Multiple Precision Arithmetic in C++ Implemented by James Pate Williams, Jr.
I have developed a long integer package in C++ using H. T. Lau’s “A Numerical Library in C for Scientists and Engineers”. That library is based on the NUMAL Numerical Algorithms in Algol library. I use 32-bit integers (long) as the basis of the LongInteger type. The base (radix) is 10000 which is the largest base using 32-bit integers. As a test of the library, I use Pollard’s original rho factorization method. I utilized the Alfred J. Menezes et al “Handbook of Applied Cryptography” Miller-Rabin algorithm and ANSI X9.17 pseudo random number generator with Triple-DES as the encryption algorithm. I translated Hans Riesel Pascal code for Euclid’s algorithm and the power modulus technique. I don’t use dynamic long integers a la Hans Riesel’s Pascal multiple precision library. The single precision is 32 32-bit longs and multiple precision 64 32-bit longs.
Here is a typical factorization:
Number to be factored, N = 3 1234 5678 9012 Factor = 3 Is Factor prime? 1 Factor = 4 Is Factor prime? 0 Factor = 102 8806 5751 Is Factor prime? 1 Function Evaluations = 6 Number to be factored, N = 0
The first number of N is the number of base 10000 digits. I verified that 10288065751 was prime using Miller-Rabin and the table found online below:
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
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Numerical Explorations 