Home > Archive > ASM370 > June 2007 > Floating point misc questions
You are viewing an archived Text-only version of the thread.
To view this thread in it's original format and/or if you want to reply to
this thread please [click here]
| Author |
Floating point misc questions
|
|
| hancock4@bbs.cpcn.com 2007-03-27, 9:59 pm |
| I was curious about the following floating point (390, Z) issues. I
tried looking these things up in Z9 Principles of Operation but I
didn't understand some of the comments. Comments would be welcome.
1) "HFP" and "BFP". It appears that BFP "Binary Floating Point" is a
new instruction group. Could someone explain the difference to the
original HFP? I thought everything was stored in binary, and hex was
simply the external representation for us humans. Also, what are the
advantages of BFP? (I am not trying to do anything, just curious
about modern features.)
2) Super computer work:
From time to time IBM announces a new supercomputer for extremely
"industrial strength" calculations. These days they seem to be many
parallel processors of PC style architecture, not S/390.
On alt.folklore.computers, there seems to be an attitude of disdain
for using the S/390 mainframe for high powered number crunching. I'm
not sure why; some say it is because of poor rounding, normalization
or lack of "IEEE" compatibility, but the Pr of Op does cover all those
issues. Indeed, "normalized" instructions have been around since
System/360 days.
Our new Z9 seems to be extremely powerful. I would think a
production machine such as that might be cheaper and just as powerful
as a specially constructed machine.
If I understand the Pr of Op correctly, the standard "extended"
floating point allows 128 bits, or about 31 digits of precision. That
seems to be quite a bit. (That seems to date back to S/370 days 30
years ago, has the precision been extended since then with newer
machines?)
Would anyone like to comment on this? Thanks!
| |
| glen herrmannsfeldt 2007-03-27, 9:59 pm |
| hancock4@bbs.cpcn.com wrote:
> 1) "HFP" and "BFP". It appears that BFP "Binary Floating Point" is a
> new instruction group. Could someone explain the difference to the
> original HFP? I thought everything was stored in binary, and hex was
> simply the external representation for us humans. Also, what are the
> advantages of BFP? (I am not trying to do anything, just curious
> about modern features.)
BFP is pretty much IEEE standard floating point, as most other
processors in use now use, and is required for Java.
For HFP, the original floating point format from S/360 carried
on to ESA/390 and Z, it is more than the external representation.
The representation of short (32 bit) HFP has six hex digits (stored
in 24 bits) of fraction, seven bits as a base 16 biased exponent,
and a sign bit. Among other differences, in HFP you can lose
precision multiplying by two.
> 2) Super computer work:
> From time to time IBM announces a new supercomputer for extremely
> "industrial strength" calculations. These days they seem to be many
> parallel processors of PC style architecture, not S/390.
> On alt.folklore.computers, there seems to be an attitude of disdain
> for using the S/390 mainframe for high powered number crunching. I'm
> not sure why; some say it is because of poor rounding, normalization
> or lack of "IEEE" compatibility, but the Pr of Op does cover all those
> issues. Indeed, "normalized" instructions have been around since
> System/360 days.
I believe it is mostly cost. Compare the price of a fast x86
or even x86-64 processor to a z/ machine. With x86-64 you
can buy a very large cluster of machines for the price of
one z/ machine.
> Our new Z9 seems to be extremely powerful. I would think a
> production machine such as that might be cheaper and just as powerful
> as a specially constructed machine.
Economy of scale. Yes compared to other specially constructed
machines, but if it can be done using off the shelf hardware
it can be much cheaper.
> If I understand the Pr of Op correctly, the standard "extended"
> floating point allows 128 bits, or about 31 digits of precision. That
> seems to be quite a bit. (That seems to date back to S/370 days 30
> years ago, has the precision been extended since then with newer
> machines?)
Actually, it dates back to the 360/85, and from there to S/370
except that DXR wasn't added until much later.
-- glen
| |
| Michel Hack 2007-04-03, 4:00 am |
| On Mar 27, 3:55 pm, hanco...@bbs.cpcn.com wrote:
> If I understand the Pr of Op correctly, the standard "extended"
> floating point allows 128 bits, or about 31 digits of precision.
Actually, the precision of both HFP128 and BFP128 is about 35 digits
(varies from 33 to 35 for HFP). The exponent of BFP128 (which will
become a standard IEEE 754 format when the revised (2007) standard
comes out as expected in a month or two) has a much wider range than
HFP128 -- but there is (was?) a software-only variant of HFP128 (for
Fortran, 20 years ago) called XEXP that has the same precision, but
an even wider exponent range, +/-9860 or so, twice as wide as BFP128.
Michel
| |
| glen herrmannsfeldt 2007-04-07, 3:57 am |
| Michel Hack wrote:
> On Mar 27, 3:55 pm, hanco...@bbs.cpcn.com wrote:
[color=darkred]
> Actually, the precision of both HFP128 and BFP128 is about 35 digits
> (varies from 33 to 35 for HFP). The exponent of BFP128 (which will
> become a standard IEEE 754 format when the revised (2007) standard
> comes out as expected in a month or two) has a much wider range than
> HFP128 -- but there is (was?) a software-only variant of HFP128 (for
> Fortran, 20 years ago) called XEXP that has the same precision, but
> an even wider exponent range, +/-9860 or so, twice as wide as BFP128.
HFP first came on the 360/85, though without support for DXR.
On machines with extended precision there was software support for
DXR, named IEAXPDXR, and for machines without all instructions were
simulated by IEAXPALL. (The source is available, though I hand
disassembled IEAXPDXR many years ago.) Like short and long precision,
it has a seven bit hex exponent. To make the software simulation
easier, both halves of extended precision have an exponent field,
with the lower half exponent 14 less (possibly wrapped). It has
a 112 bit hex fraction, so I believe between 32 and 33 decimal
digits.
The OS/360 source available through Hercules has the IEAXP routines.
-- glen
| |
|
|
|
|
|
|
|
|
|
|
|
|
|