Random Generator (Arbitrary Distribution)

Introduction link

The Random Generator (Arbitrary Distribution) block produces a stream of random values whose histogram reproduces any distribution you give it.

It implements inverse transform sampling (also called the inversion method or the Smirnov transform), the standard way to sample an arbitrary distribution:

      1. tabulate the CUMULATIVE histogram (CDF) of the wanted distribution
    2. draw a uniform random number u
    3. find the bin where u falls on the CDF
    4. that bin index IS the random value
  

Because the CDF is monotonic, step 3 is a binary search, which is what makes the block cheap: one table, one comparator, no multiplier, no divider and no DSP.

Double-click the block to open the Distribution Designer, where the distribution is chosen and the table is built.

Pin Description link

Properties link

Usage link

Where the distribution comes from link

The designer offers three sources, all ending in the same quantised table:

• Library – 58 real measured spectra shipped with the block: isotopes (Cs-137, Co-60, Am-241, Eu-152, Ba-133, K-40, Ra-226 …), samples and materials (KCl, Fiestaware, pitchblende, volcanic material, Chernobyl grass …), HpGe backgrounds and a He-3 neutron spectrum.
• Generator – 20 analytic shapes: Gaussian, uniform, exponential, log-normal, gamma, beta, Weibull, Rayleigh, Maxwell-Boltzmann, chi-squared, Student’s t, Cauchy/Lorentzian, Laplace, triangular, Landau (Moyal approximation, for energy loss), Poisson, binomial, geometric, plus a detector spectrum builder (any number of Gaussian peaks over an exponential Compton-like continuum and a flat background).
• File – CSV / TXT (one count per line, or x,y pairs) and JSON (a flat array of counts).

Shaping the distribution link

The designer maps the source onto the output range with

      out_bin = gain x src_bin + offset
  

applied when the table is built, so it costs nothing in hardware. The three plots show the original histogram, the histogram the block will actually produce (after rebinning and quantisation) and the cumulative histogram with the graphical inversion. Auto fit picks gain and offset that map the non-empty part of the source onto the whole output range.

Rebinning conserves COUNTS, not sample values: a source bin is spread over the output bins it overlaps in proportion to the overlap, so the areas – that is, the probabilities – are preserved.

Output value link

Two independent choices decide what number comes out of OUT.

Output mapping – how the bin index becomes a value:

• Bin index – OUT is the bin number itself, 0 .. Bins-1. With 1024 bins on a 16-bit port you get values 0..1023, not 0..65535. The port is simply wider than the numbers it carries.
• Rescale to full width – the index is stretched over the whole output width: OUT = index x 2^(OutputWidth - log2(Bins)) + dither. With 1024 bins on a 16-bit port you get 0..65535 in steps of 64, and the 6 spare low bits are filled by the dither.

Output format – how that span is interpreted:

• Unsigned – 0 .. Bins-1 (bin index) or 0 .. 2^OutputWidth-1 (rescaled).
• Signed – the same span shifted to sit on zero, two’s complement: -Bins/2 .. Bins/2-1 (bin index) or -2^(OutputWidth-1) .. 2^(OutputWidth-1)-1 (rescaled).

So 1024 bins on a 16-bit port can give you 0..1023, -512..511, 0..65535 or -32768..32767. The designer shows the resulting range live.

Sub-bin dithering only exists in rescale mode, because only there are there bits below the index. It is not cosmetic: a histogram asserts a constant density INSIDE a bin, so filling the sub-bin uniformly reproduces exactly the tabulated distribution. With dithering off the rescaled output is a comb of Bins codes with gaps between them. In bin index mode the setting is ignored.

Rate, and why there is a FIFO link

The binary search takes one clock per step, so one sample costs

      log2(Bins) + 2  clocks
  

(14 clocks for 4096 bins). That is the block’s natural rate – for example ~7.1 Msample/s at 100 MHz with 4096 bins. The output queue decouples that fixed rate from whatever consumes the samples.

Reading a sample: request, then strobe link

      clock N     GET pulses high for one clock
    clock N+1   OUT carries the new sample and DV is high, for exactly
                one clock
  

• DV is a strobe, not a level: it marks the clock on which a freshly delivered sample appears. Between strobes OUT simply holds the last sample delivered.
• READY tells you whether a GET will succeed: it is high while at least one sample is queued. Gate GET with it, or accept the underflow.
• UNDERFLOW pulses when GET arrives on an empty queue. It comes from the Xilinx FIFO primitive and is registered, so it appears one clock after the offending GET – in the cycle DV would have occupied had the read succeeded. On such a GET, DV does not strobe.
• When the queue is full the generator stops and restarts by itself as soon as a slot frees up. No sample is ever generated and thrown away.

Typical applications link

• Detector emulation: feed a real measured spectrum into an MCA or DPP chain without a source and without a detector.
• Monte Carlo stimulus for trigger and pile-up algorithms.
• Realistic event-rate and amplitude generation for firmware self-test.
• Any application needing noise with a prescribed, non-Gaussian shape.

Reset link

RESET clears the queue and reloads the RNG seed, so the sequence restarts identically. Two blocks with the same seed produce the same stream: give them different seeds when you need independent channels.

Resources & Timing link

• Latency: log2(Bins) + 2 clock cycles per sample (14 with the default 4096 bins)

• Throughput: one sample every log2(Bins) + 2 clocks; the FIFO decouples the reader

No DSP and no multiplier: one comparator, one adder and the table. The table costs ceil(CdfWidth/36) x ceil(Bins/1024) BRAM36 (the designer shows the live figure) plus the output FIFO. Pure VHDL, no HLS. The random source is a 64-bit xorshift generator (period 2^64-1) and the output queue is a Xilinx XPM FIFO in standard read mode (one clock of read latency), which is what gives the GET-then-strobe protocol.