xref: /linux/arch/parisc/math-emu/dfadd.c (revision ca55b2fef3a9373fcfc30f82fd26bc7fccbda732)
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 */
306 	    /* A straight forward algorithm would now shift the result
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 }
525