Olin Lathrop <olin_piclist@EMBEDINC.COM> wrote:
> A simplifying trick would be to arrange the result value to be fixed point
> with 8 fraction bits.  Then you don't need to use floating point.  Just
> multiply each value by 256 times more than in your example, then ignore the
> low byte of the result.  Using the same 273 --> 87 example:
>
>   SCALE = (115 / 360) * 256 = .3194 * 256 = 81.7778
>
>   RESULT = HUNDREDS*(SCALE*100) + TENS*(SCALE*10) + UNITS*SCALE
>          = 2*(8177) + 7*(817) + 3*81

Good approach, but it's better to round the scaling constants appropriately.
Furthermore, to get a correctly rounded result, it's also a good idea to
add in a constant equal to 1/2 LSB of the result.

        = 2*(8178) + 7*(818) + 3*82 + 127
        = 16356 + 5726 + 246 + 127
        = 22456

        22456 >> 8 = 87

Note that you would normally use 128 as the rounding offset, but a quick
simulation shows that this gives incorrect results in two cases (input
values 277 and 349). Note that all three scaling constants are rounded up.
Fudging the constant downward slightly gives correct results for all input
values.

Simulation Perl script:

for (0..360) {
    my $answer = int ($_*115/360 + 0.5);
    my $u = $_ % 10;
    $_ = int ($_/10);
    my $t = $_ % 10;
    $_ = int ($_/10);
    my $h = $_ % 10;
    my $x = int(($h*8178 + $t*818 + $u*82 + 127)/256);
    if ($x != $answer) {
        print "$answer => $x\n";
    }
}

-- Dave Tweed

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