/usr/lib/python2.7/dist-packages/mpmath/tests/test_power.py is in python-mpmath 0.19-3.
This file is owned by root:root, with mode 0o644.
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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 | from mpmath import *
from mpmath.libmp import *
import random
def test_fractional_pow():
mp.dps = 15
assert mpf(16) ** 2.5 == 1024
assert mpf(64) ** 0.5 == 8
assert mpf(64) ** -0.5 == 0.125
assert mpf(16) ** -2.5 == 0.0009765625
assert (mpf(10) ** 0.5).ae(3.1622776601683791)
assert (mpf(10) ** 2.5).ae(316.2277660168379)
assert (mpf(10) ** -0.5).ae(0.31622776601683794)
assert (mpf(10) ** -2.5).ae(0.0031622776601683794)
assert (mpf(10) ** 0.3).ae(1.9952623149688795)
assert (mpf(10) ** -0.3).ae(0.50118723362727224)
def test_pow_integer_direction():
"""
Test that inexact integer powers are rounded in the right
direction.
"""
random.seed(1234)
for prec in [10, 53, 200]:
for i in range(50):
a = random.randint(1<<(prec-1), 1<<prec)
b = random.randint(2, 100)
ab = a**b
# note: could actually be exact, but that's very unlikely!
assert to_int(mpf_pow(from_int(a), from_int(b), prec, round_down)) < ab
assert to_int(mpf_pow(from_int(a), from_int(b), prec, round_up)) > ab
def test_pow_epsilon_rounding():
"""
Stress test directed rounding for powers with integer exponents.
Basically, we look at the following cases:
>>> 1.0001 ** -5 # doctest: +SKIP
0.99950014996500702
>>> 0.9999 ** -5 # doctest: +SKIP
1.000500150035007
>>> (-1.0001) ** -5 # doctest: +SKIP
-0.99950014996500702
>>> (-0.9999) ** -5 # doctest: +SKIP
-1.000500150035007
>>> 1.0001 ** -6 # doctest: +SKIP
0.99940020994401269
>>> 0.9999 ** -6 # doctest: +SKIP
1.0006002100560125
>>> (-1.0001) ** -6 # doctest: +SKIP
0.99940020994401269
>>> (-0.9999) ** -6 # doctest: +SKIP
1.0006002100560125
etc.
We run the tests with values a very small epsilon away from 1:
small enough that the result is indistinguishable from 1 when
rounded to nearest at the output precision. We check that the
result is not erroneously rounded to 1 in cases where the
rounding should be done strictly away from 1.
"""
def powr(x, n, r):
return make_mpf(mpf_pow_int(x._mpf_, n, mp.prec, r))
for (inprec, outprec) in [(100, 20), (5000, 3000)]:
mp.prec = inprec
pos10001 = mpf(1) + mpf(2)**(-inprec+5)
pos09999 = mpf(1) - mpf(2)**(-inprec+5)
neg10001 = -pos10001
neg09999 = -pos09999
mp.prec = outprec
r = round_up
assert powr(pos10001, 5, r) > 1
assert powr(pos09999, 5, r) == 1
assert powr(neg10001, 5, r) < -1
assert powr(neg09999, 5, r) == -1
assert powr(pos10001, 6, r) > 1
assert powr(pos09999, 6, r) == 1
assert powr(neg10001, 6, r) > 1
assert powr(neg09999, 6, r) == 1
assert powr(pos10001, -5, r) == 1
assert powr(pos09999, -5, r) > 1
assert powr(neg10001, -5, r) == -1
assert powr(neg09999, -5, r) < -1
assert powr(pos10001, -6, r) == 1
assert powr(pos09999, -6, r) > 1
assert powr(neg10001, -6, r) == 1
assert powr(neg09999, -6, r) > 1
r = round_down
assert powr(pos10001, 5, r) == 1
assert powr(pos09999, 5, r) < 1
assert powr(neg10001, 5, r) == -1
assert powr(neg09999, 5, r) > -1
assert powr(pos10001, 6, r) == 1
assert powr(pos09999, 6, r) < 1
assert powr(neg10001, 6, r) == 1
assert powr(neg09999, 6, r) < 1
assert powr(pos10001, -5, r) < 1
assert powr(pos09999, -5, r) == 1
assert powr(neg10001, -5, r) > -1
assert powr(neg09999, -5, r) == -1
assert powr(pos10001, -6, r) < 1
assert powr(pos09999, -6, r) == 1
assert powr(neg10001, -6, r) < 1
assert powr(neg09999, -6, r) == 1
r = round_ceiling
assert powr(pos10001, 5, r) > 1
assert powr(pos09999, 5, r) == 1
assert powr(neg10001, 5, r) == -1
assert powr(neg09999, 5, r) > -1
assert powr(pos10001, 6, r) > 1
assert powr(pos09999, 6, r) == 1
assert powr(neg10001, 6, r) > 1
assert powr(neg09999, 6, r) == 1
assert powr(pos10001, -5, r) == 1
assert powr(pos09999, -5, r) > 1
assert powr(neg10001, -5, r) > -1
assert powr(neg09999, -5, r) == -1
assert powr(pos10001, -6, r) == 1
assert powr(pos09999, -6, r) > 1
assert powr(neg10001, -6, r) == 1
assert powr(neg09999, -6, r) > 1
r = round_floor
assert powr(pos10001, 5, r) == 1
assert powr(pos09999, 5, r) < 1
assert powr(neg10001, 5, r) < -1
assert powr(neg09999, 5, r) == -1
assert powr(pos10001, 6, r) == 1
assert powr(pos09999, 6, r) < 1
assert powr(neg10001, 6, r) == 1
assert powr(neg09999, 6, r) < 1
assert powr(pos10001, -5, r) < 1
assert powr(pos09999, -5, r) == 1
assert powr(neg10001, -5, r) == -1
assert powr(neg09999, -5, r) < -1
assert powr(pos10001, -6, r) < 1
assert powr(pos09999, -6, r) == 1
assert powr(neg10001, -6, r) < 1
assert powr(neg09999, -6, r) == 1
mp.dps = 15
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