<?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://code.haskell.org/~malcolm/hscolour/ --> <title>Data/Number/BigFloat.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <pre><a name="line-1"></a><span class='hs-comment'>-- | A simple implementation of floating point numbers with a selectable</span> <a name="line-2"></a><span class='hs-comment'>-- precision. The number of digits in the mantissa is selected by the</span> <a name="line-3"></a><span class='hs-comment'>-- 'Epsilon' type class from the "Fixed" module.</span> <a name="line-4"></a><span class='hs-comment'>--</span> <a name="line-5"></a><span class='hs-comment'>-- The numbers are stored in base 10.</span> <a name="line-6"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>BigFloat</span><span class='hs-layout'>(</span> <a name="line-7"></a> <span class='hs-conid'>BigFloat</span><span class='hs-layout'>,</span> <a name="line-8"></a> <span class='hs-conid'>Epsilon</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eps1</span><span class='hs-layout'>,</span> <span class='hs-conid'>EpsDiv10</span><span class='hs-layout'>,</span> <span class='hs-conid'>Prec10</span><span class='hs-layout'>,</span> <span class='hs-conid'>Prec50</span><span class='hs-layout'>,</span> <span class='hs-conid'>PrecPlus20</span> <a name="line-9"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-10"></a> <a name="line-11"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Numeric</span><span class='hs-layout'>(</span><span class='hs-varid'>showSigned</span><span class='hs-layout'>)</span> <a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>Fixed</span> <a name="line-13"></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'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>FixedFunctions</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>F</span> <a name="line-14"></a> <a name="line-15"></a><a name="base"></a><span class='hs-definition'>base</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <a name="line-16"></a><span class='hs-definition'>base</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>10</span> <a name="line-17"></a> <a name="line-18"></a><a name="BigFloat"></a><span class='hs-comment'>-- This representation is stupid, two Integers makes more sense,</span> <a name="line-19"></a><a name="BigFloat"></a><span class='hs-comment'>-- but is more work.</span> <a name="line-20"></a><a name="BigFloat"></a><span class='hs-comment'>-- | Floating point number where the precision is determined by the type /e/.</span> <a name="line-21"></a><a name="BigFloat"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fixed</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-conid'>Integer</span> <a name="line-22"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>)</span> <a name="line-23"></a> <a name="line-24"></a><a name="instance%20Show%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-25"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showSigned</span> <span class='hs-varid'>showBF</span> <a name="line-26"></a> <span class='hs-comment'>-- Assumes base is 10</span> <a name="line-27"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>showBF</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showsPrec</span> <span class='hs-num'>0</span> <span class='hs-varid'>m</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showString</span> <span class='hs-str'>"e"</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showsPrec</span> <span class='hs-num'>0</span> <span class='hs-varid'>e</span> <a name="line-28"></a> <a name="line-29"></a><a name="instance%20Num%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Num</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-30"></a> <span class='hs-conid'>BF</span> <span class='hs-varid'>m1</span> <span class='hs-varid'>e1</span> <span class='hs-varop'>+</span> <span class='hs-conid'>BF</span> <span class='hs-varid'>m2</span> <span class='hs-varid'>e2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>m1'</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m2'</span><span class='hs-layout'>)</span> <span class='hs-varid'>e</span> <a name="line-31"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>m1'</span><span class='hs-layout'>,</span> <span class='hs-varid'>m2'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>e</span> <span class='hs-varop'>==</span> <span class='hs-varid'>e1</span> <span class='hs-keyword'>then</span> <span class='hs-layout'>(</span><span class='hs-varid'>m1</span><span class='hs-layout'>,</span> <span class='hs-varid'>m2</span> <span class='hs-varop'>/</span> <span class='hs-varid'>base</span><span class='hs-varop'>^</span><span class='hs-layout'>(</span><span class='hs-varid'>e</span><span class='hs-comment'>-</span><span class='hs-varid'>e2</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-32"></a> <span class='hs-keyword'>else</span> <span class='hs-layout'>(</span><span class='hs-varid'>m1</span> <span class='hs-varop'>/</span> <span class='hs-varid'>base</span><span class='hs-varop'>^</span><span class='hs-layout'>(</span><span class='hs-varid'>e</span><span class='hs-comment'>-</span><span class='hs-varid'>e1</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>m2</span><span class='hs-layout'>)</span> <a name="line-33"></a> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e1</span> <span class='hs-varop'>`max`</span> <span class='hs-varid'>e2</span> <a name="line-34"></a> <span class='hs-comment'>-- Do - via negate</span> <a name="line-35"></a> <span class='hs-conid'>BF</span> <span class='hs-varid'>m1</span> <span class='hs-varid'>e1</span> <span class='hs-varop'>*</span> <span class='hs-conid'>BF</span> <span class='hs-varid'>m2</span> <span class='hs-varid'>e2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>m1</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>e1</span> <span class='hs-varop'>+</span> <span class='hs-varid'>e2</span><span class='hs-layout'>)</span> <a name="line-36"></a> <span class='hs-varid'>negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>e</span> <a name="line-37"></a> <span class='hs-varid'>abs</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-layout'>(</span><span class='hs-varid'>abs</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>e</span> <a name="line-38"></a> <span class='hs-varid'>signum</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>signum</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <a name="line-39"></a> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <a name="line-40"></a> <a name="line-41"></a><a name="instance%20Real%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Real</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-42"></a> <span class='hs-varid'>toRational</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>e</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toRational</span> <span class='hs-varid'>e</span> <span class='hs-varop'>*</span> <span class='hs-varid'>base</span><span class='hs-varop'>^^</span><span class='hs-varid'>m</span> <a name="line-43"></a> <a name="line-44"></a><a name="instance%20Ord%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Ord</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-45"></a> <span class='hs-varid'>compare</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>compare</span> <span class='hs-layout'>(</span><span class='hs-varid'>toRational</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>toRational</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <a name="line-46"></a> <a name="line-47"></a><a name="instance%20Fractional%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Fractional</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-48"></a> <span class='hs-varid'>recip</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>base</span> <span class='hs-varop'>/</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-layout'>(</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-layout'>)</span> <a name="line-49"></a> <span class='hs-comment'>-- Take care not to lose precision for small numbers</span> <a name="line-50"></a> <span class='hs-varid'>fromRational</span> <span class='hs-varid'>x</span> <a name="line-51"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-varop'>||</span> <span class='hs-varid'>abs</span> <span class='hs-varid'>x</span> <span class='hs-varop'>>=</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromRational</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <a name="line-52"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>recip</span> <span class='hs-varop'>$</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromRational</span> <span class='hs-layout'>(</span><span class='hs-varid'>recip</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <a name="line-53"></a> <a name="line-54"></a> <a name="line-55"></a><a name="bf"></a><span class='hs-comment'>-- normalizing constructor</span> <a name="line-56"></a><span class='hs-comment'>-- XXX The scaling is very inefficient</span> <a name="line-57"></a><span class='hs-definition'>bf</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Fixed</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span> <a name="line-58"></a><span class='hs-definition'>bf</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>m</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <a name="line-59"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>m</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>e</span> <a name="line-60"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>m</span> <span class='hs-varop'>>=</span> <span class='hs-varid'>base</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'>/</span> <span class='hs-varid'>base</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>e</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <a name="line-61"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>m</span> <span class='hs-varop'><</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-varid'>base</span><span class='hs-layout'>)</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-62"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span> <a name="line-63"></a> <a name="line-64"></a><a name="instance%20RealFrac%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>RealFrac</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-65"></a> <span class='hs-varid'>properFraction</span> <span class='hs-varid'>x</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-66"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>e</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-num'>0</span><span class='hs-layout'>,</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <a name="line-67"></a> <span class='hs-keyword'>else</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>properFraction</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-varid'>base</span><span class='hs-varop'>^^</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <a name="line-68"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-varid'>bf</span> <span class='hs-varid'>f</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <a name="line-69"></a> <a name="line-70"></a><a name="instance%20Floating%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Floating</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-71"></a> <span class='hs-varid'>pi</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-varid'>pi</span> <span class='hs-num'>0</span> <a name="line-72"></a> <span class='hs-varid'>sqrt</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>sqrt</span> <a name="line-73"></a> <span class='hs-varid'>exp</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>exp</span> <a name="line-74"></a> <span class='hs-varid'>log</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>log</span> <a name="line-75"></a> <span class='hs-varid'>sin</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>sin</span> <a name="line-76"></a> <span class='hs-varid'>cos</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>cos</span> <a name="line-77"></a> <span class='hs-varid'>tan</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>tan</span> <a name="line-78"></a> <span class='hs-varid'>asin</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>asin</span> <a name="line-79"></a> <span class='hs-varid'>acos</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>acos</span> <a name="line-80"></a> <span class='hs-varid'>atan</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>atan</span> <a name="line-81"></a> <span class='hs-varid'>sinh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>sinh</span> <a name="line-82"></a> <span class='hs-varid'>cosh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>cosh</span> <a name="line-83"></a> <span class='hs-varid'>tanh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>tanh</span> <a name="line-84"></a> <span class='hs-varid'>asinh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>asinh</span> <a name="line-85"></a> <span class='hs-varid'>acosh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>acosh</span> <a name="line-86"></a> <span class='hs-varid'>atanh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFloat1</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>atanh</span> <a name="line-87"></a> <a name="line-88"></a><a name="instance%20RealFloat%20(BigFloat%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>RealFloat</span> <span class='hs-layout'>(</span><span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-89"></a> <span class='hs-varid'>floatRadix</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>base</span> <a name="line-90"></a> <span class='hs-varid'>floatDigits</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-91"></a> <span class='hs-varid'>floor</span> <span class='hs-varop'>$</span> <span class='hs-varid'>logBase</span> <span class='hs-varid'>base</span> <span class='hs-varop'>$</span> <span class='hs-varid'>recip</span> <span class='hs-varop'>$</span> <span class='hs-varid'>fromRational</span> <span class='hs-varop'>$</span> <span class='hs-varid'>precision</span> <span class='hs-varid'>m</span> <a name="line-92"></a> <span class='hs-varid'>floatRange</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>minBound</span><span class='hs-layout'>,</span> <span class='hs-varid'>maxBound</span><span class='hs-layout'>)</span> <a name="line-93"></a> <span class='hs-varid'>decodeFloat</span> <span class='hs-varid'>x</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-94"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>floatDigits</span> <span class='hs-varid'>x</span> <a name="line-95"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-varid'>round</span> <span class='hs-varop'>$</span> <span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-varid'>base</span><span class='hs-varop'>^</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>e</span> <span class='hs-comment'>-</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <a name="line-96"></a> <span class='hs-varid'>encodeFloat</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInteger</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <a name="line-97"></a> <span class='hs-varid'>exponent</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>e</span> <a name="line-98"></a> <span class='hs-varid'>significand</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-num'>0</span> <a name="line-99"></a> <span class='hs-varid'>scaleFloat</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>e</span> <span class='hs-varop'>+</span> <span class='hs-varid'>toInteger</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <a name="line-100"></a> <span class='hs-varid'>isNaN</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <a name="line-101"></a> <span class='hs-varid'>isInfinite</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <a name="line-102"></a> <span class='hs-varid'>isDenormalized</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <a name="line-103"></a> <span class='hs-varid'>isNegativeZero</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <a name="line-104"></a> <span class='hs-varid'>isIEEE</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <a name="line-105"></a> <a name="line-106"></a><a name="toFloat1"></a><span class='hs-definition'>toFloat1</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Epsilon</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-conid'>Rational</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Rational</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Rational</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <a name="line-107"></a> <span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BigFloat</span> <span class='hs-varid'>e</span> <a name="line-108"></a><span class='hs-definition'>toFloat1</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>BF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-109"></a> <span class='hs-varid'>fromRational</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>precision</span> <span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-varid'>scl</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>toRational</span> <span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-varid'>scl</span><span class='hs-layout'>)</span> <a name="line-110"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>scl</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>base</span><span class='hs-varop'>^^</span><span class='hs-varid'>e</span> </pre></body> </html>
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