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Two recurring topics in asynchronous programming are exceptions and cancellation. Let s first explore some of the behavior of asynchronous programs with regard to exceptions. > let failingTask = async { do failwith "fail" };; val failingTask: Async<unit> > Async.Run failingTask;; Microsoft.FSharp.Core.FailureException: fail stopped due to error > let failingTasks = [ async { do failwith "fail A" }; async { do failwith "fail B" }; ];; val failingTasks: Async<unit> > Async.Run (Async.Parallel failingTasks);; Microsoft.FSharp.Core.FailureException: fail A stopped due to error > Async.Run (Async.Parallel failingTasks);; Microsoft.FSharp.Core.FailureException: fail B stopped due to error From this you can see the following: Tasks fail only when they are actually executed. The construction of a task using the async { ... } syntax will never fail. Tasks run using Async.Run report any failure back to the controlling thread as an exception. It is nondeterministic which task will fail first. Tasks composed using Async.Parallel report the first failure from amongst the collected set of tasks. An attempt is made to cancel other tasks by setting the cancellation flag for the group of tasks, and any further failures are ignored. You can wrap a task using the Async.Catch combinator. This has the following type:

Note that the BDD representations of x and x AND x are identical, whereas the Prop representations aren t. The Prop representation is an abstract syntax representation, whereas the BDD representation is more of a semantic or computational representation. The BDD representation incorporates all the logic necessary to prove propositional formula equivalent; in other words, this logic is built into the representation.

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You can now use BDDs to perform circuit verification For example, the following verifies that you can swap the x and y inputs to an 8-bit adder: > bddBuilderEquiv (nBitCarryRippleAdder 8 (vec 8 "x") (vec 8 "y") (vec 8 "sum") (vec 9 "carry")) (nBitCarryRippleAdder 8 (vec 8 "y") (vec 8 "x") (vec 8 "sum") (vec 9 "carry"));; val it : bool = true Thirty-three variables are involved in this circuit A naive exploration of this space would involve searching a truth table of more than eight billion entries The BDD implementation takes moments on any modern computer Efficient symbolic representations pay off! A more substantial verification problem involves checking the equivalence of circuits that have substantial structural differences To explore this, let s take a different implementation of addition called a carry select adder.

Listing 8-9. Implementation for the julian() Function (expert_udf.cc) longlong julian(UDF_INIT *initid, UDF_ARGS *args, char *is_null, char *error) { longlong jdate = 0; static int DAYS_IN_MONTH[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; int month = 0; int day = 0; int year = 0; int i; /* copy memory from the arguments */ memcpy(&month, args->args[0], args->lengths[0]); memcpy(&day, args->args[1], args->lengths[1]); memcpy(&year, args->args[2], args->lengths[2]); /* add the days in the month for each prior month */ for (i = 0; i < month - 1; i++) jdate += DAYS_IN_MONTH[i]; /* add the day of this month */ jdate += day; /* find the year */ if (((year % 100) != 0) && ((year % 4) == 0)) jdate++; /*leap year!*/ /* shift day of year to left */ jdate *= 10000; /* add the year */ jdate += year; return jdate; } Notice the first few lines after the variable declarations. This is an example of how you can marshal the values from the args array to your own local variables. In this case, I converted the first three parameters to integer values. The rest of the source code is the calculation of the Julian date value that is returned to the caller. If you are using Windows, you also need to modify the expert_udf.def file and add the methods for the JULIAN function. Listing 8-10 shows the updated expert_udf.def file.

For example: > Async.Run (Async.Catch failingTask);; val it : Choice<unit,exn> = Choice2_2 (FailureException ()) You can also handle errors by using try/finally in an async { ... } workflow.

This avoids a major problem with ripple adders caused by the fact that the carry signal must propagate along the entire length of the chain of internal adders, causing longer delays in the electrical signals and thus reducing the clock rates of a circuit or possibly increasing power consumption A carry select adder gets around this through a common hardware trick of speculative execution It divides the inputs into blocks and adds each block twice: once assuming the carry is low and once assuming it s high The result is then selected after the circuit, when the carry for the block has been computed Listing 12-16 shows the specification of the essence of the hardware layout of a carry select adder using the techniques developed so far The specification uses the slicing syntax for arrays described in 4 Listing 12-16.

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