/usr/lib/python2.7/dist-packages/mpmath/tests/test_bitwise.py is in python-mpmath 0.19-3.
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Test bit-level integer and mpf operations
"""
from mpmath import *
from mpmath.libmp import *
def test_bitcount():
assert bitcount(0) == 0
assert bitcount(1) == 1
assert bitcount(7) == 3
assert bitcount(8) == 4
assert bitcount(2**100) == 101
assert bitcount(2**100-1) == 100
def test_trailing():
assert trailing(0) == 0
assert trailing(1) == 0
assert trailing(2) == 1
assert trailing(7) == 0
assert trailing(8) == 3
assert trailing(2**100) == 100
assert trailing(2**100-1) == 0
def test_round_down():
assert from_man_exp(0, -4, 4, round_down)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_down)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_down)[:3] == (0, 15, 0)
assert from_man_exp(0xff, -4, 4, round_down)[:3] == (0, 15, 0)
assert from_man_exp(-0xf0, -4, 4, round_down)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_down)[:3] == (1, 15, 0)
assert from_man_exp(-0xff, -4, 4, round_down)[:3] == (1, 15, 0)
def test_round_up():
assert from_man_exp(0, -4, 4, round_up)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_up)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_up)[:3] == (0, 1, 4)
assert from_man_exp(0xff, -4, 4, round_up)[:3] == (0, 1, 4)
assert from_man_exp(-0xf0, -4, 4, round_up)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_up)[:3] == (1, 1, 4)
assert from_man_exp(-0xff, -4, 4, round_up)[:3] == (1, 1, 4)
def test_round_floor():
assert from_man_exp(0, -4, 4, round_floor)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_floor)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_floor)[:3] == (0, 15, 0)
assert from_man_exp(0xff, -4, 4, round_floor)[:3] == (0, 15, 0)
assert from_man_exp(-0xf0, -4, 4, round_floor)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_floor)[:3] == (1, 1, 4)
assert from_man_exp(-0xff, -4, 4, round_floor)[:3] == (1, 1, 4)
def test_round_ceiling():
assert from_man_exp(0, -4, 4, round_ceiling)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_ceiling)[:3] == (0, 15, 0)
assert from_man_exp(0xf1, -4, 4, round_ceiling)[:3] == (0, 1, 4)
assert from_man_exp(0xff, -4, 4, round_ceiling)[:3] == (0, 1, 4)
assert from_man_exp(-0xf0, -4, 4, round_ceiling)[:3] == (1, 15, 0)
assert from_man_exp(-0xf1, -4, 4, round_ceiling)[:3] == (1, 15, 0)
assert from_man_exp(-0xff, -4, 4, round_ceiling)[:3] == (1, 15, 0)
def test_round_nearest():
assert from_man_exp(0, -4, 4, round_nearest)[:3] == (0, 0, 0)
assert from_man_exp(0xf0, -4, 4, round_nearest)[:3] == (0, 15, 0)
assert from_man_exp(0xf7, -4, 4, round_nearest)[:3] == (0, 15, 0)
assert from_man_exp(0xf8, -4, 4, round_nearest)[:3] == (0, 1, 4) # 1111.1000 -> 10000.0
assert from_man_exp(0xf9, -4, 4, round_nearest)[:3] == (0, 1, 4) # 1111.1001 -> 10000.0
assert from_man_exp(0xe8, -4, 4, round_nearest)[:3] == (0, 7, 1) # 1110.1000 -> 1110.0
assert from_man_exp(0xe9, -4, 4, round_nearest)[:3] == (0, 15, 0) # 1110.1001 -> 1111.0
assert from_man_exp(-0xf0, -4, 4, round_nearest)[:3] == (1, 15, 0)
assert from_man_exp(-0xf7, -4, 4, round_nearest)[:3] == (1, 15, 0)
assert from_man_exp(-0xf8, -4, 4, round_nearest)[:3] == (1, 1, 4)
assert from_man_exp(-0xf9, -4, 4, round_nearest)[:3] == (1, 1, 4)
assert from_man_exp(-0xe8, -4, 4, round_nearest)[:3] == (1, 7, 1)
assert from_man_exp(-0xe9, -4, 4, round_nearest)[:3] == (1, 15, 0)
def test_rounding_bugs():
# 1 less than power-of-two cases
assert from_man_exp(72057594037927935, -56, 53, round_up) == (0, 1, 0, 1)
assert from_man_exp(73786976294838205979, -65, 53, round_nearest) == (0, 1, 1, 1)
assert from_man_exp(31, 0, 4, round_up) == (0, 1, 5, 1)
assert from_man_exp(-31, 0, 4, round_floor) == (1, 1, 5, 1)
assert from_man_exp(255, 0, 7, round_up) == (0, 1, 8, 1)
assert from_man_exp(-255, 0, 7, round_floor) == (1, 1, 8, 1)
def test_rounding_issue_200():
a = from_man_exp(9867,-100)
b = from_man_exp(9867,-200)
c = from_man_exp(-1,0)
z = (1, 1023, -10, 10)
assert mpf_add(a, c, 10, 'd') == z
assert mpf_add(b, c, 10, 'd') == z
assert mpf_add(c, a, 10, 'd') == z
assert mpf_add(c, b, 10, 'd') == z
def test_perturb():
a = fone
b = from_float(0.99999999999999989)
c = from_float(1.0000000000000002)
assert mpf_perturb(a, 0, 53, round_nearest) == a
assert mpf_perturb(a, 1, 53, round_nearest) == a
assert mpf_perturb(a, 0, 53, round_up) == c
assert mpf_perturb(a, 0, 53, round_ceiling) == c
assert mpf_perturb(a, 0, 53, round_down) == a
assert mpf_perturb(a, 0, 53, round_floor) == a
assert mpf_perturb(a, 1, 53, round_up) == a
assert mpf_perturb(a, 1, 53, round_ceiling) == a
assert mpf_perturb(a, 1, 53, round_down) == b
assert mpf_perturb(a, 1, 53, round_floor) == b
a = mpf_neg(a)
b = mpf_neg(b)
c = mpf_neg(c)
assert mpf_perturb(a, 0, 53, round_nearest) == a
assert mpf_perturb(a, 1, 53, round_nearest) == a
assert mpf_perturb(a, 0, 53, round_up) == a
assert mpf_perturb(a, 0, 53, round_floor) == a
assert mpf_perturb(a, 0, 53, round_down) == b
assert mpf_perturb(a, 0, 53, round_ceiling) == b
assert mpf_perturb(a, 1, 53, round_up) == c
assert mpf_perturb(a, 1, 53, round_floor) == c
assert mpf_perturb(a, 1, 53, round_down) == a
assert mpf_perturb(a, 1, 53, round_ceiling) == a
def test_add_exact():
ff = from_float
assert mpf_add(ff(3.0), ff(2.5)) == ff(5.5)
assert mpf_add(ff(3.0), ff(-2.5)) == ff(0.5)
assert mpf_add(ff(-3.0), ff(2.5)) == ff(-0.5)
assert mpf_add(ff(-3.0), ff(-2.5)) == ff(-5.5)
assert mpf_sub(mpf_add(fone, ff(1e-100)), fone) == ff(1e-100)
assert mpf_sub(mpf_add(ff(1e-100), fone), fone) == ff(1e-100)
assert mpf_sub(mpf_add(fone, ff(-1e-100)), fone) == ff(-1e-100)
assert mpf_sub(mpf_add(ff(-1e-100), fone), fone) == ff(-1e-100)
assert mpf_add(fone, fzero) == fone
assert mpf_add(fzero, fone) == fone
assert mpf_add(fzero, fzero) == fzero
def test_long_exponent_shifts():
mp.dps = 15
# Check for possible bugs due to exponent arithmetic overflow
# in a C implementation
x = mpf(1)
for p in [32, 64]:
a = ldexp(1,2**(p-1))
b = ldexp(1,2**p)
c = ldexp(1,2**(p+1))
d = ldexp(1,-2**(p-1))
e = ldexp(1,-2**p)
f = ldexp(1,-2**(p+1))
assert (x+a) == a
assert (x+b) == b
assert (x+c) == c
assert (x+d) == x
assert (x+e) == x
assert (x+f) == x
assert (a+x) == a
assert (b+x) == b
assert (c+x) == c
assert (d+x) == x
assert (e+x) == x
assert (f+x) == x
assert (x-a) == -a
assert (x-b) == -b
assert (x-c) == -c
assert (x-d) == x
assert (x-e) == x
assert (x-f) == x
assert (a-x) == a
assert (b-x) == b
assert (c-x) == c
assert (d-x) == -x
assert (e-x) == -x
assert (f-x) == -x
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