1# -*- coding: utf-8 -*-

2

3 u'''Single-instance C{float} and C{int} constants across C{pygeodesy} modules and

4 related functions L{pygeodesy.float_}, L{pygeodesy.isclose}, L{pygeodesy.isfinite},

5 L{pygeodesy.isinf}, L{pygeodesy.isint0}, L{pygeodesy.isnan}, L{pygeodesy.isnear0},

6 L{pygeodesy.isnear1}, L{pygeodesy.isnear90}, L{pygeodesy.isneg0}, L{pygeodesy.isninf},

7 L{pygeodesy.isnon0} and L{pygeodesy.remainder}.

8'''

9# make sure int/int division yields float quotient, see .basics

10 from __future__ import division as _; del _ # PYCHOK semicolon

11

12 from pygeodesy.basics import _copysign, isbool, iscomplex, isint, _0_0

13 from pygeodesy.errors import _xError, _xError2, _xkwds_get, _xkwds_item2

14# from pygeodesy.internals import _0_0 # from .basics

15 from pygeodesy.interns import _INF_, _NAN_, _UNDER_

16# from pygeodesy.lazily import _ALL_LAZY # from .unitsBase

17# from pygeodesy.streprs import Fmt # from .unitsBase

18 from pygeodesy.unitsBase import Float, Int, Radius, _ALL_LAZY, Fmt

19

20 from math import fabs, isinf, isnan, pi as _PI, sqrt

21 try:

22 from math import inf as _inf, nan as _nan # PYCHOK Python 3+

23 except ImportError: # Python 2-

24 _inf, _nan = float(_INF_), float(_NAN_)

25

26__all__ = _ALL_LAZY.constants

27__version__ = '24.05.14'

28

29

30 def _copysign_0_0(y):

31 '''(INTERNAL) copysign(0.0, y), only C{float}.

32 '''

33 return _N_0_0 if y < 0 else _0_0

34

35

36 def _copysign_1_0(y):

37 '''(INTERNAL) copysign(1.0, y), only C{float}.

38 '''

39 return _N_1_0 if y < 0 else _1_0

40

41

42 def _copysignINF(y):

43 '''(INTERNAL) copysign(INF, y), only C{float}.

44 '''

45 return NINF if y < 0 else INF

46

47

48 def _Float(**name_arg):

49 '''(INTERNAL) New named, cached C{Float}.

50 '''

51 n, arg = _xkwds_item2(name_arg)

52 return Float(_float(arg), name=n)

53

54

55 def _Radius(**name_arg):

56 '''(INTERNAL) New named, cached C{Radius}.

57 '''

58 n, arg = _xkwds_item2(name_arg)

59 return Radius(_float(arg), name=n)

60

61

62 def float_(*fs, **sets): # sets=False

63 '''Get scalars as C{float} or I{intern}'ed C{float}.

64

65 @arg fs: One more values (C{scalar}), all positional.

66 @kwarg sets: Use C{B{sets}=True} to C{intern} each

67 B{C{fs}}, otherwise don't C{intern}.

68

69 @return: A single C{float} if only one B{C{fs}} is

70 given, otherwise a tuple of C{float}s.

71

72 @raise TypeError: Some B{C{fs}} is not C{scalar}.

73 '''

74 fl = []

75 _a = fl.append

76 _f = _floats.setdefault if _xkwds_get(sets, sets=False) else \

77 _floats.get

78 try:

79 for i, f in enumerate(fs):

80 f = float(f)

81 _a(_f(f, f))

82 except Exception as x:

83 E, t = _xError2(x)

84 fs_i = Fmt.SQUARE(fs=i)

85 raise E(fs_i, f, txt=t)

86 return fl[0] if len(fl) == 1 else tuple(fl)

87

88

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

90 '''(INTERNAL) Cache initial C{float}s.

91 '''

92 f = float(f)

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

94

95

96 def float0_(*xs):

97 '''Yield C{B{x}s} as a non-NEG0 C{float}.

98 '''

99 for x in xs:

100 yield float(x) if x else _0_0

101

102

103 def _float0(f): # in .resections, .vector3dBase, ...

104 '''(INTERNAL) Return C{float(B{f})} or C{INT0}.

105 '''

106 if f:

107 f = float(f)

108 f = _floats.get(f, f)

109 elif f is not INT0:

110 f = float(f) or _0_0 # force None, NN error

111 return f

112

113

114 def _floatuple(*fs):

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

116 '''

117 return tuple(map(_float, fs))

118

119

120 try:

121 from math import log2 as _log2

122 except ImportError: # Python 3.3-

123 from math import log as _log

124

125 def _log2(x): # in .rhumb.aux_, .auxilats.auxLat

126 return _log(x, 2)

127

128

129 def _naninf(p, *xs):

130 '''(INTERNAL) Return C{NAN}, C{NINF} or C{INF}.

131 '''

132 for x in xs:

133 p *= x # fmath.fprod(xs)

134 return _copysignINF(p) if isfinite(p) else p

135

136

137 def _over(p, q):

138 '''(INTERNAL) Return C{B{p} / B{q}} avoiding C{ZeroDivisionError} exceptions.

139 '''

140 try:

141 return (p / q) # if p else _copysign_0_0(q)

142 except ZeroDivisionError:

143 return (_copysignINF(p) if isfinite(p) else NAN) if p else p

144

145

146 def _1_over(x):

147 '''(INTERNAL) Return reciprocal C{1 / B{x}} avoiding C{ZeroDivisionError} exceptions.

148 '''

149 try:

150 return _1_0 / float(x)

151 except ZeroDivisionError:

152 return NINF if isneg0(x) else INF

153

154

155_floats = {} # PYCHOK floats cache, in .__main__

156# _float = float # PYCHOK expected

157# del _floats # XXX zap floats cache never

158

159_0_0 = _float( _0_0) # PYCHOK expected

160_0_0_1T = _0_0, # PYCHOK 1-tuple

161_0_0_9T = _0_0_1T * 9 # PYCHOK 9-tuple

162_0_0001 = _float( 0.0001) # PYCHOK expected

163_0_001 = _float( 0.001) # PYCHOK expected

164_0_01 = _float( 0.01) # PYCHOK expected

165_0_1 = _float( 0.1) # PYCHOK expected

166_0_125 = _float( 0.125) # PYCHOK expected

167_0_25 = _float( 0.25) # PYCHOK expected

168_0_5 = _float( 0.5) # PYCHOK expected

169_1_0 = _float( 1) # PYCHOK expected

170_1_0_1T = _1_0, # PYCHOK 1-tuple

171_1_5 = _float( 1.5) # PYCHOK expected

172_1_75 = _float( 1.75) # PYCHOK expected

173_2_0 = _float( 2) # PYCHOK expected

174_3_0 = _float( 3) # PYCHOK expected

175_4_0 = _float( 4) # PYCHOK expected

176_5_0 = _float( 5) # PYCHOK expected

177_6_0 = _float( 6) # PYCHOK expected

178_8_0 = _float( 8) # PYCHOK expected

179_9_0 = _float( 9) # PYCHOK expected

180_10_0 = _float( 10) # PYCHOK expected

181_16_0 = _float( 16) # PYCHOK expected

182_32_0 = _float( 32) # PYCHOK expected

183_60_0 = _float( 60) # PYCHOK expected

184_90_0 = _float( 90) # PYCHOK expected

185_100_0 = _float( 100) # PYCHOK expected

186_180_0 = _float( 180) # PYCHOK expected

187_270_0 = _float( 270) # PYCHOK expected

188_360_0 = _float( 360) # PYCHOK expected

189_400_0 = _float( 400) # PYCHOK expected

190_720_0 = _float( 720) # PYCHOK expected

191_1000_0 = _float(1000) # PYCHOK expected

192_3600_0 = _float(3600) # PYCHOK expected

193

194_N_0_0 = float( '-0.0') # PYCHOK NOT _float!

195_N_0_5 = _float( -_0_5) # PYCHOK expected

196_N_1_0 = _float( -_1_0) # PYCHOK expected

197_N_2_0 = _float( -_2_0) # PYCHOK expected

198_N_90_0 = _float( -_90_0) # PYCHOK expected

199_N_180_0 = _float(-_180_0) # PYCHOK expected

200

201_M_KM = _1000_0 # meter per Kilo meter, see .utily

202_M_NM = _float(1852.0) # meter per Nautical Mile, exactly

203_M_SM = _float(1609.344) # meter per Statute Mile

204

205 try:

206 from sys import float_info as _f_i

207 # @see: <https://NumPy.org/doc/stable/reference/generated/numpy.finfo.html>

208 DIG = Int( DIG =_f_i.dig) # PYCHOK system's float decimal digits

209 EPS = _Float(EPS =_f_i.epsilon) # PYCHOK system's EPSilon

210 MANT_DIG = Int( MANT_DIG=_f_i.mant_dig) # PYCHOK system's float mantissa bits

211 MAX = _Float(MAX =_f_i.max) # PYCHOK system's MAX float 1.7976931348623157e+308

212 MAX_EXP = Int( MAX_EXP =_f_i.max_exp) # PYTHON system's max base 2 exponent

213 MIN = _Float(MIN =_f_i.min) # PYCHOK system's MIN float 2.2250738585072014e-308

214 MIN_EXP = Int( MIN_EXP =_f_i.min_exp) # PYTHON system's min base 2 exponent

215# RADIX = Int( RADIX =_f_i.radix) # PYTHON system's float base

216 del _f_i

217 except ImportError: # PYCHOK no cover

218 DIG = Int( DIG =15) # PYCHOK system's 64-bit float decimal digits

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

220 MANT_DIG = Int( MANT_DIG=53) # PYCHOK float mantissa bits ≈ 53 (C{int})

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

222 MAX_EXP = Int( MAX_ESP =_log2(MAX)) # 308 base 10

223 MIN = _Float(MIN =pow(_2_0, -1021)) # PYCHOK ≈ 10**-308

224 MIN_EXP = Int(MIN_EXP =_log2(MIN)) # -307 base 10

225# RADIX = Int(Radix =2) # base

226

227 EPS0 = _Float( EPS0 = EPS**2) # PYCHOK near-/non-zero comparison 4.930381e-32, or EPS or EPS_2

228 EPS02 = _Float( EPS02 = EPS**4) # PYCHOK near-zero-squared comparison 2.430865e-63

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

230 EPS1 = _Float( EPS1 =_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998

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

232 EPS4 = _Float( EPS4 = EPS * _4_0) # PYCHOK ≈ 8.881784197001e-16

233# _1EPS = _Float(_1EPS =_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002

234_1_EPS = _Float(_1_EPS =_1_0 / EPS) # PYCHOK = 4503599627370496.0

235# _2_EPS = _Float(_2_EPS =_2_0 / EPS) # PYCHOK = 9007199254740992.0

236_EPS2e4 = _Float(_EPS2e4 = EPS2 * 1.e4) # PYCHOK ≈ 4.440892098501e-12

237_EPS4e8 = _Float(_EPS4e8 = EPS4 * 1.e8) # PYCHOK ≈ 8.881784197001e-08

238_EPSmin = _Float(_EPSmin = sqrt(MIN)) # PYCHOK = 1.49166814624e-154

239_EPSqrt = _Float(_EPSqrt = sqrt(EPS)) # PYCHOK = 1.49011611938e5-08

240_EPStol = _Float(_EPStol =_EPSqrt * _0_1) # PYCHOK = 1.49011611938e5-09 == sqrt(EPS * _0_01)

241

242_89_999_ = _Float(_89_999_= EPS1 * _90_0) # just below 90.0

243# <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html>

244_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

245_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

246

247_1_16th = _Float(_1_16th =_1_0 / _16_0) # PYCHOK in .ellipsoids, .karney

248_1_64th = _Float(_1_64th =_1_0 / 64) # PYCHOK in .elliptic, pow(2.0, -6)

249_1_3rd = _Float(_1_3rd =_1_0 / _3_0) # PYCHOK in .fmath

250_1_6th = _Float(_1_6th =_1_0 / _6_0) # PYCHOK in .fmath

251

252_K0_UTM = _Float(_K0_UTM = 0.9996) # PYCHOK in .etm, .ktm, .utm, UTM scale at central meridian

253# sqrt(2) <https://WikiPedia.org/wiki/Square_root_of_2>

254# 1.414213562373095_048_801_688_724_209_698_078_569_671_875_376_948_073_176_679_737_99

255# _1SQRT2= _Float(_1SQRT2 =sqrt(_2_0) + 1)

256_SQRT2_2 = _Float(_SQRT2_2=sqrt(_0_5)) # PYCHOK = 0.707106781186547_6 == sqrt(2) / 2

257

258 INF = Float(INF =_inf) # PYCHOK INFinity, see function L{isinf}, L{isfinite}, NOT _Float!

259 INT0 = Int( INT0= 0) # PYCHOK unique int(0) instance, see .fsums, useZ=False

260 NAN = Float(NAN =_nan) # PYCHOK Not-A-Number, see function L{isnan}, NOT _Float!

261 NEG0 = Float(NEG0=_N_0_0) # PYCHOK NEGative 0.0, see function L{isneg0}, NOT _Float!

262 NINF = Float(NINF=-INF) # PYCHOK Negative INFinity, NOT _Float!

263

264 PI = _Float(PI =_PI) # 3.1415_9265_3589_7932_3846_2643_3832_795

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

266 PI_2 = _Float(PI_2 =_PI / _2_0) # PYCHOK Half PI, M{PI / 2}

267 PI3 = _Float(PI3 =_PI * _3_0) # PYCHOK Three PI, M{PI * 3}

268 PI3_2 = _Float(PI3_2=_PI * _1_5) # PYCHOK PI and a half, M{PI * 3 / 2}

269 PI_3 = _Float(PI_3 =_PI / _3_0) # PYCHOK One third PI, M{PI / 3}

270 PI4 = _Float(PI4 =_PI * _4_0) # PYCHOK Four PI, M{PI * 4}

271 PI_4 = _Float(PI_4 =_PI / _4_0) # PYCHOK Quarter PI, M{PI / 4}

272

273 R_MA = _Radius(R_MA=6378137.0) # PYCHOK equatorial earth radius (C{meter}), WGS84, EPSG:3785

274 R_MB = _Radius(R_MB=6356752.3) # PYCHOK polar earth radius (C{meter}), WGS84, EPSG:3785

275 R_M = _Radius(R_M =6371008.771415) # PYCHOK mean, spherical earth radius (C{meter})

276 R_KM = _Radius(R_KM=R_M / _M_KM) # PYCHOK mean, spherical earth radius (C{KM}, Kilo meter)

277 R_NM = _Radius(R_NM=R_M / _M_NM) # PYCHOK mean, spherical earth radius (C{NM}, nautical miles)

278 R_SM = _Radius(R_SM=R_M / _M_SM) # PYCHOK mean, spherical earth radius (C{SM}, statute miles)

279# See <https://www.EdWilliams.org/avform.htm>, <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf>

280# and <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> based on the

281# International Standard Nautical Mile of 1,852 meter (1' latitude)

282 R_FM = _Radius(R_FM=6371000.0) # PYCHOK former FAI Sphere earth radius (C{meter})

283 R_GM = _Radius(R_GM=6371230.0) # PYCHOK avg. radius, distance to geoid surface (C{meter})

284# <http://Wiki.GIS.com/wiki/index.php/Ellipsoidal_quadratic_mean_radius>

285 R_QM = _Radius(R_QM=6372797.560856) # PYCHOK earth' quadratic mean radius (C{meter})

286# Rtri= _Radius(Rtri=6372797.5559594) # PYCHOK Rtriaxial quadratic mean radius (C{meter}), WGS84

287# Rbi = _Radius(Rbi =6367453.6345163) # PYCHOK Rbiaxial quadratic mean radius (C{meter}), WGS84

288 R_VM = _Radius(R_VM=6366707.0194937) # PYCHOK aViation/naVigation earth radius (C{meter})

289# R_AU= Meter( R_AU=149597870700.0) # PYCHOK <https://WikiPedia.org/wiki/Astronomical_unit>

290

291_INF_NAN_NINF = INF, NAN, NINF

292_pos_self = _1_0.__pos__() is _1_0 # PYCHOK in .fsums, .vector3dBase

293

294

295 def _0_0s(n):

296 '''(INTERNAL) Return an C{B{n}-tuple} of C{_0_0} zeros.

297 '''

298 return _0_0_9T[:n] if 0 <= n <= len(_0_0_9T) else (_0_0_1T * n)

299

300

301 try:

302 from math import isclose as _isclose

303 except ImportError: # Python 3.4-

304

305 def _isclose(a, b, rel_tol=1e-9, abs_tol=0):

306 '''Mimick Python 3.5+ C{math.isclose}.

307 '''

308 t, d = abs_tol, fabs(a - b)

309 if d > t:

310 r = max(fabs(a), fabs(b)) * rel_tol

311 t = max(r, t)

312 return d <= t

313

314

315 def isclose(a, b, rel_tol=1e-12, abs_tol=EPS0):

316 '''Like C{math.isclose}, but with defaults such

317 that C{isclose(0, EPS0)} is C{True} by default.

318 '''

319 return _isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol)

320

321

322 try:

323 from math import isfinite as _isfinite # in .ellipsoids, ...

324 except ImportError: # Python 3.1-

325

326 def _isfinite(x):

327 '''Mimick Python 3.2+ C{math.isfinite}.

328 '''

329 return not (isinf(x) or isnan(x))

330

331

332 def isfinite(obj):

333 '''Check a finite C{scalar} or C{complex} value.

334

335 @arg obj: Value (C{scalar} or C{complex}).

336

337 @return: C{False} if B{C{obj}} is C{INF}, C{NINF}

338 or C{NAN}, C{True} otherwise.

339

340 @raise TypeError: Non-scalar and non-complex B{C{obj}}.

341 '''

342 try:

343 return (obj not in _INF_NAN_NINF) and _isfinite(obj)

344 except Exception as x:

345 if iscomplex(obj): # _isfinite(complex) thows TypeError

346 return isfinite(obj.real) and isfinite(obj.imag)

347 raise _xError(x, Fmt.PAREN(isfinite.__name__, obj))

348

349

350 def isint0(obj, both=False):

351 '''Check for L{INT0} or C{int(0)} value.

352

353 @arg obj: The object (any C{type}).

354 @kwarg both: If C{true}, also check C{float(0)} (C{bool}).

355

356 @return: C{True} if B{C{obj}} is L{INT0}, C{int(0)} or

357 C{float(0)}, C{False} otherwise.

358 '''

359 return (obj is INT0 or obj is int(0) or

360 bool(both and (not obj) and isint(obj, both=True))) and \

361 not isbool(obj)

362

363

364 def isnear0(x, eps0=EPS0):

365 '''Is B{C{x}} near I{zero} within a tolerance?

366

367 @arg x: Value (C{scalar}).

368 @kwarg eps0: Near-I{zero} tolerance (C{EPS0}).

369

370 @return: C{True} if C{abs(B{x}) < B{eps0}},

371 C{False} otherwise.

372

373 @see: Function L{isnon0}.

374 '''

375 return bool(eps0 > x > -eps0)

376

377

378 def isnear1(x, eps1=EPS0):

379 '''Is B{C{x}} near I{one} within a tolerance?

380

381 @arg x: Value (C{scalar}).

382 @kwarg eps1: Near-I{one} tolerance (C{EPS0}).

383

384 @return: C{isnear0(B{x} - 1, eps0=B{eps1})}.

385

386 @see: Function L{isnear0}.

387 '''

388 return bool(eps1 > (x - _1_0) > -eps1)

389

390

391 def isnear90(x, eps90=EPS0):

392 '''Is B{C{x}} near I{90} within a tolerance?

393

394 @arg x: Value (C{scalar}).

395 @kwarg eps90: Near-I{90} tolerance (C{EPS0}).

396

397 @return: C{isnear0(B{x} - 90, eps0=eps90)}.

398

399 @see: Function L{isnear0}.

400 '''

401 return bool(eps90 > (x - _90_0) > -eps90)

402

403

404 def isneg0(x):

405 '''Check for L{NEG0}, negative C{0.0}.

406

407 @arg x: Value (C{scalar}).

408

409 @return: C{True} if B{C{x}} is C{NEG0} or C{-0.0},

410 C{False} otherwise.

411 '''

412 return (not x) and _copysign(1, x) < 0

413# and str(x).startswith(_MINUS_)

414

415

416 def isninf(x):

417 '''Check for L{NINF}, negative C{INF}.

418

419 @arg x: Value (C{scalar}).

420

421 @return: C{True} if B{C{x}} is C{NINF} or C{-inf},

422 C{False} otherwise.

423 '''

424 return x is NINF or (x < 0 and not isfinite(x))

425

426

427 def isnon0(x, eps0=EPS0):

428 '''Is B{C{x}} non-zero with a tolerance?

429

430 @arg x: Value (C{scalar}).

431 @kwarg eps0: Non-zero tolerance (C{EPS0}).

432

433 @return: C{True} if C{abs(B{x}) > B{eps0}},

434 C{False} otherwise.

435

436 @see: Function L{isnear0}.

437 '''

438 return not bool(eps0 > x > -eps0) # not isnear0

439

440

441 def _off90(lat):

442 '''(INTERNAL) Off 90.0 for .gars and .wgrs.

443 '''

444 return max(min(lat, _89_999_), -_89_999_)

445

446

447 try:

448 from math import remainder

449 except ImportError: # Python 3.6-

450 from math import fmod as _fmod

451

452 def remainder(x, y):

453 '''Mimick Python 3.7+ C{math.remainder}.

454 '''

455 if isnan(y):

456 x = NAN

457 elif x and not isnan(x):

458 y = fabs(y)

459 x = _fmod(x, y)

460 h = _0_5 * y

461 if x >= h:

462 x -= y

463 elif x < -h:

464 x += y

465 return x # keep signed 0.0

466

467

468 def _umod_360(deg):

469 '''(INTERNAL) Non-negative C{deg} modulo 360, basic C{.utily.wrap360}.

470 '''

471 return (deg % _360_0) or _0_0

472

473

474 def _umod_PI2(rad):

475 '''(INTERNAL) Non-negative C{rad} modulo PI2, basic C{.utily.wrapPI2}.

476 '''

477 return (rad % PI2) or _0_0

478

479

480 if __name__ == '__main__':

481

482 from pygeodesy import itemsorted, printf

483

484 t = n = v = []

485 for n, v in itemsorted(locals()):

486 if isinstance(v, (Float, Int, Radius)):

487 printf('%9s: %r', n, v.toRepr(std=False))

488 if v.name != n:

489 raise AssertionError('%r != %r' % (n, v))

490 if v.name is not n:

491 raise AssertionError('%r is not %r' % (n, v))

492 if not n.startswith(_UNDER_):

493 t.append(n)

494 t.append(float_.__name__)

495 printf('__all__ = %r', tuple(t))

496

497# **) MIT License

498#

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

500#

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

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

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

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