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From: Jean-David Beyer <jeandavid8@verizon.net>
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Organization: Institute for Regimented Whimsey
Subject: Re: Problem in
Message-ID: <705abf29-df59-a583-1c5f-0894f2e15021@verizon.net>
Date: Fri, 17 May 2019 12:09:44 -0400
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On 4/27/19 3:32 AM, Max Lipsky wrote:
> Error comes from FSIN/FCOS instruction, but as Tom said — it’s OK (within acceptable limits).
> It was just a little unexpected for me :)

Back in my programming days, a friend was having trouble with a large
(in memory) table of floating point numbers on an IBM/360. She was
trying to do a statistical analysis of those numbers and getting strange
results. I had her add up all the numbers and print the sum. I then had
her sort the same numbers, add them up, and print the sum. The numbers
were originally in "random" order, but they were summed from large to
small after the sort. The sorted numbers summed to less than the random
ones. She finally decided that the computer hardware was bad.

In a sense, it was, though it worked within specifications.

The system/360 was a hexadecimal machine; i.e., the floating point
fraction could have up to 3 leading zeros in the fraction part of a
floating point number. And the 32-bit word size was even worse than the3
36-bit word size of the IBM/7094 binary machines she was used to. So if
you add up a bunch of large floating point numbers with small ones
following, the small ones pretty much do not count (round-off). Had she
shorted them small to large, she would have gotten the biggest answer.

The same problems were affecting her statistical analysis.

Basically, the System/360 machines were disasters as far as mathematical
calculations were concerned. Shorter word size, and inferior floating
point representation. This at a time when Burroughs machines were 48
bits and Control Data machines had 60-bit word size.

-- 
  .~.  Jean-David Beyer
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