This file is indexed.

/usr/share/pyshared/mpmath/ctx_iv.py is in python-mpmath 0.18-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
import operator

from . import libmp

from .libmp.backend import basestring

from .libmp import (
    int_types, MPZ_ONE,
    prec_to_dps, dps_to_prec, repr_dps,
    round_floor, round_ceiling,
    fzero, finf, fninf, fnan,
    mpf_le, mpf_neg,
    from_int, from_float, from_str, from_rational,
    mpi_mid, mpi_delta, mpi_str,
    mpi_abs, mpi_pos, mpi_neg, mpi_add, mpi_sub,
    mpi_mul, mpi_div, mpi_pow_int, mpi_pow,
    mpi_from_str,
    mpci_pos, mpci_neg, mpci_add, mpci_sub, mpci_mul, mpci_div, mpci_pow,
    mpci_abs, mpci_pow, mpci_exp, mpci_log,
    ComplexResult,
    mpf_hash, mpc_hash)

mpi_zero = (fzero, fzero)

from .ctx_base import StandardBaseContext

new = object.__new__

def convert_mpf_(x, prec, rounding):
    if hasattr(x, "_mpf_"): return x._mpf_
    if isinstance(x, int_types): return from_int(x, prec, rounding)
    if isinstance(x, float): return from_float(x, prec, rounding)
    if isinstance(x, basestring): return from_str(x, prec, rounding)


class ivmpf(object):
    """
    Interval arithmetic class. Precision is controlled by iv.prec.
    """

    def __new__(cls, x=0):
        return cls.ctx.convert(x)

    def __int__(self):
        a, b = self._mpi_
        if a == b:
            return int(libmp.to_int(a))
        raise ValueError

    def __hash__(self):
        a, b = self._mpi_
        if a == b:
            return mpf_hash(a)
        else:
            return hash(self._mpi_)

    @property
    def real(self): return self

    @property
    def imag(self): return self.ctx.zero

    def conjugate(self): return self

    @property
    def a(self):
        a, b = self._mpi_
        return self.ctx.make_mpf((a, a))

    @property
    def b(self):
        a, b = self._mpi_
        return self.ctx.make_mpf((b, b))

    @property
    def mid(self):
        ctx = self.ctx
        v = mpi_mid(self._mpi_, ctx.prec)
        return ctx.make_mpf((v, v))

    @property
    def delta(self):
        ctx = self.ctx
        v = mpi_delta(self._mpi_, ctx.prec)
        return ctx.make_mpf((v,v))

    @property
    def _mpci_(self):
        return self._mpi_, mpi_zero

    def _compare(*args):
        raise TypeError("no ordering relation is defined for intervals")

    __gt__ = _compare
    __le__ = _compare
    __gt__ = _compare
    __ge__ = _compare

    def __contains__(self, t):
        t = self.ctx.mpf(t)
        return (self.a <= t.a) and (t.b <= self.b)

    def __str__(self):
        return mpi_str(self._mpi_, self.ctx.prec)

    def __repr__(self):
        if self.ctx.pretty:
            return str(self)
        a, b = self._mpi_
        n = repr_dps(self.ctx.prec)
        a = libmp.to_str(a, n)
        b = libmp.to_str(b, n)
        return "mpi(%r, %r)" % (a, b)

    def _compare(s, t, cmpfun):
        if not hasattr(t, "_mpi_"):
            try:
                t = s.ctx.convert(t)
            except:
                return NotImplemented
        return cmpfun(s._mpi_, t._mpi_)

    def __eq__(s, t): return s._compare(t, libmp.mpi_eq)
    def __ne__(s, t): return s._compare(t, libmp.mpi_ne)
    def __lt__(s, t): return s._compare(t, libmp.mpi_lt)
    def __le__(s, t): return s._compare(t, libmp.mpi_le)
    def __gt__(s, t): return s._compare(t, libmp.mpi_gt)
    def __ge__(s, t): return s._compare(t, libmp.mpi_ge)

    def __abs__(self):
        return self.ctx.make_mpf(mpi_abs(self._mpi_, self.ctx.prec))
    def __pos__(self):
        return self.ctx.make_mpf(mpi_pos(self._mpi_, self.ctx.prec))
    def __neg__(self):
        return self.ctx.make_mpf(mpi_neg(self._mpi_, self.ctx.prec))

    def ae(s, t, rel_eps=None, abs_eps=None):
        return s.ctx.almosteq(s, t, rel_eps, abs_eps)

class ivmpc(object):

    def __new__(cls, re=0, im=0):
        re = cls.ctx.convert(re)
        im = cls.ctx.convert(im)
        y = new(cls)
        y._mpci_ = re._mpi_, im._mpi_
        return y

    def __hash__(self):
        (a, b), (c,d) = self._mpci_
        if a == b and c == d:
            return mpc_hash((a, c))
        else:
            return hash(self._mpci_)

    def __repr__(s):
        if s.ctx.pretty:
            return str(s)
        return "iv.mpc(%s, %s)" % (repr(s.real), repr(s.imag))

    def __str__(s):
        return "(%s + %s*j)" % (str(s.real), str(s.imag))

    @property
    def a(self):
        (a, b), (c,d) = self._mpci_
        return self.ctx.make_mpf((a, a))

    @property
    def b(self):
        (a, b), (c,d) = self._mpci_
        return self.ctx.make_mpf((b, b))

    @property
    def c(self):
        (a, b), (c,d) = self._mpci_
        return self.ctx.make_mpf((c, c))

    @property
    def d(self):
        (a, b), (c,d) = self._mpci_
        return self.ctx.make_mpf((d, d))

    @property
    def real(s):
        return s.ctx.make_mpf(s._mpci_[0])

    @property
    def imag(s):
        return s.ctx.make_mpf(s._mpci_[1])

    def conjugate(s):
        a, b = s._mpci_
        return s.ctx.make_mpc((a, mpf_neg(b)))

    def overlap(s, t):
        t = s.ctx.convert(t)
        real_overlap = (s.a <= t.a <= s.b) or (s.a <= t.b <= s.b) or (t.a <= s.a <= t.b) or (t.a <= s.b <= t.b)
        imag_overlap = (s.c <= t.c <= s.d) or (s.c <= t.d <= s.d) or (t.c <= s.c <= t.d) or (t.c <= s.d <= t.d)
        return real_overlap and imag_overlap

    def __contains__(s, t):
        t = s.ctx.convert(t)
        return t.real in s.real and t.imag in s.imag

    def _compare(s, t, ne=False):
        if not isinstance(t, s.ctx._types):
            try:
                t = s.ctx.convert(t)
            except:
                return NotImplemented
        if hasattr(t, '_mpi_'):
            tval = t._mpi_, mpi_zero
        elif hasattr(t, '_mpci_'):
            tval = t._mpci_
        if ne:
            return s._mpci_ != tval
        return s._mpci_ == tval

    def __eq__(s, t): return s._compare(t)
    def __ne__(s, t): return s._compare(t, True)

    def __lt__(s, t): raise TypeError("complex intervals cannot be ordered")
    __le__ = __gt__ = __ge__ = __lt__

    def __neg__(s): return s.ctx.make_mpc(mpci_neg(s._mpci_, s.ctx.prec))
    def __pos__(s): return s.ctx.make_mpc(mpci_pos(s._mpci_, s.ctx.prec))
    def __abs__(s): return s.ctx.make_mpf(mpci_abs(s._mpci_, s.ctx.prec))

    def ae(s, t, rel_eps=None, abs_eps=None):
        return s.ctx.almosteq(s, t, rel_eps, abs_eps)

def _binary_op(f_real, f_complex):
    def g_complex(ctx, sval, tval):
        return ctx.make_mpc(f_complex(sval, tval, ctx.prec))
    def g_real(ctx, sval, tval):
        try:
            return ctx.make_mpf(f_real(sval, tval, ctx.prec))
        except ComplexResult:
            sval = (sval, mpi_zero)
            tval = (tval, mpi_zero)
            return g_complex(ctx, sval, tval)
    def lop_real(s, t):
        ctx = s.ctx
        if not isinstance(t, ctx._types): t = ctx.convert(t)
        if hasattr(t, "_mpi_"): return g_real(ctx, s._mpi_, t._mpi_)
        if hasattr(t, "_mpci_"): return g_complex(ctx, (s._mpi_, mpi_zero), t._mpci_)
        return NotImplemented
    def rop_real(s, t):
        ctx = s.ctx
        if not isinstance(t, ctx._types): t = ctx.convert(t)
        if hasattr(t, "_mpi_"): return g_real(ctx, t._mpi_, s._mpi_)
        if hasattr(t, "_mpci_"): return g_complex(ctx, t._mpci_, (s._mpi_, mpi_zero))
        return NotImplemented
    def lop_complex(s, t):
        ctx = s.ctx
        if not isinstance(t, s.ctx._types):
            try:
                t = s.ctx.convert(t)
            except (ValueError, TypeError):
                return NotImplemented
        return g_complex(ctx, s._mpci_, t._mpci_)
    def rop_complex(s, t):
        ctx = s.ctx
        if not isinstance(t, s.ctx._types):
            t = s.ctx.convert(t)
        return g_complex(ctx, t._mpci_, s._mpci_)
    return lop_real, rop_real, lop_complex, rop_complex

ivmpf.__add__, ivmpf.__radd__, ivmpc.__add__, ivmpc.__radd__ = _binary_op(mpi_add, mpci_add)
ivmpf.__sub__, ivmpf.__rsub__, ivmpc.__sub__, ivmpc.__rsub__ = _binary_op(mpi_sub, mpci_sub)
ivmpf.__mul__, ivmpf.__rmul__, ivmpc.__mul__, ivmpc.__rmul__ = _binary_op(mpi_mul, mpci_mul)
ivmpf.__div__, ivmpf.__rdiv__, ivmpc.__div__, ivmpc.__rdiv__ = _binary_op(mpi_div, mpci_div)
ivmpf.__pow__, ivmpf.__rpow__, ivmpc.__pow__, ivmpc.__rpow__ = _binary_op(mpi_pow, mpci_pow)

ivmpf.__truediv__ = ivmpf.__div__; ivmpf.__rtruediv__ = ivmpf.__rdiv__
ivmpc.__truediv__ = ivmpc.__div__; ivmpc.__rtruediv__ = ivmpc.__rdiv__

class ivmpf_constant(ivmpf):
    def __new__(cls, f):
        self = new(cls)
        self._f = f
        return self
    def _get_mpi_(self):
        prec = self.ctx._prec[0]
        a = self._f(prec, round_floor)
        b = self._f(prec, round_ceiling)
        return a, b
    _mpi_ = property(_get_mpi_)

class MPIntervalContext(StandardBaseContext):

    def __init__(ctx):
        ctx.mpf = type('ivmpf', (ivmpf,), {})
        ctx.mpc = type('ivmpc', (ivmpc,), {})
        ctx._types = (ctx.mpf, ctx.mpc)
        ctx._constant = type('ivmpf_constant', (ivmpf_constant,), {})
        ctx._prec = [53]
        ctx._set_prec(53)
        ctx._constant._ctxdata = ctx.mpf._ctxdata = ctx.mpc._ctxdata = [ctx.mpf, new, ctx._prec]
        ctx._constant.ctx = ctx.mpf.ctx = ctx.mpc.ctx = ctx
        ctx.pretty = False
        StandardBaseContext.__init__(ctx)
        ctx._init_builtins()

    def _mpi(ctx, a, b=None):
        if b is None:
            return ctx.mpf(a)
        return ctx.mpf((a,b))

    def _init_builtins(ctx):
        ctx.one = ctx.mpf(1)
        ctx.zero = ctx.mpf(0)
        ctx.inf = ctx.mpf('inf')
        ctx.ninf = -ctx.inf
        ctx.nan = ctx.mpf('nan')
        ctx.j = ctx.mpc(0,1)
        ctx.exp = ctx._wrap_mpi_function(libmp.mpi_exp, libmp.mpci_exp)
        ctx.sqrt = ctx._wrap_mpi_function(libmp.mpi_sqrt)
        ctx.ln = ctx._wrap_mpi_function(libmp.mpi_log, libmp.mpci_log)
        ctx.cos = ctx._wrap_mpi_function(libmp.mpi_cos, libmp.mpci_cos)
        ctx.sin = ctx._wrap_mpi_function(libmp.mpi_sin, libmp.mpci_sin)
        ctx.tan = ctx._wrap_mpi_function(libmp.mpi_tan)
        ctx.gamma = ctx._wrap_mpi_function(libmp.mpi_gamma, libmp.mpci_gamma)
        ctx.loggamma = ctx._wrap_mpi_function(libmp.mpi_loggamma, libmp.mpci_loggamma)
        ctx.rgamma = ctx._wrap_mpi_function(libmp.mpi_rgamma, libmp.mpci_rgamma)
        ctx.factorial = ctx._wrap_mpi_function(libmp.mpi_factorial, libmp.mpci_factorial)
        ctx.fac = ctx.factorial

        ctx.eps = ctx._constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1))
        ctx.pi = ctx._constant(libmp.mpf_pi)
        ctx.e = ctx._constant(libmp.mpf_e)
        ctx.ln2 = ctx._constant(libmp.mpf_ln2)
        ctx.ln10 = ctx._constant(libmp.mpf_ln10)
        ctx.phi = ctx._constant(libmp.mpf_phi)
        ctx.euler = ctx._constant(libmp.mpf_euler)
        ctx.catalan = ctx._constant(libmp.mpf_catalan)
        ctx.glaisher = ctx._constant(libmp.mpf_glaisher)
        ctx.khinchin = ctx._constant(libmp.mpf_khinchin)
        ctx.twinprime = ctx._constant(libmp.mpf_twinprime)

    def _wrap_mpi_function(ctx, f_real, f_complex=None):
        def g(x, **kwargs):
            if kwargs:
                prec = kwargs.get('prec', ctx._prec[0])
            else:
                prec = ctx._prec[0]
            x = ctx.convert(x)
            if hasattr(x, "_mpi_"):
                return ctx.make_mpf(f_real(x._mpi_, prec))
            if hasattr(x, "_mpci_"):
                return ctx.make_mpc(f_complex(x._mpci_, prec))
            raise ValueError
        return g

    @classmethod
    def _wrap_specfun(cls, name, f, wrap):
        if wrap:
            def f_wrapped(ctx, *args, **kwargs):
                convert = ctx.convert
                args = [convert(a) for a in args]
                prec = ctx.prec
                try:
                    ctx.prec += 10
                    retval = f(ctx, *args, **kwargs)
                finally:
                    ctx.prec = prec
                return +retval
        else:
            f_wrapped = f
        setattr(cls, name, f_wrapped)

    def _set_prec(ctx, n):
        ctx._prec[0] = max(1, int(n))
        ctx._dps = prec_to_dps(n)

    def _set_dps(ctx, n):
        ctx._prec[0] = dps_to_prec(n)
        ctx._dps = max(1, int(n))

    prec = property(lambda ctx: ctx._prec[0], _set_prec)
    dps = property(lambda ctx: ctx._dps, _set_dps)

    def make_mpf(ctx, v):
        a = new(ctx.mpf)
        a._mpi_ = v
        return a

    def make_mpc(ctx, v):
        a = new(ctx.mpc)
        a._mpci_ = v
        return a

    def _mpq(ctx, pq):
        p, q = pq
        a = libmp.from_rational(p, q, ctx.prec, round_floor)
        b = libmp.from_rational(p, q, ctx.prec, round_ceiling)
        return ctx.make_mpf((a, b))

    def convert(ctx, x):
        if isinstance(x, (ctx.mpf, ctx.mpc)):
            return x
        if isinstance(x, ctx._constant):
            return +x
        if isinstance(x, complex) or hasattr(x, "_mpc_"):
            re = ctx.convert(x.real)
            im = ctx.convert(x.imag)
            return ctx.mpc(re,im)
        if isinstance(x, basestring):
            v = mpi_from_str(x, ctx.prec)
            return ctx.make_mpf(v)
        if hasattr(x, "_mpi_"):
            a, b = x._mpi_
        else:
            try:
                a, b = x
            except (TypeError, ValueError):
                a = b = x
            if hasattr(a, "_mpi_"):
                a = a._mpi_[0]
            else:
                a = convert_mpf_(a, ctx.prec, round_floor)
            if hasattr(b, "_mpi_"):
                b = b._mpi_[1]
            else:
                b = convert_mpf_(b, ctx.prec, round_ceiling)
        if a == fnan or b == fnan:
            a = fninf
            b = finf
        assert mpf_le(a, b), "endpoints must be properly ordered"
        return ctx.make_mpf((a, b))

    def nstr(ctx, x, n=5, **kwargs):
        x = ctx.convert(x)
        if hasattr(x, "_mpi_"):
            return libmp.mpi_to_str(x._mpi_, n, **kwargs)
        if hasattr(x, "_mpci_"):
            re = libmp.mpi_to_str(x._mpci_[0], n, **kwargs)
            im = libmp.mpi_to_str(x._mpci_[1], n, **kwargs)
            return "(%s + %s*j)" % (re, im)

    def mag(ctx, x):
        x = ctx.convert(x)
        if isinstance(x, ctx.mpc):
            return max(ctx.mag(x.real), ctx.mag(x.imag)) + 1
        a, b = libmp.mpi_abs(x._mpi_)
        sign, man, exp, bc = b
        if man:
            return exp+bc
        if b == fzero:
            return ctx.ninf
        if b == fnan:
            return ctx.nan
        return ctx.inf

    def isnan(ctx, x):
        return False

    def isinf(ctx, x):
        return x == ctx.inf

    def isint(ctx, x):
        x = ctx.convert(x)
        a, b = x._mpi_
        if a == b:
            sign, man, exp, bc = a
            if man:
                return exp >= 0
            return a == fzero
        return None

    def ldexp(ctx, x, n):
        a, b = ctx.convert(x)._mpi_
        a = libmp.mpf_shift(a, n)
        b = libmp.mpf_shift(b, n)
        return ctx.make_mpf((a,b))

    def absmin(ctx, x):
        return abs(ctx.convert(x)).a

    def absmax(ctx, x):
        return abs(ctx.convert(x)).b

    def atan2(ctx, y, x):
        y = ctx.convert(y)._mpi_
        x = ctx.convert(x)._mpi_
        return ctx.make_mpf(libmp.mpi_atan2(y,x,ctx.prec))

    def _convert_param(ctx, x):
        if isinstance(x, libmp.int_types):
            return x, 'Z'
        if isinstance(x, tuple):
            p, q = x
            return (ctx.mpf(p) / ctx.mpf(q), 'R')
        x = ctx.convert(x)
        if isinstance(x, ctx.mpf):
            return x, 'R'
        if isinstance(x, ctx.mpc):
            return x, 'C'
        raise ValueError

    def _is_real_type(ctx, z):
        return isinstance(z, ctx.mpf) or isinstance(z, int_types)

    def _is_complex_type(ctx, z):
        return isinstance(z, ctx.mpc)

    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
        coeffs = list(coeffs)
        num = range(p)
        den = range(p,p+q)
        #tol = ctx.eps
        s = t = ctx.one
        k = 0
        while 1:
            for i in num: t *= (coeffs[i]+k)
            for i in den: t /= (coeffs[i]+k)
            k += 1; t /= k; t *= z; s += t
            if t == 0:
                return s
            #if abs(t) < tol:
            #    return s
            if k > maxterms:
                raise ctx.NoConvergence


# Register with "numbers" ABC
#     We do not subclass, hence we do not use the @abstractmethod checks. While
#     this is less invasive it may turn out that we do not actually support
#     parts of the expected interfaces.  See
#     http://docs.python.org/2/library/numbers.html for list of abstract
#     methods.
try:
    import numbers
    numbers.Complex.register(ivmpc)
    numbers.Real.register(ivmpf)
except ImportError:
    pass