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