wehub-resource-sync
140 lines
6.0 KiB
Python
140 lines
6.0 KiB
Python
from random import choice, randint, seed
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from mpmath import mpf
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from mpmath.libmp import (from_int, from_str, mpf_div, mpf_mul, round_ceiling,
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round_down, round_floor, round_nearest, round_up)
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from mpmath.libmp.libintmath import trailing
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from mpmath.libmp.libmpf import mpf_rdiv_int
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def test_div_1_3():
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a = from_int(1)
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b = from_int(3)
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c = from_int(-1)
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# floor rounds down, ceiling rounds up
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assert mpf_div(a, b, 7, round_floor) == from_str('0.01010101', base=2)
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assert mpf_div(a, b, 7, round_ceiling) == from_str('0.01010110', base=2)
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assert mpf_div(a, b, 7, round_down) == from_str('0.01010101', base=2)
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assert mpf_div(a, b, 7, round_up) == from_str('0.01010110', base=2)
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assert mpf_div(a, b, 7, round_nearest) == from_str('0.01010101', base=2)
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# floor rounds up, ceiling rounds down
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assert mpf_div(c, b, 7, round_floor) == from_str('-0.01010110', base=2)
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assert mpf_div(c, b, 7, round_ceiling) == from_str('-0.01010101', base=2)
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assert mpf_div(c, b, 7, round_down) == from_str('-0.01010101', base=2)
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assert mpf_div(c, b, 7, round_up) == from_str('-0.01010110', base=2)
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assert mpf_div(c, b, 7, round_nearest) == from_str('-0.01010101', base=2)
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def test_mpf_divi_1_3():
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a = 1
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b = from_int(3)
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c = -1
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assert mpf_rdiv_int(a, b, 7, round_floor) == from_str('0.01010101', base=2)
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assert mpf_rdiv_int(a, b, 7, round_ceiling) == from_str('0.01010110', base=2)
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assert mpf_rdiv_int(a, b, 7, round_down) == from_str('0.01010101', base=2)
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assert mpf_rdiv_int(a, b, 7, round_up) == from_str('0.01010110', base=2)
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assert mpf_rdiv_int(a, b, 7, round_nearest) == from_str('0.01010101', base=2)
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assert mpf_rdiv_int(c, b, 7, round_floor) == from_str('-0.01010110', base=2)
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assert mpf_rdiv_int(c, b, 7, round_ceiling) == from_str('-0.01010101', base=2)
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assert mpf_rdiv_int(c, b, 7, round_down) == from_str('-0.01010101', base=2)
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assert mpf_rdiv_int(c, b, 7, round_up) == from_str('-0.01010110', base=2)
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assert mpf_rdiv_int(c, b, 7, round_nearest) == from_str('-0.01010101', base=2)
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def test_div_300():
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q = from_int(1000000)
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a = from_int(300499999) # a/q is a little less than a half-integer
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b = from_int(300500000) # b/q exactly a half-integer
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c = from_int(300500001) # c/q is a little more than a half-integer
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# Check nearest integer rounding (prec=9 as 2**8 < 300 < 2**9)
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assert mpf_div(a, q, 9, round_down) == from_int(300)
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assert mpf_div(b, q, 9, round_down) == from_int(300)
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assert mpf_div(c, q, 9, round_down) == from_int(300)
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assert mpf_div(a, q, 9, round_up) == from_int(301)
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assert mpf_div(b, q, 9, round_up) == from_int(301)
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assert mpf_div(c, q, 9, round_up) == from_int(301)
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# Nearest even integer is down
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assert mpf_div(a, q, 9, round_nearest) == from_int(300)
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assert mpf_div(b, q, 9, round_nearest) == from_int(300)
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assert mpf_div(c, q, 9, round_nearest) == from_int(301)
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# Nearest even integer is up
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a = from_int(301499999)
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b = from_int(301500000)
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c = from_int(301500001)
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assert mpf_div(a, q, 9, round_nearest) == from_int(301)
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assert mpf_div(b, q, 9, round_nearest) == from_int(302)
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assert mpf_div(c, q, 9, round_nearest) == from_int(302)
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def test_tight_integer_division():
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# Test that integer division at tightest possible precision is exact
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N = 100
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seed(1)
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for i in range(N):
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a = choice([1, -1]) * randint(1, 1<<randint(10, 100))
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b = choice([1, -1]) * randint(1, 1<<randint(10, 100))
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p = a * b
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width = b.bit_length() - trailing(b)
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a = from_int(a); b = from_int(b); p = from_int(p)
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for mode in [round_floor, round_ceiling, round_down,
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round_up, round_nearest]:
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assert mpf_div(p, a, int(width), mode) == b
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def test_epsilon_rounding():
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# Verify that mpf_div uses infinite precision; this result will
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# appear to be exactly 0.101 to a near-sighted algorithm
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a = from_str('0.101' + ('0'*200) + '1', base=2)
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b = from_str('1.10101', base=2)
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c = mpf_mul(a, b, 250, round_floor) # exact
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assert mpf_div(c, b, a[1].bit_length(), round_floor) == a # exact
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assert mpf_div(c, b, 2, round_down) == from_str('0.10', base=2)
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assert mpf_div(c, b, 3, round_down) == from_str('0.101', base=2)
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assert mpf_div(c, b, 2, round_up) == from_str('0.11', base=2)
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assert mpf_div(c, b, 3, round_up) == from_str('0.110', base=2)
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assert mpf_div(c, b, 2, round_floor) == from_str('0.10', base=2)
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assert mpf_div(c, b, 3, round_floor) == from_str('0.101', base=2)
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assert mpf_div(c, b, 2, round_ceiling) == from_str('0.11', base=2)
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assert mpf_div(c, b, 3, round_ceiling) == from_str('0.110', base=2)
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# The same for negative numbers
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a = from_str('-0.101' + ('0'*200) + '1', base=2)
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b = from_str('1.10101', base=2)
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c = mpf_mul(a, b, 250, round_floor)
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assert mpf_div(c, b, a[1].bit_length(), round_floor) == a
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assert mpf_div(c, b, 2, round_down) == from_str('-0.10', base=2)
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assert mpf_div(c, b, 3, round_up) == from_str('-0.110', base=2)
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# Floor goes up, ceiling goes down
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assert mpf_div(c, b, 2, round_floor) == from_str('-0.11', base=2)
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assert mpf_div(c, b, 3, round_floor) == from_str('-0.110', base=2)
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assert mpf_div(c, b, 2, round_ceiling) == from_str('-0.10', base=2)
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assert mpf_div(c, b, 3, round_ceiling) == from_str('-0.101', base=2)
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def test_mod():
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assert mpf(234) % 1 == 0
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assert mpf(-3) % 256 == 253
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assert mpf(0.25) % 23490.5 == 0.25
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assert mpf(0.25) % -23490.5 == -23490.25
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assert mpf(-0.25) % 23490.5 == 23490.25
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assert mpf(-0.25) % -23490.5 == -0.25
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# Check that these cases are handled efficiently
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assert mpf('1e10000000000') % 1 == 0
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assert mpf('1.23e-1000000000') % 1 == mpf('1.23e-1000000000')
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# test __rmod__
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assert 3 % mpf('1.75') == 1.25
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def test_div_negative_rnd_bug():
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assert (-3) / mpf('0.1531879017645047') == mpf('-19.583791966887116')
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assert mpf('-2.6342475750861301') / mpf('0.35126216427941814') == mpf('-7.4993775104985909')
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