xref: /netbsd-src/lib/libc/time/strftime.c (revision 8de7229d05dca81697c886efbd8ef69b32c94a44)
1 /*	$NetBSD: strftime.c,v 1.43 2019/04/04 19:27:28 christos Exp $	*/
2 
3 /* Convert a broken-down timestamp to a string.  */
4 
5 /* Copyright 1989 The Regents of the University of California.
6    All rights reserved.
7 
8    Redistribution and use in source and binary forms, with or without
9    modification, are permitted provided that the following conditions
10    are met:
11    1. Redistributions of source code must retain the above copyright
12       notice, this list of conditions and the following disclaimer.
13    2. Redistributions in binary form must reproduce the above copyright
14       notice, this list of conditions and the following disclaimer in the
15       documentation and/or other materials provided with the distribution.
16    3. Neither the name of the University nor the names of its contributors
17       may be used to endorse or promote products derived from this software
18       without specific prior written permission.
19 
20    THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS" AND
21    ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22    IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23    ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
24    FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25    DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26    OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27    HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29    OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30    SUCH DAMAGE.  */
31 
32 #include <sys/cdefs.h>
33 #if defined(LIBC_SCCS) && !defined(lint)
34 #if 0
35 static char	elsieid[] = "@(#)strftime.c	7.64";
36 static char	elsieid[] = "@(#)strftime.c	8.3";
37 #else
38 __RCSID("$NetBSD: strftime.c,v 1.43 2019/04/04 19:27:28 christos Exp $");
39 #endif
40 #endif /* LIBC_SCCS and not lint */
41 
42 #include "namespace.h"
43 
44 #include <stddef.h>
45 #include <assert.h>
46 #include <locale.h>
47 #include "setlocale_local.h"
48 
49 /*
50 ** Based on the UCB version with the copyright notice appearing above.
51 **
52 ** This is ANSIish only when "multibyte character == plain character".
53 */
54 
55 #include "private.h"
56 
57 /*
58 ** We don't use these extensions in strftime operation even when
59 ** supported by the local tzcode configuration.  A strictly
60 ** conforming C application may leave them in undefined state.
61 */
62 
63 #ifdef _LIBC
64 #undef TM_ZONE
65 #undef TM_GMTOFF
66 #endif
67 
68 #include <fcntl.h>
69 #include <locale.h>
70 #include <stdio.h>
71 
72 #ifndef DEPRECATE_TWO_DIGIT_YEARS
73 # define DEPRECATE_TWO_DIGIT_YEARS false
74 #endif
75 
76 #ifdef __weak_alias
77 __weak_alias(strftime_l, _strftime_l)
78 __weak_alias(strftime_lz, _strftime_lz)
79 __weak_alias(strftime_z, _strftime_z)
80 #endif
81 
82 #include "sys/localedef.h"
83 #define _TIME_LOCALE(loc) \
84     ((_TimeLocale *)((loc)->part_impl[(size_t)LC_TIME]))
85 #define c_fmt   d_t_fmt
86 
87 enum warn { IN_NONE, IN_SOME, IN_THIS, IN_ALL };
88 
89 static char *	_add(const char *, char *, const char *);
90 static char *	_conv(int, const char *, char *, const char *);
91 static char *	_fmt(const timezone_t, const char *, const struct tm *, char *,
92 			const char *, enum warn *, locale_t);
93 static char *	_yconv(int, int, bool, bool, char *, const char *);
94 
95 #ifndef YEAR_2000_NAME
96 #define YEAR_2000_NAME	"CHECK_STRFTIME_FORMATS_FOR_TWO_DIGIT_YEARS"
97 #endif /* !defined YEAR_2000_NAME */
98 
99 size_t
100 strftime_z(const timezone_t sp, char * __restrict s, size_t maxsize,
101     const char * __restrict format, const struct tm * __restrict t)
102 {
103 	return strftime_lz(sp, s, maxsize, format, t, _current_locale());
104 }
105 
106 #if HAVE_STRFTIME_L
107 size_t
108 strftime_l(char *s, size_t maxsize, char const *format, struct tm const *t,
109 	   locale_t locale)
110 {
111   /* Just call strftime, as only the C locale is supported.  */
112   return strftime(s, maxsize, format, t);
113 }
114 #endif
115 
116 size_t
117 strftime_lz(const timezone_t sp, char *const s, const size_t maxsize,
118     const char *const format, const struct tm *const t, locale_t loc)
119 {
120 	char *	p;
121 	enum warn warn = IN_NONE;
122 
123 	p = _fmt(sp, format, t, s, s + maxsize, &warn, loc);
124 	if (/*CONSTCOND*/DEPRECATE_TWO_DIGIT_YEARS
125 	    && warn != IN_NONE && getenv(YEAR_2000_NAME)) {
126 		(void) fprintf(stderr, "\n");
127 		(void) fprintf(stderr, "strftime format \"%s\" ", format);
128 		(void) fprintf(stderr, "yields only two digits of years in ");
129 		if (warn == IN_SOME)
130 			(void) fprintf(stderr, "some locales");
131 		else if (warn == IN_THIS)
132 			(void) fprintf(stderr, "the current locale");
133 		else	(void) fprintf(stderr, "all locales");
134 		(void) fprintf(stderr, "\n");
135 	}
136 	if (p == s + maxsize)
137 		return 0;
138 	*p = '\0';
139 	return p - s;
140 }
141 
142 static char *
143 _fmt(const timezone_t sp, const char *format, const struct tm *t, char *pt,
144      const char *ptlim, enum warn *warnp, locale_t loc)
145 {
146 	for ( ; *format; ++format) {
147 		if (*format == '%') {
148 label:
149 			switch (*++format) {
150 			case '\0':
151 				--format;
152 				break;
153 			case 'A':
154 				pt = _add((t->tm_wday < 0 ||
155 					t->tm_wday >= DAYSPERWEEK) ?
156 					"?" : _TIME_LOCALE(loc)->day[t->tm_wday],
157 					pt, ptlim);
158 				continue;
159 			case 'a':
160 				pt = _add((t->tm_wday < 0 ||
161 					t->tm_wday >= DAYSPERWEEK) ?
162 					"?" : _TIME_LOCALE(loc)->abday[t->tm_wday],
163 					pt, ptlim);
164 				continue;
165 			case 'B':
166 				pt = _add((t->tm_mon < 0 ||
167 					t->tm_mon >= MONSPERYEAR) ?
168 					"?" : _TIME_LOCALE(loc)->mon[t->tm_mon],
169 					pt, ptlim);
170 				continue;
171 			case 'b':
172 			case 'h':
173 				pt = _add((t->tm_mon < 0 ||
174 					t->tm_mon >= MONSPERYEAR) ?
175 					"?" : _TIME_LOCALE(loc)->abmon[t->tm_mon],
176 					pt, ptlim);
177 				continue;
178 			case 'C':
179 				/*
180 				** %C used to do a...
181 				**	_fmt("%a %b %e %X %Y", t);
182 				** ...whereas now POSIX 1003.2 calls for
183 				** something completely different.
184 				** (ado, 1993-05-24)
185 				*/
186 				pt = _yconv(t->tm_year, TM_YEAR_BASE,
187 					    true, false, pt, ptlim);
188 				continue;
189 			case 'c':
190 				{
191 				enum warn warn2 = IN_SOME;
192 
193 				pt = _fmt(sp, _TIME_LOCALE(loc)->c_fmt, t, pt,
194 				    ptlim, &warn2, loc);
195 				if (warn2 == IN_ALL)
196 					warn2 = IN_THIS;
197 				if (warn2 > *warnp)
198 					*warnp = warn2;
199 				}
200 				continue;
201 			case 'D':
202 				pt = _fmt(sp, "%m/%d/%y", t, pt, ptlim, warnp,
203 				    loc);
204 				continue;
205 			case 'd':
206 				pt = _conv(t->tm_mday, "%02d", pt, ptlim);
207 				continue;
208 			case 'E':
209 			case 'O':
210 				/*
211 				** Locale modifiers of C99 and later.
212 				** The sequences
213 				**	%Ec %EC %Ex %EX %Ey %EY
214 				**	%Od %oe %OH %OI %Om %OM
215 				**	%OS %Ou %OU %OV %Ow %OW %Oy
216 				** are supposed to provide alternative
217 				** representations.
218 				*/
219 				goto label;
220 			case 'e':
221 				pt = _conv(t->tm_mday, "%2d", pt, ptlim);
222 				continue;
223 			case 'F':
224 				pt = _fmt(sp, "%Y-%m-%d", t, pt, ptlim, warnp,
225 				    loc);
226 				continue;
227 			case 'H':
228 				pt = _conv(t->tm_hour, "%02d", pt, ptlim);
229 				continue;
230 			case 'I':
231 				pt = _conv((t->tm_hour % 12) ?
232 					(t->tm_hour % 12) : 12,
233 					"%02d", pt, ptlim);
234 				continue;
235 			case 'j':
236 				pt = _conv(t->tm_yday + 1, "%03d", pt, ptlim);
237 				continue;
238 			case 'k':
239 				/*
240 				** This used to be...
241 				**	_conv(t->tm_hour % 12 ?
242 				**		t->tm_hour % 12 : 12, 2, ' ');
243 				** ...and has been changed to the below to
244 				** match SunOS 4.1.1 and Arnold Robbins'
245 				** strftime version 3.0. That is, "%k" and
246 				** "%l" have been swapped.
247 				** (ado, 1993-05-24)
248 				*/
249 				pt = _conv(t->tm_hour, "%2d", pt, ptlim);
250 				continue;
251 #ifdef KITCHEN_SINK
252 			case 'K':
253 				/*
254 				** After all this time, still unclaimed!
255 				*/
256 				pt = _add("kitchen sink", pt, ptlim);
257 				continue;
258 #endif /* defined KITCHEN_SINK */
259 			case 'l':
260 				/*
261 				** This used to be...
262 				**	_conv(t->tm_hour, 2, ' ');
263 				** ...and has been changed to the below to
264 				** match SunOS 4.1.1 and Arnold Robbin's
265 				** strftime version 3.0. That is, "%k" and
266 				** "%l" have been swapped.
267 				** (ado, 1993-05-24)
268 				*/
269 				pt = _conv((t->tm_hour % 12) ?
270 					(t->tm_hour % 12) : 12,
271 					"%2d", pt, ptlim);
272 				continue;
273 			case 'M':
274 				pt = _conv(t->tm_min, "%02d", pt, ptlim);
275 				continue;
276 			case 'm':
277 				pt = _conv(t->tm_mon + 1, "%02d", pt, ptlim);
278 				continue;
279 			case 'n':
280 				pt = _add("\n", pt, ptlim);
281 				continue;
282 			case 'p':
283 				pt = _add((t->tm_hour >= (HOURSPERDAY / 2)) ?
284 					_TIME_LOCALE(loc)->am_pm[1] :
285 					_TIME_LOCALE(loc)->am_pm[0],
286 					pt, ptlim);
287 				continue;
288 			case 'R':
289 				pt = _fmt(sp, "%H:%M", t, pt, ptlim, warnp,
290 				    loc);
291 				continue;
292 			case 'r':
293 				pt = _fmt(sp, _TIME_LOCALE(loc)->t_fmt_ampm, t,
294 				    pt, ptlim, warnp, loc);
295 				continue;
296 			case 'S':
297 				pt = _conv(t->tm_sec, "%02d", pt, ptlim);
298 				continue;
299 			case 's':
300 				{
301 					struct tm	tm;
302 					char		buf[INT_STRLEN_MAXIMUM(
303 								time_t) + 1];
304 					time_t		mkt;
305 
306 					tm = *t;
307 					mkt = mktime_z(sp, &tm);
308 					/* CONSTCOND */
309 					if (TYPE_SIGNED(time_t))
310 						(void)snprintf(buf, sizeof(buf),
311 						    "%jd", (intmax_t) mkt);
312 					else	(void)snprintf(buf, sizeof(buf),
313 						    "%ju", (uintmax_t) mkt);
314 					pt = _add(buf, pt, ptlim);
315 				}
316 				continue;
317 			case 'T':
318 				pt = _fmt(sp, "%H:%M:%S", t, pt, ptlim, warnp,
319 				    loc);
320 				continue;
321 			case 't':
322 				pt = _add("\t", pt, ptlim);
323 				continue;
324 			case 'U':
325 				pt = _conv((t->tm_yday + DAYSPERWEEK -
326 					t->tm_wday) / DAYSPERWEEK,
327 					"%02d", pt, ptlim);
328 				continue;
329 			case 'u':
330 				/*
331 				** From Arnold Robbins' strftime version 3.0:
332 				** "ISO 8601: Weekday as a decimal number
333 				** [1 (Monday) - 7]"
334 				** (ado, 1993-05-24)
335 				*/
336 				pt = _conv((t->tm_wday == 0) ?
337 					DAYSPERWEEK : t->tm_wday,
338 					"%d", pt, ptlim);
339 				continue;
340 			case 'V':	/* ISO 8601 week number */
341 			case 'G':	/* ISO 8601 year (four digits) */
342 			case 'g':	/* ISO 8601 year (two digits) */
343 /*
344 ** From Arnold Robbins' strftime version 3.0: "the week number of the
345 ** year (the first Monday as the first day of week 1) as a decimal number
346 ** (01-53)."
347 ** (ado, 1993-05-24)
348 **
349 ** From <https://www.cl.cam.ac.uk/~mgk25/iso-time.html> by Markus Kuhn:
350 ** "Week 01 of a year is per definition the first week which has the
351 ** Thursday in this year, which is equivalent to the week which contains
352 ** the fourth day of January. In other words, the first week of a new year
353 ** is the week which has the majority of its days in the new year. Week 01
354 ** might also contain days from the previous year and the week before week
355 ** 01 of a year is the last week (52 or 53) of the previous year even if
356 ** it contains days from the new year. A week starts with Monday (day 1)
357 ** and ends with Sunday (day 7). For example, the first week of the year
358 ** 1997 lasts from 1996-12-30 to 1997-01-05..."
359 ** (ado, 1996-01-02)
360 */
361 				{
362 					int	year;
363 					int	base;
364 					int	yday;
365 					int	wday;
366 					int	w;
367 
368 					year = t->tm_year;
369 					base = TM_YEAR_BASE;
370 					yday = t->tm_yday;
371 					wday = t->tm_wday;
372 					for ( ; ; ) {
373 						int	len;
374 						int	bot;
375 						int	top;
376 
377 						len = isleap_sum(year, base) ?
378 							DAYSPERLYEAR :
379 							DAYSPERNYEAR;
380 						/*
381 						** What yday (-3 ... 3) does
382 						** the ISO year begin on?
383 						*/
384 						bot = ((yday + 11 - wday) %
385 							DAYSPERWEEK) - 3;
386 						/*
387 						** What yday does the NEXT
388 						** ISO year begin on?
389 						*/
390 						top = bot -
391 							(len % DAYSPERWEEK);
392 						if (top < -3)
393 							top += DAYSPERWEEK;
394 						top += len;
395 						if (yday >= top) {
396 							++base;
397 							w = 1;
398 							break;
399 						}
400 						if (yday >= bot) {
401 							w = 1 + ((yday - bot) /
402 								DAYSPERWEEK);
403 							break;
404 						}
405 						--base;
406 						yday += isleap_sum(year, base) ?
407 							DAYSPERLYEAR :
408 							DAYSPERNYEAR;
409 					}
410 #ifdef XPG4_1994_04_09
411 					if ((w == 52 &&
412 						t->tm_mon == TM_JANUARY) ||
413 						(w == 1 &&
414 						t->tm_mon == TM_DECEMBER))
415 							w = 53;
416 #endif /* defined XPG4_1994_04_09 */
417 					if (*format == 'V')
418 						pt = _conv(w, "%02d",
419 							pt, ptlim);
420 					else if (*format == 'g') {
421 						*warnp = IN_ALL;
422 						pt = _yconv(year, base,
423 							false, true,
424 							pt, ptlim);
425 					} else	pt = _yconv(year, base,
426 							true, true,
427 							pt, ptlim);
428 				}
429 				continue;
430 			case 'v':
431 				/*
432 				** From Arnold Robbins' strftime version 3.0:
433 				** "date as dd-bbb-YYYY"
434 				** (ado, 1993-05-24)
435 				*/
436 				pt = _fmt(sp, "%e-%b-%Y", t, pt, ptlim, warnp,
437 				    loc);
438 				continue;
439 			case 'W':
440 				pt = _conv((t->tm_yday + DAYSPERWEEK -
441 					(t->tm_wday ?
442 					(t->tm_wday - 1) :
443 					(DAYSPERWEEK - 1))) / DAYSPERWEEK,
444 					"%02d", pt, ptlim);
445 				continue;
446 			case 'w':
447 				pt = _conv(t->tm_wday, "%d", pt, ptlim);
448 				continue;
449 			case 'X':
450 				pt = _fmt(sp, _TIME_LOCALE(loc)->t_fmt, t, pt,
451 				    ptlim, warnp, loc);
452 				continue;
453 			case 'x':
454 				{
455 				enum warn warn2 = IN_SOME;
456 
457 				pt = _fmt(sp, _TIME_LOCALE(loc)->d_fmt, t, pt,
458 				    ptlim, &warn2, loc);
459 				if (warn2 == IN_ALL)
460 					warn2 = IN_THIS;
461 				if (warn2 > *warnp)
462 					*warnp = warn2;
463 				}
464 				continue;
465 			case 'y':
466 				*warnp = IN_ALL;
467 				pt = _yconv(t->tm_year, TM_YEAR_BASE,
468 					false, true,
469 					pt, ptlim);
470 				continue;
471 			case 'Y':
472 				pt = _yconv(t->tm_year, TM_YEAR_BASE,
473 					true, true,
474 					pt, ptlim);
475 				continue;
476 			case 'Z':
477 #ifdef TM_ZONE
478 				pt = _add(t->TM_ZONE, pt, ptlim);
479 #elif HAVE_TZNAME
480 				if (t->tm_isdst >= 0)
481 					pt = _add(tzgetname(sp, t->tm_isdst),
482 					    pt, ptlim);
483 #endif
484 				/*
485 				** C99 and later say that %Z must be
486 				** replaced by the empty string if the
487 				** time zone abbreviation is not
488 				** determinable.
489 				*/
490 				continue;
491 			case 'z':
492 #if defined TM_GMTOFF || USG_COMPAT || defined ALTZONE
493 				{
494 				long		diff;
495 				char const *	sign;
496 				bool negative;
497 
498 				if (t->tm_isdst < 0)
499 					continue;
500 # ifdef TM_GMTOFF
501 				diff = (int)t->TM_GMTOFF;
502 # else
503 				/*
504 				** C99 and later say that the UT offset must
505 				** be computed by looking only at
506 				** tm_isdst. This requirement is
507 				** incorrect, since it means the code
508 				** must rely on magic (in this case
509 				** altzone and timezone), and the
510 				** magic might not have the correct
511 				** offset. Doing things correctly is
512 				** tricky and requires disobeying the standard;
513 				** see GNU C strftime for details.
514 				** For now, punt and conform to the
515 				** standard, even though it's incorrect.
516 				**
517 				** C99 and later say that %z must be replaced by
518 				** the empty string if the time zone is not
519 				** determinable, so output nothing if the
520 				** appropriate variables are not available.
521 				*/
522 #  ifndef STD_INSPIRED
523 				if (t->tm_isdst == 0)
524 #   if USG_COMPAT
525 					diff = -timezone;
526 #   else
527 					continue;
528 #   endif
529 				else
530 #   ifdef ALTZONE
531 					diff = -altzone;
532 #   else
533 					continue;
534 #   endif
535 #  else
536 				{
537 					struct tm tmp;
538 					time_t lct, gct;
539 
540 					/*
541 					** Get calendar time from t
542 					** being treated as local.
543 					*/
544 					tmp = *t; /* mktime discards const */
545 					lct = mktime_z(sp, &tmp);
546 
547 					if (lct == (time_t)-1)
548 						continue;
549 
550 					/*
551 					** Get calendar time from t
552 					** being treated as GMT.
553 					**/
554 					tmp = *t; /* mktime discards const */
555 					gct = timegm(&tmp);
556 
557 					if (gct == (time_t)-1)
558 						continue;
559 
560 					/* LINTED difference will fit int */
561 					diff = (intmax_t)gct - (intmax_t)lct;
562 				}
563 #  endif
564 # endif
565 				negative = diff < 0;
566 				if (diff == 0) {
567 #ifdef TM_ZONE
568 				  negative = t->TM_ZONE[0] == '-';
569 #else
570 				  negative = t->tm_isdst < 0;
571 # if HAVE_TZNAME
572 				  if (tzname[t->tm_isdst != 0][0] == '-')
573 				    negative = true;
574 # endif
575 #endif
576 				}
577 				if (negative) {
578 					sign = "-";
579 					diff = -diff;
580 				} else	sign = "+";
581 				pt = _add(sign, pt, ptlim);
582 				diff /= SECSPERMIN;
583 				diff = (diff / MINSPERHOUR) * 100 +
584 					(diff % MINSPERHOUR);
585 				_DIAGASSERT(__type_fit(int, diff));
586 				pt = _conv((int)diff, "%04d", pt, ptlim);
587 				}
588 #endif
589 				continue;
590 #if 0
591 			case '+':
592 				pt = _fmt(sp, _TIME_LOCALE(loc)->date_fmt, t,
593 				    pt, ptlim, warnp, loc);
594 				continue;
595 #endif
596 			case '%':
597 			/*
598 			** X311J/88-090 (4.12.3.5): if conversion char is
599 			** undefined, behavior is undefined. Print out the
600 			** character itself as printf(3) also does.
601 			*/
602 			default:
603 				break;
604 			}
605 		}
606 		if (pt == ptlim)
607 			break;
608 		*pt++ = *format;
609 	}
610 	return pt;
611 }
612 
613 size_t
614 strftime(char *s, size_t maxsize, const char *format, const struct tm *t)
615 {
616 	size_t r;
617 
618 	rwlock_wrlock(&__lcl_lock);
619 	tzset_unlocked();
620 	r = strftime_z(__lclptr, s, maxsize, format, t);
621 	rwlock_unlock(&__lcl_lock);
622 
623 	return r;
624 }
625 
626 size_t
627 strftime_l(char * __restrict s, size_t maxsize, const char * __restrict format,
628     const struct tm * __restrict t, locale_t loc)
629 {
630 	size_t r;
631 
632 	rwlock_wrlock(&__lcl_lock);
633 	tzset_unlocked();
634 	r = strftime_lz(__lclptr, s, maxsize, format, t, loc);
635 	rwlock_unlock(&__lcl_lock);
636 
637 	return r;
638 }
639 
640 static char *
641 _conv(int n, const char *format, char *pt, const char *ptlim)
642 {
643 	char	buf[INT_STRLEN_MAXIMUM(int) + 1];
644 
645 	(void) snprintf(buf, sizeof(buf), format, n);
646 	return _add(buf, pt, ptlim);
647 }
648 
649 static char *
650 _add(const char *str, char *pt, const char *ptlim)
651 {
652 	while (pt < ptlim && (*pt = *str++) != '\0')
653 		++pt;
654 	return pt;
655 }
656 
657 /*
658 ** POSIX and the C Standard are unclear or inconsistent about
659 ** what %C and %y do if the year is negative or exceeds 9999.
660 ** Use the convention that %C concatenated with %y yields the
661 ** same output as %Y, and that %Y contains at least 4 bytes,
662 ** with more only if necessary.
663 */
664 
665 static char *
666 _yconv(int a, int b, bool convert_top, bool convert_yy,
667     char *pt, const char * ptlim)
668 {
669 	int	lead;
670 	int	trail;
671 
672 #define DIVISOR	100
673 	trail = a % DIVISOR + b % DIVISOR;
674 	lead = a / DIVISOR + b / DIVISOR + trail / DIVISOR;
675 	trail %= DIVISOR;
676 	if (trail < 0 && lead > 0) {
677 		trail += DIVISOR;
678 		--lead;
679 	} else if (lead < 0 && trail > 0) {
680 		trail -= DIVISOR;
681 		++lead;
682 	}
683 	if (convert_top) {
684 		if (lead == 0 && trail < 0)
685 			pt = _add("-0", pt, ptlim);
686 		else	pt = _conv(lead, "%02d", pt, ptlim);
687 	}
688 	if (convert_yy)
689 		pt = _conv(((trail < 0) ? -trail : trail), "%02d", pt, ptlim);
690 	return pt;
691 }
692