numbers [was Re: understanding probability]

[D. Hugh Redelmeier]

| From: Lennart Sorensen <lsorense-1wCw9BSqJbv44Nm34jS7GywD8/FfD2ys at public.gmane.org>

| On Mon, Aug 12, 2013 at 03:54:05PM -0400, D. Hugh Redelmeier wrote:

| > Amazing (to me) story about Kahan.  He showed that the original
| > IBM/360 floating point hardware specifications yielded significantly
| > lower precision than could be achieved.  IBM took his advice and
| > changed the specs and retrofitted a "guard digit" into every /360 in
| > the field!  This was not a trivial reflash-the-firmware kind of thing.
| > It must have cost a fortune.
| 
| Well there probably weren't that many machines, and if they were
| microcoded then if that microcode was changeable, then it probably
| wouldn't be that costly.  Even if it involved hardware swaps, the
| development cost for the machines was probably much larger than the
| actual chip manufacturing costs, so again perhaps not that bad.

- I think that they did do it early enough that there were not an
  overwhelming number of machines in the field.

- there were a half dozen different implementations of the
  architecture, and each needed to be fixed.  Most, but not all, were
  microcoded.  I think that each model used a different microcode
  store (CROS for the 30, TROS for the 40, and I don't know the
  others).

- I think that the FP instructions slowed down on the one I used (the
  model 75 in University of Waterloo).  My understanding was that
  another pass through the ALU was required to match the new specs: it
  wasn't feasible to change its width.

- /360 machines were not made of integrated circuits.  They had potted
  units with a small number of discrete compunents.

The /360 had some interesting characteristics.  IBM famously "bet the
company" on it, and won big.
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