xref: /openbmc/linux/arch/parisc/math-emu/sfadd.c (revision 7effbd18)
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  */
35 int
36 sgl_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