Mercurial > cpython-lru_cache-weakref

annotate Lib/test/test_long_future.py @ 58765:2ba7677bfa95 legacy-trunk

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testCopysign was defined twice in test_math; combine the definitions
author Mark Dickinson <dickinsm@gmail.com>
date Sat, 06 Feb 2010 23:11:25 +0000
parents ad7e4141a3eb
children b36cb4602e21
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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91533675d6cb Change long/long true division to return as many good bits as it can;
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1 from __future__ import division
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2 # When true division is the default, get rid of this and add it to
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3 # test_long.py instead. In the meantime, it's too obscure to try to
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4 # trick just part of test_long into using future division.
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5
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6 import sys
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7 import random
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8 import math
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9 import unittest
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10 from test.test_support import run_unittest
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11
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12 # decorator for skipping tests on non-IEEE 754 platforms
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13 requires_IEEE_754 = unittest.skipUnless(
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14 float.__getformat__("double").startswith("IEEE"),
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15 "test requires IEEE 754 doubles")
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16
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17 DBL_MAX = sys.float_info.max
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18 DBL_MAX_EXP = sys.float_info.max_exp
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19 DBL_MIN_EXP = sys.float_info.min_exp
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20 DBL_MANT_DIG = sys.float_info.mant_dig
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21 DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1)
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22
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23 # pure Python version of correctly-rounded true division
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24 def truediv(a, b):
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25 """Correctly-rounded true division for integers."""
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26 negative = a^b < 0
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27 a, b = abs(a), abs(b)
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28
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29 # exceptions: division by zero, overflow
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30 if not b:
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31 raise ZeroDivisionError("division by zero")
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32 if a >= DBL_MIN_OVERFLOW * b:
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33 raise OverflowError("int/int too large to represent as a float")
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34
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35 # find integer d satisfying 2**(d - 1) <= a/b < 2**d
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36 d = a.bit_length() - b.bit_length()
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37 if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
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38 d += 1
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39
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40 # compute 2**-exp * a / b for suitable exp
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41 exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
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42 a, b = a << max(-exp, 0), b << max(exp, 0)
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43 q, r = divmod(a, b)
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44
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45 # round-half-to-even: fractional part is r/b, which is > 0.5 iff
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46 # 2*r > b, and == 0.5 iff 2*r == b.
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47 if 2*r > b or 2*r == b and q % 2 == 1:
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48 q += 1
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49
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50 result = math.ldexp(float(q), exp)
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51 return -result if negative else result
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52
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53 class TrueDivisionTests(unittest.TestCase):
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54 def test(self):
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55 huge = 1L << 40000
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56 mhuge = -huge
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57 self.assertEqual(huge / huge, 1.0)
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58 self.assertEqual(mhuge / mhuge, 1.0)
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59 self.assertEqual(huge / mhuge, -1.0)
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60 self.assertEqual(mhuge / huge, -1.0)
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61 self.assertEqual(1 / huge, 0.0)
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62 self.assertEqual(1L / huge, 0.0)
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63 self.assertEqual(1 / mhuge, 0.0)
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64 self.assertEqual(1L / mhuge, 0.0)
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65 self.assertEqual((666 * huge + (huge >> 1)) / huge, 666.5)
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66 self.assertEqual((666 * mhuge + (mhuge >> 1)) / mhuge, 666.5)
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67 self.assertEqual((666 * huge + (huge >> 1)) / mhuge, -666.5)
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68 self.assertEqual((666 * mhuge + (mhuge >> 1)) / huge, -666.5)
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69 self.assertEqual(huge / (huge << 1), 0.5)
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70 self.assertEqual((1000000 * huge) / huge, 1000000)
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71
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72 namespace = {'huge': huge, 'mhuge': mhuge}
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73
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74 for overflow in ["float(huge)", "float(mhuge)",
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75 "huge / 1", "huge / 2L", "huge / -1", "huge / -2L",
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76 "mhuge / 100", "mhuge / 100L"]:
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77 # If the "eval" does not happen in this module,
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78 # true division is not enabled
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79 with self.assertRaises(OverflowError):
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80 eval(overflow, namespace)
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81
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82 for underflow in ["1 / huge", "2L / huge", "-1 / huge", "-2L / huge",
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83 "100 / mhuge", "100L / mhuge"]:
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84 result = eval(underflow, namespace)
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85 self.assertEqual(result, 0.0, 'expected underflow to 0 '
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86 'from {!r}'.format(underflow))
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87
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88 for zero in ["huge / 0", "huge / 0L", "mhuge / 0", "mhuge / 0L"]:
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89 with self.assertRaises(ZeroDivisionError):
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90 eval(zero, namespace)
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91
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92 def check_truediv(self, a, b, skip_small=True):
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93 """Verify that the result of a/b is correctly rounded, by
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94 comparing it with a pure Python implementation of correctly
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95 rounded division. b should be nonzero."""
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96
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97 a, b = long(a), long(b)
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98
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99 # skip check for small a and b: in this case, the current
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100 # implementation converts the arguments to float directly and
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101 # then applies a float division. This can give doubly-rounded
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102 # results on x87-using machines (particularly 32-bit Linux).
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103 if skip_small and max(abs(a), abs(b)) < 2**DBL_MANT_DIG:
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104 return
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105
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106 try:
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107 # use repr so that we can distinguish between -0.0 and 0.0
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108 expected = repr(truediv(a, b))
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109 except OverflowError:
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110 expected = 'overflow'
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111 except ZeroDivisionError:
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112 expected = 'zerodivision'
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113
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114 try:
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115 got = repr(a / b)
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116 except OverflowError:
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117 got = 'overflow'
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118 except ZeroDivisionError:
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119 got = 'zerodivision'
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120
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121 self.assertEqual(expected, got, "Incorrectly rounded division {}/{}: "
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122 "expected {}, got {}".format(a, b, expected, got))
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123
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124 @requires_IEEE_754
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125 def test_correctly_rounded_true_division(self):
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126 # more stringent tests than those above, checking that the
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127 # result of true division of ints is always correctly rounded.
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128 # This test should probably be considered CPython-specific.
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129
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130 # Exercise all the code paths not involving Gb-sized ints.
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131 # ... divisions involving zero
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132 self.check_truediv(123, 0)
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133 self.check_truediv(-456, 0)
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134 self.check_truediv(0, 3)
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135 self.check_truediv(0, -3)
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136 self.check_truediv(0, 0)
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137 # ... overflow or underflow by large margin
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138 self.check_truediv(671 * 12345 * 2**DBL_MAX_EXP, 12345)
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139 self.check_truediv(12345, 345678 * 2**(DBL_MANT_DIG - DBL_MIN_EXP))
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140 # ... a much larger or smaller than b
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141 self.check_truediv(12345*2**100, 98765)
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142 self.check_truediv(12345*2**30, 98765*7**81)
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143 # ... a / b near a boundary: one of 1, 2**DBL_MANT_DIG, 2**DBL_MIN_EXP,
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144 # 2**DBL_MAX_EXP, 2**(DBL_MIN_EXP-DBL_MANT_DIG)
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145 bases = (0, DBL_MANT_DIG, DBL_MIN_EXP,
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146 DBL_MAX_EXP, DBL_MIN_EXP - DBL_MANT_DIG)
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147 for base in bases:
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148 for exp in range(base - 15, base + 15):
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149 self.check_truediv(75312*2**max(exp, 0), 69187*2**max(-exp, 0))
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150 self.check_truediv(69187*2**max(exp, 0), 75312*2**max(-exp, 0))
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151
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152 # overflow corner case
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153 for m in [1, 2, 7, 17, 12345, 7**100,
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154 -1, -2, -5, -23, -67891, -41**50]:
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155 for n in range(-10, 10):
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156 self.check_truediv(m*DBL_MIN_OVERFLOW + n, m)
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157 self.check_truediv(m*DBL_MIN_OVERFLOW + n, -m)
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158
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159 # check detection of inexactness in shifting stage
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160 for n in range(250):
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161 # (2**DBL_MANT_DIG+1)/(2**DBL_MANT_DIG) lies halfway
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162 # between two representable floats, and would usually be
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163 # rounded down under round-half-to-even. The tiniest of
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164 # additions to the numerator should cause it to be rounded
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165 # up instead.
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166 self.check_truediv((2**DBL_MANT_DIG + 1)*12345*2**200 + 2**n,
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167 2**DBL_MANT_DIG*12345)
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168
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169 # 1/2731 is one of the smallest division cases that's subject
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170 # to double rounding on IEEE 754 machines working internally with
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171 # 64-bit precision. On such machines, the next check would fail,
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172 # were it not explicitly skipped in check_truediv.
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173 self.check_truediv(1, 2731)
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174
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175 # a particularly bad case for the old algorithm: gives an
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176 # error of close to 3.5 ulps.
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177 self.check_truediv(295147931372582273023, 295147932265116303360)
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178 for i in range(1000):
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179 self.check_truediv(10**(i+1), 10**i)
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180 self.check_truediv(10**i, 10**(i+1))
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181
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182 # test round-half-to-even behaviour, normal result
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183 for m in [1, 2, 4, 7, 8, 16, 17, 32, 12345, 7**100,
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184 -1, -2, -5, -23, -67891, -41**50]:
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185 for n in range(-10, 10):
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186 self.check_truediv(2**DBL_MANT_DIG*m + n, m)
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187
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188 # test round-half-to-even, subnormal result
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189 for n in range(-20, 20):
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190 self.check_truediv(n, 2**1076)
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191
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192 # largeish random divisions: a/b where |a| <= |b| <=
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193 # 2*|a|; |ans| is between 0.5 and 1.0, so error should
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194 # always be bounded by 2**-54 with equality possible only
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195 # if the least significant bit of q=ans*2**53 is zero.
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196 for M in [10**10, 10**100, 10**1000]:
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197 for i in range(1000):
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198 a = random.randrange(1, M)
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199 b = random.randrange(a, 2*a+1)
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200 self.check_truediv(a, b)
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201 self.check_truediv(-a, b)
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202 self.check_truediv(a, -b)
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203 self.check_truediv(-a, -b)
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204
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205 # and some (genuinely) random tests
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206 for _ in range(10000):
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207 a_bits = random.randrange(1000)
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208 b_bits = random.randrange(1, 1000)
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209 x = random.randrange(2**a_bits)
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210 y = random.randrange(1, 2**b_bits)
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211 self.check_truediv(x, y)
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212 self.check_truediv(x, -y)
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213 self.check_truediv(-x, y)
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214 self.check_truediv(-x, -y)
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215
19678
82db9a9006ac Fixed a typo and added more tests.
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216
41392
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217 def test_main():
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218 run_unittest(TrueDivisionTests)
41532
4b9fa8092e82 Whitespace normalization. Ugh, we really need to do this more often.
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219
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220 if __name__ == "__main__":
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221 test_main()