Debugging computer programs

Advice on Debugging and Verifying Computer Programs. The computer programs needed so far have been relatively simple. Most of the problems can... 

The third reason for our premature rejection of 5 was, as has recently been correctly guessed by Karfunkel (1992), the underdeveloped status of computational chemistry in those days computers large enough to handle C<0 were not available to us. Even when we performed the first semiempirical MO calculations of C60 and C70 in 1986, the molecules were rather too large to be studied by routine calculation and we had to work half a year debugging the program until we finally succeeded in detailed vibrational analysis (Slanina et al. 1987a,b, 1989 Rudzinski 1987). 

When you re debugging a program and one of the variables is being consistently miscalculated, there s a good chance you re a victim of the hierarchy. The quickest way to fix such an error is to liberally sprinkle parentheses throughout the suspicious equations. Your other choice is to trace through the line step by step to find how the computer is evaluating the equation. 

If you ever have to debug a computer program that calculates the dipole moment, then remember that there is a simple and elegant test at your disposal that is based on the above theorem. You just make two runs of the program for a neutral system each time using a different coordinate system (the two systems differing by a translation). The two results have to be identical. 

Software is generally more expensive to implement than hardware, but it is less expensive to duplicate. Because of the inherently sequential nature of computer programs, they are at least an order of magnitude more difficult to design, test, and debug than conventional electronics. However, once software has been correctly implemented, the cost of replicating it is very low in comparison with the equivalent amount of electronics. 

The number of radial increments can be picked arbitrarily. A good approach is to begin with a small number, /= 4, for debugging purposes. When the program is debugged, the value for / is successively doubled until a reasonable degree of accuracy is achieved or until computational times become excessive. If the latter occurs first, find a more sophisticated solution method or a faster computer. 

B1 - B2 These cells contain the values of the variable names in cells A1-A2. The association of the numbers in B1-B2 with the names in A1-A2 is accomplished with the INSERTJMAMEJDEFINE command. (The syntax INSERT NAMEJDEFINE means to use the INSERT pull-down menu, followed by the DEFINE and NAME sub-menus. In many cases there are also convenient keyboard shortcuts that avoid actually using the pull-down menu.) As much as possible, it is important to define names that appear in subsequent formulas. It is very difficult to read and debug a spreadsheet that is programmed entirely with explicit cell references. The variable name for the annulus gap thickness Delta r is in A3 and the value is computed in B3 as = r.out - r in. 

---