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# -*- coding: utf-8 -*- 

 

u'''Single-instance floats and strings, C{intern}'ed across modules. 

''' 

from math import pi as PI 

 

__all__ = ('EPS', 'EPS_2', 'EPS1', 'EPS1_2', 

'INF', 'MANTIS', 'MAX', 'MIN', 'NAN', 'NEG0', 

'NN', 

'PI', 'PI2', 'PI4', 'PI_2', 'PI_4', 

'R_M', 

'joined', 'joined_') # import by .lazily 

__version__ = '20.10.11' 

 

NN = '' # no name, empty str, Nomen Nescio <https://Wiktionary.org/wiki/N.N.> 

 

# __DUNDER__ would get mangled in classes 

_0_ = '0' # PYCHOK expected 

_1_ = '1' # PYCHOK expected 

_2_ = '2' # PYCHOK expected 

_3_ = '3' # PYCHOK expected 

_4_ = '4' # PYCHOK expected 

_areaOf_ = 'areaOf' # PYCHOK expected 

_ambiguous_ = 'ambiguous' # PYCHOK expected 

_AT_ = '@' # PYCHOK expected 

_attribute_ = 'attribute' # PYCHOK expected 

_azimuth_ = 'azimuth' # PYCHOK expected 

_band_ = 'band' # PYCHOK expected 

_bearing_ = 'bearing' # PYCHOK expected 

_C_ = 'C' # PYCHOK expected 

_Cartesian_ = 'Cartesian' # PYCHOK expected 

_coincident_ = 'coincident' # PYCHOK expected 

_colinear_ = 'colinear' # PYCHOK expected 

_COLON_ = ':' # PYCHOK expected 

_COMMA_ = ',' # PYCHOK expected 

_convergence_ = 'convergence' # PYCHOK expected 

_cubic_ = 'cubic' # PYCHOK expected 

_CURLY_ = '{%s}' # PYCHOK expected 

_datum_ = 'datum' # PYCHOK expected 

_decode3_ = 'decode3' # PYCHOK expected 

_deg_ = 'deg' # PYCHOK expected 

_degrees_ = 'degrees' # PYCHOK expected 

_degrees2_ = 'degrees2' # PYCHOK SQUARED 

_distance_ = 'distance' # PYCHOK expected 

_distanceTo_ = 'distanceTo' # PYCHOK expected 

_doesn_t_exist_ = "doesn't exist" # PYCHOK expected 

_DOT_ = '.' # PYCHOK expected 

_E_ = 'E' # PYCHOK expected 

_easting_ = 'easting' # PYCHOK expected 

_ellipsoid_ = 'ellipsoid' # PYCHOK expected 

_ellipsoidal_ = 'ellipsoidal' # PYCHOK expected 

_encode_ = 'encode' # PYCHOK expected 

_end_ = 'end' # PYCHOK expected 

_epoch_ = 'epoch' # PYCHOK expected 

_EQUAL_ = '=' # PYCHOK expected 

_exceed_PI_radians_ = 'exceed PI radians' # PYCHOK expected 

_feet_ = 'feet' # PYCHOK expected 

_fraction_ = 'fraction' # PYCHOK expected 

_gamma_ = 'gamma' # PYCHOK expected 

_h_ = 'h' # PYCHOK expected 

_H_ = 'H' # PYCHOK expected 

_height_ = 'height' # PYCHOK expected 

_hemipole_ = 'hemipole' # PYCHOK expected 

_in_ = 'in' # PYCHOK expected 

_intersection_ = 'intersection' # PYCHOK expected 

_inside_ = 'inside' # PYCHOK expected 

_invalid_ = 'invalid' # PYCHOK expected 

_isclockwise_ = 'isclockwise' # PYCHOK expected 

_ispolar_ = 'ispolar' # PYCHOK expected 

_k0_ = 'k0' # PYCHOK expected 

_knots_ = 'knots' # PYCHOK expected 

_lam_ = 'lam' # PYCHOK expected 

_lat_ = 'lat' # PYCHOK expected 

_lat0_ = 'lat0' # PYCHOK expected 

_lat1_ = 'lat1' # PYCHOK expected 

_lat2_ = 'lat2' # PYCHOK expected 

_LatLon_ = 'LatLon' # PYCHOK expected 

_len_ = 'len' # PYCHOK expected 

_linear_ = 'linear' # PYCHOK expected 

_lon_ = 'lon' # PYCHOK expected 

_lon0_ = 'lon0' # PYCHOK expected 

_m_ = 'm' # PYCHOK expected 

_M_ = 'M' # PYCHOK expected 

_meanOf_ = 'meanOf' # PYCHOK expected 

_meter_ = 'meter' # PYCHOK expected 

_MGRS_ = 'MGRS' # PYCHOK expected 

_module_ = 'module' # PYCHOK expected 

_n_ = 'n' # PYCHOK expected 

_N_ = 'N' # PYCHOK expected 

_n_a_ = 'n/a' # PYCHOK expected 

_name_ = 'name' # PYCHOK expected 

_near_concentric_ = 'near-concentric' # PYCHOK expected 

_nearestOn2_ = 'nearestOn2' # PYCHOK expected 

_negative_ = 'negative' # PYCHOK expected 

_no_ = 'no' # PYCHOK expected 

_no_intersection_ = 'no intersection' # PYCHOK expected 

_no_convergence_ = 'no convergence' # PYCHOK expected 

_no_convergence_fmt_ = 'no convergence (%g)' # PYCHOK expected 

_no_conversion_ = 'no conversion' # PYCHOK expected 

_no_overlap_ = 'no overlap' # PYCHOK expected 

_northing_ = 'northing' # PYCHOK expected 

_NorthPole_ = 'NorthPole' # PYCHOK expected 

_not_convex_ = 'not convex' # PYCHOK expected 

_not_enabled_ = 'not enabled' # PYCHOK expected 

_not_scalar_ = 'not scalar' # PYCHOK expected 

_number_ = 'number' # PYCHOK expected 

_on_ = 'on' # PYCHOK expected 

_or_ = 'or' # PYCHOK expected 

_other_ = 'other' # PYCHOK expected 

_outside_ = 'outside' # PYCHOK expected 

_PARENTH_ = '(%s)' # PYCHOK expected 

_PERCENT_ = '%' # PYCHOK expected 

_perimeterOf_ = 'perimeterOf' # PYCHOK expected 

_phi_ = 'phi' # PYCHOK expected 

_PLUS_ = '+' # PYCHOK expected 

_point_ = 'point' # PYCHOK expected 

_points_ = 'points' # PYCHOK expected 

_pole_ = 'pole' # PYCHOK expected 

_precision_ = 'precision' # PYCHOK expected 

_pygeodesy_abspath_ = 'pygeodesy_abspath' # PYCHOK expected 

_radians_ = 'radians' # PYCHOK expected 

_radians2_ = 'radians2' # PYCHOK SQUARED 

_radius_ = 'radius' # PYCHOK expected 

_radius1_ = 'radius1' # PYCHOK expected 

_radius2_ = 'radius2' # PYCHOK expected 

_range_ = 'range' # PYCHOK expected 

_reciprocal_ = 'reciprocal' # PYCHOK expected 

_resolution_ = 'resolution' # PYCHOK expected 

_S_ = 'S' # PYCHOK expected 

_scalar_ = 'scalar' # PYCHOK expected 

_scale_ = 'scale' # PYCHOK expected 

_scipy_ = 'scipy' # PYCHOK expected 

_sep_ = 'sep' # PYCHOK expected 

_spherical_ = 'spherical' # PYCHOK expected 

_SouthPole_ = 'SouthPole' # PYCHOK expected 

_SPACE_ = ' ' # PYCHOK expected 

_SQUARE_ = '[%s]' # PYCHOK expected 

_STAR_ = '*' # PYCHOK expected 

_start_ = 'start' # PYCHOK expected 

_std_ = 'std' # PYCHOK expected 

_too_distant_ = 'too distant' # PYCHOK expected 

_too_distant_fmt_ = 'too distant (%.3g)' # PYCHOK expected 

_too_few_ = 'too few' # PYCHOK expected 

_too_small_ = 'too small' # PYCHOK expected 

_transform_ = 'transform' # PYCHOK expected 

_UNDERSCORE_ = '_' # PYCHOK expected 

_units_ = 'units' # PYCHOK expected 

_UPS_ = 'UPS' # PYCHOK expected 

_utf_8_ = 'utf-8' # PYCHOK expected 

_UTM_ = 'UTM' # PYCHOK expected 

_valid_ = 'valid' # PYCHOK expected 

_version_ = 'version' # PYCHOK expected 

_W_ = 'W' # PYCHOK expected 

_x_ = 'x' # PYCHOK expected 

_y_ = 'y' # PYCHOK expected 

_z_ = 'z' # PYCHOK expected 

_zone_ = 'zone' # PYCHOK expected 

 

_COLON_SPACE_ = _COLON_ + _SPACE_ # PYCHOK expected 

_COMMA_SPACE_ = _COMMA_ + _SPACE_ # PYCHOK expected 

_DUNDER_ = _UNDERSCORE_ * 2 # PYCHOK expected 

_EW_ = _E_ + _W_ # PYCHOK common cardinals 

_NE_ = _N_ + _E_ # PYCHOK expected 

_NS_ = _N_ + _S_ # PYCHOK expected 

_NSEW_ = _NS_ + _EW_ # PYCHOK expected 

_NW_ = _N_ + _W_ # PYCHOK expected 

_SE_ = _S_ + _E_ # PYCHOK expected 

_SW_ = _S_ + _W_ # PYCHOK negative ones 

 

 

class _Missing(object): 

'''(INTERNAL) Singleton. 

''' 

def toRepr(self, **unused): 

return 'MISSING' # self.__class__.__name__.strip(_UNDERSCORE_),lower() 

 

__repr__ = toRepr 

__str__ = toRepr 

toStr = toRepr 

 

_Missing = _Missing() # PYCHOK singleton 

 

 

def _dot_(*prefix_names): 

'''(INTERNAL) Period-joined C{prefix} and C{name}s. 

''' 

return _DOT_.join(prefix_names) 

 

 

def _dunder_name(inst, *dflt): 

'''(INTERNAL) Get the double_underscore __name__ attr. 

''' 

try: 

return inst.__name__ 

except AttributeError: 

pass 

return dflt[0] if dflt else inst.__class__.__name__ 

 

 

def _float(f): # in .datums, .ellipsoids, .trf 

'''(INTERNAL) cache initial C{float}s. 

''' 

f = float(f) 

return _floats.setdefault(f, f) # PYCHOK del _floats 

 

 

def _floatuple(*fs): 

'''(INTERNAL) Cache a tuple of C{float}s. 

''' 

return tuple(map(_float, fs)) 

 

 

_floats = {} # PYCHOK floats cache, in .__main__ 

# _float = float # PYCHOK expected 

# del _floats # XXX zap floats cache never 

 

_0_0 = _float( 0) # PYCHOK expected 

_0_1 = _float( 0.1) # PYCHOK expected 

_0_5 = _float( 0.5) # PYCHOK expected 

_1_0 = _float( 1) # PYCHOK expected 

_2_0 = _float( 2) # PYCHOK expected 

_3_0 = _float( 3) # PYCHOK expected 

_4_0 = _float( 4) # PYCHOK expected 

_5_0 = _float( 5) # PYCHOK expected 

_6_0 = _float( 6) # PYCHOK expected 

_8_0 = _float( 8) # PYCHOK expected 

_16_0 = _float( 16) # PYCHOK expected 

_32_0 = _float( 32) # PYCHOK expected 

_60_0 = _float( 60) # PYCHOK expected 

_90_0 = _float( 90) # PYCHOK expected 

_180_0 = _float( 180) # PYCHOK expected 

_360_0 = _float( 360) # PYCHOK expected 

_3600_0 = _float(3600) # PYCHOK expected 

 

try: 

from sys import float_info as _float_info 

 

EPS = _float(_float_info.epsilon) # PYCHOK system's EPSilon 

MANTIS = _float_info.mant_dig # PYCHOK system's mantissa bits 

MAX = _float(_float_info.max) # PYCHOK system's MAX float 

MIN = _float(_float_info.min) # PYCHOK system's MIN float 

except (AttributeError, ImportError): # PYCHOK no cover 

EPS = _float(2.220446049250313e-16) # PYCHOK EPSilon 2**-52, M{EPS +/- 1 != 1} 

MANTIS = 53 # PYCHOK mantissa bits ≈53 (C{int}) 

MAX = _float(pow(_2_0, 1023) * (_2_0 - EPS)) # PYCHOK ≈ 10**308 

MIN = _float(pow(_2_0, -1022)) # PYCHOK ≈ 10**-308 

 

EPS2 = _float(EPS * _2_0) # PYCHOK ≈ 4.440892098501e-16 

EPS_2 = _float(EPS / _2_0) # PYCHOK ≈ 1.110223024625e-16 

EPS1 = _float(_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998 

EPS1_2 = _float(_1_0 - EPS_2) # PYCHOK ≈ 0.9999999999999999 

# _1EPS = _float(_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002 

 

if not _0_0 < EPS < EPS1 < _1_0: # for .frechet 

raise AssertionError('%s < %s: %s < %s < %.16f < %s' % ('EPS', 'EPS1', _0_0, EPS, EPS1, _1_0)) 

 

INF = _float( 'INF') # PYCHOK INFinity, see function L{isinf}, L{isfinite} 

NAN = _float( 'NAN') # PYCHOK Not-A-Number, see function L{isnan} 

NEG0 = float('-0.0') # PYCHOK NEGative 0.0, see function L{isneg0} 

 

PI2 = _float(PI * _2_0) # PYCHOK Two PI, M{PI * 2} aka I{Tau} 

PI4 = _float(PI * _4_0) # PYCHOK Four PI, M{PI * 4} 

PI_2 = _float(PI / _2_0) # PYCHOK Half PI, M{PI / 2} 

PI_4 = _float(PI / _4_0) # PYCHOK Quarter PI, M{PI / 4} 

 

R_M = _float(6371008.771415) # PYCHOK mean, spherical earth radius 

 

 

def _item_fmt(fmt, name_value_arg, name_value_kwd): 

'''(INTERNAL) Helper for C{_item_pr}, C{_item_ps} and C{_item_sq}. 

''' 

for n_v in name_value_kwd.items(): 

break 

else: 

if len(name_value_arg) > 1: 

n_v = name_value_arg[:2] 

elif name_value_arg: 

n_v = name_value_arg, _Missing 

else: 

n_v = _Missing, _Missing 

return fmt % n_v 

 

 

def _item_cs(*name_value_arg, **name_value_kwd): # PYCHOK expected 

'''(INTERNAL) Return a named value string. 

''' 

return _item_fmt('%s: %s', name_value_arg, name_value_kwd) 

 

 

def _item_pr(*name_value_arg, **name_value_kwd): # PYCHOK expected 

'''(INTERNAL) Return a parenthesized name representation. 

''' 

return _item_fmt('%s(%r)', name_value_arg, name_value_kwd) 

 

 

def _item_ps(*name_value_arg, **name_value_kwd): # PYCHOK expected 

'''(INTERNAL) Return a parenthesized name string. 

''' 

return _item_fmt('%s(%s)', name_value_arg, name_value_kwd) 

 

 

def _item_sq(*name_value_arg, **name_value_kwd): # PYCHOK expected 

'''(INTERNAL) Return an indexed or keyed name. 

''' 

return _item_fmt('%s[%r]', name_value_arg, name_value_kwd) 

 

 

def joined(*words, **sep): 

'''Joined words by separator C{sep=NN}. 

 

@arg words: One, two or more words (C{str}s). 

@kwarg sep: Separator C({str}), default C{NN}. 

 

@return: Joined B{C{words}} C({str}). 

''' 

return sep.get(_sep_, NN).join(words) 

 

 

def joined_(*words, **sep): 

'''Joined words by separator C{sep=" "}. 

 

@arg words: One, two or more words (C{str}s). 

@kwarg sep: Separator C({str}), default C{" "}. 

 

@return: Joined B{C{words}} C({str}). 

''' 

return sep.get(_sep_, _SPACE_).join(words) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE.