4 May
2024
4 May
'24
12:48 a.m.
On May 3, 2024, at 5:31 PM, Sean Conner via cctalk
<cctalk(a)classiccmp.org> wrote:
It was thus said that the Great Steve Lewis via cctalk once stated:
BASIC-PLUS (part of RSTS) had a weird floating point history. The original version,
through RSTS V3, used 3-word floating point: two words mantissa, one word exponent. Then,
presumably to match the 11/45 FPU, in version 4A they switched to your choice of 2 or 4
word float, what later in the VAX era came to be called "F" and "D"
float.
One curious thing about floating point formats of earlier computers is that they came with
wrinkles not seen either in IEEE nor in DEC float. As I recall, the 360 is really hex
float, not binary, with an exponent that gives a power of 16. CDC 6600 series mainframes
used a floating point format where the mantissa is an integer, not a fraction, and
negation is done by complementing the entire word.
The Electrologica X8 is yet another variation, which apparently came from an academic
paper of the era: it treats the mantissa as an integer too, like the CDC 6600, but with a
different normalizationn rule. THe 6600 does it like most others: shift left until all
leading zeroes have been eliminated. (It doesn't have a "hidden bit" as DEC
did.) But in the EL-X8, the normalization rule is to make the exponent as close to zero
as possible without losing bits. So an integer value is normalized to the actual integer
with exponent zero. And since there is no "excess n" bias on the exponent, the
encoding of an integer and of the identical normalized floating point value are in fact
the same.
paul
Great discussions about BASIC. I talked about
the IBM 5110 flavor of
BASIC last year (such as its FORM keyboard for quickly making structured
input forms), and recently "re-learned" that it defaults to running with
double-precision. But if you use "RUNS" instead of "RUN" then the
same
code is run using single-precision (but I haven't verified yet if that
translates into an actual runtime speed difference). I think most of the
"street BASICs" used single precision (if they supported floats at all).
But speaking of Microsoft BASIC, I think Monte Davidoff is still around
and deserves a lot of credit for doing the floating point library in the
initial Microsoft BASIC (but it's a bit sad that history has lost the names
of individual contributors
I think most of the "street BASICs" were written before IEEE-754 (floating
point standard) was ratified (1985 if I recall). Microsoft's floating point
[1] was five bytes long---four bytes for the mantissa, and one byte for the
exponent, biased by 129. I did some tests a month ago whereby I tested the
speed of the Microsoft floating point math on the 6809 (using Color Computer
BASIC) vs. the Motorola 6839 (floating point ROM implementing IEEE-754), and
the Microsoft version was faster [2].