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 */
35dbl_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