cpython/Lib/test/decimaltestdata/remainder.decTest

------------------------------------------------------------------------
-- remainder.decTest -- decimal remainder                             --
-- Copyright (c) IBM Corporation, 1981, 2007.  All rights reserved.   --
------------------------------------------------------------------------
-- Please see the document "General Decimal Arithmetic Testcases"     --
-- at http://www2.hursley.ibm.com/decimal for the description of      --
-- these testcases.                                                   --
--                                                                    --
-- These testcases are experimental ('beta' versions), and they       --
-- may contain errors.  They are offered on an as-is basis.  In       --
-- particular, achieving the same results as the tests here is not    --
-- a guarantee that an implementation complies with any Standard      --
-- or specification.  The tests are not exhaustive.                   --
--                                                                    --
-- Please send comments, suggestions, and corrections to the author:  --
--   Mike Cowlishaw, IBM Fellow                                       --
--   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         --
--   mfc@uk.ibm.com                                                   --
------------------------------------------------------------------------
version: 2.57

extended:    1
precision:   9
rounding:    half_up
maxExponent: 384
minexponent: -383

-- sanity checks (as base, above)
remx001 remainder  1     1    ->  0
remx002 remainder  2     1    ->  0
remx003 remainder  1     2    ->  1
remx004 remainder  2     2    ->  0
remx005 remainder  0     1    ->  0
remx006 remainder  0     2    ->  0
remx007 remainder  1     3    ->  1
remx008 remainder  2     3    ->  2
remx009 remainder  3     3    ->  0

remx010 remainder  2.4   1    ->  0.4
remx011 remainder  2.4   -1   ->  0.4
remx012 remainder  -2.4  1    ->  -0.4
remx013 remainder  -2.4  -1   ->  -0.4
remx014 remainder  2.40  1    ->  0.40
remx015 remainder  2.400 1    ->  0.400
remx016 remainder  2.4   2    ->  0.4
remx017 remainder  2.400 2    ->  0.400
remx018 remainder  2.    2    ->  0
remx019 remainder  20    20   ->  0

remx020 remainder  187   187    ->  0
remx021 remainder  5     2      ->  1
remx022 remainder  5     2.0    ->  1.0
remx023 remainder  5     2.000  ->  1.000
remx024 remainder  5     0.200  ->  0.000
remx025 remainder  5     0.200  ->  0.000

remx030 remainder  1     2      ->  1
remx031 remainder  1     4      ->  1
remx032 remainder  1     8      ->  1

remx033 remainder  1     16     ->  1
remx034 remainder  1     32     ->  1
remx035 remainder  1     64     ->  1
remx040 remainder  1    -2      ->  1
remx041 remainder  1    -4      ->  1
remx042 remainder  1    -8      ->  1
remx043 remainder  1    -16     ->  1
remx044 remainder  1    -32     ->  1
remx045 remainder  1    -64     ->  1
remx050 remainder -1     2      ->  -1
remx051 remainder -1     4      ->  -1
remx052 remainder -1     8      ->  -1
remx053 remainder -1     16     ->  -1
remx054 remainder -1     32     ->  -1
remx055 remainder -1     64     ->  -1
remx060 remainder -1    -2      ->  -1
remx061 remainder -1    -4      ->  -1
remx062 remainder -1    -8      ->  -1
remx063 remainder -1    -16     ->  -1
remx064 remainder -1    -32     ->  -1
remx065 remainder -1    -64     ->  -1

remx066 remainder  999999999     1  -> 0
remx067 remainder  999999999.4   1  -> 0.4
remx068 remainder  999999999.5   1  -> 0.5
remx069 remainder  999999999.9   1  -> 0.9
remx070 remainder  999999999.999 1  -> 0.999
precision: 6
remx071 remainder  999999999     1  -> NaN Division_impossible
remx072 remainder  99999999      1  -> NaN Division_impossible
remx073 remainder  9999999       1  -> NaN Division_impossible
remx074 remainder  999999        1  -> 0
remx075 remainder  99999         1  -> 0
remx076 remainder  9999          1  -> 0
remx077 remainder  999           1  -> 0
remx078 remainder  99            1  -> 0
remx079 remainder  9             1  -> 0

precision: 9
remx080 remainder  0.            1  -> 0
remx081 remainder  .0            1  -> 0.0
remx082 remainder  0.00          1  -> 0.00
remx083 remainder  0.00E+9       1  -> 0
remx084 remainder  0.00E+3       1  -> 0
remx085 remainder  0.00E+2       1  -> 0
remx086 remainder  0.00E+1       1  -> 0.0
remx087 remainder  0.00E+0       1  -> 0.00
remx088 remainder  0.00E-0       1  -> 0.00
remx089 remainder  0.00E-1       1  -> 0.000
remx090 remainder  0.00E-2       1  -> 0.0000
remx091 remainder  0.00E-3       1  -> 0.00000
remx092 remainder  0.00E-4       1  -> 0.000000
remx093 remainder  0.00E-5       1  -> 0E-7
remx094 remainder  0.00E-6       1  -> 0E-8
remx095 remainder  0.0000E-50    1  -> 0E-54

-- Various flavours of remainder by 0
precision: 9
maxexponent: 999999999
minexponent: -999999999
remx101 remainder  0       0   -> NaN Division_undefined
remx102 remainder  0      -0   -> NaN Division_undefined
remx103 remainder -0       0   -> NaN Division_undefined
remx104 remainder -0      -0   -> NaN Division_undefined
remx105 remainder  0.0E5   0   -> NaN Division_undefined
remx106 remainder  0.000   0   -> NaN Division_undefined
-- [Some think this next group should be Division_by_zero exception, but
-- IEEE 854 is explicit that it is Invalid operation .. for
-- remainder-near, anyway]
remx107 remainder  0.0001  0   -> NaN Invalid_operation
remx108 remainder  0.01    0   -> NaN Invalid_operation
remx109 remainder  0.1     0   -> NaN Invalid_operation
remx110 remainder  1       0   -> NaN Invalid_operation
remx111 remainder  1       0.0 -> NaN Invalid_operation
remx112 remainder 10       0.0 -> NaN Invalid_operation
remx113 remainder 1E+100   0.0 -> NaN Invalid_operation
remx114 remainder 1E+1000  0   -> NaN Invalid_operation
remx115 remainder  0.0001 -0   -> NaN Invalid_operation
remx116 remainder  0.01   -0   -> NaN Invalid_operation
remx119 remainder  0.1    -0   -> NaN Invalid_operation
remx120 remainder  1      -0   -> NaN Invalid_operation
remx121 remainder  1      -0.0 -> NaN Invalid_operation
remx122 remainder 10      -0.0 -> NaN Invalid_operation
remx123 remainder 1E+100  -0.0 -> NaN Invalid_operation
remx124 remainder 1E+1000 -0   -> NaN Invalid_operation
-- and zeros on left
remx130 remainder  0      1   ->  0
remx131 remainder  0     -1   ->  0
remx132 remainder  0.0    1   ->  0.0
remx133 remainder  0.0   -1   ->  0.0
remx134 remainder -0      1   -> -0
remx135 remainder -0     -1   -> -0
remx136 remainder -0.0    1   -> -0.0
remx137 remainder -0.0   -1   -> -0.0

-- 0.5ers
remx143 remainder   0.5  2     ->  0.5
remx144 remainder   0.5  2.1   ->  0.5
remx145 remainder   0.5  2.01  ->  0.50
remx146 remainder   0.5  2.001 ->  0.500
remx147 remainder   0.50 2     ->  0.50
remx148 remainder   0.50 2.01  ->  0.50
remx149 remainder   0.50 2.001 ->  0.500

-- steadies
remx150 remainder  1  1   -> 0
remx151 remainder  1  2   -> 1
remx152 remainder  1  3   -> 1
remx153 remainder  1  4   -> 1
remx154 remainder  1  5   -> 1
remx155 remainder  1  6   -> 1
remx156 remainder  1  7   -> 1
remx157 remainder  1  8   -> 1
remx158 remainder  1  9   -> 1
remx159 remainder  1  10  -> 1
remx160 remainder  1  1   -> 0
remx161 remainder  2  1   -> 0
remx162 remainder  3  1   -> 0
remx163 remainder  4  1   -> 0
remx164 remainder  5  1   -> 0
remx165 remainder  6  1   -> 0
remx166 remainder  7  1   -> 0
remx167 remainder  8  1   -> 0
remx168 remainder  9  1   -> 0
remx169 remainder  10 1   -> 0

-- some differences from remainderNear
remx171 remainder   0.4  1.020 ->  0.400
remx172 remainder   0.50 1.020 ->  0.500
remx173 remainder   0.51 1.020 ->  0.510
remx174 remainder   0.52 1.020 ->  0.520
remx175 remainder   0.6  1.020 ->  0.600


-- More flavours of remainder by 0
maxexponent: 999999999
minexponent: -999999999
remx201 remainder  0      0   -> NaN Division_undefined
remx202 remainder  0.0E5  0   -> NaN Division_undefined
remx203 remainder  0.000  0   -> NaN Division_undefined
remx204 remainder  0.0001 0   -> NaN Invalid_operation
remx205 remainder  0.01   0   -> NaN Invalid_operation
remx206 remainder  0.1    0   -> NaN Invalid_operation
remx207 remainder  1      0   -> NaN Invalid_operation
remx208 remainder  1      0.0 -> NaN Invalid_operation
remx209 remainder 10      0.0 -> NaN Invalid_operation
remx210 remainder 1E+100  0.0 -> NaN Invalid_operation
remx211 remainder 1E+1000 0   -> NaN Invalid_operation

-- some differences from remainderNear
remx231 remainder  -0.4  1.020 -> -0.400
remx232 remainder  -0.50 1.020 -> -0.500
remx233 remainder  -0.51 1.020 -> -0.510
remx234 remainder  -0.52 1.020 -> -0.520
remx235 remainder  -0.6  1.020 -> -0.600

-- high Xs
remx240 remainder  1E+2  1.00  ->  0.00


-- test some cases that are close to exponent overflow
maxexponent: 999999999
minexponent: -999999999
remx270 remainder 1 1e999999999    -> 1
remx271 remainder 1 0.9e999999999  -> 1
remx272 remainder 1 0.99e999999999 -> 1
remx273 remainder 1 0.999999999e999999999 -> 1
remx274 remainder 9e999999999          1 -> NaN Division_impossible
remx275 remainder 9.9e999999999        1 -> NaN Division_impossible
remx276 remainder 9.99e999999999       1 -> NaN Division_impossible
remx277 remainder 9.99999999e999999999 1 -> NaN Division_impossible

remx280 remainder 0.1 9e-999999999       -> NaN Division_impossible
remx281 remainder 0.1 99e-999999999      -> NaN Division_impossible
remx282 remainder 0.1 999e-999999999     -> NaN Division_impossible

remx283 remainder 0.1 9e-999999998       -> NaN Division_impossible
remx284 remainder 0.1 99e-999999998      -> NaN Division_impossible
remx285 remainder 0.1 999e-999999998     -> NaN Division_impossible
remx286 remainder 0.1 999e-999999997     -> NaN Division_impossible
remx287 remainder 0.1 9999e-999999997    -> NaN Division_impossible
remx288 remainder 0.1 99999e-999999997   -> NaN Division_impossible

-- remx3xx are from DiagBigDecimal
remx301 remainder   1    3     ->  1
remx302 remainder   5    5     ->  0
remx303 remainder   13   10    ->  3
remx304 remainder   13   50    ->  13
remx305 remainder   13   100   ->  13
remx306 remainder   13   1000  ->  13
remx307 remainder   .13    1   ->  0.13
remx308 remainder   0.133  1   ->  0.133
remx309 remainder   0.1033 1   ->  0.1033
remx310 remainder   1.033  1   ->  0.033
remx311 remainder   10.33  1   ->  0.33
remx312 remainder   10.33 10   ->  0.33
remx313 remainder   103.3  1   ->  0.3
remx314 remainder   133   10   ->  3
remx315 remainder   1033  10   ->  3
remx316 remainder   1033  50   ->  33
remx317 remainder   101.0  3   ->  2.0
remx318 remainder   102.0  3   ->  0.0
remx319 remainder   103.0  3   ->  1.0
remx320 remainder   2.40   1   ->  0.40
remx321 remainder   2.400  1   ->  0.400
remx322 remainder   2.4    1   ->  0.4
remx323 remainder   2.4    2   ->  0.4
remx324 remainder   2.400  2   ->  0.400
remx325 remainder   1   0.3    ->  0.1
remx326 remainder   1   0.30   ->  0.10
remx327 remainder   1   0.300  ->  0.100
remx328 remainder   1   0.3000 ->  0.1000
remx329 remainder   1.0    0.3 ->  0.1
remx330 remainder   1.00   0.3 ->  0.10
remx331 remainder   1.000  0.3 ->  0.100
remx332 remainder   1.0000 0.3 ->  0.1000
remx333 remainder   0.5  2     ->  0.5
remx334 remainder   0.5  2.1   ->  0.5
remx335 remainder   0.5  2.01  ->  0.50
remx336 remainder   0.5  2.001 ->  0.500
remx337 remainder   0.50 2     ->  0.50
remx338 remainder   0.50 2.01  ->  0.50
remx339 remainder   0.50 2.001 ->  0.500

remx340 remainder   0.5   0.5000001    ->  0.5000000
remx341 remainder   0.5   0.50000001    ->  0.50000000
remx342 remainder   0.5   0.500000001    ->  0.500000000
remx343 remainder   0.5   0.5000000001    ->  0.500000000  Rounded
remx344 remainder   0.5   0.50000000001    ->  0.500000000  Rounded
remx345 remainder   0.5   0.4999999    ->  1E-7
remx346 remainder   0.5   0.49999999    ->  1E-8
remx347 remainder   0.5   0.499999999    ->  1E-9
remx348 remainder   0.5   0.4999999999    ->  1E-10
remx349 remainder   0.5   0.49999999999    ->  1E-11
remx350 remainder   0.5   0.499999999999    ->  1E-12

remx351 remainder   0.03  7  ->  0.03
remx352 remainder   5   2    ->  1
remx353 remainder   4.1   2    ->  0.1
remx354 remainder   4.01   2    ->  0.01
remx355 remainder   4.001   2    ->  0.001
remx356 remainder   4.0001   2    ->  0.0001
remx357 remainder   4.00001   2    ->  0.00001
remx358 remainder   4.000001   2    ->  0.000001
remx359 remainder   4.0000001   2    ->  1E-7

remx360 remainder   1.2   0.7345 ->  0.4655
remx361 remainder   0.8   12     ->  0.8
remx362 remainder   0.8   0.2    ->  0.0
remx363 remainder   0.8   0.3    ->  0.2
remx364 remainder   0.800   12   ->  0.800
remx365 remainder   0.800   1.7  ->  0.800
remx366 remainder   2.400   2    ->  0.400

precision: 6
remx371 remainder   2.400  2        ->  0.400
precision: 3
-- long operand, rounded, case
remx372 remainder   12345678900000 12e+12 -> 3.46E+11 Inexact Rounded
--                  12000000000000

precision: 5
remx381 remainder 12345  1         ->  0
remx382 remainder 12345  1.0001    ->  0.7657
remx383 remainder 12345  1.001     ->  0.668
remx384 remainder 12345  1.01      ->  0.78
remx385 remainder 12345  1.1       ->  0.8
remx386 remainder 12355  4         ->  3
remx387 remainder 12345  4         ->  1
remx388 remainder 12355  4.0001    ->  2.6912
remx389 remainder 12345  4.0001    ->  0.6914
remx390 remainder 12345  4.9       ->  1.9
remx391 remainder 12345  4.99      ->  4.73
remx392 remainder 12345  4.999     ->  2.469
remx393 remainder 12345  4.9999    ->  0.2469
remx394 remainder 12345  5         ->  0
remx395 remainder 12345  5.0001    ->  4.7532
remx396 remainder 12345  5.001     ->  2.532
remx397 remainder 12345  5.01      ->  0.36
remx398 remainder 12345  5.1       ->  3.0

precision: 9
-- the nasty division-by-1 cases
remx401 remainder   0.5         1   ->  0.5
remx402 remainder   0.55        1   ->  0.55
remx403 remainder   0.555       1   ->  0.555
remx404 remainder   0.5555      1   ->  0.5555
remx405 remainder   0.55555     1   ->  0.55555
remx406 remainder   0.555555    1   ->  0.555555
remx407 remainder   0.5555555   1   ->  0.5555555
remx408 remainder   0.55555555  1   ->  0.55555555
remx409 remainder   0.555555555 1   ->  0.555555555

-- zero signs
remx650 remainder  1  1 ->  0
remx651 remainder -1  1 -> -0
remx652 remainder  1 -1 ->  0
remx653 remainder -1 -1 -> -0
remx654 remainder  0  1 ->  0
remx655 remainder -0  1 -> -0
remx656 remainder  0 -1 ->  0
remx657 remainder -0 -1 -> -0
remx658 remainder  0.00  1  ->  0.00
remx659 remainder -0.00  1  -> -0.00

-- Specials
remx680 remainder  Inf  -Inf   ->  NaN Invalid_operation
remx681 remainder  Inf  -1000  ->  NaN Invalid_operation
remx682 remainder  Inf  -1     ->  NaN Invalid_operation
remx683 remainder  Inf   0     ->  NaN Invalid_operation
remx684 remainder  Inf  -0     ->  NaN Invalid_operation
remx685 remainder  Inf   1     ->  NaN Invalid_operation
remx686 remainder  Inf   1000  ->  NaN Invalid_operation
remx687 remainder  Inf   Inf   ->  NaN Invalid_operation
remx688 remainder -1000  Inf   -> -1000
remx689 remainder -Inf   Inf   ->  NaN Invalid_operation
remx691 remainder -1     Inf   -> -1
remx692 remainder  0     Inf   ->  0
remx693 remainder -0     Inf   -> -0
remx694 remainder  1     Inf   ->  1
remx695 remainder  1000  Inf   ->  1000
remx696 remainder  Inf   Inf   ->  NaN Invalid_operation

remx700 remainder -Inf  -Inf   ->  NaN Invalid_operation
remx701 remainder -Inf  -1000  ->  NaN Invalid_operation
remx702 remainder -Inf  -1     ->  NaN Invalid_operation
remx703 remainder -Inf  -0     ->  NaN Invalid_operation
remx704 remainder -Inf   0     ->  NaN Invalid_operation
remx705 remainder -Inf   1     ->  NaN Invalid_operation
remx706 remainder -Inf   1000  ->  NaN Invalid_operation
remx707 remainder -Inf   Inf   ->  NaN Invalid_operation
remx708 remainder -Inf  -Inf   ->  NaN Invalid_operation
remx709 remainder -1000  Inf   -> -1000
remx710 remainder -1    -Inf   -> -1
remx711 remainder -0    -Inf   -> -0
remx712 remainder  0    -Inf   ->  0
remx713 remainder  1    -Inf   ->  1
remx714 remainder  1000 -Inf   ->  1000
remx715 remainder  Inf  -Inf   ->  NaN Invalid_operation

remx721 remainder  NaN -Inf    ->  NaN
remx722 remainder  NaN -1000   ->  NaN
remx723 remainder  NaN -1      ->  NaN
remx724 remainder  NaN -0      ->  NaN
remx725 remainder -NaN  0      -> -NaN
remx726 remainder  NaN  1      ->  NaN
remx727 remainder  NaN  1000   ->  NaN
remx728 remainder  NaN  Inf    ->  NaN
remx729 remainder  NaN -NaN    ->  NaN
remx730 remainder -Inf  NaN    ->  NaN
remx731 remainder -1000 NaN    ->  NaN
remx732 remainder -1    NaN    ->  NaN
remx733 remainder -0   -NaN    -> -NaN
remx734 remainder  0    NaN    ->  NaN
remx735 remainder  1   -NaN    -> -NaN
remx736 remainder  1000 NaN    ->  NaN
remx737 remainder  Inf  NaN    ->  NaN

remx741 remainder  sNaN -Inf   ->  NaN  Invalid_operation
remx742 remainder  sNaN -1000  ->  NaN  Invalid_operation
remx743 remainder -sNaN -1     -> -NaN  Invalid_operation
remx744 remainder  sNaN -0     ->  NaN  Invalid_operation
remx745 remainder  sNaN  0     ->  NaN  Invalid_operation
remx746 remainder  sNaN  1     ->  NaN  Invalid_operation
remx747 remainder  sNaN  1000  ->  NaN  Invalid_operation
remx749 remainder  sNaN  NaN   ->  NaN  Invalid_operation
remx750 remainder  sNaN sNaN   ->  NaN  Invalid_operation
remx751 remainder  NaN  sNaN   ->  NaN  Invalid_operation
remx752 remainder -Inf  sNaN   ->  NaN  Invalid_operation
remx753 remainder -1000 sNaN   ->  NaN  Invalid_operation
remx754 remainder -1    sNaN   ->  NaN  Invalid_operation
remx755 remainder -0    sNaN   ->  NaN  Invalid_operation
remx756 remainder  0    sNaN   ->  NaN  Invalid_operation
remx757 remainder  1    sNaN   ->  NaN  Invalid_operation
remx758 remainder  1000 sNaN   ->  NaN  Invalid_operation
remx759 remainder  Inf -sNaN   -> -NaN  Invalid_operation

-- propaging NaNs
remx760 remainder  NaN1   NaN7   ->  NaN1
remx761 remainder sNaN2   NaN8   ->  NaN2 Invalid_operation
remx762 remainder  NaN3  sNaN9   ->  NaN9 Invalid_operation
remx763 remainder sNaN4  sNaN10  ->  NaN4 Invalid_operation
remx764 remainder    15   NaN11  ->  NaN11
remx765 remainder  NaN6   NaN12  ->  NaN6
remx766 remainder  Inf    NaN13  ->  NaN13
remx767 remainder  NaN14  -Inf   ->  NaN14
remx768 remainder    0    NaN15  ->  NaN15
remx769 remainder  NaN16   -0    ->  NaN16

-- test some cases that are close to exponent overflow
maxexponent: 999999999
minexponent: -999999999
remx770 remainder 1 1e999999999    -> 1
remx771 remainder 1 0.9e999999999  -> 1
remx772 remainder 1 0.99e999999999 -> 1
remx773 remainder 1 0.999999999e999999999 -> 1
remx774 remainder 9e999999999          1 -> NaN Division_impossible
remx775 remainder 9.9e999999999        1 -> NaN Division_impossible
remx776 remainder 9.99e999999999       1 -> NaN Division_impossible
remx777 remainder 9.99999999e999999999 1 -> NaN Division_impossible

-- long operand checks
maxexponent: 999
minexponent: -999
precision: 9
remx801 remainder 12345678000 100 -> 0
remx802 remainder 1 12345678000   -> 1
remx803 remainder 1234567800  10  -> 0
remx804 remainder 1 1234567800    -> 1
remx805 remainder 1234567890  10  -> 0
remx806 remainder 1 1234567890    -> 1
remx807 remainder 1234567891  10  -> 1
remx808 remainder 1 1234567891    -> 1
remx809 remainder 12345678901 100 -> 1
remx810 remainder 1 12345678901   -> 1
remx811 remainder 1234567896  10  -> 6
remx812 remainder 1 1234567896    -> 1

precision: 15
remx821 remainder 12345678000 100 -> 0
remx822 remainder 1 12345678000   -> 1
remx823 remainder 1234567800  10  -> 0
remx824 remainder 1 1234567800    -> 1
remx825 remainder 1234567890  10  -> 0
remx826 remainder 1 1234567890    -> 1
remx827 remainder 1234567891  10  -> 1
remx828 remainder 1 1234567891    -> 1
remx829 remainder 12345678901 100 -> 1
remx830 remainder 1 12345678901   -> 1
remx831 remainder 1234567896  10  -> 6
remx832 remainder 1 1234567896    -> 1

-- worries from divideint
precision: 8
remx840 remainder  100000000.0   1  ->  NaN Division_impossible
remx841 remainder  100000000.4   1  ->  NaN Division_impossible
remx842 remainder  100000000.5   1  ->  NaN Division_impossible
remx843 remainder  100000000.9   1  ->  NaN Division_impossible
remx844 remainder  100000000.999 1  ->  NaN Division_impossible
precision: 6
remx850 remainder  100000003     5  ->  NaN Division_impossible
remx851 remainder  10000003      5  ->  NaN Division_impossible
remx852 remainder  1000003       5  ->  3
remx853 remainder  100003        5  ->  3
remx854 remainder  10003         5  ->  3
remx855 remainder  1003          5  ->  3
remx856 remainder  103           5  ->  3
remx857 remainder  13            5  ->  3
remx858 remainder  1             5  ->  1

-- Vladimir's cases
remx860 remainder 123.0e1 10000000000000000 -> 1230
remx861 remainder 1230    10000000000000000 -> 1230
remx862 remainder 12.3e2  10000000000000000 -> 1230
remx863 remainder 1.23e3  10000000000000000 -> 1230
remx864 remainder 123e1   10000000000000000 -> 1230
remx870 remainder 123e1    1000000000000000 -> 1230
remx871 remainder 123e1     100000000000000 -> 1230
remx872 remainder 123e1      10000000000000 -> 1230
remx873 remainder 123e1       1000000000000 -> 1230
remx874 remainder 123e1        100000000000 -> 1230
remx875 remainder 123e1         10000000000 -> 1230
remx876 remainder 123e1          1000000000 -> 1230
remx877 remainder 123e1           100000000 -> 1230
remx878 remainder 1230            100000000 -> 1230
remx879 remainder 123e1            10000000 -> 1230
remx880 remainder 123e1             1000000 -> 1230
remx881 remainder 123e1              100000 -> 1230
remx882 remainder 123e1               10000 -> 1230
remx883 remainder 123e1                1000 ->  230
remx884 remainder 123e1                 100 ->   30
remx885 remainder 123e1                  10 ->    0
remx886 remainder 123e1                   1 ->    0

remx889 remainder 123e1   20000000000000000 -> 1230
remx890 remainder 123e1    2000000000000000 -> 1230
remx891 remainder 123e1     200000000000000 -> 1230
remx892 remainder 123e1      20000000000000 -> 1230
remx893 remainder 123e1       2000000000000 -> 1230
remx894 remainder 123e1        200000000000 -> 1230
remx895 remainder 123e1         20000000000 -> 1230
remx896 remainder 123e1          2000000000 -> 1230
remx897 remainder 123e1           200000000 -> 1230
remx899 remainder 123e1            20000000 -> 1230
remx900 remainder 123e1             2000000 -> 1230
remx901 remainder 123e1              200000 -> 1230
remx902 remainder 123e1               20000 -> 1230
remx903 remainder 123e1                2000 -> 1230
remx904 remainder 123e1                 200 ->   30
remx905 remainder 123e1                  20 ->   10
remx906 remainder 123e1                   2 ->    0

remx909 remainder 123e1   50000000000000000 -> 1230
remx910 remainder 123e1    5000000000000000 -> 1230
remx911 remainder 123e1     500000000000000 -> 1230
remx912 remainder 123e1      50000000000000 -> 1230
remx913 remainder 123e1       5000000000000 -> 1230
remx914 remainder 123e1        500000000000 -> 1230
remx915 remainder 123e1         50000000000 -> 1230
remx916 remainder 123e1          5000000000 -> 1230
remx917 remainder 123e1           500000000 -> 1230
remx919 remainder 123e1            50000000 -> 1230
remx920 remainder 123e1             5000000 -> 1230
remx921 remainder 123e1              500000 -> 1230
remx922 remainder 123e1               50000 -> 1230
remx923 remainder 123e1                5000 -> 1230
remx924 remainder 123e1                 500 ->  230
remx925 remainder 123e1                  50 ->   30
remx926 remainder 123e1                   5 ->    0

remx929 remainder 123e1   90000000000000000 -> 1230
remx930 remainder 123e1    9000000000000000 -> 1230
remx931 remainder 123e1     900000000000000 -> 1230
remx932 remainder 123e1      90000000000000 -> 1230
remx933 remainder 123e1       9000000000000 -> 1230
remx934 remainder 123e1        900000000000 -> 1230
remx935 remainder 123e1         90000000000 -> 1230
remx936 remainder 123e1          9000000000 -> 1230
remx937 remainder 123e1           900000000 -> 1230
remx939 remainder 123e1            90000000 -> 1230
remx940 remainder 123e1             9000000 -> 1230
remx941 remainder 123e1              900000 -> 1230
remx942 remainder 123e1               90000 -> 1230
remx943 remainder 123e1                9000 -> 1230
remx944 remainder 123e1                 900 ->  330
remx945 remainder 123e1                  90 ->   60
remx946 remainder 123e1                   9 ->    6

remx950 remainder 123e1   10000000000000000 -> 1230
remx951 remainder 123e1   100000000000000000 -> 1230
remx952 remainder 123e1   1000000000000000000 -> 1230
remx953 remainder 123e1   10000000000000000000 -> 1230
remx954 remainder 123e1   100000000000000000000 -> 1230
remx955 remainder 123e1   1000000000000000000000 -> 1230
remx956 remainder 123e1   10000000000000000000000 -> 1230
remx957 remainder 123e1   100000000000000000000000 -> 1230
remx958 remainder 123e1   1000000000000000000000000 -> 1230
remx959 remainder 123e1   10000000000000000000000000 -> 1230

remx960 remainder 123e1   19999999999999999 -> 1230
remx961 remainder 123e1   199999999999999990 -> 1230
remx962 remainder 123e1   1999999999999999999 -> 1230
remx963 remainder 123e1   19999999999999999990 -> 1230
remx964 remainder 123e1   199999999999999999999 -> 1230
remx965 remainder 123e1   1999999999999999999990 -> 1230
remx966 remainder 123e1   19999999999999999999999 -> 1230
remx967 remainder 123e1   199999999999999999999990 -> 1230
remx968 remainder 123e1   1999999999999999999999999 -> 1230
remx969 remainder 123e1   19999999999999999999999990 -> 1230

remx970 remainder 1e1   10000000000000000 -> 10
remx971 remainder 1e1   100000000000000000 -> 10
remx972 remainder 1e1   1000000000000000000 -> 10
remx973 remainder 1e1   10000000000000000000 -> 10
remx974 remainder 1e1   100000000000000000000 -> 10
remx975 remainder 1e1   1000000000000000000000 -> 10
remx976 remainder 1e1   10000000000000000000000 -> 10
remx977 remainder 1e1   100000000000000000000000 -> 10
remx978 remainder 1e1   1000000000000000000000000 -> 10
remx979 remainder 1e1   10000000000000000000000000 -> 10

remx980 remainder 123e1 1000E999999 -> 1.23E+3  -- 123E+1 internally

-- overflow and underflow tests [from divide]
precision: 9
maxexponent: 999999999
minexponent: -999999999
remx990 remainder +1.23456789012345E-0 9E+999999999 -> 1.23456789 Inexact Rounded
remx991 remainder 9E+999999999 +0.23456789012345E-0 -> NaN Division_impossible
remx992 remainder +0.100 9E+999999999               -> 0.100
remx993 remainder 9E-999999999 +9.100               -> 9E-999999999
remx995 remainder -1.23456789012345E-0 9E+999999999 -> -1.23456789 Inexact Rounded
remx996 remainder 9E+999999999 -0.83456789012345E-0 -> NaN Division_impossible
remx997 remainder -0.100 9E+999999999               -> -0.100
remx998 remainder 9E-999999999 -9.100               -> 9E-999999999

-- Null tests
remx1000 remainder 10  # -> NaN Invalid_operation
remx1001 remainder  # 10 -> NaN Invalid_operation