Procedure

     RMAIND ( Remainder --- double precision )

     SUBROUTINE RMAIND ( NUM, DENOM, Q, REM )

Abstract

     Compute the integer quotient and non-negative remainder
     of NUM and DENOM.

Required_Reading

     None.

Keywords

     MATH
     UTILITY

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      NUM
     DOUBLE PRECISION      DENOM
     DOUBLE PRECISION      Q
     DOUBLE PRECISION      REM

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     NUM        I   Numerator used to compute quotient and remainder.
     DENOM      I   Denominator used to compute quotient and remainder.
     Q          O   Integer portion of the quotient NUM/DENOM.
     REM        O   Remainder of the quotient NUM/DENOM.

Detailed_Input

     NUM      is the numerator of a quotient

     DENOM    is the denominator of a quotient

Detailed_Output

     Q        is the largest integer less than or equal to the
              quotient NUM/DENOM

     REM      is the remainder of the integer division NUM/DENOM

Parameters

     None.

Exceptions

     1)  If DENOM is zero, the error SPICE(DIVIDEBYZERO) is signaled.

Files

     None.

Particulars

     Given the double precision inputs NUM and DENOM, this routine
     finds double precision numbers Q and REM that satisfy the
     following conditions:

         1) NUM = DENOM * Q + REM

         2) DENOM has integer value.

         3) REM belongs to the half open interval [0, ABS(DENOM) )

     This routine serves as a macro. In this way the code to perform
     this task can be written and maintained in a single location.

Examples

     One frequently needs to compute the  ``Two pi modulus'' of a
     number. For positive numbers the FORTRAN intrinsic mod
     function works well. However, for negative numbers the
     intrinsic will return a negative modulus. This routine
     can be used to compute the positive two pi modulus (MOD2PI) for
     any number X by the call:

         CALL RMAIND ( X, TWOPI(), I, MOD2PI )

Restrictions

     1)  Arithmetic overflows are not trapped or detected by this
         routine.

Literature_References

     None.

Author_and_Institution

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

Version

    SPICELIB Version 1.1.0, 12-AUG-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.0.0, 01-DEC-1995 (WLT)