import __builtin__
import math
import random
+import time
def median(x, use_float=True):
# there exist better algorithms...
else:
return x
+add_to_range = lambda x, (low, high): (min(low, x), max(high, x))
+
def nth(i, n=0):
i = iter(i)
for _ in xrange(n):
return 1
return int(math.log1p(-random.random()) / math.log1p(-p)) + 1
-def add_dicts(*dicts):
- res = {}
- for d in dicts:
- for k, v in d.iteritems():
- res[k] = res.get(k, 0) + v
- return dict((k, v) for k, v in res.iteritems() if v)
+def add_dicts_ext(add_func=lambda a, b: a+b, zero=0):
+ def add_dicts(*dicts):
+ res = {}
+ for d in dicts:
+ for k, v in d.iteritems():
+ res[k] = add_func(res.get(k, zero), v)
+ return dict((k, v) for k, v in res.iteritems() if v != zero)
+ return add_dicts
+add_dicts = add_dicts_ext()
+
+mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())
def format(x):
prefixes = 'kMGTPEZY'
s = '' if count == 0 else prefixes[count - 1]
return '%i' % (x,) + s
+def format_dt(dt):
+ for value, name in [(365.2425*60*60*24, 'years'), (60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]:
+ if dt > value:
+ break
+ return '%.01f %s' % (dt/value, name)
+
perfect_round = lambda x: int(x + random.random())
def erf(x):
def ierf(z):
return find_root(lambda x: (erf(x) - z)/(2*math.e**(-x**2)/math.sqrt(math.pi)), 0)
-try:
- from scipy import special
-except ImportError:
- print 'Install SciPy for more accurate confidence intervals!'
- def binomial_conf_interval(x, n, conf=0.95):
- assert 0 <= x <= n and 0 <= conf < 1
- if n == 0:
- left = random.random()*(1 - conf)
- # approximate - Wilson score interval
- z = math.sqrt(2)*ierf(conf)
- p = x/n
- topa = p + z**2/2/n
- topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
- bottom = 1 + z**2/n
- return (topa - topb)/bottom, (topa + topb)/bottom
-else:
- def binomial_conf_interval(x, n, conf=0.95):
- assert 0 <= x <= n and 0 <= conf < 1
- if n == 0:
- left = random.random()*(1 - conf)
- return left, left + conf
- b = special.beta(x+1, n-x+1)
- def f(left_a):
- left, right = max(1e-8, special.betaincinv(x+1, n-x+1, left_a)), min(1-1e-8, special.betaincinv(x+1, n-x+1, left_a + conf))
- top = right**(x+1) * (1-right)**(n-x+1) * left*(1-left) - left**(x+1) * (1-left)**(n-x+1) * right * (1-right)
- bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
- return top/bottom/b
- left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
- return special.betaincinv(x+1, n-x+1, left_a), special.betaincinv(x+1, n-x+1, left_a + conf)
-
-def binomial_conf_center_radius(x, n, conf=0.95):
+def binomial_conf_interval(x, n, conf=0.95):
assert 0 <= x <= n and 0 <= conf < 1
- left, right = binomial_conf_interval(x, n, conf)
if n == 0:
- return (left+right)/2, (right-left)/2
+ left = random.random()*(1 - conf)
+ return left, left + conf
+ # approximate - Wilson score interval
+ z = math.sqrt(2)*ierf(conf)
p = x/n
- return p, max(p - left, right - p)
+ topa = p + z**2/2/n
+ topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
+ bottom = 1 + z**2/n
+ return [clip(x, (0, 1)) for x in add_to_range(x/n, [(topa - topb)/bottom, (topa + topb)/bottom])]
minmax = lambda x: (min(x), max(x))
if n == 0:
return '???'
left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
- return '~%.1f%% (%i-%i%%)' % (100*f(x/n), int(100*left), 100-int(100-100*right))
+ return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
def reversed(x):
try:
if n < 0:
raise TypeError('n must be a natural')
if alphabet is None:
- s = '%x' % (n,)
+ s = ('%x' % (n,)).lstrip('0')
if len(s) % 2:
s = '0' + s
return s.decode('hex')
assert not s.startswith(alphabet[0])
return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
-if __name__ == '__main__':
- import random
- a = 1
- while True:
- print a, format(a) + 'H/s'
- a = a * random.randrange(2, 5)
+class RateMonitor(object):
+ def __init__(self, max_lookback_time):
+ self.max_lookback_time = max_lookback_time
+
+ self.datums = []
+ self.first_timestamp = None
+
+ def _prune(self):
+ start_time = time.time() - self.max_lookback_time
+ for i, (ts, datum) in enumerate(self.datums):
+ if ts > start_time:
+ self.datums[:] = self.datums[i:]
+ return
+
+ def get_datums_in_last(self, dt=None):
+ if dt is None:
+ dt = self.max_lookback_time
+ assert dt <= self.max_lookback_time
+ self._prune()
+ now = time.time()
+ return [datum for ts, datum in self.datums if ts > now - dt], min(dt, now - self.first_timestamp) if self.first_timestamp is not None else 0
+
+ def add_datum(self, datum):
+ self._prune()
+ t = time.time()
+ if self.first_timestamp is None:
+ self.first_timestamp = t
+ else:
+ self.datums.append((t, datum))