piclist 2001\06\06\145948a >
Thread: Looking for improved integer's math routines
www.piclist.com/techref/microchip/math/index.htm?key=math
BY : Mike Mansheim email (remove spam text)

> Post to the site and the list...

> On the site, just be sure to select code listing and put the HTML tags
> <PRE>
> before the code and
> </PRE>
> after it.

OK, here 'tis.  I don't know anything about HTML tags - are the <> part
of what is typed in?  I will post to the site as soon as I hear back.
Thanks for the help.

/*
- based on the 16 bit to 5 digit conversion written by John Payson
& explained by Scott Dattalo
- this version adds the extra bit so that the 5 digit display can
- want to express the b_i's in terms of the a_i's for the equations:
N = a4*16^4 + a3*16^3 + a2*16^2 + a1*16 + a0
N = b4*10^4 + b3*10^3 + b2*10^2 + b1*10 + b0
the solution coded below:
b0 = a0 - (4 * (a4 + a3 + a2 + a1)) - 20
b1 = (4 * a4) + (6 * a2) + (2 * a1) - 198
b2 = (5 * a4) + a3 + (2 * a2) - 140
b3 = (5 * a4) + (4 * a3) - 144
b4 = (6 * a4) + 16
- written in CCS C
- since ram was plentiful, I used a 3 byte number - only one bit
of the extra byte is actually required.  I also used three bytes
of scratchpad ram to increase the efficiency of the compiled code.
The equations can be coded in C exactly as shown above, but that
doesn't take advantage of common terms & progressive multiplies.
- even with just the one extra bit, the incoming number  can exceed
99,999, so it needs to be checked.  This code doesn't show that.
- CCS C is limited to 16 bit as the largest integer data type.  To
use a 24 bit number, I use an array to make sure the bytes are
consecutive.  This function operates on the array as a global,
because I think that is more efficient than passing arrays to
the function.
- the code could be quite a bit smaller - in John's original, the
portion of the code that isolated the nibbles and calculated the
digits took 32 instructions.  If I code that solution in C, using
two scratchpad bytes to improve things, it compiles to 64 instructions.
This version compiles to 85 instructions, so I'm sure an asm whiz
could show quite an improvement.  The C version is still much faster
than the the original way I did this, and does what I need.
*/

unsigned int  TenK, Thou, Hund, Tens, Ones;
unsigned int  num[3];

void BIN2DEC(void)
{
// operates on global variables:
// set num[0]-[3] (lo-hi) before calling
// returns with TenK...Ones set from 0-9

unsigned int a0, a1, a2, a3, a4;
unsigned int t1, t2, t3;           // scratchpad variables

// isolate the 4 bit nibbles
// for the purposes of this routine, a4 can be only 0 or 1
a4 = num[2];
a3 = num[1] / 16;
a2 = num[1] & 0b00001111;
a1 = num[0] / 16;
a0 = num[0] & 0b00001111;

// calculate the decimal digits (the b_i's are expressed here
// as TenK...Ones, as in the original)
// all are negative, except TenK
t1 = 4 * a4;
Ones = a0 - t1 - 20;
t2 = 2 * a1;
Tens = t1 + t2 - 198;
t3 = 2 * a2;
Hund = a3 + t3 - 140;
t3 = t3 * 2;              // now = 4 * a2
t2 = t2 * 2;              // now = 4 * a1
Ones = Ones - t3 - t2;
t3 = t3 + a2 + a2;        // now = 6 * a2
Tens = Tens + t3;         // Tens done
t1 = t1 + a4;             // now = 5 * a4
Hund = Hund + t1;
t3 = 4 * a3;
Thou = t1 + t3 - 144;     // Thou done
Ones = Ones - t3;         // Ones done
TenK = t1 + a4 + 16;      // Tenk done

// "normalize" the digits - this asm code was
// copied directly from the original
#asm
movlw   0x0A
Lb1:
decf    Tens,f
btfss   3,0
goto   Lb1
Lb2:
decf    Hund,f
btfss   3,0
goto   Lb2
Lb3:
decf    Thou,f
btfss   3,0
goto   Lb3
Lb4:
decf    TenK,f
btfss   3,0
goto   Lb4
#endasm
}

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