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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Private L{geodesicx} base class, functions and constants. 

 

Copyright (C) U{Charles Karney<mailto:Charles@Karney.com>} (2008-2022) 

and licensed under the MIT/X11 License. For more information, see the 

U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation. 

''' 

 

# from pygeodesy.basics import isodd # from .karney 

from pygeodesy.constants import MIN as _MIN, _0_0, _2_0 

# from pygeodesy.errors import _or # from .karney 

from pygeodesy.interns import _not_ 

from pygeodesy.karney import _CapsBase, GeodesicError, \ 

isodd, _hypot, _or, _sum2_ 

# from pygeodesy.props import Property # from .karney 

 

from math import sqrt, ldexp as _ldexp 

 

__all__ = () 

__version__ = '22.09.12' 

 

# valid C{nC4}s and C{C4order}s, see _xnC4 below 

_nC4s = {24: 2900, 27: 4032, 30: 5425} 

# underflow guard, we require _TINY * EPS > 0, _TINY + EPS == EPS 

_TINY = sqrt(_MIN) # PYCHOK exported 

# assert (_TINY * EPS) > 0 and (_TINY + EPS) == EPS 

 

 

class _GeodesicBase(_CapsBase): # in .geodsolve 

'''(INTERNAL) Base class for C{[_]Geodesic*Exact}. 

''' 

# def toRepr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

# '''Return this C{GeodesicExact*} items string. 

# 

# @kwarg prec: The C{float} precision, number of decimal digits (0..9). 

# Trailing zero decimals are stripped for B{C{prec}} values 

# of 1 and above, but kept for negative B{C{prec}} values. 

# @kwarg sep: Separator to join (C{str}). 

# 

# @return: C{GeodesicExact*} (C{str}). 

# ''' 

# return Fmt.PAREN(self.named, self.toStr(prec=prec, sep=sep)) 

pass 

 

 

def _cosSeries(c4s, sx, cx): # PYCHOK shared .geodesicx.gx and -.gxline 

'''(INTERNAL) I{Karney}'s cosine series expansion using U{Clenshaw 

summation<https://WikiPedia.org/wiki/Clenshaw_algorithm>}. 

''' 

ar = _2_0 * (cx - sx) * (cx + sx) # 2 * cos(2 * x) 

y0 = t0 = y1 = t1 = _0_0 

i = len(c4s) # c4s = list(c4s) 

if isodd(i): 

i -= 1 

y0 = c4s[i] # c4s.pop() 

_s2_ = _sum2_ 

for i in range(i - 1, 0, -2): # reversed 

# y1 = ar * y0 - y1 + c4s.pop() 

# y0 = ar * y1 - y0 + c4s.pop() 

y1, t1 = _s2_(ar * y0, ar * t0, -y1, -t1, c4s[i]) 

y0, t0 = _s2_(ar * y1, ar * t1, -y0, -t0, c4s[i - 1]) 

s, _ = _s2_(cx * y0, cx * t0, -cx * y1, -cx * t1) 

return s # cx * (y0 - y1) 

 

 

_f = float # in _f2 and .geodesicx._C4_24, _27 and _30 

 

 

def _f2(hi, lo): # in .geodesicx._C4_24, _27 and _30 

'''(INTERNAL) For C{_coeffs}. 

''' 

return _ldexp(_f(hi), 52) + _f(lo) 

 

 

def _sincos12(sin1, cos1, sin2, cos2, sineg0=False): # PYCHOK shared 

'''(INTERNAL) Compute the sine and cosine of angle 

M{ang12 = atan2(sin2, cos2) - atan2(sin1, cos1)}. 

 

Use C{-sin1} to get C{sin12} and C{cos12} of the sum 

M{ang12 = atan2(sin2, cos2) + atan2(sin1, cos1)}. 

 

@kwarg sineg0: If C{True}, make negative C{sin12} zero (C{bool}). 

 

@return: 2-Tuple C{(sin12, cos12)}. 

''' 

s = sin2 * cos1 - sin1 * cos2 

c = cos2 * cos1 + sin1 * sin2 

if sineg0 and s < 0: 

s = _0_0 # max(s, _0_0) or NEG0? 

return s, c 

 

 

def _sin1cos2(sin1, cos1, sin2, cos2): # PYCHOK shared 

'''(INTERNAL) Compute the C{sin1 * cos2} sine and its cosine. 

 

@return: 2-Tuple C{(sin1 * cos2, hypot(sin1 * sin2, cos1)}. 

''' 

s = sin1 * cos2 

c = _hypot(sin1 * sin2, cos1) 

return s, c # _norm2(s, c) 

 

 

def _xnC4(**name_nC4): 

'''(INTERNAL) Validate C{C4order}. 

''' 

n, nC4 = name_nC4.popitem() 

if nC4 not in _nC4s or not isinstance(nC4, int): 

raise GeodesicError(n, nC4, txt=_not_(_or(*map(str, _nC4s)))) 

return _nC4s[nC4] 

 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- 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.