1

2# -*- coding: utf-8 -*-

3

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

5

6 Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2008-2023)

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

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

9'''

10

11 from pygeodesy.basics import isodd, _MODS

12 from pygeodesy.constants import _0_0, _100_0

13 from pygeodesy.errors import _or, _xkwds_item2

14 from pygeodesy.fmath import hypot as _hypot

15 from pygeodesy.karney import _CapsBase, GeodesicError, _2cos2x, _sum2_

16# from pygeodesy.lazily import _MODS, printf # .basics, _MODS

17

18 from math import ldexp as _ldexp

19

20__all__ = ()

21__version__ = '24.05.19'

22

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

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

25

26

27 class _GeodesicBase(_CapsBase): # in .geodsolve

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

29 '''

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

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

32#

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

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

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

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

37#

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

39# '''

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

41 pass

42

43

44 class _Gfloats(dict):

45 '''(INTERNAL) Uniquify floats.

46 '''

47 n = 0 # total number of floats

48 nC4 = 0

49

50 def __init__(self, nC4): # PYCHOK signature

51 self.nC4 = nC4

52

53 def __call__(self, fs):

54 '''Return a tuple of "uniquified" floats.

55 '''

56 self.n += len(fs)

57 _f = self.setdefault

58 return tuple(_f(f, f) for f in map(float, fs)) # PYCHOK as attr

59

60 def prints(self):

61 n, u = self.n, len(self.keys())

62 d = (n - u) * _100_0 / n

63 _MODS.lazily.printf('_CX_%d: n=%d, u=%d, d=%.1f%%', self.nC4, n, u, d) # XXX

64

65

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

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

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

69 '''

70 ar = _2cos2x(cx, sx)

71 y0 = t0 = y1 = t1 = _0_0

72 c4 = list(c4s)

73 _c4 = c4.pop

74 _s2 = _sum2_

75 if isodd(len(c4)):

76 y0 = _c4()

77 while c4:

78 # y1 = ar * y0 - y1 + c4.pop()

79 # y0 = ar * y1 - y0 + c4.pop()

80 y1, t1 = _s2(ar * y0, ar * t0, -y1, -t1, _c4())

81 y0, t0 = _s2(ar * y1, ar * t1, -y0, -t0, _c4())

82 # s = cx * (y0 - y1)

83 s, _ = _s2(cx * y0, _0_0, cx * t0, -cx * y1, -cx * t1)

84 return s

85

86

87_f = float # in _f2 and .geodesicx._C4_24, _27 and _30

88

89

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

91 '''(INTERNAL) For C{_coeffs}.

92 '''

93 return _ldexp(_f(hi), 52) + _f(lo)

94

95

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

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

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

99

100 Negate C{sin1} to get C{sin12} and C{cos12} of the sum

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

102

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

104

105 @return: 2-Tuple C{(sin12, cos12)}.

106 '''

107 s = sin2 * cos1 - sin1 * cos2

108 c = cos2 * cos1 + sin1 * sin2

109 if sineg0 and s < 0:

110 s = _0_0 # max(s, _0_0) or NEG0?

111 return s, c

112

113

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

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

116

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

118 '''

119 s = sin1 * cos2

120 c = _hypot(sin1 * sin2, cos1)

121 return s, c # _norm2(s, c)

122

123

124 def _xnC4(**name_nC4):

125 '''(INTERNAL) Validate C{C4order}.

126 '''

127 n, nC4 = _xkwds_item2(name_nC4)

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

129 raise GeodesicError(n, nC4, txt_not_=_or(*map(str, _nC4s)))

130 return _nC4s[nC4]

131

132

133# **) MIT License

134#

135# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

136#

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

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

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

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

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

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

143#

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

145# in all copies or substantial portions of the Software.

146#

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

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

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

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

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

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

153# OTHER DEALINGS IN THE SOFTWARE.