remaindernear.dectest

eda is an estimation of distributions algorithm

-- rmnx3xx are from DiagBigDecimal
rmnx301 remaindernear   1    3     ->  1
rmnx302 remaindernear   5    5     ->  0
rmnx303 remaindernear   13   10    ->  3
rmnx304 remaindernear   13   50    ->  13
rmnx305 remaindernear   13   100   ->  13
rmnx306 remaindernear   13   1000  ->  13
rmnx307 remaindernear   .13    1   ->  0.13
rmnx308 remaindernear   0.133  1   ->  0.133
rmnx309 remaindernear   0.1033 1   ->  0.1033
rmnx310 remaindernear   1.033  1   ->  0.033
rmnx311 remaindernear   10.33  1   ->  0.33
rmnx312 remaindernear   10.33 10   ->  0.33
rmnx313 remaindernear   103.3  1   ->  0.3
rmnx314 remaindernear   133   10   ->  3
rmnx315 remaindernear   1033  10   ->  3
rmnx316 remaindernear   1033  50   -> -17
rmnx317 remaindernear   101.0  3   -> -1.0
rmnx318 remaindernear   102.0  3   ->  0
rmnx319 remaindernear   103.0  3   ->  1.0
rmnx320 remaindernear   2.40   1   ->  0.40
rmnx321 remaindernear   2.400  1   ->  0.400
rmnx322 remaindernear   2.4    1   ->  0.4
rmnx323 remaindernear   2.4    2   ->  0.4
rmnx324 remaindernear   2.400  2   ->  0.400
rmnx325 remaindernear   1   0.3    ->  0.1
rmnx326 remaindernear   1   0.30   ->  0.10
rmnx327 remaindernear   1   0.300  ->  0.100
rmnx328 remaindernear   1   0.3000 ->  0.1000
rmnx329 remaindernear   1.0    0.3 ->  0.1
rmnx330 remaindernear   1.00   0.3 ->  0.10
rmnx331 remaindernear   1.000  0.3 ->  0.100
rmnx332 remaindernear   1.0000 0.3 ->  0.1000
rmnx333 remaindernear   0.5  2     ->  0.5
rmnx334 remaindernear   0.5  2.1   ->  0.5
rmnx335 remaindernear   0.5  2.01  ->  0.5
rmnx336 remaindernear   0.5  2.001 ->  0.5
rmnx337 remaindernear   0.50 2     ->  0.50
rmnx338 remaindernear   0.50 2.01  ->  0.50
rmnx339 remaindernear   0.50 2.001 ->  0.50

rmnx340 remaindernear   0.5   0.5000001    ->  -1E-7
rmnx341 remaindernear   0.5   0.50000001    ->  -1E-8
rmnx342 remaindernear   0.5   0.500000001    ->  -1E-9
rmnx343 remaindernear   0.5   0.5000000001    ->  -1E-10
rmnx344 remaindernear   0.5   0.50000000001    ->  -1E-11
rmnx345 remaindernear   0.5   0.4999999    ->  1E-7
rmnx346 remaindernear   0.5   0.49999999    ->  1E-8
rmnx347 remaindernear   0.5   0.499999999    ->  1E-9
rmnx348 remaindernear   0.5   0.4999999999    ->  1E-10
rmnx349 remaindernear   0.5   0.49999999999    ->  1E-11

rmnx350 remaindernear   0.03  7  ->  0.03
rmnx351 remaindernear   5   2    ->  1
rmnx352 remaindernear   4.1   2    ->  0.1
rmnx353 remaindernear   4.01   2    ->  0.01
rmnx354 remaindernear   4.001   2    ->  0.001
rmnx355 remaindernear   4.0001   2    ->  0.0001
rmnx356 remaindernear   4.00001   2    ->  0.00001
rmnx357 remaindernear   4.000001   2    ->  0.000001
rmnx358 remaindernear   4.0000001   2    ->  1E-7

rmnx360 remaindernear   1.2   0.7345 -> -0.2690
rmnx361 remaindernear   0.8   12     ->  0.8
rmnx362 remaindernear   0.8   0.2    ->  0
rmnx363 remaindernear   0.8   0.3    -> -0.1
rmnx364 remaindernear   0.800   12   ->  0.800
rmnx365 remaindernear   0.800   1.7  ->  0.800
rmnx366 remaindernear   2.400   2    ->  0.400

precision: 6
rmnx371 remaindernear   2.400  2        ->  0.400
precision: 3
rmnx372 remaindernear   12345678900000 12e+12 -> 3.46E+11 Inexact Rounded

precision: 5
rmnx381 remaindernear 12345  1         ->  0
rmnx382 remaindernear 12345  1.0001    -> -0.2344
rmnx383 remaindernear 12345  1.001     -> -0.333
rmnx384 remaindernear 12345  1.01      -> -0.23
rmnx385 remaindernear 12345  1.1       -> -0.3
rmnx386 remaindernear 12355  4         -> -1
rmnx387 remaindernear 12345  4         ->  1
rmnx388 remaindernear 12355  4.0001    -> -1.3089
rmnx389 remaindernear 12345  4.0001    ->  0.6914
rmnx390 remaindernear 12345  4.9       ->  1.9
rmnx391 remaindernear 12345  4.99      -> -0.26
rmnx392 remaindernear 12345  4.999     ->  2.469
rmnx393 remaindernear 12345  4.9999    ->  0.2469
rmnx394 remaindernear 12345  5         ->  0
rmnx395 remaindernear 12345  5.0001    -> -0.2469
rmnx396 remaindernear 12345  5.001     -> -2.469
rmnx397 remaindernear 12345  5.01      ->  0.36
rmnx398 remaindernear 12345  5.1       -> -2.1

precision: 9
-- some nasty division-by-1 cases [some similar above]
rmnx401 remaindernear   0.4         1   ->  0.4
rmnx402 remaindernear   0.45        1   ->  0.45
rmnx403 remaindernear   0.455       1   ->  0.455
rmnx404 remaindernear   0.4555      1   ->  0.4555
rmnx405 remaindernear   0.45555     1   ->  0.45555
rmnx406 remaindernear   0.455555    1   ->  0.455555
rmnx407 remaindernear   0.4555555   1   ->  0.4555555
rmnx408 remaindernear   0.45555555  1   ->  0.45555555
rmnx409 remaindernear   0.455555555 1   ->  0.455555555

-- some tricky LHSs
rmnx420 remaindernear   99999999.999999999   1E+8   -> -1E-9
rmnx421 remaindernear  999999999.999999999   1E+9   -> -1E-9
precision: 9
rmnx430 remaindernear   0.455555555 1   ->  0.455555555
precision: 8
rmnx431 remaindernear   0.455555555 1   ->  0.45555556 Inexact Rounded
precision: 7
rmnx432 remaindernear   0.455555555 1   ->  0.4555556  Inexact Rounded
precision: 6
rmnx433 remaindernear   0.455555555 1   ->  0.455556   Inexact Rounded
precision: 5
rmnx434 remaindernear   0.455555555 1   ->  0.45556    Inexact Rounded
precision: 4
rmnx435 remaindernear   0.455555555 1   ->  0.4556     Inexact Rounded
precision: 3
rmnx436 remaindernear   0.455555555 1   ->  0.456      Inexact Rounded
precision: 2
rmnx437 remaindernear   0.455555555 1   ->  0.46       Inexact Rounded
precision: 1
rmnx438 remaindernear   0.455555555 1   ->  0.5        Inexact Rounded

-- early tests; from text descriptions
precision: 9
rmnx601 remaindernear  10   6  -> -2
rmnx602 remaindernear -10   6  -> 2
rmnx603 remaindernear  11   3  -> -1
rmnx604 remaindernear  11   5  -> 1
rmnx605 remaindernear   7.7 8  -> -0.3
rmnx606 remaindernear  31.5 3  -> 1.5    -- i=10
rmnx607 remaindernear  34.5 3  -> -1.5   -- i=11

-- Specials
rmnx680 remaindernear  Inf  -Inf   ->  NaN Invalid_operation
rmnx681 remaindernear  Inf  -1000  ->  NaN Invalid_operation
rmnx682 remaindernear  Inf  -1     ->  NaN Invalid_operation
rmnx683 remaindernear  Inf   0     ->  NaN Invalid_operation
rmnx684 remaindernear  Inf  -0     ->  NaN Invalid_operation
rmnx685 remaindernear  Inf   1     ->  NaN Invalid_operation
rmnx686 remaindernear  Inf   1000  ->  NaN Invalid_operation
rmnx687 remaindernear  Inf   Inf   ->  NaN Invalid_operation
rmnx688 remaindernear -1000  Inf   -> -1000
rmnx689 remaindernear -Inf   Inf   ->  NaN Invalid_operation
rmnx691 remaindernear -1     Inf   -> -1
rmnx692 remaindernear  0     Inf   ->  0
rmnx693 remaindernear -0     Inf   -> -0
rmnx694 remaindernear  1     Inf   ->  1
rmnx695 remaindernear  1000  Inf   ->  1000
rmnx696 remaindernear  Inf   Inf   ->  NaN Invalid_operation

rmnx700 remaindernear -Inf  -Inf   ->  NaN Invalid_operation
rmnx701 remaindernear -Inf  -1000  ->  NaN Invalid_operation
rmnx702 remaindernear -Inf  -1     ->  NaN Invalid_operation
rmnx703 remaindernear -Inf  -0     ->  NaN Invalid_operation
rmnx704 remaindernear -Inf   0     ->  NaN Invalid_operation
rmnx705 remaindernear -Inf   1     ->  NaN Invalid_operation
rmnx706 remaindernear -Inf   1000  ->  NaN Invalid_operation
rmnx707 remaindernear -Inf   Inf   ->  NaN Invalid_operation
rmnx708 remaindernear -Inf  -Inf   ->  NaN Invalid_operation
rmnx709 remaindernear -1000  Inf   -> -1000
rmnx710 remaindernear -1    -Inf   -> -1
rmnx711 remaindernear -0    -Inf   -> -0
rmnx712 remaindernear  0    -Inf   ->  0
rmnx713 remaindernear  1    -Inf   ->  1
rmnx714 remaindernear  1000 -Inf   ->  1000
rmnx715 remaindernear  Inf  -Inf   ->  NaN Invalid_operation

rmnx721 remaindernear  NaN -Inf    ->  NaN
rmnx722 remaindernear  NaN -1000   ->  NaN
rmnx723 remaindernear  NaN -1      ->  NaN
rmnx724 remaindernear  NaN -0      ->  NaN
rmnx725 remaindernear  NaN  0      ->  NaN
rmnx726 remaindernear  NaN  1      ->  NaN
rmnx727 remaindernear  NaN  1000   ->  NaN
rmnx728 remaindernear  NaN  Inf    ->  NaN
rmnx729 remaindernear  NaN  NaN    ->  NaN
rmnx730 remaindernear -Inf  NaN    ->  NaN
rmnx731 remaindernear -1000 NaN    ->  NaN
rmnx732 remaindernear -1    NaN    ->  NaN
rmnx733 remaindernear -0    NaN    ->  NaN
rmnx734 remaindernear  0    NaN    ->  NaN
rmnx735 remaindernear  1    NaN    ->  NaN
rmnx736 remaindernear  1000 NaN    ->  NaN
rmnx737 remaindernear  Inf  NaN    ->  NaN

rmnx741 remaindernear  sNaN -Inf   ->  NaN  Invalid_operation
rmnx742 remaindernear  sNaN -1000  ->  NaN  Invalid_operation
rmnx743 remaindernear  sNaN -1     ->  NaN  Invalid_operation
rmnx744 remaindernear  sNaN -0     ->  NaN  Invalid_operation
rmnx745 remaindernear  sNaN  0     ->  NaN  Invalid_operation
rmnx746 remaindernear  sNaN  1     ->  NaN  Invalid_operation
rmnx747 remaindernear  sNaN  1000  ->  NaN  Invalid_operation
rmnx749 remaindernear  sNaN  NaN   ->  NaN  Invalid_operation
rmnx750 remaindernear  sNaN sNaN   ->  NaN  Invalid_operation
rmnx751 remaindernear  NaN  sNaN   ->  NaN  Invalid_operation
rmnx752 remaindernear -Inf  sNaN   ->  NaN  Invalid_operation
rmnx753 remaindernear -1000 sNaN   ->  NaN  Invalid_operation
rmnx754 remaindernear -1    sNaN   ->  NaN  Invalid_operation
rmnx755 remaindernear -0    sNaN   ->  NaN  Invalid_operation
rmnx756 remaindernear  0    sNaN   ->  NaN  Invalid_operation
rmnx757 remaindernear  1    sNaN   ->  NaN  Invalid_operation
rmnx758 remaindernear  1000 sNaN   ->  NaN  Invalid_operation
rmnx759 remaindernear  Inf  sNaN   ->  NaN  Invalid_operation
rmnx760 remaindernear  NaN  sNaN   ->  NaN  Invalid_operation

-- test some cases that are close to exponent overflow
maxexponent: 999999999
rmnx770 remaindernear 1 1e999999999    -> 1
rmnx771 remaindernear 1 0.9e999999999  -> 1
rmnx772 remaindernear 1 0.99e999999999 -> 1
rmnx773 remaindernear 1 0.999999999e999999999 -> 1
rmnx774 remaindernear 9e999999999          1 -> NaN Division_impossible
rmnx775 remaindernear 9.9e999999999        1 -> NaN Division_impossible
rmnx776 remaindernear 9.99e999999999       1 -> NaN Division_impossible
rmnx777 remaindernear 9.99999999e999999999 1 -> NaN Division_impossible


-- overflow and underflow tests [from divide]
precision: 9
maxexponent: 999999999
rmnx780 remaindernear +1.23456789012345E-0 9E+999999999 -> 1.23456789 Inexact Rounded
rmnx781 remaindernear 9E+999999999 +0.23456789012345E-0 -> NaN Division_impossible
rmnx782 remaindernear +0.100 9E+999999999               -> 0.100
rmnx783 remaindernear 9E-999999999 +9.100               -> 9E-999999999
rmnx785 remaindernear -1.23456789012345E-0 9E+999999999 -> -1.23456789 Inexact Rounded
rmnx786 remaindernear 9E+999999999 -0.83456789012345E-0 -> NaN Division_impossible
rmnx787 remaindernear -0.100 9E+999999999               -> -0.100
rmnx788 remaindernear 9E-999999999 -9.100               -> 9E-999999999

-- long operands checks
maxexponent: 999
precision: 9
rmnx801 remaindernear 12345678000 100 -> 0
rmnx802 remaindernear 1 12345678000   -> 1
rmnx803 remaindernear 1234567800  10  -> 0
rmnx804 remaindernear 1 1234567800    -> 1
rmnx805 remaindernear 1234567890  10  -> 0
rmnx806 remaindernear 1 1234567890    -> 1
rmnx807 remaindernear 1234567891  10  -> 1
rmnx808 remaindernear 1 1234567891    -> 1
rmnx809 remaindernear 12345678901 100 -> 1
rmnx810 remaindernear 1 12345678901   -> 1
rmnx811 remaindernear 1234567896  10  -> -4
rmnx812 remaindernear 1 1234567896    -> 1

precision: 15
rmnx841 remaindernear 12345678000 100 -> 0
rmnx842 remaindernear 1 12345678000   -> 1
rmnx843 remaindernear 1234567800  10  -> 0
rmnx844 remaindernear 1 1234567800    -> 1
rmnx845 remaindernear 1234567890  10  -> 0
rmnx846 remaindernear 1 1234567890    -> 1
rmnx847 remaindernear 1234567891  10  -> 1
rmnx848 remaindernear 1 1234567891    -> 1
rmnx849 remaindernear 12345678901 100 -> 1
rmnx850 remaindernear 1 12345678901   -> 1
rmnx851 remaindernear 1234567896  10  -> -4
rmnx852 remaindernear 1 1234567896    -> 1

-- Null tests
rmnx900 remaindernear 10  # -> NaN Invalid_operation
rmnx901 remaindernear  # 10 -> NaN Invalid_operation