1 # Copyright (c) 2010 Python Software Foundation. All Rights Reserved. 2 # Adapted from Python's Lib/test/test_strtod.py (by Mark Dickinson) 3 4 # More test cases for deccheck.py. 5 6 import random 7 8 TEST_SIZE = 2 9 10 11 def test_short_halfway_cases(): 12 # exact halfway cases with a small number of significant digits 13 for k in 0, 5, 10, 15, 20: 14 # upper = smallest integer >= 2**54/5**k 15 upper = -(-2**54//5**k) 16 # lower = smallest odd number >= 2**53/5**k 17 lower = -(-2**53//5**k) 18 if lower % 2 == 0: 19 lower += 1 20 for i in range(10 * TEST_SIZE): 21 # Select a random odd n in [2**53/5**k, 22 # 2**54/5**k). Then n * 10**k gives a halfway case 23 # with small number of significant digits. 24 n, e = random.randrange(lower, upper, 2), k 25 26 # Remove any additional powers of 5. 27 while n % 5 == 0: 28 n, e = n // 5, e + 1 29 assert n % 10 in (1, 3, 7, 9) 30 31 # Try numbers of the form n * 2**p2 * 10**e, p2 >= 0, 32 # until n * 2**p2 has more than 20 significant digits. 33 digits, exponent = n, e 34 while digits < 10**20: 35 s = '{}e{}'.format(digits, exponent) 36 yield s 37 # Same again, but with extra trailing zeros. 38 s = '{}e{}'.format(digits * 10**40, exponent - 40) 39 yield s 40 digits *= 2 41 42 # Try numbers of the form n * 5**p2 * 10**(e - p5), p5 43 # >= 0, with n * 5**p5 < 10**20. 44 digits, exponent = n, e 45 while digits < 10**20: 46 s = '{}e{}'.format(digits, exponent) 47 yield s 48 # Same again, but with extra trailing zeros. 49 s = '{}e{}'.format(digits * 10**40, exponent - 40) 50 yield s 51 digits *= 5 52 exponent -= 1 53 54 def test_halfway_cases(): 55 # test halfway cases for the round-half-to-even rule 56 for i in range(1000): 57 for j in range(TEST_SIZE): 58 # bit pattern for a random finite positive (or +0.0) float 59 bits = random.randrange(2047*2**52) 60 61 # convert bit pattern to a number of the form m * 2**e 62 e, m = divmod(bits, 2**52) 63 if e: 64 m, e = m + 2**52, e - 1 65 e -= 1074 66 67 # add 0.5 ulps 68 m, e = 2*m + 1, e - 1 69 70 # convert to a decimal string 71 if e >= 0: 72 digits = m << e 73 exponent = 0 74 else: 75 # m * 2**e = (m * 5**-e) * 10**e 76 digits = m * 5**-e 77 exponent = e 78 s = '{}e{}'.format(digits, exponent) 79 yield s 80 81 def test_boundaries(): 82 # boundaries expressed as triples (n, e, u), where 83 # n*10**e is an approximation to the boundary value and 84 # u*10**e is 1ulp 85 boundaries = [ 86 (10000000000000000000, -19, 1110), # a power of 2 boundary (1.0) 87 (17976931348623159077, 289, 1995), # overflow boundary (2.**1024) 88 (22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022) 89 (0, -327, 4941), # zero 90 ] 91 for n, e, u in boundaries: 92 for j in range(1000): 93 for i in range(TEST_SIZE): 94 digits = n + random.randrange(-3*u, 3*u) 95 exponent = e 96 s = '{}e{}'.format(digits, exponent) 97 yield s 98 n *= 10 99 u *= 10 100 e -= 1 101 102 def test_underflow_boundary(): 103 # test values close to 2**-1075, the underflow boundary; similar 104 # to boundary_tests, except that the random error doesn't scale 105 # with n 106 for exponent in range(-400, -320): 107 base = 10**-exponent // 2**1075 108 for j in range(TEST_SIZE): 109 digits = base + random.randrange(-1000, 1000) 110 s = '{}e{}'.format(digits, exponent) 111 yield s 112 113 def test_bigcomp(): 114 for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50: 115 dig10 = 10**ndigs 116 for i in range(100 * TEST_SIZE): 117 digits = random.randrange(dig10) 118 exponent = random.randrange(-400, 400) 119 s = '{}e{}'.format(digits, exponent) 120 yield s 121 122 def test_parsing(): 123 # make '0' more likely to be chosen than other digits 124 digits = '000000123456789' 125 signs = ('+', '-', '') 126 127 # put together random short valid strings 128 # \d*[.\d*]?e 129 for i in range(1000): 130 for j in range(TEST_SIZE): 131 s = random.choice(signs) 132 intpart_len = random.randrange(5) 133 s += ''.join(random.choice(digits) for _ in range(intpart_len)) 134 if random.choice([True, False]): 135 s += '.' 136 fracpart_len = random.randrange(5) 137 s += ''.join(random.choice(digits) 138 for _ in range(fracpart_len)) 139 else: 140 fracpart_len = 0 141 if random.choice([True, False]): 142 s += random.choice(['e', 'E']) 143 s += random.choice(signs) 144 exponent_len = random.randrange(1, 4) 145 s += ''.join(random.choice(digits) 146 for _ in range(exponent_len)) 147 148 if intpart_len + fracpart_len: 149 yield s 150 151 test_particular = [ 152 # squares 153 '1.00000000100000000025', 154 '1.0000000000000000000000000100000000000000000000000' #... 155 '00025', 156 '1.0000000000000000000000000000000000000000000010000' #... 157 '0000000000000000000000000000000000000000025', 158 '1.0000000000000000000000000000000000000000000000000' #... 159 '000001000000000000000000000000000000000000000000000' #... 160 '000000000025', 161 '0.99999999900000000025', 162 '0.9999999999999999999999999999999999999999999999999' #... 163 '999000000000000000000000000000000000000000000000000' #... 164 '000025', 165 '0.9999999999999999999999999999999999999999999999999' #... 166 '999999999999999999999999999999999999999999999999999' #... 167 '999999999999999999999999999999999999999990000000000' #... 168 '000000000000000000000000000000000000000000000000000' #... 169 '000000000000000000000000000000000000000000000000000' #... 170 '0000000000000000000000000000025', 171 172 '1.0000000000000000000000000000000000000000000000000' #... 173 '000000000000000000000000000000000000000000000000000' #... 174 '100000000000000000000000000000000000000000000000000' #... 175 '000000000000000000000000000000000000000000000000001', 176 '1.0000000000000000000000000000000000000000000000000' #... 177 '000000000000000000000000000000000000000000000000000' #... 178 '500000000000000000000000000000000000000000000000000' #... 179 '000000000000000000000000000000000000000000000000005', 180 '1.0000000000000000000000000000000000000000000000000' #... 181 '000000000100000000000000000000000000000000000000000' #... 182 '000000000000000000250000000000000002000000000000000' #... 183 '000000000000000000000000000000000000000000010000000' #... 184 '000000000000000000000000000000000000000000000000000' #... 185 '0000000000000000001', 186 '1.0000000000000000000000000000000000000000000000000' #... 187 '000000000100000000000000000000000000000000000000000' #... 188 '000000000000000000249999999999999999999999999999999' #... 189 '999999999999979999999999999999999999999999999999999' #... 190 '999999999999999999999900000000000000000000000000000' #... 191 '000000000000000000000000000000000000000000000000000' #... 192 '00000000000000000000000001', 193 194 '0.9999999999999999999999999999999999999999999999999' #... 195 '999999999900000000000000000000000000000000000000000' #... 196 '000000000000000000249999999999999998000000000000000' #... 197 '000000000000000000000000000000000000000000010000000' #... 198 '000000000000000000000000000000000000000000000000000' #... 199 '0000000000000000001', 200 '0.9999999999999999999999999999999999999999999999999' #... 201 '999999999900000000000000000000000000000000000000000' #... 202 '000000000000000000250000001999999999999999999999999' #... 203 '999999999999999999999999999999999990000000000000000' #... 204 '000000000000000000000000000000000000000000000000000' #... 205 '1', 206 207 # tough cases for ln etc. 208 '1.000000000000000000000000000000000000000000000000' #... 209 '00000000000000000000000000000000000000000000000000' #... 210 '00100000000000000000000000000000000000000000000000' #... 211 '00000000000000000000000000000000000000000000000000' #... 212 '0001', 213 '0.999999999999999999999999999999999999999999999999' #... 214 '99999999999999999999999999999999999999999999999999' #... 215 '99899999999999999999999999999999999999999999999999' #... 216 '99999999999999999999999999999999999999999999999999' #... 217 '99999999999999999999999999999999999999999999999999' #... 218 '9999' 219 ] 220 221 222 TESTCASES = [ 223 [x for x in test_short_halfway_cases()], 224 [x for x in test_halfway_cases()], 225 [x for x in test_boundaries()], 226 [x for x in test_underflow_boundary()], 227 [x for x in test_bigcomp()], 228 [x for x in test_parsing()], 229 test_particular 230 ] 231 232 def un_randfloat(): 233 for i in range(1000): 234 l = random.choice(TESTCASES[:6]) 235 yield random.choice(l) 236 for v in test_particular: 237 yield v 238 239 def bin_randfloat(): 240 for i in range(1000): 241 l1 = random.choice(TESTCASES) 242 l2 = random.choice(TESTCASES) 243 yield random.choice(l1), random.choice(l2) 244 245 def tern_randfloat(): 246 for i in range(1000): 247 l1 = random.choice(TESTCASES) 248 l2 = random.choice(TESTCASES) 249 l3 = random.choice(TESTCASES) 250 yield random.choice(l1), random.choice(l2), random.choice(l3) 251
