John, all
>Has IBM established a standard in any of the various high-level languages
>for the representation of the various floating-point formats and
>precisions?
>I am specifically looking at both fixed-point and scientific notation.
> John P. Baker
Here are some references and summary info I've collected:
Standard Scientific Notation:
General description and references:
http://en.wikipedia.org/wiki/Scientific_notation
IBM Hursley generalized description of scientific notation conversion:
http://www2.hursley.ibm.com/decimal/daconvs.html#reftonum
Arithmetic Model:
http://www2.hursley.ibm.com/decimal/damodel.html
Note this model is based on IEEE 854, ANSI X3-274 standards.
Unfortunately these standards are only available in published form for a
fee. (Commentary: It would be a tremendous service to the world if a
non-profit organization could be started to move all standards
publications to the public domain to help promote understanding and use of
non-proprietary standards. Charging for them makes them all proprietary!)
So in summary the standard form would appear to be:
1. Sign (+optional)
2. Mantissa (decimal digits with optional period up to maximum
significant digits for binary format)
3. Exponent (optional)
a. E (E or e optional if sign included)
b. Sign (+optional if E or e)
c. Power of ten (exponent digits with no decimal up to maximum
exponent)
The maximum limits for each IBM fixed and floating point HFP, BFP, and DFP
format can be found in the latest Principles of Operations Manual here:
http://publibfp.boulder.ibm.com/epubs/pdf/dz9zr006.pdf
In summary the significant decimal digits and base 10 exponents are as
follows:
Summary of IBM Fixed and Floating Point Scientific Notation Limits
Type of number 32 bit 64 bit 128 bit
Fixed Point Integers
Significant digits 10 19 39
HFP Hexadecimal FP
Significant digits 7 15 34
Maximum exponent 75 75 75
BFP Binary IEEE 754 FP
Significant digits 7 16 34
Maximum exponent 38 308 4932
DFP Decimal IEEE 754r FP
Significant digits 7 16 34
Maximum exponent 96 384 6144
All of these formats are supported by z390 on Windows and Linux with CTD
and CFD conversion routine macros and supervisor calls for converting
between EBCDIC/ASCII character scientific notation and any of the above
binary formats. All corrections and comments welcome.
Don Higgins
[EMAIL PROTECTED]
www.z390.org
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