wehub-resource-sync
184 lines
7.8 KiB
Python
184 lines
7.8 KiB
Python
"""
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Test bit-level integer and mpf operations
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"""
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from mpmath import eps, fadd, ldexp, mp, mpc, mpf
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from mpmath.libmp import (MPZ, fone, from_float, from_man_exp, fzero, mpf_add,
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mpf_neg, mpf_sub, round_ceiling, round_down,
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round_floor, round_nearest, round_up, to_float)
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from mpmath.libmp.libintmath import trailing
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from mpmath.libmp.libmpf import mpf_perturb
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def test_trailing():
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assert trailing(0) == 0
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assert trailing(1) == 0
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assert trailing(2) == 1
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assert trailing(7) == 0
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assert trailing(8) == 3
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assert trailing(2**100) == 100
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assert trailing(2**100-1) == 0
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def test_round_down():
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assert from_man_exp(MPZ(0), -4, 4, round_down)[:3] == (0, 0, 0)
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assert from_man_exp(MPZ(0xf0), -4, 4, round_down)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xf1), -4, 4, round_down)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xff), -4, 4, round_down)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(-0xf0), -4, 4, round_down)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xf1), -4, 4, round_down)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xff), -4, 4, round_down)[:3] == (1, 15, 0)
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def test_round_up():
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assert from_man_exp(MPZ(0), -4, 4, round_up)[:3] == (0, 0, 0)
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assert from_man_exp(MPZ(0xf0), -4, 4, round_up)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xf1), -4, 4, round_up)[:3] == (0, 1, 4)
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assert from_man_exp(MPZ(0xff), -4, 4, round_up)[:3] == (0, 1, 4)
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assert from_man_exp(MPZ(-0xf0), -4, 4, round_up)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xf1), -4, 4, round_up)[:3] == (1, 1, 4)
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assert from_man_exp(MPZ(-0xff), -4, 4, round_up)[:3] == (1, 1, 4)
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def test_round_floor():
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assert from_man_exp(MPZ(0), -4, 4, round_floor)[:3] == (0, 0, 0)
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assert from_man_exp(MPZ(0xf0), -4, 4, round_floor)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xf1), -4, 4, round_floor)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xff), -4, 4, round_floor)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(-0xf0), -4, 4, round_floor)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xf1), -4, 4, round_floor)[:3] == (1, 1, 4)
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assert from_man_exp(MPZ(-0xff), -4, 4, round_floor)[:3] == (1, 1, 4)
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def test_round_ceiling():
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assert from_man_exp(MPZ(0), -4, 4, round_ceiling)[:3] == (0, 0, 0)
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assert from_man_exp(MPZ(0xf0), -4, 4, round_ceiling)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xf1), -4, 4, round_ceiling)[:3] == (0, 1, 4)
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assert from_man_exp(MPZ(0xff), -4, 4, round_ceiling)[:3] == (0, 1, 4)
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assert from_man_exp(MPZ(-0xf0), -4, 4, round_ceiling)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xf1), -4, 4, round_ceiling)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xff), -4, 4, round_ceiling)[:3] == (1, 15, 0)
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def test_round_nearest():
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assert from_man_exp(MPZ(0), -4, 4, round_nearest)[:3] == (0, 0, 0)
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assert from_man_exp(MPZ(0xf0), -4, 4, round_nearest)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xf7), -4, 4, round_nearest)[:3] == (0, 15, 0)
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assert from_man_exp(MPZ(0xf8), -4, 4, round_nearest)[:3] == (0, 1, 4) # 1111.1000 -> 10000.0
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assert from_man_exp(MPZ(0xf9), -4, 4, round_nearest)[:3] == (0, 1, 4) # 1111.1001 -> 10000.0
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assert from_man_exp(MPZ(0xe8), -4, 4, round_nearest)[:3] == (0, 7, 1) # 1110.1000 -> 1110.0
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assert from_man_exp(MPZ(0xe9), -4, 4, round_nearest)[:3] == (0, 15, 0) # 1110.1001 -> 1111.0
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assert from_man_exp(MPZ(-0xf0), -4, 4, round_nearest)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xf7), -4, 4, round_nearest)[:3] == (1, 15, 0)
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assert from_man_exp(MPZ(-0xf8), -4, 4, round_nearest)[:3] == (1, 1, 4)
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assert from_man_exp(MPZ(-0xf9), -4, 4, round_nearest)[:3] == (1, 1, 4)
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assert from_man_exp(MPZ(-0xe8), -4, 4, round_nearest)[:3] == (1, 7, 1)
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assert from_man_exp(MPZ(-0xe9), -4, 4, round_nearest)[:3] == (1, 15, 0)
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def test_rounding_bugs():
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# 1 less than power-of-two cases
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assert from_man_exp(MPZ(72057594037927935), -56, 53, round_up)[:3] == (0, 1, 0)
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assert from_man_exp(MPZ(73786976294838205979), -65, 53, round_nearest)[:3] == (0, 1, 1)
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assert from_man_exp(MPZ(31), 0, 4, round_up)[:3] == (0, 1, 5)
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assert from_man_exp(MPZ(-31), 0, 4, round_floor)[:3] == (1, 1, 5)
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assert from_man_exp(MPZ(255), 0, 7, round_up)[:3] == (0, 1, 8)
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assert from_man_exp(MPZ(-255), 0, 7, round_floor)[:3] == (1, 1, 8)
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def test_rounding_issue_200():
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a = from_man_exp(MPZ(9867),-100)
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b = from_man_exp(MPZ(9867),-200)
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c = from_man_exp(MPZ(-1),0)
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z = (1, 1023, -10)
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assert mpf_add(a, c, 10, 'd')[:3] == z
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assert mpf_add(b, c, 10, 'd')[:3] == z
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assert mpf_add(c, a, 10, 'd')[:3] == z
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assert mpf_add(c, b, 10, 'd')[:3] == z
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def test_perturb():
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a = fone
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b = from_float(0.99999999999999989)
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c = from_float(1.0000000000000002)
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assert mpf_perturb(a, 0, 53, round_nearest) == a
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assert mpf_perturb(a, 1, 53, round_nearest) == a
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assert mpf_perturb(a, 0, 53, round_up) == c
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assert mpf_perturb(a, 0, 53, round_ceiling) == c
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assert mpf_perturb(a, 0, 53, round_down) == a
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assert mpf_perturb(a, 0, 53, round_floor) == a
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assert mpf_perturb(a, 1, 53, round_up) == a
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assert mpf_perturb(a, 1, 53, round_ceiling) == a
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assert mpf_perturb(a, 1, 53, round_down) == b
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assert mpf_perturb(a, 1, 53, round_floor) == b
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a = mpf_neg(a)
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b = mpf_neg(b)
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c = mpf_neg(c)
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assert mpf_perturb(a, 0, 53, round_nearest) == a
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assert mpf_perturb(a, 1, 53, round_nearest) == a
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assert mpf_perturb(a, 0, 53, round_up) == a
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assert mpf_perturb(a, 0, 53, round_floor) == a
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assert mpf_perturb(a, 0, 53, round_down) == b
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assert mpf_perturb(a, 0, 53, round_ceiling) == b
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assert mpf_perturb(a, 1, 53, round_up) == c
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assert mpf_perturb(a, 1, 53, round_floor) == c
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assert mpf_perturb(a, 1, 53, round_down) == a
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assert mpf_perturb(a, 1, 53, round_ceiling) == a
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def test_add_exact():
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ff = from_float
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assert mpf_add(ff(3.0), ff(2.5)) == ff(5.5)
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assert mpf_add(ff(3.0), ff(-2.5)) == ff(0.5)
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assert mpf_add(ff(-3.0), ff(2.5)) == ff(-0.5)
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assert mpf_add(ff(-3.0), ff(-2.5)) == ff(-5.5)
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assert mpf_sub(mpf_add(fone, ff(1e-100)), fone) == ff(1e-100)
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assert mpf_sub(mpf_add(ff(1e-100), fone), fone) == ff(1e-100)
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assert mpf_sub(mpf_add(fone, ff(-1e-100)), fone) == ff(-1e-100)
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assert mpf_sub(mpf_add(ff(-1e-100), fone), fone) == ff(-1e-100)
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assert mpf_add(fone, fzero) == fone
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assert mpf_add(fzero, fone) == fone
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assert mpf_add(fzero, fzero) == fzero
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def test_long_exponent_shifts():
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# Check for possible bugs due to exponent arithmetic overflow
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# in a C implementation
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x = mpf(1)
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for p in [32, 64]:
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a = ldexp(1,2**(p-1))
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b = ldexp(1,2**p)
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c = ldexp(1,2**(p+1))
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d = ldexp(1,-2**(p-1))
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e = ldexp(1,-2**p)
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f = ldexp(1,-2**(p+1))
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assert (x+a) == a
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assert (x+b) == b
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assert (x+c) == c
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assert (x+d) == x
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assert (x+e) == x
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assert (x+f) == x
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assert (a+x) == a
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assert (b+x) == b
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assert (c+x) == c
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assert (d+x) == x
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assert (e+x) == x
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assert (f+x) == x
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assert (x-a) == -a
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assert (x-b) == -b
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assert (x-c) == -c
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assert (x-d) == x
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assert (x-e) == x
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assert (x-f) == x
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assert (a-x) == a
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assert (b-x) == b
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assert (c-x) == c
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assert (d-x) == -x
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assert (e-x) == -x
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assert (f-x) == -x
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def test_float_rounding():
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mp.prec = 64
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for x in [mpf(1), mpf(1)+eps, mpf(1)-eps, -mpf(1)+eps, -mpf(1)-eps]:
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fa = float(x)
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fb = float(fadd(x,0,prec=53,rounding='n'))
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assert fa == fb
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z = mpc(x,x)
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ca = complex(z)
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cb = complex(fadd(z,0,prec=53,rounding='n'))
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assert ca == cb
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for rnd in ['n', 'd', 'u', 'f', 'c']:
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fa = to_float(x._mpf_, rnd=rnd)
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fb = to_float(fadd(x,0,prec=53,rounding=rnd)._mpf_, rnd=rnd)
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assert fa == fb
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