mirror of
https://github.com/michaelcmartin/Ophis.git
synced 2024-09-10 01:54:25 +00:00
267 lines
5.0 KiB
HTML
267 lines
5.0 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/loose.dtd">
|
|
<HTML
|
|
><HEAD
|
|
><TITLE
|
|
>Unsigned arithmetic</TITLE
|
|
><META
|
|
NAME="GENERATOR"
|
|
CONTENT="Modular DocBook HTML Stylesheet Version 1.79"><LINK
|
|
REL="HOME"
|
|
TITLE="Programming with Ophis"
|
|
HREF="book1.html"><LINK
|
|
REL="UP"
|
|
TITLE="The Second Step"
|
|
HREF="c486.html"><LINK
|
|
REL="PREVIOUS"
|
|
TITLE="The solution"
|
|
HREF="x498.html"><LINK
|
|
REL="NEXT"
|
|
TITLE="16-bit addition and subtraction"
|
|
HREF="x527.html"></HEAD
|
|
><BODY
|
|
CLASS="SECTION"
|
|
BGCOLOR="#FFFFFF"
|
|
TEXT="#000000"
|
|
LINK="#0000FF"
|
|
VLINK="#840084"
|
|
ALINK="#0000FF"
|
|
><DIV
|
|
CLASS="NAVHEADER"
|
|
><TABLE
|
|
SUMMARY="Header navigation table"
|
|
WIDTH="100%"
|
|
BORDER="0"
|
|
CELLPADDING="0"
|
|
CELLSPACING="0"
|
|
><TR
|
|
><TH
|
|
COLSPAN="3"
|
|
ALIGN="center"
|
|
>Programming with Ophis</TH
|
|
></TR
|
|
><TR
|
|
><TD
|
|
WIDTH="10%"
|
|
ALIGN="left"
|
|
VALIGN="bottom"
|
|
><A
|
|
HREF="x498.html"
|
|
ACCESSKEY="P"
|
|
><<< Previous</A
|
|
></TD
|
|
><TD
|
|
WIDTH="80%"
|
|
ALIGN="center"
|
|
VALIGN="bottom"
|
|
>The Second Step</TD
|
|
><TD
|
|
WIDTH="10%"
|
|
ALIGN="right"
|
|
VALIGN="bottom"
|
|
><A
|
|
HREF="x527.html"
|
|
ACCESSKEY="N"
|
|
>Next >>></A
|
|
></TD
|
|
></TR
|
|
></TABLE
|
|
><HR
|
|
ALIGN="LEFT"
|
|
WIDTH="100%"></DIV
|
|
><DIV
|
|
CLASS="SECTION"
|
|
><H1
|
|
CLASS="SECTION"
|
|
><A
|
|
NAME="AEN504"
|
|
>Unsigned arithmetic</A
|
|
></H1
|
|
><P
|
|
> When writing control code that hinges on numbers, we should always
|
|
strive to have our comparison be with zero; that way, no explicit
|
|
compare is necessary, and we can branch simply
|
|
with <TT
|
|
CLASS="LITERAL"
|
|
>BEQ/BNE</TT
|
|
>, which test the zero flag.
|
|
Otherwise, we use <TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
>.
|
|
The <TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
> command subtracts its argument from the
|
|
accumulator (without borrow), updates the flags, but throws away
|
|
the result. If the value is equal, the result is zero.
|
|
(<TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
> followed by <TT
|
|
CLASS="LITERAL"
|
|
>BEQ</TT
|
|
>
|
|
branches if the argument is equal to the accumulator; this is
|
|
probably why it's called <TT
|
|
CLASS="LITERAL"
|
|
>BEQ</TT
|
|
> and not something
|
|
like <TT
|
|
CLASS="LITERAL"
|
|
>BZS</TT
|
|
>.)
|
|
</P
|
|
><P
|
|
> Intuitively, then, to check if the accumulator is <I
|
|
CLASS="EMPHASIS"
|
|
>less
|
|
than</I
|
|
> some value, we <TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
> against that
|
|
value and <TT
|
|
CLASS="LITERAL"
|
|
>BMI</TT
|
|
>. The <TT
|
|
CLASS="LITERAL"
|
|
>BMI</TT
|
|
>
|
|
command branches based on the Negative Flag, which is equal to the
|
|
seventh bit of <TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
>'s subtract. That's exactly
|
|
what we need, for signed arithmetic. However, this produces
|
|
problems if you're writing a boundary detector on your screen or
|
|
something and find that 192 < 4. 192 is outside of a signed
|
|
byte's range, and is interpreted as if it were -64. This will not
|
|
do for most graphics applications, where your values will be
|
|
ranging from 0-319 or 0-199 or 0-255.
|
|
</P
|
|
><P
|
|
> Instead, we take advantage of the implied subtraction
|
|
that <TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
> does. When subtracting, the result's
|
|
carry bit starts at 1, and gets borrowed from if necessary. Let
|
|
us consider some four-bit subtractions.
|
|
</P
|
|
><TABLE
|
|
BORDER="0"
|
|
BGCOLOR="#E0E0E0"
|
|
WIDTH="100%"
|
|
><TR
|
|
><TD
|
|
><PRE
|
|
CLASS="PROGRAMLISTING"
|
|
>C|3210 C|3210
|
|
------ ------
|
|
1|1001 9 1|1001 9
|
|
|0100 - 4 |1100 -12
|
|
------ --- ------ ---
|
|
1|0101 5 0|1101 -3</PRE
|
|
></TD
|
|
></TR
|
|
></TABLE
|
|
><P
|
|
> The <TT
|
|
CLASS="LITERAL"
|
|
>CMP</TT
|
|
> command properly modifies the carry bit
|
|
to reflect this. When computing A-B, the carry bit is set if A
|
|
>= B, and it's clear if A < B. Consider the following two
|
|
code sequences.
|
|
</P
|
|
><TABLE
|
|
BORDER="0"
|
|
BGCOLOR="#E0E0E0"
|
|
WIDTH="100%"
|
|
><TR
|
|
><TD
|
|
><PRE
|
|
CLASS="PROGRAMLISTING"
|
|
> (1) (2)
|
|
CMP #$C0 CMP #$C0
|
|
BMI label BCC label</PRE
|
|
></TD
|
|
></TR
|
|
></TABLE
|
|
><P
|
|
> The code in the first column treats the value in the accumulator
|
|
as a signed value, and branches if the value is less than -64.
|
|
(Because of overflow issues, it will actually branch for
|
|
accumulator values between $40 and $BF, even though it *should*
|
|
only be doing it for values between $80 and $BF. To see why,
|
|
compare $40 to $C0 and look at the result.) The second column
|
|
code treats the accumulator as holding an unsigned value, and
|
|
branches if the value is less than 192. It will branch for
|
|
accumulator values $00-$BF.
|
|
</P
|
|
></DIV
|
|
><DIV
|
|
CLASS="NAVFOOTER"
|
|
><HR
|
|
ALIGN="LEFT"
|
|
WIDTH="100%"><TABLE
|
|
SUMMARY="Footer navigation table"
|
|
WIDTH="100%"
|
|
BORDER="0"
|
|
CELLPADDING="0"
|
|
CELLSPACING="0"
|
|
><TR
|
|
><TD
|
|
WIDTH="33%"
|
|
ALIGN="left"
|
|
VALIGN="top"
|
|
><A
|
|
HREF="x498.html"
|
|
ACCESSKEY="P"
|
|
><<< Previous</A
|
|
></TD
|
|
><TD
|
|
WIDTH="34%"
|
|
ALIGN="center"
|
|
VALIGN="top"
|
|
><A
|
|
HREF="book1.html"
|
|
ACCESSKEY="H"
|
|
>Home</A
|
|
></TD
|
|
><TD
|
|
WIDTH="33%"
|
|
ALIGN="right"
|
|
VALIGN="top"
|
|
><A
|
|
HREF="x527.html"
|
|
ACCESSKEY="N"
|
|
>Next >>></A
|
|
></TD
|
|
></TR
|
|
><TR
|
|
><TD
|
|
WIDTH="33%"
|
|
ALIGN="left"
|
|
VALIGN="top"
|
|
>The solution</TD
|
|
><TD
|
|
WIDTH="34%"
|
|
ALIGN="center"
|
|
VALIGN="top"
|
|
><A
|
|
HREF="c486.html"
|
|
ACCESSKEY="U"
|
|
>Up</A
|
|
></TD
|
|
><TD
|
|
WIDTH="33%"
|
|
ALIGN="right"
|
|
VALIGN="top"
|
|
>16-bit addition and subtraction</TD
|
|
></TR
|
|
></TABLE
|
|
></DIV
|
|
></BODY
|
|
></HTML
|
|
> |