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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE ForeignFunctionInterface #-}</span>
<a name="line-2"></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'>Erf</span><span class='hs-layout'>(</span><span class='hs-conid'>Erf</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'>InvErf</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-3"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Foreign</span><span class='hs-varop'>.</span><span class='hs-conid'>C</span>
<a name="line-4"></a>
<a name="line-5"></a><span class='hs-keyword'>foreign</span> <span class='hs-keyword'>import</span> <span class='hs-keyword'>ccall</span> <span class='hs-str'>"erf"</span> <span class='hs-varid'>c_erf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>CDouble</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>CDouble</span>
<a name="line-6"></a><span class='hs-keyword'>foreign</span> <span class='hs-keyword'>import</span> <span class='hs-keyword'>ccall</span> <span class='hs-str'>"erfc"</span> <span class='hs-varid'>c_erfc</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>CDouble</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>CDouble</span>
<a name="line-7"></a><span class='hs-keyword'>foreign</span> <span class='hs-keyword'>import</span> <span class='hs-keyword'>ccall</span> <span class='hs-str'>"erff"</span> <span class='hs-varid'>c_erff</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>CFloat</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>CFloat</span>
<a name="line-8"></a><span class='hs-keyword'>foreign</span> <span class='hs-keyword'>import</span> <span class='hs-keyword'>ccall</span> <span class='hs-str'>"erfcf"</span> <span class='hs-varid'>c_erfcf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>CFloat</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>CFloat</span>
<a name="line-9"></a>
<a name="line-10"></a><a name="Erf"></a><span class='hs-comment'>-- |Error function related functions.</span>
<a name="line-11"></a><a name="Erf"></a><span class='hs-comment'>--</span>
<a name="line-12"></a><a name="Erf"></a><span class='hs-comment'>-- The derivative of 'erf' is @\ x -> 2 / sqrt pi * exp (x^2)@,</span>
<a name="line-13"></a><a name="Erf"></a><span class='hs-comment'>-- and this uniquely determines 'erf' by @erf 0 = 0@.</span>
<a name="line-14"></a><a name="Erf"></a><span class='hs-comment'>--</span>
<a name="line-15"></a><a name="Erf"></a><span class='hs-comment'>-- Minimal complete definition is 'erfc' or 'normcdf'.</span>
<a name="line-16"></a><a name="Erf"></a><span class='hs-keyword'>class</span> <span class='hs-layout'>(</span><span class='hs-conid'>Floating</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Erf</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-17"></a> <span class='hs-varid'>erf</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-18"></a> <span class='hs-varid'>erfc</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^@erfc x = 1 - erf x@</span>
<a name="line-19"></a> <span class='hs-varid'>erfcx</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^@erfcx x = exp (x*x) * erfc x@</span>
<a name="line-20"></a> <span class='hs-varid'>normcdf</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^@normcdf x = erfc(-x / sqrt 2) / 2@</span>
<a name="line-21"></a>
<a name="line-22"></a> <span class='hs-comment'>-- All the functions are inter-related, here's some defaults.</span>
<a name="line-23"></a> <span class='hs-varid'>erf</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1</span> <span class='hs-comment'>-</span> <span class='hs-varid'>erfc</span> <span class='hs-varid'>x</span>
<a name="line-24"></a> <span class='hs-varid'>erfc</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>normcdf</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>x</span> <span class='hs-varop'>*</span> <span class='hs-varid'>sqrt</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span>
<a name="line-25"></a> <span class='hs-varid'>erfcx</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>exp</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>erfc</span> <span class='hs-varid'>x</span>
<a name="line-26"></a> <span class='hs-varid'>normcdf</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>erfc</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>x</span> <span class='hs-varop'>/</span> <span class='hs-varid'>sqrt</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span> <span class='hs-num'>2</span>
<a name="line-27"></a>
<a name="line-28"></a><a name="instance%20Erf%20Double"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Erf</span> <span class='hs-conid'>Double</span> <span class='hs-keyword'>where</span>
<a name="line-29"></a> <span class='hs-varid'>erf</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>realToFrac</span> <span class='hs-varop'>.</span> <span class='hs-varid'>c_erf</span> <span class='hs-varop'>.</span> <span class='hs-varid'>realToFrac</span>
<a name="line-30"></a> <span class='hs-varid'>erfc</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>realToFrac</span> <span class='hs-varop'>.</span> <span class='hs-varid'>c_erfc</span> <span class='hs-varop'>.</span> <span class='hs-varid'>realToFrac</span>
<a name="line-31"></a>
<a name="line-32"></a><a name="instance%20Erf%20Float"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Erf</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span>
<a name="line-33"></a> <span class='hs-varid'>erf</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>realToFrac</span> <span class='hs-varop'>.</span> <span class='hs-varid'>c_erff</span> <span class='hs-varop'>.</span> <span class='hs-varid'>realToFrac</span>
<a name="line-34"></a> <span class='hs-varid'>erfc</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>realToFrac</span> <span class='hs-varop'>.</span> <span class='hs-varid'>c_erfcf</span> <span class='hs-varop'>.</span> <span class='hs-varid'>realToFrac</span>
<a name="line-35"></a>
<a name="line-36"></a><a name="InvErf"></a><span class='hs-comment'>-- |Inverse error functions, e.g., @inverf . erf = id@ and @erf . inverf = id@ assuming</span>
<a name="line-37"></a><a name="InvErf"></a><span class='hs-comment'>-- the appropriate codomain for 'inverf'.</span>
<a name="line-38"></a><a name="InvErf"></a><span class='hs-comment'>-- Note that the accuracy may drop radically for extreme arguments.</span>
<a name="line-39"></a><a name="InvErf"></a><span class='hs-keyword'>class</span> <span class='hs-layout'>(</span><span class='hs-conid'>Floating</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>InvErf</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-40"></a> <span class='hs-varid'>inverf</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-41"></a> <span class='hs-varid'>inverfc</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-42"></a><span class='hs-comment'>-- inverfcx :: a -> a</span>
<a name="line-43"></a> <span class='hs-varid'>invnormcdf</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-44"></a>
<a name="line-45"></a> <span class='hs-varid'>inverf</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>inverfc</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-comment'>-</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-46"></a> <span class='hs-varid'>inverfc</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span> <span class='hs-varid'>invnormcdf</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-varop'>/</span><span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span> <span class='hs-varid'>sqrt</span> <span class='hs-num'>2</span>
<a name="line-47"></a>
<a name="line-48"></a><a name="instance%20InvErf%20Double"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>InvErf</span> <span class='hs-conid'>Double</span> <span class='hs-keyword'>where</span>
<a name="line-49"></a> <span class='hs-varid'>invnormcdf</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-varop'>/</span><span class='hs-num'>0</span>
<a name="line-50"></a> <span class='hs-varid'>invnormcdf</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1</span><span class='hs-varop'>/</span><span class='hs-num'>0</span>
<a name="line-51"></a> <span class='hs-varid'>invnormcdf</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span>
<a name="line-52"></a> <span class='hs-comment'>-- Do one iteration with Halley's root finder to get a more accurate result.</span>
<a name="line-53"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>inorm</span> <span class='hs-varid'>p</span>
<a name="line-54"></a> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.5</span> <span class='hs-varop'>*</span> <span class='hs-varid'>erfc</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>x</span> <span class='hs-varop'>/</span> <span class='hs-varid'>sqrt</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-comment'>-</span> <span class='hs-varid'>p</span>
<a name="line-55"></a> <span class='hs-varid'>u</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e</span> <span class='hs-varop'>*</span> <span class='hs-varid'>sqrt</span> <span class='hs-layout'>(</span><span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>pi</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>exp</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>x</span> <span class='hs-varop'>/</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span>
<a name="line-56"></a> <span class='hs-keyword'>in</span> <span class='hs-varid'>x</span> <span class='hs-comment'>-</span> <span class='hs-varid'>u</span> <span class='hs-varop'>/</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-varid'>x</span> <span class='hs-varop'>*</span> <span class='hs-varid'>u</span> <span class='hs-varop'>/</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span>
<a name="line-57"></a>
<a name="line-58"></a><a name="instance%20InvErf%20Float"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>InvErf</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span>
<a name="line-59"></a> <span class='hs-varid'>invnormcdf</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>inorm</span>
<a name="line-60"></a>
<a name="line-61"></a><a name="inorm"></a><span class='hs-comment'>-- Taken from <a href="http://home.online.no/~pjacklam/notes/invnorm/">http://home.online.no/~pjacklam/notes/invnorm/</a></span>
<a name="line-62"></a><span class='hs-comment'>-- Accurate to about 1e-9.</span>
<a name="line-63"></a><span class='hs-definition'>inorm</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Floating</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-64"></a><span class='hs-definition'>inorm</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span>
<a name="line-65"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>a1</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>3.969683028665376e+01</span>
<a name="line-66"></a> <span class='hs-varid'>a2</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>2.209460984245205e+02</span>
<a name="line-67"></a> <span class='hs-varid'>a3</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>2.759285104469687e+02</span>
<a name="line-68"></a> <span class='hs-varid'>a4</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1.383577518672690e+02</span>
<a name="line-69"></a> <span class='hs-varid'>a5</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>3.066479806614716e+01</span>
<a name="line-70"></a> <span class='hs-varid'>a6</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>2.506628277459239e+00</span>
<a name="line-71"></a>
<a name="line-72"></a> <span class='hs-varid'>b1</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>5.447609879822406e+01</span>
<a name="line-73"></a> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1.615858368580409e+02</span>
<a name="line-74"></a> <span class='hs-varid'>b3</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1.556989798598866e+02</span>
<a name="line-75"></a> <span class='hs-varid'>b4</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>6.680131188771972e+01</span>
<a name="line-76"></a> <span class='hs-varid'>b5</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1.328068155288572e+01</span>
<a name="line-77"></a>
<a name="line-78"></a> <span class='hs-varid'>c1</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>7.784894002430293e-03</span>
<a name="line-79"></a> <span class='hs-varid'>c2</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>3.223964580411365e-01</span>
<a name="line-80"></a> <span class='hs-varid'>c3</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>2.400758277161838e+00</span>
<a name="line-81"></a> <span class='hs-varid'>c4</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>2.549732539343734e+00</span>
<a name="line-82"></a> <span class='hs-varid'>c5</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>4.374664141464968e+00</span>
<a name="line-83"></a> <span class='hs-varid'>c6</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>2.938163982698783e+00</span>
<a name="line-84"></a>
<a name="line-85"></a> <span class='hs-varid'>d1</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>7.784695709041462e-03</span>
<a name="line-86"></a> <span class='hs-varid'>d2</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>3.224671290700398e-01</span>
<a name="line-87"></a> <span class='hs-varid'>d3</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>2.445134137142996e+00</span>
<a name="line-88"></a> <span class='hs-varid'>d4</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>3.754408661907416e+00</span>
<a name="line-89"></a>
<a name="line-90"></a> <span class='hs-varid'>pLow</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0.02425</span>
<a name="line-91"></a>
<a name="line-92"></a> <span class='hs-varid'>nan</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span><span class='hs-varop'>/</span><span class='hs-num'>0</span>
<a name="line-93"></a>
<a name="line-94"></a> <span class='hs-keyword'>in</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span>
<a name="line-95"></a> <span class='hs-varid'>nan</span>
<a name="line-96"></a> <span class='hs-keyword'>else</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span>
<a name="line-97"></a> <span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-varop'>/</span><span class='hs-num'>0</span>
<a name="line-98"></a> <span class='hs-keyword'>else</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varop'><</span> <span class='hs-varid'>pLow</span> <span class='hs-keyword'>then</span>
<a name="line-99"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sqrt</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>2</span><span class='hs-varop'>*</span><span class='hs-varid'>log</span><span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-100"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>c1</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>c2</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>c3</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>c4</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>c5</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>c6</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span>
<a name="line-101"></a> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>d1</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>d2</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>d3</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-varid'>d4</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-102"></a> <span class='hs-keyword'>else</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varop'><</span> <span class='hs-num'>1</span> <span class='hs-comment'>-</span> <span class='hs-varid'>pLow</span> <span class='hs-keyword'>then</span>
<a name="line-103"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>p</span> <span class='hs-comment'>-</span> <span class='hs-num'>0.5</span>
<a name="line-104"></a> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>q</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span>
<a name="line-105"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>a1</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>a2</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>a3</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>a4</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>a5</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>a6</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>q</span> <span class='hs-varop'>/</span>
<a name="line-106"></a> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>b1</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>b2</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>b3</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>b4</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-varid'>b5</span><span class='hs-layout'>)</span><span class='hs-varop'>*</span><span class='hs-varid'>r</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-107"></a> <span class='hs-keyword'>else</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varop'><=</span> <span class='hs-num'>1</span> <span class='hs-keyword'>then</span>
<a name="line-108"></a> <span class='hs-comment'>-</span> <span class='hs-varid'>inorm</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-comment'>-</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-109"></a> <span class='hs-keyword'>else</span>
<a name="line-110"></a> <span class='hs-varid'>nan</span>
</pre></body>
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