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1.1 nbrk 1: /* $OpenBSD: sfadd.c,v 1.6 2002/11/29 09:27:34 deraadt Exp $ */
2: /*
3: (c) Copyright 1986 HEWLETT-PACKARD COMPANY
4: To anyone who acknowledges that this file is provided "AS IS"
5: without any express or implied warranty:
6: permission to use, copy, modify, and distribute this file
7: for any purpose is hereby granted without fee, provided that
8: the above copyright notice and this notice appears in all
9: copies, and that the name of Hewlett-Packard Company not be
10: used in advertising or publicity pertaining to distribution
11: of the software without specific, written prior permission.
12: Hewlett-Packard Company makes no representations about the
13: suitability of this software for any purpose.
14: */
15: /* @(#)sfadd.c: Revision: 2.7.88.1 Date: 93/12/07 15:07:00 */
16:
17: #include "float.h"
18: #include "sgl_float.h"
19:
20: /*
21: * Single_add: add two single precision values.
22: */
23: int
24: sgl_fadd(leftptr, rightptr, dstptr, status)
25: sgl_floating_point *leftptr, *rightptr, *dstptr;
26: unsigned int *status;
27: {
28: register unsigned int left, right, result, extent;
29: register unsigned int signless_upper_left, signless_upper_right, save;
30:
31:
32: register int result_exponent, right_exponent, diff_exponent;
33: register int sign_save, jumpsize;
34: register int inexact = FALSE;
35: register int underflowtrap;
36:
37: /* Create local copies of the numbers */
38: left = *leftptr;
39: right = *rightptr;
40:
41: /* A zero "save" helps discover equal operands (for later), *
42: * and is used in swapping operands (if needed). */
43: Sgl_xortointp1(left,right,/*to*/save);
44:
45: /*
46: * check first operand for NaN's or infinity
47: */
48: if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
49: {
50: if (Sgl_iszero_mantissa(left))
51: {
52: if (Sgl_isnotnan(right))
53: {
54: if (Sgl_isinfinity(right) && save!=0)
55: {
56: /*
57: * invalid since operands are opposite signed infinity's
58: */
59: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
60: Set_invalidflag();
61: Sgl_makequietnan(result);
62: *dstptr = result;
63: return(NOEXCEPTION);
64: }
65: /*
66: * return infinity
67: */
68: *dstptr = left;
69: return(NOEXCEPTION);
70: }
71: }
72: else
73: {
74: /*
75: * is NaN; signaling or quiet?
76: */
77: if (Sgl_isone_signaling(left))
78: {
79: /* trap if INVALIDTRAP enabled */
80: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
81: /* make NaN quiet */
82: Set_invalidflag();
83: Sgl_set_quiet(left);
84: }
85: /*
86: * is second operand a signaling NaN?
87: */
88: else if (Sgl_is_signalingnan(right))
89: {
90: /* trap if INVALIDTRAP enabled */
91: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
92: /* make NaN quiet */
93: Set_invalidflag();
94: Sgl_set_quiet(right);
95: *dstptr = right;
96: return(NOEXCEPTION);
97: }
98: /*
99: * return quiet NaN
100: */
101: *dstptr = left;
102: return(NOEXCEPTION);
103: }
104: } /* End left NaN or Infinity processing */
105: /*
106: * check second operand for NaN's or infinity
107: */
108: if (Sgl_isinfinity_exponent(right))
109: {
110: if (Sgl_iszero_mantissa(right))
111: {
112: /* return infinity */
113: *dstptr = right;
114: return(NOEXCEPTION);
115: }
116: /*
117: * is NaN; signaling or quiet?
118: */
119: if (Sgl_isone_signaling(right))
120: {
121: /* trap if INVALIDTRAP enabled */
122: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
123: /* make NaN quiet */
124: Set_invalidflag();
125: Sgl_set_quiet(right);
126: }
127: /*
128: * return quiet NaN
129: */
130: *dstptr = right;
131: return(NOEXCEPTION);
132: } /* End right NaN or Infinity processing */
133:
134: /* Invariant: Must be dealing with finite numbers */
135:
136: /* Compare operands by removing the sign */
137: Sgl_copytoint_exponentmantissa(left,signless_upper_left);
138: Sgl_copytoint_exponentmantissa(right,signless_upper_right);
139:
140: /* sign difference selects add or sub operation. */
141: if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
142: {
143: /* Set the left operand to the larger one by XOR swap *
144: * First finish the first word using "save" */
145: Sgl_xorfromintp1(save,right,/*to*/right);
146: Sgl_xorfromintp1(save,left,/*to*/left);
147: result_exponent = Sgl_exponent(left);
148: }
149: /* Invariant: left is not smaller than right. */
150:
151: if((right_exponent = Sgl_exponent(right)) == 0)
152: {
153: /* Denormalized operands. First look for zeroes */
154: if(Sgl_iszero_mantissa(right))
155: {
156: /* right is zero */
157: if(Sgl_iszero_exponentmantissa(left))
158: {
159: /* Both operands are zeros */
160: if(Is_rounding_mode(ROUNDMINUS))
161: {
162: Sgl_or_signs(left,/*with*/right);
163: }
164: else
165: {
166: Sgl_and_signs(left,/*with*/right);
167: }
168: }
169: else
170: {
171: /* Left is not a zero and must be the result. Trapped
172: * underflows are signaled if left is denormalized. Result
173: * is always exact. */
174: if( (result_exponent == 0) && Is_underflowtrap_enabled() )
175: {
176: /* need to normalize results mantissa */
177: sign_save = Sgl_signextendedsign(left);
178: Sgl_leftshiftby1(left);
179: Sgl_normalize(left,result_exponent);
180: Sgl_set_sign(left,/*using*/sign_save);
181: Sgl_setwrapped_exponent(left,result_exponent,unfl);
182: *dstptr = left;
183: return(UNDERFLOWEXCEPTION);
184: }
185: }
186: *dstptr = left;
187: return(NOEXCEPTION);
188: }
189:
190: /* Neither are zeroes */
191: Sgl_clear_sign(right); /* Exponent is already cleared */
192: if(result_exponent == 0 )
193: {
194: /* Both operands are denormalized. The result must be exact
195: * and is simply calculated. A sum could become normalized and a
196: * difference could cancel to a true zero. */
197: if( (/*signed*/int) save < 0 )
198: {
199: Sgl_subtract(left,/*minus*/right,/*into*/result);
200: if(Sgl_iszero_mantissa(result))
201: {
202: if(Is_rounding_mode(ROUNDMINUS))
203: {
204: Sgl_setone_sign(result);
205: }
206: else
207: {
208: Sgl_setzero_sign(result);
209: }
210: *dstptr = result;
211: return(NOEXCEPTION);
212: }
213: }
214: else
215: {
216: Sgl_addition(left,right,/*into*/result);
217: if(Sgl_isone_hidden(result))
218: {
219: *dstptr = result;
220: return(NOEXCEPTION);
221: }
222: }
223: if(Is_underflowtrap_enabled())
224: {
225: /* need to normalize result */
226: sign_save = Sgl_signextendedsign(result);
227: Sgl_leftshiftby1(result);
228: Sgl_normalize(result,result_exponent);
229: Sgl_set_sign(result,/*using*/sign_save);
230: Sgl_setwrapped_exponent(result,result_exponent,unfl);
231: *dstptr = result;
232: return(UNDERFLOWEXCEPTION);
233: }
234: *dstptr = result;
235: return(NOEXCEPTION);
236: }
237: right_exponent = 1; /* Set exponent to reflect different bias
238: * with denomalized numbers. */
239: }
240: else
241: {
242: Sgl_clear_signexponent_set_hidden(right);
243: }
244: Sgl_clear_exponent_set_hidden(left);
245: diff_exponent = result_exponent - right_exponent;
246:
247: /*
248: * Special case alignment of operands that would force alignment
249: * beyond the extent of the extension. A further optimization
250: * could special case this but only reduces the path length for this
251: * infrequent case.
252: */
253: if(diff_exponent > SGL_THRESHOLD)
254: {
255: diff_exponent = SGL_THRESHOLD;
256: }
257:
258: /* Align right operand by shifting to right */
259: Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
260: /*and lower to*/extent);
261:
262: /* Treat sum and difference of the operands separately. */
263: if( (/*signed*/int) save < 0 )
264: {
265: /*
266: * Difference of the two operands. Their can be no overflow. A
267: * borrow can occur out of the hidden bit and force a post
268: * normalization phase.
269: */
270: Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
271: if(Sgl_iszero_hidden(result))
272: {
273: /* Handle normalization */
274: /* A straight forward algorithm would now shift the result
275: * and extension left until the hidden bit becomes one. Not
276: * all of the extension bits need participate in the shift.
277: * Only the two most significant bits (round and guard) are
278: * needed. If only a single shift is needed then the guard
279: * bit becomes a significant low order bit and the extension
280: * must participate in the rounding. If more than a single
281: * shift is needed, then all bits to the right of the guard
282: * bit are zeros, and the guard bit may or may not be zero. */
283: sign_save = Sgl_signextendedsign(result);
284: Sgl_leftshiftby1_withextent(result,extent,result);
285:
286: /* Need to check for a zero result. The sign and exponent
287: * fields have already been zeroed. The more efficient test
288: * of the full object can be used.
289: */
290: if(Sgl_iszero(result))
291: /* Must have been "x-x" or "x+(-x)". */
292: {
293: if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
294: *dstptr = result;
295: return(NOEXCEPTION);
296: }
297: result_exponent--;
298: /* Look to see if normalization is finished. */
299: if(Sgl_isone_hidden(result))
300: {
301: if(result_exponent==0)
302: {
303: /* Denormalized, exponent should be zero. Left operand *
304: * was normalized, so extent (guard, round) was zero */
305: goto underflow;
306: }
307: else
308: {
309: /* No further normalization is needed. */
310: Sgl_set_sign(result,/*using*/sign_save);
311: Ext_leftshiftby1(extent);
312: goto round;
313: }
314: }
315:
316: /* Check for denormalized, exponent should be zero. Left *
317: * operand was normalized, so extent (guard, round) was zero */
318: if(!(underflowtrap = Is_underflowtrap_enabled()) &&
319: result_exponent==0) goto underflow;
320:
321: /* Shift extension to complete one bit of normalization and
322: * update exponent. */
323: Ext_leftshiftby1(extent);
324:
325: /* Discover first one bit to determine shift amount. Use a
326: * modified binary search. We have already shifted the result
327: * one position right and still not found a one so the remainder
328: * of the extension must be zero and simplifies rounding. */
329: /* Scan bytes */
330: while(Sgl_iszero_hiddenhigh7mantissa(result))
331: {
332: Sgl_leftshiftby8(result);
333: if((result_exponent -= 8) <= 0 && !underflowtrap)
334: goto underflow;
335: }
336: /* Now narrow it down to the nibble */
337: if(Sgl_iszero_hiddenhigh3mantissa(result))
338: {
339: /* The lower nibble contains the normalizing one */
340: Sgl_leftshiftby4(result);
341: if((result_exponent -= 4) <= 0 && !underflowtrap)
342: goto underflow;
343: }
344: /* Select case were first bit is set (already normalized)
345: * otherwise select the proper shift. */
346: if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
347: {
348: /* Already normalized */
349: if(result_exponent <= 0) goto underflow;
350: Sgl_set_sign(result,/*using*/sign_save);
351: Sgl_set_exponent(result,/*using*/result_exponent);
352: *dstptr = result;
353: return(NOEXCEPTION);
354: }
355: Sgl_sethigh4bits(result,/*using*/sign_save);
356: switch(jumpsize)
357: {
358: case 1:
359: {
360: Sgl_leftshiftby3(result);
361: result_exponent -= 3;
362: break;
363: }
364: case 2:
365: case 3:
366: {
367: Sgl_leftshiftby2(result);
368: result_exponent -= 2;
369: break;
370: }
371: case 4:
372: case 5:
373: case 6:
374: case 7:
375: {
376: Sgl_leftshiftby1(result);
377: result_exponent -= 1;
378: break;
379: }
380: }
381: if(result_exponent > 0)
382: {
383: Sgl_set_exponent(result,/*using*/result_exponent);
384: *dstptr = result;
385: return(NOEXCEPTION); /* Sign bit is already set */
386: }
387: /* Fixup potential underflows */
388: underflow:
389: if(Is_underflowtrap_enabled())
390: {
391: Sgl_set_sign(result,sign_save);
392: Sgl_setwrapped_exponent(result,result_exponent,unfl);
393: *dstptr = result;
394: /* inexact = FALSE; */
395: return(UNDERFLOWEXCEPTION);
396: }
397: /*
398: * Since we cannot get an inexact denormalized result,
399: * we can now return.
400: */
401: Sgl_right_align(result,/*by*/(1-result_exponent),extent);
402: Sgl_clear_signexponent(result);
403: Sgl_set_sign(result,sign_save);
404: *dstptr = result;
405: return(NOEXCEPTION);
406: } /* end if(hidden...)... */
407: /* Fall through and round */
408: } /* end if(save < 0)... */
409: else
410: {
411: /* Add magnitudes */
412: Sgl_addition(left,right,/*to*/result);
413: if(Sgl_isone_hiddenoverflow(result))
414: {
415: /* Prenormalization required. */
416: Sgl_rightshiftby1_withextent(result,extent,extent);
417: Sgl_arithrightshiftby1(result);
418: result_exponent++;
419: } /* end if hiddenoverflow... */
420: } /* end else ...add magnitudes... */
421:
422: /* Round the result. If the extension is all zeros,then the result is
423: * exact. Otherwise round in the correct direction. No underflow is
424: * possible. If a postnormalization is necessary, then the mantissa is
425: * all zeros so no shift is needed. */
426: round:
427: if(Ext_isnotzero(extent))
428: {
429: inexact = TRUE;
430: switch(Rounding_mode())
431: {
432: case ROUNDNEAREST: /* The default. */
433: if(Ext_isone_sign(extent))
434: {
435: /* at least 1/2 ulp */
436: if(Ext_isnotzero_lower(extent) ||
437: Sgl_isone_lowmantissa(result))
438: {
439: /* either exactly half way and odd or more than 1/2ulp */
440: Sgl_increment(result);
441: }
442: }
443: break;
444:
445: case ROUNDPLUS:
446: if(Sgl_iszero_sign(result))
447: {
448: /* Round up positive results */
449: Sgl_increment(result);
450: }
451: break;
452:
453: case ROUNDMINUS:
454: if(Sgl_isone_sign(result))
455: {
456: /* Round down negative results */
457: Sgl_increment(result);
458: }
459:
460: case ROUNDZERO:;
461: /* truncate is simple */
462: } /* end switch... */
463: if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
464: }
465: if(result_exponent == SGL_INFINITY_EXPONENT)
466: {
467: /* Overflow */
468: if(Is_overflowtrap_enabled())
469: {
470: Sgl_setwrapped_exponent(result,result_exponent,ovfl);
471: *dstptr = result;
472: if (inexact) {
473: if (Is_inexacttrap_enabled())
474: return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
475: else Set_inexactflag();
476: }
477: return(OVERFLOWEXCEPTION);
478: }
479: else
480: {
481: Set_overflowflag();
482: inexact = TRUE;
483: Sgl_setoverflow(result);
484: }
485: }
486: else Sgl_set_exponent(result,result_exponent);
487: *dstptr = result;
488: if(inexact) {
489: if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
490: else Set_inexactflag();
491: }
492: return(NOEXCEPTION);
493: }