September Morn Update

Task/Gamma-function/Python/gamma-function-2.py

@@ -0,0 +1,82 @@
+'''Gamma function'''
+
+from functools import reduce
+
+
+# gamma_ :: [Float] -> Float -> Float
+def gamma_(tbl):
+    '''Gamma function.'''
+    def go(x):
+        y = float(x) - 1.0
+        return 1.0 / reduce(
+            lambda a, x: a * y + x,
+            tbl[-2::-1],
+            tbl[-1]
+        )
+    return lambda x: go(x)
+
+
+# TBL :: [Float]
+TBL = [
+    1.00000000000000000000, 0.57721566490153286061,
+    -0.65587807152025388108, -0.04200263503409523553,
+    0.16653861138229148950, -0.04219773455554433675,
+    -0.00962197152787697356, 0.00721894324666309954,
+    -0.00116516759185906511, -0.00021524167411495097,
+    0.00012805028238811619, -0.00002013485478078824,
+    -0.00000125049348214267, 0.00000113302723198170,
+    -0.00000020563384169776, 0.00000000611609510448,
+    0.00000000500200764447, -0.00000000118127457049,
+    0.00000000010434267117, 0.00000000000778226344,
+    -0.00000000000369680562, 0.00000000000051003703,
+    -0.00000000000002058326, -0.00000000000000534812,
+    0.00000000000000122678, -0.00000000000000011813,
+    0.00000000000000000119, 0.00000000000000000141,
+    -0.00000000000000000023, 0.00000000000000000002
+]
+
+
+# TEST ----------------------------------------------------
+# main :: IO()
+def main():
+    '''Gamma function over a range of values.'''
+
+    gamma = gamma_(TBL)
+    print(
+        fTable(' i -> gamma(i/3):\n')(repr)(lambda x: "%0.7e" % x)(
+            lambda x: gamma(x / 3.0)
+        )(enumFromTo(1)(10))
+    )
+
+
+# GENERIC -------------------------------------------------
+
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+
+
+# FORMATTING -------------------------------------------------
+
+# fTable :: String -> (a -> String) ->
+#                     (b -> String) -> (a -> b) -> [a] -> String
+def fTable(s):
+    '''Heading -> x display function -> fx display function ->
+                     f -> xs -> tabular string.
+    '''
+    def go(xShow, fxShow, f, xs):
+        ys = [xShow(x) for x in xs]
+        w = max(map(len, ys))
+        return s + '\n' + '\n'.join(map(
+            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
+            xs, ys
+        ))
+    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
+        xShow, fxShow, f, xs
+    )
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()