X-Git-Url: https://git.novaco.in/?a=blobdiff_plain;f=p2pool%2Futil%2Fmath.py;h=04ed3ffa2ed2d2f0cf78c5292a68f5f3be702bc9;hb=62a65ed608004510a8207ba16a2acacfd3aaef24;hp=9268e574f100ed01dda7364990d20d582526ea18;hpb=5e903ce09ae9fdf7fbf012a703feaa9141e8b011;p=p2pool.git diff --git a/p2pool/util/math.py b/p2pool/util/math.py index 9268e57..04ed3ff 100644 --- a/p2pool/util/math.py +++ b/p2pool/util/math.py @@ -3,6 +3,7 @@ from __future__ import absolute_import, division import __builtin__ import math import random +import time def median(x, use_float=True): # there exist better algorithms... @@ -44,6 +45,8 @@ def clip(x, (low, high)): 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): @@ -57,12 +60,17 @@ def geometric(p): 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' @@ -74,7 +82,7 @@ def format(x): return '%i' % (x,) + s def format_dt(dt): - for value, name in [(60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]: + 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) @@ -114,43 +122,18 @@ def find_root(y_over_dy, start, steps=10, bounds=(None, None)): 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 - 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)) - -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)) @@ -158,7 +141,7 @@ 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), 100*left-1/2, 100*right+1/2) + return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right)) def reversed(x): try: @@ -196,7 +179,7 @@ def natural_to_string(n, alphabet=None): 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') @@ -218,9 +201,32 @@ def string_to_natural(s, alphabet=None): 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))