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/sfsub.c $Revision: 1.1 $
26 *
27 * Purpose:
28 * Single_subtract: subtract two single precision values.
29 *
30 * External Interfaces:
31 * sgl_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 "sgl_float.h"
44
45 /*
46 * Single_subtract: subtract two single precision values.
47 */
48 int
sgl_fsub(sgl_floating_point * leftptr,sgl_floating_point * rightptr,sgl_floating_point * dstptr,unsigned int * status)49 sgl_fsub(
50 sgl_floating_point *leftptr,
51 sgl_floating_point *rightptr,
52 sgl_floating_point *dstptr,
53 unsigned int *status)
54 {
55 register unsigned int left, right, result, extent;
56 register unsigned int signless_upper_left, signless_upper_right, save;
57
58 register int result_exponent, right_exponent, diff_exponent;
59 register int sign_save, jumpsize;
60 register boolean inexact = FALSE, underflowtrap;
61
62 /* Create local copies of the numbers */
63 left = *leftptr;
64 right = *rightptr;
65
66 /* A zero "save" helps discover equal operands (for later), *
67 * and is used in swapping operands (if needed). */
68 Sgl_xortointp1(left,right,/*to*/save);
69
70 /*
71 * check first operand for NaN's or infinity
72 */
73 if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
74 {
75 if (Sgl_iszero_mantissa(left))
76 {
77 if (Sgl_isnotnan(right))
78 {
79 if (Sgl_isinfinity(right) && save==0)
80 {
81 /*
82 * invalid since operands are same signed infinity's
83 */
84 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
85 Set_invalidflag();
86 Sgl_makequietnan(result);
87 *dstptr = result;
88 return(NOEXCEPTION);
89 }
90 /*
91 * return infinity
92 */
93 *dstptr = left;
94 return(NOEXCEPTION);
95 }
96 }
97 else
98 {
99 /*
100 * is NaN; signaling or quiet?
101 */
102 if (Sgl_isone_signaling(left))
103 {
104 /* trap if INVALIDTRAP enabled */
105 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
106 /* make NaN quiet */
107 Set_invalidflag();
108 Sgl_set_quiet(left);
109 }
110 /*
111 * is second operand a signaling NaN?
112 */
113 else if (Sgl_is_signalingnan(right))
114 {
115 /* trap if INVALIDTRAP enabled */
116 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
117 /* make NaN quiet */
118 Set_invalidflag();
119 Sgl_set_quiet(right);
120 *dstptr = right;
121 return(NOEXCEPTION);
122 }
123 /*
124 * return quiet NaN
125 */
126 *dstptr = left;
127 return(NOEXCEPTION);
128 }
129 } /* End left NaN or Infinity processing */
130 /*
131 * check second operand for NaN's or infinity
132 */
133 if (Sgl_isinfinity_exponent(right))
134 {
135 if (Sgl_iszero_mantissa(right))
136 {
137 /* return infinity */
138 Sgl_invert_sign(right);
139 *dstptr = right;
140 return(NOEXCEPTION);
141 }
142 /*
143 * is NaN; signaling or quiet?
144 */
145 if (Sgl_isone_signaling(right))
146 {
147 /* trap if INVALIDTRAP enabled */
148 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
149 /* make NaN quiet */
150 Set_invalidflag();
151 Sgl_set_quiet(right);
152 }
153 /*
154 * return quiet NaN
155 */
156 *dstptr = right;
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 Sgl_copytoint_exponentmantissa(left,signless_upper_left);
164 Sgl_copytoint_exponentmantissa(right,signless_upper_right);
165
166 /* sign difference selects sub or add operation. */
167 if(Sgl_ismagnitudeless(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 Sgl_xorfromintp1(save,right,/*to*/right);
172 Sgl_xorfromintp1(save,left,/*to*/left);
173 result_exponent = Sgl_exponent(left);
174 Sgl_invert_sign(left);
175 }
176 /* Invariant: left is not smaller than right. */
177
178 if((right_exponent = Sgl_exponent(right)) == 0)
179 {
180 /* Denormalized operands. First look for zeroes */
181 if(Sgl_iszero_mantissa(right))
182 {
183 /* right is zero */
184 if(Sgl_iszero_exponentmantissa(left))
185 {
186 /* Both operands are zeros */
187 Sgl_invert_sign(right);
188 if(Is_rounding_mode(ROUNDMINUS))
189 {
190 Sgl_or_signs(left,/*with*/right);
191 }
192 else
193 {
194 Sgl_and_signs(left,/*with*/right);
195 }
196 }
197 else
198 {
199 /* Left is not a zero and must be the result. Trapped
200 * underflows are signaled if left is denormalized. Result
201 * is always exact. */
202 if( (result_exponent == 0) && Is_underflowtrap_enabled() )
203 {
204 /* need to normalize results mantissa */
205 sign_save = Sgl_signextendedsign(left);
206 Sgl_leftshiftby1(left);
207 Sgl_normalize(left,result_exponent);
208 Sgl_set_sign(left,/*using*/sign_save);
209 Sgl_setwrapped_exponent(left,result_exponent,unfl);
210 *dstptr = left;
211 /* inexact = FALSE */
212 return(UNDERFLOWEXCEPTION);
213 }
214 }
215 *dstptr = left;
216 return(NOEXCEPTION);
217 }
218
219 /* Neither are zeroes */
220 Sgl_clear_sign(right); /* Exponent is already cleared */
221 if(result_exponent == 0 )
222 {
223 /* Both operands are denormalized. The result must be exact
224 * and is simply calculated. A sum could become normalized and a
225 * difference could cancel to a true zero. */
226 if( (/*signed*/int) save >= 0 )
227 {
228 Sgl_subtract(left,/*minus*/right,/*into*/result);
229 if(Sgl_iszero_mantissa(result))
230 {
231 if(Is_rounding_mode(ROUNDMINUS))
232 {
233 Sgl_setone_sign(result);
234 }
235 else
236 {
237 Sgl_setzero_sign(result);
238 }
239 *dstptr = result;
240 return(NOEXCEPTION);
241 }
242 }
243 else
244 {
245 Sgl_addition(left,right,/*into*/result);
246 if(Sgl_isone_hidden(result))
247 {
248 *dstptr = result;
249 return(NOEXCEPTION);
250 }
251 }
252 if(Is_underflowtrap_enabled())
253 {
254 /* need to normalize result */
255 sign_save = Sgl_signextendedsign(result);
256 Sgl_leftshiftby1(result);
257 Sgl_normalize(result,result_exponent);
258 Sgl_set_sign(result,/*using*/sign_save);
259 Sgl_setwrapped_exponent(result,result_exponent,unfl);
260 *dstptr = result;
261 /* inexact = FALSE */
262 return(UNDERFLOWEXCEPTION);
263 }
264 *dstptr = result;
265 return(NOEXCEPTION);
266 }
267 right_exponent = 1; /* Set exponent to reflect different bias
268 * with denomalized numbers. */
269 }
270 else
271 {
272 Sgl_clear_signexponent_set_hidden(right);
273 }
274 Sgl_clear_exponent_set_hidden(left);
275 diff_exponent = result_exponent - right_exponent;
276
277 /*
278 * Special case alignment of operands that would force alignment
279 * beyond the extent of the extension. A further optimization
280 * could special case this but only reduces the path length for this
281 * infrequent case.
282 */
283 if(diff_exponent > SGL_THRESHOLD)
284 {
285 diff_exponent = SGL_THRESHOLD;
286 }
287
288 /* Align right operand by shifting to right */
289 Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
290 /*and lower to*/extent);
291
292 /* Treat sum and difference of the operands separately. */
293 if( (/*signed*/int) save >= 0 )
294 {
295 /*
296 * Difference of the two operands. Their can be no overflow. A
297 * borrow can occur out of the hidden bit and force a post
298 * normalization phase.
299 */
300 Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
301 if(Sgl_iszero_hidden(result))
302 {
303 /* Handle normalization */
304 /* A straight foward algorithm would now shift the result
305 * and extension left until the hidden bit becomes one. Not
306 * all of the extension bits need participate in the shift.
307 * Only the two most significant bits (round and guard) are
308 * needed. If only a single shift is needed then the guard
309 * bit becomes a significant low order bit and the extension
310 * must participate in the rounding. If more than a single
311 * shift is needed, then all bits to the right of the guard
312 * bit are zeros, and the guard bit may or may not be zero. */
313 sign_save = Sgl_signextendedsign(result);
314 Sgl_leftshiftby1_withextent(result,extent,result);
315
316 /* Need to check for a zero result. The sign and exponent
317 * fields have already been zeroed. The more efficient test
318 * of the full object can be used.
319 */
320 if(Sgl_iszero(result))
321 /* Must have been "x-x" or "x+(-x)". */
322 {
323 if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
324 *dstptr = result;
325 return(NOEXCEPTION);
326 }
327 result_exponent--;
328 /* Look to see if normalization is finished. */
329 if(Sgl_isone_hidden(result))
330 {
331 if(result_exponent==0)
332 {
333 /* Denormalized, exponent should be zero. Left operand *
334 * was normalized, so extent (guard, round) was zero */
335 goto underflow;
336 }
337 else
338 {
339 /* No further normalization is needed. */
340 Sgl_set_sign(result,/*using*/sign_save);
341 Ext_leftshiftby1(extent);
342 goto round;
343 }
344 }
345
346 /* Check for denormalized, exponent should be zero. Left *
347 * operand was normalized, so extent (guard, round) was zero */
348 if(!(underflowtrap = Is_underflowtrap_enabled()) &&
349 result_exponent==0) goto underflow;
350
351 /* Shift extension to complete one bit of normalization and
352 * update exponent. */
353 Ext_leftshiftby1(extent);
354
355 /* Discover first one bit to determine shift amount. Use a
356 * modified binary search. We have already shifted the result
357 * one position right and still not found a one so the remainder
358 * of the extension must be zero and simplifies rounding. */
359 /* Scan bytes */
360 while(Sgl_iszero_hiddenhigh7mantissa(result))
361 {
362 Sgl_leftshiftby8(result);
363 if((result_exponent -= 8) <= 0 && !underflowtrap)
364 goto underflow;
365 }
366 /* Now narrow it down to the nibble */
367 if(Sgl_iszero_hiddenhigh3mantissa(result))
368 {
369 /* The lower nibble contains the normalizing one */
370 Sgl_leftshiftby4(result);
371 if((result_exponent -= 4) <= 0 && !underflowtrap)
372 goto underflow;
373 }
374 /* Select case were first bit is set (already normalized)
375 * otherwise select the proper shift. */
376 if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
377 {
378 /* Already normalized */
379 if(result_exponent <= 0) goto underflow;
380 Sgl_set_sign(result,/*using*/sign_save);
381 Sgl_set_exponent(result,/*using*/result_exponent);
382 *dstptr = result;
383 return(NOEXCEPTION);
384 }
385 Sgl_sethigh4bits(result,/*using*/sign_save);
386 switch(jumpsize)
387 {
388 case 1:
389 {
390 Sgl_leftshiftby3(result);
391 result_exponent -= 3;
392 break;
393 }
394 case 2:
395 case 3:
396 {
397 Sgl_leftshiftby2(result);
398 result_exponent -= 2;
399 break;
400 }
401 case 4:
402 case 5:
403 case 6:
404 case 7:
405 {
406 Sgl_leftshiftby1(result);
407 result_exponent -= 1;
408 break;
409 }
410 }
411 if(result_exponent > 0)
412 {
413 Sgl_set_exponent(result,/*using*/result_exponent);
414 *dstptr = result; /* Sign bit is already set */
415 return(NOEXCEPTION);
416 }
417 /* Fixup potential underflows */
418 underflow:
419 if(Is_underflowtrap_enabled())
420 {
421 Sgl_set_sign(result,sign_save);
422 Sgl_setwrapped_exponent(result,result_exponent,unfl);
423 *dstptr = result;
424 /* inexact = FALSE */
425 return(UNDERFLOWEXCEPTION);
426 }
427 /*
428 * Since we cannot get an inexact denormalized result,
429 * we can now return.
430 */
431 Sgl_right_align(result,/*by*/(1-result_exponent),extent);
432 Sgl_clear_signexponent(result);
433 Sgl_set_sign(result,sign_save);
434 *dstptr = result;
435 return(NOEXCEPTION);
436 } /* end if(hidden...)... */
437 /* Fall through and round */
438 } /* end if(save >= 0)... */
439 else
440 {
441 /* Add magnitudes */
442 Sgl_addition(left,right,/*to*/result);
443 if(Sgl_isone_hiddenoverflow(result))
444 {
445 /* Prenormalization required. */
446 Sgl_rightshiftby1_withextent(result,extent,extent);
447 Sgl_arithrightshiftby1(result);
448 result_exponent++;
449 } /* end if hiddenoverflow... */
450 } /* end else ...sub magnitudes... */
451
452 /* Round the result. If the extension is all zeros,then the result is
453 * exact. Otherwise round in the correct direction. No underflow is
454 * possible. If a postnormalization is necessary, then the mantissa is
455 * all zeros so no shift is needed. */
456 round:
457 if(Ext_isnotzero(extent))
458 {
459 inexact = TRUE;
460 switch(Rounding_mode())
461 {
462 case ROUNDNEAREST: /* The default. */
463 if(Ext_isone_sign(extent))
464 {
465 /* at least 1/2 ulp */
466 if(Ext_isnotzero_lower(extent) ||
467 Sgl_isone_lowmantissa(result))
468 {
469 /* either exactly half way and odd or more than 1/2ulp */
470 Sgl_increment(result);
471 }
472 }
473 break;
474
475 case ROUNDPLUS:
476 if(Sgl_iszero_sign(result))
477 {
478 /* Round up positive results */
479 Sgl_increment(result);
480 }
481 break;
482
483 case ROUNDMINUS:
484 if(Sgl_isone_sign(result))
485 {
486 /* Round down negative results */
487 Sgl_increment(result);
488 }
489
490 case ROUNDZERO:;
491 /* truncate is simple */
492 } /* end switch... */
493 if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
494 }
495 if(result_exponent == SGL_INFINITY_EXPONENT)
496 {
497 /* Overflow */
498 if(Is_overflowtrap_enabled())
499 {
500 Sgl_setwrapped_exponent(result,result_exponent,ovfl);
501 *dstptr = result;
502 if (inexact)
503 if (Is_inexacttrap_enabled())
504 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
505 else Set_inexactflag();
506 return(OVERFLOWEXCEPTION);
507 }
508 else
509 {
510 Set_overflowflag();
511 inexact = TRUE;
512 Sgl_setoverflow(result);
513 }
514 }
515 else Sgl_set_exponent(result,result_exponent);
516 *dstptr = result;
517 if(inexact)
518 if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
519 else Set_inexactflag();
520 return(NOEXCEPTION);
521 }
522