Let's visit some other conversion activities in the 1970's. The gig was at a company implementing a customized insurance application. The actuaries used a PDP-10 (and Fortran) to compute their various tables and summaries.

I was roped into rewriting an actuarial Fortran programs into PL/1 for an IBM 370.

This program, clearly, encodes deep business knowledge. It must be preserved very precisely, since the actuarial calculations are directly tied to the financial expectations for the particular line of business.

The good news about Fortran to PL/1 conversion is that PL/1 offers features (and syntax) that are similar to Fortran. It's not an exact match, but it's close enough to make the conversion relatively risk-free.

There are, of course, issues.

In particular, Fortran IV was not big on the "structured if-then-else" features of Algol-like languages. PL/1, like Pascal, followed on the heels of Algol 60. Fortran didn't follow Algol; Fortran depended on GOTO statements instead of nested IF-THEN-ELSE statements.

This meant that some logic expressions were rather tangled and difficult to fully understand. Patience and and care were required to unwind the logic from it's tangled nest of Fortran GOTO's into neater PL/1 BEGIN-END blocks.

It was the 70's. Testing was---at best---primitive. The languages and tools didn't support very much in the way of automated testing.

Compounding the problem, IT management was so late in getting the project started that we had to do repeated overnighters to get things running. The fog of sleep deprivation doesn't facilitate high quality software.

Further compounding the problem, we don't really have access to the PDP-10 that the actuaries use. We can't run any controlled tests.

And. Bonus.

We were doing "test-in-production". As soon as it worked, that was the official production run. Everything prior to the one that worked was discard as a test run.

The test strategy was simply to do a side-by-side comparison with the legacy PDP-10 output. While it's tedious to read hundreds of pages of mainframe computer print-out, that was the job.

At some point, the output would disagree. The PDP-10 Fortran, of course, was deemed to be "right."

So it was a matter of discovering what was unique about the case where there was a difference. Lots of deduction and puzzle solving.

Finally, we got down to one really subtle issue.

The numbers were slightly different. Slightly.

What does this slight discrepancy mean?

Is it a bug? Do we have to chase down some math error? It's unlikely to be a math error, since the expressions convert trivially from Fortran to PL/1. And the numbers are close.

Is it a feature? Is there something in Fortran or PL/1 that we simply failed to understand? Unlikely.

Everything else works.

It's a "quirk". It's not a "bug" because it's not clearly wrong. It's not a feature, because we're not going to define it as being clearly right. It's in this middle realm of behavior best described as quirky.

Decimal hardware, BTW, was part of the IBM 370 system. Decimal-mode arithmetic was often faster then floating-point.

The PL/1 rules have some odd features regarding division and multiplication.

The PL/1 version provides exact decimal answers. Lots of decimal places exact.

The Fortran version involved approximations. All floating-point calculation must be looked at as an approximation. Many numbers have an exact binary representation. But numbers without an exact binary representation will have tiny errors. The tiny errors are magnified through calculations. Generally, subtracting two nearly-equal floating-point values elevates the erroneous parts of the approximation to lofty heights of visibility.

It was not as important to preserve the quirks of single-precision floating-point math.

Clearly, we have to distinguish between three separate considerations.

I was roped into rewriting an actuarial Fortran programs into PL/1 for an IBM 370.

This program, clearly, encodes deep business knowledge. It must be preserved very precisely, since the actuarial calculations are directly tied to the financial expectations for the particular line of business.

The good news about Fortran to PL/1 conversion is that PL/1 offers features (and syntax) that are similar to Fortran. It's not an exact match, but it's close enough to make the conversion relatively risk-free.

There are, of course, issues.

In particular, Fortran IV was not big on the "structured if-then-else" features of Algol-like languages. PL/1, like Pascal, followed on the heels of Algol 60. Fortran didn't follow Algol; Fortran depended on GOTO statements instead of nested IF-THEN-ELSE statements.

This meant that some logic expressions were rather tangled and difficult to fully understand. Patience and and care were required to unwind the logic from it's tangled nest of Fortran GOTO's into neater PL/1 BEGIN-END blocks.

## Test Case

Perhaps the most important gap here was the lack of any kind of definitive test case.It was the 70's. Testing was---at best---primitive. The languages and tools didn't support very much in the way of automated testing.

Compounding the problem, IT management was so late in getting the project started that we had to do repeated overnighters to get things running. The fog of sleep deprivation doesn't facilitate high quality software.

Further compounding the problem, we don't really have access to the PDP-10 that the actuaries use. We can't run any controlled tests.

And. Bonus.

We were doing "test-in-production". As soon as it worked, that was the official production run. Everything prior to the one that worked was discard as a test run.

The test strategy was simply to do a side-by-side comparison with the legacy PDP-10 output. While it's tedious to read hundreds of pages of mainframe computer print-out, that was the job.

## Results

For the first attempts, there were significant logic issues. Regions of IF-GOTO that hadn't been properly rewritten into IF-THEN-ELSE.At some point, the output would disagree. The PDP-10 Fortran, of course, was deemed to be "right."

So it was a matter of discovering what was unique about the case where there was a difference. Lots of deduction and puzzle solving.

Finally, we got down to one really subtle issue.

The numbers were slightly different. Slightly.

What does this slight discrepancy mean?

Is it a bug? Do we have to chase down some math error? It's unlikely to be a math error, since the expressions convert trivially from Fortran to PL/1. And the numbers are close.

Is it a feature? Is there something in Fortran or PL/1 that we simply failed to understand? Unlikely.

Everything else works.

It's a "quirk". It's not a "bug" because it's not clearly wrong. It's not a feature, because we're not going to define it as being clearly right. It's in this middle realm of behavior best described as quirky.

## Quirks

What we've uncovered, it turns out, is the difference between Fortran floating point calculations and PL/1's fixed-point decimal calculations. PL/1's compiler reasons out the proper number of decimal places in the intermediate results and generates fixed-point decimal code appropriately.Decimal hardware, BTW, was part of the IBM 370 system. Decimal-mode arithmetic was often faster then floating-point.

The PL/1 rules have some odd features regarding division and multiplication.

`A*0.001`and

`A/1000`have different deduced number of decimal places. Other than that, the rules are obvious and mathematically sound.

The PL/1 version provides exact decimal answers. Lots of decimal places exact.

The Fortran version involved approximations. All floating-point calculation must be looked at as an approximation. Many numbers have an exact binary representation. But numbers without an exact binary representation will have tiny errors. The tiny errors are magnified through calculations. Generally, subtracting two nearly-equal floating-point values elevates the erroneous parts of the approximation to lofty heights of visibility.

## Preservation

It was important to preserve the essential actuarial knowledge encoded in Fortran into PL/1.It was not as important to preserve the quirks of single-precision floating-point math.

Clearly, we have to distinguish between three separate considerations.

- Valuable Features: encoded business knowledge.
- Implementation Details: technology knowledge.
- Quirks. Aspects of the implementation that lead to low-value discrepancies in the output.

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