Re: Fortran or Ada?

["James Giles" <jamesgiles@worldnet.att.net>]

dewarr@my-dejanews.com wrote in message <6vdfq4$p1$1@nnrp1.dejanews.com>...
>In article <YGdS1.73461$hx3.8968466@HME2.newscontent-01.sprint.ca>,
>  "Ian St. John" <istjohn@sprint.ca> wrote:
>>
>> Testing by itself can never guarantee correct code. The testing is just to
>> determine syntax errors, oversights, etc.
>
>That's a bit strong, there are definitely cases where testing can be
>exhaustive, e.g. in checking out a sqrt routine for IEEE short form
>arithmetic. Indeed it is almost practical to do exhaustive testing on
>long format division (which would have saved Intel many millions of
>dollars :-)

There are 2^128 different possible divide operations (each operand
having 2^64 different possible values) - and that's assuming that you
don't have to test each pair of operands for each possible value of
the exponent and sign (in which case there are nearly 2^160 different
operand pairs - each operand having 2^80 different values).  Now,
assuming that a Pentium class machine can test 100 million operations
per second (an overestimate to say the least), it would take over 10^30
seconds to test all 2^128 divides.  This still assumes you have an
independent source of the correct answer for each divide to test
against!  Running, say, 1000 machines in parallel, each testing different
divides, would reduce the time needed to "just" 10^27 seconds.  A
year has on the order of 3*10^7 seconds.

Now, there are other kinds of tests.  A "correctness proof" is a test
which does not work by actual execution of the code or hardware,
but by logical examination of the components of them.  This is still
only a test, since the "proof" has the same complexity as the thing
being tested - and the same likelyhood of error.  However, to a
certain extent, such errors are independent of the errors in the actual
code or hardware (not always: especially in cases where the "proof"
is generated with automated tools, an error in one can be completely
transcribed into the other).  This makes it a useful exercise, especially
for mission-critical code or hardware.

--
J. Giles