ACIS

Appendix A - FEP Timing Budget

      Purpose

This section describes the timing budget for the science and bias processing modes of the Front End Processor. It details the conditions under which the data throughput requirements of the ACIS Contract End Item Specification (§3.1.3.2a of 36-01101-06) are to be met. These are stated as follows:

"The digital processing system shall be capable of continuous operation in event mode with any input data stream with all of the following characteristics: 1) containing at least 1000 pixels above threshold per second per CCD data stream (due to valid X-ray events, background events, and hot pixels); and ii) containing a total valid X-ray event rate (in all six CCD data streams) of a rate of at least 750 events per second."

These requirements only apply to event mode, not to either histogram or raw mode, since these are for diagnostic purposes only. However, in the interest of completeness, timing budgets have been constructed for all modes.

      Overall Approach

Since the FEP software has been designed according to function rather than performance, timing requirements were not imposed a priori in the design, but rather as a set of a posteriori qualifications to which the prototype designs were subjected. The process is went follows:

A detailed design of a particular FEP science mode was performed and a preliminary design document written.
Prototype C-language source code was written.
The design document and prototype code were reviewed. Obvious errors were corrected and re-design suggestions implemented.
The prototype code was converted to assembler instructions by the gcc compiler (S option) on an R3000 DecStation using maximal optimization.
The assembler code was inspected, and the number of machine instructions required to perform the various stages of the FEP science modes were counted, along with the number of accesses (always entire 32-bit words) to non-cache memory.

      Results

The results are shown in Table 49. The "cycles" column lists the number of machine instructions that were generated for each function, and the "access" column lists the number of 32-bit accesses to non-cache memory, assuming each row contains 1024 pixels and 128 overclocks (a maximum of 32 from each of 4 output nodes).

The rightmost column estimates the execution time of each function, assuming that all cache accesses occupy a single machine cycle (0.1 ľsec), and that non-cache accesses require an additional 2 cycles to perform.

TABLE 49. FEP machine cycles and non-cache memory accesses

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Science Mode          Function             Sub-function     Cycles   Access    Msec   
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Timed Event   Set Up                                          237           0.023  
              Per CCD row             Set Up                   71           0.007  
                                      Overclocks             1600      64   0.173  
                                      Threshold detection    7424      32   0.755  
                                      Total                  9095      96   0.935  
              Per threshold crossing  Set Up                   57       2   0.006  
                                      Detect event            179      12   0.021  
                                      Copy to BEP             152      11   0.018  
                                      Total                   388      25   0.045  
              Per CCD frame(a)        Set Up                  237           0.023  
                                      Total (msec per frame)             1074.500  
Raw Pixels    Set Up                                          150           0.015  
              Per CCD row             Set Up                   57           0.006  
                                      Format pixels          3584     512   0.461  
                                      Format overclocks       768      64   0.090  
                                      Copy to BEP            5762     574   0.691  
                                      Total                 10114    1150   1.248  
              Per CCD frame(b)        Set Up                  119           0.012  
                                      Total (msec per frame)             1277.970  
Histogram     Set Up                                          162           0.017  
              Per CCD row             Set Up                   45           0.005  
                                      Pixel histogram        7860     512   0.885  
                                      Average overclocks     5376      64   0.551  
                                      Total                 13281     576   1.441  
              Report buffer           Clear buffer          65561           6.556  
                                      Copy to BEP          163992   16395  19.679  
              Per CCD frame(c)        Set Up                  124           0.013  
                                      Total (msec per frame)             1475.600  
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(a): assuming 1024 rows per frame and 2600 threshold crossings, each a local maximum
(b): assuming 1024 rows per CCD frame
(c): assuming 1024 rows per CCD frame, with the histogram arrays in cache memory

The times quoted in Table 49 were based on the most pessimistic assumptions for a full-frame timed exposure---a readout time of 2.6 seconds, and hence a total of 2600 threshold crossings, each of which is a local maximum and therefore causes an event record to be sent to the BEP. The figure of 1.074 seconds of CPU time per frame represents a performance margin of 59%. Note, however, that most of the processor time is spent in locating the threshold crossings---the overhead incurred in determining whether a particular crossing is a local minimum, and then copying the event record to the ring buffer, is very small. Inverting the argument, Figure 201 shows how the maximum number of threshold crossings per second is expected to vary with the time between exposures. The break at 2.6 seconds marks the point at which shorter readout times can only be achieved by clocking the CCD in sub-frame readout mode.

FIGURE 201. Threshold Crossings vs. Inter-Exposure Time

There are two conditions under which the CEI specification may not be met. First, when partial frames are read from the CCDs (sub-frame mode) and the inter-exposure time is less than about 0.2 second. In this situation, the need to synchronize the FEP processors via frequent BEP handshakes, coupled with the overhead of generating exposure records, will cause the performance to deteriorate in a TBD manner.

Second, when a disproportionate number of threshold crossings are concentrated at the bottom of the image frame, i.e. the part that is examined last, the FEP may not have sufficient time to process the pixels before they are overwritten by the next frame. This would cause the BEP to command all FEPs to skip a frame. If this condition persists, the overall duty cycle would be halved.

Table 49 also shows that histogram mode possesses a 43% margin in its ability to process full 1024-line image frames at an inter-exposure time of 2.6 seconds. However, each set of histogram arrays occupies 66 Kbytes, which will eventually saturate the 24 Kbaud telemetry downlink if reported more frequently than once per 22 seconds (once per 18 minutes in 500 baud "next-in-line" mode). Similarly, the FEPs possess adequate margin in raw mode, but will quickly fill available buffer space in the BEP and FEPs.

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