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):
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, bounds=(None, None)):
+def find_root(y_over_dy, start, steps=10, bounds=(None, None)):
guess = start
for i in xrange(steps):
- guess = guess - f(guess)/fp(guess)
+ 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)
-
-try:
- from scipy import special
-except ImportError:
- print 'Install SciPy for more accurate confidence intervals!'
- def binomial_conf_interval(x, n, conf=0.95):
- if n == 0:
- return (1-conf)/2, 1-(1-conf)/2
- # 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):
- if n == 0:
- left = random.random()*(1 - conf)
- return left, left + conf
- pdf = lambda p: p**x * (1-p)**(n-x) /special.beta(x+1, n-x+1)
- dpdf = lambda p: ((x*p**(x-1) * (1-p)**(n-x) - p**x * (n-x)*(1-p)**(n-x-1))/special.beta(x+1, n-x+1) \
- if p != 0 else {0: -n, 1: 1}.get(x, 0)) \
- if p != 1 else {n-1: -1, n: n}.get(x, 0)
- cdf = lambda p: special.betainc(x+1, n-x+1, p)
- dcdf = pdf
- invcdf = lambda i: special.betaincinv(x+1, n-x+1, i)
- dinvcdf = lambda i: 1/pdf(invcdf(i))
- left_to_right = lambda left: invcdf(cdf(left) + conf)
- dleft_to_right = lambda left: dinvcdf(cdf(left) + conf)*dcdf(left)
- f = lambda left: pdf(left_to_right(left)) - pdf(left)
- df = lambda left: dpdf(left_to_right(left))*dleft_to_right(left) - dpdf(left)
- left = find_root(f, df, invcdf((1-conf)/2), 8, (0, invcdf(1-conf)))
- return left, left_to_right(left)
-
-def binomial_conf_center_radius(x, n, conf=0.95):
- left, right = binomial_conf_interval(x, n, conf)
+ return find_root(lambda x: (erf(x) - z)/(2*math.e**(-x**2)/math.sqrt(math.pi)), 0)
+
+def binomial_conf_interval(x, n, conf=0.95):
+ assert 0 <= x <= n and 0 <= conf < 1
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))
+
+def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
+ if n == 0:
+ 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()
-if __name__ == '__main__':
- import random
- a = 1
- while True:
- print a, format(a) + 'H/s'
- a = a * random.randrange(2, 5)
+def natural_to_string(n, alphabet=None):
+ if n < 0:
+ raise TypeError('n must be a natural')
+ if alphabet is None:
+ s = ('%x' % (n,)).lstrip('0')
+ 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()
+ if self.first_timestamp is None:
+ self.first_timestamp = t
+ else:
+ self.datums.append((t, datum))
git://git.novaco.in / p2pool.git / blobdiff