Procedure

     LSTLTD ( Last double precision element less than )

      INTEGER FUNCTION  LSTLTD ( X, N, ARRAY )

Abstract

     Find the index of the largest array element less than 
     a given number X in an array of non-decreasing numbers.

Required_Reading

     None.

Keywords

     ARRAY
     SEARCH

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   X
     INTEGER            N
     DOUBLE PRECISION   ARRAY ( * )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     X          I   Upper bound value to search against.
     N          I   Number of elements in ARRAY.
     ARRAY      I   Array of possible lower bounds.

     The function returns the index of the last element of ARRAY that
     is less than X.

Detailed_Input

     X        is a double precision value acting as an upper bound: the
              element of ARRAY that is the greatest element less than X
              is to be found.

     N        is the total number of elements in ARRAY.

     ARRAY    is an array of double precision numbers that forms a
              non-decreasing sequence. The elements of array need not
              be distinct.

Detailed_Output

     The function returns the index of the highest-indexed element in
     the input array that is less than X. The routine assumes the array
     elements are sorted in non-decreasing order.

     Indices range from 1 to N.

     If all elements of ARRAY are greater than or equal to X, the
     routine returns the value 0. If N is less than or equal to zero,
     the routine returns the value 0.

Parameters

     None.

Exceptions

     Error free.

     1)  If N is less than or equal to zero, the function returns 0.
         This case is not treated as an error.

     2)  If the input array is not sorted in non-decreasing order, the
         output of this routine is undefined. No error is signaled.

Files

     None.

Particulars

     This routine uses a binary search algorithm and so requires
     at most on the order of

        log (N)
           2

     steps to compute the value of LSTLTD.

     Note: If you need to find the first element of the array that is
     greater than or equal to X, simply add 1 to the result returned by
     this function and check to see if the result is within the array
     bounds given by N.

Examples

     If ARRAY(I) = -1 + 4*I/3 (real arithmetic implied here)

        N        = 10
        X        = 7.12

     then

        LSTLTD will be I where

             (4*I/3) - 1       <      7.12

     but

             (4*(I+1)/3) - 1   > or = 7.12 .

     In this case our subsequence is:

            1/3, 5/3, 9/3, 13/3, 17/3, 21/3, 25/3, .... 37/3

     index:  1    2    3    4     5     6     7    ....  10

     Thus LSTLTD will be returned as 6

     The following table shows the values of LSTLTD that would be
     returned for various values of X

            X       LSTLTD
          -----     -------
           0.12        0
           1.34        1
           5.13        4
           8.00        6
          15.10       10

Restrictions

     1)  If the sequence of double precision numbers in the input array
         ARRAY is not non-decreasing, the program will run to
         completion but the index found will not mean anything.

Literature_References

     None.

Author_and_Institution

     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 26-OCT-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Removed
        unnecessary $Revisions section. Improved $Detailed_Input,
        $Detailed_Output, $Particulars, $Exceptions and $Restrictions
        sections.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WLT) (NJB)