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<title>src/Data/Trie/BitTwiddle.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# OPTIONS_GHC -Wall -fwarn-tabs -fno-warn-name-shadowing #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>-- The MagicHash is for unboxed primitives (-fglasgow-exts also works)</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE CPP, MagicHash #-}</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'>-- ~ 2009.01.05</span>
<a name="line-8"></a><span class='hs-comment'>-- |</span>
<a name="line-9"></a><span class='hs-comment'>-- Module : Data.Trie.BitTwiddle</span>
<a name="line-10"></a><span class='hs-comment'>-- Copyright : Copyright (c) 2002 Daan Leijen</span>
<a name="line-11"></a><span class='hs-comment'>-- License : BSD3</span>
<a name="line-12"></a><span class='hs-comment'>-- Maintainer : libraries@haskell.org, wren@community.haskell.org</span>
<a name="line-13"></a><span class='hs-comment'>-- Stability : stable</span>
<a name="line-14"></a><span class='hs-comment'>-- Portability : portable (with CPP)</span>
<a name="line-15"></a><span class='hs-comment'>--</span>
<a name="line-16"></a><span class='hs-comment'>-- Functions to treat 'Word' as a bit-vector for big-endian patricia</span>
<a name="line-17"></a><span class='hs-comment'>-- trees. This code is duplicated from "Data.IntMap". The only</span>
<a name="line-18"></a><span class='hs-comment'>-- differences are that some of the conversion functions are</span>
<a name="line-19"></a><span class='hs-comment'>-- specialized to 'Word8' for bytestrings, instead of being specialized</span>
<a name="line-20"></a><span class='hs-comment'>-- to 'Int'.</span>
<a name="line-21"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-22"></a>
<a name="line-23"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Trie</span><span class='hs-varop'>.</span><span class='hs-conid'>BitTwiddle</span>
<a name="line-24"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Prefix</span><span class='hs-layout'>,</span> <span class='hs-conid'>Mask</span>
<a name="line-25"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>elemToNat</span>
<a name="line-26"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>zero</span><span class='hs-layout'>,</span> <span class='hs-varid'>nomatch</span>
<a name="line-27"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>mask</span><span class='hs-layout'>,</span> <span class='hs-varid'>shorter</span><span class='hs-layout'>,</span> <span class='hs-varid'>branchMask</span>
<a name="line-28"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-29"></a>
<a name="line-30"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Trie</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteStringInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>ByteStringElem</span><span class='hs-layout'>)</span>
<a name="line-31"></a>
<a name="line-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Bits</span>
<a name="line-33"></a>
<a name="line-34"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 503</span>
<a name="line-35"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>GHC</span><span class='hs-varop'>.</span><span class='hs-conid'>Exts</span> <span class='hs-layout'>(</span> <span class='hs-conid'>Word</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>Int</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>shiftRL</span><span class='hs-cpp'>#</span> <span class='hs-layout'>)</span>
<a name="line-36"></a><span class='hs-cpp'>#elif __GLASGOW_HASKELL__</span>
<a name="line-37"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>GlaExts</span> <span class='hs-layout'>(</span> <span class='hs-conid'>Word</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>Int</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>shiftRL</span><span class='hs-cpp'>#</span> <span class='hs-layout'>)</span>
<a name="line-38"></a><span class='hs-cpp'>#else</span>
<a name="line-39"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Word</span> <span class='hs-layout'>(</span><span class='hs-conid'>Word</span><span class='hs-layout'>)</span>
<a name="line-40"></a><span class='hs-cpp'>#endif</span>
<a name="line-41"></a>
<a name="line-42"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-43"></a>
<a name="line-44"></a><a name="KeyElem"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>KeyElem</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ByteStringElem</span>
<a name="line-45"></a><a name="Prefix"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Prefix</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>KeyElem</span>
<a name="line-46"></a><a name="Mask"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Mask</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>KeyElem</span>
<a name="line-47"></a>
<a name="line-48"></a><a name="elemToNat"></a><span class='hs-definition'>elemToNat</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>KeyElem</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Word</span>
<a name="line-49"></a><span class='hs-comment'>{-# INLINE elemToNat #-}</span>
<a name="line-50"></a><span class='hs-definition'>elemToNat</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromIntegral</span>
<a name="line-51"></a>
<a name="line-52"></a><a name="natToElem"></a><span class='hs-definition'>natToElem</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Word</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>KeyElem</span>
<a name="line-53"></a><span class='hs-comment'>{-# INLINE natToElem #-}</span>
<a name="line-54"></a><span class='hs-definition'>natToElem</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromIntegral</span>
<a name="line-55"></a>
<a name="line-56"></a><a name="shiftRL"></a><span class='hs-definition'>shiftRL</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Word</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Word</span>
<a name="line-57"></a><span class='hs-comment'>{-# INLINE shiftRL #-}</span>
<a name="line-58"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__</span>
<a name="line-59"></a><span class='hs-comment'>-- GHC: use unboxing to get @shiftRL@ inlined.</span>
<a name="line-60"></a><span class='hs-definition'>shiftRL</span> <span class='hs-layout'>(</span><span class='hs-conid'>W</span><span class='hs-cpp'>#</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>I</span><span class='hs-cpp'>#</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>W</span><span class='hs-cpp'>#</span> <span class='hs-layout'>(</span><span class='hs-varid'>shiftRL</span><span class='hs-cpp'>#</span> <span class='hs-varid'>x</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span>
<a name="line-61"></a><span class='hs-cpp'>#else</span>
<a name="line-62"></a><span class='hs-definition'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>shiftR</span> <span class='hs-varid'>x</span> <span class='hs-varid'>i</span>
<a name="line-63"></a><span class='hs-cpp'>#endif</span>
<a name="line-64"></a>
<a name="line-65"></a>
<a name="line-66"></a><span class='hs-comment'>{---------------------------------------------------------------
<a name="line-67"></a>-- Endian independent bit twiddling (Trie endianness, not architecture)
<a name="line-68"></a>---------------------------------------------------------------}</span>
<a name="line-69"></a>
<a name="line-70"></a><span class='hs-comment'>-- TODO: should we use the (Bits Word8) instance instead of 'elemToNat' and (Bits Nat)? We need to compare Core, C--, or ASM in order to decide this. The choice will apply to 'zero', 'mask', 'maskW',... If we shouldn't, then we should probably send a patch upstream to fix the (Bits Word8) instance.</span>
<a name="line-71"></a>
<a name="line-72"></a><a name="zero"></a><span class='hs-comment'>-- | Is the value under the mask zero?</span>
<a name="line-73"></a><span class='hs-definition'>zero</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>KeyElem</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Mask</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-74"></a><span class='hs-comment'>{-# INLINE zero #-}</span>
<a name="line-75"></a><span class='hs-definition'>zero</span> <span class='hs-varid'>i</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>elemToNat</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-varop'>.&.</span> <span class='hs-layout'>(</span><span class='hs-varid'>elemToNat</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span>
<a name="line-76"></a>
<a name="line-77"></a><a name="nomatch"></a><span class='hs-comment'>-- | Does a value /not/ match some prefix, for all the bits preceding</span>
<a name="line-78"></a><span class='hs-comment'>-- a masking bit? (Hence a subtree matching the value doesn't exist.)</span>
<a name="line-79"></a><span class='hs-definition'>nomatch</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>KeyElem</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Prefix</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Mask</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-80"></a><span class='hs-comment'>{-# INLINE nomatch #-}</span>
<a name="line-81"></a><span class='hs-definition'>nomatch</span> <span class='hs-varid'>i</span> <span class='hs-varid'>p</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mask</span> <span class='hs-varid'>i</span> <span class='hs-varid'>m</span> <span class='hs-varop'>/=</span> <span class='hs-varid'>p</span>
<a name="line-82"></a>
<a name="line-83"></a><a name="mask"></a><span class='hs-definition'>mask</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>KeyElem</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Mask</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Prefix</span>
<a name="line-84"></a><span class='hs-comment'>{-# INLINE mask #-}</span>
<a name="line-85"></a><span class='hs-definition'>mask</span> <span class='hs-varid'>i</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>maskW</span> <span class='hs-layout'>(</span><span class='hs-varid'>elemToNat</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>elemToNat</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-86"></a>
<a name="line-87"></a>
<a name="line-88"></a><span class='hs-comment'>{---------------------------------------------------------------
<a name="line-89"></a>-- Big endian operations (Trie endianness, not architecture)
<a name="line-90"></a>---------------------------------------------------------------}</span>
<a name="line-91"></a>
<a name="line-92"></a><a name="maskW"></a><span class='hs-comment'>-- | Get mask by setting all bits higher than the smallest bit in</span>
<a name="line-93"></a><span class='hs-comment'>-- @m@. Then apply that mask to @i@.</span>
<a name="line-94"></a><span class='hs-definition'>maskW</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Word</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Word</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Prefix</span>
<a name="line-95"></a><span class='hs-comment'>{-# INLINE maskW #-}</span>
<a name="line-96"></a><span class='hs-definition'>maskW</span> <span class='hs-varid'>i</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>natToElem</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span> <span class='hs-varop'>.&.</span> <span class='hs-layout'>(</span><span class='hs-varid'>complement</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'>`xor`</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-97"></a><span class='hs-comment'>-- TODO: try the alternatives mentioned in the Containers paper:</span>
<a name="line-98"></a><span class='hs-comment'>-- \i m -> natToElem (i .&. (negate m - m))</span>
<a name="line-99"></a><span class='hs-comment'>-- \i m -> natToElem (i .&. (m * complement 1))</span>
<a name="line-100"></a><span class='hs-comment'>-- N.B. these return /all/ the low bits, and therefore they are not equal functions for all m. They are, however, equal when only one bit of m is set.</span>
<a name="line-101"></a>
<a name="line-102"></a><a name="shorter"></a><span class='hs-comment'>-- | Determine whether the first mask denotes a shorter prefix than</span>
<a name="line-103"></a><span class='hs-comment'>-- the second.</span>
<a name="line-104"></a><span class='hs-definition'>shorter</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Mask</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Mask</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-105"></a><span class='hs-comment'>{-# INLINE shorter #-}</span>
<a name="line-106"></a><span class='hs-definition'>shorter</span> <span class='hs-varid'>m1</span> <span class='hs-varid'>m2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>elemToNat</span> <span class='hs-varid'>m1</span> <span class='hs-varop'>></span> <span class='hs-varid'>elemToNat</span> <span class='hs-varid'>m2</span>
<a name="line-107"></a>
<a name="line-108"></a><a name="branchMask"></a><span class='hs-comment'>-- | Determine first differing bit of two prefixes.</span>
<a name="line-109"></a><span class='hs-definition'>branchMask</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Prefix</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Prefix</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Mask</span>
<a name="line-110"></a><span class='hs-comment'>{-# INLINE branchMask #-}</span>
<a name="line-111"></a><span class='hs-definition'>branchMask</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span>
<a name="line-112"></a> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>natToElem</span> <span class='hs-layout'>(</span><span class='hs-varid'>highestBitMask</span> <span class='hs-layout'>(</span><span class='hs-varid'>elemToNat</span> <span class='hs-varid'>p1</span> <span class='hs-varop'>`xor`</span> <span class='hs-varid'>elemToNat</span> <span class='hs-varid'>p2</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-113"></a>
<a name="line-114"></a><span class='hs-comment'>{---------------------------------------------------------------
<a name="line-115"></a> Finding the highest bit (mask) in a word [x] can be done efficiently
<a name="line-116"></a> in three ways:
<a name="line-117"></a> * convert to a floating point value and the mantissa tells us the
<a name="line-118"></a> [log2(x)] that corresponds with the highest bit position. The
<a name="line-119"></a> mantissa is retrieved either via the standard C function [frexp]
<a name="line-120"></a> or by some bit twiddling on IEEE compatible numbers (float).
<a name="line-121"></a> Note that one needs to use at least [double] precision for an
<a name="line-122"></a> accurate mantissa of 32 bit numbers.
<a name="line-123"></a> * use bit twiddling, a logarithmic sequence of bitwise or's and
<a name="line-124"></a> shifts (bit).
<a name="line-125"></a> * use processor specific assembler instruction (asm).
<a name="line-126"></a>
<a name="line-127"></a> The most portable way would be [bit], but is it efficient enough?
<a name="line-128"></a> I have measured the cycle counts of the different methods on an
<a name="line-129"></a> AMD Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC
<a name="line-130"></a> instruction:
<a name="line-131"></a>
<a name="line-132"></a> highestBitMask: method cycles
<a name="line-133"></a> --------------
<a name="line-134"></a> frexp 200
<a name="line-135"></a> float 33
<a name="line-136"></a> bit 11
<a name="line-137"></a> asm 12
<a name="line-138"></a>
<a name="line-139"></a> highestBit: method cycles
<a name="line-140"></a> --------------
<a name="line-141"></a> frexp 195
<a name="line-142"></a> float 33
<a name="line-143"></a> bit 11
<a name="line-144"></a> asm 11
<a name="line-145"></a>
<a name="line-146"></a> Wow, the bit twiddling is on today's RISC like machines even
<a name="line-147"></a> faster than a single CISC instruction (BSR)!
<a name="line-148"></a>---------------------------------------------------------------}</span>
<a name="line-149"></a>
<a name="line-150"></a><a name="highestBitMask"></a><span class='hs-comment'>{---------------------------------------------------------------
<a name="line-151"></a> [highestBitMask] returns a word where only the highest bit is
<a name="line-152"></a> set. It is found by first setting all bits in lower positions
<a name="line-153"></a> than the highest bit and than taking an exclusive or with the
<a name="line-154"></a> original value. Allthough the function may look expensive, GHC
<a name="line-155"></a> compiles this into excellent C code that subsequently compiled
<a name="line-156"></a> into highly efficient machine code. The algorithm is derived from
<a name="line-157"></a> Jorg Arndt's FXT library.
<a name="line-158"></a>---------------------------------------------------------------}</span>
<a name="line-159"></a><span class='hs-definition'>highestBitMask</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Word</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Word</span>
<a name="line-160"></a><span class='hs-comment'>{-# INLINE highestBitMask #-}</span>
<a name="line-161"></a><span class='hs-definition'>highestBitMask</span> <span class='hs-varid'>x</span>
<a name="line-162"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-163"></a> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-164"></a> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>4</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-165"></a> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>8</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-166"></a> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>16</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-167"></a> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>32</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span> <span class='hs-comment'>-- for 64 bit platforms</span>
<a name="line-168"></a> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`xor`</span> <span class='hs-varid'>shiftRL</span> <span class='hs-varid'>x</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-169"></a>
<a name="line-170"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-171"></a><span class='hs-comment'>----------------------------------------------------------- fin.</span>
</pre></body>
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