python-mpmath 0.19-3 / usr / lib / python2.7 / dist-packages / mpmath / tests / test_basic_ops.py

This file is indexed.

/usr/lib/python2.7/dist-packages/mpmath/tests/test_basic_ops.py is in python-mpmath 0.19-3.

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
import mpmath
from mpmath import *
from mpmath.libmp import *
import random
import sys

try:
    long = long
except NameError:
    long = int

def test_type_compare():
    assert mpf(2) == mpc(2,0)
    assert mpf(0) == mpc(0)
    assert mpf(2) != mpc(2, 0.00001)
    assert mpf(2) == 2.0
    assert mpf(2) != 3.0
    assert mpf(2) == 2
    assert mpf(2) != '2.0'
    assert mpc(2) != '2.0'

def test_add():
    assert mpf(2.5) + mpf(3) == 5.5
    assert mpf(2.5) + 3 == 5.5
    assert mpf(2.5) + 3.0 == 5.5
    assert 3 + mpf(2.5) == 5.5
    assert 3.0 + mpf(2.5) == 5.5
    assert (3+0j) + mpf(2.5) == 5.5
    assert mpc(2.5) + mpf(3) == 5.5
    assert mpc(2.5) + 3 == 5.5
    assert mpc(2.5) + 3.0 == 5.5
    assert mpc(2.5) + (3+0j) == 5.5
    assert 3 + mpc(2.5) == 5.5
    assert 3.0 + mpc(2.5) == 5.5
    assert (3+0j) + mpc(2.5) == 5.5

def test_sub():
    assert mpf(2.5) - mpf(3) == -0.5
    assert mpf(2.5) - 3 == -0.5
    assert mpf(2.5) - 3.0 == -0.5
    assert 3 - mpf(2.5) == 0.5
    assert 3.0 - mpf(2.5) == 0.5
    assert (3+0j) - mpf(2.5) == 0.5
    assert mpc(2.5) - mpf(3) == -0.5
    assert mpc(2.5) - 3 == -0.5
    assert mpc(2.5) - 3.0 == -0.5
    assert mpc(2.5) - (3+0j) == -0.5
    assert 3 - mpc(2.5) == 0.5
    assert 3.0 - mpc(2.5) == 0.5
    assert (3+0j) - mpc(2.5) == 0.5

def test_mul():
    assert mpf(2.5) * mpf(3) == 7.5
    assert mpf(2.5) * 3 == 7.5
    assert mpf(2.5) * 3.0 == 7.5
    assert 3 * mpf(2.5) == 7.5
    assert 3.0 * mpf(2.5) == 7.5
    assert (3+0j) * mpf(2.5) == 7.5
    assert mpc(2.5) * mpf(3) == 7.5
    assert mpc(2.5) * 3 == 7.5
    assert mpc(2.5) * 3.0 == 7.5
    assert mpc(2.5) * (3+0j) == 7.5
    assert 3 * mpc(2.5) == 7.5
    assert 3.0 * mpc(2.5) == 7.5
    assert (3+0j) * mpc(2.5) == 7.5

def test_div():
    assert mpf(6) / mpf(3) == 2.0
    assert mpf(6) / 3 == 2.0
    assert mpf(6) / 3.0 == 2.0
    assert 6 / mpf(3) == 2.0
    assert 6.0 / mpf(3) == 2.0
    assert (6+0j) / mpf(3.0) == 2.0
    assert mpc(6) / mpf(3) == 2.0
    assert mpc(6) / 3 == 2.0
    assert mpc(6) / 3.0 == 2.0
    assert mpc(6) / (3+0j) == 2.0
    assert 6 / mpc(3) == 2.0
    assert 6.0 / mpc(3) == 2.0
    assert (6+0j) / mpc(3) == 2.0

def test_pow():
    assert mpf(6) ** mpf(3) == 216.0
    assert mpf(6) ** 3 == 216.0
    assert mpf(6) ** 3.0 == 216.0
    assert 6 ** mpf(3) == 216.0
    assert 6.0 ** mpf(3) == 216.0
    assert (6+0j) ** mpf(3.0) == 216.0
    assert mpc(6) ** mpf(3) == 216.0
    assert mpc(6) ** 3 == 216.0
    assert mpc(6) ** 3.0 == 216.0
    assert mpc(6) ** (3+0j) == 216.0
    assert 6 ** mpc(3) == 216.0
    assert 6.0 ** mpc(3) == 216.0
    assert (6+0j) ** mpc(3) == 216.0

def test_mixed_misc():
    assert 1 + mpf(3) == mpf(3) + 1 == 4
    assert 1 - mpf(3) == -(mpf(3) - 1) == -2
    assert 3 * mpf(2) == mpf(2) * 3 == 6
    assert 6 / mpf(2) == mpf(6) / 2 == 3
    assert 1.0 + mpf(3) == mpf(3) + 1.0 == 4
    assert 1.0 - mpf(3) == -(mpf(3) - 1.0) == -2
    assert 3.0 * mpf(2) == mpf(2) * 3.0 == 6
    assert 6.0 / mpf(2) == mpf(6) / 2.0 == 3

def test_add_misc():
    mp.dps = 15
    assert mpf(4) + mpf(-70) == -66
    assert mpf(1) + mpf(1.1)/80 == 1 + 1.1/80
    assert mpf((1, 10000000000)) + mpf(3) == mpf((1, 10000000000))
    assert mpf(3) + mpf((1, 10000000000)) == mpf((1, 10000000000))
    assert mpf((1, -10000000000)) + mpf(3) == mpf(3)
    assert mpf(3) + mpf((1, -10000000000)) == mpf(3)
    assert mpf(1) + 1e-15 != 1
    assert mpf(1) + 1e-20 == 1
    assert mpf(1.07e-22) + 0 == mpf(1.07e-22)
    assert mpf(0) + mpf(1.07e-22) == mpf(1.07e-22)

def test_complex_misc():
    # many more tests needed
    assert 1 + mpc(2) == 3
    assert not mpc(2).ae(2 + 1e-13)
    assert mpc(2+1e-15j).ae(2)

def test_complex_zeros():
    for a in [0,2]:
      for b in [0,3]:
        for c in [0,4]:
          for d in [0,5]:
            assert mpc(a,b)*mpc(c,d) == complex(a,b)*complex(c,d)

def test_hash():
    for i in range(-256, 256):
        assert hash(mpf(i)) == hash(i)
    assert hash(mpf(0.5)) == hash(0.5)
    assert hash(mpc(2,3)) == hash(2+3j)
    # Check that this doesn't fail
    assert hash(inf)
    # Check that overflow doesn't assign equal hashes to large numbers
    assert hash(mpf('1e1000')) != hash('1e10000')
    assert hash(mpc(100,'1e1000')) != hash(mpc(200,'1e1000'))
    from mpmath.rational import mpq
    assert hash(mp.mpq(1,3))
    assert hash(mp.mpq(0,1)) == 0
    assert hash(mp.mpq(-1,1)) == hash(-1)
    assert hash(mp.mpq(1,1)) == hash(1)
    assert hash(mp.mpq(5,1)) == hash(5)
    assert hash(mp.mpq(1,2)) == hash(0.5)
    if sys.version >= "3.2":
        assert hash(mpf(1)*2**2000) == hash(2**2000)
        assert hash(mpf(1)/2**2000) == hash(mpq(1,2**2000))

# Advanced rounding test
def test_add_rounding():
    mp.dps = 15
    a = from_float(1e-50)
    assert mpf_sub(mpf_add(fone, a, 53, round_up), fone, 53, round_up) == from_float(2.2204460492503131e-16)
    assert mpf_sub(fone, a, 53, round_up) == fone
    assert mpf_sub(fone, mpf_sub(fone, a, 53, round_down), 53, round_down) == from_float(1.1102230246251565e-16)
    assert mpf_add(fone, a, 53, round_down) == fone

def test_almost_equal():
    assert mpf(1.2).ae(mpf(1.20000001), 1e-7)
    assert not mpf(1.2).ae(mpf(1.20000001), 1e-9)
    assert not mpf(-0.7818314824680298).ae(mpf(-0.774695868667929))

def test_arithmetic_functions():
    import operator
    ops = [(operator.add, fadd), (operator.sub, fsub), (operator.mul, fmul),
        (operator.truediv, fdiv)]
    a = mpf(0.27)
    b = mpf(1.13)
    c = mpc(0.51+2.16j)
    d = mpc(1.08-0.99j)
    for x in [a,b,c,d]:
        for y in [a,b,c,d]:
            for op, fop in ops:
                if fop is not fdiv:
                    mp.prec = 200
                    z0 = op(x,y)
                mp.prec = 60
                z1 = op(x,y)
                mp.prec = 53
                z2 = op(x,y)
                assert fop(x, y, prec=60) == z1
                assert fop(x, y) == z2
                if fop is not fdiv:
                    assert fop(x, y, prec=inf) == z0
                    assert fop(x, y, dps=inf) == z0
                    assert fop(x, y, exact=True) == z0
                assert fneg(fneg(z1, exact=True), prec=inf) == z1
                assert fneg(z1) == -(+z1)
    mp.dps = 15

def test_exact_integer_arithmetic():
    # XXX: re-fix this so that all operations are tested with all rounding modes
    random.seed(0)
    for prec in [6, 10, 25, 40, 100, 250, 725]:
      for rounding in ['d', 'u', 'f', 'c', 'n']:
        mp.dps = prec
        M = 10**(prec-2)
        M2 = 10**(prec//2-2)
        for i in range(10):
            a = random.randint(-M, M)
            b = random.randint(-M, M)
            assert mpf(a, rounding=rounding) == a
            assert int(mpf(a, rounding=rounding)) == a
            assert int(mpf(str(a), rounding=rounding)) == a
            assert mpf(a) + mpf(b) == a + b
            assert mpf(a) - mpf(b) == a - b
            assert -mpf(a) == -a
            a = random.randint(-M2, M2)
            b = random.randint(-M2, M2)
            assert mpf(a) * mpf(b) == a*b
            assert mpf_mul(from_int(a), from_int(b), mp.prec, rounding) == from_int(a*b)
    mp.dps = 15

def test_odd_int_bug():
    assert to_int(from_int(3), round_nearest) == 3

def test_str_1000_digits():
    mp.dps = 1001
    # last digit may be wrong
    assert str(mpf(2)**0.5)[-10:-1] == '9518488472'[:9]
    assert str(pi)[-10:-1] == '2164201989'[:9]
    mp.dps = 15

def test_str_10000_digits():
    mp.dps = 10001
    # last digit may be wrong
    assert str(mpf(2)**0.5)[-10:-1] == '5873258351'[:9]
    assert str(pi)[-10:-1] == '5256375678'[:9]
    mp.dps = 15

def test_monitor():
    f = lambda x: x**2
    a = []
    b = []
    g = monitor(f, a.append, b.append)
    assert g(3) == 9
    assert g(4) == 16
    assert a[0] == ((3,), {})
    assert b[0] == 9

def test_nint_distance():
    assert nint_distance(mpf(-3)) == (-3, -inf)
    assert nint_distance(mpc(-3)) == (-3, -inf)
    assert nint_distance(mpf(-3.1)) == (-3, -3)
    assert nint_distance(mpf(-3.01)) == (-3, -6)
    assert nint_distance(mpf(-3.001)) == (-3, -9)
    assert nint_distance(mpf(-3.0001)) == (-3, -13)
    assert nint_distance(mpf(-2.9)) == (-3, -3)
    assert nint_distance(mpf(-2.99)) == (-3, -6)
    assert nint_distance(mpf(-2.999)) == (-3, -9)
    assert nint_distance(mpf(-2.9999)) == (-3, -13)
    assert nint_distance(mpc(-3+0.1j)) == (-3, -3)
    assert nint_distance(mpc(-3+0.01j)) == (-3, -6)
    assert nint_distance(mpc(-3.1+0.1j)) == (-3, -3)
    assert nint_distance(mpc(-3.01+0.01j)) == (-3, -6)
    assert nint_distance(mpc(-3.001+0.001j)) == (-3, -9)
    assert nint_distance(mpf(0)) == (0, -inf)
    assert nint_distance(mpf(0.01)) == (0, -6)
    assert nint_distance(mpf('1e-100')) == (0, -332)

def test_floor_ceil_nint_frac():
    mp.dps = 15
    for n in range(-10,10):
        assert floor(n) == n
        assert floor(n+0.5) == n
        assert ceil(n) == n
        assert ceil(n+0.5) == n+1
        assert nint(n) == n
        # nint rounds to even
        if n % 2 == 1:
            assert nint(n+0.5) == n+1
        else:
            assert nint(n+0.5) == n
    assert floor(inf) == inf
    assert floor(ninf) == ninf
    assert isnan(floor(nan))
    assert ceil(inf) == inf
    assert ceil(ninf) == ninf
    assert isnan(ceil(nan))
    assert nint(inf) == inf
    assert nint(ninf) == ninf
    assert isnan(nint(nan))
    assert floor(0.1) == 0
    assert floor(0.9) == 0
    assert floor(-0.1) == -1
    assert floor(-0.9) == -1
    assert floor(10000000000.1) == 10000000000
    assert floor(10000000000.9) == 10000000000
    assert floor(-10000000000.1) == -10000000000-1
    assert floor(-10000000000.9) == -10000000000-1
    assert floor(1e-100) == 0
    assert floor(-1e-100) == -1
    assert floor(1e100) == 1e100
    assert floor(-1e100) == -1e100
    assert ceil(0.1) == 1
    assert ceil(0.9) == 1
    assert ceil(-0.1) == 0
    assert ceil(-0.9) == 0
    assert ceil(10000000000.1) == 10000000000+1
    assert ceil(10000000000.9) == 10000000000+1
    assert ceil(-10000000000.1) == -10000000000
    assert ceil(-10000000000.9) == -10000000000
    assert ceil(1e-100) == 1
    assert ceil(-1e-100) == 0
    assert ceil(1e100) == 1e100
    assert ceil(-1e100) == -1e100
    assert nint(0.1) == 0
    assert nint(0.9) == 1
    assert nint(-0.1) == 0
    assert nint(-0.9) == -1
    assert nint(10000000000.1) == 10000000000
    assert nint(10000000000.9) == 10000000000+1
    assert nint(-10000000000.1) == -10000000000
    assert nint(-10000000000.9) == -10000000000-1
    assert nint(1e-100) == 0
    assert nint(-1e-100) == 0
    assert nint(1e100) == 1e100
    assert nint(-1e100) == -1e100
    assert floor(3.2+4.6j) == 3+4j
    assert ceil(3.2+4.6j) == 4+5j
    assert nint(3.2+4.6j) == 3+5j
    for n in range(-10,10):
        assert frac(n) == 0
    assert frac(0.25) == 0.25
    assert frac(1.25) == 0.25
    assert frac(2.25) == 0.25
    assert frac(-0.25) == 0.75
    assert frac(-1.25) == 0.75
    assert frac(-2.25) == 0.75
    assert frac('1e100000000000000') == 0
    u = mpf('1e-100000000000000')
    assert frac(u) == u
    assert frac(-u) == 1  # rounding!
    u = mpf('1e-400')
    assert frac(-u, prec=0) == fsub(1, u, exact=True)
    assert frac(3.25+4.75j) == 0.25+0.75j

def test_isnan_etc():
    from mpmath.rational import mpq
    assert isnan(nan) == True
    assert isnan(3) == False
    assert isnan(mpf(3)) == False
    assert isnan(inf) == False
    assert isnan(mpc(2,nan)) == True
    assert isnan(mpc(2,nan)) == True
    assert isnan(mpc(nan,nan)) == True
    assert isnan(mpc(2,2)) == False
    assert isnan(mpc(nan,inf)) == True
    assert isnan(mpc(inf,inf)) == False
    assert isnan(mpq((3,2))) == False
    assert isnan(mpq((0,1))) == False
    assert isinf(inf) == True
    assert isinf(-inf) == True
    assert isinf(3) == False
    assert isinf(nan) == False
    assert isinf(3+4j) == False
    assert isinf(mpc(inf)) == True
    assert isinf(mpc(3,inf)) == True
    assert isinf(mpc(inf,3)) == True
    assert isinf(mpc(inf,inf)) == True
    assert isinf(mpc(nan,inf)) == True
    assert isinf(mpc(inf,nan)) == True
    assert isinf(mpc(nan,nan)) == False
    assert isinf(mpq((3,2))) == False
    assert isinf(mpq((0,1))) == False
    assert isnormal(3) == True
    assert isnormal(3.5) == True
    assert isnormal(mpf(3.5)) == True
    assert isnormal(0) == False
    assert isnormal(mpf(0)) == False
    assert isnormal(0.0) == False
    assert isnormal(inf) == False
    assert isnormal(-inf) == False
    assert isnormal(nan) == False
    assert isnormal(float(inf)) == False
    assert isnormal(mpc(0,0)) == False
    assert isnormal(mpc(3,0)) == True
    assert isnormal(mpc(0,3)) == True
    assert isnormal(mpc(3,3)) == True
    assert isnormal(mpc(0,nan)) == False
    assert isnormal(mpc(0,inf)) == False
    assert isnormal(mpc(3,nan)) == False
    assert isnormal(mpc(3,inf)) == False
    assert isnormal(mpc(3,-inf)) == False
    assert isnormal(mpc(nan,0)) == False
    assert isnormal(mpc(inf,0)) == False
    assert isnormal(mpc(nan,3)) == False
    assert isnormal(mpc(inf,3)) == False
    assert isnormal(mpc(inf,nan)) == False
    assert isnormal(mpc(nan,inf)) == False
    assert isnormal(mpc(nan,nan)) == False
    assert isnormal(mpc(inf,inf)) == False
    assert isnormal(mpq((3,2))) == True
    assert isnormal(mpq((0,1))) == False
    assert isint(3) == True
    assert isint(0) == True
    assert isint(long(3)) == True
    assert isint(long(0)) == True
    assert isint(mpf(3)) == True
    assert isint(mpf(0)) == True
    assert isint(mpf(-3)) == True
    assert isint(mpf(3.2)) == False
    assert isint(3.2) == False
    assert isint(nan) == False
    assert isint(inf) == False
    assert isint(-inf) == False
    assert isint(mpc(0)) == True
    assert isint(mpc(3)) == True
    assert isint(mpc(3.2)) == False
    assert isint(mpc(3,inf)) == False
    assert isint(mpc(inf)) == False
    assert isint(mpc(3,2)) == False
    assert isint(mpc(0,2)) == False
    assert isint(mpc(3,2),gaussian=True) == True
    assert isint(mpc(3,0),gaussian=True) == True
    assert isint(mpc(0,3),gaussian=True) == True
    assert isint(3+4j) == False
    assert isint(3+4j, gaussian=True) == True
    assert isint(3+0j) == True
    assert isint(mpq((3,2))) == False
    assert isint(mpq((3,9))) == False
    assert isint(mpq((9,3))) == True
    assert isint(mpq((0,4))) == True
    assert isint(mpq((1,1))) == True
    assert isint(mpq((-1,1))) == True
    assert mp.isnpint(0) == True
    assert mp.isnpint(1) == False
    assert mp.isnpint(-1) == True
    assert mp.isnpint(-1.1) == False
    assert mp.isnpint(-1.0) == True
    assert mp.isnpint(mp.mpq(1,2)) == False
    assert mp.isnpint(mp.mpq(-1,2)) == False
    assert mp.isnpint(mp.mpq(-3,1)) == True
    assert mp.isnpint(mp.mpq(0,1)) == True
    assert mp.isnpint(mp.mpq(1,1)) == False
    assert mp.isnpint(0+0j) == True
    assert mp.isnpint(-1+0j) == True
    assert mp.isnpint(-1.1+0j) == False
    assert mp.isnpint(-1+0.1j) == False
    assert mp.isnpint(0+0.1j) == False

APT Browse - Built by Thomas Orozco.