157 lines
5.1 KiB
Python
157 lines
5.1 KiB
Python
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
|