<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html> <head> <!-- Generated by HsColour, http://www.cs.york.ac.uk/fp/darcs/hscolour/ --> <title>Lava/Arithmetic.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <pre><a name="line-1"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Lava</span><span class='hs-varop'>.</span><span class='hs-conid'>Arithmetic</span> <span class='hs-keyword'>where</span> <a name="line-2"></a> <a name="line-3"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Lava</span> <a name="line-4"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Lava</span><span class='hs-varop'>.</span><span class='hs-conid'>Patterns</span> <a name="line-5"></a> <a name="line-6"></a><span class='hs-comment'>----------------------------------------------------------------</span> <a name="line-7"></a><span class='hs-comment'>-- Basic Components</span> <a name="line-8"></a> <a name="line-9"></a><a name="halfAdd"></a><span class='hs-definition'>halfAdd</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>sum</span><span class='hs-layout'>,</span> <span class='hs-varid'>carry</span><span class='hs-layout'>)</span> <a name="line-10"></a> <span class='hs-keyword'>where</span> <a name="line-11"></a> <span class='hs-varid'>sum</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xor2</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <a name="line-12"></a> <span class='hs-varid'>carry</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>and2</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <a name="line-13"></a> <a name="line-14"></a><a name="fullAdd"></a><span class='hs-definition'>fullAdd</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>sum</span><span class='hs-layout'>,</span> <span class='hs-varid'>carryOut</span><span class='hs-layout'>)</span> <a name="line-15"></a> <span class='hs-keyword'>where</span> <a name="line-16"></a> <span class='hs-layout'>(</span><span class='hs-varid'>sum1</span><span class='hs-layout'>,</span> <span class='hs-varid'>carry1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>halfAdd</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <a name="line-17"></a> <span class='hs-layout'>(</span><span class='hs-varid'>sum</span><span class='hs-layout'>,</span> <span class='hs-varid'>carry2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>halfAdd</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-varid'>sum1</span><span class='hs-layout'>)</span> <a name="line-18"></a> <span class='hs-varid'>carryOut</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xor2</span> <span class='hs-layout'>(</span><span class='hs-varid'>carry1</span><span class='hs-layout'>,</span> <span class='hs-varid'>carry2</span><span class='hs-layout'>)</span> <a name="line-19"></a> <a name="line-20"></a><a name="bitAdder"></a><span class='hs-definition'>bitAdder</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>row</span> <span class='hs-varid'>halfAdd</span> <a name="line-21"></a> <a name="line-22"></a><a name="adder"></a><span class='hs-definition'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-varid'>carryIn</span><span class='hs-layout'>)</span> <a name="line-23"></a><span class='hs-definition'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bitAdder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <a name="line-24"></a><span class='hs-definition'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bitAdder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <a name="line-25"></a><span class='hs-definition'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-conop'>:</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-conop'>:</span><span class='hs-varid'>bs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span><span class='hs-conop'>:</span><span class='hs-varid'>ss</span><span class='hs-layout'>,</span> <span class='hs-varid'>carryOut</span><span class='hs-layout'>)</span> <a name="line-26"></a> <span class='hs-keyword'>where</span> <a name="line-27"></a> <span class='hs-layout'>(</span><span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-varid'>carry</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fullAdd</span> <span class='hs-layout'>(</span><span class='hs-varid'>carryIn</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-28"></a> <span class='hs-layout'>(</span><span class='hs-varid'>ss</span><span class='hs-layout'>,</span> <span class='hs-varid'>carryOut</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>carry</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-29"></a> <a name="line-30"></a><a name="binAdder"></a><span class='hs-definition'>binAdder</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sum</span> <span class='hs-varop'>++</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>carryOut</span><span class='hs-keyglyph'>]</span> <a name="line-31"></a> <span class='hs-keyword'>where</span> <a name="line-32"></a> <span class='hs-layout'>(</span><span class='hs-varid'>sum</span><span class='hs-layout'>,</span> <span class='hs-varid'>carryOut</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>low</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-33"></a> <a name="line-34"></a><a name="bitMulti"></a><span class='hs-definition'>bitMulti</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span> <span class='hs-varid'>and2</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>bs</span> <span class='hs-keyglyph'>]</span> <a name="line-35"></a> <a name="line-36"></a><a name="multi"></a><span class='hs-definition'>multi</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span> <a name="line-37"></a><span class='hs-definition'>multi</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>replicate</span> <span class='hs-layout'>(</span><span class='hs-varid'>length</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-varid'>low</span> <a name="line-38"></a><span class='hs-definition'>multi</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>replicate</span> <span class='hs-layout'>(</span><span class='hs-varid'>length</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-varid'>low</span> <a name="line-39"></a><span class='hs-definition'>multi</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-conop'>:</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>m</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ms</span> <a name="line-40"></a> <span class='hs-keyword'>where</span> <a name="line-41"></a> <span class='hs-layout'>(</span><span class='hs-varid'>m</span><span class='hs-conop'>:</span><span class='hs-varid'>abs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bitMulti</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <a name="line-42"></a> <span class='hs-varid'>asbs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>multi</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <a name="line-43"></a> <span class='hs-layout'>(</span><span class='hs-varid'>ms</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>adder</span> <span class='hs-layout'>(</span><span class='hs-varid'>low</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>abs</span><span class='hs-layout'>,</span> <span class='hs-varid'>asbs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-44"></a> <a name="line-45"></a><a name="numBreak"></a><span class='hs-definition'>numBreak</span> <span class='hs-varid'>num</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>bit</span><span class='hs-layout'>,</span> <span class='hs-varid'>num'</span><span class='hs-layout'>)</span> <a name="line-46"></a> <span class='hs-keyword'>where</span> <a name="line-47"></a> <span class='hs-varid'>digit</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>imod</span> <span class='hs-layout'>(</span><span class='hs-varid'>num</span><span class='hs-layout'>,</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <a name="line-48"></a> <span class='hs-varid'>bit</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>int2bit</span> <span class='hs-varid'>digit</span> <a name="line-49"></a> <span class='hs-varid'>num'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>idiv</span> <span class='hs-layout'>(</span><span class='hs-varid'>num</span><span class='hs-layout'>,</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <a name="line-50"></a> <a name="line-51"></a><a name="int2bin"></a><span class='hs-definition'>int2bin</span> <span class='hs-num'>0</span> <span class='hs-varid'>num</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span> <a name="line-52"></a><span class='hs-definition'>int2bin</span> <span class='hs-varid'>n</span> <span class='hs-varid'>num</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>bit</span><span class='hs-conop'>:</span><span class='hs-varid'>bits</span><span class='hs-layout'>)</span> <a name="line-53"></a> <span class='hs-keyword'>where</span> <a name="line-54"></a> <span class='hs-layout'>(</span><span class='hs-varid'>bit</span><span class='hs-layout'>,</span><span class='hs-varid'>num'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>numBreak</span> <span class='hs-varid'>num</span> <a name="line-55"></a> <span class='hs-varid'>bits</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>int2bin</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>num'</span> <a name="line-56"></a> <a name="line-57"></a><a name="bin2int"></a><span class='hs-definition'>bin2int</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span> <a name="line-58"></a><span class='hs-definition'>bin2int</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-conop'>:</span><span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>num</span> <a name="line-59"></a> <span class='hs-keyword'>where</span> <a name="line-60"></a> <span class='hs-varid'>num'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bin2int</span> <span class='hs-varid'>bs</span> <a name="line-61"></a> <span class='hs-varid'>num</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bit2int</span> <span class='hs-varid'>b</span> <span class='hs-varop'>+</span> <span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>num'</span> <a name="line-62"></a> <a name="line-63"></a><span class='hs-comment'>----------------------------------------------------------------</span> <a name="line-64"></a><span class='hs-comment'>-- the end.</span> <a name="line-65"></a> <a name="line-66"></a> </pre></body> </html>
