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PROJECTS BY BRADLEY BERG


WHITE PAPERS

CLIMATE EMERGENCY ESSENTIAL LINKS




A GENERAL PURPOSE PROGRAMMING LANGUAGE AND COMPILER

The Gilda language is intended to make it easier and to build high quality
software. This is achieved by addressing issues with portability, reuse, ease of
use, software maintenance, reliability, testing, and debugging. The language
integrates several innovations with a clean and simple syntax.



Overview of the Gilda Programming Language


Design and Implementation of Iterative Loops


Examples:   
Hello World
Phonecode




64 BIT PRIMALITY TEST

These primality tests extend Steve Worley's 32 bit primality test. They improve
on Jim Sinclair's test that uses 7 SPRP tests. 32 bit numbers are checked with a
single SPRP test, two are used for 49 bit numbers, and three for 64 bit numbers.

Numbers under 2^32 can be tested using the SPRP bases in: is.prime.32.base.data

Numbers from 2^32 to 2^64 can be tested using the base pairs in:
is.prime.64.base.data

The is.prime.gg Gilda function determines if any 64 bit number is prime.
The list.is.prime.32.g program lists the bases used to test 32 bit numbers for
primality.
It uses this sprp.gg implementation of the Strong Probable Prime test.

The sprp test can be substantially sped up with negligible overhead by
interleaving it with trial division over small primes. A modulus by a small
prime is computed in each iteration of the loop for Base ^ D mod N.

Numbers with 49 or fewer bits fit in a floating point double. The modulus can be
computed by multiplying by the reciprocal of small primes that are pre-computed
and stored in an array. Division is avoided and processors can perform floating
point operations in parallel with integer operations.

This Visual C code, sprp_two_trial_49.c, computes 2^E mod N and trial division
for small primes.

Likewise numbers with 50 to 64 bits needs to use integer division. Arithmetic
operations can still be issued in parallel with the divisions to reduce the
overhead of trial division. The sprp_two_trial.c procedure illustrates this
strategy.

Primality testing was 1.4 times faster for 32 bit numbers, 2.4 times faster for
numbers with 33 to 49 bits, and 4.75 times faster for 50 to 64 bit numbers. Even
though integrating trial division finds more numbers to be composite, it's not
that many more. These procedures can also be used as the first stage of
factorization routines to take advantage of the trial division results.

Please let me know if you can verify any of these algorithms or suggest
improvements. If you revise the Visual C code to work with other compilers, pass
them along to me and I'll merge it with the samples and post them. You can also
visit this page for recent progress involving the Miller-Rabin primality test.




COLLATZ CONJECTURE

The Collatz sequence is chaotic and cannot be resolved using conventional
algebra. Consequently proof strategies attempting to cover all possible values
in sequence runs will not work. They often appear to cover all values, but there
are always some cases that are overlooked. Terence Tao's important paper
generalizes this phenomenon and reduces the bounds to minuscule limits.

There are two different problems to consider here - a linear sequence problem
and a circular sequence problem. Instead of looking for patterns in the values
produced by the sequence, these papers analyze the underlying mechanics of the
sequence. For anyone interested in the topic they give the reader insight into
the workings of these two problems and lay out compelling strategies that
address both.

After this talk in the Q&A Terence Tao said about the linear problem, "If you
get to randomize N every time you pass through this [region] it becomes like
this [linear downward] drift." He also limited his paper to the linear problem
saying, "The only way to disprove it is to produce a cycle."

This first paper uses Shannon entropy to analyze the linear problem for the
Collatz Conjecture. For a pseudo random number generator to be unbiased it must
use operations that generate values with an equal distribution of zero and one
bits. The sequence does just that, however, an infinitely long run requires
values biased towards one so it cannot be generated.

The second paper addresses the circular problem for the Collatz Conjecture by
deriving bounds on the sequence. One set of bounds show that the starting seed
value has to be relatively large to form a loop of a given length. Another
contradictory set of bounds show that the seed is limited to much smaller
values.




INTEGRATED PREAMP / CROSSOVER / TWEETER-MIDRANGE AUDIO AMPLIFIER

Design notes for a high fidelity low cost stereo system.




COMPUTER MEMORY

Nano-Memory Simulation


Securing Personal Portable Storage


New Computers Based On Non-Volatile Random Access Memory








LOGIC PROGRAMMING

B. A. Berg, "Modeling Access Control Policy With The RW Language", Brown
University, May 14, 2006
https://www.techneon.com/paper/rw_access.html









PUBLICATIONS

B. A. Berg, "Disentangling Exceptions", Brown University, December, 2008

https://cs.brown.edu/research/pubs/theses/masters/2009/berg.pdf






Ahmad, Berg, Cetintemel, Humphrey, Hwang, Jhingran, Maskey, Papaemmanouil,
Rasin, Tatbul, Xing, Zdonik,
"Distributed Operation in the Borealis Stream Processing Engine", 2nd
International Conference on Geosensor Networks, Boston, MA, October 2006

https://www.cs.brown.edu/research/borealis/public/publications/sigmod05.demo.pdf






B. A. Berg, "A Distributed Catalog for the Borealis Stream Processing Engine",
Brown University, May 31, 2006

https://www.cs.brown.edu/research/borealis/public/publications/distributed_catalog.pdf






Daniel V. Bailey, Bradley Berg, "Remote management interface using credentials
associated with respective access control intervals",
United States Patent: 9,455,977, September 27, 2016

https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/9455977






LAST UPDATED: OCTOBER 14, 2023