1 # Tests for the correctly-rounded string -> float conversions
2 # introduced in Python 2.7 and 3.1.
3
4 import random
5 import unittest
6 import re
7 import sys
8 import test.support
9
10 if getattr(sys, 'float_repr_style', '') != 'short':
11 raise unittest.SkipTest('correctly-rounded string->float conversions '
12 'not available on this system')
13
14 # Correctly rounded str -> float in pure Python, for comparison.
15
16 strtod_parser = re.compile(r""" # A numeric string consists of:
17 (?P<sign>[-+])? # an optional sign, followed by
18 (?=\d|\.\d) # a number with at least one digit
19 (?P<int>\d*) # having a (possibly empty) integer part
20 (?:\.(?P<frac>\d*))? # followed by an optional fractional part
21 (?:E(?P<exp>[-+]?\d+))? # and an optional exponent
22 \Z
23 """, re.VERBOSE | re.IGNORECASE).match
24
25 # Pure Python version of correctly rounded string->float conversion.
26 # Avoids any use of floating-point by returning the result as a hex string.
27 def strtod(s, mant_dig=53, min_exp = -1021, max_exp = 1024):
28 """Convert a finite decimal string to a hex string representing an
29 IEEE 754 binary64 float. Return 'inf' or '-inf' on overflow.
30 This function makes no use of floating-point arithmetic at any
31 stage."""
32
33 # parse string into a pair of integers 'a' and 'b' such that
34 # abs(decimal value) = a/b, along with a boolean 'negative'.
35 m = strtod_parser(s)
36 if m is None:
37 raise ValueError('invalid numeric string')
38 fraction = m.group('frac') or ''
39 intpart = int(m.group('int') + fraction)
40 exp = int(m.group('exp') or '0') - len(fraction)
41 negative = m.group('sign') == '-'
42 a, b = intpart*10**max(exp, 0), 10**max(0, -exp)
43
44 # quick return for zeros
45 if not a:
46 return '-0x0.0p+0' if negative else '0x0.0p+0'
47
48 # compute exponent e for result; may be one too small in the case
49 # that the rounded value of a/b lies in a different binade from a/b
50 d = a.bit_length() - b.bit_length()
51 d += (a >> d if d >= 0 else a << -d) >= b
52 e = max(d, min_exp) - mant_dig
53
54 # approximate a/b by number of the form q * 2**e; adjust e if necessary
55 a, b = a << max(-e, 0), b << max(e, 0)
56 q, r = divmod(a, b)
57 if 2*r > b or 2*r == b and q & 1:
58 q += 1
59 if q.bit_length() == mant_dig+1:
60 q //= 2
61 e += 1
62
63 # double check that (q, e) has the right form
64 assert q.bit_length() <= mant_dig and e >= min_exp - mant_dig
65 assert q.bit_length() == mant_dig or e == min_exp - mant_dig
66
67 # check for overflow and underflow
68 if e + q.bit_length() > max_exp:
69 return '-inf' if negative else 'inf'
70 if not q:
71 return '-0x0.0p+0' if negative else '0x0.0p+0'
72
73 # for hex representation, shift so # bits after point is a multiple of 4
74 hexdigs = 1 + (mant_dig-2)//4
75 shift = 3 - (mant_dig-2)%4
76 q, e = q << shift, e - shift
77 return '{}0x{:x}.{:0{}x}p{:+d}'.format(
78 '-' if negative else '',
79 q // 16**hexdigs,
80 q % 16**hexdigs,
81 hexdigs,
82 e + 4*hexdigs)
83
84 TEST_SIZE = 10
85
86 class ESC[4;38;5;81mStrtodTests(ESC[4;38;5;149munittestESC[4;38;5;149m.ESC[4;38;5;149mTestCase):
87 def check_strtod(self, s):
88 """Compare the result of Python's builtin correctly rounded
89 string->float conversion (using float) to a pure Python
90 correctly rounded string->float implementation. Fail if the
91 two methods give different results."""
92
93 try:
94 fs = float(s)
95 except OverflowError:
96 got = '-inf' if s[0] == '-' else 'inf'
97 except MemoryError:
98 got = 'memory error'
99 else:
100 got = fs.hex()
101 expected = strtod(s)
102 self.assertEqual(expected, got,
103 "Incorrectly rounded str->float conversion for {}: "
104 "expected {}, got {}".format(s, expected, got))
105
106 def test_short_halfway_cases(self):
107 # exact halfway cases with a small number of significant digits
108 for k in 0, 5, 10, 15, 20:
109 # upper = smallest integer >= 2**54/5**k
110 upper = -(-2**54//5**k)
111 # lower = smallest odd number >= 2**53/5**k
112 lower = -(-2**53//5**k)
113 if lower % 2 == 0:
114 lower += 1
115 for i in range(TEST_SIZE):
116 # Select a random odd n in [2**53/5**k,
117 # 2**54/5**k). Then n * 10**k gives a halfway case
118 # with small number of significant digits.
119 n, e = random.randrange(lower, upper, 2), k
120
121 # Remove any additional powers of 5.
122 while n % 5 == 0:
123 n, e = n // 5, e + 1
124 assert n % 10 in (1, 3, 7, 9)
125
126 # Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
127 # until n * 2**p2 has more than 20 significant digits.
128 digits, exponent = n, e
129 while digits < 10**20:
130 s = '{}e{}'.format(digits, exponent)
131 self.check_strtod(s)
132 # Same again, but with extra trailing zeros.
133 s = '{}e{}'.format(digits * 10**40, exponent - 40)
134 self.check_strtod(s)
135 digits *= 2
136
137 # Try numbers of the form n * 5**p2 * 10**(e - p5), p5
138 # >= 0, with n * 5**p5 < 10**20.
139 digits, exponent = n, e
140 while digits < 10**20:
141 s = '{}e{}'.format(digits, exponent)
142 self.check_strtod(s)
143 # Same again, but with extra trailing zeros.
144 s = '{}e{}'.format(digits * 10**40, exponent - 40)
145 self.check_strtod(s)
146 digits *= 5
147 exponent -= 1
148
149 def test_halfway_cases(self):
150 # test halfway cases for the round-half-to-even rule
151 for i in range(100 * TEST_SIZE):
152 # bit pattern for a random finite positive (or +0.0) float
153 bits = random.randrange(2047*2**52)
154
155 # convert bit pattern to a number of the form m * 2**e
156 e, m = divmod(bits, 2**52)
157 if e:
158 m, e = m + 2**52, e - 1
159 e -= 1074
160
161 # add 0.5 ulps
162 m, e = 2*m + 1, e - 1
163
164 # convert to a decimal string
165 if e >= 0:
166 digits = m << e
167 exponent = 0
168 else:
169 # m * 2**e = (m * 5**-e) * 10**e
170 digits = m * 5**-e
171 exponent = e
172 s = '{}e{}'.format(digits, exponent)
173 self.check_strtod(s)
174
175 def test_boundaries(self):
176 # boundaries expressed as triples (n, e, u), where
177 # n*10**e is an approximation to the boundary value and
178 # u*10**e is 1ulp
179 boundaries = [
180 (10000000000000000000, -19, 1110), # a power of 2 boundary (1.0)
181 (17976931348623159077, 289, 1995), # overflow boundary (2.**1024)
182 (22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022)
183 (0, -327, 4941), # zero
184 ]
185 for n, e, u in boundaries:
186 for j in range(1000):
187 digits = n + random.randrange(-3*u, 3*u)
188 exponent = e
189 s = '{}e{}'.format(digits, exponent)
190 self.check_strtod(s)
191 n *= 10
192 u *= 10
193 e -= 1
194
195 def test_underflow_boundary(self):
196 # test values close to 2**-1075, the underflow boundary; similar
197 # to boundary_tests, except that the random error doesn't scale
198 # with n
199 for exponent in range(-400, -320):
200 base = 10**-exponent // 2**1075
201 for j in range(TEST_SIZE):
202 digits = base + random.randrange(-1000, 1000)
203 s = '{}e{}'.format(digits, exponent)
204 self.check_strtod(s)
205
206 def test_bigcomp(self):
207 for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
208 dig10 = 10**ndigs
209 for i in range(10 * TEST_SIZE):
210 digits = random.randrange(dig10)
211 exponent = random.randrange(-400, 400)
212 s = '{}e{}'.format(digits, exponent)
213 self.check_strtod(s)
214
215 def test_parsing(self):
216 # make '0' more likely to be chosen than other digits
217 digits = '000000123456789'
218 signs = ('+', '-', '')
219
220 # put together random short valid strings
221 # \d*[.\d*]?e
222 for i in range(1000):
223 for j in range(TEST_SIZE):
224 s = random.choice(signs)
225 intpart_len = random.randrange(5)
226 s += ''.join(random.choice(digits) for _ in range(intpart_len))
227 if random.choice([True, False]):
228 s += '.'
229 fracpart_len = random.randrange(5)
230 s += ''.join(random.choice(digits)
231 for _ in range(fracpart_len))
232 else:
233 fracpart_len = 0
234 if random.choice([True, False]):
235 s += random.choice(['e', 'E'])
236 s += random.choice(signs)
237 exponent_len = random.randrange(1, 4)
238 s += ''.join(random.choice(digits)
239 for _ in range(exponent_len))
240
241 if intpart_len + fracpart_len:
242 self.check_strtod(s)
243 else:
244 try:
245 float(s)
246 except ValueError:
247 pass
248 else:
249 assert False, "expected ValueError"
250
251 @test.support.bigmemtest(size=test.support._2G+10, memuse=3, dry_run=False)
252 def test_oversized_digit_strings(self, maxsize):
253 # Input string whose length doesn't fit in an INT.
254 s = "1." + "1" * maxsize
255 with self.assertRaises(ValueError):
256 float(s)
257 del s
258
259 s = "0." + "0" * maxsize + "1"
260 with self.assertRaises(ValueError):
261 float(s)
262 del s
263
264 def test_large_exponents(self):
265 # Verify that the clipping of the exponent in strtod doesn't affect the
266 # output values.
267 def positive_exp(n):
268 """ Long string with value 1.0 and exponent n"""
269 return '0.{}1e+{}'.format('0'*(n-1), n)
270
271 def negative_exp(n):
272 """ Long string with value 1.0 and exponent -n"""
273 return '1{}e-{}'.format('0'*n, n)
274
275 self.assertEqual(float(positive_exp(10000)), 1.0)
276 self.assertEqual(float(positive_exp(20000)), 1.0)
277 self.assertEqual(float(positive_exp(30000)), 1.0)
278 self.assertEqual(float(negative_exp(10000)), 1.0)
279 self.assertEqual(float(negative_exp(20000)), 1.0)
280 self.assertEqual(float(negative_exp(30000)), 1.0)
281
282 def test_particular(self):
283 # inputs that produced crashes or incorrectly rounded results with
284 # previous versions of dtoa.c, for various reasons
285 test_strings = [
286 # issue 7632 bug 1, originally reported failing case
287 '2183167012312112312312.23538020374420446192e-370',
288 # 5 instances of issue 7632 bug 2
289 '12579816049008305546974391768996369464963024663104e-357',
290 '17489628565202117263145367596028389348922981857013e-357',
291 '18487398785991994634182916638542680759613590482273e-357',
292 '32002864200581033134358724675198044527469366773928e-358',
293 '94393431193180696942841837085033647913224148539854e-358',
294 '73608278998966969345824653500136787876436005957953e-358',
295 '64774478836417299491718435234611299336288082136054e-358',
296 '13704940134126574534878641876947980878824688451169e-357',
297 '46697445774047060960624497964425416610480524760471e-358',
298 # failing case for bug introduced by METD in r77451 (attempted
299 # fix for issue 7632, bug 2), and fixed in r77482.
300 '28639097178261763178489759107321392745108491825303e-311',
301 # two numbers demonstrating a flaw in the bigcomp 'dig == 0'
302 # correction block (issue 7632, bug 3)
303 '1.00000000000000001e44',
304 '1.0000000000000000100000000000000000000001e44',
305 # dtoa.c bug for numbers just smaller than a power of 2 (issue
306 # 7632, bug 4)
307 '99999999999999994487665465554760717039532578546e-47',
308 # failing case for off-by-one error introduced by METD in
309 # r77483 (dtoa.c cleanup), fixed in r77490
310 '965437176333654931799035513671997118345570045914469' #...
311 '6213413350821416312194420007991306908470147322020121018368e0',
312 # incorrect lsb detection for round-half-to-even when
313 # bc->scale != 0 (issue 7632, bug 6).
314 '104308485241983990666713401708072175773165034278685' #...
315 '682646111762292409330928739751702404658197872319129' #...
316 '036519947435319418387839758990478549477777586673075' #...
317 '945844895981012024387992135617064532141489278815239' #...
318 '849108105951619997829153633535314849999674266169258' #...
319 '928940692239684771590065027025835804863585454872499' #...
320 '320500023126142553932654370362024104462255244034053' #...
321 '203998964360882487378334860197725139151265590832887' #...
322 '433736189468858614521708567646743455601905935595381' #...
323 '852723723645799866672558576993978025033590728687206' #...
324 '296379801363024094048327273913079612469982585674824' #...
325 '156000783167963081616214710691759864332339239688734' #...
326 '656548790656486646106983450809073750535624894296242' #...
327 '072010195710276073042036425579852459556183541199012' #...
328 '652571123898996574563824424330960027873516082763671875e-1075',
329 # demonstration that original fix for issue 7632 bug 1 was
330 # buggy; the exit condition was too strong
331 '247032822920623295e-341',
332 # demonstrate similar problem to issue 7632 bug1: crash
333 # with 'oversized quotient in quorem' message.
334 '99037485700245683102805043437346965248029601286431e-373',
335 '99617639833743863161109961162881027406769510558457e-373',
336 '98852915025769345295749278351563179840130565591462e-372',
337 '99059944827693569659153042769690930905148015876788e-373',
338 '98914979205069368270421829889078356254059760327101e-372',
339 # issue 7632 bug 5: the following 2 strings convert differently
340 '1000000000000000000000000000000000000000e-16',
341 '10000000000000000000000000000000000000000e-17',
342 # issue 7632 bug 7
343 '991633793189150720000000000000000000000000000000000000000e-33',
344 # And another, similar, failing halfway case
345 '4106250198039490000000000000000000000000000000000000000e-38',
346 # issue 7632 bug 8: the following produced 10.0
347 '10.900000000000000012345678912345678912345',
348
349 # two humongous values from issue 7743
350 '116512874940594195638617907092569881519034793229385' #...
351 '228569165191541890846564669771714896916084883987920' #...
352 '473321268100296857636200926065340769682863349205363' #...
353 '349247637660671783209907949273683040397979984107806' #...
354 '461822693332712828397617946036239581632976585100633' #...
355 '520260770761060725403904123144384571612073732754774' #...
356 '588211944406465572591022081973828448927338602556287' #...
357 '851831745419397433012491884869454462440536895047499' #...
358 '436551974649731917170099387762871020403582994193439' #...
359 '761933412166821484015883631622539314203799034497982' #...
360 '130038741741727907429575673302461380386596501187482' #...
361 '006257527709842179336488381672818798450229339123527' #...
362 '858844448336815912020452294624916993546388956561522' #...
363 '161875352572590420823607478788399460162228308693742' #...
364 '05287663441403533948204085390898399055004119873046875e-1075',
365
366 '525440653352955266109661060358202819561258984964913' #...
367 '892256527849758956045218257059713765874251436193619' #...
368 '443248205998870001633865657517447355992225852945912' #...
369 '016668660000210283807209850662224417504752264995360' #...
370 '631512007753855801075373057632157738752800840302596' #...
371 '237050247910530538250008682272783660778181628040733' #...
372 '653121492436408812668023478001208529190359254322340' #...
373 '397575185248844788515410722958784640926528544043090' #...
374 '115352513640884988017342469275006999104519620946430' #...
375 '818767147966495485406577703972687838176778993472989' #...
376 '561959000047036638938396333146685137903018376496408' #...
377 '319705333868476925297317136513970189073693314710318' #...
378 '991252811050501448326875232850600451776091303043715' #...
379 '157191292827614046876950225714743118291034780466325' #...
380 '085141343734564915193426994587206432697337118211527' #...
381 '278968731294639353354774788602467795167875117481660' #...
382 '4738791256853675690543663283782215866825e-1180',
383
384 # exercise exit conditions in bigcomp comparison loop
385 '2602129298404963083833853479113577253105939995688e2',
386 '260212929840496308383385347911357725310593999568896e0',
387 '26021292984049630838338534791135772531059399956889601e-2',
388 '260212929840496308383385347911357725310593999568895e0',
389 '260212929840496308383385347911357725310593999568897e0',
390 '260212929840496308383385347911357725310593999568996e0',
391 '260212929840496308383385347911357725310593999568866e0',
392 # 2**53
393 '9007199254740992.00',
394 # 2**1024 - 2**970: exact overflow boundary. All values
395 # smaller than this should round to something finite; any value
396 # greater than or equal to this one overflows.
397 '179769313486231580793728971405303415079934132710037' #...
398 '826936173778980444968292764750946649017977587207096' #...
399 '330286416692887910946555547851940402630657488671505' #...
400 '820681908902000708383676273854845817711531764475730' #...
401 '270069855571366959622842914819860834936475292719074' #...
402 '168444365510704342711559699508093042880177904174497792',
403 # 2**1024 - 2**970 - tiny
404 '179769313486231580793728971405303415079934132710037' #...
405 '826936173778980444968292764750946649017977587207096' #...
406 '330286416692887910946555547851940402630657488671505' #...
407 '820681908902000708383676273854845817711531764475730' #...
408 '270069855571366959622842914819860834936475292719074' #...
409 '168444365510704342711559699508093042880177904174497791.999',
410 # 2**1024 - 2**970 + tiny
411 '179769313486231580793728971405303415079934132710037' #...
412 '826936173778980444968292764750946649017977587207096' #...
413 '330286416692887910946555547851940402630657488671505' #...
414 '820681908902000708383676273854845817711531764475730' #...
415 '270069855571366959622842914819860834936475292719074' #...
416 '168444365510704342711559699508093042880177904174497792.001',
417 # 1 - 2**-54, +-tiny
418 '999999999999999944488848768742172978818416595458984375e-54',
419 '9999999999999999444888487687421729788184165954589843749999999e-54',
420 '9999999999999999444888487687421729788184165954589843750000001e-54',
421 # Value found by Rick Regan that gives a result of 2**-968
422 # under Gay's dtoa.c (as of Nov 04, 2010); since fixed.
423 # (Fixed some time ago in Python's dtoa.c.)
424 '0.0000000000000000000000000000000000000000100000000' #...
425 '000000000576129113423785429971690421191214034235435' #...
426 '087147763178149762956868991692289869941246658073194' #...
427 '51982237978882039897143840789794921875',
428 ]
429 for s in test_strings:
430 self.check_strtod(s)
431
432 if __name__ == "__main__":
433 unittest.main()