Minor code beautifications in statistics.py (gh-124866)

Author: rhettinger

Lib/statistics.py

@@ -248,6 +248,7 @@ def count_positive(iterable):
                 found_zero = True
             else:
                 raise StatisticsError('No negative inputs allowed', x)
+
     total = fsum(map(log, count_positive(data)))
 
     if not n:
@@ -710,6 +711,7 @@ def correlation(x, y, /, *, method='linear'):
         start = (n - 1) / -2            # Center rankings around zero
         x = _rank(x, start=start)
         y = _rank(y, start=start)
+
     else:
         xbar = fsum(x) / n
         ybar = fsum(y) / n
@@ -1213,91 +1215,6 @@ def quantiles(data, *, n=4, method='exclusive'):
 
 ## Normal Distribution #####################################################
 
-def _normal_dist_inv_cdf(p, mu, sigma):
-    # There is no closed-form solution to the inverse CDF for the normal
-    # distribution, so we use a rational approximation instead:
-    # Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
-    # Normal Distribution".  Applied Statistics. Blackwell Publishing. 37
-    # (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
-    q = p - 0.5
-
-    if fabs(q) <= 0.425:
-        r = 0.180625 - q * q
-        # Hash sum: 55.88319_28806_14901_4439
-        num = (((((((2.50908_09287_30122_6727e+3 * r +
-                     3.34305_75583_58812_8105e+4) * r +
-                     6.72657_70927_00870_0853e+4) * r +
-                     4.59219_53931_54987_1457e+4) * r +
-                     1.37316_93765_50946_1125e+4) * r +
-                     1.97159_09503_06551_4427e+3) * r +
-                     1.33141_66789_17843_7745e+2) * r +
-                     3.38713_28727_96366_6080e+0) * q
-        den = (((((((5.22649_52788_52854_5610e+3 * r +
-                     2.87290_85735_72194_2674e+4) * r +
-                     3.93078_95800_09271_0610e+4) * r +
-                     2.12137_94301_58659_5867e+4) * r +
-                     5.39419_60214_24751_1077e+3) * r +
-                     6.87187_00749_20579_0830e+2) * r +
-                     4.23133_30701_60091_1252e+1) * r +
-                     1.0)
-        x = num / den
-        return mu + (x * sigma)
-
-    r = p if q <= 0.0 else 1.0 - p
-    r = sqrt(-log(r))
-    if r <= 5.0:
-        r = r - 1.6
-        # Hash sum: 49.33206_50330_16102_89036
-        num = (((((((7.74545_01427_83414_07640e-4 * r +
-                     2.27238_44989_26918_45833e-2) * r +
-                     2.41780_72517_74506_11770e-1) * r +
-                     1.27045_82524_52368_38258e+0) * r +
-                     3.64784_83247_63204_60504e+0) * r +
-                     5.76949_72214_60691_40550e+0) * r +
-                     4.63033_78461_56545_29590e+0) * r +
-                     1.42343_71107_49683_57734e+0)
-        den = (((((((1.05075_00716_44416_84324e-9 * r +
-                     5.47593_80849_95344_94600e-4) * r +
-                     1.51986_66563_61645_71966e-2) * r +
-                     1.48103_97642_74800_74590e-1) * r +
-                     6.89767_33498_51000_04550e-1) * r +
-                     1.67638_48301_83803_84940e+0) * r +
-                     2.05319_16266_37758_82187e+0) * r +
-                     1.0)
-    else:
-        r = r - 5.0
-        # Hash sum: 47.52583_31754_92896_71629
-        num = (((((((2.01033_43992_92288_13265e-7 * r +
-                     2.71155_55687_43487_57815e-5) * r +
-                     1.24266_09473_88078_43860e-3) * r +
-                     2.65321_89526_57612_30930e-2) * r +
-                     2.96560_57182_85048_91230e-1) * r +
-                     1.78482_65399_17291_33580e+0) * r +
-                     5.46378_49111_64114_36990e+0) * r +
-                     6.65790_46435_01103_77720e+0)
-        den = (((((((2.04426_31033_89939_78564e-15 * r +
-                     1.42151_17583_16445_88870e-7) * r +
-                     1.84631_83175_10054_68180e-5) * r +
-                     7.86869_13114_56132_59100e-4) * r +
-                     1.48753_61290_85061_48525e-2) * r +
-                     1.36929_88092_27358_05310e-1) * r +
-                     5.99832_20655_58879_37690e-1) * r +
-                     1.0)
-
-    x = num / den
-    if q < 0.0:
-        x = -x
-
-    return mu + (x * sigma)
-
-
-# If available, use C implementation
-try:
-    from _statistics import _normal_dist_inv_cdf
-except ImportError:
-    pass
-
-
 class NormalDist:
     "Normal distribution of a random variable"
     # https://en.wikipedia.org/wiki/Normal_distribution
@@ -1561,11 +1478,13 @@ def _sum(data):
     types_add = types.add
     partials = {}
     partials_get = partials.get
+
     for typ, values in groupby(data, type):
         types_add(typ)
         for n, d in map(_exact_ratio, values):
             count += 1
             partials[d] = partials_get(d, 0) + n
+
     if None in partials:
         # The sum will be a NAN or INF. We can ignore all the finite
         # partials, and just look at this special one.
@@ -1574,6 +1493,7 @@ def _sum(data):
     else:
         # Sum all the partial sums using builtin sum.
         total = sum(Fraction(n, d) for d, n in partials.items())
+
     T = reduce(_coerce, types, int)  # or raise TypeError
     return (T, total, count)
 
@@ -1596,6 +1516,7 @@ def _ss(data, c=None):
     types_add = types.add
     sx_partials = defaultdict(int)
     sxx_partials = defaultdict(int)
+
     for typ, values in groupby(data, type):
         types_add(typ)
         for n, d in map(_exact_ratio, values):
@@ -1605,11 +1526,13 @@ def _ss(data, c=None):
 
     if not count:
         ssd = c = Fraction(0)
+
     elif None in sx_partials:
         # The sum will be a NAN or INF. We can ignore all the finite
         # partials, and just look at this special one.
         ssd = c = sx_partials[None]
         assert not _isfinite(ssd)
+
     else:
         sx = sum(Fraction(n, d) for d, n in sx_partials.items())
         sxx = sum(Fraction(n, d*d) for d, n in sxx_partials.items())
@@ -1693,8 +1616,10 @@ def _convert(value, T):
         # This covers the cases where T is Fraction, or where value is
         # a NAN or INF (Decimal or float).
         return value
+
     if issubclass(T, int) and value.denominator != 1:
         T = float
+
     try:
         # FIXME: what do we do if this overflows?
         return T(value)
@@ -1857,3 +1782,88 @@ def _sqrtprod(x: float, y: float) -> float:
     # https://www.wolframalpha.com/input/?i=Maclaurin+series+sqrt%28h**2+%2B+x%29+at+x%3D0
     d = sumprod((x, h), (y, -h))
     return h + d / (2.0 * h)
+
+
+def _normal_dist_inv_cdf(p, mu, sigma):
+    # There is no closed-form solution to the inverse CDF for the normal
+    # distribution, so we use a rational approximation instead:
+    # Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
+    # Normal Distribution".  Applied Statistics. Blackwell Publishing. 37
+    # (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
+    q = p - 0.5
+
+    if fabs(q) <= 0.425:
+        r = 0.180625 - q * q
+        # Hash sum: 55.88319_28806_14901_4439
+        num = (((((((2.50908_09287_30122_6727e+3 * r +
+                     3.34305_75583_58812_8105e+4) * r +
+                     6.72657_70927_00870_0853e+4) * r +
+                     4.59219_53931_54987_1457e+4) * r +
+                     1.37316_93765_50946_1125e+4) * r +
+                     1.97159_09503_06551_4427e+3) * r +
+                     1.33141_66789_17843_7745e+2) * r +
+                     3.38713_28727_96366_6080e+0) * q
+        den = (((((((5.22649_52788_52854_5610e+3 * r +
+                     2.87290_85735_72194_2674e+4) * r +
+                     3.93078_95800_09271_0610e+4) * r +
+                     2.12137_94301_58659_5867e+4) * r +
+                     5.39419_60214_24751_1077e+3) * r +
+                     6.87187_00749_20579_0830e+2) * r +
+                     4.23133_30701_60091_1252e+1) * r +
+                     1.0)
+        x = num / den
+        return mu + (x * sigma)
+
+    r = p if q <= 0.0 else 1.0 - p
+    r = sqrt(-log(r))
+    if r <= 5.0:
+        r = r - 1.6
+        # Hash sum: 49.33206_50330_16102_89036
+        num = (((((((7.74545_01427_83414_07640e-4 * r +
+                     2.27238_44989_26918_45833e-2) * r +
+                     2.41780_72517_74506_11770e-1) * r +
+                     1.27045_82524_52368_38258e+0) * r +
+                     3.64784_83247_63204_60504e+0) * r +
+                     5.76949_72214_60691_40550e+0) * r +
+                     4.63033_78461_56545_29590e+0) * r +
+                     1.42343_71107_49683_57734e+0)
+        den = (((((((1.05075_00716_44416_84324e-9 * r +
+                     5.47593_80849_95344_94600e-4) * r +
+                     1.51986_66563_61645_71966e-2) * r +
+                     1.48103_97642_74800_74590e-1) * r +
+                     6.89767_33498_51000_04550e-1) * r +
+                     1.67638_48301_83803_84940e+0) * r +
+                     2.05319_16266_37758_82187e+0) * r +
+                     1.0)
+    else:
+        r = r - 5.0
+        # Hash sum: 47.52583_31754_92896_71629
+        num = (((((((2.01033_43992_92288_13265e-7 * r +
+                     2.71155_55687_43487_57815e-5) * r +
+                     1.24266_09473_88078_43860e-3) * r +
+                     2.65321_89526_57612_30930e-2) * r +
+                     2.96560_57182_85048_91230e-1) * r +
+                     1.78482_65399_17291_33580e+0) * r +
+                     5.46378_49111_64114_36990e+0) * r +
+                     6.65790_46435_01103_77720e+0)
+        den = (((((((2.04426_31033_89939_78564e-15 * r +
+                     1.42151_17583_16445_88870e-7) * r +
+                     1.84631_83175_10054_68180e-5) * r +
+                     7.86869_13114_56132_59100e-4) * r +
+                     1.48753_61290_85061_48525e-2) * r +
+                     1.36929_88092_27358_05310e-1) * r +
+                     5.99832_20655_58879_37690e-1) * r +
+                     1.0)
+
+    x = num / den
+    if q < 0.0:
+        x = -x
+
+    return mu + (x * sigma)
+
+
+# If available, use C implementation
+try:
+    from _statistics import _normal_dist_inv_cdf
+except ImportError:
+    pass