Author: jamespatewilliamsjr
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.
Rice-Golomb Encoder and Decoder Copyright (c) Thursday, April 3, 2025, to Sunday, April 6, 2025, by James Pate Williams, Jr. BA, BS, Master of Software Engineering, Doctor of Philosophy Computer Science
Online references:
https://en.wikipedia.org/wiki/Golomb_coding
// Rice-Golomb Encoder and Decoder
// Copyright (c) Thursday, April 3, 2025
// by James Pate Williams, Jr.
// BA, BS, Master of Software Engineering
// Doctor of Philosophy Computer Science
// Online references:
// https://en.wikipedia.org/wiki/Golomb_coding
// https://ntrs.nasa.gov/api/citations/19790014634/downloads/19790014634.pdf
#include <iostream>
#include <string>
#include <vector>
//#include <stdlib.h>
bool Encode(const char* NChars, size_t NCharsCount,
long M, long long& N, std::vector<char>& qBits,
std::vector<char>& rBits, unsigned int& qSize, unsigned int& rSize,
long long& q, long long& r, unsigned int& NSize) {
N = NChars[0] - (long long)'0';
for (unsigned int i = 1; i < NCharsCount; i++) {
N = 10 * N + (long long)NChars[i] - (long long)'0';
}
q = N / M;
r = N % M;
qSize = 0;
while (qSize < q) {
qBits.push_back('1');
qSize++;
}
qBits.push_back('0');
qSize++;
rSize = 0;
unsigned int b = (unsigned int)floor(log2(M));
if (b > 62) {
return false;
}
long long p = (long long)pow(2, b + 1);
if (r < p - M) {
long long rr = r;
while (rr > 0) {
long long digit = (rr & 1) == 1 ? 1 : 0;
rBits.push_back((char)digit + '0');
rSize++;
rr >>= 1;
}
rBits.push_back('0');
rSize++;
}
else {
long long rr = r + p - M;
while (rSize < b + 1) {
long long digit = rr & 1 ? 1 : 0;
rBits.push_back((char)digit + '0');
rSize++;
rr >>= 1;
}
}
long long rValue = rBits[0];
for (size_t i = 1; i < rSize; i++) {
rValue = rValue * 2 + rBits[i];
}
long long NBitCount = 0;
while (N > 0) {
N >>= 1;
NBitCount++;
}
std::cout << "q-bits size = " << qSize << std::endl;
std::cout << "r-bits size = " << rSize << std::endl;
std::cout << "N-bits size = " << qSize + rSize << std::endl;
std::cout << "N-Chars * 8-Bits per Char = " << NCharsCount * 8 << std::endl;
std::cout << "% Compression = " << 100.0 * (1.0 - (qSize + rSize) /
(NCharsCount * 8.0)) << std::endl;
return true;
}
void Decode(long long M, long long& N,
std::vector<char> qBits, std::vector<char> rBits,
unsigned int& qSize, unsigned int& rSize,
long long& q, long long& r) {
int count = 0;
while (qBits[count] != '0') {
count++;
}
q = count;
int c = (int)rSize - 1;
unsigned int b = (unsigned int)floor(log2(M));
long long p = (long long)pow(2, b + 1);
long long s = 0;
r = rBits[c--] - (long long)'0';
do {
r = 2 * r + rBits[c] - (long long)'0';
c--;
} while (c >= 0);
if (r < p - M) {
s = r;
}
else {
s = r + p - M;
c = 1;
r = rBits[0] - (long long)'0';
while (c < (int)(b + 1)) {
r = 2 * r + rBits[c] - (long long)'0';
c++;
}
s = r;
}
r = s;
N = q * M + r;
}
int main() {
char line[128] = { };
size_t NSize = 0, qSize = 0, rSize = 0;
long long M = 10, N = 42, q = -1, r = -1;
std::vector<char> qBits, rBits;
std::cout << "M = ";
std::cin.getline(line, 127);
std::string str1(line);
M = std::stoi(str1);
std::cout << "N = ";
std::cin.getline(line, 127);
std::string str2(line);
Encode(str2.c_str(), strlen(str2.c_str()), M, N,
qBits, rBits, qSize, rSize, q, r, NSize);
std::cout << "q = " << q << std::endl;
std::cout << "r = " << r << std::endl;
std::cout << "q-size = " << qSize << std::endl;
std::cout << "r-size = " << rSize << std::endl;
std::cout << "q ";
for (unsigned int i = 0; i < qSize; i++) {
std::cout << qBits[i] << ' ';
}
std::cout << std::endl;
std::cout << "r ";
for (int i = (int)rSize - 1; i >= 0; i--) {
std::cout << rBits[i] << ' ';
}
std::cout << std::endl;
Decode(M, N, qBits, rBits, qSize, rSize, q, r);
std::cout << "q = " << q << std::endl;
std::cout << "r = " << r << std::endl;
std::cout << "q-size = " << qSize << std::endl;
std::cout << "r-size = " << rSize << std::endl;
std::cout << "q ";
for (unsigned int i = 0; i < qSize; i++) {
std::cout << qBits[i] << ' ';
}
std::cout << std::endl;
std::cout << "r ";
for (int i = rSize - 1; i >= 0; i--) {
std::cout << rBits[i] << ' ';
}
std::cout << std::endl;
std::cout << "N = " << N << std::endl;
return 0;
}
M = 64
N = 1027
q-bits size = 17
r-bits size = 3
N-bits size = 20
N-Chars * 8-Bits per Char = 32
% Compression = 37.5
q = 16
r = 3
q-size = 17
r-size = 3
q 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
r 0 1 1
q = 16
r = 3
q-size = 17
r-size = 3
q 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
r 0 1 1
N = 1027
Lexical.cpp Copyright (c) Friday, April 4, 2025, by James Pate Williams, Jr. Reference: “Modern Compiler Implementation in Java Second Edition” (c) 2002 by Andrew W. Appel with Jens Palsberg Chapter Two, Lexical Analysis
// Lexical.cpp
// Copyright (c) Friday, April 4, 2025, by
// James Pate Williams, Jr.
// Reference: "Modern Compiler Implementation
// in Java Second Edition" (c) 2002
// Andrew W. Appel with Jens Palsberg
// Chapter Two, Lexical Analysis
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
std::vector<char> AlphabeticChars = { 'A', 'B', 'C', 'D', 'E', 'F',
'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R',
'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e',
'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r',
's', 't', 'u', 'v', 'w', 'x', 'y', 'z' };
std::vector<char> BracketChars = { '(', ')', '{', '}', '[', ']' };
std::vector<char> ArithmeticOps = { '+', '-', '*', '/', '%' };
std::vector<char> LogicalOps = { '&', '^', '|' };
std::vector<char> DecimalDigits = { '0', '1', '2', '4', '5', '6',
'7', '8', '9' };
std::vector<char> WhiteSpace = { ' ', '\t', '\n' };
std::vector<std::string> ReservedWords = {
"do", "double", "else", "for", "if", "int", "long", "while" };
char reservedWordsAscii[8][8] = { { } };
std::vector<char> AlphaNumericChars;
bool TokenScan(
std::string wline,
bool& arithmeticOp,
bool& bracket,
bool& endOfLine,
bool& id,
bool& intNumber,
bool& logicalOp,
bool& realNumber,
bool& reservedWord,
bool& whiteSpace,
char& arithmeticOpChar,
char& bracketChar,
char& ch,
char& endOfLineChar,
char& whiteSpaceChar,
size_t& cptr,
std::string& idStr,
std::string& intNumberStr,
std::string& realNumberStr,
std::string& reservedWordStr) {
const char* line = wline.c_str();
ch = line[cptr];
while (ch == ' ' || ch == '\t' || ch == '\n' && cptr < strlen(line)) {
cptr++;
ch = line[cptr];
}
if (ch == '\n' || cptr == strlen(line)) {
endOfLine = true;
endOfLineChar = '\n';
return true;
}
ch = line[cptr];
if (ch >= 'A' && ch <= 'Z' ||
ch >= 'a' && ch <= 'z') {
idStr += ch;
cptr++;
while (cptr < strlen(line)) {
ch = line[cptr];
if (ch >= '0' && ch <= '9' ||
ch >= 'A' && ch <= 'Z' ||
ch >= 'a' && ch <= 'z' ||
ch == '_') {
idStr += ch;
cptr++;
}
else if (ch == ' ' || ch == '\t' || ch == '\n') {
cptr++;
break;
}
else {
id = false;
return false;
}
}
id = true;
char reservedWordAscii[8] = { };
reservedWordStr = "";
for (size_t i = 0; i < strlen(idStr.c_str()); i++) {
reservedWordAscii[i] = idStr.c_str()[i];
}
reservedWordAscii[strlen(idStr.c_str())] = '\0';
for (size_t i = 0; i < 8; i++) {
size_t count = 0;
reservedWord = false;
reservedWordStr = "";
for (size_t j = 0; j < strlen(reservedWordsAscii[i]); j++) {
if (reservedWordAscii[j] == reservedWordsAscii[i][j]) {
reservedWord = true;
reservedWordStr += idStr[j];
count++;
}
}
if (reservedWord && count == strlen(reservedWordsAscii[i])) {
break;
}
}
if (reservedWord) {
id = false;
}
if (id) {
id = true;
reservedWord = false;
reservedWordStr = "";
}
else {
id = false;
idStr = "";
}
return id || reservedWord;
}
else if (ch >= '0' && ch <= '9')
{
intNumberStr = "";
realNumberStr = "";
intNumberStr += ch;
realNumberStr += ch;
cptr++;
ch = line[cptr];
if (ch >= '0' && ch <= '9') {
intNumberStr += ch;
cptr++;
ch = line[cptr];
while (cptr < strlen(line)) {
ch = line[cptr];
if (ch >= '0' && ch <= '9') {
intNumberStr += ch;
cptr++;
}
else if (ch == ' ' || ch == '\t' || ch == '\n') {
cptr++;
break;
}
else {
intNumber = false;
return false;
}
}
intNumber = true;
return true;
}
else if (ch == '.') {
realNumberStr += ch;
cptr++;
ch = line[cptr];
if (ch >= '0' && ch <= '9') {
realNumberStr += ch;
cptr++;
while (cptr < (int)strlen(line)) {
ch = line[cptr];
if (ch >= '0' && ch <= '9') {
realNumberStr += ch;
cptr++;
}
else if (ch == ' ' || ch == '\t' || ch == '\n') {
cptr++;
break;
}
else {
realNumber = false;
return false;
}
}
realNumber = true;
return true;
}
}
}
else if (ch == '.') {
realNumberStr += ch;
cptr++;
ch = line[cptr];
if (ch >= '0' && ch <= '9') {
realNumberStr += ch;
cptr++;
while (cptr < (int)strlen(line)) {
ch = line[cptr];
if (ch >= '0' && ch <= '9') {
realNumberStr += ch;
cptr++;
}
else if (ch == ' ' || ch == '\t' || ch == '\n') {
cptr++;
break;
}
else {
realNumber = false;
return false;
}
}
realNumber = true;
return true;
}
else {
realNumber = false;
return false;
}
}
return false;
}
bool LineScan(
std::string wline,
bool& arithmeticOp,
bool& bracket,
bool& endOfLine,
bool& id,
bool& intNumber,
bool& logicalOp,
bool& realNumber,
bool& reservedWord,
bool& whiteSpace,
char& arithmeticOpChar,
char& bracketChar,
char& ch,
char& endOfLineChar,
char& whiteSpaceChar,
size_t& cptr,
std::string& idStr,
std::string& intNumberStr,
std::string& realNumberStr,
std::string& reservedWordStr)
{
const char* line = wline.c_str();
ch = line[cptr];
while (ch == ' ' || ch == '\t' || ch == '\n' && cptr < strlen(line)) {
cptr++;
ch = line[cptr];
}
if (ch == '\n' || cptr == strlen(line)) {
endOfLine = true;
endOfLineChar = '\n';
return true;
}
arithmeticOp = bracket = endOfLine = id = false;
intNumber = logicalOp = realNumber = whiteSpace = false;
arithmeticOpChar = '\0', bracketChar = '\0', ch = '\0';
endOfLineChar = '\0', whiteSpaceChar = '\0';
if (TokenScan(
line,
arithmeticOp,
bracket,
endOfLine,
id,
intNumber,
logicalOp,
realNumber,
reservedWord,
whiteSpace,
arithmeticOpChar,
bracketChar,
ch,
endOfLineChar,
whiteSpaceChar,
cptr,
idStr,
intNumberStr,
realNumberStr,
reservedWordStr)) {
if (id || intNumber || realNumber || reservedWord) {
return true;
}
if (endOfLine) {
return true;
}
ch = line[cptr];
if (ch == ' ' || ch == '\t' || ch == '\n') {
cptr++;
ch = line[cptr];
}
else if (ch == '\n') {
cptr++;
ch = line[cptr];
endOfLine = true;
return true;
}
}
else if (ch == '\\') {
cptr++;
if (cptr == strlen(line)) {
return false;
}
ch = line[cptr];
if (ch == '\\') {
// found a one-line comment
// skip until end-of-line
cptr++;
ch = line[cptr];
while (cptr < strlen(line) && ch != '\n') {
ch = line[cptr++];
}
return ch == '\n';
}
else {
// single \ found
return false;
}
}
const auto itao = std::find(ArithmeticOps.begin(), ArithmeticOps.end(), ch);
if (itao != ArithmeticOps.end()) {
arithmeticOp = true;
return true;
}
const auto itbc = std::find(BracketChars.begin(), BracketChars.end(), ch);
if (itbc != BracketChars.end()) {
bracketChar = true;
return true;
}
const auto itlo = std::find(LogicalOps.begin(), LogicalOps.end(), ch);
if (itlo != LogicalOps.end()) {
logicalOp = true;
return true;
}
const auto itdd = std::find(DecimalDigits.begin(), DecimalDigits.end(), ch);
if (itdd != DecimalDigits.end()) {
intNumberStr += ch;
cptr++;
ch = line[cptr];
while (ch >= '0' && ch <= '9') {
intNumberStr += ch;
}
const auto iws = std::find(WhiteSpace.begin(), WhiteSpace.end(), ch);
if (iws != WhiteSpace.end()) {
intNumber = intNumberStr.size() > 1;
whiteSpace = true;
return true;
}
else {
return false;
}
}
return false;
}
int main()
{
for (size_t i = 0; i < AlphabeticChars.size(); i++) {
AlphaNumericChars.push_back(AlphabeticChars[i]);
}
for (size_t i = 0; i < DecimalDigits.size(); i++) {
AlphaNumericChars.push_back(DecimalDigits[i]);
}
for (size_t i = 0; i < 8; i++) {
for (size_t j = 0; j < strlen(ReservedWords[i].c_str()); j++) {
reservedWordsAscii[i][j] = ReservedWords[i].c_str()[j];
}
reservedWordsAscii[i][strlen(ReservedWords[i].c_str())] = '\0';
}
const char* line0 = { };
std::string line1 = "abc4 def_5 amp c1\n";
std::string line2 = ".1234 0.4567 9876 while for\n";
std::string line3 = "\\\\this is a one-line comment\n";
std::string line4 = "a + b / c\n";
for (int i = 1; i <= 4; i++) {
bool arithmeticOp = false, bracket = false, endOfLine = false;
bool id = false, intNumber = false, logicalOp = false, realNumber = false;
bool reservedWord = false, whiteSpace = false;
char arithmeticOpChar = '\0', bracketChar = '\0', ch = '\0';
char endOfLineChar = '\0', logicalOpChar = '\0', whiteSpaceChar = '\0';
size_t cptr = 0;
std::string idStr, intNumberStr, realNumberStr, reservedWordStr;
if (i == 1) {
line0 = line1.c_str();
}
else if (i == 2) {
line0 = line2.c_str();
}
else if (i == 3) {
line0 = line3.c_str();
}
else if (i == 4) {
line0 = line4.c_str();
}
while (cptr < strlen(line0) && ch != '\n') {
if (LineScan(
line0,
arithmeticOp,
bracket,
endOfLine,
id,
intNumber,
logicalOp,
realNumber,
reservedWord,
whiteSpace,
arithmeticOpChar,
bracketChar,
ch,
endOfLineChar,
whiteSpaceChar,
cptr,
idStr,
intNumberStr,
realNumberStr,
reservedWordStr)) {
if (id) {
ch = line0[cptr];
std::cout << "id = " << idStr << std::endl;
std::cout << "cptr = " << cptr << std::endl;
std::cout << "ch = " << ch << std::endl;
id = false;
idStr = "";
}
else if (intNumber) {
std::cout << "int number = " << intNumberStr << std::endl;
std::cout << "cptr = " << cptr << std::endl;
std::cout << "ch = " << ch << std::endl;
intNumber = false;
intNumberStr = "";
}
else if (realNumber) {
std::cout << "real number = " << realNumberStr << std::endl;
std::cout << "cptr = " << cptr << std::endl;
std::cout << "ch = " << ch << std::endl;
realNumber = false;
realNumberStr = "";
}
else if (reservedWord) {
std::cout << "reserved word = " << reservedWordStr << std::endl;
std::cout << "cptr = " << cptr << std::endl;
std::cout << "ch = " << ch << std::endl;
reservedWord = false;
reservedWordStr = "";
}
else {
if (arithmeticOp) {
arithmeticOpChar = ch = line0[cptr++];
std::cout << "Arithmetic operator character = ";
std::cout << arithmeticOpChar << std::endl;
}
}
if (ch == '\0' || ch == '\n' || cptr >= strlen(line0)) {
break;
}
}
}
}
return 0;
}
Chapter One Straight-Line Program Interpreter from “Modern Compiler Implementation in Java Second Edition” (c) 2002 by Andrew W. Appel, Translation to C++ by James Pate Williams, Jr. on Thursday, April 3, 2025
Wayback in the Spring Semester of 2006, after I was awarded my Doctor of Philosophy Degree in Computer Science, I partially audited a Compiler Design Course. Due to my mental aberrations, I was unable to complete the course. The instructor was on a Sabbatical from the United States Air Force Academy in Colorado Springs, Colorado. The textbook we used, and I still have a copy, was “Modern Compiler Implementation in Java Second Edition” © 2002 by Andrew W. Appel. Below is a translation from Java to C++ that I just completed.
// Chapter One program translated from Java to C++ by
// James Pate Williams, Jr. (c) Wednesday April 3, 2025
// Reference: "Modern Complier Implementation in Java
// Second Edition" (c) 2002 by Andrew W. Appel
#ifndef _SLPInterpreter_H
#include <iostream>
#include <stack>
#include <string>
#include <vector>
class TableEntry {
public:
std::string symbol, value;
TableEntry(std::string symbol, std::string value) {
this->symbol = symbol;
this->value = value;
}
};
std::stack<std::string> sStack;
std::vector<TableEntry> symbolTable;
class Exp {
public:
Exp() { };
virtual ~Exp() { };
};
std::stack<Exp> eStack;
class ExpList {
public:
ExpList() { };
virtual ~ExpList() { };
};
class Stm {
public:
Stm() { };
virtual ~Stm() { };
};
class CompoundStm : public Stm {
public:
Stm stm1, stm2;
CompoundStm(Stm stm1, Stm stm2) {
this->stm1 = stm1;
this->stm2 = stm2;
};
};
class AssignStm : public Stm {
public:
std::string id;
Exp exp;
AssignStm(std::string id, Exp exp) {
this->id = id;
this->exp = exp;
bool found = false;
for (int i = 0; !found && i < (int)symbolTable.size(); i++) {
if (symbolTable[i].symbol == id) {
found = true;
}
}
if (!found) {
symbolTable.push_back(TableEntry(id, ""));
}
};
void Print() {
std::cout << this->id << ' ';
};
};
class PrintStm : public Stm {
public:
ExpList exps;
PrintStm(ExpList exps) {
this->exps = exps;
};
};
class IdExp : public Exp {
public:
std::string id;
IdExp(std::string id) {
this->id = id;
Print();
TableEntry te(id, "");
};
void Print() {
std::cout << id << ' ';
};
};
class NumExp : public Exp {
public:
int num;
NumExp(int num) {
this->num = num;
Print();
char buffer[128] = { };
_itoa_s(num, buffer, 127, 10);
sStack.push(std::string(buffer));
};
void Print() {
std::cout << num << ' ';
};
};
enum class ArithmeticOp {
Plus, Minus, Times, Div
};
class OpExp : public Exp {
public:
Exp left, right;
ArithmeticOp op;
OpExp(Exp left, ArithmeticOp op, Exp right) {
this->left = left;
this->op = op;
this->right = right;
std::string ops = "";
switch (op) {
case ArithmeticOp::Plus:
ops = "+";
break;
case ArithmeticOp::Minus:
ops = "-";
break;
case ArithmeticOp::Times:
ops = "*";
break;
case ArithmeticOp::Div:
ops = "/";
break;
};
std::cout << ops << std::endl;
eStack.push(left);
eStack.push(right);
sStack.push(ops);
};
};
class EseqExp : public Exp {
public:
Stm stm; Exp exp;
EseqExp(Stm stm, Exp exp) {
this->stm = stm;
this->exp = exp;
};
};
class PairExpList : public ExpList {
public:
Exp head;
ExpList tail;
PairExpList(Exp head, ExpList tail) {
this->head = head;
this->tail = tail;
};
};
class LastExpList : public ExpList {
public:
Exp head;
LastExpList(Exp head) {
this->head = head;
};
};
#endif _SLPInterpreter_H
int main() {
int a = 0, b = 0;
Stm prog(CompoundStm(AssignStm("a",
OpExp(NumExp(5), ArithmeticOp::Plus, NumExp(3))),
CompoundStm(AssignStm("b",
EseqExp(PrintStm(PairExpList(IdExp("a"),
LastExpList(OpExp(IdExp("a"),
ArithmeticOp::Minus, NumExp(1))))),
OpExp(NumExp(10), ArithmeticOp::Times, IdExp("a")))),
PrintStm(LastExpList(IdExp("b"))))));
bool first = true;
int result = 0;
//sStack.push("0");
while (!sStack.empty()) {
std::string lts, ops, rts;
if (first) {
ops = sStack.top();
sStack.pop();
lts = sStack.top();
sStack.pop();
rts = sStack.top();
sStack.pop();
first = false;
}
else {
lts = sStack.top();
sStack.pop();
ops = sStack.top();
sStack.pop();
rts = sStack.top();
sStack.pop();
}
int lvi = std::stoi(lts);
int rvi = std::stoi(rts);
if (ops == "+") {
result = lvi + rvi;
}
else if (ops == "-") {
result = lvi - rvi;
}
else if (ops == "*") {
result = lvi * rvi;
}
else if (ops == "/") {
result = lvi / rvi;
}
char ascii[128] = { };
_itoa_s(result, ascii, 10);
if (sStack.size() != 0) {
sStack.push(std::string(ascii));
}
}
std::cout << "Result = " << result << std::endl;
return 0;
}
Approximation of the Ground-State Total Energy of a Beryllium Atom © Sunday, March 30 to Tuesday April 1, 2025, by James Pate Williams, Jr., BA, BS, Master of Software Engineering, PhD Computer Science
Blog Entry © Sunday, March 29, 2025, by James Pate Williams, Jr., BA, BS, Master of Software Engineering, PhD Slater Determinant Coefficients for Z = 2 to 4
Enter the atomic number Z (2 to 6 or 0 to quit): 2
2 1 1 + a(1)b(2)
1 0 0 - a(2)b(1)
# Even Permutations = 1
Enter the atomic number Z (2 to 6 or 0 to quit): 3
6 3 1 + a(1)b(2)c(3)
5 2 0 - a(1)b(3)c(2)
4 2 0 - a(2)b(1)c(3)
3 1 1 + a(2)b(3)c(1)
2 1 1 + a(3)b(1)c(2)
1 0 0 - a(3)b(2)c(1)
# Even Permutations = 3
Enter the atomic number Z (2 to 6 or 0 to quit): 4
24 12 0 + a(1)b(2)c(3)d(4)
23 11 1 - a(1)b(2)c(4)d(3)
22 11 1 - a(1)b(3)c(2)d(4)
21 10 0 + a(1)b(3)c(4)d(2)
20 10 0 + a(1)b(4)c(2)d(3)
19 9 1 - a(1)b(4)c(3)d(2)
18 9 1 - a(2)b(1)c(3)d(4)
17 8 0 + a(2)b(1)c(4)d(3)
16 8 0 + a(2)b(3)c(1)d(4)
15 7 1 - a(2)b(3)c(4)d(1)
14 7 1 - a(2)b(4)c(1)d(3)
13 6 0 + a(2)b(4)c(3)d(1)
12 6 0 + a(3)b(1)c(2)d(4)
11 5 1 - a(3)b(1)c(4)d(2)
10 5 1 - a(3)b(2)c(1)d(4)
9 4 0 + a(3)b(2)c(4)d(1)
8 4 0 + a(3)b(4)c(1)d(2)
7 3 1 - a(3)b(4)c(2)d(1)
6 3 1 - a(4)b(1)c(2)d(3)
5 2 0 + a(4)b(1)c(3)d(2)
4 2 0 + a(4)b(2)c(1)d(3)
3 1 1 - a(4)b(2)c(3)d(1)
2 1 1 - a(4)b(3)c(1)d(2)
1 0 0 + a(4)b(3)c(2)d(1)
# Even Permutations = 12
Enter the atomic number Z (2 to 6 or 0 to quit):
// AOPermutations.cpp : This file contains the 'main' function.
// Program execution begins and ends there.
// Copyright (c) Saturday, March 29, 2025
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Signs of the atomic orbitals in a Slater Determinant
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
int main()
{
char alpha[] = { 'a', 'b', 'c', 'd', 'e', 'f' }, line[128] = {};
int factorial[7] = { 1, 1, 2, 6, 24, 120, 720 };
while (true)
{
int col = 0, counter = 0, row = 0, sign = 1, t = 0, Z = 0, zfact = 0;
int numberEven = 0;
std::cout << "Enter the atomic number Z (2 to 6 or 0 to quit): ";
std::cin.getline(line, 127);
std::string str(line);
Z = std::stoi(str);
if (Z == 0)
{
break;
}
if (Z < 2 || Z > 6)
{
std::cout << "Illegal Z, please try again" << std::endl;
continue;
}
zfact = factorial[Z];
std::vector<char> orb(Z);
std::vector<int> tmp(Z), vec(Z);
for (int i = 0; i < Z; i++)
{
orb[i] = alpha[i];
vec[i] = i + 1;
}
do
{
for (int i = 0; i < (int)vec.size(); i++)
{
tmp[i] = vec[i];
}
t = 0;
do
{
t++;
} while (std::next_permutation(tmp.begin(), tmp.end()));
std::cout << t << '\t' << t / 2 << '\t';
std::cout << (t / 2 & 1) << '\t';
if (Z == 2 || Z == 3)
{
if ((t / 2 & 1) == 0)
{
std::cout << "-\t";
}
else
{
std::cout << "+\t";
numberEven++;
}
}
else
{
if ((t / 2 & 1) == 1)
{
std::cout << "-\t";
}
else
{
std::cout << "+\t";
numberEven++;
}
}
for (int i = 0; i < Z; i++)
{
std::cout << orb[i] << '(' << vec[i] << ')';
}
row++;
std::cout << std::endl;
if (zfact != 2 && row == zfact)
{
std::cout << std::endl;
break;
}
row %= Z;
} while (std::next_permutation(vec.begin(), vec.end()));
std::cout << "# Even Permutations = ";
std::cout << numberEven << std::endl;
}
return 0;
}
Numerical Explorations 