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# -*- coding: utf-8 -*- 

 

u'''Base L{geodesicx} classes, functions and constants. 

 

Copyright (C) Charles Karney (2012-2021) <Charles@Karney.com> 

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

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

''' 

 

# from pygeodesy.basics import isodd # from .karney 

# from pygeodesy.errors import _or # from .karney 

from pygeodesy.interns import MIN as _MIN, _not_, \ 

_0_0, _1_0, _N_1_0, _2_0 

from pygeodesy.karney import GeodesicError, isodd, _or, \ 

_NamedBase, Property, _sum2_ 

from pygeodesy.lazily import _ALL_DOCS 

# from pygeodesy.named import _NamedBase # from .karney 

# from pygeodesy.props import Property # from .karney 

 

from math import sqrt, ldexp as _ldexp 

 

__all__ = () 

__version__ = '22.04.29' 

 

# 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 

 

 

class Caps(object): # PYCHOK 

'''(INTERNAL) Overriden by C{Caps} below. 

''' 

EMPTY = 0 # formerly aka NONE 

LATITUDE = 1 << 7 # compute latitude C{lat2} (0x80) 

LONGITUDE = 1 << 8 # compute longitude C{lon2} 

AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2} 

DISTANCE = 1 << 10 # compute distance C{s12} 

DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct 

REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} 

GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} 

AREA = 1 << 14 # compute area C{S12} (0x4000) 

 

STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE 

ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_* 

 

LINE_OFF = 1 << 15 # Line without updates from parent GeodesicExact 

LONG_UNROLL = 1 << 16 # unroll C{lon2} in GeodesicExact.Direct 

REVERSE2 = 1 << 17 # reverse C{azi2} 

 

_ANGLE_ONLY = 1 << 18 # angular distance C{a12} only 

_SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse 

 

_DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details 

_DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details 

_DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details 

_DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details 

_DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

_DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs 

 

_OUT_ALL = ALL 

_OUTMASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

 

_AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

_AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

_LINE = AZIMUTH | LATITUDE | LONG_UNROLL 

_REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

 

Caps = Caps() # PYCHOK singleton 

'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic 

capabilities (C{caps}) and expected results (C{outmask}). 

 

C{AREA} - compute area C{S12}, 

 

C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

 

C{DISTANCE} - compute distance C{s12}, 

 

C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

 

C{EMPTY} - nothing, formerly aka C{NONE}, 

 

C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

 

C{LATITUDE} - compute latitude C{lat2}, 

 

C{LONGITUDE} - compute longitude C{lon2}, 

 

C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

 

C{REDUCEDLENGTH} - compute reduced length C{m12}, 

 

C{REVERSE2} - reverse C{azi2}, 

 

and C{ALL} - all of the above. 

 

C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

 

 

class _GeodesicBase(_NamedBase): # in .geodsolve 

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

''' 

ALL = Caps.ALL 

AREA = Caps.AREA 

AZIMUTH = Caps.AZIMUTH 

DISTANCE = Caps.DISTANCE 

DISTANCE_IN = Caps.DISTANCE_IN 

EMPTY = Caps.EMPTY # aka NONE 

GEODESICSCALE = Caps.GEODESICSCALE 

LATITUDE = Caps.LATITUDE 

LINE_OFF = Caps.LINE_OFF 

LONGITUDE = Caps.LONGITUDE 

LONG_UNROLL = Caps.LONG_UNROLL 

REDUCEDLENGTH = Caps.REDUCEDLENGTH 

STANDARD = Caps.STANDARD 

 

_debug = 0 # or Caps._DEBUG_... 

 

# 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)) 

 

@Property 

def debug(self): 

'''Get the C{debug} option (C{bool}). 

''' 

return bool(self._debug) 

 

@debug.setter # PYCHOK setter! 

def debug(self, debug): 

'''Set the C{debug} option. 

 

@arg debug: Include more details in results (C{bool}). 

''' 

self._debug = Caps._DEBUG_ALL if debug else 0 

 

 

def _all_caps(_caps, caps): # PYCHOK shared 

'''(INTERNAL) Check all available capabilities: C{True} 

if I{all} B{C{caps}} are available in B{C{_caps}}, 

C{False} otherwise (C{bool}). 

''' 

caps &= Caps._OUT_ALL 

return (_caps & caps) == caps 

 

 

def _coSeries(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() 

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

# y1 = ar * y0 - y1 + c4s.pop() 

# y0 = ar * y1 - y0 + c4s.pop() 

y1, t1 = _sum2_(ar * y0, ar * t0, -y1, -t1, c4s[i]) 

y0, t0 = _sum2_(ar * y1, ar * t1, -y0, -t0, c4s[i - 1]) 

s, _ = _sum2_(_1_0, cx * y0, cx * t0, -cx * y1, -cx * t1, _N_1_0) 

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 _polynomial(x, c4s, i, j): # PYCHOK shared 

'''(INTERNAL) Like C{GeographicLib.Math.hpp.polyval} but with a 

different signature and cascaded summation as C{karney._fsum2}. 

 

@return: M{sum(c4s[k] * x**(j - k - 1) for k in range(i, j)} 

''' 

s, t = c4s[i], _0_0 

for i in range(i + 1, j): 

s, t = _sum2_(s * x, t * x, c4s[i]) 

return s # + t 

 

 

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

'''(INTERNAL) Compute the C{sin12} and C{cos12} of 

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 noneg: Limit C{sin12} to non-negative (C{bool}). 

 

@return: 2-Tuple C{(sin12, cos12)}. 

''' 

s = sin2 * cos1 - sin1 * cos2 

c = cos2 * cos1 + sin1 * sin2 

if noneg and s < 0: 

s = _0_0 # max(s, _0_0) or NEG0? 

return 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] 

 

 

__all__ += _ALL_DOCS(Caps) 

 

# **) 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.