overflows, the largest integer with the same sign as `a' is | |
4829 | | returned. | |
4830 | *----------------------------------------------------------------------------*/ | |
4831 | ||
4832 | int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) | |
4833 | { | |
4834 | flag aSign; | |
4835 | int32 aExp, shiftCount; | |
bb98fe42 | 4836 | uint64_t aSig0, aSig1; |
158142c2 FB |
4837 | int64 z; |
4838 | ||
4839 | aSig1 = extractFloat128Frac1( a ); | |
4840 | aSig0 = extractFloat128Frac0( a ); | |
4841 | aExp = extractFloat128Exp( a ); | |
4842 | aSign = extractFloat128Sign( a ); | |
4843 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); | |
4844 | shiftCount = aExp - 0x402F; | |
4845 | if ( 0 < shiftCount ) { | |
4846 | if ( 0x403E <= aExp ) { | |
4847 | aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); | |
4848 | if ( ( a.high == LIT64( 0xC03E000000000000 ) ) | |
4849 | && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { | |
4850 | if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
4851 | } | |
4852 | else { | |
4853 | float_raise( float_flag_invalid STATUS_VAR); | |
4854 | if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { | |
4855 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
4856 | } | |
4857 | } | |
bb98fe42 | 4858 | return (int64_t) LIT64( 0x8000000000000000 ); |
158142c2 FB |
4859 | } |
4860 | z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); | |
bb98fe42 | 4861 | if ( (uint64_t) ( aSig1<<shiftCount ) ) { |
158142c2 FB |
4862 | STATUS(float_exception_flags) |= float_flag_inexact; |
4863 | } | |
4864 | } | |
4865 | else { | |
4866 | if ( aExp < 0x3FFF ) { | |
4867 | if ( aExp | aSig0 | aSig1 ) { | |
4868 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4869 | } | |
4870 | return 0; | |
4871 | } | |
4872 | z = aSig0>>( - shiftCount ); | |
4873 | if ( aSig1 | |
bb98fe42 | 4874 | || ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) { |
158142c2 FB |
4875 | STATUS(float_exception_flags) |= float_flag_inexact; |
4876 | } | |
4877 | } | |
4878 | if ( aSign ) z = - z; | |
4879 | return z; | |
4880 | ||
4881 | } | |
4882 | ||
4883 | /*---------------------------------------------------------------------------- | |
4884 | | Returns the result of converting the quadruple-precision floating-point | |
4885 | | value `a' to the single-precision floating-point format. The conversion | |
4886 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4887 | | Arithmetic. | |
4888 | *----------------------------------------------------------------------------*/ | |
4889 | ||
4890 | float32 float128_to_float32( float128 a STATUS_PARAM ) | |
4891 | { | |
4892 | flag aSign; | |
4893 | int32 aExp; | |
bb98fe42 AF |
4894 | uint64_t aSig0, aSig1; |
4895 | uint32_t zSig; | |
158142c2 FB |
4896 | |
4897 | aSig1 = extractFloat128Frac1( a ); | |
4898 | aSig0 = extractFloat128Frac0( a ); | |
4899 | aExp = extractFloat128Exp( a ); | |
4900 | aSign = extractFloat128Sign( a ); | |
4901 | if ( aExp == 0x7FFF ) { | |
4902 | if ( aSig0 | aSig1 ) { | |
bcd4d9af | 4903 | return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
4904 | } |
4905 | return packFloat32( aSign, 0xFF, 0 ); | |
4906 | } | |
4907 | aSig0 |= ( aSig1 != 0 ); | |
4908 | shift64RightJamming( aSig0, 18, &aSig0 ); | |
4909 | zSig = aSig0; | |
4910 | if ( aExp || zSig ) { | |
4911 | zSig |= 0x40000000; | |
4912 | aExp -= 0x3F81; | |
4913 | } | |
4914 | return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); | |
4915 | ||
4916 | } | |
4917 | ||
4918 | /*---------------------------------------------------------------------------- | |
4919 | | Returns the result of converting the quadruple-precision floating-point | |
4920 | | value `a' to the double-precision floating-point format. The conversion | |
4921 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4922 | | Arithmetic. | |
4923 | *----------------------------------------------------------------------------*/ | |
4924 | ||
4925 | float64 float128_to_float64( float128 a STATUS_PARAM ) | |
4926 | { | |
4927 | flag aSign; | |
4928 | int32 aExp; | |
bb98fe42 | 4929 | uint64_t aSig0, aSig1; |
158142c2 FB |
4930 | |
4931 | aSig1 = extractFloat128Frac1( a ); | |
4932 | aSig0 = extractFloat128Frac0( a ); | |
4933 | aExp = extractFloat128Exp( a ); | |
4934 | aSign = extractFloat128Sign( a ); | |
4935 | if ( aExp == 0x7FFF ) { | |
4936 | if ( aSig0 | aSig1 ) { | |
bcd4d9af | 4937 | return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
4938 | } |
4939 | return packFloat64( aSign, 0x7FF, 0 ); | |
4940 | } | |
4941 | shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); | |
4942 | aSig0 |= ( aSig1 != 0 ); | |
4943 | if ( aExp || aSig0 ) { | |
4944 | aSig0 |= LIT64( 0x4000000000000000 ); | |
4945 | aExp -= 0x3C01; | |
4946 | } | |
4947 | return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR ); | |
4948 | ||
4949 | } | |
4950 | ||
4951 | #ifdef FLOATX80 | |
4952 | ||
4953 | /*---------------------------------------------------------------------------- | |
4954 | | Returns the result of converting the quadruple-precision floating-point | |
4955 | | value `a' to the extended double-precision floating-point format. The | |
4956 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
4957 | | Floating-Point Arithmetic. | |
4958 | *----------------------------------------------------------------------------*/ | |
4959 | ||
4960 | floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) | |
4961 | { | |
4962 | flag aSign; | |
4963 | int32 aExp; | |
bb98fe42 | 4964 | uint64_t aSig0, aSig1; |
158142c2 FB |
4965 | |
4966 | aSig1 = extractFloat128Frac1( a ); | |
4967 | aSig0 = extractFloat128Frac0( a ); | |
4968 | aExp = extractFloat128Exp( a ); | |
4969 | aSign = extractFloat128Sign( a ); | |
4970 | if ( aExp == 0x7FFF ) { | |
4971 | if ( aSig0 | aSig1 ) { | |
bcd4d9af | 4972 | return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
158142c2 FB |
4973 | } |
4974 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
4975 | } | |
4976 | if ( aExp == 0 ) { | |
4977 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); | |
4978 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
4979 | } | |
4980 | else { | |
4981 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4982 | } | |
4983 | shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); | |
4984 | return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); | |
4985 | ||
4986 | } | |
4987 | ||
4988 | #endif | |
4989 | ||
4990 | /*---------------------------------------------------------------------------- | |
4991 | | Rounds the quadruple-precision floating-point value `a' to an integer, and | |
4992 | | returns the result as a quadruple-precision floating-point value. The | |
4993 | | operation is performed according to the IEC/IEEE Standard for Binary | |
4994 | | Floating-Point Arithmetic. | |
4995 | *----------------------------------------------------------------------------*/ | |
4996 | ||
4997 | float128 float128_round_to_int( float128 a STATUS_PARAM ) | |
4998 | { | |
4999 | flag aSign; | |
5000 | int32 aExp; | |
bb98fe42 | 5001 | uint64_t lastBitMask, roundBitsMask; |
158142c2 FB |
5002 | int8 roundingMode; |
5003 | float128 z; | |
5004 | ||
5005 | aExp = extractFloat128Exp( a ); | |
5006 | if ( 0x402F <= aExp ) { | |
5007 | if ( 0x406F <= aExp ) { | |
5008 | if ( ( aExp == 0x7FFF ) | |
5009 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) | |
5010 | ) { | |
5011 | return propagateFloat128NaN( a, a STATUS_VAR ); | |
5012 | } | |
5013 | return a; | |
5014 | } | |
5015 | lastBitMask = 1; | |
5016 | lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; | |
5017 | roundBitsMask = lastBitMask - 1; | |
5018 | z = a; | |
5019 | roundingMode = STATUS(float_rounding_mode); | |
5020 | if ( roundingMode == float_round_nearest_even ) { | |
5021 | if ( lastBitMask ) { | |
5022 | add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); | |
5023 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; | |
5024 | } | |
5025 | else { | |
bb98fe42 | 5026 | if ( (int64_t) z.low < 0 ) { |
158142c2 | 5027 | ++z.high; |
bb98fe42 | 5028 | if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1; |
158142c2 FB |
5029 | } |
5030 | } | |
5031 | } | |
5032 | else if ( roundingMode != float_round_to_zero ) { | |
5033 | if ( extractFloat128Sign( z ) | |
5034 | ^ ( roundingMode == float_round_up ) ) { | |
5035 | add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low ); | |
5036 | } | |
5037 | } | |
5038 | z.low &= ~ roundBitsMask; | |
5039 | } | |
5040 | else { | |
5041 | if ( aExp < 0x3FFF ) { | |
bb98fe42 | 5042 | if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a; |
158142c2 FB |
5043 | STATUS(float_exception_flags) |= float_flag_inexact; |
5044 | aSign = extractFloat128Sign( a ); | |
5045 | switch ( STATUS(float_rounding_mode) ) { | |
5046 | case float_round_nearest_even: | |
5047 | if ( ( aExp == 0x3FFE ) | |
5048 | && ( extractFloat128Frac0( a ) | |
5049 | | extractFloat128Frac1( a ) ) | |
5050 | ) { | |
5051 | return packFloat128( aSign, 0x3FFF, 0, 0 ); | |
5052 | } | |
5053 | break; | |
5054 | case float_round_down: | |
5055 | return | |
5056 | aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) | |
5057 | : packFloat128( 0, 0, 0, 0 ); | |
5058 | case float_round_up: | |
5059 | return | |
5060 | aSign ? packFloat128( 1, 0, 0, 0 ) | |
5061 | : packFloat128( 0, 0x3FFF, 0, 0 ); | |
5062 | } | |
5063 | return packFloat128( aSign, 0, 0, 0 ); | |
5064 | } | |
5065 | lastBitMask = 1; | |
5066 | lastBitMask <<= 0x402F - aExp; | |
5067 | roundBitsMask = lastBitMask - 1; | |
5068 | z.low = 0; | |
5069 | z.high = a.high; | |
5070 | roundingMode = STATUS(float_rounding_mode); | |
5071 | if ( roundingMode == float_round_nearest_even ) { | |
5072 | z.high += lastBitMask>>1; | |
5073 | if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { | |
5074 | z.high &= ~ lastBitMask; | |
5075 | } | |
5076 | } | |
5077 | else if ( roundingMode != float_round_to_zero ) { | |
5078 | if ( extractFloat128Sign( z ) | |
5079 | ^ ( roundingMode == float_round_up ) ) { | |
5080 | z.high |= ( a.low != 0 ); | |
5081 | z.high += roundBitsMask; | |
5082 | } | |
5083 | } | |
5084 | z.high &= ~ roundBitsMask; | |
5085 | } | |
5086 | if ( ( z.low != a.low ) || ( z.high != a.high ) ) { | |
5087 | STATUS(float_exception_flags) |= float_flag_inexact; | |
5088 | } | |
5089 | return z; | |
5090 | ||
5091 | } | |
5092 | ||
5093 | /*---------------------------------------------------------------------------- | |
5094 | | Returns the result of adding the absolute values of the quadruple-precision | |
5095 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated | |
5096 | | before being returned. `zSign' is ignored if the result is a NaN. | |
5097 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
5098 | | Floating-Point Arithmetic. | |
5099 | *----------------------------------------------------------------------------*/ | |
5100 | ||
5101 | static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) | |
5102 | { | |
5103 | int32 aExp, bExp, zExp; | |
bb98fe42 | 5104 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
158142c2 FB |
5105 | int32 expDiff; |
5106 | ||
5107 | aSig1 = extractFloat128Frac1( a ); | |
5108 | aSig0 = extractFloat128Frac0( a ); | |
5109 | aExp = extractFloat128Exp( a ); | |
5110 | bSig1 = extractFloat128Frac1( b ); | |
5111 | bSig0 = extractFloat128Frac0( b ); | |
5112 | bExp = extractFloat128Exp( b ); | |
5113 | expDiff = aExp - bExp; | |
5114 | if ( 0 < expDiff ) { | |
5115 | if ( aExp == 0x7FFF ) { | |
5116 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5117 | return a; | |
5118 | } | |
5119 | if ( bExp == 0 ) { | |
5120 | --expDiff; | |
5121 | } | |
5122 | else { | |
5123 | bSig0 |= LIT64( 0x0001000000000000 ); | |
5124 | } | |
5125 | shift128ExtraRightJamming( | |
5126 | bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); | |
5127 | zExp = aExp; | |
5128 | } | |
5129 | else if ( expDiff < 0 ) { | |
5130 | if ( bExp == 0x7FFF ) { | |
5131 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5132 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
5133 | } | |
5134 | if ( aExp == 0 ) { | |
5135 | ++expDiff; | |
5136 | } | |
5137 | else { | |
5138 | aSig0 |= LIT64( 0x0001000000000000 ); | |
5139 | } | |
5140 | shift128ExtraRightJamming( | |
5141 | aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); | |
5142 | zExp = bExp; | |
5143 | } | |
5144 | else { | |
5145 | if ( aExp == 0x7FFF ) { | |
5146 | if ( aSig0 | aSig1 | bSig0 | bSig1 ) { | |
5147 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
5148 | } | |
5149 | return a; | |
5150 | } | |
5151 | add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); | |
fe76d976 PB |
5152 | if ( aExp == 0 ) { |
5153 | if ( STATUS(flush_to_zero) ) return packFloat128( zSign, 0, 0, 0 ); | |
5154 | return packFloat128( zSign, 0, zSig0, zSig1 ); | |
5155 | } | |
158142c2 FB |
5156 | zSig2 = 0; |
5157 | zSig0 |= LIT64( 0x0002000000000000 ); | |
5158 | zExp = aExp; | |
5159 | goto shiftRight1; | |
5160 | } | |
5161 | aSig0 |= LIT64( 0x0001000000000000 ); | |
5162 | add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); | |
5163 | --zExp; | |
5164 | if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; | |
5165 | ++zExp; | |
5166 | shiftRight1: | |
5167 | shift128ExtraRightJamming( | |
5168 | zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); | |
5169 | roundAndPack: | |
5170 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
5171 | ||
5172 | } | |
5173 | ||
5174 | /*---------------------------------------------------------------------------- | |
5175 | | Returns the result of subtracting the absolute values of the quadruple- | |
5176 | | precision floating-point values `a' and `b'. If `zSign' is 1, the | |
5177 | | difference is negated before being returned. `zSign' is ignored if the | |
5178 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
5179 | | Standard for Binary Floating-Point Arithmetic. | |
5180 | *----------------------------------------------------------------------------*/ | |
5181 | ||
5182 | static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) | |
5183 | { | |
5184 | int32 aExp, bExp, zExp; | |
bb98fe42 | 5185 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; |
158142c2 FB |
5186 | int32 expDiff; |
5187 | float128 z; | |
5188 | ||
5189 | aSig1 = extractFloat128Frac1( a ); | |
5190 | aSig0 = extractFloat128Frac0( a ); | |
5191 | aExp = extractFloat128Exp( a ); | |
5192 | bSig1 = extractFloat128Frac1( b ); | |
5193 | bSig0 = extractFloat128Frac0( b ); | |
5194 | bExp = extractFloat128Exp( b ); | |
5195 | expDiff = aExp - bExp; | |
5196 | shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); | |
5197 | shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); | |
5198 | if ( 0 < expDiff ) goto aExpBigger; | |
5199 | if ( expDiff < 0 ) goto bExpBigger; | |
5200 | if ( aExp == 0x7FFF ) { | |
5201 | if ( aSig0 | aSig1 | bSig0 | bSig1 ) { | |
5202 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
5203 | } | |
5204 | float_raise( float_flag_invalid STATUS_VAR); | |
5205 | z.low = float128_default_nan_low; | |
5206 | z.high = float128_default_nan_high; | |
5207 | return z; | |
5208 | } | |
5209 | if ( aExp == 0 ) { | |
5210 | aExp = 1; | |
5211 | bExp = 1; | |
5212 | } | |
5213 | if ( bSig0 < aSig0 ) goto aBigger; | |
5214 | if ( aSig0 < bSig0 ) goto bBigger; | |
5215 | if ( bSig1 < aSig1 ) goto aBigger; | |
5216 | if ( aSig1 < bSig1 ) goto bBigger; | |
5217 | return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); | |
5218 | bExpBigger: | |
5219 | if ( bExp == 0x7FFF ) { | |
5220 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5221 | return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); | |
5222 | } | |
5223 | if ( aExp == 0 ) { | |
5224 | ++expDiff; | |
5225 | } | |
5226 | else { | |
5227 | aSig0 |= LIT64( 0x4000000000000000 ); | |
5228 | } | |
5229 | shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); | |
5230 | bSig0 |= LIT64( 0x4000000000000000 ); | |
5231 | bBigger: | |
5232 | sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); | |
5233 | zExp = bExp; | |
5234 | zSign ^= 1; | |
5235 | goto normalizeRoundAndPack; | |
5236 | aExpBigger: | |
5237 | if ( aExp == 0x7FFF ) { | |
5238 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5239 | return a; | |
5240 | } | |
5241 | if ( bExp == 0 ) { | |
5242 | --expDiff; | |
5243 | } | |
5244 | else { | |
5245 | bSig0 |= LIT64( 0x4000000000000000 ); | |
5246 | } | |
5247 | shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); | |
5248 | aSig0 |= LIT64( 0x4000000000000000 ); | |
5249 | aBigger: | |
5250 | sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); | |
5251 | zExp = aExp; | |
5252 | normalizeRoundAndPack: | |
5253 | --zExp; | |
5254 | return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); | |
5255 | ||
5256 | } | |
5257 | ||
5258 | /*---------------------------------------------------------------------------- | |
5259 | | Returns the result of adding the quadruple-precision floating-point values | |
5260 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
5261 | | for Binary Floating-Point Arithmetic. | |
5262 | *----------------------------------------------------------------------------*/ | |
5263 | ||
5264 | float128 float128_add( float128 a, float128 b STATUS_PARAM ) | |
5265 | { | |
5266 | flag aSign, bSign; | |
5267 | ||
5268 | aSign = extractFloat128Sign( a ); | |
5269 | bSign = extractFloat128Sign( b ); | |
5270 | if ( aSign == bSign ) { | |
5271 | return addFloat128Sigs( a, b, aSign STATUS_VAR ); | |
5272 | } | |
5273 | else { | |
5274 | return subFloat128Sigs( a, b, aSign STATUS_VAR ); | |
5275 | } | |
5276 | ||
5277 | } | |
5278 | ||
5279 | /*---------------------------------------------------------------------------- | |
5280 | | Returns the result of subtracting the quadruple-precision floating-point | |
5281 | | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
5282 | | Standard for Binary Floating-Point Arithmetic. | |
5283 | *----------------------------------------------------------------------------*/ | |
5284 | ||
5285 | float128 float128_sub( float128 a, float128 b STATUS_PARAM ) | |
5286 | { | |
5287 | flag aSign, bSign; | |
5288 | ||
5289 | aSign = extractFloat128Sign( a ); | |
5290 | bSign = extractFloat128Sign( b ); | |
5291 | if ( aSign == bSign ) { | |
5292 | return subFloat128Sigs( a, b, aSign STATUS_VAR ); | |
5293 | } | |
5294 | else { | |
5295 | return addFloat128Sigs( a, b, aSign STATUS_VAR ); | |
5296 | } | |
5297 | ||
5298 | } | |
5299 | ||
5300 | /*---------------------------------------------------------------------------- | |
5301 | | Returns the result of multiplying the quadruple-precision floating-point | |
5302 | | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
5303 | | Standard for Binary Floating-Point Arithmetic. | |
5304 | *----------------------------------------------------------------------------*/ | |
5305 | ||
5306 | float128 float128_mul( float128 a, float128 b STATUS_PARAM ) | |
5307 | { | |
5308 | flag aSign, bSign, zSign; | |
5309 | int32 aExp, bExp, zExp; | |
bb98fe42 | 5310 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; |
158142c2 FB |
5311 | float128 z; |
5312 | ||
5313 | aSig1 = extractFloat128Frac1( a ); | |
5314 | aSig0 = extractFloat128Frac0( a ); | |
5315 | aExp = extractFloat128Exp( a ); | |
5316 | aSign = extractFloat128Sign( a ); | |
5317 | bSig1 = extractFloat128Frac1( b ); | |
5318 | bSig0 = extractFloat128Frac0( b ); | |
5319 | bExp = extractFloat128Exp( b ); | |
5320 | bSign = extractFloat128Sign( b ); | |
5321 | zSign = aSign ^ bSign; | |
5322 | if ( aExp == 0x7FFF ) { | |
5323 | if ( ( aSig0 | aSig1 ) | |
5324 | || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { | |
5325 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
5326 | } | |
5327 | if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; | |
5328 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
5329 | } | |
5330 | if ( bExp == 0x7FFF ) { | |
5331 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5332 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) { | |
5333 | invalid: | |
5334 | float_raise( float_flag_invalid STATUS_VAR); | |
5335 | z.low = float128_default_nan_low; | |
5336 | z.high = float128_default_nan_high; | |
5337 | return z; | |
5338 | } | |
5339 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
5340 | } | |
5341 | if ( aExp == 0 ) { | |
5342 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); | |
5343 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
5344 | } | |
5345 | if ( bExp == 0 ) { | |
5346 | if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); | |
5347 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); | |
5348 | } | |
5349 | zExp = aExp + bExp - 0x4000; | |
5350 | aSig0 |= LIT64( 0x0001000000000000 ); | |
5351 | shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); | |
5352 | mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); | |
5353 | add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); | |
5354 | zSig2 |= ( zSig3 != 0 ); | |
5355 | if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { | |
5356 | shift128ExtraRightJamming( | |
5357 | zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); | |
5358 | ++zExp; | |
5359 | } | |
5360 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
5361 | ||
5362 | } | |
5363 | ||
5364 | /*---------------------------------------------------------------------------- | |
5365 | | Returns the result of dividing the quadruple-precision floating-point value | |
5366 | | `a' by the corresponding value `b'. The operation is performed according to | |
5367 | | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5368 | *----------------------------------------------------------------------------*/ | |
5369 | ||
5370 | float128 float128_div( float128 a, float128 b STATUS_PARAM ) | |
5371 | { | |
5372 | flag aSign, bSign, zSign; | |
5373 | int32 aExp, bExp, zExp; | |
bb98fe42 AF |
5374 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
5375 | uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
158142c2 FB |
5376 | float128 z; |
5377 | ||
5378 | aSig1 = extractFloat128Frac1( a ); | |
5379 | aSig0 = extractFloat128Frac0( a ); | |
5380 | aExp = extractFloat128Exp( a ); | |
5381 | aSign = extractFloat128Sign( a ); | |
5382 | bSig1 = extractFloat128Frac1( b ); | |
5383 | bSig0 = extractFloat128Frac0( b ); | |
5384 | bExp = extractFloat128Exp( b ); | |
5385 | bSign = extractFloat128Sign( b ); | |
5386 | zSign = aSign ^ bSign; | |
5387 | if ( aExp == 0x7FFF ) { | |
5388 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5389 | if ( bExp == 0x7FFF ) { | |
5390 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5391 | goto invalid; | |
5392 | } | |
5393 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
5394 | } | |
5395 | if ( bExp == 0x7FFF ) { | |
5396 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5397 | return packFloat128( zSign, 0, 0, 0 ); | |
5398 | } | |
5399 | if ( bExp == 0 ) { | |
5400 | if ( ( bSig0 | bSig1 ) == 0 ) { | |
5401 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) { | |
5402 | invalid: | |
5403 | float_raise( float_flag_invalid STATUS_VAR); | |
5404 | z.low = float128_default_nan_low; | |
5405 | z.high = float128_default_nan_high; | |
5406 | return z; | |
5407 | } | |
5408 | float_raise( float_flag_divbyzero STATUS_VAR); | |
5409 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
5410 | } | |
5411 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); | |
5412 | } | |
5413 | if ( aExp == 0 ) { | |
5414 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); | |
5415 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
5416 | } | |
5417 | zExp = aExp - bExp + 0x3FFD; | |
5418 | shortShift128Left( | |
5419 | aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); | |
5420 | shortShift128Left( | |
5421 | bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); | |
5422 | if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { | |
5423 | shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); | |
5424 | ++zExp; | |
5425 | } | |
5426 | zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); | |
5427 | mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); | |
5428 | sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); | |
bb98fe42 | 5429 | while ( (int64_t) rem0 < 0 ) { |
158142c2 FB |
5430 | --zSig0; |
5431 | add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); | |
5432 | } | |
5433 | zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); | |
5434 | if ( ( zSig1 & 0x3FFF ) <= 4 ) { | |
5435 | mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); | |
5436 | sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); | |
bb98fe42 | 5437 | while ( (int64_t) rem1 < 0 ) { |
158142c2 FB |
5438 | --zSig1; |
5439 | add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); | |
5440 | } | |
5441 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
5442 | } | |
5443 | shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); | |
5444 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
5445 | ||
5446 | } | |
5447 | ||
5448 | /*---------------------------------------------------------------------------- | |
5449 | | Returns the remainder of the quadruple-precision floating-point value `a' | |
5450 | | with respect to the corresponding value `b'. The operation is performed | |
5451 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5452 | *----------------------------------------------------------------------------*/ | |
5453 | ||
5454 | float128 float128_rem( float128 a, float128 b STATUS_PARAM ) | |
5455 | { | |
ed086f3d | 5456 | flag aSign, zSign; |
158142c2 | 5457 | int32 aExp, bExp, expDiff; |
bb98fe42 AF |
5458 | uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; |
5459 | uint64_t allZero, alternateASig0, alternateASig1, sigMean1; | |
5460 | int64_t sigMean0; | |
158142c2 FB |
5461 | float128 z; |
5462 | ||
5463 | aSig1 = extractFloat128Frac1( a ); | |
5464 | aSig0 = extractFloat128Frac0( a ); | |
5465 | aExp = extractFloat128Exp( a ); | |
5466 | aSign = extractFloat128Sign( a ); | |
5467 | bSig1 = extractFloat128Frac1( b ); | |
5468 | bSig0 = extractFloat128Frac0( b ); | |
5469 | bExp = extractFloat128Exp( b ); | |
158142c2 FB |
5470 | if ( aExp == 0x7FFF ) { |
5471 | if ( ( aSig0 | aSig1 ) | |
5472 | || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { | |
5473 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
5474 | } | |
5475 | goto invalid; | |
5476 | } | |
5477 | if ( bExp == 0x7FFF ) { | |
5478 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
5479 | return a; | |
5480 | } | |
5481 | if ( bExp == 0 ) { | |
5482 | if ( ( bSig0 | bSig1 ) == 0 ) { | |
5483 | invalid: | |
5484 | float_raise( float_flag_invalid STATUS_VAR); | |
5485 | z.low = float128_default_nan_low; | |
5486 | z.high = float128_default_nan_high; | |
5487 | return z; | |
5488 | } | |
5489 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); | |
5490 | } | |
5491 | if ( aExp == 0 ) { | |
5492 | if ( ( aSig0 | aSig1 ) == 0 ) return a; | |
5493 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
5494 | } | |
5495 | expDiff = aExp - bExp; | |
5496 | if ( expDiff < -1 ) return a; | |
5497 | shortShift128Left( | |
5498 | aSig0 | LIT64( 0x0001000000000000 ), | |
5499 | aSig1, | |
5500 | 15 - ( expDiff < 0 ), | |
5501 | &aSig0, | |
5502 | &aSig1 | |
5503 | ); | |
5504 | shortShift128Left( | |
5505 | bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); | |
5506 | q = le128( bSig0, bSig1, aSig0, aSig1 ); | |
5507 | if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); | |
5508 | expDiff -= 64; | |
5509 | while ( 0 < expDiff ) { | |
5510 | q = estimateDiv128To64( aSig0, aSig1, bSig0 ); | |
5511 | q = ( 4 < q ) ? q - 4 : 0; | |
5512 | mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); | |
5513 | shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); | |
5514 | shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); | |
5515 | sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); | |
5516 | expDiff -= 61; | |
5517 | } | |
5518 | if ( -64 < expDiff ) { | |
5519 | q = estimateDiv128To64( aSig0, aSig1, bSig0 ); | |
5520 | q = ( 4 < q ) ? q - 4 : 0; | |
5521 | q >>= - expDiff; | |
5522 | shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); | |
5523 | expDiff += 52; | |
5524 | if ( expDiff < 0 ) { | |
5525 | shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); | |
5526 | } | |
5527 | else { | |
5528 | shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); | |
5529 | } | |
5530 | mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); | |
5531 | sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); | |
5532 | } | |
5533 | else { | |
5534 | shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); | |
5535 | shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); | |
5536 | } | |
5537 | do { | |
5538 | alternateASig0 = aSig0; | |
5539 | alternateASig1 = aSig1; | |
5540 | ++q; | |
5541 | sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); | |
bb98fe42 | 5542 | } while ( 0 <= (int64_t) aSig0 ); |
158142c2 | 5543 | add128( |
bb98fe42 | 5544 | aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 ); |
158142c2 FB |
5545 | if ( ( sigMean0 < 0 ) |
5546 | || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { | |
5547 | aSig0 = alternateASig0; | |
5548 | aSig1 = alternateASig1; | |
5549 | } | |
bb98fe42 | 5550 | zSign = ( (int64_t) aSig0 < 0 ); |
158142c2 FB |
5551 | if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); |
5552 | return | |
5553 | normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR ); | |
5554 | ||
5555 | } | |
5556 | ||
5557 | /*---------------------------------------------------------------------------- | |
5558 | | Returns the square root of the quadruple-precision floating-point value `a'. | |
5559 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
5560 | | Floating-Point Arithmetic. | |
5561 | *----------------------------------------------------------------------------*/ | |
5562 | ||
5563 | float128 float128_sqrt( float128 a STATUS_PARAM ) | |
5564 | { | |
5565 | flag aSign; | |
5566 | int32 aExp, zExp; | |
bb98fe42 AF |
5567 | uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; |
5568 | uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
158142c2 FB |
5569 | float128 z; |
5570 | ||
5571 | aSig1 = extractFloat128Frac1( a ); | |
5572 | aSig0 = extractFloat128Frac0( a ); | |
5573 | aExp = extractFloat128Exp( a ); | |
5574 | aSign = extractFloat128Sign( a ); | |
5575 | if ( aExp == 0x7FFF ) { | |
5576 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); | |
5577 | if ( ! aSign ) return a; | |
5578 | goto invalid; | |
5579 | } | |
5580 | if ( aSign ) { | |
5581 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; | |
5582 | invalid: | |
5583 | float_raise( float_flag_invalid STATUS_VAR); | |
5584 | z.low = float128_default_nan_low; | |
5585 | z.high = float128_default_nan_high; | |
5586 | return z; | |
5587 | } | |
5588 | if ( aExp == 0 ) { | |
5589 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); | |
5590 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
5591 | } | |
5592 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; | |
5593 | aSig0 |= LIT64( 0x0001000000000000 ); | |
5594 | zSig0 = estimateSqrt32( aExp, aSig0>>17 ); | |
5595 | shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); | |
5596 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); | |
5597 | doubleZSig0 = zSig0<<1; | |
5598 | mul64To128( zSig0, zSig0, &term0, &term1 ); | |
5599 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); | |
bb98fe42 | 5600 | while ( (int64_t) rem0 < 0 ) { |
158142c2 FB |
5601 | --zSig0; |
5602 | doubleZSig0 -= 2; | |
5603 | add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); | |
5604 | } | |
5605 | zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); | |
5606 | if ( ( zSig1 & 0x1FFF ) <= 5 ) { | |
5607 | if ( zSig1 == 0 ) zSig1 = 1; | |
5608 | mul64To128( doubleZSig0, zSig1, &term1, &term2 ); | |
5609 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
5610 | mul64To128( zSig1, zSig1, &term2, &term3 ); | |
5611 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
bb98fe42 | 5612 | while ( (int64_t) rem1 < 0 ) { |
158142c2 FB |
5613 | --zSig1; |
5614 | shortShift128Left( 0, zSig1, 1, &term2, &term3 ); | |
5615 | term3 |= 1; | |
5616 | term2 |= doubleZSig0; | |
5617 | add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
5618 | } | |
5619 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
5620 | } | |
5621 | shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); | |
5622 | return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
5623 | ||
5624 | } | |
5625 | ||
5626 | /*---------------------------------------------------------------------------- | |
5627 | | Returns 1 if the quadruple-precision floating-point value `a' is equal to | |
5628 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
5629 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5630 | *----------------------------------------------------------------------------*/ | |
5631 | ||
750afe93 | 5632 | int float128_eq( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5633 | { |
5634 | ||
5635 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5636 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5637 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5638 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5639 | ) { | |
5640 | if ( float128_is_signaling_nan( a ) | |
5641 | || float128_is_signaling_nan( b ) ) { | |
5642 | float_raise( float_flag_invalid STATUS_VAR); | |
5643 | } | |
5644 | return 0; | |
5645 | } | |
5646 | return | |
5647 | ( a.low == b.low ) | |
5648 | && ( ( a.high == b.high ) | |
5649 | || ( ( a.low == 0 ) | |
bb98fe42 | 5650 | && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
158142c2 FB |
5651 | ); |
5652 | ||
5653 | } | |
5654 | ||
5655 | /*---------------------------------------------------------------------------- | |
5656 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5657 | | or equal to the corresponding value `b', and 0 otherwise. The comparison | |
5658 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
5659 | | Arithmetic. | |
5660 | *----------------------------------------------------------------------------*/ | |
5661 | ||
750afe93 | 5662 | int float128_le( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5663 | { |
5664 | flag aSign, bSign; | |
5665 | ||
5666 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5667 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5668 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5669 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5670 | ) { | |
5671 | float_raise( float_flag_invalid STATUS_VAR); | |
5672 | return 0; | |
5673 | } | |
5674 | aSign = extractFloat128Sign( a ); | |
5675 | bSign = extractFloat128Sign( b ); | |
5676 | if ( aSign != bSign ) { | |
5677 | return | |
5678 | aSign | |
bb98fe42 | 5679 | || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
5680 | == 0 ); |
5681 | } | |
5682 | return | |
5683 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
5684 | : le128( a.high, a.low, b.high, b.low ); | |
5685 | ||
5686 | } | |
5687 | ||
5688 | /*---------------------------------------------------------------------------- | |
5689 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5690 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
5691 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5692 | *----------------------------------------------------------------------------*/ | |
5693 | ||
750afe93 | 5694 | int float128_lt( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5695 | { |
5696 | flag aSign, bSign; | |
5697 | ||
5698 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5699 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5700 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5701 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5702 | ) { | |
5703 | float_raise( float_flag_invalid STATUS_VAR); | |
5704 | return 0; | |
5705 | } | |
5706 | aSign = extractFloat128Sign( a ); | |
5707 | bSign = extractFloat128Sign( b ); | |
5708 | if ( aSign != bSign ) { | |
5709 | return | |
5710 | aSign | |
bb98fe42 | 5711 | && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
5712 | != 0 ); |
5713 | } | |
5714 | return | |
5715 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
5716 | : lt128( a.high, a.low, b.high, b.low ); | |
5717 | ||
5718 | } | |
5719 | ||
5720 | /*---------------------------------------------------------------------------- | |
5721 | | Returns 1 if the quadruple-precision floating-point value `a' is equal to | |
5722 | | the corresponding value `b', and 0 otherwise. The invalid exception is | |
5723 | | raised if either operand is a NaN. Otherwise, the comparison is performed | |
5724 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5725 | *----------------------------------------------------------------------------*/ | |
5726 | ||
750afe93 | 5727 | int float128_eq_signaling( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5728 | { |
5729 | ||
5730 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5731 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5732 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5733 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5734 | ) { | |
5735 | float_raise( float_flag_invalid STATUS_VAR); | |
5736 | return 0; | |
5737 | } | |
5738 | return | |
5739 | ( a.low == b.low ) | |
5740 | && ( ( a.high == b.high ) | |
5741 | || ( ( a.low == 0 ) | |
bb98fe42 | 5742 | && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
158142c2 FB |
5743 | ); |
5744 | ||
5745 | } | |
5746 | ||
5747 | /*---------------------------------------------------------------------------- | |
5748 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5749 | | or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
5750 | | cause an exception. Otherwise, the comparison is performed according to the | |
5751 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5752 | *----------------------------------------------------------------------------*/ | |
5753 | ||
750afe93 | 5754 | int float128_le_quiet( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5755 | { |
5756 | flag aSign, bSign; | |
5757 | ||
5758 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5759 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5760 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5761 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5762 | ) { | |
5763 | if ( float128_is_signaling_nan( a ) | |
5764 | || float128_is_signaling_nan( b ) ) { | |
5765 | float_raise( float_flag_invalid STATUS_VAR); | |
5766 | } | |
5767 | return 0; | |
5768 | } | |
5769 | aSign = extractFloat128Sign( a ); | |
5770 | bSign = extractFloat128Sign( b ); | |
5771 | if ( aSign != bSign ) { | |
5772 | return | |
5773 | aSign | |
bb98fe42 | 5774 | || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
5775 | == 0 ); |
5776 | } | |
5777 | return | |
5778 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
5779 | : le128( a.high, a.low, b.high, b.low ); | |
5780 | ||
5781 | } | |
5782 | ||
5783 | /*---------------------------------------------------------------------------- | |
5784 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5785 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
5786 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
5787 | | Standard for Binary Floating-Point Arithmetic. | |
5788 | *----------------------------------------------------------------------------*/ | |
5789 | ||
750afe93 | 5790 | int float128_lt_quiet( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5791 | { |
5792 | flag aSign, bSign; | |
5793 | ||
5794 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5795 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5796 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5797 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5798 | ) { | |
5799 | if ( float128_is_signaling_nan( a ) | |
5800 | || float128_is_signaling_nan( b ) ) { | |
5801 | float_raise( float_flag_invalid STATUS_VAR); | |
5802 | } | |
5803 | return 0; | |
5804 | } | |
5805 | aSign = extractFloat128Sign( a ); | |
5806 | bSign = extractFloat128Sign( b ); | |
5807 | if ( aSign != bSign ) { | |
5808 | return | |
5809 | aSign | |
bb98fe42 | 5810 | && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
158142c2 FB |
5811 | != 0 ); |
5812 | } | |
5813 | return | |
5814 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
5815 | : lt128( a.high, a.low, b.high, b.low ); | |
5816 | ||
5817 | } | |
5818 | ||
5819 | #endif | |
5820 | ||
1d6bda35 FB |
5821 | /* misc functions */ |
5822 | float32 uint32_to_float32( unsigned int a STATUS_PARAM ) | |
5823 | { | |
5824 | return int64_to_float32(a STATUS_VAR); | |
5825 | } | |
5826 | ||
5827 | float64 uint32_to_float64( unsigned int a STATUS_PARAM ) | |
5828 | { | |
5829 | return int64_to_float64(a STATUS_VAR); | |
5830 | } | |
5831 | ||
5832 | unsigned int float32_to_uint32( float32 a STATUS_PARAM ) | |
5833 | { | |
5834 | int64_t v; | |
5835 | unsigned int res; | |
5836 | ||
5837 | v = float32_to_int64(a STATUS_VAR); | |
5838 | if (v < 0) { | |
5839 | res = 0; | |
5840 | float_raise( float_flag_invalid STATUS_VAR); | |
5841 | } else if (v > 0xffffffff) { | |
5842 | res = 0xffffffff; | |
5843 | float_raise( float_flag_invalid STATUS_VAR); | |
5844 | } else { | |
5845 | res = v; | |
5846 | } | |
5847 | return res; | |
5848 | } | |
5849 | ||
5850 | unsigned int float32_to_uint32_round_to_zero( float32 a STATUS_PARAM ) | |
5851 | { | |
5852 | int64_t v; | |
5853 | unsigned int res; | |
5854 | ||
5855 | v = float32_to_int64_round_to_zero(a STATUS_VAR); | |
5856 | if (v < 0) { | |
5857 | res = 0; | |
5858 | float_raise( float_flag_invalid STATUS_VAR); | |
5859 | } else if (v > 0xffffffff) { | |
5860 | res = 0xffffffff; | |
5861 | float_raise( float_flag_invalid STATUS_VAR); | |
5862 | } else { | |
5863 | res = v; | |
5864 | } | |
5865 | return res; | |
5866 | } | |
5867 | ||
cbcef455 PM |
5868 | unsigned int float32_to_uint16_round_to_zero( float32 a STATUS_PARAM ) |
5869 | { | |
5870 | int64_t v; | |
5871 | unsigned int res; | |
5872 | ||
5873 | v = float32_to_int64_round_to_zero(a STATUS_VAR); | |
5874 | if (v < 0) { | |
5875 | res = 0; | |
5876 | float_raise( float_flag_invalid STATUS_VAR); | |
5877 | } else if (v > 0xffff) { | |
5878 | res = 0xffff; | |
5879 | float_raise( float_flag_invalid STATUS_VAR); | |
5880 | } else { | |
5881 | res = v; | |
5882 | } | |
5883 | return res; | |
5884 | } | |
5885 | ||
1d6bda35 FB |
5886 | unsigned int float64_to_uint32( float64 a STATUS_PARAM ) |
5887 | { | |
5888 | int64_t v; | |
5889 | unsigned int res; | |
5890 | ||
5891 | v = float64_to_int64(a STATUS_VAR); | |
5892 | if (v < 0) { | |
5893 | res = 0; | |
5894 | float_raise( float_flag_invalid STATUS_VAR); | |
5895 | } else if (v > 0xffffffff) { | |
5896 | res = 0xffffffff; | |
5897 | float_raise( float_flag_invalid STATUS_VAR); | |
5898 | } else { | |
5899 | res = v; | |
5900 | } | |
5901 | return res; | |
5902 | } | |
5903 | ||
5904 | unsigned int float64_to_uint32_round_to_zero( float64 a STATUS_PARAM ) | |
5905 | { | |
5906 | int64_t v; | |
5907 | unsigned int res; | |
5908 | ||
5909 | v = float64_to_int64_round_to_zero(a STATUS_VAR); | |
5910 | if (v < 0) { | |
5911 | res = 0; | |
5912 | float_raise( float_flag_invalid STATUS_VAR); | |
5913 | } else if (v > 0xffffffff) { | |
5914 | res = 0xffffffff; | |
5915 | float_raise( float_flag_invalid STATUS_VAR); | |
5916 | } else { | |
5917 | res = v; | |
5918 | } | |
5919 | return res; | |
5920 | } | |
5921 | ||
cbcef455 PM |
5922 | unsigned int float64_to_uint16_round_to_zero( float64 a STATUS_PARAM ) |
5923 | { | |
5924 | int64_t v; | |
5925 | unsigned int res; | |
5926 | ||
5927 | v = float64_to_int64_round_to_zero(a STATUS_VAR); | |
5928 | if (v < 0) { | |
5929 | res = 0; | |
5930 | float_raise( float_flag_invalid STATUS_VAR); | |
5931 | } else if (v > 0xffff) { | |
5932 | res = 0xffff; | |
5933 | float_raise( float_flag_invalid STATUS_VAR); | |
5934 | } else { | |
5935 | res = v; | |
5936 | } | |
5937 | return res; | |
5938 | } | |
5939 | ||
f090c9d4 | 5940 | /* FIXME: This looks broken. */ |
75d62a58 JM |
5941 | uint64_t float64_to_uint64 (float64 a STATUS_PARAM) |
5942 | { | |
5943 | int64_t v; | |
5944 | ||
f090c9d4 PB |
5945 | v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); |
5946 | v += float64_val(a); | |
5947 | v = float64_to_int64(make_float64(v) STATUS_VAR); | |
75d62a58 JM |
5948 | |
5949 | return v - INT64_MIN; | |
5950 | } | |
5951 | ||
5952 | uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM) | |
5953 | { | |
5954 | int64_t v; | |
5955 | ||
f090c9d4 PB |
5956 | v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); |
5957 | v += float64_val(a); | |
5958 | v = float64_to_int64_round_to_zero(make_float64(v) STATUS_VAR); | |
75d62a58 JM |
5959 | |
5960 | return v - INT64_MIN; | |
5961 | } | |
5962 | ||
1d6bda35 | 5963 | #define COMPARE(s, nan_exp) \ |
750afe93 | 5964 | INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \ |
1d6bda35 FB |
5965 | int is_quiet STATUS_PARAM ) \ |
5966 | { \ | |
5967 | flag aSign, bSign; \ | |
bb98fe42 | 5968 | uint ## s ## _t av, bv; \ |
37d18660 PM |
5969 | a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ |
5970 | b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ | |
1d6bda35 FB |
5971 | \ |
5972 | if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ | |
5973 | extractFloat ## s ## Frac( a ) ) || \ | |
5974 | ( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ | |
5975 | extractFloat ## s ## Frac( b ) )) { \ | |
5976 | if (!is_quiet || \ | |
5977 | float ## s ## _is_signaling_nan( a ) || \ | |
5978 | float ## s ## _is_signaling_nan( b ) ) { \ | |
5979 | float_raise( float_flag_invalid STATUS_VAR); \ | |
5980 | } \ | |
5981 | return float_relation_unordered; \ | |
5982 | } \ | |
5983 | aSign = extractFloat ## s ## Sign( a ); \ | |
5984 | bSign = extractFloat ## s ## Sign( b ); \ | |
f090c9d4 | 5985 | av = float ## s ## _val(a); \ |
cd8a2533 | 5986 | bv = float ## s ## _val(b); \ |
1d6bda35 | 5987 | if ( aSign != bSign ) { \ |
bb98fe42 | 5988 | if ( (uint ## s ## _t) ( ( av | bv )<<1 ) == 0 ) { \ |
1d6bda35 FB |
5989 | /* zero case */ \ |
5990 | return float_relation_equal; \ | |
5991 | } else { \ | |
5992 | return 1 - (2 * aSign); \ | |
5993 | } \ | |
5994 | } else { \ | |
f090c9d4 | 5995 | if (av == bv) { \ |
1d6bda35 FB |
5996 | return float_relation_equal; \ |
5997 | } else { \ | |
f090c9d4 | 5998 | return 1 - 2 * (aSign ^ ( av < bv )); \ |
1d6bda35 FB |
5999 | } \ |
6000 | } \ | |
6001 | } \ | |
6002 | \ | |
750afe93 | 6003 | int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \ |
1d6bda35 FB |
6004 | { \ |
6005 | return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \ | |
6006 | } \ | |
6007 | \ | |
750afe93 | 6008 | int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \ |
1d6bda35 FB |
6009 | { \ |
6010 | return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \ | |
6011 | } | |
6012 | ||
6013 | COMPARE(32, 0xff) | |
6014 | COMPARE(64, 0x7ff) | |
9ee6e8bb | 6015 | |
1f587329 BS |
6016 | INLINE int float128_compare_internal( float128 a, float128 b, |
6017 | int is_quiet STATUS_PARAM ) | |
6018 | { | |
6019 | flag aSign, bSign; | |
6020 | ||
6021 | if (( ( extractFloat128Exp( a ) == 0x7fff ) && | |
6022 | ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) || | |
6023 | ( ( extractFloat128Exp( b ) == 0x7fff ) && | |
6024 | ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) { | |
6025 | if (!is_quiet || | |
6026 | float128_is_signaling_nan( a ) || | |
6027 | float128_is_signaling_nan( b ) ) { | |
6028 | float_raise( float_flag_invalid STATUS_VAR); | |
6029 | } | |
6030 | return float_relation_unordered; | |
6031 | } | |
6032 | aSign = extractFloat128Sign( a ); | |
6033 | bSign = extractFloat128Sign( b ); | |
6034 | if ( aSign != bSign ) { | |
6035 | if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) { | |
6036 | /* zero case */ | |
6037 | return float_relation_equal; | |
6038 | } else { | |
6039 | return 1 - (2 * aSign); | |
6040 | } | |
6041 | } else { | |
6042 | if (a.low == b.low && a.high == b.high) { | |
6043 | return float_relation_equal; | |
6044 | } else { | |
6045 | return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); | |
6046 | } | |
6047 | } | |
6048 | } | |
6049 | ||
6050 | int float128_compare( float128 a, float128 b STATUS_PARAM ) | |
6051 | { | |
6052 | return float128_compare_internal(a, b, 0 STATUS_VAR); | |
6053 | } | |
6054 | ||
6055 | int float128_compare_quiet( float128 a, float128 b STATUS_PARAM ) | |
6056 | { | |
6057 | return float128_compare_internal(a, b, 1 STATUS_VAR); | |
6058 | } | |
6059 | ||
9ee6e8bb PB |
6060 | /* Multiply A by 2 raised to the power N. */ |
6061 | float32 float32_scalbn( float32 a, int n STATUS_PARAM ) | |
6062 | { | |
6063 | flag aSign; | |
6064 | int16 aExp; | |
bb98fe42 | 6065 | uint32_t aSig; |
9ee6e8bb | 6066 | |
37d18660 | 6067 | a = float32_squash_input_denormal(a STATUS_VAR); |
9ee6e8bb PB |
6068 | aSig = extractFloat32Frac( a ); |
6069 | aExp = extractFloat32Exp( a ); | |
6070 | aSign = extractFloat32Sign( a ); | |
6071 | ||
6072 | if ( aExp == 0xFF ) { | |
6073 | return a; | |
6074 | } | |
69397542 PB |
6075 | if ( aExp != 0 ) |
6076 | aSig |= 0x00800000; | |
6077 | else if ( aSig == 0 ) | |
6078 | return a; | |
6079 | ||
6080 | aExp += n - 1; | |
6081 | aSig <<= 7; | |
6082 | return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); | |
9ee6e8bb PB |
6083 | } |
6084 | ||
6085 | float64 float64_scalbn( float64 a, int n STATUS_PARAM ) | |
6086 | { | |
6087 | flag aSign; | |
6088 | int16 aExp; | |
bb98fe42 | 6089 | uint64_t aSig; |
9ee6e8bb | 6090 | |
37d18660 | 6091 | a = float64_squash_input_denormal(a STATUS_VAR); |
9ee6e8bb PB |
6092 | aSig = extractFloat64Frac( a ); |
6093 | aExp = extractFloat64Exp( a ); | |
6094 | aSign = extractFloat64Sign( a ); | |
6095 | ||
6096 | if ( aExp == 0x7FF ) { | |
6097 | return a; | |
6098 | } | |
69397542 PB |
6099 | if ( aExp != 0 ) |
6100 | aSig |= LIT64( 0x0010000000000000 ); | |
6101 | else if ( aSig == 0 ) | |
6102 | return a; | |
6103 | ||
6104 | aExp += n - 1; | |
6105 | aSig <<= 10; | |
6106 | return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR ); | |
9ee6e8bb PB |
6107 | } |
6108 | ||
6109 | #ifdef FLOATX80 | |
6110 | floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM ) | |
6111 | { | |
6112 | flag aSign; | |
6113 | int16 aExp; | |
bb98fe42 | 6114 | uint64_t aSig; |
9ee6e8bb PB |
6115 | |
6116 | aSig = extractFloatx80Frac( a ); | |
6117 | aExp = extractFloatx80Exp( a ); | |
6118 | aSign = extractFloatx80Sign( a ); | |
6119 | ||
6120 | if ( aExp == 0x7FF ) { | |
6121 | return a; | |
6122 | } | |
69397542 PB |
6123 | if (aExp == 0 && aSig == 0) |
6124 | return a; | |
6125 | ||
9ee6e8bb | 6126 | aExp += n; |
69397542 PB |
6127 | return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision), |
6128 | aSign, aExp, aSig, 0 STATUS_VAR ); | |
9ee6e8bb PB |
6129 | } |
6130 | #endif | |
6131 | ||
6132 | #ifdef FLOAT128 | |
6133 | float128 float128_scalbn( float128 a, int n STATUS_PARAM ) | |
6134 | { | |
6135 | flag aSign; | |
6136 | int32 aExp; | |
bb98fe42 | 6137 | uint64_t aSig0, aSig1; |
9ee6e8bb PB |
6138 | |
6139 | aSig1 = extractFloat128Frac1( a ); | |
6140 | aSig0 = extractFloat128Frac0( a ); | |
6141 | aExp = extractFloat128Exp( a ); | |
6142 | aSign = extractFloat128Sign( a ); | |
6143 | if ( aExp == 0x7FFF ) { | |
6144 | return a; | |
6145 | } | |
69397542 PB |
6146 | if ( aExp != 0 ) |
6147 | aSig0 |= LIT64( 0x0001000000000000 ); | |
6148 | else if ( aSig0 == 0 && aSig1 == 0 ) | |
6149 | return a; | |
6150 | ||
6151 | aExp += n - 1; | |
6152 | return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1 | |
6153 | STATUS_VAR ); | |
9ee6e8bb PB |
6154 | |
6155 | } | |
6156 | #endif |