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 NGP0 Coordinates to Device

Specific Coordinates

Conversion of NGP0 coordinates to floating point PDP10 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 signmagnitude 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
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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
In 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
PDP10, this multiply can usually be performed with no access to
memory since Q is usually small.
In
We are now left with the 2 factor. This can be accomplished with an
arithmetic shift left by (In) or an arithmetic shift right by (nI)
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 (In)
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 ]
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