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@ -7,15 +7,6 @@ import random |
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import math |
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import array |
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# Used for lazy formatting of failure messages |
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class Frm(object): |
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def __init__(self, format, *args): |
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self.format = format |
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self.args = args |
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def __str__(self): |
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return self.format % self.args |
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# SHIFT should match the value in longintrepr.h for best testing. |
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SHIFT = sys.int_info.bits_per_digit |
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BASE = 2 ** SHIFT |
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@ -163,17 +154,18 @@ class LongTest(unittest.TestCase): |
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def check_division(self, x, y): |
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eq = self.assertEqual |
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q, r = divmod(x, y) |
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q2, r2 = x//y, x%y |
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pab, pba = x*y, y*x |
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eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y)) |
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eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y)) |
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eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y)) |
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eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y)) |
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if y > 0: |
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self.assertTrue(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y)) |
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else: |
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self.assertTrue(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y)) |
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with self.subTest(x=x, y=y): |
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q, r = divmod(x, y) |
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q2, r2 = x//y, x%y |
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pab, pba = x*y, y*x |
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eq(pab, pba, "multiplication does not commute") |
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eq(q, q2, "divmod returns different quotient than /") |
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eq(r, r2, "divmod returns different mod than %") |
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eq(x, q*y + r, "x != q*y + r after divmod") |
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if y > 0: |
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self.assertTrue(0 <= r < y, "bad mod from divmod") |
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else: |
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self.assertTrue(y < r <= 0, "bad mod from divmod") |
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def test_division(self): |
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digits = list(range(1, MAXDIGITS+1)) + list(range(KARATSUBA_CUTOFF, |
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@ -228,72 +220,63 @@ class LongTest(unittest.TestCase): |
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for bbits in bits: |
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if bbits < abits: |
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continue |
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b = (1 << bbits) - 1 |
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x = a * b |
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y = ((1 << (abits + bbits)) - |
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(1 << abits) - |
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(1 << bbits) + |
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1) |
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self.assertEqual(x, y, |
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Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y)) |
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with self.subTest(abits=abits, bbits=bbits): |
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b = (1 << bbits) - 1 |
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x = a * b |
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y = ((1 << (abits + bbits)) - |
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(1 << abits) - |
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(1 << bbits) + |
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1) |
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self.assertEqual(x, y) |
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def check_bitop_identities_1(self, x): |
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eq = self.assertEqual |
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eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x)) |
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eq(x | 0, x, Frm("x | 0 != x for x=%r", x)) |
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eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x)) |
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eq(x & -1, x, Frm("x & -1 != x for x=%r", x)) |
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eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x)) |
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eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x)) |
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eq(x, ~~x, Frm("x != ~~x for x=%r", x)) |
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eq(x & x, x, Frm("x & x != x for x=%r", x)) |
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eq(x | x, x, Frm("x | x != x for x=%r", x)) |
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eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x)) |
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eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x)) |
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eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x)) |
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eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x)) |
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eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x)) |
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eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x)) |
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with self.subTest(x=x): |
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eq(x & 0, 0) |
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eq(x | 0, x) |
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eq(x ^ 0, x) |
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eq(x & -1, x) |
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eq(x | -1, -1) |
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eq(x ^ -1, ~x) |
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eq(x, ~~x) |
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eq(x & x, x) |
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eq(x | x, x) |
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eq(x ^ x, 0) |
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eq(x & ~x, 0) |
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eq(x | ~x, -1) |
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eq(x ^ ~x, -1) |
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eq(-x, 1 + ~x) |
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eq(-x, ~(x-1)) |
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for n in range(2*SHIFT): |
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p2 = 2 ** n |
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eq(x << n >> n, x, |
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Frm("x << n >> n != x for x=%r, n=%r", (x, n))) |
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eq(x // p2, x >> n, |
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Frm("x // p2 != x >> n for x=%r n=%r p2=%r", (x, n, p2))) |
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eq(x * p2, x << n, |
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Frm("x * p2 != x << n for x=%r n=%r p2=%r", (x, n, p2))) |
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eq(x & -p2, x >> n << n, |
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Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", (x, n, p2))) |
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eq(x & -p2, x & ~(p2 - 1), |
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Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", (x, n, p2))) |
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with self.subTest(x=x, n=n, p2=p2): |
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eq(x << n >> n, x) |
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eq(x // p2, x >> n) |
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eq(x * p2, x << n) |
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eq(x & -p2, x >> n << n) |
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eq(x & -p2, x & ~(p2 - 1)) |
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def check_bitop_identities_2(self, x, y): |
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eq = self.assertEqual |
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eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", (x, y))) |
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eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", (x, y))) |
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eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", (x, y))) |
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eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", (x, y))) |
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eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", (x, y))) |
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eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", (x, y))) |
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eq(x ^ y, (x | y) & ~(x & y), |
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Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", (x, y))) |
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eq(x ^ y, (x & ~y) | (~x & y), |
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Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", (x, y))) |
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eq(x ^ y, (x | y) & (~x | ~y), |
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Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", (x, y))) |
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with self.subTest(x=x, y=y): |
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eq(x & y, y & x) |
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eq(x | y, y | x) |
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eq(x ^ y, y ^ x) |
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eq(x ^ y ^ x, y) |
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eq(x & y, ~(~x | ~y)) |
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eq(x | y, ~(~x & ~y)) |
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eq(x ^ y, (x | y) & ~(x & y)) |
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eq(x ^ y, (x & ~y) | (~x & y)) |
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eq(x ^ y, (x | y) & (~x | ~y)) |
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def check_bitop_identities_3(self, x, y, z): |
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eq = self.assertEqual |
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eq((x & y) & z, x & (y & z), |
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Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", (x, y, z))) |
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eq((x | y) | z, x | (y | z), |
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Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", (x, y, z))) |
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eq((x ^ y) ^ z, x ^ (y ^ z), |
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Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", (x, y, z))) |
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eq(x & (y | z), (x & y) | (x & z), |
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Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", (x, y, z))) |
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eq(x | (y & z), (x | y) & (x | z), |
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Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", (x, y, z))) |
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with self.subTest(x=x, y=y, z=z): |
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eq((x & y) & z, x & (y & z)) |
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eq((x | y) | z, x | (y | z)) |
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eq((x ^ y) ^ z, x ^ (y ^ z)) |
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eq(x & (y | z), (x & y) | (x & z)) |
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eq(x | (y & z), (x | y) & (x | z)) |
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def test_bitop_identities(self): |
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for x in special: |
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@ -324,11 +307,11 @@ class LongTest(unittest.TestCase): |
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def check_format_1(self, x): |
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for base, mapper in (2, bin), (8, oct), (10, str), (10, repr), (16, hex): |
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got = mapper(x) |
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expected = self.slow_format(x, base) |
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msg = Frm("%s returned %r but expected %r for %r", |
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mapper.__name__, got, expected, x) |
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self.assertEqual(got, expected, msg) |
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self.assertEqual(int(got, 0), x, Frm('int("%s", 0) != %r', got, x)) |
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with self.subTest(x=x, mapper=mapper.__name__): |
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expected = self.slow_format(x, base) |
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self.assertEqual(got, expected) |
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with self.subTest(got=got): |
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self.assertEqual(int(got, 0), x) |
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def test_format(self): |
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for x in special: |
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@ -627,14 +610,15 @@ class LongTest(unittest.TestCase): |
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for y in cases: |
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Ry = Rat(y) |
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Rcmp = (Rx > Ry) - (Rx < Ry) |
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xycmp = (x > y) - (x < y) |
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eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp)) |
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eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp)) |
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eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp)) |
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eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp)) |
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eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp)) |
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eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp)) |
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eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp)) |
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with self.subTest(x=x, y=y, Rcmp=Rcmp): |
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xycmp = (x > y) - (x < y) |
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eq(Rcmp, xycmp) |
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eq(x == y, Rcmp == 0) |
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eq(x != y, Rcmp != 0) |
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eq(x < y, Rcmp < 0) |
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eq(x <= y, Rcmp <= 0) |
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eq(x > y, Rcmp > 0) |
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eq(x >= y, Rcmp >= 0) |
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def test__format__(self): |
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self.assertEqual(format(123456789, 'd'), '123456789') |
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