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
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
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