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Linux/arch/parisc/math-emu/dfsub.c

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  1 /*
  2  * Linux/PA-RISC Project (http://www.parisc-linux.org/)
  3  *
  4  * Floating-point emulation code
  5  *  Copyright (C) 2001 Hewlett-Packard (Paul Bame) <bame@debian.org>
  6  *
  7  *    This program is free software; you can redistribute it and/or modify
  8  *    it under the terms of the GNU General Public License as published by
  9  *    the Free Software Foundation; either version 2, or (at your option)
 10  *    any later version.
 11  *
 12  *    This program is distributed in the hope that it will be useful,
 13  *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 14  *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 15  *    GNU General Public License for more details.
 16  *
 17  *    You should have received a copy of the GNU General Public License
 18  *    along with this program; if not, write to the Free Software
 19  *    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 20  */
 21 /*
 22  * BEGIN_DESC
 23  *
 24  *  File:
 25  *      @(#)    pa/spmath/dfsub.c               $Revision: 1.1 $
 26  *
 27  *  Purpose:
 28  *      Double_subtract: subtract two double precision values.
 29  *
 30  *  External Interfaces:
 31  *      dbl_fsub(leftptr, rightptr, dstptr, status)
 32  *
 33  *  Internal Interfaces:
 34  *
 35  *  Theory:
 36  *      <<please update with a overview of the operation of this file>>
 37  *
 38  * END_DESC
 39 */
 40 
 41 
 42 #include "float.h"
 43 #include "dbl_float.h"
 44 
 45 /*
 46  * Double_subtract: subtract two double precision values.
 47  */
 48 int
 49 dbl_fsub(
 50             dbl_floating_point *leftptr,
 51             dbl_floating_point *rightptr,
 52             dbl_floating_point *dstptr,
 53             unsigned int *status)
 54     {
 55     register unsigned int signless_upper_left, signless_upper_right, save;
 56     register unsigned int leftp1, leftp2, rightp1, rightp2, extent;
 57     register unsigned int resultp1 = 0, resultp2 = 0;
 58     
 59     register int result_exponent, right_exponent, diff_exponent;
 60     register int sign_save, jumpsize;
 61     register boolean inexact = FALSE, underflowtrap;
 62         
 63     /* Create local copies of the numbers */
 64     Dbl_copyfromptr(leftptr,leftp1,leftp2);
 65     Dbl_copyfromptr(rightptr,rightp1,rightp2);
 66 
 67     /* A zero "save" helps discover equal operands (for later),  *
 68      * and is used in swapping operands (if needed).             */
 69     Dbl_xortointp1(leftp1,rightp1,/*to*/save);
 70 
 71     /*
 72      * check first operand for NaN's or infinity
 73      */
 74     if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT)
 75         {
 76         if (Dbl_iszero_mantissa(leftp1,leftp2)) 
 77             {
 78             if (Dbl_isnotnan(rightp1,rightp2)) 
 79                 {
 80                 if (Dbl_isinfinity(rightp1,rightp2) && save==0) 
 81                     {
 82                     /* 
 83                      * invalid since operands are same signed infinity's
 84                      */
 85                     if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
 86                     Set_invalidflag();
 87                     Dbl_makequietnan(resultp1,resultp2);
 88                     Dbl_copytoptr(resultp1,resultp2,dstptr);
 89                     return(NOEXCEPTION);
 90                     }
 91                 /*
 92                  * return infinity
 93                  */
 94                 Dbl_copytoptr(leftp1,leftp2,dstptr);
 95                 return(NOEXCEPTION);
 96                 }
 97             }
 98         else 
 99             {
100             /*
101              * is NaN; signaling or quiet?
102              */
103             if (Dbl_isone_signaling(leftp1)) 
104                 {
105                 /* trap if INVALIDTRAP enabled */
106                 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
107                 /* make NaN quiet */
108                 Set_invalidflag();
109                 Dbl_set_quiet(leftp1);
110                 }
111             /* 
112              * is second operand a signaling NaN? 
113              */
114             else if (Dbl_is_signalingnan(rightp1)) 
115                 {
116                 /* trap if INVALIDTRAP enabled */
117                 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
118                 /* make NaN quiet */
119                 Set_invalidflag();
120                 Dbl_set_quiet(rightp1);
121                 Dbl_copytoptr(rightp1,rightp2,dstptr);
122                 return(NOEXCEPTION);
123                 }
124             /*
125              * return quiet NaN
126              */
127             Dbl_copytoptr(leftp1,leftp2,dstptr);
128             return(NOEXCEPTION);
129             }
130         } /* End left NaN or Infinity processing */
131     /*
132      * check second operand for NaN's or infinity
133      */
134     if (Dbl_isinfinity_exponent(rightp1)) 
135         {
136         if (Dbl_iszero_mantissa(rightp1,rightp2)) 
137             {
138             /* return infinity */
139             Dbl_invert_sign(rightp1);
140             Dbl_copytoptr(rightp1,rightp2,dstptr);
141             return(NOEXCEPTION);
142             }
143         /*
144          * is NaN; signaling or quiet?
145          */
146         if (Dbl_isone_signaling(rightp1)) 
147             {
148             /* trap if INVALIDTRAP enabled */
149             if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
150             /* make NaN quiet */
151             Set_invalidflag();
152             Dbl_set_quiet(rightp1);
153             }
154         /*
155          * return quiet NaN
156          */
157         Dbl_copytoptr(rightp1,rightp2,dstptr);
158         return(NOEXCEPTION);
159         } /* End right NaN or Infinity processing */
160 
161     /* Invariant: Must be dealing with finite numbers */
162 
163     /* Compare operands by removing the sign */
164     Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left);
165     Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right);
166 
167     /* sign difference selects add or sub operation. */
168     if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right))
169         {
170         /* Set the left operand to the larger one by XOR swap *
171          *  First finish the first word using "save"          */
172         Dbl_xorfromintp1(save,rightp1,/*to*/rightp1);
173         Dbl_xorfromintp1(save,leftp1,/*to*/leftp1);
174         Dbl_swap_lower(leftp2,rightp2);
175         result_exponent = Dbl_exponent(leftp1);
176         Dbl_invert_sign(leftp1);
177         }
178     /* Invariant:  left is not smaller than right. */ 
179 
180     if((right_exponent = Dbl_exponent(rightp1)) == 0)
181         {
182         /* Denormalized operands.  First look for zeroes */
183         if(Dbl_iszero_mantissa(rightp1,rightp2)) 
184             {
185             /* right is zero */
186             if(Dbl_iszero_exponentmantissa(leftp1,leftp2))
187                 {
188                 /* Both operands are zeros */
189                 Dbl_invert_sign(rightp1);
190                 if(Is_rounding_mode(ROUNDMINUS))
191                     {
192                     Dbl_or_signs(leftp1,/*with*/rightp1);
193                     }
194                 else
195                     {
196                     Dbl_and_signs(leftp1,/*with*/rightp1);
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 = Dbl_signextendedsign(leftp1);
208                     Dbl_leftshiftby1(leftp1,leftp2);
209                     Dbl_normalize(leftp1,leftp2,result_exponent);
210                     Dbl_set_sign(leftp1,/*using*/sign_save);
211                     Dbl_setwrapped_exponent(leftp1,result_exponent,unfl);
212                     Dbl_copytoptr(leftp1,leftp2,dstptr);
213                     /* inexact = FALSE */
214                     return(UNDERFLOWEXCEPTION);
215                     }
216                 }
217             Dbl_copytoptr(leftp1,leftp2,dstptr);
218             return(NOEXCEPTION);
219             }
220 
221         /* Neither are zeroes */
222         Dbl_clear_sign(rightp1);        /* 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                 Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2,
231                  /*into*/resultp1,resultp2);
232                 if(Dbl_iszero_mantissa(resultp1,resultp2))
233                     {
234                     if(Is_rounding_mode(ROUNDMINUS))
235                         {
236                         Dbl_setone_sign(resultp1);
237                         }
238                     else
239                         {
240                         Dbl_setzero_sign(resultp1);
241                         }
242                     Dbl_copytoptr(resultp1,resultp2,dstptr);
243                     return(NOEXCEPTION);
244                     }
245                 }
246             else
247                 {
248                 Dbl_addition(leftp1,leftp2,rightp1,rightp2,
249                  /*into*/resultp1,resultp2);
250                 if(Dbl_isone_hidden(resultp1))
251                     {
252                     Dbl_copytoptr(resultp1,resultp2,dstptr);
253                     return(NOEXCEPTION);
254                     }
255                 }
256             if(Is_underflowtrap_enabled())
257                 {
258                 /* need to normalize result */
259                 sign_save = Dbl_signextendedsign(resultp1);
260                 Dbl_leftshiftby1(resultp1,resultp2);
261                 Dbl_normalize(resultp1,resultp2,result_exponent);
262                 Dbl_set_sign(resultp1,/*using*/sign_save);
263                 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl);
264                 Dbl_copytoptr(resultp1,resultp2,dstptr);
265                 /* inexact = FALSE */
266                 return(UNDERFLOWEXCEPTION);
267                 }
268             Dbl_copytoptr(resultp1,resultp2,dstptr);
269             return(NOEXCEPTION);
270             }
271         right_exponent = 1;     /* Set exponent to reflect different bias
272                                  * with denomalized numbers. */
273         }
274     else
275         {
276         Dbl_clear_signexponent_set_hidden(rightp1);
277         }
278     Dbl_clear_exponent_set_hidden(leftp1);
279     diff_exponent = result_exponent - right_exponent;
280 
281     /* 
282      * Special case alignment of operands that would force alignment 
283      * beyond the extent of the extension.  A further optimization
284      * could special case this but only reduces the path length for this
285      * infrequent case.
286      */
287     if(diff_exponent > DBL_THRESHOLD)
288         {
289         diff_exponent = DBL_THRESHOLD;
290         }
291     
292     /* Align right operand by shifting to right */
293     Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent,
294      /*and lower to*/extent);
295 
296     /* Treat sum and difference of the operands separately. */
297     if( (/*signed*/int) save >= 0 )
298         {
299         /*
300          * Difference of the two operands.  Their can be no overflow.  A
301          * borrow can occur out of the hidden bit and force a post
302          * normalization phase.
303          */
304         Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2,
305          /*with*/extent,/*into*/resultp1,resultp2);
306         if(Dbl_iszero_hidden(resultp1))
307             {
308             /* Handle normalization */
309             /* A straight forward algorithm would now shift the result
310              * and extension left until the hidden bit becomes one.  Not
311              * all of the extension bits need participate in the shift.
312              * Only the two most significant bits (round and guard) are
313              * needed.  If only a single shift is needed then the guard
314              * bit becomes a significant low order bit and the extension
315              * must participate in the rounding.  If more than a single 
316              * shift is needed, then all bits to the right of the guard 
317              * bit are zeros, and the guard bit may or may not be zero. */
318             sign_save = Dbl_signextendedsign(resultp1);
319             Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2);
320 
321             /* Need to check for a zero result.  The sign and exponent
322              * fields have already been zeroed.  The more efficient test
323              * of the full object can be used.
324              */
325             if(Dbl_iszero(resultp1,resultp2))
326                 /* Must have been "x-x" or "x+(-x)". */
327                 {
328                 if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1);
329                 Dbl_copytoptr(resultp1,resultp2,dstptr);
330                 return(NOEXCEPTION);
331                 }
332             result_exponent--;
333             /* Look to see if normalization is finished. */
334             if(Dbl_isone_hidden(resultp1))
335                 {
336                 if(result_exponent==0)
337                     {
338                     /* Denormalized, exponent should be zero.  Left operand *
339                      * was normalized, so extent (guard, round) was zero    */
340                     goto underflow;
341                     }
342                 else
343                     {
344                     /* No further normalization is needed. */
345                     Dbl_set_sign(resultp1,/*using*/sign_save);
346                     Ext_leftshiftby1(extent);
347                     goto round;
348                     }
349                 }
350 
351             /* Check for denormalized, exponent should be zero.  Left    *
352              * operand was normalized, so extent (guard, round) was zero */
353             if(!(underflowtrap = Is_underflowtrap_enabled()) &&
354                result_exponent==0) goto underflow;
355 
356             /* Shift extension to complete one bit of normalization and
357              * update exponent. */
358             Ext_leftshiftby1(extent);
359 
360             /* Discover first one bit to determine shift amount.  Use a
361              * modified binary search.  We have already shifted the result
362              * one position right and still not found a one so the remainder
363              * of the extension must be zero and simplifies rounding. */
364             /* Scan bytes */
365             while(Dbl_iszero_hiddenhigh7mantissa(resultp1))
366                 {
367                 Dbl_leftshiftby8(resultp1,resultp2);
368                 if((result_exponent -= 8) <= 0  && !underflowtrap)
369                     goto underflow;
370                 }
371             /* Now narrow it down to the nibble */
372             if(Dbl_iszero_hiddenhigh3mantissa(resultp1))
373                 {
374                 /* The lower nibble contains the normalizing one */
375                 Dbl_leftshiftby4(resultp1,resultp2);
376                 if((result_exponent -= 4) <= 0 && !underflowtrap)
377                     goto underflow;
378                 }
379             /* Select case were first bit is set (already normalized)
380              * otherwise select the proper shift. */
381             if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7)
382                 {
383                 /* Already normalized */
384                 if(result_exponent <= 0) goto underflow;
385                 Dbl_set_sign(resultp1,/*using*/sign_save);
386                 Dbl_set_exponent(resultp1,/*using*/result_exponent);
387                 Dbl_copytoptr(resultp1,resultp2,dstptr);
388                 return(NOEXCEPTION);
389                 }
390             Dbl_sethigh4bits(resultp1,/*using*/sign_save);
391             switch(jumpsize) 
392                 {
393                 case 1:
394                     {
395                     Dbl_leftshiftby3(resultp1,resultp2);
396                     result_exponent -= 3;
397                     break;
398                     }
399                 case 2:
400                 case 3:
401                     {
402                     Dbl_leftshiftby2(resultp1,resultp2);
403                     result_exponent -= 2;
404                     break;
405                     }
406                 case 4:
407                 case 5:
408                 case 6:
409                 case 7:
410                     {
411                     Dbl_leftshiftby1(resultp1,resultp2);
412                     result_exponent -= 1;
413                     break;
414                     }
415                 }
416             if(result_exponent > 0) 
417                 {
418                 Dbl_set_exponent(resultp1,/*using*/result_exponent);
419                 Dbl_copytoptr(resultp1,resultp2,dstptr);
420                 return(NOEXCEPTION);            /* Sign bit is already set */
421                 }
422             /* Fixup potential underflows */
423           underflow:
424             if(Is_underflowtrap_enabled())
425                 {
426                 Dbl_set_sign(resultp1,sign_save);
427                 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl);
428                 Dbl_copytoptr(resultp1,resultp2,dstptr);
429                 /* inexact = FALSE */
430                 return(UNDERFLOWEXCEPTION);
431                 }
432             /* 
433              * Since we cannot get an inexact denormalized result,
434              * we can now return.
435              */
436             Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent);
437             Dbl_clear_signexponent(resultp1);
438             Dbl_set_sign(resultp1,sign_save);
439             Dbl_copytoptr(resultp1,resultp2,dstptr);
440             return(NOEXCEPTION);
441             } /* end if(hidden...)... */
442         /* Fall through and round */
443         } /* end if(save >= 0)... */
444     else 
445         {
446         /* Subtract magnitudes */
447         Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2);
448         if(Dbl_isone_hiddenoverflow(resultp1))
449             {
450             /* Prenormalization required. */
451             Dbl_rightshiftby1_withextent(resultp2,extent,extent);
452             Dbl_arithrightshiftby1(resultp1,resultp2);
453             result_exponent++;
454             } /* end if hiddenoverflow... */
455         } /* end else ...subtract magnitudes... */
456     
457     /* Round the result.  If the extension is all zeros,then the result is
458      * exact.  Otherwise round in the correct direction.  No underflow is
459      * possible. If a postnormalization is necessary, then the mantissa is
460      * all zeros so no shift is needed. */
461   round:
462     if(Ext_isnotzero(extent))
463         {
464         inexact = TRUE;
465         switch(Rounding_mode())
466             {
467             case ROUNDNEAREST: /* The default. */
468             if(Ext_isone_sign(extent))
469                 {
470                 /* at least 1/2 ulp */
471                 if(Ext_isnotzero_lower(extent)  ||
472                   Dbl_isone_lowmantissap2(resultp2))
473                     {
474                     /* either exactly half way and odd or more than 1/2ulp */
475                     Dbl_increment(resultp1,resultp2);
476                     }
477                 }
478             break;
479 
480             case ROUNDPLUS:
481             if(Dbl_iszero_sign(resultp1))
482                 {
483                 /* Round up positive results */
484                 Dbl_increment(resultp1,resultp2);
485                 }
486             break;
487             
488             case ROUNDMINUS:
489             if(Dbl_isone_sign(resultp1))
490                 {
491                 /* Round down negative results */
492                 Dbl_increment(resultp1,resultp2);
493                 }
494             
495             case ROUNDZERO:;
496             /* truncate is simple */
497             } /* end switch... */
498         if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++;
499         }
500     if(result_exponent == DBL_INFINITY_EXPONENT)
501         {
502         /* Overflow */
503         if(Is_overflowtrap_enabled())
504             {
505             Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl);
506             Dbl_copytoptr(resultp1,resultp2,dstptr);
507             if (inexact)
508             if (Is_inexacttrap_enabled())
509                 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
510                 else Set_inexactflag();
511             return(OVERFLOWEXCEPTION);
512             }
513         else
514             {
515             inexact = TRUE;
516             Set_overflowflag();
517             Dbl_setoverflow(resultp1,resultp2);
518             }
519         }
520     else Dbl_set_exponent(resultp1,result_exponent);
521     Dbl_copytoptr(resultp1,resultp2,dstptr);
522     if(inexact) 
523         if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
524         else Set_inexactflag();
525     return(NOEXCEPTION);
526     }
527 

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