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# Copyright (c) 2010 Python Software Foundation. All Rights Reserved.
# Adapted from Python's Lib/test/test_strtod.py (by Mark Dickinson)
# More test cases for deccheck.py.
import random
TEST_SIZE = 2
def test_short_halfway_cases():
# exact halfway cases with a small number of significant digits
for k in 0, 5, 10, 15, 20:
# upper = smallest integer >= 2**54/5**k
upper = -(-2**54//5**k)
# lower = smallest odd number >= 2**53/5**k
lower = -(-2**53//5**k)
if lower % 2 == 0:
lower += 1
for i in range(10 * TEST_SIZE):
# Select a random odd n in [2**53/5**k,
# 2**54/5**k). Then n * 10**k gives a halfway case
# with small number of significant digits.
n, e = random.randrange(lower, upper, 2), k
# Remove any additional powers of 5.
while n % 5 == 0:
n, e = n // 5, e + 1
assert n % 10 in (1, 3, 7, 9)
# Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
# until n * 2**p2 has more than 20 significant digits.
digits, exponent = n, e
while digits < 10**20:
s = '{}e{}'.format(digits, exponent)
yield s
# Same again, but with extra trailing zeros.
s = '{}e{}'.format(digits * 10**40, exponent - 40)
yield s
digits *= 2
# Try numbers of the form n * 5**p2 * 10**(e - p5), p5
# >= 0, with n * 5**p5 < 10**20.
digits, exponent = n, e
while digits < 10**20:
s = '{}e{}'.format(digits, exponent)
yield s
# Same again, but with extra trailing zeros.
s = '{}e{}'.format(digits * 10**40, exponent - 40)
yield s
digits *= 5
exponent -= 1
def test_halfway_cases():
# test halfway cases for the round-half-to-even rule
for i in range(1000):
for j in range(TEST_SIZE):
# bit pattern for a random finite positive (or +0.0) float
bits = random.randrange(2047*2**52)
# convert bit pattern to a number of the form m * 2**e
e, m = divmod(bits, 2**52)
if e:
m, e = m + 2**52, e - 1
e -= 1074
# add 0.5 ulps
m, e = 2*m + 1, e - 1
# convert to a decimal string
if e >= 0:
digits = m << e
exponent = 0
else:
# m * 2**e = (m * 5**-e) * 10**e
digits = m * 5**-e
exponent = e
s = '{}e{}'.format(digits, exponent)
yield s
def test_boundaries():
# boundaries expressed as triples (n, e, u), where
# n*10**e is an approximation to the boundary value and
# u*10**e is 1ulp
boundaries = [
(10000000000000000000, -19, 1110), # a power of 2 boundary (1.0)
(17976931348623159077, 289, 1995), # overflow boundary (2.**1024)
(22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022)
(0, -327, 4941), # zero
]
for n, e, u in boundaries:
for j in range(1000):
for i in range(TEST_SIZE):
digits = n + random.randrange(-3*u, 3*u)
exponent = e
s = '{}e{}'.format(digits, exponent)
yield s
n *= 10
u *= 10
e -= 1
def test_underflow_boundary():
# test values close to 2**-1075, the underflow boundary; similar
# to boundary_tests, except that the random error doesn't scale
# with n
for exponent in range(-400, -320):
base = 10**-exponent // 2**1075
for j in range(TEST_SIZE):
digits = base + random.randrange(-1000, 1000)
s = '{}e{}'.format(digits, exponent)
yield s
def test_bigcomp():
for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
dig10 = 10**ndigs
for i in range(100 * TEST_SIZE):
digits = random.randrange(dig10)
exponent = random.randrange(-400, 400)
s = '{}e{}'.format(digits, exponent)
yield s
def test_parsing():
# make '0' more likely to be chosen than other digits
digits = '000000123456789'
signs = ('+', '-', '')
# put together random short valid strings
# \d*[.\d*]?e
for i in range(1000):
for j in range(TEST_SIZE):
s = random.choice(signs)
intpart_len = random.randrange(5)
s += ''.join(random.choice(digits) for _ in range(intpart_len))
if random.choice([True, False]):
s += '.'
fracpart_len = random.randrange(5)
s += ''.join(random.choice(digits)
for _ in range(fracpart_len))
else:
fracpart_len = 0
if random.choice([True, False]):
s += random.choice(['e', 'E'])
s += random.choice(signs)
exponent_len = random.randrange(1, 4)
s += ''.join(random.choice(digits)
for _ in range(exponent_len))
if intpart_len + fracpart_len:
yield s
test_particular = [
# squares
'1.00000000100000000025',
'1.0000000000000000000000000100000000000000000000000' #...
'00025',
'1.0000000000000000000000000000000000000000000010000' #...
'0000000000000000000000000000000000000000025',
'1.0000000000000000000000000000000000000000000000000' #...
'000001000000000000000000000000000000000000000000000' #...
'000000000025',
'0.99999999900000000025',
'0.9999999999999999999999999999999999999999999999999' #...
'999000000000000000000000000000000000000000000000000' #...
'000025',
'0.9999999999999999999999999999999999999999999999999' #...
'999999999999999999999999999999999999999999999999999' #...
'999999999999999999999999999999999999999990000000000' #...
'000000000000000000000000000000000000000000000000000' #...
'000000000000000000000000000000000000000000000000000' #...
'0000000000000000000000000000025',
'1.0000000000000000000000000000000000000000000000000' #...
'000000000000000000000000000000000000000000000000000' #...
'100000000000000000000000000000000000000000000000000' #...
'000000000000000000000000000000000000000000000000001',
'1.0000000000000000000000000000000000000000000000000' #...
'000000000000000000000000000000000000000000000000000' #...
'500000000000000000000000000000000000000000000000000' #...
'000000000000000000000000000000000000000000000000005',
'1.0000000000000000000000000000000000000000000000000' #...
'000000000100000000000000000000000000000000000000000' #...
'000000000000000000250000000000000002000000000000000' #...
'000000000000000000000000000000000000000000010000000' #...
'000000000000000000000000000000000000000000000000000' #...
'0000000000000000001',
'1.0000000000000000000000000000000000000000000000000' #...
'000000000100000000000000000000000000000000000000000' #...
'000000000000000000249999999999999999999999999999999' #...
'999999999999979999999999999999999999999999999999999' #...
'999999999999999999999900000000000000000000000000000' #...
'000000000000000000000000000000000000000000000000000' #...
'00000000000000000000000001',
'0.9999999999999999999999999999999999999999999999999' #...
'999999999900000000000000000000000000000000000000000' #...
'000000000000000000249999999999999998000000000000000' #...
'000000000000000000000000000000000000000000010000000' #...
'000000000000000000000000000000000000000000000000000' #...
'0000000000000000001',
'0.9999999999999999999999999999999999999999999999999' #...
'999999999900000000000000000000000000000000000000000' #...
'000000000000000000250000001999999999999999999999999' #...
'999999999999999999999999999999999990000000000000000' #...
'000000000000000000000000000000000000000000000000000' #...
'1',
# tough cases for ln etc.
'1.000000000000000000000000000000000000000000000000' #...
'00000000000000000000000000000000000000000000000000' #...
'00100000000000000000000000000000000000000000000000' #...
'00000000000000000000000000000000000000000000000000' #...
'0001',
'0.999999999999999999999999999999999999999999999999' #...
'99999999999999999999999999999999999999999999999999' #...
'99899999999999999999999999999999999999999999999999' #...
'99999999999999999999999999999999999999999999999999' #...
'99999999999999999999999999999999999999999999999999' #...
'9999'
]
TESTCASES = [
[x for x in test_short_halfway_cases()],
[x for x in test_halfway_cases()],
[x for x in test_boundaries()],
[x for x in test_underflow_boundary()],
[x for x in test_bigcomp()],
[x for x in test_parsing()],
test_particular
]
def un_randfloat():
for i in range(1000):
l = random.choice(TESTCASES[:6])
yield random.choice(l)
for v in test_particular:
yield v
def bin_randfloat():
for i in range(1000):
l1 = random.choice(TESTCASES)
l2 = random.choice(TESTCASES)
yield random.choice(l1), random.choice(l2)
def tern_randfloat():
for i in range(1000):
l1 = random.choice(TESTCASES)
l2 = random.choice(TESTCASES)
l3 = random.choice(TESTCASES)
yield random.choice(l1), random.choice(l2), random.choice(l3)
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