Improve mutlipleOf validator with floating point value.

[vpelletier]

Example:

>>> 150.0 % 0.01
0.009999999999996878
>>> 0.01 - 0.009999999999996878
3.1225022567582528e-15
>>> 150.0 / 0.01
15000.0

I've prepared a commit against json-schema/JSON-Schema-Test-Suite adding following test case:

    {
        "schema": {"multipleOf": 0.01},
        "tests": [
            {
                "description": "150.0 is multiple of 0.01",
                "data": 150.0,
                "valid": true
            },
            {
                "description": "150.0001 is not multiple of 0.01",
                "data": 150.0001,
                "valid": false
            }
        ]
    }

but am not sure it is the right place to put such test nor how to choose "better" values without relying on implementation (does implementatio use modulo ? on double or single precision ? etc). As a result, I could not come up with a meaningful description. Anyway, this test fails with current implementation with:
ValidationError: 150.0 is not a multiple of 0.01
and is fixed with attached patch.

[vpelletier]

Anything wrong with this change ?

[Julian]

Hey, sorry, been a bit backed up but appreciate the patch certainly. I'm not sure, I have to think about it a bit more. It seems the answer is no, nothing wrong :), because all the tests pass, but I have to look closer since I haven't convinced myself that this actually doesn't just shift the imprecision someplace else.

[vpelletier]

Good point, I'm not really sure of this either actually.
At least for 150.0-family values (ie, same mantisa but varying exponent) /-division seems to consistently behave well while remainder precision gets worse as exponent increases.
Adding a small-ish value gives expected results up to the point where adding 0.00001 doesn't actually change the value.
I do not know if this can be extrapolated to other mantises.

150.0 * 2**x

>>> print '\n'.join(['%20.5f /:%30.12f %5s %%:%.18f %5s' % (y, y/0.01, int(y/0.01) != y/0.01, y%0.01, (y%0.01 > FLOAT_TOLERANCE) and (0.01 - y%0.01) > FLOAT_TOLERANCE) for y in [150 * 2**x for x in xrange(40)]])
           150.00000 /:            15000.000000000000 False %:0.009999999999996878  True
           300.00000 /:            30000.000000000000 False %:0.009999999999993755  True
           600.00000 /:            60000.000000000000 False %:0.009999999999987510  True
          1200.00000 /:           120000.000000000000 False %:0.009999999999975020  True
          2400.00000 /:           240000.000000000000 False %:0.009999999999950040  True
          4800.00000 /:           480000.000000000000 False %:0.009999999999900080  True
          9600.00000 /:           960000.000000000000 False %:0.009999999999800160  True
         19200.00000 /:          1920000.000000000000 False %:0.009999999999600320  True
         38400.00000 /:          3840000.000000000000 False %:0.009999999999200640  True
         76800.00000 /:          7680000.000000000000 False %:0.009999999998401279  True
        153600.00000 /:         15360000.000000000000 False %:0.009999999996802558  True
        307200.00000 /:         30720000.000000000000 False %:0.009999999993605116  True
        614400.00000 /:         61440000.000000000000 False %:0.009999999987210231  True
       1228800.00000 /:        122880000.000000000000 False %:0.009999999974420462  True
       2457600.00000 /:        245760000.000000000000 False %:0.009999999948840923  True
       4915200.00000 /:        491520000.000000000000 False %:0.009999999897681846  True
       9830400.00000 /:        983040000.000000000000 False %:0.009999999795363692  True
      19660800.00000 /:       1966080000.000000000000 False %:0.009999999590727384  True
      39321600.00000 /:       3932160000.000000000000 False %:0.009999999181454769  True
      78643200.00000 /:       7864320000.000000000000 False %:0.009999998362909537  True
     157286400.00000 /:      15728640000.000000000000 False %:0.009999996725819074  True
     314572800.00000 /:      31457280000.000000000000 False %:0.009999993451638147  True
     629145600.00000 /:      62914560000.000000000000 False %:0.009999986903276295  True
    1258291200.00000 /:     125829120000.000000000000 False %:0.009999973806552589  True
    2516582400.00000 /:     251658240000.000000000000 False %:0.009999947613105178  True
    5033164800.00000 /:     503316480000.000000000000 False %:0.009999895226210356  True
   10066329600.00000 /:    1006632960000.000000000000 False %:0.009999790452420712  True
   20132659200.00000 /:    2013265920000.000000000000 False %:0.009999580904841423  True
   40265318400.00000 /:    4026531840000.000000000000 False %:0.009999161809682846  True
   80530636800.00000 /:    8053063680000.000000000000 False %:0.009998323619365692  True
  161061273600.00000 /:   16106127360000.000000000000 False %:0.009996647238731384  True
  322122547200.00000 /:   32212254720000.000000000000 False %:0.009993294477462769  True
  644245094400.00000 /:   64424509440000.000000000000 False %:0.009986588954925537  True
 1288490188800.00000 /:  128849018880000.000000000000 False %:0.009973177909851074  True
 2576980377600.00000 /:  257698037760000.000000000000 False %:0.009946355819702149  True
 5153960755200.00000 /:  515396075520000.000000000000 False %:0.009892711639404297  True
10307921510400.00000 /: 1030792151040000.000000000000 False %:0.009785423278808594  True
20615843020800.00000 /: 2061584302080000.000000000000 False %:0.009570846557617188  True
41231686041600.00000 /: 4123168604160000.000000000000 False %:0.009141693115234375  True
82463372083200.00000 /: 8246337208320000.000000000000 False %:0.008283386230468750  True

0.00001 + 150.0 * 2**x

>>> print '\n'.join(['%20.5f /:%30.12f %5s %%:%.18f %5s' % (y, y/0.01, int(y/0.01) != y/0.01, y%0.01, (y%0.01 > FLOAT_TOLERANCE) and (0.01 - y%0.01) > FLOAT_TOLERANCE) for y in [0.00001 + 150 * 2**x for x in xrange(40)]])
           150.00001 /:            15000.001000000000  True %:0.000010000000000052  True
           300.00001 /:            30000.000999999997  True %:0.000009999999968507  True
           600.00001 /:            60000.000999999997  True %:0.000009999999962262  True
          1200.00001 /:           120000.000999999989  True %:0.000009999999949772  True
          2400.00001 /:           240000.001000000018  True %:0.000010000000152166  True
          4800.00001 /:           480000.000999999989  True %:0.000009999999647459  True
          9600.00001 /:           960000.000999999931  True %:0.000009999999547539  True
         19200.00001 /:          1920000.000999999931  True %:0.000009999999347698  True
         38400.00001 /:          3840000.001000000164  True %:0.000010000002585997  True
         76800.00001 /:          7680000.001000000164  True %:0.000010000001786636  True
        153600.00001 /:         15360000.000999998301  True %:0.000009999985636000  True
        307200.00001 /:         30720000.001000002027  True %:0.000010000011542388  True
        614400.00001 /:         61440000.000999994576  True %:0.000009999946939843  True
       1228800.00001 /:        122880000.001000002027  True %:0.000010000050565395  True
       2457600.00001 /:        245760000.001000016928  True %:0.000010000024985857  True
       4915200.00001 /:        491520000.000999927521  True %:0.000009999508165492  True
       9830400.00001 /:        983040000.001000046730  True %:0.000010000337169913  True
      19660800.00001 /:       1966080000.000999927521  True %:0.000009998269888456  True
      39321600.00001 /:       3932160000.000999927521  True %:0.000009997860615840  True
      78643200.00001 /:       7864320000.000999450684  True %:0.000009997042070609  True
     157286400.00001 /:      15728640000.001001358032  True %:0.000010010306141339  True
     314572800.00001 /:      31457280000.000999450684  True %:0.000010007031960413  True
     629145600.00001 /:      62914560000.000999450684  True %:0.000010000483598560  True
    1258291200.00001 /:     125829120000.000991821289  True %:0.000009987386874855  True
    2516582400.00001 /:     251658240000.001007080078  True %:0.000009961193427444  True
    5033164800.00001 /:     503316480000.000915527344  True %:0.000009431969374418  True
   10066329600.00001 /:    1006632960000.000976562500  True %:0.000009327195584774  True
   20132659200.00001 /:    2013265920000.001220703125  True %:0.000011024996638298  True
   40265318400.00001 /:    4026531840000.000488281250  True %:0.000006791204214096  True
   80530636800.00002 /:    8053063680000.000976562500  True %:0.000013582408428192  True
  161061273600.00000 /:   16106127360000.000000000000 False %:0.009996647238731384  True
  322122547200.00000 /:   32212254720000.000000000000 False %:0.009993294477462769  True
  644245094400.00000 /:   64424509440000.000000000000 False %:0.009986588954925537  True
 1288490188800.00000 /:  128849018880000.000000000000 False %:0.009973177909851074  True
 2576980377600.00000 /:  257698037760000.000000000000 False %:0.009946355819702149  True
 5153960755200.00000 /:  515396075520000.000000000000 False %:0.009892711639404297  True
10307921510400.00000 /: 1030792151040000.000000000000 False %:0.009785423278808594  True
20615843020800.00000 /: 2061584302080000.000000000000 False %:0.009570846557617188  True
41231686041600.00000 /: 4123168604160000.000000000000 False %:0.009141693115234375  True
82463372083200.00000 /: 8246337208320000.000000000000 False %:0.008283386230468750  True

[Julian]

OK, think you've convinced me for now that this is better than what's there at least, and whenever my brain gets a minute to relax I can try to think a bit harder about it, but merging, appreciated!

[vpelletier]

I'm sorry, I just found a case where my code doesn't work:

> 10.1/0.1
100.99999999999999

I've not yet decided where I wan to go from there. While I understand there is no golden bullet for floats, I would like such "simple" (only 4 significant digits in result...) cases to just work.