1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
|
<pre>Network Working Group Karl C. Kelley
Request for Comments: 387 Jaacov Meir
NIC: 11359 8/10/72
Categories: D.6, F
Obsoletes:
References: RFC #292
SOME EXPERIENCES IN IMPLEMENTING NETWORK GRAPHICS PROTOCOL LEVEL 0
We are in the process of implementing NGP-0 at several hosts. For
the time being, we are forced to consider the remote host as the "last
intelligent machine". We are attempting to translate NGP-0 to a machine
dependent code for the Computek display. The remote hosts are CCN, UCSD,
and soon RANDCSG. More comments about that work will be made in
subsequent RFC's. The concern of this RFC is twofold:
1. Clarify the coordinate number system.
2. Puzzle over how to do TEXTR string without either:
a. Reading current position and saving it while the text string
is being output, or
b. Monitoring the beam position for each NGP command and saving
this information somewhere.
An appendix to this RFC will outline the conversion from the NGP
coordinate system to the floating point arithmetic on the PDP-1O.
The Coordinate Data
The document for NGP-0 (<a href="./rfc292">RFC 292</a>) does not say specifically that the
format of coordinate data is the same whether the command is in absolute
or relative mode. The only thing stated is that they are in two's
complement notation with the leftmost bit being the sign bit. It is
possible to use two different 2's complement schemes:
<span class="grey">Kelley & Meir [Page 1]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-2" ></span>
<span class="grey"><a href="./rfc387">RFC 387</a> Experience Implementing Net Graphics Protocol August 1972</span>
System A System B
(Absolute Coordinates) (Relative Coordinates)
-1 -2 -3 -16 0 -1 -2 -15
-2 2 2 ... ...2 -2 2 2 ... <a href="#page-2">2</a>
+--+--+--+--+---------+--+--+ +--+--+--+--+---------+--+--+
| | | | | | | | | | | | | | | |
+--+--+--+--+---------+--+--+ +--+--+--+--+---------+--+--+
^ ^
.0111 ...............11 = +1/2-e 0.11 ..............11 = 1-e
.00 .................01 = +e 0.100 .............00 = 1/2
.00 .................0 = 0 0.00...............01 = e
.111 ................11 = -e 0.00 ..............00 = 0
.100 ................ = 1/2 1.11 ..............11 = -e
1.10 ..............00 = -1/2
1.00 ..............01 = -1+e = -(1-e)
1.00 ..............00 = -1
-16 -15
Where: e = 2 Where: e = 2
-16 -15
Range: -1/2 to +1/2 - 2 Range: -1 to +1 - 2
I submit that one could interpret the requirement for absolute
coordinate data to be in the range -1/2 to +1/2 - e as requiring that
two different number systems should be used. Thinking along those
lines, System A has the advantage that you never get handed a number out
of range, which saves some checking worries. It also has one whole bit
more of precision.
I further submit that having two systems to contend with merely
clouds the issue and requires extra coding. It makes more sense just to
stick with System B above. Among the advantages in its use are:
1. The single system can handle both absolute and relative
coordinates.
<span class="grey">Kelley & Meir [Page 2]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-3" ></span>
<span class="grey"><a href="./rfc387">RFC 387</a> Experience Implementing Net Graphics Protocol August 1972</span>
2. If an absolute coordinate exceeds range, simply forcing the sign
bit on causes a nice wrap-around.
3. The representation is the same as the mantissa for floating
point numbers on most machines. Notice, however, that mantissas
of normalized floating point numbers are not in the range for
absolute coordinates. The program will have to shift the
mantissa until exponent is 0.
It may be that few of us interpreted the NGP document to mean two
number systems were needed. If that is the case, so much the better.
In any case, until shaken from the position by the overwhelming force of
contrary logic, we will, in all of our implementations, use System B
above for both absolute and relative coordinates.
The TEXTR Command
-----------------
The last paragraph on page 4 of <a href="./rfc292">RFC 292</a> says, "...a command be
included only if its output is a function solely of the current command
and the "beam position" current at the start of the command. In other
words, the interpreter for level 0 need have no internal storage for
'modes' or pushdown stacks."
In the case of the Computek display, most of the NGP commands
correspond to capabilities of the device. The lone exception is the
TEXTR command. There are two ways to know what beam position to return
to after the string is displayed. One way is to read the cursor position
from the display just before doing the string output. This is no good
because it requires reading from the device (which we can't do until
input protocols are implemented). Also, on this device, the cursor
position is accurate only to within 4 scope points.
The second way to know what beam position to return to is to monitor
all motions of the beam in software. Thus our implementations of NGP-0
to Computek translations will employ a software X register and Y
register. On absolute commands, the registers will be set to the
coordinates for that command. On relative commands, the coordinate data
will be added to the registers. At the beginning and end of picture,
these registers will be set to 0.
The TEXTR command will also cause these software beam registers to
be changed. That is, the X register will be incremented for each
character of the string to correspond to what is happening in the
display itself.
<span class="grey">Kelley & Meir [Page 3]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-4" ></span>
<span class="grey"><a href="./rfc387">RFC 387</a> Experience Implementing Net Graphics Protocol August 1972</span>
APPENDIX
NGP-0 to PDP-10 Floating Point
------------------------------
The NGP-0 looks at all data numbers (X and Y parameters) as a
fraction number in the following format (16 bits per number).
+--+--+--+--+--+--+-----------------+--+--+--+--+
| | | | | | | ... ... | | | | |
+--.--+--+--+--+--+-----------------+--+--+--+--+
Bit position 0 1 2 3 ...... 14 15
with the binary point assumed between bits 0 and 1. Bit 0 is the sign
bit and all negative numbers are represented as their two's complement.
The PDP-10 machine code representation of fractions in floating point
(mantissa part) is very similar to the above (with one exception--the
number -1), so the transformation could be obtained simply by two
operations, move and substitute.
Data (X,Y) Conversion
---------------------
NGP (extreme points) Floating Point (PDP-10)
(16 bits) (36 bits)
exp mantissa
1/2 0.1000 . . . . . .0 0 10000000 10 . . . . . .<a href="#page-0">0</a>
-1/2 1.1000 . . . . . .0 1 01111111 10 . . . . . .<a href="#page-0">0</a>
-1 1.00 . . . . . .0 1 01111101 10 . . . . . .<a href="#page-0">0</a>
Special case
1-e 0.11 . . . . . .1 0 10000000 1111 . . . . .<a href="#page-1">1</a>
<span class="grey">Kelley & Meir [Page 4]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-5" ></span>
<span class="grey"><a href="./rfc387">RFC 387</a> Experience Implementing Net Graphics Protocol August 1972</span>
Translation from NGP into floating point for PDP-1O:
1. Move sign bit (leftmost one) to sign bit.
2. Move fraction part (15 bits) to mantissa part (left justified;
fill with zero's to right).
3. Fill in exponent part (8 bits) according to:
a. If positive number exp = 10000000 = (80) hex
b. If negative number exp = 01111111 = (7F) hex
c. Exception _in_only_ one number
-1 in NGP (negative sign and fraction all zero's)
(1) mantissa becomes same as -1/2
(2) exponent becomes the one's complement of (82) hex
= (7D) hex
The methods of conversion will remain the same regardless of the
number of bits (up to 24) that are used for the NGP fraction.
[ This RFC was put into machine readable form for entry ]
[ into the online RFC archives by Alex McKenzie with ]
[ support from GTE, formerly BBN Corp. 9/99 ]
Kelley & Meir [Page 5]
</pre>
|
