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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE BangPatterns, CPP, MagicHash, OverloadedStrings, UnboxedTuples #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>-- Module: Blaze.Text.Double.Native</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright: (c) 2011 MailRank, Inc.</span>
<a name="line-5"></a><span class='hs-comment'>-- License: BSD3</span>
<a name="line-6"></a><span class='hs-comment'>-- Maintainer: Bryan O'Sullivan <bos@serpentine.com></span>
<a name="line-7"></a><span class='hs-comment'>-- Stability: experimental</span>
<a name="line-8"></a><span class='hs-comment'>-- Portability: portable</span>
<a name="line-9"></a><span class='hs-comment'>--</span>
<a name="line-10"></a><span class='hs-comment'>-- Efficiently serialize a Double as a lazy 'L.ByteString'.</span>
<a name="line-11"></a>
<a name="line-12"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Blaze</span><span class='hs-varop'>.</span><span class='hs-conid'>Text</span><span class='hs-varop'>.</span><span class='hs-conid'>Double</span><span class='hs-varop'>.</span><span class='hs-conid'>Native</span>
<a name="line-13"></a> <span class='hs-layout'>(</span>
<a name="line-14"></a> <span class='hs-varid'>float</span>
<a name="line-15"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>double</span>
<a name="line-16"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-17"></a>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Blaze</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span><span class='hs-varop'>.</span><span class='hs-conid'>Builder</span> <span class='hs-layout'>(</span><span class='hs-conid'>Builder</span><span class='hs-layout'>,</span> <span class='hs-varid'>fromByteString</span><span class='hs-layout'>)</span>
<a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Blaze</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span><span class='hs-varop'>.</span><span class='hs-conid'>Builder</span><span class='hs-varop'>.</span><span class='hs-conid'>Char8</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromChar</span><span class='hs-layout'>)</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Blaze</span><span class='hs-varop'>.</span><span class='hs-conid'>Text</span><span class='hs-varop'>.</span><span class='hs-conid'>Int</span> <span class='hs-layout'>(</span><span class='hs-varid'>digit</span><span class='hs-layout'>,</span> <span class='hs-varid'>integral</span><span class='hs-layout'>,</span> <span class='hs-varid'>minus</span><span class='hs-layout'>)</span>
<a name="line-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span><span class='hs-varop'>.</span><span class='hs-conid'>Char8</span> <span class='hs-conid'>()</span>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span><span class='hs-layout'>,</span> <span class='hs-varid'>mconcat</span><span class='hs-layout'>,</span> <span class='hs-varid'>mempty</span><span class='hs-layout'>)</span>
<a name="line-23"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Vector</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>V</span>
<a name="line-24"></a>
<a name="line-25"></a><span class='hs-comment'>-- The code below is originally from GHC.Float, but has been optimised</span>
<a name="line-26"></a><span class='hs-comment'>-- in quite a few ways.</span>
<a name="line-27"></a>
<a name="line-28"></a><a name="T"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>T</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>T</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Int</span><span class='hs-keyglyph'>]</span> <span class='hs-comment'>{-# UNPACK #-}</span> <span class='hs-varop'>!</span><span class='hs-conid'>Int</span>
<a name="line-29"></a>
<a name="line-30"></a><a name="float"></a><span class='hs-definition'>float</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Float</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Builder</span>
<a name="line-31"></a><span class='hs-definition'>float</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>double</span> <span class='hs-varop'>.</span> <span class='hs-varid'>realToFrac</span>
<a name="line-32"></a>
<a name="line-33"></a><a name="double"></a><span class='hs-definition'>double</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Builder</span>
<a name="line-34"></a><span class='hs-definition'>double</span> <span class='hs-varid'>f</span>
<a name="line-35"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isInfinite</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromByteString</span> <span class='hs-varop'>$</span>
<a name="line-36"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>f</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span> <span class='hs-str'>"Infinity"</span> <span class='hs-keyword'>else</span> <span class='hs-str'>"-Infinity"</span>
<a name="line-37"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>f</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span> <span class='hs-varop'>||</span> <span class='hs-varid'>isNegativeZero</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>minus</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>goGeneric</span> <span class='hs-layout'>(</span><span class='hs-varid'>floatToDigits</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>f</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-38"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>f</span> <span class='hs-varop'>>=</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>goGeneric</span> <span class='hs-layout'>(</span><span class='hs-varid'>floatToDigits</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-39"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromByteString</span> <span class='hs-str'>"NaN"</span>
<a name="line-40"></a> <span class='hs-keyword'>where</span>
<a name="line-41"></a> <span class='hs-varid'>goGeneric</span> <span class='hs-varid'>p</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>T</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span>
<a name="line-42"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>e</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span> <span class='hs-varop'>||</span> <span class='hs-varid'>e</span> <span class='hs-varop'>></span> <span class='hs-num'>7</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>goExponent</span> <span class='hs-varid'>p</span>
<a name="line-43"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>goFixed</span> <span class='hs-varid'>p</span>
<a name="line-44"></a> <span class='hs-varid'>goExponent</span> <span class='hs-layout'>(</span><span class='hs-conid'>T</span> <span class='hs-varid'>is</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-45"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>is</span> <span class='hs-keyword'>of</span>
<a name="line-46"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>error</span> <span class='hs-str'>"putFormattedFloat"</span>
<a name="line-47"></a> <span class='hs-keyglyph'>[</span><span class='hs-num'>0</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>fromByteString</span> <span class='hs-str'>"0.0e0"</span>
<a name="line-48"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>d</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>digit</span> <span class='hs-varid'>d</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>fromByteString</span> <span class='hs-str'>".0e"</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>integral</span> <span class='hs-layout'>(</span><span class='hs-varid'>e</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-49"></a> <span class='hs-layout'>(</span><span class='hs-varid'>d</span><span class='hs-conop'>:</span><span class='hs-varid'>ds</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>digit</span> <span class='hs-varid'>d</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'.'</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>digits</span> <span class='hs-varid'>ds</span> <span class='hs-varop'>`mappend`</span>
<a name="line-50"></a> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'e'</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>integral</span> <span class='hs-layout'>(</span><span class='hs-varid'>e</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-51"></a> <span class='hs-varid'>goFixed</span> <span class='hs-layout'>(</span><span class='hs-conid'>T</span> <span class='hs-varid'>is</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span>
<a name="line-52"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>e</span> <span class='hs-varop'><=</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'0'</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'.'</span> <span class='hs-varop'>`mappend`</span>
<a name="line-53"></a> <span class='hs-varid'>mconcat</span> <span class='hs-layout'>(</span><span class='hs-varid'>replicate</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromChar</span> <span class='hs-chr'>'0'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>`mappend`</span>
<a name="line-54"></a> <span class='hs-varid'>digits</span> <span class='hs-varid'>is</span>
<a name="line-55"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-varid'>g</span> <span class='hs-num'>0</span> <span class='hs-varid'>rs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'.'</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>mk0</span> <span class='hs-varid'>rs</span>
<a name="line-56"></a> <span class='hs-varid'>g</span> <span class='hs-varid'>n</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'0'</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>g</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-conid'>[]</span>
<a name="line-57"></a> <span class='hs-varid'>g</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span><span class='hs-conop'>:</span><span class='hs-varid'>rs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>digit</span> <span class='hs-varid'>r</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>g</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'>rs</span>
<a name="line-58"></a> <span class='hs-keyword'>in</span> <span class='hs-varid'>g</span> <span class='hs-varid'>e</span> <span class='hs-varid'>is</span>
<a name="line-59"></a> <span class='hs-varid'>mk0</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromChar</span> <span class='hs-chr'>'0'</span>
<a name="line-60"></a> <span class='hs-varid'>mk0</span> <span class='hs-varid'>rs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>digits</span> <span class='hs-varid'>rs</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="digits"></a><span class='hs-definition'>digits</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Int</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Builder</span>
<a name="line-63"></a><span class='hs-definition'>digits</span> <span class='hs-layout'>(</span><span class='hs-varid'>d</span><span class='hs-conop'>:</span><span class='hs-varid'>ds</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>digit</span> <span class='hs-varid'>d</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>digits</span> <span class='hs-varid'>ds</span>
<a name="line-64"></a><span class='hs-definition'>digits</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mempty</span>
<a name="line-65"></a><span class='hs-comment'>{-# INLINE digits #-}</span>
<a name="line-66"></a>
<a name="line-67"></a><a name="floatToDigits"></a><span class='hs-definition'>floatToDigits</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>T</span>
<a name="line-68"></a><span class='hs-definition'>floatToDigits</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>T</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>0</span><span class='hs-keyglyph'>]</span> <span class='hs-num'>0</span>
<a name="line-69"></a><span class='hs-definition'>floatToDigits</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>T</span> <span class='hs-layout'>(</span><span class='hs-varid'>reverse</span> <span class='hs-varid'>rds</span><span class='hs-layout'>)</span> <span class='hs-varid'>k</span>
<a name="line-70"></a> <span class='hs-keyword'>where</span>
<a name="line-71"></a> <span class='hs-layout'>(</span><span class='hs-varid'>f0</span><span class='hs-layout'>,</span> <span class='hs-varid'>e0</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>decodeFloat</span> <span class='hs-varid'>x</span>
<a name="line-72"></a> <span class='hs-layout'>(</span><span class='hs-varid'>minExp0</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'>floatRange</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span><span class='hs-keyglyph'>::</span><span class='hs-conid'>Double</span><span class='hs-layout'>)</span>
<a name="line-73"></a> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>floatDigits</span> <span class='hs-varid'>x</span>
<a name="line-74"></a> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>floatRadix</span> <span class='hs-varid'>x</span>
<a name="line-75"></a> <span class='hs-varid'>minExp</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>minExp0</span> <span class='hs-comment'>-</span> <span class='hs-varid'>p</span> <span class='hs-comment'>-- the real minimum exponent</span>
<a name="line-76"></a> <span class='hs-comment'>-- Haskell requires that f be adjusted so denormalized numbers</span>
<a name="line-77"></a> <span class='hs-comment'>-- will have an impossibly low exponent. Adjust for this.</span>
<a name="line-78"></a> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-varid'>e</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-79"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>minExp</span> <span class='hs-comment'>-</span> <span class='hs-varid'>e0</span> <span class='hs-keyword'>in</span>
<a name="line-80"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>n</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f0</span> <span class='hs-varop'>`div`</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-varop'>^</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>e0</span><span class='hs-varop'>+</span><span class='hs-varid'>n</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyword'>else</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f0</span><span class='hs-layout'>,</span> <span class='hs-varid'>e0</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span>
<a name="line-81"></a> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>r</span><span class='hs-layout'>,</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-varid'>mUp</span><span class='hs-layout'>,</span> <span class='hs-varid'>mDn</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-82"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>e</span> <span class='hs-varop'>>=</span> <span class='hs-num'>0</span>
<a name="line-83"></a> <span class='hs-keyword'>then</span> <span class='hs-keyword'>let</span> <span class='hs-varid'>be</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span><span class='hs-varop'>^</span> <span class='hs-varid'>e</span>
<a name="line-84"></a> <span class='hs-keyword'>in</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>f</span> <span class='hs-varop'>==</span> <span class='hs-varid'>b</span><span class='hs-varop'>^</span><span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-85"></a> <span class='hs-keyword'>then</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>be</span><span class='hs-varop'>*</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>be</span><span class='hs-varop'>*</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span>
<a name="line-86"></a> <span class='hs-keyword'>else</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>be</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-varid'>be</span><span class='hs-layout'>,</span> <span class='hs-varid'>be</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span>
<a name="line-87"></a> <span class='hs-keyword'>else</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>e</span> <span class='hs-varop'>></span> <span class='hs-varid'>minExp</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>f</span> <span class='hs-varop'>==</span> <span class='hs-varid'>b</span><span class='hs-varop'>^</span><span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-88"></a> <span class='hs-keyword'>then</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-varop'>^</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>e</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-num'>1</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span>
<a name="line-89"></a> <span class='hs-keyword'>else</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-varop'>^</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-num'>2</span><span class='hs-layout'>,</span> <span class='hs-num'>1</span><span class='hs-layout'>,</span> <span class='hs-num'>1</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span>
<a name="line-90"></a> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fixup</span> <span class='hs-varid'>k0</span>
<a name="line-91"></a> <span class='hs-keyword'>where</span>
<a name="line-92"></a> <span class='hs-varid'>k0</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>b</span> <span class='hs-varop'>==</span> <span class='hs-num'>2</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-varid'>e0</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-num'>3</span> <span class='hs-varop'>`div`</span> <span class='hs-num'>10</span>
<a name="line-93"></a> <span class='hs-comment'>-- logBase 10 2 is slightly bigger than 3/10 so the following</span>
<a name="line-94"></a> <span class='hs-comment'>-- will err on the low side. Ignoring the fraction will make</span>
<a name="line-95"></a> <span class='hs-comment'>-- it err even more. Haskell promises that p-1 <= logBase b f</span>
<a name="line-96"></a> <span class='hs-comment'>-- < p.</span>
<a name="line-97"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ceiling</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>log</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span>
<a name="line-98"></a> <span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>e</span> <span class='hs-varop'>*</span> <span class='hs-varid'>log</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span> <span class='hs-varid'>log</span> <span class='hs-num'>10</span><span class='hs-layout'>)</span>
<a name="line-99"></a> <span class='hs-varid'>fixup</span> <span class='hs-varid'>n</span>
<a name="line-100"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>>=</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>r</span> <span class='hs-varop'>+</span> <span class='hs-varid'>mUp</span> <span class='hs-varop'><=</span> <span class='hs-varid'>exp10</span> <span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>n</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>fixup</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-101"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>exp10</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span> <span class='hs-varop'>+</span> <span class='hs-varid'>mUp</span><span class='hs-layout'>)</span> <span class='hs-varop'><=</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>n</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>fixup</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-102"></a>
<a name="line-103"></a> <span class='hs-varid'>gen</span> <span class='hs-varid'>ds</span> <span class='hs-varop'>!</span><span class='hs-varid'>rn</span> <span class='hs-varop'>!</span><span class='hs-varid'>sN</span> <span class='hs-varop'>!</span><span class='hs-varid'>mUpN</span> <span class='hs-varop'>!</span><span class='hs-varid'>mDnN</span> <span class='hs-keyglyph'>=</span>
<a name="line-104"></a> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>dn0</span><span class='hs-layout'>,</span> <span class='hs-varid'>rn'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>rn</span> <span class='hs-varop'>*</span> <span class='hs-num'>10</span><span class='hs-layout'>)</span> <span class='hs-varop'>`divMod`</span> <span class='hs-varid'>sN</span>
<a name="line-105"></a> <span class='hs-varid'>mUpN'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mUpN</span> <span class='hs-varop'>*</span> <span class='hs-num'>10</span>
<a name="line-106"></a> <span class='hs-varid'>mDnN'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mDnN</span> <span class='hs-varop'>*</span> <span class='hs-num'>10</span>
<a name="line-107"></a> <span class='hs-varop'>!</span><span class='hs-varid'>dn</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>dn0</span>
<a name="line-108"></a> <span class='hs-varop'>!</span><span class='hs-varid'>dn'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dn</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span>
<a name="line-109"></a> <span class='hs-keyword'>in</span> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-varid'>rn'</span> <span class='hs-varop'><</span> <span class='hs-varid'>mDnN'</span><span class='hs-layout'>,</span> <span class='hs-varid'>rn'</span> <span class='hs-varop'>+</span> <span class='hs-varid'>mUpN'</span> <span class='hs-varop'>></span> <span class='hs-varid'>sN</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-110"></a> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-conid'>True</span><span class='hs-layout'>,</span> <span class='hs-conid'>False</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>dn</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ds</span>
<a name="line-111"></a> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-conid'>False</span><span class='hs-layout'>,</span> <span class='hs-conid'>True</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>dn'</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ds</span>
<a name="line-112"></a> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-conid'>True</span><span class='hs-layout'>,</span> <span class='hs-conid'>True</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>if</span> <span class='hs-varid'>rn'</span> <span class='hs-varop'>*</span> <span class='hs-num'>2</span> <span class='hs-varop'><</span> <span class='hs-varid'>sN</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>dn</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ds</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>dn'</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ds</span>
<a name="line-113"></a> <span class='hs-layout'>(</span><span class='hs-cpp'>#</span> <span class='hs-conid'>False</span><span class='hs-layout'>,</span> <span class='hs-conid'>False</span> <span class='hs-cpp'>#</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>gen</span> <span class='hs-layout'>(</span><span class='hs-varid'>dn</span><span class='hs-conop'>:</span><span class='hs-varid'>ds</span><span class='hs-layout'>)</span> <span class='hs-varid'>rn'</span> <span class='hs-varid'>sN</span> <span class='hs-varid'>mUpN'</span> <span class='hs-varid'>mDnN'</span>
<a name="line-114"></a>
<a name="line-115"></a> <span class='hs-varid'>rds</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>k</span> <span class='hs-varop'>>=</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>gen</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>r</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-varop'>*</span> <span class='hs-varid'>exp10</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-varid'>mUp</span> <span class='hs-varid'>mDn</span>
<a name="line-116"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>gen</span> <span class='hs-conid'>[]</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span> <span class='hs-varop'>*</span> <span class='hs-varid'>bk</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-varid'>mUp</span> <span class='hs-varop'>*</span> <span class='hs-varid'>bk</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>mDn</span> <span class='hs-varop'>*</span> <span class='hs-varid'>bk</span><span class='hs-layout'>)</span>
<a name="line-117"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>bk</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>exp10</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>k</span><span class='hs-layout'>)</span>
<a name="line-118"></a>
<a name="line-119"></a><a name="exp10"></a><span class='hs-definition'>exp10</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Integer</span>
<a name="line-120"></a><span class='hs-definition'>exp10</span> <span class='hs-varid'>n</span>
<a name="line-121"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>>=</span> <span class='hs-num'>0</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>n</span> <span class='hs-varop'><</span> <span class='hs-varid'>maxExpt</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>unsafeIndex</span> <span class='hs-varid'>expts</span> <span class='hs-varid'>n</span>
<a name="line-122"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>10</span> <span class='hs-varop'>^</span> <span class='hs-varid'>n</span>
<a name="line-123"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>expts</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>V</span><span class='hs-varop'>.</span><span class='hs-varid'>generate</span> <span class='hs-varid'>maxExpt</span> <span class='hs-layout'>(</span><span class='hs-num'>10</span><span class='hs-varop'>^</span><span class='hs-layout'>)</span>
<a name="line-124"></a> <span class='hs-comment'>{-# NOINLINE expts #-}</span>
<a name="line-125"></a> <span class='hs-varid'>maxExpt</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>17</span>
<a name="line-126"></a><span class='hs-comment'>{-# INLINE exp10 #-}</span>
</pre></body>
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