Converting Between Floating Point and Human Readable Format

In my last post I mentioned 6502 code that can convert between ASCII and floating point formats that was written by Marvin L De Jong and published in the February and April 1981 issues of COMPUTE! magazine.

I've now entered it and ported it to the CC65 assembler to run on the Replica 1.

As often seems to be the case, there were a number of errors in the printed code, such as symbols that were never defined. The "#" sign was also not used to specify immediate addressing (this was apparently a coding convention that the author followed in all of his published code).

Fortunately it seemed that the generated machine code in the listing was correct, so in most cases I was able to use that as a reference to determine what the code should be.

I also had to combine the code in the first article with changes in the second one as there was no complete listing of the final software.

The code used some i/o routines for the AIM-65 machine so those needed to be be replaced with equivalents for the Replica 1.

After a couple of evenings of porting and testing I had the string to floating point and floating point to string functions working (De Jong refers to it as "BCD format" but it is really an ASCII string format). So, for example, I could now convert a string like "+6.02214E23" or "-1.2E-19" to floating point and back to ASCII. I then updated my little test/demo program to support calling the new routines.

The floating point format used by the De Jong code is a little different from the format used by the Woz code, but I was able to convert them easily enough.

The final result is the demo program which exercises all the functions. Here is an example run:

FLOATING POINT DEMONSTRATION PROGRAM

F - FIXED TO FLOATING POINT
P - FLOATING TO FIXED POINT
L - NATURAL LOG
N - COMMON LOG
E - EXPONENTIAL
A - FLOATING POINT ADD
S - FLOATING POINT SUBTRACT
M - FLOATING POINT MULTIPLY
D - FLOATING POINT DIVIDE
B - STRING TO FLOATING POINT
T - FLOATING POINT TO STRING
? - THIS HELP SCREEN
X - EXIT

SELECT A FUNCTION: B
STRING TO FLOATING POINT
ENTER FP STRING: 1234
FLOATING POINT IS: 8A 4D2000

SELECT A FUNCTION: T
FLOATING POINT TO STRING
ENTER EXPONENT AND MANTISSA: 8A 4D2000
FLOATING POINT IS: 1234

SELECT A FUNCTION: B
STRING TO FLOATING POINT
ENTER FP STRING: 6.02214E23
FLOATING POINT IS: CE 7F8616

SELECT A FUNCTION: T
FLOATING POINT TO STRING
ENTER EXPONENT AND MANTISSA: CE 7F8616
FLOATING POINT IS: 60221399.E16

With the facilities here you could implement a math program like a scientific calculator. I may do that at some point.

I learned a little about floating point code with this project. It also reminded me that back at the time this code was written there was no standard for representing floating point numbers. That was addressed by the IEEE Standard for Floating-Point Arithmetic (IEEE 754) and most modern CPU chips that have floating point hardware now support this standard, and language compilers typically support it in their run-time libraries. CPUs that lack floating point hardware typically emulate it in software, using code much like the 6502 code here, but more complex and typically written in C.

As usual, all of the code can be found here and you are welcome to use it.