Path: utzoo!utgpu!water!watmath!clyde!rutgers!sri-spam!ames!oliveb!intelca!mipos3!td2cad!cpocd2!howard
From: howard@cpocd2.UUCP (Howard A. Landman)
Newsgroups: comp.arch
Subject: Re: Round-off
Message-ID: <1069@cpocd2.UUCP>
Date: 19 Jan 88 21:53:49 GMT
References: <189@mithras> <614@PT.CS.CMU.EDU> <4404@ecsvax.UUCP>
Reply-To: howard@cpocd2.UUCP (Howard A. Landman)
Organization: Intel Corp. ASIC Systems Organization, Chandler AZ
Lines: 35

In article <4404@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes:
>This tradeoff goes back to the original 360 - and seems to have originated
>with the desire to have a floating point word fit in 4 bytes, and so the
>exponent was in 1 byte.  In order to have an acceptable range of
>magnitude, the exponent had to shift more than binary, and HEX was chosen.
>magnitude, the exponent had to shift more than binary, and HEX was chosen.
>Of course with hex normalization, any hex digit could be most significant,
>part of the leading non-zero hex digit.

Given that hex rounding effectively trashes three bits of mantissa accuracy,
it would have been just as good to use an 11-bit exponent and a 21-bit
mantissa with normal rounding.  I can remember learning to program in PL-I
on an IBM and being REAL SURPRISED when simple calculations gave results that
were off by more than 1%.  Someone finally explained to me that you NEVER,
were off by more than 1%.  Someone finally explained to me that you NEVER,
NEVER, NEVER use what he called IBM's "half precision" floating point format,
unless you only care about the first significant digit.

It was precisely the awfulness of IBM single precision that led Kernighan and
Ritchie to make it a required feature of the C language that all floating
point computations be done in double precision.

I seem to recall Gene Amdahl saying once that if he had it to do over again,
he would have done it differently.  Of course, once I heard someone ask him
whether he thought the IBM 360 architecture was really the best that could be
achieved (it was over 15 years old at the time), and he said something like
"Why don't you ask me if I thought it was the best that could be achieved
THEN?".  A yes answer would imply that it was dated, and a no answer would
imply that some of the decisions were compromises over which he had no control
and with which he didn't agree.

-- 
	Howard A. Landman
	{oliveb,hplabs}!intelca!mipos3!cpocd2!howard
	howard%cpocd2.intel.com@RELAY.CS.N