import __builtin__
import math
import random
+import time
def median(x, use_float=True):
# there exist better algorithms...
res[k] = res.get(k, 0) + v
return dict((k, v) for k, v in res.iteritems() if v)
+mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())
+
def format(x):
prefixes = 'kMGTPEZY'
count = 0
s = '' if count == 0 else prefixes[count - 1]
return '%i' % (x,) + s
+def format_dt(dt):
+ for value, name in [(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):
y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
return sign*y # erf(-x) = -erf(x)
-def find_root(f, fp, start, steps=10):
- guess = 0
+def find_root(y_over_dy, start, steps=10, bounds=(None, None)):
+ guess = start
for i in xrange(steps):
- d = fp(guess)
- guess = guess - f(guess)/d
+ prev, guess = guess, guess - y_over_dy(guess)
+ if bounds[0] is not None and guess < bounds[0]: guess = bounds[0]
+ if bounds[1] is not None and guess > bounds[1]: guess = bounds[1]
+ if guess == prev:
+ break
return guess
def ierf(z):
- return find_root(lambda x: erf(x) - z, lambda guess: 2*math.e**(-guess**2)/math.sqrt(math.pi), 0)
+ 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:
- return (1-conf)/2, 1-(1-conf)/2
+ left = random.random()*(1 - conf)
+ return left, left + conf
# approximate - Wilson score interval
z = math.sqrt(2)*ierf(conf)
p = x/n
bottom = 1 + z**2/n
return (topa - topb)/bottom, (topa + topb)/bottom
else:
- def binomial_conf_interval(x, n, conf=0.95, steps=11):
- a = 1 - conf
+ def binomial_conf_interval(x, n, conf=0.95):
+ assert 0 <= x <= n and 0 <= conf < 1
if n == 0:
- left = random.random()*a
+ left = random.random()*(1 - conf)
return left, left + conf
- res = None
- for left_a_i in xrange(steps):
- left_a = a * left_a_i / (steps - 1)
- this_left, this_right = special.betaincinv(x+1, n-x+1, left_a), special.betaincinv(x+1, n-x+1, 1 - (a - left_a))
- if res is None or this_right - this_left < res[1] - res[0]:
- res = this_left, this_right
- return res
-
-def binomial_conf_center_radius(x, n, conf=0.95):
- left, right = binomial_conf_interval(x, n, conf)
+ bl = float(special.betaln(x+1, n-x+1))
+ def f(left_a):
+ left, right = max(1e-8, float(special.betaincinv(x+1, n-x+1, left_a))), min(1-1e-8, float(special.betaincinv(x+1, n-x+1, left_a + conf)))
+ top = math.exp(math.log(right)*(x+1) + math.log(1-right)*(n-x+1) + math.log(left) + math.log(1-left) - bl) - math.exp(math.log(left)*(x+1) + math.log(1-left)*(n-x+1) + math.log(right) + math.log(1-right) - bl)
+ bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
+ return top/bottom
+ left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
+ return float(special.betaincinv(x+1, n-x+1, left_a)), float(special.betaincinv(x+1, n-x+1, left_a + conf))
+
+minmax = lambda x: (min(x), max(x))
+
+def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
if n == 0:
- return (left+right)/2, (right-left)/2
- p = x/n
- return p, max(p - left, right - p)
+ return '???'
+ left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
+ return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
def reversed(x):
try:
target -= weight
raise AssertionError()
+def natural_to_string(n, alphabet=None):
+ if n < 0:
+ raise TypeError('n must be a natural')
+ if alphabet is None:
+ s = '%x' % (n,)
+ if len(s) % 2:
+ s = '0' + s
+ return s.decode('hex')
+ else:
+ assert len(set(alphabet)) == len(alphabet)
+ res = []
+ while n:
+ n, x = divmod(n, len(alphabet))
+ res.append(alphabet[x])
+ res.reverse()
+ return ''.join(res)
+
+def string_to_natural(s, alphabet=None):
+ if alphabet is None:
+ assert not s.startswith('\x00')
+ return int(s.encode('hex'), 16) if s else 0
+ else:
+ assert len(set(alphabet)) == len(alphabet)
+ assert not s.startswith(alphabet[0])
+ return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
+
+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()
+ self.datums.append((t, datum))
+ if self.first_timestamp is None:
+ self.first_timestamp = t
+
if __name__ == '__main__':
import random
a = 1
git://git.novaco.in / p2pool.git / blobdiff