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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 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 [ 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 ] [Page 2]