1 | // SPDX-License-Identifier: GPL-2.0-or-later |
2 | /* |
3 | * Linux/PA-RISC Project (http://www.parisc-linux.org/) |
4 | * |
5 | * Floating-point emulation code |
6 | * Copyright (C) 2001 Hewlett-Packard (Paul Bame) <bame@debian.org> |
7 | */ |
8 | /* |
9 | * BEGIN_DESC |
10 | * |
11 | * File: |
12 | * @(#) pa/spmath/dfsub.c $Revision: 1.1 $ |
13 | * |
14 | * Purpose: |
15 | * Double_subtract: subtract two double precision values. |
16 | * |
17 | * External Interfaces: |
18 | * dbl_fsub(leftptr, rightptr, dstptr, status) |
19 | * |
20 | * Internal Interfaces: |
21 | * |
22 | * Theory: |
23 | * <<please update with a overview of the operation of this file>> |
24 | * |
25 | * END_DESC |
26 | */ |
27 | |
28 | |
29 | #include "float.h" |
30 | #include "dbl_float.h" |
31 | |
32 | /* |
33 | * Double_subtract: subtract two double precision values. |
34 | */ |
35 | int |
36 | dbl_fsub( |
37 | dbl_floating_point *leftptr, |
38 | dbl_floating_point *rightptr, |
39 | dbl_floating_point *dstptr, |
40 | unsigned int *status) |
41 | { |
42 | register unsigned int signless_upper_left, signless_upper_right, save; |
43 | register unsigned int leftp1, leftp2, rightp1, rightp2, extent; |
44 | register unsigned int resultp1 = 0, resultp2 = 0; |
45 | |
46 | register int result_exponent, right_exponent, diff_exponent; |
47 | register int sign_save, jumpsize; |
48 | register boolean inexact = FALSE, underflowtrap; |
49 | |
50 | /* Create local copies of the numbers */ |
51 | Dbl_copyfromptr(leftptr,leftp1,leftp2); |
52 | Dbl_copyfromptr(rightptr,rightp1,rightp2); |
53 | |
54 | /* A zero "save" helps discover equal operands (for later), * |
55 | * and is used in swapping operands (if needed). */ |
56 | Dbl_xortointp1(leftp1,rightp1,/*to*/save); |
57 | |
58 | /* |
59 | * check first operand for NaN's or infinity |
60 | */ |
61 | if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT) |
62 | { |
63 | if (Dbl_iszero_mantissa(leftp1,leftp2)) |
64 | { |
65 | if (Dbl_isnotnan(rightp1,rightp2)) |
66 | { |
67 | if (Dbl_isinfinity(rightp1,rightp2) && save==0) |
68 | { |
69 | /* |
70 | * invalid since operands are same signed infinity's |
71 | */ |
72 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
73 | Set_invalidflag(); |
74 | Dbl_makequietnan(resultp1,resultp2); |
75 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
76 | return(NOEXCEPTION); |
77 | } |
78 | /* |
79 | * return infinity |
80 | */ |
81 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
82 | return(NOEXCEPTION); |
83 | } |
84 | } |
85 | else |
86 | { |
87 | /* |
88 | * is NaN; signaling or quiet? |
89 | */ |
90 | if (Dbl_isone_signaling(leftp1)) |
91 | { |
92 | /* trap if INVALIDTRAP enabled */ |
93 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
94 | /* make NaN quiet */ |
95 | Set_invalidflag(); |
96 | Dbl_set_quiet(leftp1); |
97 | } |
98 | /* |
99 | * is second operand a signaling NaN? |
100 | */ |
101 | else if (Dbl_is_signalingnan(rightp1)) |
102 | { |
103 | /* trap if INVALIDTRAP enabled */ |
104 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
105 | /* make NaN quiet */ |
106 | Set_invalidflag(); |
107 | Dbl_set_quiet(rightp1); |
108 | Dbl_copytoptr(rightp1,rightp2,dstptr); |
109 | return(NOEXCEPTION); |
110 | } |
111 | /* |
112 | * return quiet NaN |
113 | */ |
114 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
115 | return(NOEXCEPTION); |
116 | } |
117 | } /* End left NaN or Infinity processing */ |
118 | /* |
119 | * check second operand for NaN's or infinity |
120 | */ |
121 | if (Dbl_isinfinity_exponent(rightp1)) |
122 | { |
123 | if (Dbl_iszero_mantissa(rightp1,rightp2)) |
124 | { |
125 | /* return infinity */ |
126 | Dbl_invert_sign(rightp1); |
127 | Dbl_copytoptr(rightp1,rightp2,dstptr); |
128 | return(NOEXCEPTION); |
129 | } |
130 | /* |
131 | * is NaN; signaling or quiet? |
132 | */ |
133 | if (Dbl_isone_signaling(rightp1)) |
134 | { |
135 | /* trap if INVALIDTRAP enabled */ |
136 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
137 | /* make NaN quiet */ |
138 | Set_invalidflag(); |
139 | Dbl_set_quiet(rightp1); |
140 | } |
141 | /* |
142 | * return quiet NaN |
143 | */ |
144 | Dbl_copytoptr(rightp1,rightp2,dstptr); |
145 | return(NOEXCEPTION); |
146 | } /* End right NaN or Infinity processing */ |
147 | |
148 | /* Invariant: Must be dealing with finite numbers */ |
149 | |
150 | /* Compare operands by removing the sign */ |
151 | Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); |
152 | Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); |
153 | |
154 | /* sign difference selects add or sub operation. */ |
155 | if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) |
156 | { |
157 | /* Set the left operand to the larger one by XOR swap * |
158 | * First finish the first word using "save" */ |
159 | Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); |
160 | Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); |
161 | Dbl_swap_lower(leftp2,rightp2); |
162 | result_exponent = Dbl_exponent(leftp1); |
163 | Dbl_invert_sign(leftp1); |
164 | } |
165 | /* Invariant: left is not smaller than right. */ |
166 | |
167 | if((right_exponent = Dbl_exponent(rightp1)) == 0) |
168 | { |
169 | /* Denormalized operands. First look for zeroes */ |
170 | if(Dbl_iszero_mantissa(rightp1,rightp2)) |
171 | { |
172 | /* right is zero */ |
173 | if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) |
174 | { |
175 | /* Both operands are zeros */ |
176 | Dbl_invert_sign(rightp1); |
177 | if(Is_rounding_mode(ROUNDMINUS)) |
178 | { |
179 | Dbl_or_signs(leftp1,/*with*/rightp1); |
180 | } |
181 | else |
182 | { |
183 | Dbl_and_signs(leftp1,/*with*/rightp1); |
184 | } |
185 | } |
186 | else |
187 | { |
188 | /* Left is not a zero and must be the result. Trapped |
189 | * underflows are signaled if left is denormalized. Result |
190 | * is always exact. */ |
191 | if( (result_exponent == 0) && Is_underflowtrap_enabled() ) |
192 | { |
193 | /* need to normalize results mantissa */ |
194 | sign_save = Dbl_signextendedsign(leftp1); |
195 | Dbl_leftshiftby1(leftp1,leftp2); |
196 | Dbl_normalize(leftp1,leftp2,result_exponent); |
197 | Dbl_set_sign(leftp1,/*using*/sign_save); |
198 | Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); |
199 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
200 | /* inexact = FALSE */ |
201 | return(UNDERFLOWEXCEPTION); |
202 | } |
203 | } |
204 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
205 | return(NOEXCEPTION); |
206 | } |
207 | |
208 | /* Neither are zeroes */ |
209 | Dbl_clear_sign(rightp1); /* Exponent is already cleared */ |
210 | if(result_exponent == 0 ) |
211 | { |
212 | /* Both operands are denormalized. The result must be exact |
213 | * and is simply calculated. A sum could become normalized and a |
214 | * difference could cancel to a true zero. */ |
215 | if( (/*signed*/int) save >= 0 ) |
216 | { |
217 | Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, |
218 | /*into*/resultp1,resultp2); |
219 | if(Dbl_iszero_mantissa(resultp1,resultp2)) |
220 | { |
221 | if(Is_rounding_mode(ROUNDMINUS)) |
222 | { |
223 | Dbl_setone_sign(resultp1); |
224 | } |
225 | else |
226 | { |
227 | Dbl_setzero_sign(resultp1); |
228 | } |
229 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
230 | return(NOEXCEPTION); |
231 | } |
232 | } |
233 | else |
234 | { |
235 | Dbl_addition(leftp1,leftp2,rightp1,rightp2, |
236 | /*into*/resultp1,resultp2); |
237 | if(Dbl_isone_hidden(resultp1)) |
238 | { |
239 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
240 | return(NOEXCEPTION); |
241 | } |
242 | } |
243 | if(Is_underflowtrap_enabled()) |
244 | { |
245 | /* need to normalize result */ |
246 | sign_save = Dbl_signextendedsign(resultp1); |
247 | Dbl_leftshiftby1(resultp1,resultp2); |
248 | Dbl_normalize(resultp1,resultp2,result_exponent); |
249 | Dbl_set_sign(resultp1,/*using*/sign_save); |
250 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); |
251 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
252 | /* inexact = FALSE */ |
253 | return(UNDERFLOWEXCEPTION); |
254 | } |
255 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
256 | return(NOEXCEPTION); |
257 | } |
258 | right_exponent = 1; /* Set exponent to reflect different bias |
259 | * with denormalized numbers. */ |
260 | } |
261 | else |
262 | { |
263 | Dbl_clear_signexponent_set_hidden(rightp1); |
264 | } |
265 | Dbl_clear_exponent_set_hidden(leftp1); |
266 | diff_exponent = result_exponent - right_exponent; |
267 | |
268 | /* |
269 | * Special case alignment of operands that would force alignment |
270 | * beyond the extent of the extension. A further optimization |
271 | * could special case this but only reduces the path length for this |
272 | * infrequent case. |
273 | */ |
274 | if(diff_exponent > DBL_THRESHOLD) |
275 | { |
276 | diff_exponent = DBL_THRESHOLD; |
277 | } |
278 | |
279 | /* Align right operand by shifting to right */ |
280 | Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, |
281 | /*and lower to*/extent); |
282 | |
283 | /* Treat sum and difference of the operands separately. */ |
284 | if( (/*signed*/int) save >= 0 ) |
285 | { |
286 | /* |
287 | * Difference of the two operands. Their can be no overflow. A |
288 | * borrow can occur out of the hidden bit and force a post |
289 | * normalization phase. |
290 | */ |
291 | Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, |
292 | /*with*/extent,/*into*/resultp1,resultp2); |
293 | if(Dbl_iszero_hidden(resultp1)) |
294 | { |
295 | /* Handle normalization */ |
296 | /* A straight forward algorithm would now shift the result |
297 | * and extension left until the hidden bit becomes one. Not |
298 | * all of the extension bits need participate in the shift. |
299 | * Only the two most significant bits (round and guard) are |
300 | * needed. If only a single shift is needed then the guard |
301 | * bit becomes a significant low order bit and the extension |
302 | * must participate in the rounding. If more than a single |
303 | * shift is needed, then all bits to the right of the guard |
304 | * bit are zeros, and the guard bit may or may not be zero. */ |
305 | sign_save = Dbl_signextendedsign(resultp1); |
306 | Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); |
307 | |
308 | /* Need to check for a zero result. The sign and exponent |
309 | * fields have already been zeroed. The more efficient test |
310 | * of the full object can be used. |
311 | */ |
312 | if(Dbl_iszero(resultp1,resultp2)) |
313 | /* Must have been "x-x" or "x+(-x)". */ |
314 | { |
315 | if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); |
316 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
317 | return(NOEXCEPTION); |
318 | } |
319 | result_exponent--; |
320 | /* Look to see if normalization is finished. */ |
321 | if(Dbl_isone_hidden(resultp1)) |
322 | { |
323 | if(result_exponent==0) |
324 | { |
325 | /* Denormalized, exponent should be zero. Left operand * |
326 | * was normalized, so extent (guard, round) was zero */ |
327 | goto underflow; |
328 | } |
329 | else |
330 | { |
331 | /* No further normalization is needed. */ |
332 | Dbl_set_sign(resultp1,/*using*/sign_save); |
333 | Ext_leftshiftby1(extent); |
334 | goto round; |
335 | } |
336 | } |
337 | |
338 | /* Check for denormalized, exponent should be zero. Left * |
339 | * operand was normalized, so extent (guard, round) was zero */ |
340 | if(!(underflowtrap = Is_underflowtrap_enabled()) && |
341 | result_exponent==0) goto underflow; |
342 | |
343 | /* Shift extension to complete one bit of normalization and |
344 | * update exponent. */ |
345 | Ext_leftshiftby1(extent); |
346 | |
347 | /* Discover first one bit to determine shift amount. Use a |
348 | * modified binary search. We have already shifted the result |
349 | * one position right and still not found a one so the remainder |
350 | * of the extension must be zero and simplifies rounding. */ |
351 | /* Scan bytes */ |
352 | while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) |
353 | { |
354 | Dbl_leftshiftby8(resultp1,resultp2); |
355 | if((result_exponent -= 8) <= 0 && !underflowtrap) |
356 | goto underflow; |
357 | } |
358 | /* Now narrow it down to the nibble */ |
359 | if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) |
360 | { |
361 | /* The lower nibble contains the normalizing one */ |
362 | Dbl_leftshiftby4(resultp1,resultp2); |
363 | if((result_exponent -= 4) <= 0 && !underflowtrap) |
364 | goto underflow; |
365 | } |
366 | /* Select case were first bit is set (already normalized) |
367 | * otherwise select the proper shift. */ |
368 | if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) |
369 | { |
370 | /* Already normalized */ |
371 | if(result_exponent <= 0) goto underflow; |
372 | Dbl_set_sign(resultp1,/*using*/sign_save); |
373 | Dbl_set_exponent(resultp1,/*using*/result_exponent); |
374 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
375 | return(NOEXCEPTION); |
376 | } |
377 | Dbl_sethigh4bits(resultp1,/*using*/sign_save); |
378 | switch(jumpsize) |
379 | { |
380 | case 1: |
381 | { |
382 | Dbl_leftshiftby3(resultp1,resultp2); |
383 | result_exponent -= 3; |
384 | break; |
385 | } |
386 | case 2: |
387 | case 3: |
388 | { |
389 | Dbl_leftshiftby2(resultp1,resultp2); |
390 | result_exponent -= 2; |
391 | break; |
392 | } |
393 | case 4: |
394 | case 5: |
395 | case 6: |
396 | case 7: |
397 | { |
398 | Dbl_leftshiftby1(resultp1,resultp2); |
399 | result_exponent -= 1; |
400 | break; |
401 | } |
402 | } |
403 | if(result_exponent > 0) |
404 | { |
405 | Dbl_set_exponent(resultp1,/*using*/result_exponent); |
406 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
407 | return(NOEXCEPTION); /* Sign bit is already set */ |
408 | } |
409 | /* Fixup potential underflows */ |
410 | underflow: |
411 | if(Is_underflowtrap_enabled()) |
412 | { |
413 | Dbl_set_sign(resultp1,sign_save); |
414 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); |
415 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
416 | /* inexact = FALSE */ |
417 | return(UNDERFLOWEXCEPTION); |
418 | } |
419 | /* |
420 | * Since we cannot get an inexact denormalized result, |
421 | * we can now return. |
422 | */ |
423 | Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); |
424 | Dbl_clear_signexponent(resultp1); |
425 | Dbl_set_sign(resultp1,sign_save); |
426 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
427 | return(NOEXCEPTION); |
428 | } /* end if(hidden...)... */ |
429 | /* Fall through and round */ |
430 | } /* end if(save >= 0)... */ |
431 | else |
432 | { |
433 | /* Subtract magnitudes */ |
434 | Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); |
435 | if(Dbl_isone_hiddenoverflow(resultp1)) |
436 | { |
437 | /* Prenormalization required. */ |
438 | Dbl_rightshiftby1_withextent(resultp2,extent,extent); |
439 | Dbl_arithrightshiftby1(resultp1,resultp2); |
440 | result_exponent++; |
441 | } /* end if hiddenoverflow... */ |
442 | } /* end else ...subtract magnitudes... */ |
443 | |
444 | /* Round the result. If the extension is all zeros,then the result is |
445 | * exact. Otherwise round in the correct direction. No underflow is |
446 | * possible. If a postnormalization is necessary, then the mantissa is |
447 | * all zeros so no shift is needed. */ |
448 | round: |
449 | if(Ext_isnotzero(extent)) |
450 | { |
451 | inexact = TRUE; |
452 | switch(Rounding_mode()) |
453 | { |
454 | case ROUNDNEAREST: /* The default. */ |
455 | if(Ext_isone_sign(extent)) |
456 | { |
457 | /* at least 1/2 ulp */ |
458 | if(Ext_isnotzero_lower(extent) || |
459 | Dbl_isone_lowmantissap2(resultp2)) |
460 | { |
461 | /* either exactly half way and odd or more than 1/2ulp */ |
462 | Dbl_increment(resultp1,resultp2); |
463 | } |
464 | } |
465 | break; |
466 | |
467 | case ROUNDPLUS: |
468 | if(Dbl_iszero_sign(resultp1)) |
469 | { |
470 | /* Round up positive results */ |
471 | Dbl_increment(resultp1,resultp2); |
472 | } |
473 | break; |
474 | |
475 | case ROUNDMINUS: |
476 | if(Dbl_isone_sign(resultp1)) |
477 | { |
478 | /* Round down negative results */ |
479 | Dbl_increment(resultp1,resultp2); |
480 | } |
481 | |
482 | case ROUNDZERO:; |
483 | /* truncate is simple */ |
484 | } /* end switch... */ |
485 | if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; |
486 | } |
487 | if(result_exponent == DBL_INFINITY_EXPONENT) |
488 | { |
489 | /* Overflow */ |
490 | if(Is_overflowtrap_enabled()) |
491 | { |
492 | Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); |
493 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
494 | if (inexact) |
495 | if (Is_inexacttrap_enabled()) |
496 | return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); |
497 | else Set_inexactflag(); |
498 | return(OVERFLOWEXCEPTION); |
499 | } |
500 | else |
501 | { |
502 | inexact = TRUE; |
503 | Set_overflowflag(); |
504 | Dbl_setoverflow(resultp1,resultp2); |
505 | } |
506 | } |
507 | else Dbl_set_exponent(resultp1,result_exponent); |
508 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
509 | if(inexact) |
510 | if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION); |
511 | else Set_inexactflag(); |
512 | return(NOEXCEPTION); |
513 | } |
514 | |