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diff --git a/doc/rfc/rfc401.txt b/doc/rfc/rfc401.txt new file mode 100644 index 0000000..35c15dc --- /dev/null +++ b/doc/rfc/rfc401.txt @@ -0,0 +1,112 @@ + + + + + + +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] + |