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