# Coverage for pygeodesy/constants.py : 100%

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''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import _0_0, _copysign, isbool, iscomplex, isint from pygeodesy.errors import _ALL_LAZY, _xError, _xError2 from pygeodesy.interns import _INF_, _NAN_, _sets_, _UNDER_ # from pygeodesy.lazily import _ALL_LAZY # from .errors # from pygeodesy.streprs import Fmt # from .unitsBase from pygeodesy.unitsBase import Float, Fmt, Int, Radius from math import isinf, isnan, pi as _pi, sqrt try: from math import inf as _inf, nan as _nan # PYCHOK Python 3+ except ImportError: # Python 2- _inf, _nan = float(_INF_), float(_NAN_) __all__ = _ALL_LAZY.constants __version__ = '22.09.20' def _Float(**name_arg): '''(INTERNAL) New named, cached C{Float}. ''' n, arg = name_arg.popitem() return Float(_float(arg), name=n) def _Radius(**name_arg): '''(INTERNAL) New named, cached C{Radius}. ''' n, arg = name_arg.popitem() return Radius(_float(arg), name=n) def float_(*fs, **sets): '''Get scalars as C{float} or I{intern}'ed C{float}. @arg fs: One more values (C{scalar}), all positional. @kwarg sets: Use keyword argument C{B{sets}=True} to C{intern} each B{C{fs}}, otherwise don't. @return: Single C{float} if only one B{C{fs}} is given, otherwise a tuple of C{float}s. @raise TypeError: Some B{C{fs}} not C{scalar}. ''' _f = _floats.setdefault if sets.get(_sets_, False) else \ _floats.get fl = [] try: for i, f in enumerate(fs): f = float(f) fl.append(_f(f, f)) except Exception as x: _E, t = _xError2(x) _fs_i = Fmt.SQUARE(fs=i) raise _E(_fs_i, f, txt=t) return fl[0] if len(fl) == 1 else tuple(fl) def _float(f): # in .datums, .ellipsoids, ... '''(INTERNAL) Cache initial C{float}s. ''' f = float(f) return _floats.setdefault(f, f) # PYCHOK del _floats def float0(*xs): '''Yield as C{B{x}s} as a non-NEG0 C{float}. ''' for x in xs: yield float(x) or _0_0 def _float0(f): # in .resections, .vector3dBase, ... '''(INTERNAL) Return C{float(B{f})} or C{INT0}. ''' if f: f = float(f) f = _floats.get(f, f) elif f is not INT0: f = _0_0 return f def _floatuple(*fs): '''(INTERNAL) Cache a tuple of C{float}s. ''' return tuple(map(_float, fs)) def _1_over(x): '''(INTERNAL) Return reciprocal C{1 / B{x}}. ''' return _float(_1_0 / float(x)) _floats = {} # PYCHOK floats cache, in .__main__ # _float = float # PYCHOK expected # del _floats # XXX zap floats cache never _0_0 = _float( _0_0) # PYCHOK expected _0_0_1T = _0_0, # PYCHOK 1-tuple _0_0_9T = _0_0_1T * 9 # PYCHOK 9-tuple _0_0001 = _float( 0.0001) # PYCHOK expected _0_001 = _float( 0.001) # PYCHOK expected _0_01 = _float( 0.01) # PYCHOK expected _0_1 = _float( 0.1) # PYCHOK expected _0_125 = _float( 0.125) # PYCHOK expected _0_25 = _float( 0.25) # PYCHOK expected _0_26 = _float( 0.26) # PYCHOK expected _0_5 = _float( 0.5) # PYCHOK expected _1_0 = _float( 1) # PYCHOK expected _1_0_1T = _1_0, # PYCHOK 1-tuple _1_5 = _float( 1.5) # PYCHOK expected _1_75 = _float( 1.75) # 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 _9_0 = _float( 9) # PYCHOK expected _10_0 = _float( 10) # 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 _270_0 = _float( 270) # PYCHOK expected _360_0 = _float( 360) # PYCHOK expected _400_0 = _float( 400) # PYCHOK expected _720_0 = _float( 720) # PYCHOK expected _1000_0 = _float(1000) # PYCHOK expected _3600_0 = _float(3600) # PYCHOK expected _N_0_0 = float( '-0.0') # PYCHOK NOT _float! _N_1_0 = _float( -1) # PYCHOK expected _N_2_0 = _float( -2) # PYCHOK expected _N_90_0 = _float( -90) # PYCHOK expected _N_180_0 = _float(-180) # PYCHOK expected _M_KM = _1000_0 # meter per Kilo meter, see .utily _M_NM = _float(1852.0) # meter per Nautical Mile _M_SM = _float(1609.344) # meter per Statute Mile try: from sys import float_info as _f_i DIG = Int( DIG =_f_i.dig) # PYCHOK system's float decimal digits EPS = _Float(EPS =_f_i.epsilon) # PYCHOK system's EPSilon MANT_DIG = Int( MANT_DIG=_f_i.mant_dig) # PYCHOK system's float mantissa bits MAX = _Float(MAX =_f_i.max) # PYCHOK system's MAX float 1.7976931348623157e+308 # MAX_EXP = Int( MAX_EXP =_f_i.max_exp) # PYTHON system's max base 2 exponent MIN = _Float(MIN =_f_i.min) # PYCHOK system's MIN float 2.2250738585072014e-308 # MIN_EXP = Int( MIN_EXP =_f_i.min_exp) # PYTHON system's min base 2 exponent # RADIX = Int( RADIX =_f_i.radix) # PYTHON system's float base del _f_i except ImportError: # PYCHOK no cover DIG = Int( DIG =15) # PYCHOK system's 64-bit float decimal digits EPS = _Float(EPS =2.220446049250313e-16) # PYCHOK EPSilon 2**-52, M{EPS +/- 1 != 1} MANT_DIG = Int( MANT_DIG=53) # PYCHOK float mantissa bits ≈ 53 (C{int}) MAX = _Float(MAX =pow(_2_0, 1023) * (_2_0 - EPS)) # PYCHOK ≈ 10**308 # MAX_EXP = Int( MAX_ESP =1024) # 308 base 10 MIN = _Float(MIN =pow(_2_0, -1021)) # PYCHOK ≈ 10**-308 # MIN_EXP = Int(MIN_EXP =-1021) # -307 base 10 # RADIX = Int(Radix =2) # base EPS0 = _Float( EPS0 = EPS**2) # PYCHOK near-/non-zero comparison 4.930381e-32, or EPS or EPS_2 EPS02 = _Float( EPS02 = EPS**4) # PYCHOK near-zero-squared comparison 2.430865e-63 EPS_2 = _Float( EPS_2 = EPS / _2_0) # PYCHOK ≈ 1.110223024625e-16 EPS1 = _Float( EPS1 =_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998 EPS2 = _Float( EPS2 = EPS * _2_0) # PYCHOK ≈ 4.440892098501e-16 EPS4 = _Float( EPS4 = EPS * _4_0) # PYCHOK ≈ 8.881784197001e-16 # _1EPS = _Float(_1EPS =_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002 _1_EPS = _Float(_1_EPS =_1_0 / EPS) # PYCHOK = 4503599627370496.0 # _2_EPS = _Float(_2_EPS =_2_0 / EPS) # PYCHOK = 9007199254740992.0 _EPS4e8 = _Float(_EPS4e8 = EPS4 * 1.e8) # PYCHOK ≈ 8.881784197001e-08 _EPSmin = _Float(_EPSmin = sqrt(MIN)) # PYCHOK = 1.49166814624e-154 _EPSqrt = _Float(_EPSqrt = sqrt(EPS)) # PYCHOK = 1.49011611938e5-08 _EPStol = _Float(_EPStol =_EPSqrt * _0_1) # PYCHOK = 1.49011611938e5-09 == sqrt(EPS * _0_01) _89_999_ = _Float(_89_999_=EPS1 * _90_0) # just below 90.0 # <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html> _1__90 = _Float(_1__90 =_1_0 / _90_0) # PYCHOK = 0.011_111_111_111_111_111_111_111_111_111_111_111_111_111_111_11111 _2__PI = _Float(_2__PI =_2_0 / _pi) # PYCHOK = 0.636_619_772_367_581_343_075_535_053_490_057_448_137_838_582_96182 _1_16th = _Float(_1_16th =_1_0 / _16_0) # PYCHOK in .ellipsoids, .karney _1_64th = _Float(_1_64th =_1_0 / 64) # PYCHOK in .elliptic, pow(2.0, -6) _1_3rd = _Float(_1_3rd =_1_0 / _3_0) # PYCHOK in .fmath _2_3rd = _Float(_2_3rd =_2_0 / _3_0) # PYCHOK in .fmath _K0_UTM = _Float(_K0_UTM = 0.9996) # PYCHOK in .etm, .ktm, .utm, UTM scale at central meridian # sqrt(2) <https://WikiPedia.org/wiki/Square_root_of_2> # 1.414213562373095_048_801_688_724_209_698_078_569_671_875_376_948_073_176_679_737_99 # _1SQRT2 = _Float(_1SQRT2 =sqrt(_2_0) + 1) _SQRT2_2 = _Float(_SQRT2_2=sqrt(_0_5)) # PYCHOK = 0.707106781186547_6 == sqrt(2) / 2 INF = Float(INF =_inf) # PYCHOK INFinity, see function L{isinf}, L{isfinite}, NOT _Float! INT0 = Int( INT0= 0) # PYCHOK unique int(0) instance, see .fsums, useZ=False NAN = Float(NAN =_nan) # PYCHOK Not-A-Number, see function L{isnan}, NOT _Float! NEG0 = Float(NEG0=_N_0_0) # PYCHOK NEGative 0.0, see function L{isneg0}, NOT _Float! NINF = Float(NINF=-INF) # PYCHOK Negative INFinity, NOT _Float! PI = _Float(PI =_pi) PI2 = _Float(PI2 =_pi * _2_0) # PYCHOK Two PI, M{PI * 2} aka I{Tau} PI_2 = _Float(PI_2 =_pi / _2_0) # PYCHOK Half PI, M{PI / 2} PI3 = _Float(PI3 =_pi * _3_0) # PYCHOK Three PI, M{PI * 3} PI3_2 = _Float(PI3_2=_pi * _1_5) # PYCHOK PI and a half, M{PI * 3 / 2} PI4 = _Float(PI4 =_pi * _4_0) # PYCHOK Four PI, M{PI * 4} PI_4 = _Float(PI_4 =_pi / _4_0) # PYCHOK Quarter PI, M{PI / 4} R_MA = _Radius(R_MA=6378137.0) # PYCHOK equatorial earth radius (C{meter}), WGS84, EPSG:3785 R_MB = _Radius(R_MB=6356752.3) # PYCHOK polar earth radius (C{meter}), WGS84, EPSG:3785 R_M = _Radius(R_M =6371008.771415) # PYCHOK mean, spherical earth radius (C{meter}) R_KM = _Radius(R_KM=R_M / _M_KM) # PYCHOK mean, spherical earth radius (C{KM}, kilo meter) R_NM = _Radius(R_NM=R_M / _M_NM) # PYCHOK mean, spherical earth radius (C{NM}, nautical miles) R_SM = _Radius(R_SM=R_M / _M_SM) # PYCHOK mean, spherical earth radius (C{SM}, statute miles) # See <https://www.EdWilliams.org/avform.htm>, <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf> # and <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> based on the # International Standard Nautical Mile of 1,852 meter (1' latitude) R_FM = _Radius(R_FM=6371000.0) # PYCHOK former FAI Sphere earth radius (C{meter}) R_GM = _Radius(R_GM=6371230.0) # PYCHOK avg. radius, distance to geoid surface (C{meter}) # <http://Wiki.GIS.com/wiki/index.php/Ellipsoidal_quadratic_mean_radius> R_QM = _Radius(R_QM=6372797.560856) # PYCHOK earth' quadratic mean radius (C{meter}) # Rtri= _Radius(Rtri=6372797.5559594) # PYCHOK Rtriaxial quadratic mean radius (C{meter}), WGS84 # Rbi = _Radius(Rbi =6367453.6345163) # PYCHOK Rbiaxial quadratic mean radius (C{meter}), WGS84 R_VM = _Radius(R_VM=6366707.0194937) # PYCHOK aViation/naVigation earth radius (C{meter}) _INF_NAN_NINF = INF, NAN, NINF def _0_0s(n): '''(INTERNAL) Return an C{B{n}-tuple} of C{_0_0} zeros. ''' return _0_0_9T[:n] if 0 <= n <= len(_0_0_9T) else (_0_0_1T * n) try: from math import isclose as _isclose except ImportError: # Python 3.4- def _isclose(a, b, rel_tol=1e-9, abs_tol=0): '''Mimick Python 3.5+ C{math.isclose}. ''' t, d = abs_tol, abs(a - b) if d > t: r = max(abs(a), abs(b)) * rel_tol t = max(r, t) return d <= t def isclose(a, b, rel_tol=1e-12, abs_tol=EPS0): '''Like C{math.isclose}, but with defaults such that C{isclose(0, EPS0)} is C{True} by default. ''' return _isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol) try: from math import isfinite as _isfinite # in .ellipsoids, .fsums, .karney except ImportError: # Python 3.1- def _isfinite(x): '''Mimick Python 3.2+ C{math.isfinite}. ''' return not (isinf(x) or isnan(x)) def isfinite(obj): '''Check a finite C{scalar} or C{complex} value. @arg obj: Value (C{scalar} or C{complex}). @return: C{False} if B{C{obj}} is C{INF}, C{NINF} or C{NAN}, C{True} otherwise. @raise TypeError: Non-scalar and non-complex B{C{obj}}. ''' try: return (obj not in _INF_NAN_NINF) and _isfinite(obj) except Exception as x: if iscomplex(obj): # _isfinite(complex) thows TypeError return isfinite(obj.real) and isfinite(obj.imag) raise _xError(x, Fmt.PAREN(isfinite.__name__, obj)) def isint0(obj, both=False): '''Check for L{INT0} or C{int(0)} value. @arg obj: The object (any C{type}). @kwarg both: If C{true}, also check C{float(0)} (C{bool}). @return: C{True} if B{C{obj}} is L{INT0}, C{int(0)} or C{float(0)}, C{False} otherwise. ''' return (obj is INT0 or obj is int(0) or bool(both and (not obj) and isint(obj, both=True))) and not isbool(obj) def isnear0(x, eps0=EPS0): '''Is B{C{x}} near zero within a tolerance? @arg x: Value (C{scalar}). @kwarg eps0: Near-zero tolerance (C{EPS0}). @return: C{True} if C{abs(B{x}) < B{eps0}}, C{False} otherwise. @see: Function L{isnon0}. ''' return bool(eps0 > x > -eps0) def isnear1(x, eps1=EPS0): '''Is B{C{x}} near one within a tolerance? @arg x: Value (C{scalar}). @kwarg eps1: Near-one tolerance (C{EPS0}). @return: C{isnear0(B{x} - 1)}. @see: Function L{isnear0}. ''' return isnear0(x - _1_0, eps0=eps1) def isnear90(x, eps90=EPS0): '''Is B{C{x}} near one within a tolerance? @arg x: Value (C{scalar}). @kwarg eps90: Near-90 tolerance (C{EPS0}). @return: C{isnear0(B{x} - 90)}. @see: Function L{isnear0}. ''' return isnear0(x - _90_0, eps0=eps90) def isneg0(x): '''Check for L{NEG0}, negative C{0.0}. @arg x: Value (C{scalar}). @return: C{True} if B{C{x}} is C{NEG0} or C{-0.0}, C{False} otherwise. ''' return x in (_0_0, NEG0) and _copysign(1, x) < 0 # and str(x).startswith(_MINUS_) def isninf(x): '''Check for L{NINF}, negative C{INF}. @arg x: Value (C{scalar}). @return: C{True} if B{C{x}} is C{NINF} or C{-inf}, C{False} otherwise. ''' return x is NINF or ((not isfinite(x)) and x < 0) def isnon0(x, eps0=EPS0): '''Is B{C{x}} non-zero with a tolerance? @arg x: Value (C{scalar}). @kwarg eps0: Non-zero tolerance (C{EPS0}). @return: C{True} if C{abs(B{x}) > B{eps0}}, C{False} otherwise. @see: Function L{isnear0}. ''' return not bool(eps0 > x > -eps0) # not isnear0 def _off90(lat): '''(INTERNAL) Off 90.0 for .gars and .wgrs. ''' return max(min(lat, _89_999_), -_89_999_) try: from math import remainder except ImportError: # Python 3.6- from math import fmod as _fmod def remainder(x, y): '''Mimick Python 3.7+ C{math.remainder}. ''' if isnan(y): x = NAN elif x and not isnan(x): y = abs(y) x = _fmod(x, y) h = _0_5 * y if x >= h: x -= y elif x < -h: x += y return x # keep signed 0.0 def _umod_360(deg): '''(INTERNAL) Non-negative C{deg} modulo 360, basic C{.utily.wrap360}. ''' return (deg % _360_0) or _0_0 if __name__ == '__main__': from pygeodesy.errors import itemsorted from pygeodesy.lazily import printf t = n = v = [] for n, v in itemsorted(locals()): if isinstance(v, (Float, Int, Radius)): printf('%9s: %r', n, v.toRepr(std=False)) if v.name != n: raise AssertionError('%r != %r' % (n, v)) if v.name is not n: raise AssertionError('%r is not %r' % (n, v)) if not n.startswith(_UNDER_): t.append(n) t.append(float_.__name__) printf('__all__ = %r', tuple(t)) # **) 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.