Mercurial > cpython-lru_cache-weakref
annotate Lib/test/test_long.py @ 73798:6cde416ef03b
Credit Per Øyvind Karlsen for the initial implementation of the lzma module (issue #6715).
| author | Nadeem Vawda <nadeem.vawda@gmail.com> |
|---|---|
| date | Thu, 01 Dec 2011 01:18:27 +0200 |
| parents | 117d51d3dd7d |
| children | c7b0f711dc15 |
| rev | line source |
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1 import unittest |
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2 from test import support |
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Issue #10624: Use support.requires_IEEE_754 in all appropriate tests.
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4 import sys |
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5 |
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6 import random |
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7 import math |
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8 import array |
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9 |
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10 # Used for lazy formatting of failure messages |
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11 class Frm(object): |
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12 def __init__(self, format, *args): |
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13 self.format = format |
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14 self.args = args |
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15 |
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16 def __str__(self): |
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17 return self.format % self.args |
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18 |
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19 # SHIFT should match the value in longintrepr.h for best testing. |
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20 SHIFT = sys.int_info.bits_per_digit |
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21 BASE = 2 ** SHIFT |
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22 MASK = BASE - 1 |
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23 KARATSUBA_CUTOFF = 70 # from longobject.c |
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24 |
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25 # Max number of base BASE digits to use in test cases. Doubling |
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26 # this will more than double the runtime. |
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27 MAXDIGITS = 15 |
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28 |
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29 # build some special values |
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30 special = [0, 1, 2, BASE, BASE >> 1, 0x5555555555555555, 0xaaaaaaaaaaaaaaaa] |
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31 # some solid strings of one bits |
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32 p2 = 4 # 0 and 1 already added |
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33 for i in range(2*SHIFT): |
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34 special.append(p2 - 1) |
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35 p2 = p2 << 1 |
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36 del p2 |
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37 # add complements & negations |
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38 special += [~x for x in special] + [-x for x in special] |
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39 |
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40 DBL_MAX = sys.float_info.max |
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41 DBL_MAX_EXP = sys.float_info.max_exp |
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42 DBL_MIN_EXP = sys.float_info.min_exp |
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43 DBL_MANT_DIG = sys.float_info.mant_dig |
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44 DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1) |
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45 |
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46 |
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47 # Pure Python version of correctly-rounded integer-to-float conversion. |
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48 def int_to_float(n): |
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49 """ |
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50 Correctly-rounded integer-to-float conversion. |
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51 |
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52 """ |
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53 # Constants, depending only on the floating-point format in use. |
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54 # We use an extra 2 bits of precision for rounding purposes. |
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55 PRECISION = sys.float_info.mant_dig + 2 |
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56 SHIFT_MAX = sys.float_info.max_exp - PRECISION |
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57 Q_MAX = 1 << PRECISION |
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58 ROUND_HALF_TO_EVEN_CORRECTION = [0, -1, -2, 1, 0, -1, 2, 1] |
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59 |
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60 # Reduce to the case where n is positive. |
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61 if n == 0: |
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62 return 0.0 |
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63 elif n < 0: |
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64 return -int_to_float(-n) |
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65 |
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66 # Convert n to a 'floating-point' number q * 2**shift, where q is an |
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67 # integer with 'PRECISION' significant bits. When shifting n to create q, |
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68 # the least significant bit of q is treated as 'sticky'. That is, the |
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69 # least significant bit of q is set if either the corresponding bit of n |
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70 # was already set, or any one of the bits of n lost in the shift was set. |
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71 shift = n.bit_length() - PRECISION |
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72 q = n << -shift if shift < 0 else (n >> shift) | bool(n & ~(-1 << shift)) |
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73 |
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74 # Round half to even (actually rounds to the nearest multiple of 4, |
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75 # rounding ties to a multiple of 8). |
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76 q += ROUND_HALF_TO_EVEN_CORRECTION[q & 7] |
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77 |
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78 # Detect overflow. |
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79 if shift + (q == Q_MAX) > SHIFT_MAX: |
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80 raise OverflowError("integer too large to convert to float") |
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81 |
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82 # Checks: q is exactly representable, and q**2**shift doesn't overflow. |
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83 assert q % 4 == 0 and q // 4 <= 2**(sys.float_info.mant_dig) |
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84 assert q * 2**shift <= sys.float_info.max |
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85 |
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86 # Some circularity here, since float(q) is doing an int-to-float |
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87 # conversion. But here q is of bounded size, and is exactly representable |
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88 # as a float. In a low-level C-like language, this operation would be a |
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89 # simple cast (e.g., from unsigned long long to double). |
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90 return math.ldexp(float(q), shift) |
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91 |
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92 |
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93 # pure Python version of correctly-rounded true division |
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94 def truediv(a, b): |
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95 """Correctly-rounded true division for integers.""" |
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96 negative = a^b < 0 |
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97 a, b = abs(a), abs(b) |
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98 |
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99 # exceptions: division by zero, overflow |
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100 if not b: |
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101 raise ZeroDivisionError("division by zero") |
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102 if a >= DBL_MIN_OVERFLOW * b: |
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103 raise OverflowError("int/int too large to represent as a float") |
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104 |
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105 # find integer d satisfying 2**(d - 1) <= a/b < 2**d |
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106 d = a.bit_length() - b.bit_length() |
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107 if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b: |
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108 d += 1 |
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109 |
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110 # compute 2**-exp * a / b for suitable exp |
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111 exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG |
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112 a, b = a << max(-exp, 0), b << max(exp, 0) |
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113 q, r = divmod(a, b) |
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114 |
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115 # round-half-to-even: fractional part is r/b, which is > 0.5 iff |
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116 # 2*r > b, and == 0.5 iff 2*r == b. |
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117 if 2*r > b or 2*r == b and q % 2 == 1: |
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118 q += 1 |
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119 |
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120 result = math.ldexp(q, exp) |
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121 return -result if negative else result |
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122 |
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123 |
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124 class LongTest(unittest.TestCase): |
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125 |
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126 # Get quasi-random long consisting of ndigits digits (in base BASE). |
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127 # quasi == the most-significant digit will not be 0, and the number |
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128 # is constructed to contain long strings of 0 and 1 bits. These are |
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129 # more likely than random bits to provoke digit-boundary errors. |
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130 # The sign of the number is also random. |
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131 |
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132 def getran(self, ndigits): |
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133 self.assertTrue(ndigits > 0) |
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134 nbits_hi = ndigits * SHIFT |
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135 nbits_lo = nbits_hi - SHIFT + 1 |
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136 answer = 0 |
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137 nbits = 0 |
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138 r = int(random.random() * (SHIFT * 2)) | 1 # force 1 bits to start |
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139 while nbits < nbits_lo: |
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140 bits = (r >> 1) + 1 |
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141 bits = min(bits, nbits_hi - nbits) |
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142 self.assertTrue(1 <= bits <= SHIFT) |
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143 nbits = nbits + bits |
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144 answer = answer << bits |
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145 if r & 1: |
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146 answer = answer | ((1 << bits) - 1) |
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147 r = int(random.random() * (SHIFT * 2)) |
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148 self.assertTrue(nbits_lo <= nbits <= nbits_hi) |
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149 if random.random() < 0.5: |
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150 answer = -answer |
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151 return answer |
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152 |
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153 # Get random long consisting of ndigits random digits (relative to base |
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154 # BASE). The sign bit is also random. |
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155 |
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156 def getran2(ndigits): |
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157 answer = 0 |
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158 for i in range(ndigits): |
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159 answer = (answer << SHIFT) | random.randint(0, MASK) |
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160 if random.random() < 0.5: |
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161 answer = -answer |
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162 return answer |
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163 |
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164 def check_division(self, x, y): |
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165 eq = self.assertEqual |
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166 q, r = divmod(x, y) |
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167 q2, r2 = x//y, x%y |
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168 pab, pba = x*y, y*x |
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169 eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y)) |
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170 eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y)) |
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171 eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y)) |
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172 eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y)) |
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173 if y > 0: |
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174 self.assertTrue(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y)) |
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175 else: |
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176 self.assertTrue(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y)) |
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177 |
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178 def test_division(self): |
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179 digits = list(range(1, MAXDIGITS+1)) + list(range(KARATSUBA_CUTOFF, |
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180 KARATSUBA_CUTOFF + 14)) |
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181 digits.append(KARATSUBA_CUTOFF * 3) |
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182 for lenx in digits: |
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183 x = self.getran(lenx) |
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184 for leny in digits: |
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185 y = self.getran(leny) or 1 |
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186 self.check_division(x, y) |
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187 |
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188 # specific numbers chosen to exercise corner cases of the |
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189 # current long division implementation |
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190 |
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191 # 30-bit cases involving a quotient digit estimate of BASE+1 |
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192 self.check_division(1231948412290879395966702881, |
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193 1147341367131428698) |
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194 self.check_division(815427756481275430342312021515587883, |
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195 707270836069027745) |
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196 self.check_division(627976073697012820849443363563599041, |
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197 643588798496057020) |
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198 self.check_division(1115141373653752303710932756325578065, |
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199 1038556335171453937726882627) |
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200 # 30-bit cases that require the post-subtraction correction step |
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201 self.check_division(922498905405436751940989320930368494, |
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202 949985870686786135626943396) |
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203 self.check_division(768235853328091167204009652174031844, |
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204 1091555541180371554426545266) |
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205 |
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206 # 15-bit cases involving a quotient digit estimate of BASE+1 |
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207 self.check_division(20172188947443, 615611397) |
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208 self.check_division(1020908530270155025, 950795710) |
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209 self.check_division(128589565723112408, 736393718) |
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210 self.check_division(609919780285761575, 18613274546784) |
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211 # 15-bit cases that require the post-subtraction correction step |
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212 self.check_division(710031681576388032, 26769404391308) |
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213 self.check_division(1933622614268221, 30212853348836) |
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214 |
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215 |
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216 |
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217 def test_karatsuba(self): |
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218 digits = list(range(1, 5)) + list(range(KARATSUBA_CUTOFF, |
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219 KARATSUBA_CUTOFF + 10)) |
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220 digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100]) |
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221 |
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222 bits = [digit * SHIFT for digit in digits] |
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223 |
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224 # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) == |
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225 # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check. |
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226 for abits in bits: |
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227 a = (1 << abits) - 1 |
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228 for bbits in bits: |
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229 if bbits < abits: |
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230 continue |
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231 b = (1 << bbits) - 1 |
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232 x = a * b |
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233 y = ((1 << (abits + bbits)) - |
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234 (1 << abits) - |
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235 (1 << bbits) + |
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236 1) |
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237 self.assertEqual(x, y, |
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238 Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y)) |
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239 |
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240 def check_bitop_identities_1(self, x): |
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241 eq = self.assertEqual |
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242 eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x)) |
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243 eq(x | 0, x, Frm("x | 0 != x for x=%r", x)) |
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244 eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x)) |
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245 eq(x & -1, x, Frm("x & -1 != x for x=%r", x)) |
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246 eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x)) |
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247 eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x)) |
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248 eq(x, ~~x, Frm("x != ~~x for x=%r", x)) |
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249 eq(x & x, x, Frm("x & x != x for x=%r", x)) |
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250 eq(x | x, x, Frm("x | x != x for x=%r", x)) |
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251 eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x)) |
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252 eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x)) |
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253 eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x)) |
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254 eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x)) |
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255 eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x)) |
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256 eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x)) |
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257 for n in range(2*SHIFT): |
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258 p2 = 2 ** n |
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259 eq(x << n >> n, x, |
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260 Frm("x << n >> n != x for x=%r, n=%r", (x, n))) |
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261 eq(x // p2, x >> n, |
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262 Frm("x // p2 != x >> n for x=%r n=%r p2=%r", (x, n, p2))) |
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263 eq(x * p2, x << n, |
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264 Frm("x * p2 != x << n for x=%r n=%r p2=%r", (x, n, p2))) |
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265 eq(x & -p2, x >> n << n, |
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266 Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", (x, n, p2))) |
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267 eq(x & -p2, x & ~(p2 - 1), |
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268 Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", (x, n, p2))) |
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269 |
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270 def check_bitop_identities_2(self, x, y): |
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271 eq = self.assertEqual |
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272 eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", (x, y))) |
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273 eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", (x, y))) |
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274 eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", (x, y))) |
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275 eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", (x, y))) |
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276 eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", (x, y))) |
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277 eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", (x, y))) |
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278 eq(x ^ y, (x | y) & ~(x & y), |
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279 Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", (x, y))) |
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280 eq(x ^ y, (x & ~y) | (~x & y), |
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281 Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", (x, y))) |
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282 eq(x ^ y, (x | y) & (~x | ~y), |
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283 Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", (x, y))) |
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284 |
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285 def check_bitop_identities_3(self, x, y, z): |
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286 eq = self.assertEqual |
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287 eq((x & y) & z, x & (y & z), |
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288 Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", (x, y, z))) |
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289 eq((x | y) | z, x | (y | z), |
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290 Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", (x, y, z))) |
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291 eq((x ^ y) ^ z, x ^ (y ^ z), |
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292 Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", (x, y, z))) |
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293 eq(x & (y | z), (x & y) | (x & z), |
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294 Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", (x, y, z))) |
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295 eq(x | (y & z), (x | y) & (x | z), |
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296 Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", (x, y, z))) |
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297 |
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298 def test_bitop_identities(self): |
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299 for x in special: |
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300 self.check_bitop_identities_1(x) |
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301 digits = range(1, MAXDIGITS+1) |
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302 for lenx in digits: |
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303 x = self.getran(lenx) |
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304 self.check_bitop_identities_1(x) |
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305 for leny in digits: |
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306 y = self.getran(leny) |
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307 self.check_bitop_identities_2(x, y) |
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308 self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2)) |
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309 |
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310 def slow_format(self, x, base): |
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311 digits = [] |
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312 sign = 0 |
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313 if x < 0: |
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314 sign, x = 1, -x |
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315 while x: |
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316 x, r = divmod(x, base) |
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317 digits.append(int(r)) |
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318 digits.reverse() |
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319 digits = digits or [0] |
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320 return '-'[:sign] + \ |
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321 {2: '0b', 8: '0o', 10: '', 16: '0x'}[base] + \ |
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322 "".join("0123456789abcdef"[i] for i in digits) |
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323 |
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324 def check_format_1(self, x): |
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325 for base, mapper in (8, oct), (10, repr), (16, hex): |
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326 got = mapper(x) |
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327 expected = self.slow_format(x, base) |
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328 msg = Frm("%s returned %r but expected %r for %r", |
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329 mapper.__name__, got, expected, x) |
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330 self.assertEqual(got, expected, msg) |
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331 self.assertEqual(int(got, 0), x, Frm('int("%s", 0) != %r', got, x)) |
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332 # str() has to be checked a little differently since there's no |
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333 # trailing "L" |
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334 got = str(x) |
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335 expected = self.slow_format(x, 10) |
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336 msg = Frm("%s returned %r but expected %r for %r", |
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337 mapper.__name__, got, expected, x) |
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338 self.assertEqual(got, expected, msg) |
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339 |
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340 def test_format(self): |
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341 for x in special: |
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342 self.check_format_1(x) |
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343 for i in range(10): |
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344 for lenx in range(1, MAXDIGITS+1): |
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345 x = self.getran(lenx) |
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346 self.check_format_1(x) |
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347 |
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348 def test_long(self): |
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349 # Check conversions from string |
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350 LL = [ |
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351 ('1' + '0'*20, 10**20), |
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352 ('1' + '0'*100, 10**100) |
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353 ] |
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354 for s, v in LL: |
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355 for sign in "", "+", "-": |
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356 for prefix in "", " ", "\t", " \t\t ": |
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357 ss = prefix + sign + s |
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358 vv = v |
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359 if sign == "-" and v is not ValueError: |
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360 vv = -v |
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361 try: |
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362 self.assertEqual(int(ss), vv) |
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363 except ValueError: |
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364 pass |
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366 # trailing L should no longer be accepted... |
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367 self.assertRaises(ValueError, int, '123L') |
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368 self.assertRaises(ValueError, int, '123l') |
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369 self.assertRaises(ValueError, int, '0L') |
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370 self.assertRaises(ValueError, int, '-37L') |
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371 self.assertRaises(ValueError, int, '0x32L', 16) |
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372 self.assertRaises(ValueError, int, '1L', 21) |
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373 # ... but it's just a normal digit if base >= 22 |
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374 self.assertEqual(int('1L', 22), 43) |
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375 |
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376 # tests with base 0 |
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377 self.assertEqual(int('000', 0), 0) |
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378 self.assertEqual(int('0o123', 0), 83) |
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379 self.assertEqual(int('0x123', 0), 291) |
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380 self.assertEqual(int('0b100', 0), 4) |
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381 self.assertEqual(int(' 0O123 ', 0), 83) |
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382 self.assertEqual(int(' 0X123 ', 0), 291) |
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383 self.assertEqual(int(' 0B100 ', 0), 4) |
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384 self.assertEqual(int('0', 0), 0) |
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385 self.assertEqual(int('+0', 0), 0) |
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386 self.assertEqual(int('-0', 0), 0) |
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387 self.assertEqual(int('00', 0), 0) |
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388 self.assertRaises(ValueError, int, '08', 0) |
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389 self.assertRaises(ValueError, int, '-012395', 0) |
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390 |
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391 # invalid bases |
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392 invalid_bases = [-909, |
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393 2**31-1, 2**31, -2**31, -2**31-1, |
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394 2**63-1, 2**63, -2**63, -2**63-1, |
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395 2**100, -2**100, |
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396 ] |
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397 for base in invalid_bases: |
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398 self.assertRaises(ValueError, int, '42', base) |
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399 |
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400 |
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401 def test_conversion(self): |
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402 |
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403 class JustLong: |
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404 # test that __long__ no longer used in 3.x |
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405 def __long__(self): |
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406 return 42 |
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407 self.assertRaises(TypeError, int, JustLong()) |
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408 |
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409 class LongTrunc: |
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410 # __long__ should be ignored in 3.x |
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411 def __long__(self): |
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412 return 42 |
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413 def __trunc__(self): |
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414 return 1729 |
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415 self.assertEqual(int(LongTrunc()), 1729) |
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416 |
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417 def check_float_conversion(self, n): |
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418 # Check that int -> float conversion behaviour matches |
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419 # that of the pure Python version above. |
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420 try: |
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421 actual = float(n) |
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422 except OverflowError: |
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423 actual = 'overflow' |
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424 |
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425 try: |
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426 expected = int_to_float(n) |
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427 except OverflowError: |
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428 expected = 'overflow' |
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429 |
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430 msg = ("Error in conversion of integer {} to float. " |
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431 "Got {}, expected {}.".format(n, actual, expected)) |
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432 self.assertEqual(actual, expected, msg) |
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433 |
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434 @support.requires_IEEE_754 |
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435 def test_float_conversion(self): |
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436 |
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437 exact_values = [0, 1, 2, |
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438 2**53-3, |
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439 2**53-2, |
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440 2**53-1, |
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441 2**53, |
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442 2**53+2, |
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443 2**54-4, |
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444 2**54-2, |
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445 2**54, |
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446 2**54+4] |
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447 for x in exact_values: |
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448 self.assertEqual(float(x), x) |
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449 self.assertEqual(float(-x), -x) |
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450 |
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451 # test round-half-even |
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452 for x, y in [(1, 0), (2, 2), (3, 4), (4, 4), (5, 4), (6, 6), (7, 8)]: |
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453 for p in range(15): |
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454 self.assertEqual(int(float(2**p*(2**53+x))), 2**p*(2**53+y)) |
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455 |
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456 for x, y in [(0, 0), (1, 0), (2, 0), (3, 4), (4, 4), (5, 4), (6, 8), |
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457 (7, 8), (8, 8), (9, 8), (10, 8), (11, 12), (12, 12), |
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458 (13, 12), (14, 16), (15, 16)]: |
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459 for p in range(15): |
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460 self.assertEqual(int(float(2**p*(2**54+x))), 2**p*(2**54+y)) |
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461 |
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462 # behaviour near extremes of floating-point range |
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463 int_dbl_max = int(DBL_MAX) |
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464 top_power = 2**DBL_MAX_EXP |
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465 halfway = (int_dbl_max + top_power)//2 |
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466 self.assertEqual(float(int_dbl_max), DBL_MAX) |
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467 self.assertEqual(float(int_dbl_max+1), DBL_MAX) |
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468 self.assertEqual(float(halfway-1), DBL_MAX) |
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469 self.assertRaises(OverflowError, float, halfway) |
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470 self.assertEqual(float(1-halfway), -DBL_MAX) |
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471 self.assertRaises(OverflowError, float, -halfway) |
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472 self.assertRaises(OverflowError, float, top_power-1) |
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473 self.assertRaises(OverflowError, float, top_power) |
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474 self.assertRaises(OverflowError, float, top_power+1) |
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475 self.assertRaises(OverflowError, float, 2*top_power-1) |
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476 self.assertRaises(OverflowError, float, 2*top_power) |
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477 self.assertRaises(OverflowError, float, top_power*top_power) |
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478 |
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479 for p in range(100): |
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480 x = 2**p * (2**53 + 1) + 1 |
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481 y = 2**p * (2**53 + 2) |
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482 self.assertEqual(int(float(x)), y) |
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483 |
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484 x = 2**p * (2**53 + 1) |
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485 y = 2**p * 2**53 |
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486 self.assertEqual(int(float(x)), y) |
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487 |
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488 # Compare builtin float conversion with pure Python int_to_float |
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489 # function above. |
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490 test_values = [ |
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491 int_dbl_max-1, int_dbl_max, int_dbl_max+1, |
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492 halfway-1, halfway, halfway + 1, |
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493 top_power-1, top_power, top_power+1, |
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494 2*top_power-1, 2*top_power, top_power*top_power, |
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495 ] |
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496 test_values.extend(exact_values) |
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497 for p in range(-4, 8): |
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498 for x in range(-128, 128): |
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499 test_values.append(2**(p+53) + x) |
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500 for value in test_values: |
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501 self.check_float_conversion(value) |
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502 self.check_float_conversion(-value) |
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503 |
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504 def test_float_overflow(self): |
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505 for x in -2.0, -1.0, 0.0, 1.0, 2.0: |
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506 self.assertEqual(float(int(x)), x) |
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507 |
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508 shuge = '12345' * 120 |
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509 huge = 1 << 30000 |
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510 mhuge = -huge |
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511 namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math} |
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512 for test in ["float(huge)", "float(mhuge)", |
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513 "complex(huge)", "complex(mhuge)", |
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514 "complex(huge, 1)", "complex(mhuge, 1)", |
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515 "complex(1, huge)", "complex(1, mhuge)", |
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516 "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.", |
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517 "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.", |
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518 "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.", |
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519 "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.", |
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520 "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.", |
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521 "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.", |
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522 "math.sin(huge)", "math.sin(mhuge)", |
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523 "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better |
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524 # math.floor() of an int returns an int now |
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525 ##"math.floor(huge)", "math.floor(mhuge)", |
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526 ]: |
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527 |
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528 self.assertRaises(OverflowError, eval, test, namespace) |
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529 |
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530 # XXX Perhaps float(shuge) can raise OverflowError on some box? |
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531 # The comparison should not. |
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532 self.assertNotEqual(float(shuge), int(shuge), |
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533 "float(shuge) should not equal int(shuge)") |
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534 |
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535 def test_logs(self): |
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536 LOG10E = math.log10(math.e) |
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537 |
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538 for exp in list(range(10)) + [100, 1000, 10000]: |
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539 value = 10 ** exp |
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540 log10 = math.log10(value) |
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541 self.assertAlmostEqual(log10, exp) |
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542 |
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543 # log10(value) == exp, so log(value) == log10(value)/log10(e) == |
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544 # exp/LOG10E |
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545 expected = exp / LOG10E |
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546 log = math.log(value) |
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547 self.assertAlmostEqual(log, expected) |
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548 |
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549 for bad in -(1 << 10000), -2, 0: |
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550 self.assertRaises(ValueError, math.log, bad) |
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551 self.assertRaises(ValueError, math.log10, bad) |
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552 |
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553 def test_mixed_compares(self): |
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554 eq = self.assertEqual |
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555 |
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556 # We're mostly concerned with that mixing floats and longs does the |
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557 # right stuff, even when longs are too large to fit in a float. |
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558 # The safest way to check the results is to use an entirely different |
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559 # method, which we do here via a skeletal rational class (which |
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560 # represents all Python ints, longs and floats exactly). |
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561 class Rat: |
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562 def __init__(self, value): |
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563 if isinstance(value, int): |
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564 self.n = value |
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565 self.d = 1 |
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566 elif isinstance(value, float): |
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567 # Convert to exact rational equivalent. |
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568 f, e = math.frexp(abs(value)) |
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569 assert f == 0 or 0.5 <= f < 1.0 |
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570 # |value| = f * 2**e exactly |
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571 |
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572 # Suck up CHUNK bits at a time; 28 is enough so that we suck |
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573 # up all bits in 2 iterations for all known binary double- |
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574 # precision formats, and small enough to fit in an int. |
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575 CHUNK = 28 |
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576 top = 0 |
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577 # invariant: |value| = (top + f) * 2**e exactly |
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578 while f: |
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579 f = math.ldexp(f, CHUNK) |
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580 digit = int(f) |
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581 assert digit >> CHUNK == 0 |
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582 top = (top << CHUNK) | digit |
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583 f -= digit |
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584 assert 0.0 <= f < 1.0 |
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585 e -= CHUNK |
|
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586 |
|
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587 # Now |value| = top * 2**e exactly. |
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588 if e >= 0: |
|
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589 n = top << e |
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590 d = 1 |
|
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591 else: |
|
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592 n = top |
|
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593 d = 1 << -e |
|
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594 if value < 0: |
|
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595 n = -n |
|
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596 self.n = n |
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597 self.d = d |
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598 assert float(n) / float(d) == value |
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599 else: |
|
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600 raise TypeError("can't deal with %r" % value) |
|
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601 |
|
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602 def _cmp__(self, other): |
|
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603 if not isinstance(other, Rat): |
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604 other = Rat(other) |
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605 x, y = self.n * other.d, self.d * other.n |
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606 return (x > y) - (x < y) |
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607 def __eq__(self, other): |
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608 return self._cmp__(other) == 0 |
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609 def __ne__(self, other): |
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610 return self._cmp__(other) != 0 |
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611 def __ge__(self, other): |
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612 return self._cmp__(other) >= 0 |
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613 def __gt__(self, other): |
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614 return self._cmp__(other) > 0 |
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615 def __le__(self, other): |
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616 return self._cmp__(other) <= 0 |
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617 def __lt__(self, other): |
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618 return self._cmp__(other) < 0 |
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619 |
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620 cases = [0, 0.001, 0.99, 1.0, 1.5, 1e20, 1e200] |
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621 # 2**48 is an important boundary in the internals. 2**53 is an |
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622 # important boundary for IEEE double precision. |
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623 for t in 2.0**48, 2.0**50, 2.0**53: |
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624 cases.extend([t - 1.0, t - 0.3, t, t + 0.3, t + 1.0, |
|
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625 int(t-1), int(t), int(t+1)]) |
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626 cases.extend([0, 1, 2, sys.maxsize, float(sys.maxsize)]) |
|
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627 # 1 << 20000 should exceed all double formats. int(1e200) is to |
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628 # check that we get equality with 1e200 above. |
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629 t = int(1e200) |
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630 cases.extend([0, 1, 2, 1 << 20000, t-1, t, t+1]) |
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631 cases.extend([-x for x in cases]) |
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632 for x in cases: |
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633 Rx = Rat(x) |
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634 for y in cases: |
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635 Ry = Rat(y) |
|
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636 Rcmp = (Rx > Ry) - (Rx < Ry) |
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637 xycmp = (x > y) - (x < y) |
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638 eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp)) |
|
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639 eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp)) |
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640 eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp)) |
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641 eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp)) |
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642 eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp)) |
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643 eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp)) |
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644 eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp)) |
|
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645 |
|
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646 def test__format__(self): |
|
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647 self.assertEqual(format(123456789, 'd'), '123456789') |
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648 self.assertEqual(format(123456789, 'd'), '123456789') |
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649 |
| 43097 | 650 # sign and aligning are interdependent |
| 651 self.assertEqual(format(1, "-"), '1') | |
| 652 self.assertEqual(format(-1, "-"), '-1') | |
| 653 self.assertEqual(format(1, "-3"), ' 1') | |
| 654 self.assertEqual(format(-1, "-3"), ' -1') | |
| 655 self.assertEqual(format(1, "+3"), ' +1') | |
| 656 self.assertEqual(format(-1, "+3"), ' -1') | |
| 657 self.assertEqual(format(1, " 3"), ' 1') | |
| 658 self.assertEqual(format(-1, " 3"), ' -1') | |
| 659 self.assertEqual(format(1, " "), ' 1') | |
| 660 self.assertEqual(format(-1, " "), '-1') | |
| 661 | |
|
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662 # hex |
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663 self.assertEqual(format(3, "x"), "3") |
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664 self.assertEqual(format(3, "X"), "3") |
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665 self.assertEqual(format(1234, "x"), "4d2") |
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666 self.assertEqual(format(-1234, "x"), "-4d2") |
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667 self.assertEqual(format(1234, "8x"), " 4d2") |
| 43097 | 668 self.assertEqual(format(-1234, "8x"), " -4d2") |
|
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669 self.assertEqual(format(1234, "x"), "4d2") |
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670 self.assertEqual(format(-1234, "x"), "-4d2") |
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671 self.assertEqual(format(-3, "x"), "-3") |
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672 self.assertEqual(format(-3, "X"), "-3") |
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673 self.assertEqual(format(int('be', 16), "x"), "be") |
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674 self.assertEqual(format(int('be', 16), "X"), "BE") |
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675 self.assertEqual(format(-int('be', 16), "x"), "-be") |
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676 self.assertEqual(format(-int('be', 16), "X"), "-BE") |
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677 |
|
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678 # octal |
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679 self.assertEqual(format(3, "b"), "11") |
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680 self.assertEqual(format(-3, "b"), "-11") |
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681 self.assertEqual(format(1234, "b"), "10011010010") |
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682 self.assertEqual(format(-1234, "b"), "-10011010010") |
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683 self.assertEqual(format(1234, "-b"), "10011010010") |
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684 self.assertEqual(format(-1234, "-b"), "-10011010010") |
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685 self.assertEqual(format(1234, " b"), " 10011010010") |
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686 self.assertEqual(format(-1234, " b"), "-10011010010") |
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687 self.assertEqual(format(1234, "+b"), "+10011010010") |
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688 self.assertEqual(format(-1234, "+b"), "-10011010010") |
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689 |
|
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690 # make sure these are errors |
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691 self.assertRaises(ValueError, format, 3, "1.3") # precision disallowed |
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692 self.assertRaises(ValueError, format, 3, "+c") # sign not allowed |
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693 # with 'c' |
|
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694 |
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695 # ensure that only int and float type specifiers work |
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696 for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + |
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697 [chr(x) for x in range(ord('A'), ord('Z')+1)]): |
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698 if not format_spec in 'bcdoxXeEfFgGn%': |
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699 self.assertRaises(ValueError, format, 0, format_spec) |
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700 self.assertRaises(ValueError, format, 1, format_spec) |
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701 self.assertRaises(ValueError, format, -1, format_spec) |
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702 self.assertRaises(ValueError, format, 2**100, format_spec) |
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703 self.assertRaises(ValueError, format, -(2**100), format_spec) |
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704 |
|
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705 # ensure that float type specifiers work; format converts |
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706 # the int to a float |
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707 for format_spec in 'eEfFgG%': |
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708 for value in [0, 1, -1, 100, -100, 1234567890, -1234567890]: |
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709 self.assertEqual(format(value, format_spec), |
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710 format(float(value), format_spec)) |
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712 def test_nan_inf(self): |
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714 self.assertRaises(OverflowError, int, float('-inf')) |
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715 self.assertRaises(ValueError, int, float('nan')) |
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716 |
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717 def test_true_division(self): |
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718 huge = 1 << 40000 |
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719 mhuge = -huge |
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720 self.assertEqual(huge / huge, 1.0) |
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721 self.assertEqual(mhuge / mhuge, 1.0) |
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722 self.assertEqual(huge / mhuge, -1.0) |
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723 self.assertEqual(mhuge / huge, -1.0) |
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724 self.assertEqual(1 / huge, 0.0) |
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725 self.assertEqual(1 / huge, 0.0) |
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726 self.assertEqual(1 / mhuge, 0.0) |
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727 self.assertEqual(1 / mhuge, 0.0) |
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728 self.assertEqual((666 * huge + (huge >> 1)) / huge, 666.5) |
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729 self.assertEqual((666 * mhuge + (mhuge >> 1)) / mhuge, 666.5) |
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730 self.assertEqual((666 * huge + (huge >> 1)) / mhuge, -666.5) |
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731 self.assertEqual((666 * mhuge + (mhuge >> 1)) / huge, -666.5) |
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732 self.assertEqual(huge / (huge << 1), 0.5) |
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733 self.assertEqual((1000000 * huge) / huge, 1000000) |
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734 |
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735 namespace = {'huge': huge, 'mhuge': mhuge} |
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736 |
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737 for overflow in ["float(huge)", "float(mhuge)", |
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738 "huge / 1", "huge / 2", "huge / -1", "huge / -2", |
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739 "mhuge / 100", "mhuge / 200"]: |
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740 self.assertRaises(OverflowError, eval, overflow, namespace) |
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741 |
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742 for underflow in ["1 / huge", "2 / huge", "-1 / huge", "-2 / huge", |
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743 "100 / mhuge", "200 / mhuge"]: |
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744 result = eval(underflow, namespace) |
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745 self.assertEqual(result, 0.0, |
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746 "expected underflow to 0 from %r" % underflow) |
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747 |
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748 for zero in ["huge / 0", "mhuge / 0"]: |
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749 self.assertRaises(ZeroDivisionError, eval, zero, namespace) |
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750 |
|
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751 def check_truediv(self, a, b, skip_small=True): |
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752 """Verify that the result of a/b is correctly rounded, by |
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753 comparing it with a pure Python implementation of correctly |
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754 rounded division. b should be nonzero.""" |
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755 |
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756 # skip check for small a and b: in this case, the current |
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757 # implementation converts the arguments to float directly and |
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758 # then applies a float division. This can give doubly-rounded |
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759 # results on x87-using machines (particularly 32-bit Linux). |
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760 if skip_small and max(abs(a), abs(b)) < 2**DBL_MANT_DIG: |
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761 return |
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762 |
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763 try: |
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764 # use repr so that we can distinguish between -0.0 and 0.0 |
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765 expected = repr(truediv(a, b)) |
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766 except OverflowError: |
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767 expected = 'overflow' |
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768 except ZeroDivisionError: |
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769 expected = 'zerodivision' |
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770 |
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771 try: |
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772 got = repr(a / b) |
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773 except OverflowError: |
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774 got = 'overflow' |
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775 except ZeroDivisionError: |
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776 got = 'zerodivision' |
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777 |
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778 self.assertEqual(expected, got, "Incorrectly rounded division {}/{}: " |
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779 "expected {}, got {}".format(a, b, expected, got)) |
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780 |
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781 @support.requires_IEEE_754 |
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782 def test_correctly_rounded_true_division(self): |
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783 # more stringent tests than those above, checking that the |
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784 # result of true division of ints is always correctly rounded. |
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785 # This test should probably be considered CPython-specific. |
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786 |
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787 # Exercise all the code paths not involving Gb-sized ints. |
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788 # ... divisions involving zero |
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789 self.check_truediv(123, 0) |
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790 self.check_truediv(-456, 0) |
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791 self.check_truediv(0, 3) |
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792 self.check_truediv(0, -3) |
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793 self.check_truediv(0, 0) |
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794 # ... overflow or underflow by large margin |
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795 self.check_truediv(671 * 12345 * 2**DBL_MAX_EXP, 12345) |
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796 self.check_truediv(12345, 345678 * 2**(DBL_MANT_DIG - DBL_MIN_EXP)) |
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797 # ... a much larger or smaller than b |
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798 self.check_truediv(12345*2**100, 98765) |
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799 self.check_truediv(12345*2**30, 98765*7**81) |
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800 # ... a / b near a boundary: one of 1, 2**DBL_MANT_DIG, 2**DBL_MIN_EXP, |
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801 # 2**DBL_MAX_EXP, 2**(DBL_MIN_EXP-DBL_MANT_DIG) |
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802 bases = (0, DBL_MANT_DIG, DBL_MIN_EXP, |
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803 DBL_MAX_EXP, DBL_MIN_EXP - DBL_MANT_DIG) |
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804 for base in bases: |
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805 for exp in range(base - 15, base + 15): |
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806 self.check_truediv(75312*2**max(exp, 0), 69187*2**max(-exp, 0)) |
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807 self.check_truediv(69187*2**max(exp, 0), 75312*2**max(-exp, 0)) |
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808 |
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809 # overflow corner case |
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810 for m in [1, 2, 7, 17, 12345, 7**100, |
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811 -1, -2, -5, -23, -67891, -41**50]: |
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812 for n in range(-10, 10): |
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813 self.check_truediv(m*DBL_MIN_OVERFLOW + n, m) |
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814 self.check_truediv(m*DBL_MIN_OVERFLOW + n, -m) |
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815 |
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816 # check detection of inexactness in shifting stage |
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817 for n in range(250): |
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818 # (2**DBL_MANT_DIG+1)/(2**DBL_MANT_DIG) lies halfway |
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819 # between two representable floats, and would usually be |
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820 # rounded down under round-half-to-even. The tiniest of |
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821 # additions to the numerator should cause it to be rounded |
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822 # up instead. |
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823 self.check_truediv((2**DBL_MANT_DIG + 1)*12345*2**200 + 2**n, |
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824 2**DBL_MANT_DIG*12345) |
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825 |
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826 # 1/2731 is one of the smallest division cases that's subject |
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827 # to double rounding on IEEE 754 machines working internally with |
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828 # 64-bit precision. On such machines, the next check would fail, |
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829 # were it not explicitly skipped in check_truediv. |
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830 self.check_truediv(1, 2731) |
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831 |
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832 # a particularly bad case for the old algorithm: gives an |
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833 # error of close to 3.5 ulps. |
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834 self.check_truediv(295147931372582273023, 295147932265116303360) |
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835 for i in range(1000): |
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836 self.check_truediv(10**(i+1), 10**i) |
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837 self.check_truediv(10**i, 10**(i+1)) |
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838 |
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839 # test round-half-to-even behaviour, normal result |
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840 for m in [1, 2, 4, 7, 8, 16, 17, 32, 12345, 7**100, |
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841 -1, -2, -5, -23, -67891, -41**50]: |
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842 for n in range(-10, 10): |
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843 self.check_truediv(2**DBL_MANT_DIG*m + n, m) |
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844 |
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845 # test round-half-to-even, subnormal result |
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846 for n in range(-20, 20): |
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847 self.check_truediv(n, 2**1076) |
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848 |
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849 # largeish random divisions: a/b where |a| <= |b| <= |
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850 # 2*|a|; |ans| is between 0.5 and 1.0, so error should |
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851 # always be bounded by 2**-54 with equality possible only |
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852 # if the least significant bit of q=ans*2**53 is zero. |
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853 for M in [10**10, 10**100, 10**1000]: |
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854 for i in range(1000): |
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855 a = random.randrange(1, M) |
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856 b = random.randrange(a, 2*a+1) |
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857 self.check_truediv(a, b) |
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858 self.check_truediv(-a, b) |
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859 self.check_truediv(a, -b) |
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860 self.check_truediv(-a, -b) |
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861 |
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862 # and some (genuinely) random tests |
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863 for _ in range(10000): |
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864 a_bits = random.randrange(1000) |
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865 b_bits = random.randrange(1, 1000) |
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866 x = random.randrange(2**a_bits) |
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867 y = random.randrange(1, 2**b_bits) |
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868 self.check_truediv(x, y) |
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869 self.check_truediv(x, -y) |
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870 self.check_truediv(-x, y) |
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871 self.check_truediv(-x, -y) |
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872 |
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873 def test_small_ints(self): |
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874 for i in range(-5, 257): |
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875 self.assertTrue(i is i + 0) |
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876 self.assertTrue(i is i * 1) |
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877 self.assertTrue(i is i - 0) |
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878 self.assertTrue(i is i // 1) |
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879 self.assertTrue(i is i & -1) |
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880 self.assertTrue(i is i | 0) |
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881 self.assertTrue(i is i ^ 0) |
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882 self.assertTrue(i is ~~i) |
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883 self.assertTrue(i is i**1) |
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884 self.assertTrue(i is int(str(i))) |
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885 self.assertTrue(i is i<<2>>2, str(i)) |
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886 # corner cases |
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887 i = 1 << 70 |
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888 self.assertTrue(i - i is 0) |
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889 self.assertTrue(0 * i is 0) |
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890 |
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891 def test_bit_length(self): |
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892 tiny = 1e-10 |
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893 for x in range(-65000, 65000): |
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894 k = x.bit_length() |
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895 # Check equivalence with Python version |
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896 self.assertEqual(k, len(bin(x).lstrip('-0b'))) |
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897 # Behaviour as specified in the docs |
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898 if x != 0: |
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899 self.assertTrue(2**(k-1) <= abs(x) < 2**k) |
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900 else: |
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901 self.assertEqual(k, 0) |
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|
902 # Alternative definition: x.bit_length() == 1 + floor(log_2(x)) |
|
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|
903 if x != 0: |
|
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|
904 # When x is an exact power of 2, numeric errors can |
|
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changeset
|
905 # cause floor(log(x)/log(2)) to be one too small; for |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
906 # small x this can be fixed by adding a small quantity |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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changeset
|
907 # to the quotient before taking the floor. |
|
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|
908 self.assertEqual(k, 1 + math.floor( |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
909 math.log(abs(x))/math.log(2) + tiny)) |
|
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|
910 |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
911 self.assertEqual((0).bit_length(), 0) |
|
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|
912 self.assertEqual((1).bit_length(), 1) |
|
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|
913 self.assertEqual((-1).bit_length(), 1) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
914 self.assertEqual((2).bit_length(), 2) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
915 self.assertEqual((-2).bit_length(), 2) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
916 for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64, 234]: |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
917 a = 2**i |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
918 self.assertEqual((a-1).bit_length(), i) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
919 self.assertEqual((1-a).bit_length(), i) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
920 self.assertEqual((a).bit_length(), i+1) |
|
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|
921 self.assertEqual((-a).bit_length(), i+1) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
922 self.assertEqual((a+1).bit_length(), i+1) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
923 self.assertEqual((-a-1).bit_length(), i+1) |
|
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Forward merge of r67822 to py3k: add bit_length method to int.
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|
924 |
|
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925 def test_round(self): |
|
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|
926 # check round-half-even algorithm. For round to nearest ten; |
|
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|
927 # rounding map is invariant under adding multiples of 20 |
|
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|
928 test_dict = {0:0, 1:0, 2:0, 3:0, 4:0, 5:0, |
|
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|
929 6:10, 7:10, 8:10, 9:10, 10:10, 11:10, 12:10, 13:10, 14:10, |
|
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|
930 15:20, 16:20, 17:20, 18:20, 19:20} |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
931 for offset in range(-520, 520, 20): |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
932 for k, v in test_dict.items(): |
|
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|
933 got = round(k+offset, -1) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
934 expected = v+offset |
|
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|
935 self.assertEqual(got, expected) |
|
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|
936 self.assertTrue(type(got) is int) |
|
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|
937 |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
938 # larger second argument |
|
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|
939 self.assertEqual(round(-150, -2), -200) |
|
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940 self.assertEqual(round(-149, -2), -100) |
|
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|
941 self.assertEqual(round(-51, -2), -100) |
|
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|
942 self.assertEqual(round(-50, -2), 0) |
|
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|
943 self.assertEqual(round(-49, -2), 0) |
|
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|
944 self.assertEqual(round(-1, -2), 0) |
|
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|
945 self.assertEqual(round(0, -2), 0) |
|
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|
946 self.assertEqual(round(1, -2), 0) |
|
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|
947 self.assertEqual(round(49, -2), 0) |
|
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|
948 self.assertEqual(round(50, -2), 0) |
|
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|
949 self.assertEqual(round(51, -2), 100) |
|
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|
950 self.assertEqual(round(149, -2), 100) |
|
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|
951 self.assertEqual(round(150, -2), 200) |
|
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|
952 self.assertEqual(round(250, -2), 200) |
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|
953 self.assertEqual(round(251, -2), 300) |
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|
954 self.assertEqual(round(172500, -3), 172000) |
|
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955 self.assertEqual(round(173500, -3), 174000) |
|
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956 self.assertEqual(round(31415926535, -1), 31415926540) |
|
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957 self.assertEqual(round(31415926535, -2), 31415926500) |
|
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|
958 self.assertEqual(round(31415926535, -3), 31415927000) |
|
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|
959 self.assertEqual(round(31415926535, -4), 31415930000) |
|
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|
960 self.assertEqual(round(31415926535, -5), 31415900000) |
|
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|
961 self.assertEqual(round(31415926535, -6), 31416000000) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
962 self.assertEqual(round(31415926535, -7), 31420000000) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
963 self.assertEqual(round(31415926535, -8), 31400000000) |
|
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|
964 self.assertEqual(round(31415926535, -9), 31000000000) |
|
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|
965 self.assertEqual(round(31415926535, -10), 30000000000) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
966 self.assertEqual(round(31415926535, -11), 0) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
967 self.assertEqual(round(31415926535, -12), 0) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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changeset
|
968 self.assertEqual(round(31415926535, -999), 0) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
969 |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
970 # should get correct results even for huge inputs |
|
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|
971 for k in range(10, 100): |
|
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|
972 got = round(10**k + 324678, -3) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
973 expect = 10**k + 325000 |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
974 self.assertEqual(got, expect) |
|
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|
975 self.assertTrue(type(got) is int) |
|
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|
976 |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
977 # nonnegative second argument: round(x, n) should just return x |
|
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978 for n in range(5): |
|
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|
979 for i in range(100): |
|
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|
980 x = random.randrange(-10000, 10000) |
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|
981 got = round(x, n) |
|
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|
982 self.assertEqual(got, x) |
|
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|
983 self.assertTrue(type(got) is int) |
|
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|
984 for huge_n in 2**31-1, 2**31, 2**63-1, 2**63, 2**100, 10**100: |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
985 self.assertEqual(round(8979323, huge_n), 8979323) |
|
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|
986 |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
987 # omitted second argument |
|
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988 for i in range(100): |
|
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|
989 x = random.randrange(-10000, 10000) |
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990 got = round(x) |
|
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991 self.assertEqual(got, x) |
|
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992 self.assertTrue(type(got) is int) |
|
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|
993 |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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|
994 # bad second argument |
|
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|
995 bad_exponents = ('brian', 2.0, 0j, None) |
|
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Issue #4707: round(x, n) now returns an integer when x is an integer.
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996 for e in bad_exponents: |
|
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|
997 self.assertRaises(TypeError, round, 3, e) |
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|
998 |
|
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999 def test_to_bytes(self): |
|
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1000 def check(tests, byteorder, signed=False): |
|
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|
1001 for test, expected in tests.items(): |
|
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|
1002 try: |
|
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|
1003 self.assertEqual( |
|
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|
1004 test.to_bytes(len(expected), byteorder, signed=signed), |
|
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|
1005 expected) |
|
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|
1006 except Exception as err: |
|
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|
1007 raise AssertionError( |
|
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|
1008 "failed to convert {0} with byteorder={1} and signed={2}" |
|
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|
1009 .format(test, byteorder, signed)) from err |
|
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|
1010 |
|
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|
1011 # Convert integers to signed big-endian byte arrays. |
|
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|
1012 tests1 = { |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1013 0: b'\x00', |
|
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|
1014 1: b'\x01', |
|
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|
1015 -1: b'\xff', |
|
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|
1016 -127: b'\x81', |
|
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|
1017 -128: b'\x80', |
|
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|
1018 -129: b'\xff\x7f', |
|
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|
1019 127: b'\x7f', |
|
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|
1020 129: b'\x00\x81', |
|
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|
1021 -255: b'\xff\x01', |
|
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|
1022 -256: b'\xff\x00', |
|
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|
1023 255: b'\x00\xff', |
|
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1024 256: b'\x01\x00', |
|
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|
1025 32767: b'\x7f\xff', |
|
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|
1026 -32768: b'\xff\x80\x00', |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1027 65535: b'\x00\xff\xff', |
|
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|
1028 -65536: b'\xff\x00\x00', |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1029 -8388608: b'\x80\x00\x00' |
|
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|
1030 } |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1031 check(tests1, 'big', signed=True) |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1032 |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1033 # Convert integers to signed little-endian byte arrays. |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1034 tests2 = { |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1035 0: b'\x00', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1036 1: b'\x01', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1037 -1: b'\xff', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1038 -127: b'\x81', |
|
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|
1039 -128: b'\x80', |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1040 -129: b'\x7f\xff', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1041 127: b'\x7f', |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1042 129: b'\x81\x00', |
|
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|
1043 -255: b'\x01\xff', |
|
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|
1044 -256: b'\x00\xff', |
|
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|
1045 255: b'\xff\x00', |
|
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|
1046 256: b'\x00\x01', |
|
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|
1047 32767: b'\xff\x7f', |
|
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|
1048 -32768: b'\x00\x80', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1049 65535: b'\xff\xff\x00', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1050 -65536: b'\x00\x00\xff', |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1051 -8388608: b'\x00\x00\x80' |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1052 } |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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diff
changeset
|
1053 check(tests2, 'little', signed=True) |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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57951
diff
changeset
|
1054 |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1055 # Convert integers to unsigned big-endian byte arrays. |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1056 tests3 = { |
|
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1057 0: b'\x00', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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diff
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|
1058 1: b'\x01', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1059 127: b'\x7f', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1060 128: b'\x80', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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diff
changeset
|
1061 255: b'\xff', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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diff
changeset
|
1062 256: b'\x01\x00', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1063 32767: b'\x7f\xff', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1064 32768: b'\x80\x00', |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1065 65535: b'\xff\xff', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1066 65536: b'\x01\x00\x00' |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1067 } |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1068 check(tests3, 'big', signed=False) |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1069 |
|
f9c0c411f80c
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Alexandre Vassalotti <alexandre@peadrop.com>
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|
1070 # Convert integers to unsigned little-endian byte arrays. |
|
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|
1071 tests4 = { |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1072 0: b'\x00', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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diff
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|
1073 1: b'\x01', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1074 127: b'\x7f', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1075 128: b'\x80', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1076 255: b'\xff', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1077 256: b'\x00\x01', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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57951
diff
changeset
|
1078 32767: b'\xff\x7f', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1079 32768: b'\x00\x80', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1080 65535: b'\xff\xff', |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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diff
changeset
|
1081 65536: b'\x00\x00\x01' |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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parents:
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changeset
|
1082 } |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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changeset
|
1083 check(tests4, 'little', signed=False) |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1084 |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1085 self.assertRaises(OverflowError, (256).to_bytes, 1, 'big', signed=False) |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1086 self.assertRaises(OverflowError, (256).to_bytes, 1, 'big', signed=True) |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1087 self.assertRaises(OverflowError, (256).to_bytes, 1, 'little', signed=False) |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1088 self.assertRaises(OverflowError, (256).to_bytes, 1, 'little', signed=True) |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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1089 self.assertRaises(OverflowError, (-1).to_bytes, 2, 'big', signed=False), |
|
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1090 self.assertRaises(OverflowError, (-1).to_bytes, 2, 'little', signed=False) |
|
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1091 self.assertEqual((0).to_bytes(0, 'big'), b'') |
|
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1092 self.assertEqual((1).to_bytes(5, 'big'), b'\x00\x00\x00\x00\x01') |
|
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1093 self.assertEqual((0).to_bytes(5, 'big'), b'\x00\x00\x00\x00\x00') |
|
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1094 self.assertEqual((-1).to_bytes(5, 'big', signed=True), |
|
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1095 b'\xff\xff\xff\xff\xff') |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1096 self.assertRaises(OverflowError, (1).to_bytes, 0, 'big') |
|
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|
1097 |
|
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1098 def test_from_bytes(self): |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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1099 def check(tests, byteorder, signed=False): |
|
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1100 for test, expected in tests.items(): |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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1101 try: |
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1102 self.assertEqual( |
|
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|
1103 int.from_bytes(test, byteorder, signed=signed), |
|
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|
1104 expected) |
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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1105 except Exception as err: |
|
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|
1106 raise AssertionError( |
|
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|
1107 "failed to convert {0} with byteorder={1!r} and signed={2}" |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1108 .format(test, byteorder, signed)) from err |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1109 |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1110 # Convert signed big-endian byte arrays to integers. |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1111 tests1 = { |
|
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1112 b'': 0, |
|
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1113 b'\x00': 0, |
|
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|
1114 b'\x00\x00': 0, |
|
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1115 b'\x01': 1, |
|
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|
1116 b'\x00\x01': 1, |
|
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1117 b'\xff': -1, |
|
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|
1118 b'\xff\xff': -1, |
|
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1119 b'\x81': -127, |
|
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1120 b'\x80': -128, |
|
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1121 b'\xff\x7f': -129, |
|
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1122 b'\x7f': 127, |
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1123 b'\x00\x81': 129, |
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|
1124 b'\xff\x01': -255, |
|
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1125 b'\xff\x00': -256, |
|
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1126 b'\x00\xff': 255, |
|
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|
1127 b'\x01\x00': 256, |
|
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1128 b'\x7f\xff': 32767, |
|
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|
1129 b'\x80\x00': -32768, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1130 b'\x00\xff\xff': 65535, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1131 b'\xff\x00\x00': -65536, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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1132 b'\x80\x00\x00': -8388608 |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1133 } |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1134 check(tests1, 'big', signed=True) |
|
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|
1135 |
|
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|
1136 # Convert signed little-endian byte arrays to integers. |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1137 tests2 = { |
|
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1138 b'': 0, |
|
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|
1139 b'\x00': 0, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1140 b'\x00\x00': 0, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1141 b'\x01': 1, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1142 b'\x00\x01': 256, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1143 b'\xff': -1, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1144 b'\xff\xff': -1, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1145 b'\x81': -127, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1146 b'\x80': -128, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
Alexandre Vassalotti <alexandre@peadrop.com>
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|
1147 b'\x7f\xff': -129, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1148 b'\x7f': 127, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1149 b'\x81\x00': 129, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1150 b'\x01\xff': -255, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1151 b'\x00\xff': -256, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1152 b'\xff\x00': 255, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1153 b'\x00\x01': 256, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1154 b'\xff\x7f': 32767, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1155 b'\x00\x80': -32768, |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1156 b'\xff\xff\x00': 65535, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1157 b'\x00\x00\xff': -65536, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1158 b'\x00\x00\x80': -8388608 |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1159 } |
|
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|
1160 check(tests2, 'little', signed=True) |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1161 |
|
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|
1162 # Convert unsigned big-endian byte arrays to integers. |
|
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|
1163 tests3 = { |
|
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|
1164 b'': 0, |
|
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|
1165 b'\x00': 0, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1166 b'\x01': 1, |
|
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|
1167 b'\x7f': 127, |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1168 b'\x80': 128, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1169 b'\xff': 255, |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1170 b'\x01\x00': 256, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1171 b'\x7f\xff': 32767, |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1172 b'\x80\x00': 32768, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1173 b'\xff\xff': 65535, |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1174 b'\x01\x00\x00': 65536, |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1175 } |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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|
1176 check(tests3, 'big', signed=False) |
|
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Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1177 |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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changeset
|
1178 # Convert integers to unsigned little-endian byte arrays. |
|
f9c0c411f80c
Issue #1023290: Added API for the conversion of longs to bytes and vice-versa.
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1179 tests4 = { |
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1180 b'': 0, |
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1181 b'\x00': 0, |
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1182 b'\x01': 1, |
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1183 b'\x7f': 127, |
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1184 b'\x80': 128, |
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1185 b'\xff': 255, |
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1186 b'\x00\x01': 256, |
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1187 b'\xff\x7f': 32767, |
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1188 b'\x00\x80': 32768, |
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1189 b'\xff\xff': 65535, |
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1190 b'\x00\x00\x01': 65536, |
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1191 } |
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1192 check(tests4, 'little', signed=False) |
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1193 |
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1194 class myint(int): |
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1195 pass |
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1196 |
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1197 self.assertTrue(type(myint.from_bytes(b'\x00', 'big')) is myint) |
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1198 self.assertEqual(myint.from_bytes(b'\x01', 'big'), 1) |
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1199 self.assertTrue( |
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1200 type(myint.from_bytes(b'\x00', 'big', signed=False)) is myint) |
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1201 self.assertEqual(myint.from_bytes(b'\x01', 'big', signed=False), 1) |
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1202 self.assertTrue(type(myint.from_bytes(b'\x00', 'little')) is myint) |
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1203 self.assertEqual(myint.from_bytes(b'\x01', 'little'), 1) |
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1204 self.assertTrue(type(myint.from_bytes( |
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1205 b'\x00', 'little', signed=False)) is myint) |
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1206 self.assertEqual(myint.from_bytes(b'\x01', 'little', signed=False), 1) |
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1207 self.assertEqual( |
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1208 int.from_bytes([255, 0, 0], 'big', signed=True), -65536) |
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1209 self.assertEqual( |
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1210 int.from_bytes((255, 0, 0), 'big', signed=True), -65536) |
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1211 self.assertEqual(int.from_bytes( |
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1212 bytearray(b'\xff\x00\x00'), 'big', signed=True), -65536) |
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1213 self.assertEqual(int.from_bytes( |
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1214 bytearray(b'\xff\x00\x00'), 'big', signed=True), -65536) |
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1215 self.assertEqual(int.from_bytes( |
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1216 array.array('B', b'\xff\x00\x00'), 'big', signed=True), -65536) |
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1217 self.assertEqual(int.from_bytes( |
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1218 memoryview(b'\xff\x00\x00'), 'big', signed=True), -65536) |
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1219 self.assertRaises(ValueError, int.from_bytes, [256], 'big') |
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1220 self.assertRaises(ValueError, int.from_bytes, [0], 'big\x00') |
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1221 self.assertRaises(ValueError, int.from_bytes, [0], 'little\x00') |
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1222 self.assertRaises(TypeError, int.from_bytes, "", 'big') |
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1223 self.assertRaises(TypeError, int.from_bytes, "\x00", 'big') |
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1224 self.assertRaises(TypeError, int.from_bytes, 0, 'big') |
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1225 self.assertRaises(TypeError, int.from_bytes, 0, 'big', True) |
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1226 self.assertRaises(TypeError, myint.from_bytes, "", 'big') |
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1227 self.assertRaises(TypeError, myint.from_bytes, "\x00", 'big') |
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1228 self.assertRaises(TypeError, myint.from_bytes, 0, 'big') |
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1229 self.assertRaises(TypeError, int.from_bytes, 0, 'big', True) |
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1230 |
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1231 |
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1232 def test_main(): |
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1233 support.run_unittest(LongTest) |
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1234 |
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1235 if __name__ == "__main__": |
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1236 test_main() |
