**Maths
Errors**

Mathematical functions can be
delicate animals. There exist mathematical functions which simply cannot
produce sensible answers in all possible cases. Mathematical functions are not
"user friendly"! One example of an unfriendly function is the inverse
sine function asin(x) which only works for values of x
in the range +1.0 to -1.0. The reason for this is a mathematical one: namely
that the sine function (of which asin() is the opposite) only has values in
this range. The statement

y = asin (25.3);

is nonsense and it cannot possibly
produce a value for y, because none exists. Similarly, there is no simple number
which is the square root of a negative value, so an expression such as:

x = sqrt(-2.0);

would also be nonsense. This doesn't
stop the programmer from writing these statements though and it doesn't stop a
faulty program from straying out of bounds. What happens then when an erroneous
statement is executed? Some sort of error condition would certainly have to
result.

In many languages, errors, like the
ones above, are terminal: they cause a program to stop without any option to
recover the damage. In C, as the reader might have come to expect, this is not
the case. It is possible (in principle) to recover from any error, whilst still
maintaining firm control of a program.

Errors like the ones above are
called domain errors (the set of values which a function can accept is called
the domain of the function). There are other errors which can occur too. For
example, division by zero is illegal, because dividing by zero is
"mathematical nonsense" - it can be done, but the answer can be all
the numbers which exist at the same time! Obviously a program cannot work with
any idea as vague as this. Finally, in addition to these "pathological"
cases, mathematical operations can fail just because the numbers they deal with
get too large for the computer to handle, or too small, as the case may be.

*Domain error*

Illegal value put into function

*Division by zero*

Dividing by zero is nonsense.

*Overflow*

Number became too large

*Underflow*

Number became too small.

*Loss of accuracy*

No meaningful answer could be calculated

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