# Request For Comments - RFC401

You are here: irt.org | RFCs | RFC401 [ previous next ]

```

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

[Page 1]

```

```
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
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

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)

This procedure would generally be much faster than:

1.   move coordinate to register and extend sign
2.   float fractional coordinate
3.   floating point multiply