1/*	$NetBSD: sfsub.c,v 1.4 2007/02/22 05:46:31 thorpej Exp $	*/
2
3/*	$OpenBSD: sfsub.c,v 1.4 2001/03/29 03:58:19 mickey Exp $	*/
4
5/*
6 * Copyright 1996 1995 by Open Software Foundation, Inc.
7 *              All Rights Reserved
8 *
9 * Permission to use, copy, modify, and distribute this software and
10 * its documentation for any purpose and without fee is hereby granted,
11 * provided that the above copyright notice appears in all copies and
12 * that both the copyright notice and this permission notice appear in
13 * supporting documentation.
14 *
15 * OSF DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE
16 * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
17 * FOR A PARTICULAR PURPOSE.
18 *
19 * IN NO EVENT SHALL OSF BE LIABLE FOR ANY SPECIAL, INDIRECT, OR
20 * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
21 * LOSS OF USE, DATA OR PROFITS, WHETHER IN ACTION OF CONTRACT,
22 * NEGLIGENCE, OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
23 * WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
24 *
25 */
26/*
27 * pmk1.1
28 */
29/*
30 * (c) Copyright 1986 HEWLETT-PACKARD COMPANY
31 *
32 * To anyone who acknowledges that this file is provided "AS IS"
33 * without any express or implied warranty:
34 *     permission to use, copy, modify, and distribute this file
35 * for any purpose is hereby granted without fee, provided that
36 * the above copyright notice and this notice appears in all
37 * copies, and that the name of Hewlett-Packard Company not be
38 * used in advertising or publicity pertaining to distribution
39 * of the software without specific, written prior permission.
40 * Hewlett-Packard Company makes no representations about the
41 * suitability of this software for any purpose.
42 */
43
44#include <sys/cdefs.h>
45__KERNEL_RCSID(0, "$NetBSD: sfsub.c,v 1.4 2007/02/22 05:46:31 thorpej Exp $");
46
47#include "../spmath/float.h"
48#include "../spmath/sgl_float.h"
49
50/*
51 * Single_subtract: subtract two single precision values.
52 */
53int
54sgl_fsub(sgl_floating_point *leftptr, sgl_floating_point *rightptr,
55    sgl_floating_point *dstptr, unsigned int *status)
56{
57    register unsigned int left, right, result, extent;
58    register unsigned int signless_upper_left, signless_upper_right, save;
59
60    register int result_exponent, right_exponent, diff_exponent;
61    register int sign_save, jumpsize;
62    register int inexact = false, underflowtrap;
63
64    /* Create local copies of the numbers */
65    left = *leftptr;
66    right = *rightptr;
67
68    /* A zero "save" helps discover equal operands (for later),	*
69     * and is used in swapping operands (if needed).		*/
70    Sgl_xortointp1(left,right,/*to*/save);
71
72    /*
73     * check first operand for NaN's or infinity
74     */
75    if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
76	{
77	if (Sgl_iszero_mantissa(left))
78	    {
79	    if (Sgl_isnotnan(right))
80		{
81		if (Sgl_isinfinity(right) && save==0)
82		    {
83		    /*
84		     * invalid since operands are same signed infinity's
85		     */
86		    if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
87		    Set_invalidflag();
88		    Sgl_makequietnan(result);
89		    *dstptr = result;
90		    return(NOEXCEPTION);
91		    }
92		/*
93		 * return infinity
94		 */
95		*dstptr = left;
96		return(NOEXCEPTION);
97		}
98	    }
99	else
100	    {
101	    /*
102	     * is NaN; signaling or quiet?
103	     */
104	    if (Sgl_isone_signaling(left))
105		{
106		/* trap if INVALIDTRAP enabled */
107		if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
108		/* make NaN quiet */
109		Set_invalidflag();
110		Sgl_set_quiet(left);
111		}
112	    /*
113	     * is second operand a signaling NaN?
114	     */
115	    else if (Sgl_is_signalingnan(right))
116		{
117		/* trap if INVALIDTRAP enabled */
118		if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
119		/* make NaN quiet */
120		Set_invalidflag();
121		Sgl_set_quiet(right);
122		*dstptr = right;
123		return(NOEXCEPTION);
124		}
125	    /*
126	     * return quiet NaN
127	     */
128	    *dstptr = left;
129	    return(NOEXCEPTION);
130	    }
131	} /* End left NaN or Infinity processing */
132    /*
133     * check second operand for NaN's or infinity
134     */
135    if (Sgl_isinfinity_exponent(right))
136	{
137	if (Sgl_iszero_mantissa(right))
138	    {
139	    /* return infinity */
140	    Sgl_invert_sign(right);
141	    *dstptr = right;
142	    return(NOEXCEPTION);
143	    }
144	/*
145	 * is NaN; signaling or quiet?
146	 */
147	if (Sgl_isone_signaling(right))
148	    {
149	    /* trap if INVALIDTRAP enabled */
150	    if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
151	    /* make NaN quiet */
152	    Set_invalidflag();
153	    Sgl_set_quiet(right);
154	    }
155	/*
156	 * return quiet NaN
157	 */
158	*dstptr = right;
159	return(NOEXCEPTION);
160	} /* End right NaN or Infinity processing */
161
162    /* Invariant: Must be dealing with finite numbers */
163
164    /* Compare operands by removing the sign */
165    Sgl_copytoint_exponentmantissa(left,signless_upper_left);
166    Sgl_copytoint_exponentmantissa(right,signless_upper_right);
167
168    /* sign difference selects sub or add operation. */
169    if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
170	{
171	/* Set the left operand to the larger one by XOR swap *
172	 *  First finish the first word using "save"	  */
173	Sgl_xorfromintp1(save,right,/*to*/right);
174	Sgl_xorfromintp1(save,left,/*to*/left);
175	result_exponent = Sgl_exponent(left);
176	Sgl_invert_sign(left);
177	}
178    /* Invariant:  left is not smaller than right. */
179
180    if((right_exponent = Sgl_exponent(right)) == 0)
181	{
182	/* Denormalized operands.  First look for zeroes */
183	if(Sgl_iszero_mantissa(right))
184	    {
185	    /* right is zero */
186	    if(Sgl_iszero_exponentmantissa(left))
187		{
188		/* Both operands are zeros */
189		Sgl_invert_sign(right);
190		if(Is_rounding_mode(ROUNDMINUS))
191		    {
192		    Sgl_or_signs(left,/*with*/right);
193		    }
194		else
195		    {
196		    Sgl_and_signs(left,/*with*/right);
197		    }
198		}
199	    else
200		{
201		/* Left is not a zero and must be the result.  Trapped
202		 * underflows are signaled if left is denormalized.  Result
203		 * is always exact. */
204		if( (result_exponent == 0) && Is_underflowtrap_enabled() )
205		    {
206		    /* need to normalize results mantissa */
207		    sign_save = Sgl_signextendedsign(left);
208		    Sgl_leftshiftby1(left);
209		    Sgl_normalize(left,result_exponent);
210		    Sgl_set_sign(left,/*using*/sign_save);
211		    Sgl_setwrapped_exponent(left,result_exponent,unfl);
212		    *dstptr = left;
213		    /* inexact = false */
214		    return(UNDERFLOWEXCEPTION);
215		    }
216		}
217	    *dstptr = left;
218	    return(NOEXCEPTION);
219	    }
220
221	/* Neither are zeroes */
222	Sgl_clear_sign(right);	/* Exponent is already cleared */
223	if(result_exponent == 0 )
224	    {
225	    /* Both operands are denormalized.  The result must be exact
226	     * and is simply calculated.  A sum could become normalized and a
227	     * difference could cancel to a true zero. */
228	    if( (/*signed*/int) save >= 0 )
229		{
230		Sgl_subtract(left,/*minus*/right,/*into*/result);
231		if(Sgl_iszero_mantissa(result))
232		    {
233		    if(Is_rounding_mode(ROUNDMINUS))
234			{
235			Sgl_setone_sign(result);
236			}
237		    else
238			{
239			Sgl_setzero_sign(result);
240			}
241		    *dstptr = result;
242		    return(NOEXCEPTION);
243		    }
244		}
245	    else
246		{
247		Sgl_addition(left,right,/*into*/result);
248		if(Sgl_isone_hidden(result))
249		    {
250		    *dstptr = result;
251		    return(NOEXCEPTION);
252		    }
253		}
254	    if(Is_underflowtrap_enabled())
255		{
256		/* need to normalize result */
257		sign_save = Sgl_signextendedsign(result);
258		Sgl_leftshiftby1(result);
259		Sgl_normalize(result,result_exponent);
260		Sgl_set_sign(result,/*using*/sign_save);
261		Sgl_setwrapped_exponent(result,result_exponent,unfl);
262		*dstptr = result;
263		/* inexact = false */
264		return(UNDERFLOWEXCEPTION);
265		}
266	    *dstptr = result;
267	    return(NOEXCEPTION);
268	    }
269	right_exponent = 1;	/* Set exponent to reflect different bias
270				 * with denomalized numbers. */
271	}
272    else
273	{
274	Sgl_clear_signexponent_set_hidden(right);
275	}
276    Sgl_clear_exponent_set_hidden(left);
277    diff_exponent = result_exponent - right_exponent;
278
279    /*
280     * Special case alignment of operands that would force alignment
281     * beyond the extent of the extension.  A further optimization
282     * could special case this but only reduces the path length for this
283     * infrequent case.
284     */
285    if(diff_exponent > SGL_THRESHOLD)
286	{
287	diff_exponent = SGL_THRESHOLD;
288	}
289
290    /* Align right operand by shifting to right */
291    Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
292      /*and lower to*/extent);
293
294    /* Treat sum and difference of the operands separately. */
295    if( (/*signed*/int) save >= 0 )
296	{
297	/*
298	 * Difference of the two operands.  Their can be no overflow.  A
299	 * borrow can occur out of the hidden bit and force a post
300	 * normalization phase.
301	 */
302	Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
303	if(Sgl_iszero_hidden(result))
304	    {
305	    /* Handle normalization */
306	    /* A straight foward 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 = Sgl_signextendedsign(result);
316	    Sgl_leftshiftby1_withextent(result,extent,result);
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(Sgl_iszero(result))
323		/* Must have been "x-x" or "x+(-x)". */
324		{
325		if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
326		*dstptr = result;
327		return(NOEXCEPTION);
328		}
329	    result_exponent--;
330	    /* Look to see if normalization is finished. */
331	    if(Sgl_isone_hidden(result))
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		    Sgl_set_sign(result,/*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(Sgl_iszero_hiddenhigh7mantissa(result))
363		{
364		Sgl_leftshiftby8(result);
365		if((result_exponent -= 8) <= 0  && !underflowtrap)
366		    goto underflow;
367		}
368	    /* Now narrow it down to the nibble */
369	    if(Sgl_iszero_hiddenhigh3mantissa(result))
370		{
371		/* The lower nibble contains the normalizing one */
372		Sgl_leftshiftby4(result);
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 = Sgl_hiddenhigh3mantissa(result)) > 7)
379		{
380		/* Already normalized */
381		if(result_exponent <= 0) goto underflow;
382		Sgl_set_sign(result,/*using*/sign_save);
383		Sgl_set_exponent(result,/*using*/result_exponent);
384		*dstptr = result;
385		return(NOEXCEPTION);
386		}
387	    Sgl_sethigh4bits(result,/*using*/sign_save);
388	    switch(jumpsize)
389		{
390		case 1:
391		    {
392		    Sgl_leftshiftby3(result);
393		    result_exponent -= 3;
394		    break;
395		    }
396		case 2:
397		case 3:
398		    {
399		    Sgl_leftshiftby2(result);
400		    result_exponent -= 2;
401		    break;
402		    }
403		case 4:
404		case 5:
405		case 6:
406		case 7:
407		    {
408		    Sgl_leftshiftby1(result);
409		    result_exponent -= 1;
410		    break;
411		    }
412		}
413	    if(result_exponent > 0)
414		{
415		Sgl_set_exponent(result,/*using*/result_exponent);
416		*dstptr = result;	/* Sign bit is already set */
417		return(NOEXCEPTION);
418		}
419	    /* Fixup potential underflows */
420	  underflow:
421	    if(Is_underflowtrap_enabled())
422		{
423		Sgl_set_sign(result,sign_save);
424		Sgl_setwrapped_exponent(result,result_exponent,unfl);
425		*dstptr = result;
426		/* inexact = false */
427		return(UNDERFLOWEXCEPTION);
428		}
429	    /*
430	     * Since we cannot get an inexact denormalized result,
431	     * we can now return.
432	     */
433	    Sgl_right_align(result,/*by*/(1-result_exponent),extent);
434	    Sgl_clear_signexponent(result);
435	    Sgl_set_sign(result,sign_save);
436	    *dstptr = result;
437	    return(NOEXCEPTION);
438	    } /* end if(hidden...)... */
439	/* Fall through and round */
440	} /* end if(save >= 0)... */
441    else
442	{
443	/* Add magnitudes */
444	Sgl_addition(left,right,/*to*/result);
445	if(Sgl_isone_hiddenoverflow(result))
446	    {
447	    /* Prenormalization required. */
448	    Sgl_rightshiftby1_withextent(result,extent,extent);
449	    Sgl_arithrightshiftby1(result);
450	    result_exponent++;
451	    } /* end if hiddenoverflow... */
452	} /* end else ...sub 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		  Sgl_isone_lowmantissa(result))
470		    {
471		    /* either exactly half way and odd or more than 1/2ulp */
472		    Sgl_increment(result);
473		    }
474		}
475	    break;
476
477	    case ROUNDPLUS:
478	    if(Sgl_iszero_sign(result))
479		{
480		/* Round up positive results */
481		Sgl_increment(result);
482		}
483	    break;
484
485	    case ROUNDMINUS:
486	    if(Sgl_isone_sign(result))
487		{
488		/* Round down negative results */
489		Sgl_increment(result);
490		}
491
492	    case ROUNDZERO:;
493	    /* truncate is simple */
494	    } /* end switch... */
495	if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
496	}
497    if(result_exponent == SGL_INFINITY_EXPONENT)
498	{
499	/* Overflow */
500	if(Is_overflowtrap_enabled())
501	    {
502	    Sgl_setwrapped_exponent(result,result_exponent,ovfl);
503	    *dstptr = result;
504	    if (inexact) {
505		if (Is_inexacttrap_enabled())
506		    return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
507		else Set_inexactflag();
508	    }
509	    return(OVERFLOWEXCEPTION);
510	    }
511	else
512	    {
513	    Set_overflowflag();
514	    inexact = true;
515	    Sgl_setoverflow(result);
516	    }
517	}
518    else Sgl_set_exponent(result,result_exponent);
519    *dstptr = result;
520    if(inexact) {
521	if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
522	else Set_inexactflag();
523    }
524    return(NOEXCEPTION);
525    }
526