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/sfadd.c		$Revision: 1.1 $
13 *
14 *  Purpose:
15 *	Single_add: add two single precision values.
16 *
17 *  External Interfaces:
18 *	sgl_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 "sgl_float.h"
31
32/*
33 * Single_add: add two single precision values.
34 */
35int
36sgl_fadd(
37    sgl_floating_point *leftptr,
38    sgl_floating_point *rightptr,
39    sgl_floating_point *dstptr,
40    unsigned int *status)
41    {
42    register unsigned int left, right, result, extent;
43    register unsigned int signless_upper_left, signless_upper_right, save;
44
45
46    register int result_exponent, right_exponent, diff_exponent;
47    register int sign_save, jumpsize;
48    register boolean inexact = FALSE;
49    register boolean underflowtrap;
50
51    /* Create local copies of the numbers */
52    left = *leftptr;
53    right = *rightptr;
54
55    /* A zero "save" helps discover equal operands (for later),  *
56     * and is used in swapping operands (if needed).             */
57    Sgl_xortointp1(left,right,/*to*/save);
58
59    /*
60     * check first operand for NaN's or infinity
61     */
62    if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
63	{
64	if (Sgl_iszero_mantissa(left))
65	    {
66	    if (Sgl_isnotnan(right))
67		{
68		if (Sgl_isinfinity(right) && save!=0)
69		    {
70		    /*
71		     * invalid since operands are opposite signed infinity's
72		     */
73		    if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
74                    Set_invalidflag();
75                    Sgl_makequietnan(result);
76		    *dstptr = result;
77		    return(NOEXCEPTION);
78		    }
79		/*
80	 	 * return infinity
81	 	 */
82		*dstptr = left;
83		return(NOEXCEPTION);
84		}
85	    }
86	else
87	    {
88            /*
89             * is NaN; signaling or quiet?
90             */
91            if (Sgl_isone_signaling(left))
92		{
93               	/* trap if INVALIDTRAP enabled */
94		if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
95        	/* make NaN quiet */
96        	Set_invalidflag();
97        	Sgl_set_quiet(left);
98        	}
99	    /*
100	     * is second operand a signaling NaN?
101	     */
102	    else if (Sgl_is_signalingnan(right))
103		{
104        	/* trap if INVALIDTRAP enabled */
105               	if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
106		/* make NaN quiet */
107		Set_invalidflag();
108		Sgl_set_quiet(right);
109		*dstptr = right;
110		return(NOEXCEPTION);
111		}
112	    /*
113 	     * return quiet NaN
114 	     */
115 	    *dstptr = left;
116 	    return(NOEXCEPTION);
117	    }
118	} /* End left NaN or Infinity processing */
119    /*
120     * check second operand for NaN's or infinity
121     */
122    if (Sgl_isinfinity_exponent(right))
123	{
124	if (Sgl_iszero_mantissa(right))
125	    {
126	    /* return infinity */
127	    *dstptr = right;
128	    return(NOEXCEPTION);
129	    }
130        /*
131         * is NaN; signaling or quiet?
132         */
133        if (Sgl_isone_signaling(right))
134	    {
135            /* trap if INVALIDTRAP enabled */
136	    if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
137	    /* make NaN quiet */
138	    Set_invalidflag();
139	    Sgl_set_quiet(right);
140	    }
141	/*
142	 * return quiet NaN
143 	 */
144	*dstptr = right;
145	return(NOEXCEPTION);
146    	} /* End right NaN or Infinity processing */
147
148    /* Invariant: Must be dealing with finite numbers */
149
150    /* Compare operands by removing the sign */
151    Sgl_copytoint_exponentmantissa(left,signless_upper_left);
152    Sgl_copytoint_exponentmantissa(right,signless_upper_right);
153
154    /* sign difference selects add or sub operation. */
155    if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
156	{
157	/* Set the left operand to the larger one by XOR swap *
158	 *  First finish the first word using "save"          */
159	Sgl_xorfromintp1(save,right,/*to*/right);
160	Sgl_xorfromintp1(save,left,/*to*/left);
161	result_exponent = Sgl_exponent(left);
162	}
163    /* Invariant:  left is not smaller than right. */
164
165    if((right_exponent = Sgl_exponent(right)) == 0)
166        {
167	/* Denormalized operands.  First look for zeroes */
168	if(Sgl_iszero_mantissa(right))
169	    {
170	    /* right is zero */
171	    if(Sgl_iszero_exponentmantissa(left))
172		{
173		/* Both operands are zeros */
174		if(Is_rounding_mode(ROUNDMINUS))
175		    {
176		    Sgl_or_signs(left,/*with*/right);
177		    }
178		else
179		    {
180		    Sgl_and_signs(left,/*with*/right);
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 = Sgl_signextendedsign(left);
192		    Sgl_leftshiftby1(left);
193		    Sgl_normalize(left,result_exponent);
194		    Sgl_set_sign(left,/*using*/sign_save);
195		    Sgl_setwrapped_exponent(left,result_exponent,unfl);
196		    *dstptr = left;
197		    return(UNDERFLOWEXCEPTION);
198		    }
199		}
200	    *dstptr = left;
201	    return(NOEXCEPTION);
202	    }
203
204	/* Neither are zeroes */
205	Sgl_clear_sign(right);	/* Exponent is already cleared */
206	if(result_exponent == 0 )
207	    {
208	    /* Both operands are denormalized.  The result must be exact
209	     * and is simply calculated.  A sum could become normalized and a
210	     * difference could cancel to a true zero. */
211	    if( (/*signed*/int) save < 0 )
212		{
213		Sgl_subtract(left,/*minus*/right,/*into*/result);
214		if(Sgl_iszero_mantissa(result))
215		    {
216		    if(Is_rounding_mode(ROUNDMINUS))
217			{
218			Sgl_setone_sign(result);
219			}
220		    else
221			{
222			Sgl_setzero_sign(result);
223			}
224		    *dstptr = result;
225		    return(NOEXCEPTION);
226		    }
227		}
228	    else
229		{
230		Sgl_addition(left,right,/*into*/result);
231		if(Sgl_isone_hidden(result))
232		    {
233		    *dstptr = result;
234		    return(NOEXCEPTION);
235		    }
236		}
237	    if(Is_underflowtrap_enabled())
238		{
239		/* need to normalize result */
240	    	sign_save = Sgl_signextendedsign(result);
241		Sgl_leftshiftby1(result);
242		Sgl_normalize(result,result_exponent);
243		Sgl_set_sign(result,/*using*/sign_save);
244                Sgl_setwrapped_exponent(result,result_exponent,unfl);
245		*dstptr = result;
246		return(UNDERFLOWEXCEPTION);
247		}
248	    *dstptr = result;
249	    return(NOEXCEPTION);
250	    }
251	right_exponent = 1;	/* Set exponent to reflect different bias
252				 * with denormalized numbers. */
253	}
254    else
255	{
256	Sgl_clear_signexponent_set_hidden(right);
257	}
258    Sgl_clear_exponent_set_hidden(left);
259    diff_exponent = result_exponent - right_exponent;
260
261    /*
262     * Special case alignment of operands that would force alignment
263     * beyond the extent of the extension.  A further optimization
264     * could special case this but only reduces the path length for this
265     * infrequent case.
266     */
267    if(diff_exponent > SGL_THRESHOLD)
268	{
269	diff_exponent = SGL_THRESHOLD;
270	}
271
272    /* Align right operand by shifting to right */
273    Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
274     /*and lower to*/extent);
275
276    /* Treat sum and difference of the operands separately. */
277    if( (/*signed*/int) save < 0 )
278	{
279	/*
280	 * Difference of the two operands.  Their can be no overflow.  A
281	 * borrow can occur out of the hidden bit and force a post
282	 * normalization phase.
283	 */
284	Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
285	if(Sgl_iszero_hidden(result))
286	    {
287	    /* Handle normalization */
288	    /* A straightforward algorithm would now shift the result
289	     * and extension left until the hidden bit becomes one.  Not
290	     * all of the extension bits need participate in the shift.
291	     * Only the two most significant bits (round and guard) are
292	     * needed.  If only a single shift is needed then the guard
293	     * bit becomes a significant low order bit and the extension
294	     * must participate in the rounding.  If more than a single
295	     * shift is needed, then all bits to the right of the guard
296	     * bit are zeros, and the guard bit may or may not be zero. */
297	    sign_save = Sgl_signextendedsign(result);
298            Sgl_leftshiftby1_withextent(result,extent,result);
299
300            /* Need to check for a zero result.  The sign and exponent
301	     * fields have already been zeroed.  The more efficient test
302	     * of the full object can be used.
303	     */
304    	    if(Sgl_iszero(result))
305		/* Must have been "x-x" or "x+(-x)". */
306		{
307		if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
308		*dstptr = result;
309		return(NOEXCEPTION);
310		}
311	    result_exponent--;
312	    /* Look to see if normalization is finished. */
313	    if(Sgl_isone_hidden(result))
314		{
315		if(result_exponent==0)
316		    {
317		    /* Denormalized, exponent should be zero.  Left operand *
318 		     * was normalized, so extent (guard, round) was zero    */
319		    goto underflow;
320		    }
321		else
322		    {
323		    /* No further normalization is needed. */
324		    Sgl_set_sign(result,/*using*/sign_save);
325	    	    Ext_leftshiftby1(extent);
326		    goto round;
327		    }
328		}
329
330	    /* Check for denormalized, exponent should be zero.  Left    *
331	     * operand was normalized, so extent (guard, round) was zero */
332	    if(!(underflowtrap = Is_underflowtrap_enabled()) &&
333	       result_exponent==0) goto underflow;
334
335	    /* Shift extension to complete one bit of normalization and
336	     * update exponent. */
337	    Ext_leftshiftby1(extent);
338
339	    /* Discover first one bit to determine shift amount.  Use a
340	     * modified binary search.  We have already shifted the result
341	     * one position right and still not found a one so the remainder
342	     * of the extension must be zero and simplifies rounding. */
343	    /* Scan bytes */
344	    while(Sgl_iszero_hiddenhigh7mantissa(result))
345		{
346		Sgl_leftshiftby8(result);
347		if((result_exponent -= 8) <= 0  && !underflowtrap)
348		    goto underflow;
349		}
350	    /* Now narrow it down to the nibble */
351	    if(Sgl_iszero_hiddenhigh3mantissa(result))
352		{
353		/* The lower nibble contains the normalizing one */
354		Sgl_leftshiftby4(result);
355		if((result_exponent -= 4) <= 0 && !underflowtrap)
356		    goto underflow;
357		}
358	    /* Select case were first bit is set (already normalized)
359	     * otherwise select the proper shift. */
360	    if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
361		{
362		/* Already normalized */
363		if(result_exponent <= 0) goto underflow;
364		Sgl_set_sign(result,/*using*/sign_save);
365		Sgl_set_exponent(result,/*using*/result_exponent);
366		*dstptr = result;
367		return(NOEXCEPTION);
368		}
369	    Sgl_sethigh4bits(result,/*using*/sign_save);
370	    switch(jumpsize)
371		{
372		case 1:
373		    {
374		    Sgl_leftshiftby3(result);
375		    result_exponent -= 3;
376		    break;
377		    }
378		case 2:
379		case 3:
380		    {
381		    Sgl_leftshiftby2(result);
382		    result_exponent -= 2;
383		    break;
384		    }
385		case 4:
386		case 5:
387		case 6:
388		case 7:
389		    {
390		    Sgl_leftshiftby1(result);
391		    result_exponent -= 1;
392		    break;
393		    }
394		}
395	    if(result_exponent > 0)
396		{
397		Sgl_set_exponent(result,/*using*/result_exponent);
398		*dstptr = result;
399		return(NOEXCEPTION); /* Sign bit is already set */
400		}
401	    /* Fixup potential underflows */
402	  underflow:
403	    if(Is_underflowtrap_enabled())
404		{
405		Sgl_set_sign(result,sign_save);
406                Sgl_setwrapped_exponent(result,result_exponent,unfl);
407		*dstptr = result;
408		/* inexact = FALSE; */
409		return(UNDERFLOWEXCEPTION);
410		}
411	    /*
412	     * Since we cannot get an inexact denormalized result,
413	     * we can now return.
414	     */
415	    Sgl_right_align(result,/*by*/(1-result_exponent),extent);
416	    Sgl_clear_signexponent(result);
417	    Sgl_set_sign(result,sign_save);
418	    *dstptr = result;
419	    return(NOEXCEPTION);
420	    } /* end if(hidden...)... */
421	/* Fall through and round */
422	} /* end if(save < 0)... */
423    else
424	{
425	/* Add magnitudes */
426	Sgl_addition(left,right,/*to*/result);
427	if(Sgl_isone_hiddenoverflow(result))
428	    {
429	    /* Prenormalization required. */
430	    Sgl_rightshiftby1_withextent(result,extent,extent);
431	    Sgl_arithrightshiftby1(result);
432	    result_exponent++;
433	    } /* end if hiddenoverflow... */
434	} /* end else ...add magnitudes... */
435
436    /* Round the result.  If the extension is all zeros,then the result is
437     * exact.  Otherwise round in the correct direction.  No underflow is
438     * possible. If a postnormalization is necessary, then the mantissa is
439     * all zeros so no shift is needed. */
440  round:
441    if(Ext_isnotzero(extent))
442	{
443	inexact = TRUE;
444	switch(Rounding_mode())
445	    {
446	    case ROUNDNEAREST: /* The default. */
447	    if(Ext_isone_sign(extent))
448		{
449		/* at least 1/2 ulp */
450		if(Ext_isnotzero_lower(extent)  ||
451		  Sgl_isone_lowmantissa(result))
452		    {
453		    /* either exactly half way and odd or more than 1/2ulp */
454		    Sgl_increment(result);
455		    }
456		}
457	    break;
458
459	    case ROUNDPLUS:
460	    if(Sgl_iszero_sign(result))
461		{
462		/* Round up positive results */
463		Sgl_increment(result);
464		}
465	    break;
466
467	    case ROUNDMINUS:
468	    if(Sgl_isone_sign(result))
469		{
470		/* Round down negative results */
471		Sgl_increment(result);
472		}
473
474	    case ROUNDZERO:;
475	    /* truncate is simple */
476	    } /* end switch... */
477	if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
478	}
479    if(result_exponent == SGL_INFINITY_EXPONENT)
480        {
481        /* Overflow */
482        if(Is_overflowtrap_enabled())
483	    {
484	    Sgl_setwrapped_exponent(result,result_exponent,ovfl);
485	    *dstptr = result;
486	    if (inexact)
487		if (Is_inexacttrap_enabled())
488		    return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
489		else Set_inexactflag();
490	    return(OVERFLOWEXCEPTION);
491	    }
492        else
493	    {
494	    Set_overflowflag();
495	    inexact = TRUE;
496	    Sgl_setoverflow(result);
497	    }
498	}
499    else Sgl_set_exponent(result,result_exponent);
500    *dstptr = result;
501    if(inexact)
502	if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
503	else Set_inexactflag();
504    return(NOEXCEPTION);
505    }
506