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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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