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import sys, py, math
from rpython.rlib.rfloat import float_as_rbigint_ratio
from rpython.rlib.rfloat import round_away
from rpython.rlib.rfloat import round_double
from rpython.rlib.rfloat import erf, erfc, gamma, lgamma
from rpython.rlib.rfloat import ulps_check, acc_check
from rpython.rlib.rfloat import string_to_float
from rpython.rlib.rbigint import rbigint
def test_round_away():
assert round_away(.1) == 0.
assert round_away(.5) == 1.
assert round_away(.7) == 1.
assert round_away(1.) == 1.
assert round_away(-.5) == -1.
assert round_away(-.1) == 0.
assert round_away(-.7) == -1.
assert round_away(0.) == 0.
def test_round_double():
def almost_equal(x, y):
assert abs(x-y) < 1e-7
almost_equal(round_double(0.125, 2), 0.13)
almost_equal(round_double(0.375, 2), 0.38)
almost_equal(round_double(0.625, 2), 0.63)
almost_equal(round_double(0.875, 2), 0.88)
almost_equal(round_double(-0.125, 2), -0.13)
almost_equal(round_double(-0.375, 2), -0.38)
almost_equal(round_double(-0.625, 2), -0.63)
almost_equal(round_double(-0.875, 2), -0.88)
almost_equal(round_double(0.25, 1), 0.3)
almost_equal(round_double(0.75, 1), 0.8)
almost_equal(round_double(-0.25, 1), -0.3)
almost_equal(round_double(-0.75, 1), -0.8)
assert round_double(-6.5, 0) == -7.0
assert round_double(-5.5, 0) == -6.0
assert round_double(-1.5, 0) == -2.0
assert round_double(-0.5, 0) == -1.0
assert round_double(0.5, 0) == 1.0
assert round_double(1.5, 0) == 2.0
assert round_double(2.5, 0) == 3.0
assert round_double(3.5, 0) == 4.0
assert round_double(4.5, 0) == 5.0
assert round_double(5.5, 0) == 6.0
assert round_double(6.5, 0) == 7.0
assert round_double(-25.0, -1) == -30.0
assert round_double(-15.0, -1) == -20.0
assert round_double(-5.0, -1) == -10.0
assert round_double(5.0, -1) == 10.0
assert round_double(15.0, -1) == 20.0
assert round_double(25.0, -1) == 30.0
assert round_double(35.0, -1) == 40.0
assert round_double(45.0, -1) == 50.0
assert round_double(55.0, -1) == 60.0
assert round_double(65.0, -1) == 70.0
assert round_double(75.0, -1) == 80.0
assert round_double(85.0, -1) == 90.0
assert round_double(95.0, -1) == 100.0
assert round_double(12325.0, -1) == 12330.0
assert round_double(350.0, -2) == 400.0
assert round_double(450.0, -2) == 500.0
almost_equal(round_double(0.5e21, -21), 1e21)
almost_equal(round_double(1.5e21, -21), 2e21)
almost_equal(round_double(2.5e21, -21), 3e21)
almost_equal(round_double(5.5e21, -21), 6e21)
almost_equal(round_double(8.5e21, -21), 9e21)
almost_equal(round_double(-1.5e22, -22), -2e22)
almost_equal(round_double(-0.5e22, -22), -1e22)
almost_equal(round_double(0.5e22, -22), 1e22)
almost_equal(round_double(1.5e22, -22), 2e22)
exact_integral = 5e15 + 1
assert round_double(exact_integral, 0) == exact_integral
assert round_double(exact_integral/2.0, 0) == 5e15/2.0 + 1.0
exact_integral = 5e15 - 1
assert round_double(exact_integral, 0) == exact_integral
assert round_double(exact_integral/2.0, 0) == 5e15/2.0
def test_round_half_even():
from rpython.rlib import rfloat
func = rfloat.round_double
# 2.x behavior
assert func(2.5, 0, False) == 3.0
# 3.x behavior
assert func(2.5, 0, True) == 2.0
for i in range(-10, 10):
assert func(i + 0.5, 0, True) == i + (i & 1)
assert func(i * 10 + 5, -1, True) == (i + (i & 1)) * 10
exact_integral = 5e15 + 1
assert round_double(exact_integral, 0, True) == exact_integral
assert round_double(exact_integral/2.0, 0, True) == 5e15/2.0
exact_integral = 5e15 - 1
assert round_double(exact_integral, 0, True) == exact_integral
assert round_double(exact_integral/2.0, 0, True) == 5e15/2.0
def test_float_as_rbigint_ratio():
for f, ratio in [
(0.875, (7, 8)),
(-0.875, (-7, 8)),
(0.0, (0, 1)),
(11.5, (23, 2)),
]:
num, den = float_as_rbigint_ratio(f)
assert num.eq(rbigint.fromint(ratio[0]))
assert den.eq(rbigint.fromint(ratio[1]))
with py.test.raises(OverflowError):
float_as_rbigint_ratio(float('inf'))
with py.test.raises(OverflowError):
float_as_rbigint_ratio(float('-inf'))
with py.test.raises(ValueError):
float_as_rbigint_ratio(float('nan'))
def test_mtestfile():
from rpython.rlib import rfloat
import zipfile
import os
def _parse_mtestfile(fname):
"""Parse a file with test values
-- starts a comment
blank lines, or lines containing only a comment, are ignored
other lines are expected to have the form
id fn arg -> expected [flag]*
"""
with open(fname) as fp:
for line in fp:
# strip comments, and skip blank lines
if '--' in line:
line = line[:line.index('--')]
if not line.strip():
continue
lhs, rhs = line.split('->')
id, fn, arg = lhs.split()
rhs_pieces = rhs.split()
exp = rhs_pieces[0]
flags = rhs_pieces[1:]
yield (id, fn, float(arg), float(exp), flags)
ALLOWED_ERROR = 20 # permitted error, in ulps
fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}"
failures = []
math_testcases = os.path.join(os.path.dirname(__file__),
"math_testcases.txt")
for id, fn, arg, expected, flags in _parse_mtestfile(math_testcases):
func = getattr(rfloat, fn)
if 'invalid' in flags or 'divide-by-zero' in flags:
expected = 'ValueError'
elif 'overflow' in flags:
expected = 'OverflowError'
try:
got = func(arg)
except ValueError:
got = 'ValueError'
except OverflowError:
got = 'OverflowError'
accuracy_failure = None
if isinstance(got, float) and isinstance(expected, float):
if math.isnan(expected) and math.isnan(got):
continue
if not math.isnan(expected) and not math.isnan(got):
if fn == 'lgamma':
# we use a weaker accuracy test for lgamma;
# lgamma only achieves an absolute error of
# a few multiples of the machine accuracy, in
# general.
accuracy_failure = acc_check(expected, got,
rel_err = 5e-15,
abs_err = 5e-15)
elif fn == 'erfc':
# erfc has less-than-ideal accuracy for large
# arguments (x ~ 25 or so), mainly due to the
# error involved in computing exp(-x*x).
#
# XXX Would be better to weaken this test only
# for large x, instead of for all x.
accuracy_failure = ulps_check(expected, got, 2000)
else:
accuracy_failure = ulps_check(expected, got, 20)
if accuracy_failure is None:
continue
if isinstance(got, str) and isinstance(expected, str):
if got == expected:
continue
fail_msg = fail_fmt.format(id, fn, arg, expected, got)
if accuracy_failure is not None:
fail_msg += ' ({})'.format(accuracy_failure)
failures.append(fail_msg)
assert not failures
def test_gamma_overflow_translated():
from rpython.translator.c.test.test_genc import compile
def wrapper(arg):
try:
return gamma(arg)
except OverflowError:
return -42
f = compile(wrapper, [float])
assert f(10.0) == 362880.0
assert f(1720.0) == -42
assert f(172.0) == -42
def test_string_to_float():
from rpython.rlib.rstring import ParseStringError
import random
assert string_to_float('0') == 0.0
assert string_to_float('1') == 1.0
assert string_to_float('-1.5') == -1.5
assert string_to_float('1.5E2') == 150.0
assert string_to_float('2.5E-1') == 0.25
assert string_to_float('1e1111111111111') == float('1e1111111111111')
assert string_to_float('1e-1111111111111') == float('1e-1111111111111')
assert string_to_float('-1e1111111111111') == float('-1e1111111111111')
assert string_to_float('-1e-1111111111111') == float('-1e-1111111111111')
assert string_to_float('1e111111111111111111111') == float('1e111111111111111111111')
assert string_to_float('1e-111111111111111111111') == float('1e-111111111111111111111')
assert string_to_float('-1e111111111111111111111') == float('-1e111111111111111111111')
assert string_to_float('-1e-111111111111111111111') == float('-1e-111111111111111111111')
valid_parts = [['', ' ', ' \f\n\r\t\v'],
['', '+', '-'],
['00', '90', '.5', '2.4', '3.', '0.07',
'12.3489749871982471987198371293717398256187563298638726'
'2187362820947193247129871083561249818451804287437824015'
'013816418758104762348932657836583048761487632840726386'],
['', 'e0', 'E+1', 'E-01', 'E42'],
['', ' ', ' \f\n\r\t\v'],
]
invalid_parts = [['#'],
['++', '+-', '-+', '--'],
['', '1.2.3', '.', '5..6'],
['E+', 'E-', 'e', 'e++', 'E++2'],
['#'],
]
for part0 in valid_parts[0]:
for part1 in valid_parts[1]:
for part2 in valid_parts[2]:
for part3 in valid_parts[3]:
for part4 in valid_parts[4]:
s = part0+part1+part2+part3+part4
assert (abs(string_to_float(s) - float(s)) <=
1E-13 * abs(float(s)))
for j in range(len(invalid_parts)):
for invalid in invalid_parts[j]:
for i in range(20):
parts = [random.choice(lst) for lst in valid_parts]
parts[j] = invalid
s = ''.join(parts)
print repr(s)
if s.strip(): # empty s raises OperationError directly
py.test.raises(ParseStringError, string_to_float, s)
py.test.raises(ParseStringError, string_to_float, "")
def test_log2():
from rpython.rlib import rfloat
assert rfloat.log2(1.0) == 0.0
assert rfloat.log2(2.0) == 1.0
assert rfloat.log2(2.0**1023) == 1023.0
assert 1.584 < rfloat.log2(3.0) < 1.585
py.test.raises(ValueError, rfloat.log2, 0)
py.test.raises(ValueError, rfloat.log2, -1)
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