RFC401

Network Working Group Jim Hansen Request for Comment #401 Center for Advanced NIC #11923 Computation Category: D.6 University of Illinois Updates: RFC #387 October 23, 1972 Obsoletes: None

           Conversion of NGP-0 Coordinates to Device
           -----------------------------------------
                      Specific Coordinates
                      --------------------

Conversion of NGP-0 coordinates to floating point PDP-10 coordinates was discussed in RFC #387. In general, however, it is undesirable to convert NGP coordinates to floating point coordinates because real devices require integer addressing. To this end, a means is described to convert NGP coordi- nates to integer coordinates in the range zero to M, where M is the maximum address of the device screen on a machine using 2's complement arithmetic. It would not, however, be difficult to modify this algorithm to operate on machines using one's complement or sign-magnitude arithmetic.

First consider the NGP coordinate format:

               +--+-----------+
               |  |   n       |
               +--+-----------+
                s ^  FRACTION
                i
                g
                n

Where the sign occupies the most significant bit of the coordinate followed by bits of numerical information (initial implementation of NGP requires N=15). Negative numbers are represented by 2's complement. Conversion to device coordinates is accomplished by:

                D = S * f + S

Where D =>integer device coordinate

  S =>scaling factor (typically M/2)
  f =>NGP fractional coordinate

Let us rewrite this as:

                        n     n
                D = S*(2 *f)/2 +S

Now factor S into two terms:

                        I
                S= Q * 2

Where Q is an odd integer and I is an integer.

When: I n n

                D = Q * 2 *(2 *f)/2  +S

                         I-n   n
                  = Q * 2   *(2 *f)  +S
         n

The factor (2 *f) is represented in 2's complement form simply by extending the sign bit of f into the upper portion of the computer word, If Q = 1 (as it would be with many devices), it can be ignored. If Q >< 1, we may console ourselves that an integer multiply is faster on most machines than a floating point multiply. In fact, on a PDP-10, this multiply can usually be performed with no access to memory since Q is usually small.

                      I-n

We are now left with the 2 factor. This can be accomplished with an arithmetic shift left by (I-n) or an arithmetic shift right by (n-I) as is appropriate. The offset factor, S, may now be added using an integer add.

The procedure for converting NGP coordinates to integer device coordinates is then:

           1.   move coordinate to a register and extend sign
           2.   integer multiply by Q (if necessary)
           3.   arithmetic shift left by (I-n)
           4.   integer add S

This procedure would generally be much faster than:

           1.   move coordinate to register and extend sign
           2.   float fractional coordinate
           3.   floating point multiply
           4.   floating point add
           5.   conversion to fixed point

   [ This RFC was put into machine readable form for entry ]
   [ into the online RFC archives by BBN Corp. under the   ]
   [ direction of Alex McKenzie.                      1/97 ]