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