254 lines
6.4 KiB
Python
254 lines
6.4 KiB
Python
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from .ctx_base import StandardBaseContext
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import math
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import cmath
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from . import math2
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from . import function_docs
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from .libmp import mpf_bernoulli, to_float, int_types
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from . import libmp
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class FPContext(StandardBaseContext):
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"""
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Context for fast low-precision arithmetic (53-bit precision, giving at most
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about 15-digit accuracy), using Python's builtin float and complex.
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"""
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def __init__(ctx):
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StandardBaseContext.__init__(ctx)
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# Override SpecialFunctions implementation
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ctx.loggamma = math2.loggamma
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ctx._bernoulli_cache = {}
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ctx.pretty = False
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ctx._init_aliases()
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_mpq = lambda cls, x: float(x[0])/x[1]
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NoConvergence = libmp.NoConvergence
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def _get_prec(ctx): return 53
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def _set_prec(ctx, p): return
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def _get_dps(ctx): return 15
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def _set_dps(ctx, p): return
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_fixed_precision = True
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prec = property(_get_prec, _set_prec)
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dps = property(_get_dps, _set_dps)
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zero = 0.0
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one = 1.0
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eps = math2.EPS
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inf = math2.INF
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ninf = math2.NINF
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nan = math2.NAN
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j = 1j
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# Called by SpecialFunctions.__init__()
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@classmethod
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def _wrap_specfun(cls, name, f, wrap):
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if wrap:
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def f_wrapped(ctx, *args, **kwargs):
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convert = ctx.convert
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args = [convert(a) for a in args]
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return f(ctx, *args, **kwargs)
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else:
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f_wrapped = f
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f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
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setattr(cls, name, f_wrapped)
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def bernoulli(ctx, n):
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cache = ctx._bernoulli_cache
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if n in cache:
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return cache[n]
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cache[n] = to_float(mpf_bernoulli(n, 53, 'n'), strict=True)
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return cache[n]
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pi = math2.pi
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e = math2.e
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euler = math2.euler
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sqrt2 = 1.4142135623730950488
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sqrt5 = 2.2360679774997896964
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phi = 1.6180339887498948482
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ln2 = 0.69314718055994530942
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ln10 = 2.302585092994045684
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euler = 0.57721566490153286061
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catalan = 0.91596559417721901505
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khinchin = 2.6854520010653064453
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apery = 1.2020569031595942854
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glaisher = 1.2824271291006226369
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absmin = absmax = abs
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def is_special(ctx, x):
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return x - x != 0.0
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def isnan(ctx, x):
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return x != x
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def isinf(ctx, x):
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return abs(x) == math2.INF
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def isnormal(ctx, x):
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if x:
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return x - x == 0.0
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return False
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def isnpint(ctx, x):
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if type(x) is complex:
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if x.imag:
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return False
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x = x.real
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return x <= 0.0 and round(x) == x
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mpf = float
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mpc = complex
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def convert(ctx, x):
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try:
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return float(x)
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except:
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return complex(x)
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power = staticmethod(math2.pow)
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sqrt = staticmethod(math2.sqrt)
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exp = staticmethod(math2.exp)
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ln = log = staticmethod(math2.log)
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cos = staticmethod(math2.cos)
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sin = staticmethod(math2.sin)
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tan = staticmethod(math2.tan)
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cos_sin = staticmethod(math2.cos_sin)
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acos = staticmethod(math2.acos)
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asin = staticmethod(math2.asin)
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atan = staticmethod(math2.atan)
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cosh = staticmethod(math2.cosh)
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sinh = staticmethod(math2.sinh)
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tanh = staticmethod(math2.tanh)
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gamma = staticmethod(math2.gamma)
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rgamma = staticmethod(math2.rgamma)
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fac = factorial = staticmethod(math2.factorial)
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floor = staticmethod(math2.floor)
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ceil = staticmethod(math2.ceil)
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cospi = staticmethod(math2.cospi)
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sinpi = staticmethod(math2.sinpi)
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cbrt = staticmethod(math2.cbrt)
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_nthroot = staticmethod(math2.nthroot)
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_ei = staticmethod(math2.ei)
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_e1 = staticmethod(math2.e1)
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_zeta = _zeta_int = staticmethod(math2.zeta)
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# XXX: math2
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def arg(ctx, z):
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z = complex(z)
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return math.atan2(z.imag, z.real)
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def expj(ctx, x):
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return ctx.exp(ctx.j*x)
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def expjpi(ctx, x):
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return ctx.exp(ctx.j*ctx.pi*x)
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ldexp = math.ldexp
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frexp = math.frexp
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def mag(ctx, z):
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if z:
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return ctx.frexp(abs(z))[1]
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return ctx.ninf
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def isint(ctx, z):
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if hasattr(z, "imag"): # float/int don't have .real/.imag in py2.5
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if z.imag:
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return False
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z = z.real
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try:
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return z == int(z)
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except:
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return False
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def nint_distance(ctx, z):
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if hasattr(z, "imag"): # float/int don't have .real/.imag in py2.5
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n = round(z.real)
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else:
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n = round(z)
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if n == z:
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return n, ctx.ninf
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return n, ctx.mag(abs(z-n))
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def _convert_param(ctx, z):
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if type(z) is tuple:
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p, q = z
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return ctx.mpf(p) / q, 'R'
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if hasattr(z, "imag"): # float/int don't have .real/.imag in py2.5
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intz = int(z.real)
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else:
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intz = int(z)
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if z == intz:
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return intz, 'Z'
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return z, 'R'
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def _is_real_type(ctx, z):
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return isinstance(z, float) or isinstance(z, int_types)
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def _is_complex_type(ctx, z):
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return isinstance(z, complex)
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def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
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coeffs = list(coeffs)
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num = range(p)
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den = range(p,p+q)
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tol = ctx.eps
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s = t = 1.0
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k = 0
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while 1:
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for i in num: t *= (coeffs[i]+k)
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for i in den: t /= (coeffs[i]+k)
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k += 1; t /= k; t *= z; s += t
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if abs(t) < tol:
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return s
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if k > maxterms:
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raise ctx.NoConvergence
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def atan2(ctx, x, y):
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return math.atan2(x, y)
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def psi(ctx, m, z):
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m = int(m)
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if m == 0:
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return ctx.digamma(z)
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return (-1)**(m+1) * ctx.fac(m) * ctx.zeta(m+1, z)
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digamma = staticmethod(math2.digamma)
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def harmonic(ctx, x):
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x = ctx.convert(x)
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if x == 0 or x == 1:
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return x
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return ctx.digamma(x+1) + ctx.euler
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nstr = str
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def to_fixed(ctx, x, prec):
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return int(math.ldexp(x, prec))
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def rand(ctx):
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import random
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return random.random()
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_erf = staticmethod(math2.erf)
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_erfc = staticmethod(math2.erfc)
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def sum_accurately(ctx, terms, check_step=1):
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s = ctx.zero
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k = 0
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for term in terms():
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s += term
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if (not k % check_step) and term:
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if abs(term) <= 1e-18*abs(s):
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break
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k += 1
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return s
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