8.5 Diagnostic messages

ode is always in one of two states:

• Reading input. The input includes a specification of a system of ordinary differential equations, together with instructions for solving it numerically: a ‘print’ line and a ‘step’ line.
• Numerically solving a system, and printing the resulting output.

ode moves from the first to the second state after it sees and processes a ‘step’ line. It returns to the first state after the generated output has been printed. Errors may occur in the `reading' state or the `solving' state, and may terminate computations or even cause ode to exit. We now explain the possible sorts of error.

While reading input, ode may encounter a syntax error: an ungrammatical line that it is unable to parse. (For a summary of its input grammar, see Input Language.) If so, it emits the error message

     ode::nnn: syntax error

where ‘nnn’ is the number of the line containing the error. When the ‘-f filename’ option is used to specify an input file, the error message will read

     ode:filename:nnn: syntax error

for errors encountered inside the input file. Subsequently, when ode begins reading the standard input, line numbers will start over again from 1.

No effort is made to recover from syntax errors in the input. However, there is a meager effort to resynchronize, so that more than one syntax error in a file may be found at the same time.

It is also possible that a fatal arithmetic exception (such as a division by zero, or a floating point overflow) may occur while ode is reading input. If such an exception occurs, ode will print an “Floating point exception” error message and exit. Arithmetic exceptions are machine-dependent. On some machines, the line

     y = 1/0

would induce an arithmetic exception. Also on some machines (not necessarily the same ones), the lines

     y = 1e100
     z = y^4

would induce an arithmetic exception. That is because on most machines, the double precision quantities that ode uses internally are limited to a maximum size of approximately 1.8x10^308.

When ode is in the `solving' state, i.e., computing a numerical solution, similar arithmetic exceptions may occur. If so, the solution will be interrupted and a message resembling

     ode: arithmetic exception while calculating y'

will be printed. However, ode will not exit; the exception will be `caught'. ode itself recognizes the following exceptional conditions: square root of a negative number, logarithm of a non-positive number, and negative number raised to a non-integer power. ode will catch any of these operations before it is performed, and print an error message specifying which illegal operation it has encountered.

     ode: square root of a negative number while calculating y'

would be a typical error message.

If the machine on which ode is running supports the ‘matherr’ facility for reporting errors in the computation of standard mathematical functions, it will be used. This facility reports domain errors and range errors (overflows, underflows, and losses of significance) that could occur when evaluating such functions as ‘log’, ‘gamma’, etc.; again, before they are performed. If the matherr facility is present, the error message will be fairly informative. For example, the error message

     ode: range error (overflow) in lgamma while calculating y'

could be generated if the logarithmic gamma function ‘lgamma’ is evaluated at a value of its argument that is too large. The generation of any such message, except a message warning of an underflow, will cause the numerical solution to be interrupted.

There is another sort of error that may occur during numerical solution: the condition that an error ceiling, which the user may set with the ‘-r’ option or the ‘-e’ option, is exceeded. This too will cause the numerical solution to be abandoned, and ode to switch back to reading input.