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      1 -- 'f' code formatting, with explicit precision (>= 0).  Output always
      2 -- has the given number of places after the point;  zeros are added if
      3 -- necessary to make this true.
      4 
      5 -- zeros
      6 %.0f 0 -> 0
      7 %.1f 0 -> 0.0
      8 %.2f 0 -> 0.00
      9 %.3f 0 -> 0.000
     10 %.50f 0 -> 0.00000000000000000000000000000000000000000000000000
     11 
     12 -- precision 0;  result should never include a .
     13 %.0f 1.5 -> 2
     14 %.0f 2.5 -> 2
     15 %.0f 3.5 -> 4
     16 %.0f 0.0 -> 0
     17 %.0f 0.1 -> 0
     18 %.0f 0.001 -> 0
     19 %.0f 10.0 -> 10
     20 %.0f 10.1 -> 10
     21 %.0f 10.01 -> 10
     22 %.0f 123.456 -> 123
     23 %.0f 1234.56 -> 1235
     24 %.0f 1e49 -> 9999999999999999464902769475481793196872414789632
     25 %.0f 9.9999999999999987e+49 -> 99999999999999986860582406952576489172979654066176
     26 %.0f 1e50 -> 100000000000000007629769841091887003294964970946560
     27 
     28 -- precision 1
     29 %.1f 0.0001 -> 0.0
     30 %.1f 0.001 -> 0.0
     31 %.1f 0.01 -> 0.0
     32 %.1f 0.04 -> 0.0
     33 %.1f 0.06 -> 0.1
     34 %.1f 0.25 -> 0.2
     35 %.1f 0.75 -> 0.8
     36 %.1f 1.4 -> 1.4
     37 %.1f 1.5 -> 1.5
     38 %.1f 10.0 -> 10.0
     39 %.1f 1000.03 -> 1000.0
     40 %.1f 1234.5678 -> 1234.6
     41 %.1f 1234.7499 -> 1234.7
     42 %.1f 1234.75 -> 1234.8
     43 
     44 -- precision 2
     45 %.2f 0.0001 -> 0.00
     46 %.2f 0.001 -> 0.00
     47 %.2f 0.004999 -> 0.00
     48 %.2f 0.005001 -> 0.01
     49 %.2f 0.01 -> 0.01
     50 %.2f 0.125 -> 0.12
     51 %.2f 0.375 -> 0.38
     52 %.2f 1234500 -> 1234500.00
     53 %.2f 1234560 -> 1234560.00
     54 %.2f 1234567 -> 1234567.00
     55 %.2f 1234567.8 -> 1234567.80
     56 %.2f 1234567.89 -> 1234567.89
     57 %.2f 1234567.891 -> 1234567.89
     58 %.2f 1234567.8912 -> 1234567.89
     59 
     60 -- alternate form always includes a decimal point.  This only
     61 -- makes a difference when the precision is 0.
     62 %#.0f 0 -> 0.
     63 %#.1f 0 -> 0.0
     64 %#.0f 1.5 -> 2.
     65 %#.0f 2.5 -> 2.
     66 %#.0f 10.1 -> 10.
     67 %#.0f 1234.56 -> 1235.
     68 %#.1f 1.4 -> 1.4
     69 %#.2f 0.375 -> 0.38
     70 
     71 -- if precision is omitted it defaults to 6
     72 %f 0 -> 0.000000
     73 %f 1230000 -> 1230000.000000
     74 %f 1234567 -> 1234567.000000
     75 %f 123.4567 -> 123.456700
     76 %f 1.23456789 -> 1.234568
     77 %f 0.00012 -> 0.000120
     78 %f 0.000123 -> 0.000123
     79 %f 0.00012345 -> 0.000123
     80 %f 0.000001 -> 0.000001
     81 %f 0.0000005001 -> 0.000001
     82 %f 0.0000004999 -> 0.000000
     83 
     84 -- nans and infinities
     85 %f nan -> nan
     86 %f inf -> inf
     87 %f -infinity -> -inf
     88 %F nan -> NAN
     89 %F infinity -> INF
     90 %F -inf -> -INF
     91 
     92 -- 'e' code formatting with explicit precision (>= 0). Output should
     93 -- always have exactly the number of places after the point that were
     94 -- requested.
     95 
     96 -- zeros
     97 %.0e 0 -> 0e+00
     98 %.1e 0 -> 0.0e+00
     99 %.2e 0 -> 0.00e+00
    100 %.10e 0 -> 0.0000000000e+00
    101 %.50e 0 -> 0.00000000000000000000000000000000000000000000000000e+00
    102 
    103 -- precision 0.  no decimal point in the output
    104 %.0e 0.01 -> 1e-02
    105 %.0e 0.1 -> 1e-01
    106 %.0e 1 -> 1e+00
    107 %.0e 10 -> 1e+01
    108 %.0e 100 -> 1e+02
    109 %.0e 0.012 -> 1e-02
    110 %.0e 0.12 -> 1e-01
    111 %.0e 1.2 -> 1e+00
    112 %.0e 12 -> 1e+01
    113 %.0e 120 -> 1e+02
    114 %.0e 123.456 -> 1e+02
    115 %.0e 0.000123456 -> 1e-04
    116 %.0e 123456000 -> 1e+08
    117 %.0e 0.5 -> 5e-01
    118 %.0e 1.4 -> 1e+00
    119 %.0e 1.5 -> 2e+00
    120 %.0e 1.6 -> 2e+00
    121 %.0e 2.4999999 -> 2e+00
    122 %.0e 2.5 -> 2e+00
    123 %.0e 2.5000001 -> 3e+00
    124 %.0e 3.499999999999 -> 3e+00
    125 %.0e 3.5 -> 4e+00
    126 %.0e 4.5 -> 4e+00
    127 %.0e 5.5 -> 6e+00
    128 %.0e 6.5 -> 6e+00
    129 %.0e 7.5 -> 8e+00
    130 %.0e 8.5 -> 8e+00
    131 %.0e 9.4999 -> 9e+00
    132 %.0e 9.5 -> 1e+01
    133 %.0e 10.5 -> 1e+01
    134 %.0e 14.999 -> 1e+01
    135 %.0e 15 -> 2e+01
    136 
    137 -- precision 1
    138 %.1e 0.0001 -> 1.0e-04
    139 %.1e 0.001 -> 1.0e-03
    140 %.1e 0.01 -> 1.0e-02
    141 %.1e 0.1 -> 1.0e-01
    142 %.1e 1 -> 1.0e+00
    143 %.1e 10 -> 1.0e+01
    144 %.1e 100 -> 1.0e+02
    145 %.1e 120 -> 1.2e+02
    146 %.1e 123 -> 1.2e+02
    147 %.1e 123.4 -> 1.2e+02
    148 
    149 -- precision 2
    150 %.2e 0.00013 -> 1.30e-04
    151 %.2e 0.000135 -> 1.35e-04
    152 %.2e 0.0001357 -> 1.36e-04
    153 %.2e 0.0001 -> 1.00e-04
    154 %.2e 0.001 -> 1.00e-03
    155 %.2e 0.01 -> 1.00e-02
    156 %.2e 0.1 -> 1.00e-01
    157 %.2e 1 -> 1.00e+00
    158 %.2e 10 -> 1.00e+01
    159 %.2e 100 -> 1.00e+02
    160 %.2e 1000 -> 1.00e+03
    161 %.2e 1500 -> 1.50e+03
    162 %.2e 1590 -> 1.59e+03
    163 %.2e 1598 -> 1.60e+03
    164 %.2e 1598.7 -> 1.60e+03
    165 %.2e 1598.76 -> 1.60e+03
    166 %.2e 9999 -> 1.00e+04
    167 
    168 -- omitted precision defaults to 6
    169 %e 0 -> 0.000000e+00
    170 %e 165 -> 1.650000e+02
    171 %e 1234567 -> 1.234567e+06
    172 %e 12345678 -> 1.234568e+07
    173 %e 1.1 -> 1.100000e+00
    174 
    175 -- alternate form always contains a decimal point.  This only makes
    176 -- a difference when precision is 0.
    177 
    178 %#.0e 0.01 -> 1.e-02
    179 %#.0e 0.1 -> 1.e-01
    180 %#.0e 1 -> 1.e+00
    181 %#.0e 10 -> 1.e+01
    182 %#.0e 100 -> 1.e+02
    183 %#.0e 0.012 -> 1.e-02
    184 %#.0e 0.12 -> 1.e-01
    185 %#.0e 1.2 -> 1.e+00
    186 %#.0e 12 -> 1.e+01
    187 %#.0e 120 -> 1.e+02
    188 %#.0e 123.456 -> 1.e+02
    189 %#.0e 0.000123456 -> 1.e-04
    190 %#.0e 123456000 -> 1.e+08
    191 %#.0e 0.5 -> 5.e-01
    192 %#.0e 1.4 -> 1.e+00
    193 %#.0e 1.5 -> 2.e+00
    194 %#.0e 1.6 -> 2.e+00
    195 %#.0e 2.4999999 -> 2.e+00
    196 %#.0e 2.5 -> 2.e+00
    197 %#.0e 2.5000001 -> 3.e+00
    198 %#.0e 3.499999999999 -> 3.e+00
    199 %#.0e 3.5 -> 4.e+00
    200 %#.0e 4.5 -> 4.e+00
    201 %#.0e 5.5 -> 6.e+00
    202 %#.0e 6.5 -> 6.e+00
    203 %#.0e 7.5 -> 8.e+00
    204 %#.0e 8.5 -> 8.e+00
    205 %#.0e 9.4999 -> 9.e+00
    206 %#.0e 9.5 -> 1.e+01
    207 %#.0e 10.5 -> 1.e+01
    208 %#.0e 14.999 -> 1.e+01
    209 %#.0e 15 -> 2.e+01
    210 %#.1e 123.4 -> 1.2e+02
    211 %#.2e 0.0001357 -> 1.36e-04
    212 
    213 -- nans and infinities
    214 %e nan -> nan
    215 %e inf -> inf
    216 %e -infinity -> -inf
    217 %E nan -> NAN
    218 %E infinity -> INF
    219 %E -inf -> -INF
    220 
    221 -- 'g' code formatting.
    222 
    223 -- zeros
    224 %.0g 0 -> 0
    225 %.1g 0 -> 0
    226 %.2g 0 -> 0
    227 %.3g 0 -> 0
    228 %.4g 0 -> 0
    229 %.10g 0 -> 0
    230 %.50g 0 -> 0
    231 %.100g 0 -> 0
    232 
    233 -- precision 0 doesn't make a lot of sense for the 'g' code (what does
    234 -- it mean to have no significant digits?); in practice, it's interpreted
    235 -- as identical to precision 1
    236 %.0g 1000 -> 1e+03
    237 %.0g 100 -> 1e+02
    238 %.0g 10 -> 1e+01
    239 %.0g 1 -> 1
    240 %.0g 0.1 -> 0.1
    241 %.0g 0.01 -> 0.01
    242 %.0g 1e-3 -> 0.001
    243 %.0g 1e-4 -> 0.0001
    244 %.0g 1e-5 -> 1e-05
    245 %.0g 1e-6 -> 1e-06
    246 %.0g 12 -> 1e+01
    247 %.0g 120 -> 1e+02
    248 %.0g 1.2 -> 1
    249 %.0g 0.12 -> 0.1
    250 %.0g 0.012 -> 0.01
    251 %.0g 0.0012 -> 0.001
    252 %.0g 0.00012 -> 0.0001
    253 %.0g 0.000012 -> 1e-05
    254 %.0g 0.0000012 -> 1e-06
    255 
    256 -- precision 1 identical to precision 0
    257 %.1g 1000 -> 1e+03
    258 %.1g 100 -> 1e+02
    259 %.1g 10 -> 1e+01
    260 %.1g 1 -> 1
    261 %.1g 0.1 -> 0.1
    262 %.1g 0.01 -> 0.01
    263 %.1g 1e-3 -> 0.001
    264 %.1g 1e-4 -> 0.0001
    265 %.1g 1e-5 -> 1e-05
    266 %.1g 1e-6 -> 1e-06
    267 %.1g 12 -> 1e+01
    268 %.1g 120 -> 1e+02
    269 %.1g 1.2 -> 1
    270 %.1g 0.12 -> 0.1
    271 %.1g 0.012 -> 0.01
    272 %.1g 0.0012 -> 0.001
    273 %.1g 0.00012 -> 0.0001
    274 %.1g 0.000012 -> 1e-05
    275 %.1g 0.0000012 -> 1e-06
    276 
    277 -- precision 2
    278 %.2g 1000 -> 1e+03
    279 %.2g 100 -> 1e+02
    280 %.2g 10 -> 10
    281 %.2g 1 -> 1
    282 %.2g 0.1 -> 0.1
    283 %.2g 0.01 -> 0.01
    284 %.2g 0.001 -> 0.001
    285 %.2g 1e-4 -> 0.0001
    286 %.2g 1e-5 -> 1e-05
    287 %.2g 1e-6 -> 1e-06
    288 %.2g 1234 -> 1.2e+03
    289 %.2g 123 -> 1.2e+02
    290 %.2g 12.3 -> 12
    291 %.2g 1.23 -> 1.2
    292 %.2g 0.123 -> 0.12
    293 %.2g 0.0123 -> 0.012
    294 %.2g 0.00123 -> 0.0012
    295 %.2g 0.000123 -> 0.00012
    296 %.2g 0.0000123 -> 1.2e-05
    297 
    298 -- alternate g formatting:  always include decimal point and
    299 -- exactly <precision> significant digits.
    300 %#.0g 0 -> 0.
    301 %#.1g 0 -> 0.
    302 %#.2g 0 -> 0.0
    303 %#.3g 0 -> 0.00
    304 %#.4g 0 -> 0.000
    305 
    306 %#.0g 0.2 -> 0.2
    307 %#.1g 0.2 -> 0.2
    308 %#.2g 0.2 -> 0.20
    309 %#.3g 0.2 -> 0.200
    310 %#.4g 0.2 -> 0.2000
    311 %#.10g 0.2 -> 0.2000000000
    312 
    313 %#.0g 2 -> 2.
    314 %#.1g 2 -> 2.
    315 %#.2g 2 -> 2.0
    316 %#.3g 2 -> 2.00
    317 %#.4g 2 -> 2.000
    318 
    319 %#.0g 20 -> 2.e+01
    320 %#.1g 20 -> 2.e+01
    321 %#.2g 20 -> 20.
    322 %#.3g 20 -> 20.0
    323 %#.4g 20 -> 20.00
    324 
    325 %#.0g 234.56 -> 2.e+02
    326 %#.1g 234.56 -> 2.e+02
    327 %#.2g 234.56 -> 2.3e+02
    328 %#.3g 234.56 -> 235.
    329 %#.4g 234.56 -> 234.6
    330 %#.5g 234.56 -> 234.56
    331 %#.6g 234.56 -> 234.560
    332 
    333 -- nans and infinities
    334 %g nan -> nan
    335 %g inf -> inf
    336 %g -infinity -> -inf
    337 %G nan -> NAN
    338 %G infinity -> INF
    339 %G -inf -> -INF
    340 
    341 -- for repr formatting see the separate test_short_repr test in
    342 -- test_float.py.  Not all platforms use short repr for floats.
    343 
    344 -- str formatting.  Result always includes decimal point and at
    345 -- least one digit after the point, or an exponent.
    346 %s 0 -> 0.0
    347 %s 1 -> 1.0
    348 
    349 %s 0.01 -> 0.01
    350 %s 0.02 -> 0.02
    351 %s 0.03 -> 0.03
    352 %s 0.04 -> 0.04
    353 %s 0.05 -> 0.05
    354 
    355 -- str truncates to 12 significant digits
    356 %s 1.234123412341 -> 1.23412341234
    357 %s 1.23412341234 -> 1.23412341234
    358 %s 1.2341234123 -> 1.2341234123
    359 
    360 -- values >= 1e11 get an exponent
    361 %s 10 -> 10.0
    362 %s 100 -> 100.0
    363 %s 1e10 -> 10000000000.0
    364 %s 9.999e10 -> 99990000000.0
    365 %s 99999999999 -> 99999999999.0
    366 %s 99999999999.9 -> 99999999999.9
    367 %s 99999999999.99 -> 1e+11
    368 %s 1e11 -> 1e+11
    369 %s 1e12 -> 1e+12
    370 
    371 -- as do values < 1e-4
    372 %s 1e-3 -> 0.001
    373 %s 1.001e-4 -> 0.0001001
    374 %s 1.000000000001e-4 -> 0.0001
    375 %s 1.00000000001e-4 -> 0.000100000000001
    376 %s 1.0000000001e-4 -> 0.00010000000001
    377 %s 1e-4 -> 0.0001
    378 %s 0.999999999999e-4 -> 9.99999999999e-05
    379 %s 0.999e-4 -> 9.99e-05
    380 %s 1e-5 -> 1e-05
    381