blob: 008d721b5d2270a595f244e80c37c99532edf87b [file] [log] [blame]
Linus Torvalds1da177e2005-04-16 15:20:36 -07001/*
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/sfadd.c $Revision: 1.1 $
26 *
27 * Purpose:
28 * Single_add: add two single precision values.
29 *
30 * External Interfaces:
31 * sgl_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 "sgl_float.h"
44
45/*
46 * Single_add: add two single precision values.
47 */
48int
49sgl_fadd(
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
59 register int result_exponent, right_exponent, diff_exponent;
60 register int sign_save, jumpsize;
61 register boolean inexact = FALSE;
62 register boolean underflowtrap;
63
64 /* Create local copies of the numbers */
65 left = *leftptr;
66 right = *rightptr;
67
68 /* A zero "save" helps discover equal operands (for later), *
69 * and is used in swapping operands (if needed). */
70 Sgl_xortointp1(left,right,/*to*/save);
71
72 /*
73 * check first operand for NaN's or infinity
74 */
75 if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
76 {
77 if (Sgl_iszero_mantissa(left))
78 {
79 if (Sgl_isnotnan(right))
80 {
81 if (Sgl_isinfinity(right) && save!=0)
82 {
83 /*
84 * invalid since operands are opposite signed infinity's
85 */
86 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
87 Set_invalidflag();
88 Sgl_makequietnan(result);
89 *dstptr = result;
90 return(NOEXCEPTION);
91 }
92 /*
93 * return infinity
94 */
95 *dstptr = left;
96 return(NOEXCEPTION);
97 }
98 }
99 else
100 {
101 /*
102 * is NaN; signaling or quiet?
103 */
104 if (Sgl_isone_signaling(left))
105 {
106 /* trap if INVALIDTRAP enabled */
107 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
108 /* make NaN quiet */
109 Set_invalidflag();
110 Sgl_set_quiet(left);
111 }
112 /*
113 * is second operand a signaling NaN?
114 */
115 else if (Sgl_is_signalingnan(right))
116 {
117 /* trap if INVALIDTRAP enabled */
118 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
119 /* make NaN quiet */
120 Set_invalidflag();
121 Sgl_set_quiet(right);
122 *dstptr = right;
123 return(NOEXCEPTION);
124 }
125 /*
126 * return quiet NaN
127 */
128 *dstptr = left;
129 return(NOEXCEPTION);
130 }
131 } /* End left NaN or Infinity processing */
132 /*
133 * check second operand for NaN's or infinity
134 */
135 if (Sgl_isinfinity_exponent(right))
136 {
137 if (Sgl_iszero_mantissa(right))
138 {
139 /* return infinity */
140 *dstptr = right;
141 return(NOEXCEPTION);
142 }
143 /*
144 * is NaN; signaling or quiet?
145 */
146 if (Sgl_isone_signaling(right))
147 {
148 /* trap if INVALIDTRAP enabled */
149 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
150 /* make NaN quiet */
151 Set_invalidflag();
152 Sgl_set_quiet(right);
153 }
154 /*
155 * return quiet NaN
156 */
157 *dstptr = right;
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 Sgl_copytoint_exponentmantissa(left,signless_upper_left);
165 Sgl_copytoint_exponentmantissa(right,signless_upper_right);
166
167 /* sign difference selects add or sub operation. */
168 if(Sgl_ismagnitudeless(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 Sgl_xorfromintp1(save,right,/*to*/right);
173 Sgl_xorfromintp1(save,left,/*to*/left);
174 result_exponent = Sgl_exponent(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 if(Is_rounding_mode(ROUNDMINUS))
188 {
189 Sgl_or_signs(left,/*with*/right);
190 }
191 else
192 {
193 Sgl_and_signs(left,/*with*/right);
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 = Sgl_signextendedsign(left);
205 Sgl_leftshiftby1(left);
206 Sgl_normalize(left,result_exponent);
207 Sgl_set_sign(left,/*using*/sign_save);
208 Sgl_setwrapped_exponent(left,result_exponent,unfl);
209 *dstptr = left;
210 return(UNDERFLOWEXCEPTION);
211 }
212 }
213 *dstptr = left;
214 return(NOEXCEPTION);
215 }
216
217 /* Neither are zeroes */
218 Sgl_clear_sign(right); /* Exponent is already cleared */
219 if(result_exponent == 0 )
220 {
221 /* Both operands are denormalized. The result must be exact
222 * and is simply calculated. A sum could become normalized and a
223 * difference could cancel to a true zero. */
224 if( (/*signed*/int) save < 0 )
225 {
226 Sgl_subtract(left,/*minus*/right,/*into*/result);
227 if(Sgl_iszero_mantissa(result))
228 {
229 if(Is_rounding_mode(ROUNDMINUS))
230 {
231 Sgl_setone_sign(result);
232 }
233 else
234 {
235 Sgl_setzero_sign(result);
236 }
237 *dstptr = result;
238 return(NOEXCEPTION);
239 }
240 }
241 else
242 {
243 Sgl_addition(left,right,/*into*/result);
244 if(Sgl_isone_hidden(result))
245 {
246 *dstptr = result;
247 return(NOEXCEPTION);
248 }
249 }
250 if(Is_underflowtrap_enabled())
251 {
252 /* need to normalize result */
253 sign_save = Sgl_signextendedsign(result);
254 Sgl_leftshiftby1(result);
255 Sgl_normalize(result,result_exponent);
256 Sgl_set_sign(result,/*using*/sign_save);
257 Sgl_setwrapped_exponent(result,result_exponent,unfl);
258 *dstptr = result;
259 return(UNDERFLOWEXCEPTION);
260 }
261 *dstptr = result;
262 return(NOEXCEPTION);
263 }
264 right_exponent = 1; /* Set exponent to reflect different bias
265 * with denomalized numbers. */
266 }
267 else
268 {
269 Sgl_clear_signexponent_set_hidden(right);
270 }
271 Sgl_clear_exponent_set_hidden(left);
272 diff_exponent = result_exponent - right_exponent;
273
274 /*
275 * Special case alignment of operands that would force alignment
276 * beyond the extent of the extension. A further optimization
277 * could special case this but only reduces the path length for this
278 * infrequent case.
279 */
280 if(diff_exponent > SGL_THRESHOLD)
281 {
282 diff_exponent = SGL_THRESHOLD;
283 }
284
285 /* Align right operand by shifting to right */
286 Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
287 /*and lower to*/extent);
288
289 /* Treat sum and difference of the operands separately. */
290 if( (/*signed*/int) save < 0 )
291 {
292 /*
293 * Difference of the two operands. Their can be no overflow. A
294 * borrow can occur out of the hidden bit and force a post
295 * normalization phase.
296 */
297 Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
298 if(Sgl_iszero_hidden(result))
299 {
300 /* Handle normalization */
301 /* A straight foward algorithm would now shift the result
302 * and extension left until the hidden bit becomes one. Not
303 * all of the extension bits need participate in the shift.
304 * Only the two most significant bits (round and guard) are
305 * needed. If only a single shift is needed then the guard
306 * bit becomes a significant low order bit and the extension
307 * must participate in the rounding. If more than a single
308 * shift is needed, then all bits to the right of the guard
309 * bit are zeros, and the guard bit may or may not be zero. */
310 sign_save = Sgl_signextendedsign(result);
311 Sgl_leftshiftby1_withextent(result,extent,result);
312
313 /* Need to check for a zero result. The sign and exponent
314 * fields have already been zeroed. The more efficient test
315 * of the full object can be used.
316 */
317 if(Sgl_iszero(result))
318 /* Must have been "x-x" or "x+(-x)". */
319 {
320 if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
321 *dstptr = result;
322 return(NOEXCEPTION);
323 }
324 result_exponent--;
325 /* Look to see if normalization is finished. */
326 if(Sgl_isone_hidden(result))
327 {
328 if(result_exponent==0)
329 {
330 /* Denormalized, exponent should be zero. Left operand *
331 * was normalized, so extent (guard, round) was zero */
332 goto underflow;
333 }
334 else
335 {
336 /* No further normalization is needed. */
337 Sgl_set_sign(result,/*using*/sign_save);
338 Ext_leftshiftby1(extent);
339 goto round;
340 }
341 }
342
343 /* Check for denormalized, exponent should be zero. Left *
344 * operand was normalized, so extent (guard, round) was zero */
345 if(!(underflowtrap = Is_underflowtrap_enabled()) &&
346 result_exponent==0) goto underflow;
347
348 /* Shift extension to complete one bit of normalization and
349 * update exponent. */
350 Ext_leftshiftby1(extent);
351
352 /* Discover first one bit to determine shift amount. Use a
353 * modified binary search. We have already shifted the result
354 * one position right and still not found a one so the remainder
355 * of the extension must be zero and simplifies rounding. */
356 /* Scan bytes */
357 while(Sgl_iszero_hiddenhigh7mantissa(result))
358 {
359 Sgl_leftshiftby8(result);
360 if((result_exponent -= 8) <= 0 && !underflowtrap)
361 goto underflow;
362 }
363 /* Now narrow it down to the nibble */
364 if(Sgl_iszero_hiddenhigh3mantissa(result))
365 {
366 /* The lower nibble contains the normalizing one */
367 Sgl_leftshiftby4(result);
368 if((result_exponent -= 4) <= 0 && !underflowtrap)
369 goto underflow;
370 }
371 /* Select case were first bit is set (already normalized)
372 * otherwise select the proper shift. */
373 if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
374 {
375 /* Already normalized */
376 if(result_exponent <= 0) goto underflow;
377 Sgl_set_sign(result,/*using*/sign_save);
378 Sgl_set_exponent(result,/*using*/result_exponent);
379 *dstptr = result;
380 return(NOEXCEPTION);
381 }
382 Sgl_sethigh4bits(result,/*using*/sign_save);
383 switch(jumpsize)
384 {
385 case 1:
386 {
387 Sgl_leftshiftby3(result);
388 result_exponent -= 3;
389 break;
390 }
391 case 2:
392 case 3:
393 {
394 Sgl_leftshiftby2(result);
395 result_exponent -= 2;
396 break;
397 }
398 case 4:
399 case 5:
400 case 6:
401 case 7:
402 {
403 Sgl_leftshiftby1(result);
404 result_exponent -= 1;
405 break;
406 }
407 }
408 if(result_exponent > 0)
409 {
410 Sgl_set_exponent(result,/*using*/result_exponent);
411 *dstptr = result;
412 return(NOEXCEPTION); /* Sign bit is already set */
413 }
414 /* Fixup potential underflows */
415 underflow:
416 if(Is_underflowtrap_enabled())
417 {
418 Sgl_set_sign(result,sign_save);
419 Sgl_setwrapped_exponent(result,result_exponent,unfl);
420 *dstptr = result;
421 /* inexact = FALSE; */
422 return(UNDERFLOWEXCEPTION);
423 }
424 /*
425 * Since we cannot get an inexact denormalized result,
426 * we can now return.
427 */
428 Sgl_right_align(result,/*by*/(1-result_exponent),extent);
429 Sgl_clear_signexponent(result);
430 Sgl_set_sign(result,sign_save);
431 *dstptr = result;
432 return(NOEXCEPTION);
433 } /* end if(hidden...)... */
434 /* Fall through and round */
435 } /* end if(save < 0)... */
436 else
437 {
438 /* Add magnitudes */
439 Sgl_addition(left,right,/*to*/result);
440 if(Sgl_isone_hiddenoverflow(result))
441 {
442 /* Prenormalization required. */
443 Sgl_rightshiftby1_withextent(result,extent,extent);
444 Sgl_arithrightshiftby1(result);
445 result_exponent++;
446 } /* end if hiddenoverflow... */
447 } /* end else ...add magnitudes... */
448
449 /* Round the result. If the extension is all zeros,then the result is
450 * exact. Otherwise round in the correct direction. No underflow is
451 * possible. If a postnormalization is necessary, then the mantissa is
452 * all zeros so no shift is needed. */
453 round:
454 if(Ext_isnotzero(extent))
455 {
456 inexact = TRUE;
457 switch(Rounding_mode())
458 {
459 case ROUNDNEAREST: /* The default. */
460 if(Ext_isone_sign(extent))
461 {
462 /* at least 1/2 ulp */
463 if(Ext_isnotzero_lower(extent) ||
464 Sgl_isone_lowmantissa(result))
465 {
466 /* either exactly half way and odd or more than 1/2ulp */
467 Sgl_increment(result);
468 }
469 }
470 break;
471
472 case ROUNDPLUS:
473 if(Sgl_iszero_sign(result))
474 {
475 /* Round up positive results */
476 Sgl_increment(result);
477 }
478 break;
479
480 case ROUNDMINUS:
481 if(Sgl_isone_sign(result))
482 {
483 /* Round down negative results */
484 Sgl_increment(result);
485 }
486
487 case ROUNDZERO:;
488 /* truncate is simple */
489 } /* end switch... */
490 if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
491 }
492 if(result_exponent == SGL_INFINITY_EXPONENT)
493 {
494 /* Overflow */
495 if(Is_overflowtrap_enabled())
496 {
497 Sgl_setwrapped_exponent(result,result_exponent,ovfl);
498 *dstptr = result;
499 if (inexact)
500 if (Is_inexacttrap_enabled())
501 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
502 else Set_inexactflag();
503 return(OVERFLOWEXCEPTION);
504 }
505 else
506 {
507 Set_overflowflag();
508 inexact = TRUE;
509 Sgl_setoverflow(result);
510 }
511 }
512 else Sgl_set_exponent(result,result_exponent);
513 *dstptr = result;
514 if(inexact)
515 if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
516 else Set_inexactflag();
517 return(NOEXCEPTION);
518 }