from itertools import groupby, repeat
from bisect import bisect_left, bisect_right
from math import hypot, sqrt, fabs, exp, erf, tau, log, fsum
+from functools import reduce
from operator import mul
from collections import Counter, namedtuple, defaultdict
allowed.
"""
count = 0
+ types = set()
+ types_add = types.add
partials = {}
partials_get = partials.get
- T = int
for typ, values in groupby(data, type):
- T = _coerce(T, typ) # or raise TypeError
+ types_add(typ)
for n, d in map(_exact_ratio, values):
count += 1
partials[d] = partials_get(d, 0) + n
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)
T, total, count = _sum((d := x - c) * d for x in data)
return (T, total, count)
count = 0
+ types = set()
+ types_add = types.add
sx_partials = defaultdict(int)
sxx_partials = defaultdict(int)
- T = int
for typ, values in groupby(data, type):
- T = _coerce(T, typ) # or raise TypeError
+ types_add(typ)
for n, d in map(_exact_ratio, values):
count += 1
sx_partials[d] += n
# This formula has poor numeric properties for floats,
# but with fractions it is exact.
total = (count * sxx - sx * sx) / count
+ T = reduce(_coerce, types, int) # or raise TypeError
return (T, total, count)