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