41 MCODE - Floating FIX Mode (Fix ALL)

[Ángel Martin]

Floating FIX Mode

As discussed in a forum thread, it's often valuable to see the maximum number of digits with a meaningful contribution to the result value. The idea for the 41 was to use the I/O_SVC interrupt polling point to adjust the FIX setting in a dynamic fashion, depending on the value stored in the stack register X.

Some folks call this a FIX ALL mode, but I favor the Floating FIX terminology - after all a fix ALL would always be a static FIX_9, for it isn't about ALL digits but ALL NEEDED ones. Bur semantics aside, the code below shows the core of the routine, i.e. the actual determination of the FIX settings.

The formulas used are as follows:

Let x be represented by the following convention used in the 41 platform, with one digit for the mantissa sign, 10 digits for the mantissa, one for the exponent sign and two for the exponent. This enables a numeric range between +/-9,999999999 E99, with a "whole" around zero defined by the interval +/-1E-99.

Then the fix setting to use is a function of the number in X , represented as follows:

" s|abcdefghij|xyz "

1. If number >=1 (or x="0")

let z# = number of mantissa digits equal to zero, starting from the most significant one (i.e. from PT= 3 to PT=12), and XP = value of exponent (yz). Then we have:
FIX = max { 0 , [(9-z#) + XP }

2. if number < 1 (or x="9")

let |XP| = 100 - xyz, and z# as defined above. Then we have:
FIX = min { 9 , [(9-z#) + |XP| }

And here is the code to be executed by the OS upon each qualifying I/O_SVC event:

Code:


384    CLRF 0    default is  XP > 0
0F8    READ 3(X)    
2FA    ?C#0 M    is it zero??
15B    JNC +43d    (has 10 zeroes in mantissa)
2A0    SETDEC    decimal math
01C    PT= 3    
006    A=0 S&X    
2E2    ?C#0 @PT    
037    JC  +06    [EXIT]
166    A=A+1 S&X    # of zero digits in A[S&X]
354    ?PT= 12    
01F    JC  +03    [EXIT]
3DC    PT=PT+1    
3D3    JNC -06    
130    LDI S&X    
009    CON:    mantissa field length
0A6    A<>C S&X    #z in C[S&X]
1C6    A=A-C S&X    mant# = (9 - z#)
086    B=A S&X    keep copy in B[S&X]
0F8    READ 3(X)    
106    A=C S&X    put it in A[S&X]
356    ?A#0 XS    lower than one?
03B    JNC  +07    no, jump to section
388    SETF 0    marks  XP < 0
016    A=0 XS    yes, remove sign
130    LDI S&X    
100    CON:    normalize constant
0A6    A<>C S&X    
1C6    A=A-C S&X    |XP| = (100 - XP)  in A[S&X]
130    LDI S&X    
009    CON:    maximum FIX setting
260    SETHEX    HEX mode
306    ?A<C S&X    is |XP| < 9 ?
063    JNC  +12d    no, out of bounds
0A6    A<>C S&X    put |XP| in C[S&X]
066    A<>B S&X    put (9-z#) in A[S&X]
38C    ?FSET 0    
01B    JNC +03    
206    C=C+A S&X    mant# + |XP|
03B    JNC +07    
246    C=A-C S&X    mant# - |XP|
2F6    ?C#0 XS    zeros in tens, hundreds...
023    JNC  +04    no, stay put
046    C=0 S&X    yes, it was integer!
013    JNC +02    skip next
0C6    C=B S&X    put (9-z#) in C[S&X]
0FC    RCR 10    puts it in C<4>
10E    A=C ALL    save result in A<4>
3B8    READ 14(d)    read flag register
158    M=C  ALL    save it for later
05C    PT= 4    
0A2    A<>C @PT    get fix# to C<4>
01C    PT= 3    
210    LD@PT- 8    FIX mode
3A8    WRIT 14(d)    temporary settings
0F8    READ 3(X)    puts value in C
099    ?NC XQ    Sends C to display - sets HEX
02C    ->0B26    [DSPCRG]
198    C=M  ALL    recall original FIX settings
205    ?NC GO    Set MSG flag (from C)
00E    ->0381    [STMSF]+3