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
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Specific Coordinates
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- Conversion of NGP-0 coordinates to floating point PDP-10 coordinates
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- was discussed in RFC #387. In general, however, it is undesirable to
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- convert NGP coordinates to floating point coordinates because real
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- devices require integer addressing. To this end, a means is described
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- to convert NGP coordi- nates to integer coordinates in the range zero
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- to M, where M is the maximum address of the device screen on a machine
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- using 2's complement arithmetic. It would not, however, be difficult
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- to modify this algorithm to operate on machines using one's complement
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- or sign-magnitude arithmetic.
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- First consider the NGP coordinate format:
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+--+-----------+
| | n |
+--+-----------+
s ^ FRACTION
i
g
n
- Where the sign occupies the most significant bit of the coordinate
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- followed by bits of numerical information (initial implementation of
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- NGP requires N=15). Negative numbers are represented by 2's
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- complement. Conversion to device coordinates is accomplished by:
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D = S * f + S
- Where D =>integer device coordinate
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S =>scaling factor (typically M/2)
f =>NGP fractional coordinate
- Let us rewrite this as:
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n n
D = S*(2 *f)/2 +S
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-
I
S= Q * 2
- Where Q is an odd integer and I is an integer.
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- When: I n n
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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
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- extending the sign bit of f into the upper portion of the computer
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- word, If Q = 1 (as it would be with many devices), it can be ignored.
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- If Q >< 1, we may console ourselves that an integer multiply is faster
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- on most machines than a floating point multiply. In fact, on a
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- PDP-10, this multiply can usually be performed with no access to
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- memory since Q is usually small.
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I-n
- We are now left with the 2 factor. This can be accomplished with an
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- arithmetic shift left by (I-n) or an arithmetic shift right by (n-I)
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- as is appropriate. The offset factor, S, may now be added using an
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- integer add.
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- The procedure for converting NGP coordinates to integer device
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- coordinates is then:
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- 1. move coordinate to a register and extend sign
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2. integer multiply by Q (if necessary)
- 3. arithmetic shift left by (I-n)
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4. integer add S
- This procedure would generally be much faster than:
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- 1. move coordinate to register and extend sign
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2. float fractional coordinate
- 3. floating point multiply
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4. floating point add
- 5. conversion to fixed point
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[ 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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