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1da177e4 LT |
1 | /* |
2 | * Linux/PA-RISC Project (http://www.parisc-linux.org/) | |
3 | * | |
4 | * Floating-point emulation code | |
5 | * Copyright (C) 2001 Hewlett-Packard (Paul Bame) <bame@debian.org> | |
6 | * | |
7 | * This program is free software; you can redistribute it and/or modify | |
8 | * it under the terms of the GNU General Public License as published by | |
9 | * the Free Software Foundation; either version 2, or (at your option) | |
10 | * any later version. | |
11 | * | |
12 | * This program is distributed in the hope that it will be useful, | |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
15 | * GNU General Public License for more details. | |
16 | * | |
17 | * You should have received a copy of the GNU General Public License | |
18 | * along with this program; if not, write to the Free Software | |
19 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | |
20 | */ | |
21 | /* | |
22 | * BEGIN_DESC | |
23 | * | |
24 | * File: | |
25 | * @(#) pa/spmath/dfsub.c $Revision: 1.1 $ | |
26 | * | |
27 | * Purpose: | |
28 | * Double_subtract: subtract two double precision values. | |
29 | * | |
30 | * External Interfaces: | |
31 | * dbl_fsub(leftptr, rightptr, dstptr, status) | |
32 | * | |
33 | * Internal Interfaces: | |
34 | * | |
35 | * Theory: | |
36 | * <<please update with a overview of the operation of this file>> | |
37 | * | |
38 | * END_DESC | |
39 | */ | |
40 | ||
41 | ||
42 | #include "float.h" | |
43 | #include "dbl_float.h" | |
44 | ||
45 | /* | |
46 | * Double_subtract: subtract two double precision values. | |
47 | */ | |
48 | int | |
49 | dbl_fsub( | |
50 | dbl_floating_point *leftptr, | |
51 | dbl_floating_point *rightptr, | |
52 | dbl_floating_point *dstptr, | |
53 | unsigned int *status) | |
54 | { | |
55 | register unsigned int signless_upper_left, signless_upper_right, save; | |
56 | register unsigned int leftp1, leftp2, rightp1, rightp2, extent; | |
57 | register unsigned int resultp1 = 0, resultp2 = 0; | |
58 | ||
59 | register int result_exponent, right_exponent, diff_exponent; | |
60 | register int sign_save, jumpsize; | |
61 | register boolean inexact = FALSE, underflowtrap; | |
62 | ||
63 | /* Create local copies of the numbers */ | |
64 | Dbl_copyfromptr(leftptr,leftp1,leftp2); | |
65 | Dbl_copyfromptr(rightptr,rightp1,rightp2); | |
66 | ||
67 | /* A zero "save" helps discover equal operands (for later), * | |
68 | * and is used in swapping operands (if needed). */ | |
69 | Dbl_xortointp1(leftp1,rightp1,/*to*/save); | |
70 | ||
71 | /* | |
72 | * check first operand for NaN's or infinity | |
73 | */ | |
74 | if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT) | |
75 | { | |
76 | if (Dbl_iszero_mantissa(leftp1,leftp2)) | |
77 | { | |
78 | if (Dbl_isnotnan(rightp1,rightp2)) | |
79 | { | |
80 | if (Dbl_isinfinity(rightp1,rightp2) && save==0) | |
81 | { | |
82 | /* | |
83 | * invalid since operands are same signed infinity's | |
84 | */ | |
85 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); | |
86 | Set_invalidflag(); | |
87 | Dbl_makequietnan(resultp1,resultp2); | |
88 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
89 | return(NOEXCEPTION); | |
90 | } | |
91 | /* | |
92 | * return infinity | |
93 | */ | |
94 | Dbl_copytoptr(leftp1,leftp2,dstptr); | |
95 | return(NOEXCEPTION); | |
96 | } | |
97 | } | |
98 | else | |
99 | { | |
100 | /* | |
101 | * is NaN; signaling or quiet? | |
102 | */ | |
103 | if (Dbl_isone_signaling(leftp1)) | |
104 | { | |
105 | /* trap if INVALIDTRAP enabled */ | |
106 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); | |
107 | /* make NaN quiet */ | |
108 | Set_invalidflag(); | |
109 | Dbl_set_quiet(leftp1); | |
110 | } | |
111 | /* | |
112 | * is second operand a signaling NaN? | |
113 | */ | |
114 | else if (Dbl_is_signalingnan(rightp1)) | |
115 | { | |
116 | /* trap if INVALIDTRAP enabled */ | |
117 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); | |
118 | /* make NaN quiet */ | |
119 | Set_invalidflag(); | |
120 | Dbl_set_quiet(rightp1); | |
121 | Dbl_copytoptr(rightp1,rightp2,dstptr); | |
122 | return(NOEXCEPTION); | |
123 | } | |
124 | /* | |
125 | * return quiet NaN | |
126 | */ | |
127 | Dbl_copytoptr(leftp1,leftp2,dstptr); | |
128 | return(NOEXCEPTION); | |
129 | } | |
130 | } /* End left NaN or Infinity processing */ | |
131 | /* | |
132 | * check second operand for NaN's or infinity | |
133 | */ | |
134 | if (Dbl_isinfinity_exponent(rightp1)) | |
135 | { | |
136 | if (Dbl_iszero_mantissa(rightp1,rightp2)) | |
137 | { | |
138 | /* return infinity */ | |
139 | Dbl_invert_sign(rightp1); | |
140 | Dbl_copytoptr(rightp1,rightp2,dstptr); | |
141 | return(NOEXCEPTION); | |
142 | } | |
143 | /* | |
144 | * is NaN; signaling or quiet? | |
145 | */ | |
146 | if (Dbl_isone_signaling(rightp1)) | |
147 | { | |
148 | /* trap if INVALIDTRAP enabled */ | |
149 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); | |
150 | /* make NaN quiet */ | |
151 | Set_invalidflag(); | |
152 | Dbl_set_quiet(rightp1); | |
153 | } | |
154 | /* | |
155 | * return quiet NaN | |
156 | */ | |
157 | Dbl_copytoptr(rightp1,rightp2,dstptr); | |
158 | return(NOEXCEPTION); | |
159 | } /* End right NaN or Infinity processing */ | |
160 | ||
161 | /* Invariant: Must be dealing with finite numbers */ | |
162 | ||
163 | /* Compare operands by removing the sign */ | |
164 | Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); | |
165 | Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); | |
166 | ||
167 | /* sign difference selects add or sub operation. */ | |
168 | if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) | |
169 | { | |
170 | /* Set the left operand to the larger one by XOR swap * | |
171 | * First finish the first word using "save" */ | |
172 | Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); | |
173 | Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); | |
174 | Dbl_swap_lower(leftp2,rightp2); | |
175 | result_exponent = Dbl_exponent(leftp1); | |
176 | Dbl_invert_sign(leftp1); | |
177 | } | |
178 | /* Invariant: left is not smaller than right. */ | |
179 | ||
180 | if((right_exponent = Dbl_exponent(rightp1)) == 0) | |
181 | { | |
182 | /* Denormalized operands. First look for zeroes */ | |
183 | if(Dbl_iszero_mantissa(rightp1,rightp2)) | |
184 | { | |
185 | /* right is zero */ | |
186 | if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) | |
187 | { | |
188 | /* Both operands are zeros */ | |
189 | Dbl_invert_sign(rightp1); | |
190 | if(Is_rounding_mode(ROUNDMINUS)) | |
191 | { | |
192 | Dbl_or_signs(leftp1,/*with*/rightp1); | |
193 | } | |
194 | else | |
195 | { | |
196 | Dbl_and_signs(leftp1,/*with*/rightp1); | |
197 | } | |
198 | } | |
199 | else | |
200 | { | |
201 | /* Left is not a zero and must be the result. Trapped | |
202 | * underflows are signaled if left is denormalized. Result | |
203 | * is always exact. */ | |
204 | if( (result_exponent == 0) && Is_underflowtrap_enabled() ) | |
205 | { | |
206 | /* need to normalize results mantissa */ | |
207 | sign_save = Dbl_signextendedsign(leftp1); | |
208 | Dbl_leftshiftby1(leftp1,leftp2); | |
209 | Dbl_normalize(leftp1,leftp2,result_exponent); | |
210 | Dbl_set_sign(leftp1,/*using*/sign_save); | |
211 | Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); | |
212 | Dbl_copytoptr(leftp1,leftp2,dstptr); | |
213 | /* inexact = FALSE */ | |
214 | return(UNDERFLOWEXCEPTION); | |
215 | } | |
216 | } | |
217 | Dbl_copytoptr(leftp1,leftp2,dstptr); | |
218 | return(NOEXCEPTION); | |
219 | } | |
220 | ||
221 | /* Neither are zeroes */ | |
222 | Dbl_clear_sign(rightp1); /* Exponent is already cleared */ | |
223 | if(result_exponent == 0 ) | |
224 | { | |
225 | /* Both operands are denormalized. The result must be exact | |
226 | * and is simply calculated. A sum could become normalized and a | |
227 | * difference could cancel to a true zero. */ | |
228 | if( (/*signed*/int) save >= 0 ) | |
229 | { | |
230 | Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, | |
231 | /*into*/resultp1,resultp2); | |
232 | if(Dbl_iszero_mantissa(resultp1,resultp2)) | |
233 | { | |
234 | if(Is_rounding_mode(ROUNDMINUS)) | |
235 | { | |
236 | Dbl_setone_sign(resultp1); | |
237 | } | |
238 | else | |
239 | { | |
240 | Dbl_setzero_sign(resultp1); | |
241 | } | |
242 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
243 | return(NOEXCEPTION); | |
244 | } | |
245 | } | |
246 | else | |
247 | { | |
248 | Dbl_addition(leftp1,leftp2,rightp1,rightp2, | |
249 | /*into*/resultp1,resultp2); | |
250 | if(Dbl_isone_hidden(resultp1)) | |
251 | { | |
252 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
253 | return(NOEXCEPTION); | |
254 | } | |
255 | } | |
256 | if(Is_underflowtrap_enabled()) | |
257 | { | |
258 | /* need to normalize result */ | |
259 | sign_save = Dbl_signextendedsign(resultp1); | |
260 | Dbl_leftshiftby1(resultp1,resultp2); | |
261 | Dbl_normalize(resultp1,resultp2,result_exponent); | |
262 | Dbl_set_sign(resultp1,/*using*/sign_save); | |
263 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); | |
264 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
265 | /* inexact = FALSE */ | |
266 | return(UNDERFLOWEXCEPTION); | |
267 | } | |
268 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
269 | return(NOEXCEPTION); | |
270 | } | |
271 | right_exponent = 1; /* Set exponent to reflect different bias | |
272 | * with denomalized numbers. */ | |
273 | } | |
274 | else | |
275 | { | |
276 | Dbl_clear_signexponent_set_hidden(rightp1); | |
277 | } | |
278 | Dbl_clear_exponent_set_hidden(leftp1); | |
279 | diff_exponent = result_exponent - right_exponent; | |
280 | ||
281 | /* | |
282 | * Special case alignment of operands that would force alignment | |
283 | * beyond the extent of the extension. A further optimization | |
284 | * could special case this but only reduces the path length for this | |
285 | * infrequent case. | |
286 | */ | |
287 | if(diff_exponent > DBL_THRESHOLD) | |
288 | { | |
289 | diff_exponent = DBL_THRESHOLD; | |
290 | } | |
291 | ||
292 | /* Align right operand by shifting to right */ | |
293 | Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, | |
294 | /*and lower to*/extent); | |
295 | ||
296 | /* Treat sum and difference of the operands separately. */ | |
297 | if( (/*signed*/int) save >= 0 ) | |
298 | { | |
299 | /* | |
300 | * Difference of the two operands. Their can be no overflow. A | |
301 | * borrow can occur out of the hidden bit and force a post | |
302 | * normalization phase. | |
303 | */ | |
304 | Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, | |
305 | /*with*/extent,/*into*/resultp1,resultp2); | |
306 | if(Dbl_iszero_hidden(resultp1)) | |
307 | { | |
308 | /* Handle normalization */ | |
25985edc | 309 | /* A straight forward algorithm would now shift the result |
1da177e4 LT |
310 | * and extension left until the hidden bit becomes one. Not |
311 | * all of the extension bits need participate in the shift. | |
312 | * Only the two most significant bits (round and guard) are | |
313 | * needed. If only a single shift is needed then the guard | |
314 | * bit becomes a significant low order bit and the extension | |
315 | * must participate in the rounding. If more than a single | |
316 | * shift is needed, then all bits to the right of the guard | |
317 | * bit are zeros, and the guard bit may or may not be zero. */ | |
318 | sign_save = Dbl_signextendedsign(resultp1); | |
319 | Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); | |
320 | ||
321 | /* Need to check for a zero result. The sign and exponent | |
322 | * fields have already been zeroed. The more efficient test | |
323 | * of the full object can be used. | |
324 | */ | |
325 | if(Dbl_iszero(resultp1,resultp2)) | |
326 | /* Must have been "x-x" or "x+(-x)". */ | |
327 | { | |
328 | if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); | |
329 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
330 | return(NOEXCEPTION); | |
331 | } | |
332 | result_exponent--; | |
333 | /* Look to see if normalization is finished. */ | |
334 | if(Dbl_isone_hidden(resultp1)) | |
335 | { | |
336 | if(result_exponent==0) | |
337 | { | |
338 | /* Denormalized, exponent should be zero. Left operand * | |
339 | * was normalized, so extent (guard, round) was zero */ | |
340 | goto underflow; | |
341 | } | |
342 | else | |
343 | { | |
344 | /* No further normalization is needed. */ | |
345 | Dbl_set_sign(resultp1,/*using*/sign_save); | |
346 | Ext_leftshiftby1(extent); | |
347 | goto round; | |
348 | } | |
349 | } | |
350 | ||
351 | /* Check for denormalized, exponent should be zero. Left * | |
352 | * operand was normalized, so extent (guard, round) was zero */ | |
353 | if(!(underflowtrap = Is_underflowtrap_enabled()) && | |
354 | result_exponent==0) goto underflow; | |
355 | ||
356 | /* Shift extension to complete one bit of normalization and | |
357 | * update exponent. */ | |
358 | Ext_leftshiftby1(extent); | |
359 | ||
360 | /* Discover first one bit to determine shift amount. Use a | |
361 | * modified binary search. We have already shifted the result | |
362 | * one position right and still not found a one so the remainder | |
363 | * of the extension must be zero and simplifies rounding. */ | |
364 | /* Scan bytes */ | |
365 | while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) | |
366 | { | |
367 | Dbl_leftshiftby8(resultp1,resultp2); | |
368 | if((result_exponent -= 8) <= 0 && !underflowtrap) | |
369 | goto underflow; | |
370 | } | |
371 | /* Now narrow it down to the nibble */ | |
372 | if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) | |
373 | { | |
374 | /* The lower nibble contains the normalizing one */ | |
375 | Dbl_leftshiftby4(resultp1,resultp2); | |
376 | if((result_exponent -= 4) <= 0 && !underflowtrap) | |
377 | goto underflow; | |
378 | } | |
379 | /* Select case were first bit is set (already normalized) | |
380 | * otherwise select the proper shift. */ | |
381 | if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) | |
382 | { | |
383 | /* Already normalized */ | |
384 | if(result_exponent <= 0) goto underflow; | |
385 | Dbl_set_sign(resultp1,/*using*/sign_save); | |
386 | Dbl_set_exponent(resultp1,/*using*/result_exponent); | |
387 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
388 | return(NOEXCEPTION); | |
389 | } | |
390 | Dbl_sethigh4bits(resultp1,/*using*/sign_save); | |
391 | switch(jumpsize) | |
392 | { | |
393 | case 1: | |
394 | { | |
395 | Dbl_leftshiftby3(resultp1,resultp2); | |
396 | result_exponent -= 3; | |
397 | break; | |
398 | } | |
399 | case 2: | |
400 | case 3: | |
401 | { | |
402 | Dbl_leftshiftby2(resultp1,resultp2); | |
403 | result_exponent -= 2; | |
404 | break; | |
405 | } | |
406 | case 4: | |
407 | case 5: | |
408 | case 6: | |
409 | case 7: | |
410 | { | |
411 | Dbl_leftshiftby1(resultp1,resultp2); | |
412 | result_exponent -= 1; | |
413 | break; | |
414 | } | |
415 | } | |
416 | if(result_exponent > 0) | |
417 | { | |
418 | Dbl_set_exponent(resultp1,/*using*/result_exponent); | |
419 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
420 | return(NOEXCEPTION); /* Sign bit is already set */ | |
421 | } | |
422 | /* Fixup potential underflows */ | |
423 | underflow: | |
424 | if(Is_underflowtrap_enabled()) | |
425 | { | |
426 | Dbl_set_sign(resultp1,sign_save); | |
427 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); | |
428 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
429 | /* inexact = FALSE */ | |
430 | return(UNDERFLOWEXCEPTION); | |
431 | } | |
432 | /* | |
433 | * Since we cannot get an inexact denormalized result, | |
434 | * we can now return. | |
435 | */ | |
436 | Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); | |
437 | Dbl_clear_signexponent(resultp1); | |
438 | Dbl_set_sign(resultp1,sign_save); | |
439 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
440 | return(NOEXCEPTION); | |
441 | } /* end if(hidden...)... */ | |
442 | /* Fall through and round */ | |
443 | } /* end if(save >= 0)... */ | |
444 | else | |
445 | { | |
446 | /* Subtract magnitudes */ | |
447 | Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); | |
448 | if(Dbl_isone_hiddenoverflow(resultp1)) | |
449 | { | |
450 | /* Prenormalization required. */ | |
451 | Dbl_rightshiftby1_withextent(resultp2,extent,extent); | |
452 | Dbl_arithrightshiftby1(resultp1,resultp2); | |
453 | result_exponent++; | |
454 | } /* end if hiddenoverflow... */ | |
455 | } /* end else ...subtract magnitudes... */ | |
456 | ||
457 | /* Round the result. If the extension is all zeros,then the result is | |
458 | * exact. Otherwise round in the correct direction. No underflow is | |
459 | * possible. If a postnormalization is necessary, then the mantissa is | |
460 | * all zeros so no shift is needed. */ | |
461 | round: | |
462 | if(Ext_isnotzero(extent)) | |
463 | { | |
464 | inexact = TRUE; | |
465 | switch(Rounding_mode()) | |
466 | { | |
467 | case ROUNDNEAREST: /* The default. */ | |
468 | if(Ext_isone_sign(extent)) | |
469 | { | |
470 | /* at least 1/2 ulp */ | |
471 | if(Ext_isnotzero_lower(extent) || | |
472 | Dbl_isone_lowmantissap2(resultp2)) | |
473 | { | |
474 | /* either exactly half way and odd or more than 1/2ulp */ | |
475 | Dbl_increment(resultp1,resultp2); | |
476 | } | |
477 | } | |
478 | break; | |
479 | ||
480 | case ROUNDPLUS: | |
481 | if(Dbl_iszero_sign(resultp1)) | |
482 | { | |
483 | /* Round up positive results */ | |
484 | Dbl_increment(resultp1,resultp2); | |
485 | } | |
486 | break; | |
487 | ||
488 | case ROUNDMINUS: | |
489 | if(Dbl_isone_sign(resultp1)) | |
490 | { | |
491 | /* Round down negative results */ | |
492 | Dbl_increment(resultp1,resultp2); | |
493 | } | |
494 | ||
495 | case ROUNDZERO:; | |
496 | /* truncate is simple */ | |
497 | } /* end switch... */ | |
498 | if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; | |
499 | } | |
500 | if(result_exponent == DBL_INFINITY_EXPONENT) | |
501 | { | |
502 | /* Overflow */ | |
503 | if(Is_overflowtrap_enabled()) | |
504 | { | |
505 | Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); | |
506 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
507 | if (inexact) | |
508 | if (Is_inexacttrap_enabled()) | |
509 | return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); | |
510 | else Set_inexactflag(); | |
511 | return(OVERFLOWEXCEPTION); | |
512 | } | |
513 | else | |
514 | { | |
515 | inexact = TRUE; | |
516 | Set_overflowflag(); | |
517 | Dbl_setoverflow(resultp1,resultp2); | |
518 | } | |
519 | } | |
520 | else Dbl_set_exponent(resultp1,result_exponent); | |
521 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
522 | if(inexact) | |
523 | if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION); | |
524 | else Set_inexactflag(); | |
525 | return(NOEXCEPTION); | |
526 | } |