I have read the sequence of contributions to this thread with more dismay than usual. Working with leap seconds poses no particular difficulties, and in particular Paul Gilmartin's suggestions are otiose. (I single him out only because he almost always knows what he is talking about, even when I disagree strongly with him.) A table is needed but IBM supplies one, which it updates well in advance of the effective insertion time of a new leap second, indeed almost as soon as the BIPM issues its notification that an insertion will occur. Currently, the table takes the (somewhat edited, but substantively correct) form
year m dom doy Σls STCKE (9 high bytes) 1900 1 1 1 0 x'000000000000000000' 1972 1 1 1 0 x'008126d60e46000000' 1972 7 1 183 1 x'00820ba9811e240000' 1973 1 1 1 2 x'0082f300eee2480000' 1974 1 1 1 3 x'0084bde971446c0000' 1975 1 1 1 4 x'008688d23346900000' 1976 1 1 1 5 x'008853baf578b40000' 1977 1 1 1 6 x'008a1fe59520d80000' 1978 1 1 1 7 x'008beace5752fc0000' 1979 1 1 1 8 x'008db5b71985200000' 1980 1 1 1 9 x'008f809fdbb7440000' 1981 7 1 182 10 x'0092305c0fcd680000' 1982 7 1 182 11 x'0093fb44d1ff8c0000' 1983 7 1 182 12 x'0095c62f9431b00000' 1985 7 1 182 13 x'00995d40f517d00000' 1988 1 1 1 14 x'009dda69a557f80000' 1990 1 1 1 15 x'00a1117d063e1c0000' 1991 1 1 1 16 x'00a33c65c780400000' 1992 7 1 182 17 x'00a3ec21fc86640000' 1993 7 1 182 18 x'00a7b70abeb8880000' 1994 7 1 182 19 x'00a981f380eaac0000' 1996 1 1 1 20 x'00ac34336fecd00000' 1997 7 1 182 21 x'00aee3efa40df40000' 1999 1 1 1 22 x'00b1962f9305180000' 2005 1 1 1 23 x'00BE251097973C0000' Suppose now that we have a copy of this table, call it T, and a (truncated) STCKE value, call it S, for which we need the corresponding cumulative leap-seconds-inserted value. Traditional match-seeking binary search in this table is unavailable to us because we need not a match for but a greatest lower bound (glb), which may occasionally also be a match, on S. A binary-search scheme that I devised long ago for evaluating tabular step functions can, however, be used for this purpose. A PL/I version of it, specialized for this use, is leapsecs: procedure(Tp, S, cumLS) /* cumulative LSs for STCKE */ returns(aligned bit) reorder ; /* returns '1'b with cumLS set if S is bounded in T; returns '0'b, false, if S is not bounded in T. */ /* parameters */ declare (Tp pointer, /* table pointer */ S aligned bit(72)) /* search argument, truncated STCKE */ parameter nonassignable, cumLS signed binary fixed(31,0) /* cumulative leap seconds */ parameter assignable ; /* table to search */ declare 1 T based(Tp), /* table */ 2 tls /* low table subscript */ signed binary fixed(31,0), 2 ths /* high table subscript */ signed binary fixed(31,0), 2 tab dimension(ls refer(T.tls); hs refer(T.ths), 3 year signed binary fixed(31,0), /* Gregorian year */ 3 moy signed binary fixed(7,0), /* month of year */ 3 dom signed binary fixed(7,0), /* day of month */ 3 doy signed binary fixed(15,0), /* day of year */ 3 cls signed binary fixed(31,0), /* cumulative LSs */ 3 STCKE9 aligned bit(72), /* STCKE value */ 3 * character(3) ; /* DW alignment */ /* named constants */ declare (F1 value (1b), F2 value(10b)) signed binary fixed(31,0) ; /* LIFO scratch storage */ declare (h, /* high search subscript */ l, /* low search subscript */ m, /* middling search subscript */ hmin, /* minimal bounding subscript */ (ls, hs)) /* unused dynamic-allocation values */ signed binary fixed(31,0), (bounded, /* is S bounded in T? */ search, /* table not yet exhausted? */ search_higher) /* search following T.STCKE9(m)? */ aligned bit ; l, hmin = T.tls ; h = T.ths ; do search = (l <= h) while(search) ; m = l + (h - l)/F2 ; /* fixedoverflow! */ search_higher = (S >= T.STCKE9(m)) ; if search_higher then l = m + F1 ; else h = m - F1 ; end ; bounded = (h >= hmin) ; if bounded then cumLS = T.cls(h) ; return(bounded) ; end leapsecs ; Here no STCKE value can be without a glb in T, but I have left the code that deals with search arguments smaller than the smallest table value in place to illustrate how the algorithm works for such values. In general, of course, the smallest element in a table like T may be greater than some search argument value S; and in this case S has no glb in T and this procedure returns '0'b, false. The elements of a table T may comprise either an ordered set of unique elements or a partially ordered multiset that in general contains duplicate elements; and one of the merits of this scheme is that it yields unequivocal results for such multisets. John Gilmore Ashland, MA 01721-1817 USA _________________________________________________________________ See how Windows connects the people, information, and fun that are part of your life. http://clk.atdmt.com/MRT/go/msnnkwxp1020093175mrt/direct/01/ ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to [EMAIL PROTECTED] with the message: GET IBM-MAIN INFO Search the archives at http://bama.ua.edu/archives/ibm-main.html
