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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/dfadd.c $Revision: 1.1 $ | |
26 | * | |
27 | * Purpose: | |
28 | * Double_add: add two double precision values. | |
29 | * | |
30 | * External Interfaces: | |
31 | * dbl_fadd(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_add: add two double precision values. | |
47 | */ | |
48 | dbl_fadd( | |
49 | dbl_floating_point *leftptr, | |
50 | dbl_floating_point *rightptr, | |
51 | dbl_floating_point *dstptr, | |
52 | unsigned int *status) | |
53 | { | |
54 | register unsigned int signless_upper_left, signless_upper_right, save; | |
55 | register unsigned int leftp1, leftp2, rightp1, rightp2, extent; | |
56 | register unsigned int resultp1 = 0, resultp2 = 0; | |
57 | ||
58 | register int result_exponent, right_exponent, diff_exponent; | |
59 | register int sign_save, jumpsize; | |
60 | register boolean inexact = FALSE; | |
61 | register boolean 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 opposite 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_copytoptr(rightp1,rightp2,dstptr); | |
140 | return(NOEXCEPTION); | |
141 | } | |
142 | /* | |
143 | * is NaN; signaling or quiet? | |
144 | */ | |
145 | if (Dbl_isone_signaling(rightp1)) | |
146 | { | |
147 | /* trap if INVALIDTRAP enabled */ | |
148 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); | |
149 | /* make NaN quiet */ | |
150 | Set_invalidflag(); | |
151 | Dbl_set_quiet(rightp1); | |
152 | } | |
153 | /* | |
154 | * return quiet NaN | |
155 | */ | |
156 | Dbl_copytoptr(rightp1,rightp2,dstptr); | |
157 | return(NOEXCEPTION); | |
158 | } /* End right NaN or Infinity processing */ | |
159 | ||
160 | /* Invariant: Must be dealing with finite numbers */ | |
161 | ||
162 | /* Compare operands by removing the sign */ | |
163 | Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); | |
164 | Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); | |
165 | ||
166 | /* sign difference selects add or sub operation. */ | |
167 | if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) | |
168 | { | |
169 | /* Set the left operand to the larger one by XOR swap * | |
170 | * First finish the first word using "save" */ | |
171 | Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); | |
172 | Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); | |
173 | Dbl_swap_lower(leftp2,rightp2); | |
174 | result_exponent = Dbl_exponent(leftp1); | |
175 | } | |
176 | /* Invariant: left is not smaller than right. */ | |
177 | ||
178 | if((right_exponent = Dbl_exponent(rightp1)) == 0) | |
179 | { | |
180 | /* Denormalized operands. First look for zeroes */ | |
181 | if(Dbl_iszero_mantissa(rightp1,rightp2)) | |
182 | { | |
183 | /* right is zero */ | |
184 | if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) | |
185 | { | |
186 | /* Both operands are zeros */ | |
187 | if(Is_rounding_mode(ROUNDMINUS)) | |
188 | { | |
189 | Dbl_or_signs(leftp1,/*with*/rightp1); | |
190 | } | |
191 | else | |
192 | { | |
193 | Dbl_and_signs(leftp1,/*with*/rightp1); | |
194 | } | |
195 | } | |
196 | else | |
197 | { | |
198 | /* Left is not a zero and must be the result. Trapped | |
199 | * underflows are signaled if left is denormalized. Result | |
200 | * is always exact. */ | |
201 | if( (result_exponent == 0) && Is_underflowtrap_enabled() ) | |
202 | { | |
203 | /* need to normalize results mantissa */ | |
204 | sign_save = Dbl_signextendedsign(leftp1); | |
205 | Dbl_leftshiftby1(leftp1,leftp2); | |
206 | Dbl_normalize(leftp1,leftp2,result_exponent); | |
207 | Dbl_set_sign(leftp1,/*using*/sign_save); | |
208 | Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); | |
209 | Dbl_copytoptr(leftp1,leftp2,dstptr); | |
210 | /* inexact = FALSE */ | |
211 | return(UNDERFLOWEXCEPTION); | |
212 | } | |
213 | } | |
214 | Dbl_copytoptr(leftp1,leftp2,dstptr); | |
215 | return(NOEXCEPTION); | |
216 | } | |
217 | ||
218 | /* Neither are zeroes */ | |
219 | Dbl_clear_sign(rightp1); /* Exponent is already cleared */ | |
220 | if(result_exponent == 0 ) | |
221 | { | |
222 | /* Both operands are denormalized. The result must be exact | |
223 | * and is simply calculated. A sum could become normalized and a | |
224 | * difference could cancel to a true zero. */ | |
225 | if( (/*signed*/int) save < 0 ) | |
226 | { | |
227 | Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, | |
228 | /*into*/resultp1,resultp2); | |
229 | if(Dbl_iszero_mantissa(resultp1,resultp2)) | |
230 | { | |
231 | if(Is_rounding_mode(ROUNDMINUS)) | |
232 | { | |
233 | Dbl_setone_sign(resultp1); | |
234 | } | |
235 | else | |
236 | { | |
237 | Dbl_setzero_sign(resultp1); | |
238 | } | |
239 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
240 | return(NOEXCEPTION); | |
241 | } | |
242 | } | |
243 | else | |
244 | { | |
245 | Dbl_addition(leftp1,leftp2,rightp1,rightp2, | |
246 | /*into*/resultp1,resultp2); | |
247 | if(Dbl_isone_hidden(resultp1)) | |
248 | { | |
249 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
250 | return(NOEXCEPTION); | |
251 | } | |
252 | } | |
253 | if(Is_underflowtrap_enabled()) | |
254 | { | |
255 | /* need to normalize result */ | |
256 | sign_save = Dbl_signextendedsign(resultp1); | |
257 | Dbl_leftshiftby1(resultp1,resultp2); | |
258 | Dbl_normalize(resultp1,resultp2,result_exponent); | |
259 | Dbl_set_sign(resultp1,/*using*/sign_save); | |
260 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); | |
261 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
262 | /* inexact = FALSE */ | |
263 | return(UNDERFLOWEXCEPTION); | |
264 | } | |
265 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
266 | return(NOEXCEPTION); | |
267 | } | |
268 | right_exponent = 1; /* Set exponent to reflect different bias | |
269 | * with denomalized numbers. */ | |
270 | } | |
271 | else | |
272 | { | |
273 | Dbl_clear_signexponent_set_hidden(rightp1); | |
274 | } | |
275 | Dbl_clear_exponent_set_hidden(leftp1); | |
276 | diff_exponent = result_exponent - right_exponent; | |
277 | ||
278 | /* | |
279 | * Special case alignment of operands that would force alignment | |
280 | * beyond the extent of the extension. A further optimization | |
281 | * could special case this but only reduces the path length for this | |
282 | * infrequent case. | |
283 | */ | |
284 | if(diff_exponent > DBL_THRESHOLD) | |
285 | { | |
286 | diff_exponent = DBL_THRESHOLD; | |
287 | } | |
288 | ||
289 | /* Align right operand by shifting to right */ | |
290 | Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, | |
291 | /*and lower to*/extent); | |
292 | ||
293 | /* Treat sum and difference of the operands separately. */ | |
294 | if( (/*signed*/int) save < 0 ) | |
295 | { | |
296 | /* | |
297 | * Difference of the two operands. Their can be no overflow. A | |
298 | * borrow can occur out of the hidden bit and force a post | |
299 | * normalization phase. | |
300 | */ | |
301 | Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, | |
302 | /*with*/extent,/*into*/resultp1,resultp2); | |
303 | if(Dbl_iszero_hidden(resultp1)) | |
304 | { | |
305 | /* Handle normalization */ | |
25985edc | 306 | /* A straight forward algorithm would now shift the result |
1da177e4 LT |
307 | * and extension left until the hidden bit becomes one. Not |
308 | * all of the extension bits need participate in the shift. | |
309 | * Only the two most significant bits (round and guard) are | |
310 | * needed. If only a single shift is needed then the guard | |
311 | * bit becomes a significant low order bit and the extension | |
312 | * must participate in the rounding. If more than a single | |
313 | * shift is needed, then all bits to the right of the guard | |
314 | * bit are zeros, and the guard bit may or may not be zero. */ | |
315 | sign_save = Dbl_signextendedsign(resultp1); | |
316 | Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); | |
317 | ||
318 | /* Need to check for a zero result. The sign and exponent | |
319 | * fields have already been zeroed. The more efficient test | |
320 | * of the full object can be used. | |
321 | */ | |
322 | if(Dbl_iszero(resultp1,resultp2)) | |
323 | /* Must have been "x-x" or "x+(-x)". */ | |
324 | { | |
325 | if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); | |
326 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
327 | return(NOEXCEPTION); | |
328 | } | |
329 | result_exponent--; | |
330 | /* Look to see if normalization is finished. */ | |
331 | if(Dbl_isone_hidden(resultp1)) | |
332 | { | |
333 | if(result_exponent==0) | |
334 | { | |
335 | /* Denormalized, exponent should be zero. Left operand * | |
336 | * was normalized, so extent (guard, round) was zero */ | |
337 | goto underflow; | |
338 | } | |
339 | else | |
340 | { | |
341 | /* No further normalization is needed. */ | |
342 | Dbl_set_sign(resultp1,/*using*/sign_save); | |
343 | Ext_leftshiftby1(extent); | |
344 | goto round; | |
345 | } | |
346 | } | |
347 | ||
348 | /* Check for denormalized, exponent should be zero. Left * | |
349 | * operand was normalized, so extent (guard, round) was zero */ | |
350 | if(!(underflowtrap = Is_underflowtrap_enabled()) && | |
351 | result_exponent==0) goto underflow; | |
352 | ||
353 | /* Shift extension to complete one bit of normalization and | |
354 | * update exponent. */ | |
355 | Ext_leftshiftby1(extent); | |
356 | ||
357 | /* Discover first one bit to determine shift amount. Use a | |
358 | * modified binary search. We have already shifted the result | |
359 | * one position right and still not found a one so the remainder | |
360 | * of the extension must be zero and simplifies rounding. */ | |
361 | /* Scan bytes */ | |
362 | while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) | |
363 | { | |
364 | Dbl_leftshiftby8(resultp1,resultp2); | |
365 | if((result_exponent -= 8) <= 0 && !underflowtrap) | |
366 | goto underflow; | |
367 | } | |
368 | /* Now narrow it down to the nibble */ | |
369 | if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) | |
370 | { | |
371 | /* The lower nibble contains the normalizing one */ | |
372 | Dbl_leftshiftby4(resultp1,resultp2); | |
373 | if((result_exponent -= 4) <= 0 && !underflowtrap) | |
374 | goto underflow; | |
375 | } | |
376 | /* Select case were first bit is set (already normalized) | |
377 | * otherwise select the proper shift. */ | |
378 | if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) | |
379 | { | |
380 | /* Already normalized */ | |
381 | if(result_exponent <= 0) goto underflow; | |
382 | Dbl_set_sign(resultp1,/*using*/sign_save); | |
383 | Dbl_set_exponent(resultp1,/*using*/result_exponent); | |
384 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
385 | return(NOEXCEPTION); | |
386 | } | |
387 | Dbl_sethigh4bits(resultp1,/*using*/sign_save); | |
388 | switch(jumpsize) | |
389 | { | |
390 | case 1: | |
391 | { | |
392 | Dbl_leftshiftby3(resultp1,resultp2); | |
393 | result_exponent -= 3; | |
394 | break; | |
395 | } | |
396 | case 2: | |
397 | case 3: | |
398 | { | |
399 | Dbl_leftshiftby2(resultp1,resultp2); | |
400 | result_exponent -= 2; | |
401 | break; | |
402 | } | |
403 | case 4: | |
404 | case 5: | |
405 | case 6: | |
406 | case 7: | |
407 | { | |
408 | Dbl_leftshiftby1(resultp1,resultp2); | |
409 | result_exponent -= 1; | |
410 | break; | |
411 | } | |
412 | } | |
413 | if(result_exponent > 0) | |
414 | { | |
415 | Dbl_set_exponent(resultp1,/*using*/result_exponent); | |
416 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
417 | return(NOEXCEPTION); /* Sign bit is already set */ | |
418 | } | |
419 | /* Fixup potential underflows */ | |
420 | underflow: | |
421 | if(Is_underflowtrap_enabled()) | |
422 | { | |
423 | Dbl_set_sign(resultp1,sign_save); | |
424 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); | |
425 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
426 | /* inexact = FALSE */ | |
427 | return(UNDERFLOWEXCEPTION); | |
428 | } | |
429 | /* | |
430 | * Since we cannot get an inexact denormalized result, | |
431 | * we can now return. | |
432 | */ | |
433 | Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); | |
434 | Dbl_clear_signexponent(resultp1); | |
435 | Dbl_set_sign(resultp1,sign_save); | |
436 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
437 | return(NOEXCEPTION); | |
438 | } /* end if(hidden...)... */ | |
439 | /* Fall through and round */ | |
440 | } /* end if(save < 0)... */ | |
441 | else | |
442 | { | |
443 | /* Add magnitudes */ | |
444 | Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); | |
445 | if(Dbl_isone_hiddenoverflow(resultp1)) | |
446 | { | |
447 | /* Prenormalization required. */ | |
448 | Dbl_rightshiftby1_withextent(resultp2,extent,extent); | |
449 | Dbl_arithrightshiftby1(resultp1,resultp2); | |
450 | result_exponent++; | |
451 | } /* end if hiddenoverflow... */ | |
452 | } /* end else ...add magnitudes... */ | |
453 | ||
454 | /* Round the result. If the extension is all zeros,then the result is | |
455 | * exact. Otherwise round in the correct direction. No underflow is | |
456 | * possible. If a postnormalization is necessary, then the mantissa is | |
457 | * all zeros so no shift is needed. */ | |
458 | round: | |
459 | if(Ext_isnotzero(extent)) | |
460 | { | |
461 | inexact = TRUE; | |
462 | switch(Rounding_mode()) | |
463 | { | |
464 | case ROUNDNEAREST: /* The default. */ | |
465 | if(Ext_isone_sign(extent)) | |
466 | { | |
467 | /* at least 1/2 ulp */ | |
468 | if(Ext_isnotzero_lower(extent) || | |
469 | Dbl_isone_lowmantissap2(resultp2)) | |
470 | { | |
471 | /* either exactly half way and odd or more than 1/2ulp */ | |
472 | Dbl_increment(resultp1,resultp2); | |
473 | } | |
474 | } | |
475 | break; | |
476 | ||
477 | case ROUNDPLUS: | |
478 | if(Dbl_iszero_sign(resultp1)) | |
479 | { | |
480 | /* Round up positive results */ | |
481 | Dbl_increment(resultp1,resultp2); | |
482 | } | |
483 | break; | |
484 | ||
485 | case ROUNDMINUS: | |
486 | if(Dbl_isone_sign(resultp1)) | |
487 | { | |
488 | /* Round down negative results */ | |
489 | Dbl_increment(resultp1,resultp2); | |
490 | } | |
491 | ||
492 | case ROUNDZERO:; | |
493 | /* truncate is simple */ | |
494 | } /* end switch... */ | |
495 | if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; | |
496 | } | |
497 | if(result_exponent == DBL_INFINITY_EXPONENT) | |
498 | { | |
499 | /* Overflow */ | |
500 | if(Is_overflowtrap_enabled()) | |
501 | { | |
502 | Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); | |
503 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
504 | if (inexact) | |
505 | if (Is_inexacttrap_enabled()) | |
506 | return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); | |
507 | else Set_inexactflag(); | |
508 | return(OVERFLOWEXCEPTION); | |
509 | } | |
510 | else | |
511 | { | |
512 | inexact = TRUE; | |
513 | Set_overflowflag(); | |
514 | Dbl_setoverflow(resultp1,resultp2); | |
515 | } | |
516 | } | |
517 | else Dbl_set_exponent(resultp1,result_exponent); | |
518 | Dbl_copytoptr(resultp1,resultp2,dstptr); | |
519 | if(inexact) | |
520 | if(Is_inexacttrap_enabled()) | |
521 | return(INEXACTEXCEPTION); | |
522 | else Set_inexactflag(); | |
523 | return(NOEXCEPTION); | |
524 | } |