1 /* $OpenBSD: sfadd.c,v 1.6 2002/11/29 09:27:34 deraadt Exp $ */
2 /*
3 (c) Copyright 1986 HEWLETT-PACKARD COMPANY
4 To anyone who acknowledges that this file is provided "AS IS"
5 without any express or implied warranty:
6 permission to use, copy, modify, and distribute this file
7 for any purpose is hereby granted without fee, provided that
8 the above copyright notice and this notice appears in all
9 copies, and that the name of Hewlett-Packard Company not be
10 used in advertising or publicity pertaining to distribution
11 of the software without specific, written prior permission.
12 Hewlett-Packard Company makes no representations about the
13 suitability of this software for any purpose.
14 */
15 /* @(#)sfadd.c: Revision: 2.7.88.1 Date: 93/12/07 15:07:00 */
16
17 #include "float.h"
18 #include "sgl_float.h"
19
20 /*
21 * Single_add: add two single precision values.
22 */
23 int
sgl_fadd(leftptr,rightptr,dstptr,status)24 sgl_fadd(leftptr, rightptr, dstptr, status)
25 sgl_floating_point *leftptr, *rightptr, *dstptr;
26 unsigned int *status;
27 {
28 register unsigned int left, right, result, extent;
29 register unsigned int signless_upper_left, signless_upper_right, save;
30
31
32 register int result_exponent, right_exponent, diff_exponent;
33 register int sign_save, jumpsize;
34 register int inexact = FALSE;
35 register int underflowtrap;
36
37 /* Create local copies of the numbers */
38 left = *leftptr;
39 right = *rightptr;
40
41 /* A zero "save" helps discover equal operands (for later), *
42 * and is used in swapping operands (if needed). */
43 Sgl_xortointp1(left,right,/*to*/save);
44
45 /*
46 * check first operand for NaN's or infinity
47 */
48 if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
49 {
50 if (Sgl_iszero_mantissa(left))
51 {
52 if (Sgl_isnotnan(right))
53 {
54 if (Sgl_isinfinity(right) && save!=0)
55 {
56 /*
57 * invalid since operands are opposite signed infinity's
58 */
59 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
60 Set_invalidflag();
61 Sgl_makequietnan(result);
62 *dstptr = result;
63 return(NOEXCEPTION);
64 }
65 /*
66 * return infinity
67 */
68 *dstptr = left;
69 return(NOEXCEPTION);
70 }
71 }
72 else
73 {
74 /*
75 * is NaN; signaling or quiet?
76 */
77 if (Sgl_isone_signaling(left))
78 {
79 /* trap if INVALIDTRAP enabled */
80 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
81 /* make NaN quiet */
82 Set_invalidflag();
83 Sgl_set_quiet(left);
84 }
85 /*
86 * is second operand a signaling NaN?
87 */
88 else if (Sgl_is_signalingnan(right))
89 {
90 /* trap if INVALIDTRAP enabled */
91 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
92 /* make NaN quiet */
93 Set_invalidflag();
94 Sgl_set_quiet(right);
95 *dstptr = right;
96 return(NOEXCEPTION);
97 }
98 /*
99 * return quiet NaN
100 */
101 *dstptr = left;
102 return(NOEXCEPTION);
103 }
104 } /* End left NaN or Infinity processing */
105 /*
106 * check second operand for NaN's or infinity
107 */
108 if (Sgl_isinfinity_exponent(right))
109 {
110 if (Sgl_iszero_mantissa(right))
111 {
112 /* return infinity */
113 *dstptr = right;
114 return(NOEXCEPTION);
115 }
116 /*
117 * is NaN; signaling or quiet?
118 */
119 if (Sgl_isone_signaling(right))
120 {
121 /* trap if INVALIDTRAP enabled */
122 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
123 /* make NaN quiet */
124 Set_invalidflag();
125 Sgl_set_quiet(right);
126 }
127 /*
128 * return quiet NaN
129 */
130 *dstptr = right;
131 return(NOEXCEPTION);
132 } /* End right NaN or Infinity processing */
133
134 /* Invariant: Must be dealing with finite numbers */
135
136 /* Compare operands by removing the sign */
137 Sgl_copytoint_exponentmantissa(left,signless_upper_left);
138 Sgl_copytoint_exponentmantissa(right,signless_upper_right);
139
140 /* sign difference selects add or sub operation. */
141 if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
142 {
143 /* Set the left operand to the larger one by XOR swap *
144 * First finish the first word using "save" */
145 Sgl_xorfromintp1(save,right,/*to*/right);
146 Sgl_xorfromintp1(save,left,/*to*/left);
147 result_exponent = Sgl_exponent(left);
148 }
149 /* Invariant: left is not smaller than right. */
150
151 if((right_exponent = Sgl_exponent(right)) == 0)
152 {
153 /* Denormalized operands. First look for zeroes */
154 if(Sgl_iszero_mantissa(right))
155 {
156 /* right is zero */
157 if(Sgl_iszero_exponentmantissa(left))
158 {
159 /* Both operands are zeros */
160 if(Is_rounding_mode(ROUNDMINUS))
161 {
162 Sgl_or_signs(left,/*with*/right);
163 }
164 else
165 {
166 Sgl_and_signs(left,/*with*/right);
167 }
168 }
169 else
170 {
171 /* Left is not a zero and must be the result. Trapped
172 * underflows are signaled if left is denormalized. Result
173 * is always exact. */
174 if( (result_exponent == 0) && Is_underflowtrap_enabled() )
175 {
176 /* need to normalize results mantissa */
177 sign_save = Sgl_signextendedsign(left);
178 Sgl_leftshiftby1(left);
179 Sgl_normalize(left,result_exponent);
180 Sgl_set_sign(left,/*using*/sign_save);
181 Sgl_setwrapped_exponent(left,result_exponent,unfl);
182 *dstptr = left;
183 return(UNDERFLOWEXCEPTION);
184 }
185 }
186 *dstptr = left;
187 return(NOEXCEPTION);
188 }
189
190 /* Neither are zeroes */
191 Sgl_clear_sign(right); /* Exponent is already cleared */
192 if(result_exponent == 0 )
193 {
194 /* Both operands are denormalized. The result must be exact
195 * and is simply calculated. A sum could become normalized and a
196 * difference could cancel to a true zero. */
197 if( (/*signed*/int) save < 0 )
198 {
199 Sgl_subtract(left,/*minus*/right,/*into*/result);
200 if(Sgl_iszero_mantissa(result))
201 {
202 if(Is_rounding_mode(ROUNDMINUS))
203 {
204 Sgl_setone_sign(result);
205 }
206 else
207 {
208 Sgl_setzero_sign(result);
209 }
210 *dstptr = result;
211 return(NOEXCEPTION);
212 }
213 }
214 else
215 {
216 Sgl_addition(left,right,/*into*/result);
217 if(Sgl_isone_hidden(result))
218 {
219 *dstptr = result;
220 return(NOEXCEPTION);
221 }
222 }
223 if(Is_underflowtrap_enabled())
224 {
225 /* need to normalize result */
226 sign_save = Sgl_signextendedsign(result);
227 Sgl_leftshiftby1(result);
228 Sgl_normalize(result,result_exponent);
229 Sgl_set_sign(result,/*using*/sign_save);
230 Sgl_setwrapped_exponent(result,result_exponent,unfl);
231 *dstptr = result;
232 return(UNDERFLOWEXCEPTION);
233 }
234 *dstptr = result;
235 return(NOEXCEPTION);
236 }
237 right_exponent = 1; /* Set exponent to reflect different bias
238 * with denomalized numbers. */
239 }
240 else
241 {
242 Sgl_clear_signexponent_set_hidden(right);
243 }
244 Sgl_clear_exponent_set_hidden(left);
245 diff_exponent = result_exponent - right_exponent;
246
247 /*
248 * Special case alignment of operands that would force alignment
249 * beyond the extent of the extension. A further optimization
250 * could special case this but only reduces the path length for this
251 * infrequent case.
252 */
253 if(diff_exponent > SGL_THRESHOLD)
254 {
255 diff_exponent = SGL_THRESHOLD;
256 }
257
258 /* Align right operand by shifting to right */
259 Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
260 /*and lower to*/extent);
261
262 /* Treat sum and difference of the operands separately. */
263 if( (/*signed*/int) save < 0 )
264 {
265 /*
266 * Difference of the two operands. Their can be no overflow. A
267 * borrow can occur out of the hidden bit and force a post
268 * normalization phase.
269 */
270 Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
271 if(Sgl_iszero_hidden(result))
272 {
273 /* Handle normalization */
274 /* A straight forward algorithm would now shift the result
275 * and extension left until the hidden bit becomes one. Not
276 * all of the extension bits need participate in the shift.
277 * Only the two most significant bits (round and guard) are
278 * needed. If only a single shift is needed then the guard
279 * bit becomes a significant low order bit and the extension
280 * must participate in the rounding. If more than a single
281 * shift is needed, then all bits to the right of the guard
282 * bit are zeros, and the guard bit may or may not be zero. */
283 sign_save = Sgl_signextendedsign(result);
284 Sgl_leftshiftby1_withextent(result,extent,result);
285
286 /* Need to check for a zero result. The sign and exponent
287 * fields have already been zeroed. The more efficient test
288 * of the full object can be used.
289 */
290 if(Sgl_iszero(result))
291 /* Must have been "x-x" or "x+(-x)". */
292 {
293 if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
294 *dstptr = result;
295 return(NOEXCEPTION);
296 }
297 result_exponent--;
298 /* Look to see if normalization is finished. */
299 if(Sgl_isone_hidden(result))
300 {
301 if(result_exponent==0)
302 {
303 /* Denormalized, exponent should be zero. Left operand *
304 * was normalized, so extent (guard, round) was zero */
305 goto underflow;
306 }
307 else
308 {
309 /* No further normalization is needed. */
310 Sgl_set_sign(result,/*using*/sign_save);
311 Ext_leftshiftby1(extent);
312 goto round;
313 }
314 }
315
316 /* Check for denormalized, exponent should be zero. Left *
317 * operand was normalized, so extent (guard, round) was zero */
318 if(!(underflowtrap = Is_underflowtrap_enabled()) &&
319 result_exponent==0) goto underflow;
320
321 /* Shift extension to complete one bit of normalization and
322 * update exponent. */
323 Ext_leftshiftby1(extent);
324
325 /* Discover first one bit to determine shift amount. Use a
326 * modified binary search. We have already shifted the result
327 * one position right and still not found a one so the remainder
328 * of the extension must be zero and simplifies rounding. */
329 /* Scan bytes */
330 while(Sgl_iszero_hiddenhigh7mantissa(result))
331 {
332 Sgl_leftshiftby8(result);
333 if((result_exponent -= 8) <= 0 && !underflowtrap)
334 goto underflow;
335 }
336 /* Now narrow it down to the nibble */
337 if(Sgl_iszero_hiddenhigh3mantissa(result))
338 {
339 /* The lower nibble contains the normalizing one */
340 Sgl_leftshiftby4(result);
341 if((result_exponent -= 4) <= 0 && !underflowtrap)
342 goto underflow;
343 }
344 /* Select case were first bit is set (already normalized)
345 * otherwise select the proper shift. */
346 if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
347 {
348 /* Already normalized */
349 if(result_exponent <= 0) goto underflow;
350 Sgl_set_sign(result,/*using*/sign_save);
351 Sgl_set_exponent(result,/*using*/result_exponent);
352 *dstptr = result;
353 return(NOEXCEPTION);
354 }
355 Sgl_sethigh4bits(result,/*using*/sign_save);
356 switch(jumpsize)
357 {
358 case 1:
359 {
360 Sgl_leftshiftby3(result);
361 result_exponent -= 3;
362 break;
363 }
364 case 2:
365 case 3:
366 {
367 Sgl_leftshiftby2(result);
368 result_exponent -= 2;
369 break;
370 }
371 case 4:
372 case 5:
373 case 6:
374 case 7:
375 {
376 Sgl_leftshiftby1(result);
377 result_exponent -= 1;
378 break;
379 }
380 }
381 if(result_exponent > 0)
382 {
383 Sgl_set_exponent(result,/*using*/result_exponent);
384 *dstptr = result;
385 return(NOEXCEPTION); /* Sign bit is already set */
386 }
387 /* Fixup potential underflows */
388 underflow:
389 if(Is_underflowtrap_enabled())
390 {
391 Sgl_set_sign(result,sign_save);
392 Sgl_setwrapped_exponent(result,result_exponent,unfl);
393 *dstptr = result;
394 /* inexact = FALSE; */
395 return(UNDERFLOWEXCEPTION);
396 }
397 /*
398 * Since we cannot get an inexact denormalized result,
399 * we can now return.
400 */
401 Sgl_right_align(result,/*by*/(1-result_exponent),extent);
402 Sgl_clear_signexponent(result);
403 Sgl_set_sign(result,sign_save);
404 *dstptr = result;
405 return(NOEXCEPTION);
406 } /* end if(hidden...)... */
407 /* Fall through and round */
408 } /* end if(save < 0)... */
409 else
410 {
411 /* Add magnitudes */
412 Sgl_addition(left,right,/*to*/result);
413 if(Sgl_isone_hiddenoverflow(result))
414 {
415 /* Prenormalization required. */
416 Sgl_rightshiftby1_withextent(result,extent,extent);
417 Sgl_arithrightshiftby1(result);
418 result_exponent++;
419 } /* end if hiddenoverflow... */
420 } /* end else ...add magnitudes... */
421
422 /* Round the result. If the extension is all zeros,then the result is
423 * exact. Otherwise round in the correct direction. No underflow is
424 * possible. If a postnormalization is necessary, then the mantissa is
425 * all zeros so no shift is needed. */
426 round:
427 if(Ext_isnotzero(extent))
428 {
429 inexact = TRUE;
430 switch(Rounding_mode())
431 {
432 case ROUNDNEAREST: /* The default. */
433 if(Ext_isone_sign(extent))
434 {
435 /* at least 1/2 ulp */
436 if(Ext_isnotzero_lower(extent) ||
437 Sgl_isone_lowmantissa(result))
438 {
439 /* either exactly half way and odd or more than 1/2ulp */
440 Sgl_increment(result);
441 }
442 }
443 break;
444
445 case ROUNDPLUS:
446 if(Sgl_iszero_sign(result))
447 {
448 /* Round up positive results */
449 Sgl_increment(result);
450 }
451 break;
452
453 case ROUNDMINUS:
454 if(Sgl_isone_sign(result))
455 {
456 /* Round down negative results */
457 Sgl_increment(result);
458 }
459
460 case ROUNDZERO:;
461 /* truncate is simple */
462 } /* end switch... */
463 if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
464 }
465 if(result_exponent == SGL_INFINITY_EXPONENT)
466 {
467 /* Overflow */
468 if(Is_overflowtrap_enabled())
469 {
470 Sgl_setwrapped_exponent(result,result_exponent,ovfl);
471 *dstptr = result;
472 if (inexact) {
473 if (Is_inexacttrap_enabled())
474 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
475 else Set_inexactflag();
476 }
477 return(OVERFLOWEXCEPTION);
478 }
479 else
480 {
481 Set_overflowflag();
482 inexact = TRUE;
483 Sgl_setoverflow(result);
484 }
485 }
486 else Sgl_set_exponent(result,result_exponent);
487 *dstptr = result;
488 if(inexact) {
489 if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
490 else Set_inexactflag();
491 }
492 return(NOEXCEPTION);
493 }
494