144 lines
5.2 KiB
Python
144 lines
5.2 KiB
Python
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from mpmath.libmp import *
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from mpmath import mpf, mp
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from random import randint, choice, seed
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all_modes = [round_floor, round_ceiling, round_down, round_up, round_nearest]
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fb = from_bstr
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fi = from_int
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ff = from_float
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def test_div_1_3():
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a = fi(1)
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b = fi(3)
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c = fi(-1)
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# floor rounds down, ceiling rounds up
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assert mpf_div(a, b, 7, round_floor) == fb('0.01010101')
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assert mpf_div(a, b, 7, round_ceiling) == fb('0.01010110')
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assert mpf_div(a, b, 7, round_down) == fb('0.01010101')
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assert mpf_div(a, b, 7, round_up) == fb('0.01010110')
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assert mpf_div(a, b, 7, round_nearest) == fb('0.01010101')
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# floor rounds up, ceiling rounds down
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assert mpf_div(c, b, 7, round_floor) == fb('-0.01010110')
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assert mpf_div(c, b, 7, round_ceiling) == fb('-0.01010101')
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assert mpf_div(c, b, 7, round_down) == fb('-0.01010101')
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assert mpf_div(c, b, 7, round_up) == fb('-0.01010110')
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assert mpf_div(c, b, 7, round_nearest) == fb('-0.01010101')
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def test_mpf_divi_1_3():
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a = 1
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b = fi(3)
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c = -1
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assert mpf_rdiv_int(a, b, 7, round_floor) == fb('0.01010101')
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assert mpf_rdiv_int(a, b, 7, round_ceiling) == fb('0.01010110')
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assert mpf_rdiv_int(a, b, 7, round_down) == fb('0.01010101')
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assert mpf_rdiv_int(a, b, 7, round_up) == fb('0.01010110')
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assert mpf_rdiv_int(a, b, 7, round_nearest) == fb('0.01010101')
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assert mpf_rdiv_int(c, b, 7, round_floor) == fb('-0.01010110')
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assert mpf_rdiv_int(c, b, 7, round_ceiling) == fb('-0.01010101')
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assert mpf_rdiv_int(c, b, 7, round_down) == fb('-0.01010101')
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assert mpf_rdiv_int(c, b, 7, round_up) == fb('-0.01010110')
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assert mpf_rdiv_int(c, b, 7, round_nearest) == fb('-0.01010101')
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def test_div_300():
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q = fi(1000000)
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a = fi(300499999) # a/q is a little less than a half-integer
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b = fi(300500000) # b/q exactly a half-integer
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c = fi(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) == fi(300)
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assert mpf_div(b, q, 9, round_down) == fi(300)
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assert mpf_div(c, q, 9, round_down) == fi(300)
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assert mpf_div(a, q, 9, round_up) == fi(301)
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assert mpf_div(b, q, 9, round_up) == fi(301)
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assert mpf_div(c, q, 9, round_up) == fi(301)
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# Nearest even integer is down
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assert mpf_div(a, q, 9, round_nearest) == fi(300)
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assert mpf_div(b, q, 9, round_nearest) == fi(300)
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assert mpf_div(c, q, 9, round_nearest) == fi(301)
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# Nearest even integer is up
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a = fi(301499999)
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b = fi(301500000)
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c = fi(301500001)
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assert mpf_div(a, q, 9, round_nearest) == fi(301)
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assert mpf_div(b, q, 9, round_nearest) == fi(302)
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assert mpf_div(c, q, 9, round_nearest) == fi(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 = bitcount(abs(b)) - trailing(b)
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a = fi(a); b = fi(b); p = fi(p)
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for mode in all_modes:
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assert mpf_div(p, a, 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 = fb('0.101' + ('0'*200) + '1')
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b = fb('1.10101')
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c = mpf_mul(a, b, 250, round_floor) # exact
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assert mpf_div(c, b, bitcount(a[1]), round_floor) == a # exact
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assert mpf_div(c, b, 2, round_down) == fb('0.10')
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assert mpf_div(c, b, 3, round_down) == fb('0.101')
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assert mpf_div(c, b, 2, round_up) == fb('0.11')
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assert mpf_div(c, b, 3, round_up) == fb('0.110')
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assert mpf_div(c, b, 2, round_floor) == fb('0.10')
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assert mpf_div(c, b, 3, round_floor) == fb('0.101')
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assert mpf_div(c, b, 2, round_ceiling) == fb('0.11')
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assert mpf_div(c, b, 3, round_ceiling) == fb('0.110')
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# The same for negative numbers
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a = fb('-0.101' + ('0'*200) + '1')
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b = fb('1.10101')
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c = mpf_mul(a, b, 250, round_floor)
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assert mpf_div(c, b, bitcount(a[1]), round_floor) == a
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assert mpf_div(c, b, 2, round_down) == fb('-0.10')
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assert mpf_div(c, b, 3, round_up) == fb('-0.110')
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# Floor goes up, ceiling goes down
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assert mpf_div(c, b, 2, round_floor) == fb('-0.11')
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assert mpf_div(c, b, 3, round_floor) == fb('-0.110')
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assert mpf_div(c, b, 2, round_ceiling) == fb('-0.10')
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assert mpf_div(c, b, 3, round_ceiling) == fb('-0.101')
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def test_mod():
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mp.dps = 15
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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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mp.dps = 15
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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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