cpython/Lib/test/decimaltestdata/ddRemainder.decTest

------------------------------------------------------------------------
-- ddRemainder.decTest -- decDouble remainder                         --
-- Copyright (c) IBM Corporation, 1981, 2008.  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: 2.59

precision:   16
maxExponent: 384
minExponent: -383
extended:    1
clamp:       1
rounding:    half_even

-- sanity checks (as base, above)
ddrem001 remainder  1     1    ->  0
ddrem002 remainder  2     1    ->  0
ddrem003 remainder  1     2    ->  1
ddrem004 remainder  2     2    ->  0
ddrem005 remainder  0     1    ->  0
ddrem006 remainder  0     2    ->  0
ddrem007 remainder  1     3    ->  1
ddrem008 remainder  2     3    ->  2
ddrem009 remainder  3     3    ->  0

ddrem010 remainder  2.4   1    ->  0.4
ddrem011 remainder  2.4   -1   ->  0.4
ddrem012 remainder  -2.4  1    ->  -0.4
ddrem013 remainder  -2.4  -1   ->  -0.4
ddrem014 remainder  2.40  1    ->  0.40
ddrem015 remainder  2.400 1    ->  0.400
ddrem016 remainder  2.4   2    ->  0.4
ddrem017 remainder  2.400 2    ->  0.400
ddrem018 remainder  2.    2    ->  0
ddrem019 remainder  20    20   ->  0

ddrem020 remainder  187   187    ->  0
ddrem021 remainder  5     2      ->  1
ddrem022 remainder  5     2.0    ->  1.0
ddrem023 remainder  5     2.000  ->  1.000
ddrem024 remainder  5     0.200  ->  0.000
ddrem025 remainder  5     0.200  ->  0.000

ddrem030 remainder  1     2      ->  1
ddrem031 remainder  1     4      ->  1
ddrem032 remainder  1     8      ->  1

ddrem033 remainder  1     16     ->  1
ddrem034 remainder  1     32     ->  1
ddrem035 remainder  1     64     ->  1
ddrem040 remainder  1    -2      ->  1
ddrem041 remainder  1    -4      ->  1
ddrem042 remainder  1    -8      ->  1
ddrem043 remainder  1    -16     ->  1
ddrem044 remainder  1    -32     ->  1
ddrem045 remainder  1    -64     ->  1
ddrem050 remainder -1     2      ->  -1
ddrem051 remainder -1     4      ->  -1
ddrem052 remainder -1     8      ->  -1
ddrem053 remainder -1     16     ->  -1
ddrem054 remainder -1     32     ->  -1
ddrem055 remainder -1     64     ->  -1
ddrem060 remainder -1    -2      ->  -1
ddrem061 remainder -1    -4      ->  -1
ddrem062 remainder -1    -8      ->  -1
ddrem063 remainder -1    -16     ->  -1
ddrem064 remainder -1    -32     ->  -1
ddrem065 remainder -1    -64     ->  -1

ddrem066 remainder  999999999     1  -> 0
ddrem067 remainder  999999999.4   1  -> 0.4
ddrem068 remainder  999999999.5   1  -> 0.5
ddrem069 remainder  999999999.9   1  -> 0.9
ddrem070 remainder  999999999.999 1  -> 0.999
ddrem071 remainder  999999.999999 1  -> 0.999999
ddrem072 remainder  9             1  -> 0
ddrem073 remainder  9999999999999999 1  -> 0
ddrem074 remainder  9999999999999999 2  -> 1
ddrem075 remainder  9999999999999999 3  -> 0
ddrem076 remainder  9999999999999999 4  -> 3

ddrem080 remainder  0.            1  -> 0
ddrem081 remainder  .0            1  -> 0.0
ddrem082 remainder  0.00          1  -> 0.00
ddrem083 remainder  0.00E+9       1  -> 0
ddrem084 remainder  0.00E+3       1  -> 0
ddrem085 remainder  0.00E+2       1  -> 0
ddrem086 remainder  0.00E+1       1  -> 0.0
ddrem087 remainder  0.00E+0       1  -> 0.00
ddrem088 remainder  0.00E-0       1  -> 0.00
ddrem089 remainder  0.00E-1       1  -> 0.000
ddrem090 remainder  0.00E-2       1  -> 0.0000
ddrem091 remainder  0.00E-3       1  -> 0.00000
ddrem092 remainder  0.00E-4       1  -> 0.000000
ddrem093 remainder  0.00E-5       1  -> 0E-7
ddrem094 remainder  0.00E-6       1  -> 0E-8
ddrem095 remainder  0.0000E-50    1  -> 0E-54

-- Various flavours of remainder by 0
ddrem101 remainder  0       0   -> NaN Division_undefined
ddrem102 remainder  0      -0   -> NaN Division_undefined
ddrem103 remainder -0       0   -> NaN Division_undefined
ddrem104 remainder -0      -0   -> NaN Division_undefined
ddrem105 remainder  0.0E5   0   -> NaN Division_undefined
ddrem106 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]
ddrem107 remainder  0.0001  0   -> NaN Invalid_operation
ddrem108 remainder  0.01    0   -> NaN Invalid_operation
ddrem109 remainder  0.1     0   -> NaN Invalid_operation
ddrem110 remainder  1       0   -> NaN Invalid_operation
ddrem111 remainder  1       0.0 -> NaN Invalid_operation
ddrem112 remainder 10       0.0 -> NaN Invalid_operation
ddrem113 remainder 1E+100   0.0 -> NaN Invalid_operation
ddrem114 remainder 1E+380   0   -> NaN Invalid_operation
ddrem115 remainder  0.0001 -0   -> NaN Invalid_operation
ddrem116 remainder  0.01   -0   -> NaN Invalid_operation
ddrem119 remainder  0.1    -0   -> NaN Invalid_operation
ddrem120 remainder  1      -0   -> NaN Invalid_operation
ddrem121 remainder  1      -0.0 -> NaN Invalid_operation
ddrem122 remainder 10      -0.0 -> NaN Invalid_operation
ddrem123 remainder 1E+100  -0.0 -> NaN Invalid_operation
ddrem124 remainder 1E+384  -0   -> NaN Invalid_operation
-- and zeros on left
ddrem130 remainder  0      1   ->  0
ddrem131 remainder  0     -1   ->  0
ddrem132 remainder  0.0    1   ->  0.0
ddrem133 remainder  0.0   -1   ->  0.0
ddrem134 remainder -0      1   -> -0
ddrem135 remainder -0     -1   -> -0
ddrem136 remainder -0.0    1   -> -0.0
ddrem137 remainder -0.0   -1   -> -0.0

-- 0.5ers
ddrem143 remainder   0.5  2     ->  0.5
ddrem144 remainder   0.5  2.1   ->  0.5
ddrem145 remainder   0.5  2.01  ->  0.50
ddrem146 remainder   0.5  2.001 ->  0.500
ddrem147 remainder   0.50 2     ->  0.50
ddrem148 remainder   0.50 2.01  ->  0.50
ddrem149 remainder   0.50 2.001 ->  0.500

-- steadies
ddrem150 remainder  1  1   -> 0
ddrem151 remainder  1  2   -> 1
ddrem152 remainder  1  3   -> 1
ddrem153 remainder  1  4   -> 1
ddrem154 remainder  1  5   -> 1
ddrem155 remainder  1  6   -> 1
ddrem156 remainder  1  7   -> 1
ddrem157 remainder  1  8   -> 1
ddrem158 remainder  1  9   -> 1
ddrem159 remainder  1  10  -> 1
ddrem160 remainder  1  1   -> 0
ddrem161 remainder  2  1   -> 0
ddrem162 remainder  3  1   -> 0
ddrem163 remainder  4  1   -> 0
ddrem164 remainder  5  1   -> 0
ddrem165 remainder  6  1   -> 0
ddrem166 remainder  7  1   -> 0
ddrem167 remainder  8  1   -> 0
ddrem168 remainder  9  1   -> 0
ddrem169 remainder  10 1   -> 0

-- some differences from remainderNear
ddrem171 remainder   0.4  1.020 ->  0.400
ddrem172 remainder   0.50 1.020 ->  0.500
ddrem173 remainder   0.51 1.020 ->  0.510
ddrem174 remainder   0.52 1.020 ->  0.520
ddrem175 remainder   0.6  1.020 ->  0.600

-- More flavours of remainder by 0
ddrem201 remainder  0      0   -> NaN Division_undefined
ddrem202 remainder  0.0E5  0   -> NaN Division_undefined
ddrem203 remainder  0.000  0   -> NaN Division_undefined
ddrem204 remainder  0.0001 0   -> NaN Invalid_operation
ddrem205 remainder  0.01   0   -> NaN Invalid_operation
ddrem206 remainder  0.1    0   -> NaN Invalid_operation
ddrem207 remainder  1      0   -> NaN Invalid_operation
ddrem208 remainder  1      0.0 -> NaN Invalid_operation
ddrem209 remainder 10      0.0 -> NaN Invalid_operation
ddrem210 remainder 1E+100  0.0 -> NaN Invalid_operation
ddrem211 remainder 1E+380  0   -> NaN Invalid_operation

-- some differences from remainderNear
ddrem231 remainder  -0.4  1.020 -> -0.400
ddrem232 remainder  -0.50 1.020 -> -0.500
ddrem233 remainder  -0.51 1.020 -> -0.510
ddrem234 remainder  -0.52 1.020 -> -0.520
ddrem235 remainder  -0.6  1.020 -> -0.600

-- high Xs
ddrem240 remainder  1E+2  1.00  ->  0.00

-- ddrem3xx are from DiagBigDecimal
ddrem301 remainder   1    3     ->  1
ddrem302 remainder   5    5     ->  0
ddrem303 remainder   13   10    ->  3
ddrem304 remainder   13   50    ->  13
ddrem305 remainder   13   100   ->  13
ddrem306 remainder   13   1000  ->  13
ddrem307 remainder   .13    1   ->  0.13
ddrem308 remainder   0.133  1   ->  0.133
ddrem309 remainder   0.1033 1   ->  0.1033
ddrem310 remainder   1.033  1   ->  0.033
ddrem311 remainder   10.33  1   ->  0.33
ddrem312 remainder   10.33 10   ->  0.33
ddrem313 remainder   103.3  1   ->  0.3
ddrem314 remainder   133   10   ->  3
ddrem315 remainder   1033  10   ->  3
ddrem316 remainder   1033  50   ->  33
ddrem317 remainder   101.0  3   ->  2.0
ddrem318 remainder   102.0  3   ->  0.0
ddrem319 remainder   103.0  3   ->  1.0
ddrem320 remainder   2.40   1   ->  0.40
ddrem321 remainder   2.400  1   ->  0.400
ddrem322 remainder   2.4    1   ->  0.4
ddrem323 remainder   2.4    2   ->  0.4
ddrem324 remainder   2.400  2   ->  0.400
ddrem325 remainder   1   0.3    ->  0.1
ddrem326 remainder   1   0.30   ->  0.10
ddrem327 remainder   1   0.300  ->  0.100
ddrem328 remainder   1   0.3000 ->  0.1000
ddrem329 remainder   1.0    0.3 ->  0.1
ddrem330 remainder   1.00   0.3 ->  0.10
ddrem331 remainder   1.000  0.3 ->  0.100
ddrem332 remainder   1.0000 0.3 ->  0.1000
ddrem333 remainder   0.5  2     ->  0.5
ddrem334 remainder   0.5  2.1   ->  0.5
ddrem335 remainder   0.5  2.01  ->  0.50
ddrem336 remainder   0.5  2.001 ->  0.500
ddrem337 remainder   0.50 2     ->  0.50
ddrem338 remainder   0.50 2.01  ->  0.50
ddrem339 remainder   0.50 2.001 ->  0.500

ddrem340 remainder   0.5   0.5000001    ->  0.5000000
ddrem341 remainder   0.5   0.50000001    ->  0.50000000
ddrem342 remainder   0.5   0.500000001    ->  0.500000000
ddrem343 remainder   0.5   0.5000000001    ->  0.5000000000
ddrem344 remainder   0.5   0.50000000001    ->  0.50000000000
ddrem345 remainder   0.5   0.4999999    ->  1E-7
ddrem346 remainder   0.5   0.49999999    ->  1E-8
ddrem347 remainder   0.5   0.499999999    ->  1E-9
ddrem348 remainder   0.5   0.4999999999    ->  1E-10
ddrem349 remainder   0.5   0.49999999999    ->  1E-11
ddrem350 remainder   0.5   0.499999999999    ->  1E-12

ddrem351 remainder   0.03  7  ->  0.03
ddrem352 remainder   5   2    ->  1
ddrem353 remainder   4.1   2    ->  0.1
ddrem354 remainder   4.01   2    ->  0.01
ddrem355 remainder   4.001   2    ->  0.001
ddrem356 remainder   4.0001   2    ->  0.0001
ddrem357 remainder   4.00001   2    ->  0.00001
ddrem358 remainder   4.000001   2    ->  0.000001
ddrem359 remainder   4.0000001   2    ->  1E-7

ddrem360 remainder   1.2   0.7345 ->  0.4655
ddrem361 remainder   0.8   12     ->  0.8
ddrem362 remainder   0.8   0.2    ->  0.0
ddrem363 remainder   0.8   0.3    ->  0.2
ddrem364 remainder   0.800   12   ->  0.800
ddrem365 remainder   0.800   1.7  ->  0.800
ddrem366 remainder   2.400   2    ->  0.400

ddrem371 remainder   2.400  2        ->  0.400

ddrem381 remainder 12345  1         ->  0
ddrem382 remainder 12345  1.0001    ->  0.7657
ddrem383 remainder 12345  1.001     ->  0.668
ddrem384 remainder 12345  1.01      ->  0.78
ddrem385 remainder 12345  1.1       ->  0.8
ddrem386 remainder 12355  4         ->  3
ddrem387 remainder 12345  4         ->  1
ddrem388 remainder 12355  4.0001    ->  2.6912
ddrem389 remainder 12345  4.0001    ->  0.6914
ddrem390 remainder 12345  4.9       ->  1.9
ddrem391 remainder 12345  4.99      ->  4.73
ddrem392 remainder 12345  4.999     ->  2.469
ddrem393 remainder 12345  4.9999    ->  0.2469
ddrem394 remainder 12345  5         ->  0
ddrem395 remainder 12345  5.0001    ->  4.7532
ddrem396 remainder 12345  5.001     ->  2.532
ddrem397 remainder 12345  5.01      ->  0.36
ddrem398 remainder 12345  5.1       ->  3.0

-- the nasty division-by-1 cases
ddrem401 remainder   0.5         1   ->  0.5
ddrem402 remainder   0.55        1   ->  0.55
ddrem403 remainder   0.555       1   ->  0.555
ddrem404 remainder   0.5555      1   ->  0.5555
ddrem405 remainder   0.55555     1   ->  0.55555
ddrem406 remainder   0.555555    1   ->  0.555555
ddrem407 remainder   0.5555555   1   ->  0.5555555
ddrem408 remainder   0.55555555  1   ->  0.55555555
ddrem409 remainder   0.555555555 1   ->  0.555555555

-- folddowns
ddrem421 remainder   1E+384       1  ->   NaN Division_impossible
ddrem422 remainder   1E+384  1E+383  ->   0E+369 Clamped
ddrem423 remainder   1E+384  2E+383  ->   0E+369 Clamped
ddrem424 remainder   1E+384  3E+383  ->   1.00000000000000E+383 Clamped
ddrem425 remainder   1E+384  4E+383  ->   2.00000000000000E+383 Clamped
ddrem426 remainder   1E+384  5E+383  ->   0E+369 Clamped
ddrem427 remainder   1E+384  6E+383  ->   4.00000000000000E+383 Clamped
ddrem428 remainder   1E+384  7E+383  ->   3.00000000000000E+383 Clamped
ddrem429 remainder   1E+384  8E+383  ->   2.00000000000000E+383 Clamped
ddrem430 remainder   1E+384  9E+383  ->   1.00000000000000E+383 Clamped
-- tinies
ddrem431 remainder   1E-397  1E-398  ->   0E-398
ddrem432 remainder   1E-397  2E-398  ->   0E-398
ddrem433 remainder   1E-397  3E-398  ->   1E-398 Subnormal
ddrem434 remainder   1E-397  4E-398  ->   2E-398 Subnormal
ddrem435 remainder   1E-397  5E-398  ->   0E-398
ddrem436 remainder   1E-397  6E-398  ->   4E-398 Subnormal
ddrem437 remainder   1E-397  7E-398  ->   3E-398 Subnormal
ddrem438 remainder   1E-397  8E-398  ->   2E-398 Subnormal
ddrem439 remainder   1E-397  9E-398  ->   1E-398 Subnormal
ddrem440 remainder   1E-397 10E-398  ->   0E-398
ddrem441 remainder   1E-397 11E-398  -> 1.0E-397 Subnormal
ddrem442 remainder 100E-397 11E-398  -> 1.0E-397 Subnormal
ddrem443 remainder 100E-397 20E-398  ->   0E-398
ddrem444 remainder 100E-397 21E-398  -> 1.3E-397 Subnormal
ddrem445 remainder 100E-397 30E-398  -> 1.0E-397 Subnormal

-- zero signs
ddrem650 remainder  1  1 ->  0
ddrem651 remainder -1  1 -> -0
ddrem652 remainder  1 -1 ->  0
ddrem653 remainder -1 -1 -> -0
ddrem654 remainder  0  1 ->  0
ddrem655 remainder -0  1 -> -0
ddrem656 remainder  0 -1 ->  0
ddrem657 remainder -0 -1 -> -0
ddrem658 remainder  0.00  1  ->  0.00
ddrem659 remainder -0.00  1  -> -0.00

-- Specials
ddrem680 remainder  Inf  -Inf   ->  NaN Invalid_operation
ddrem681 remainder  Inf  -1000  ->  NaN Invalid_operation
ddrem682 remainder  Inf  -1     ->  NaN Invalid_operation
ddrem683 remainder  Inf   0     ->  NaN Invalid_operation
ddrem684 remainder  Inf  -0     ->  NaN Invalid_operation
ddrem685 remainder  Inf   1     ->  NaN Invalid_operation
ddrem686 remainder  Inf   1000  ->  NaN Invalid_operation
ddrem687 remainder  Inf   Inf   ->  NaN Invalid_operation
ddrem688 remainder -1000  Inf   -> -1000
ddrem689 remainder -Inf   Inf   ->  NaN Invalid_operation
ddrem691 remainder -1     Inf   -> -1
ddrem692 remainder  0     Inf   ->  0
ddrem693 remainder -0     Inf   -> -0
ddrem694 remainder  1     Inf   ->  1
ddrem695 remainder  1000  Inf   ->  1000
ddrem696 remainder  Inf   Inf   ->  NaN Invalid_operation

ddrem700 remainder -Inf  -Inf   ->  NaN Invalid_operation
ddrem701 remainder -Inf  -1000  ->  NaN Invalid_operation
ddrem702 remainder -Inf  -1     ->  NaN Invalid_operation
ddrem703 remainder -Inf  -0     ->  NaN Invalid_operation
ddrem704 remainder -Inf   0     ->  NaN Invalid_operation
ddrem705 remainder -Inf   1     ->  NaN Invalid_operation
ddrem706 remainder -Inf   1000  ->  NaN Invalid_operation
ddrem707 remainder -Inf   Inf   ->  NaN Invalid_operation
ddrem708 remainder -Inf  -Inf   ->  NaN Invalid_operation
ddrem709 remainder -1000  Inf   -> -1000
ddrem710 remainder -1    -Inf   -> -1
ddrem711 remainder -0    -Inf   -> -0
ddrem712 remainder  0    -Inf   ->  0
ddrem713 remainder  1    -Inf   ->  1
ddrem714 remainder  1000 -Inf   ->  1000
ddrem715 remainder  Inf  -Inf   ->  NaN Invalid_operation

ddrem721 remainder  NaN -Inf    ->  NaN
ddrem722 remainder  NaN -1000   ->  NaN
ddrem723 remainder  NaN -1      ->  NaN
ddrem724 remainder  NaN -0      ->  NaN
ddrem725 remainder -NaN  0      -> -NaN
ddrem726 remainder  NaN  1      ->  NaN
ddrem727 remainder  NaN  1000   ->  NaN
ddrem728 remainder  NaN  Inf    ->  NaN
ddrem729 remainder  NaN -NaN    ->  NaN
ddrem730 remainder -Inf  NaN    ->  NaN
ddrem731 remainder -1000 NaN    ->  NaN
ddrem732 remainder -1    NaN    ->  NaN
ddrem733 remainder -0   -NaN    -> -NaN
ddrem734 remainder  0    NaN    ->  NaN
ddrem735 remainder  1   -NaN    -> -NaN
ddrem736 remainder  1000 NaN    ->  NaN
ddrem737 remainder  Inf  NaN    ->  NaN

ddrem741 remainder  sNaN -Inf   ->  NaN  Invalid_operation
ddrem742 remainder  sNaN -1000  ->  NaN  Invalid_operation
ddrem743 remainder -sNaN -1     -> -NaN  Invalid_operation
ddrem744 remainder  sNaN -0     ->  NaN  Invalid_operation
ddrem745 remainder  sNaN  0     ->  NaN  Invalid_operation
ddrem746 remainder  sNaN  1     ->  NaN  Invalid_operation
ddrem747 remainder  sNaN  1000  ->  NaN  Invalid_operation
ddrem749 remainder  sNaN  NaN   ->  NaN  Invalid_operation
ddrem750 remainder  sNaN sNaN   ->  NaN  Invalid_operation
ddrem751 remainder  NaN  sNaN   ->  NaN  Invalid_operation
ddrem752 remainder -Inf  sNaN   ->  NaN  Invalid_operation
ddrem753 remainder -1000 sNaN   ->  NaN  Invalid_operation
ddrem754 remainder -1    sNaN   ->  NaN  Invalid_operation
ddrem755 remainder -0    sNaN   ->  NaN  Invalid_operation
ddrem756 remainder  0    sNaN   ->  NaN  Invalid_operation
ddrem757 remainder  1    sNaN   ->  NaN  Invalid_operation
ddrem758 remainder  1000 sNaN   ->  NaN  Invalid_operation
ddrem759 remainder  Inf -sNaN   -> -NaN  Invalid_operation

-- propaging NaNs
ddrem760 remainder  NaN1   NaN7   ->  NaN1
ddrem761 remainder sNaN2   NaN8   ->  NaN2 Invalid_operation
ddrem762 remainder  NaN3  sNaN9   ->  NaN9 Invalid_operation
ddrem763 remainder sNaN4  sNaN10  ->  NaN4 Invalid_operation
ddrem764 remainder    15   NaN11  ->  NaN11
ddrem765 remainder  NaN6   NaN12  ->  NaN6
ddrem766 remainder  Inf    NaN13  ->  NaN13
ddrem767 remainder  NaN14  -Inf   ->  NaN14
ddrem768 remainder    0    NaN15  ->  NaN15
ddrem769 remainder  NaN16   -0    ->  NaN16

-- edge cases of impossible
ddrem770  remainder  1234567890123456  10    ->  6
ddrem771  remainder  1234567890123456   1    ->  0
ddrem772  remainder  1234567890123456   0.1  ->  NaN Division_impossible
ddrem773  remainder  1234567890123456   0.01 ->  NaN Division_impossible

-- long operand checks
ddrem801 remainder 12345678000 100 -> 0
ddrem802 remainder 1 12345678000   -> 1
ddrem803 remainder 1234567800  10  -> 0
ddrem804 remainder 1 1234567800    -> 1
ddrem805 remainder 1234567890  10  -> 0
ddrem806 remainder 1 1234567890    -> 1
ddrem807 remainder 1234567891  10  -> 1
ddrem808 remainder 1 1234567891    -> 1
ddrem809 remainder 12345678901 100 -> 1
ddrem810 remainder 1 12345678901   -> 1
ddrem811 remainder 1234567896  10  -> 6
ddrem812 remainder 1 1234567896    -> 1

ddrem821 remainder 12345678000 100 -> 0
ddrem822 remainder 1 12345678000   -> 1
ddrem823 remainder 1234567800  10  -> 0
ddrem824 remainder 1 1234567800    -> 1
ddrem825 remainder 1234567890  10  -> 0
ddrem826 remainder 1 1234567890    -> 1
ddrem827 remainder 1234567891  10  -> 1
ddrem828 remainder 1 1234567891    -> 1
ddrem829 remainder 12345678901 100 -> 1
ddrem830 remainder 1 12345678901   -> 1
ddrem831 remainder 1234567896  10  -> 6
ddrem832 remainder 1 1234567896    -> 1

-- from divideint
ddrem840 remainder  100000000.0   1  ->  0.0
ddrem841 remainder  100000000.4   1  ->  0.4
ddrem842 remainder  100000000.5   1  ->  0.5
ddrem843 remainder  100000000.9   1  ->  0.9
ddrem844 remainder  100000000.999 1  ->  0.999
ddrem850 remainder  100000003     5  ->  3
ddrem851 remainder  10000003      5  ->  3
ddrem852 remainder  1000003       5  ->  3
ddrem853 remainder  100003        5  ->  3
ddrem854 remainder  10003         5  ->  3
ddrem855 remainder  1003          5  ->  3
ddrem856 remainder  103           5  ->  3
ddrem857 remainder  13            5  ->  3
ddrem858 remainder  1             5  ->  1

-- Vladimir's cases         1234567890123456
ddrem860 remainder 123.0e1 1000000000000000  -> 1230
ddrem861 remainder 1230    1000000000000000  -> 1230
ddrem862 remainder 12.3e2  1000000000000000  -> 1230
ddrem863 remainder 1.23e3  1000000000000000  -> 1230
ddrem864 remainder 123e1   1000000000000000  -> 1230
ddrem870 remainder 123e1    1000000000000000 -> 1230
ddrem871 remainder 123e1     100000000000000 -> 1230
ddrem872 remainder 123e1      10000000000000 -> 1230
ddrem873 remainder 123e1       1000000000000 -> 1230
ddrem874 remainder 123e1        100000000000 -> 1230
ddrem875 remainder 123e1         10000000000 -> 1230
ddrem876 remainder 123e1          1000000000 -> 1230
ddrem877 remainder 123e1           100000000 -> 1230
ddrem878 remainder 1230            100000000 -> 1230
ddrem879 remainder 123e1            10000000 -> 1230
ddrem880 remainder 123e1             1000000 -> 1230
ddrem881 remainder 123e1              100000 -> 1230
ddrem882 remainder 123e1               10000 -> 1230
ddrem883 remainder 123e1                1000 ->  230
ddrem884 remainder 123e1                 100 ->   30
ddrem885 remainder 123e1                  10 ->    0
ddrem886 remainder 123e1                   1 ->    0

ddrem890 remainder 123e1    2000000000000000 -> 1230
ddrem891 remainder 123e1     200000000000000 -> 1230
ddrem892 remainder 123e1      20000000000000 -> 1230
ddrem893 remainder 123e1       2000000000000 -> 1230
ddrem894 remainder 123e1        200000000000 -> 1230
ddrem895 remainder 123e1         20000000000 -> 1230
ddrem896 remainder 123e1          2000000000 -> 1230
ddrem897 remainder 123e1           200000000 -> 1230
ddrem899 remainder 123e1            20000000 -> 1230
ddrem900 remainder 123e1             2000000 -> 1230
ddrem901 remainder 123e1              200000 -> 1230
ddrem902 remainder 123e1               20000 -> 1230
ddrem903 remainder 123e1                2000 -> 1230
ddrem904 remainder 123e1                 200 ->   30
ddrem905 remainder 123e1                  20 ->   10
ddrem906 remainder 123e1                   2 ->    0

ddrem910 remainder 123e1    5000000000000000 -> 1230
ddrem911 remainder 123e1     500000000000000 -> 1230
ddrem912 remainder 123e1      50000000000000 -> 1230
ddrem913 remainder 123e1       5000000000000 -> 1230
ddrem914 remainder 123e1        500000000000 -> 1230
ddrem915 remainder 123e1         50000000000 -> 1230
ddrem916 remainder 123e1          5000000000 -> 1230
ddrem917 remainder 123e1           500000000 -> 1230
ddrem919 remainder 123e1            50000000 -> 1230
ddrem920 remainder 123e1             5000000 -> 1230
ddrem921 remainder 123e1              500000 -> 1230
ddrem922 remainder 123e1               50000 -> 1230
ddrem923 remainder 123e1                5000 -> 1230
ddrem924 remainder 123e1                 500 ->  230
ddrem925 remainder 123e1                  50 ->   30
ddrem926 remainder 123e1                   5 ->    0

ddrem930 remainder 123e1    9000000000000000 -> 1230
ddrem931 remainder 123e1     900000000000000 -> 1230
ddrem932 remainder 123e1      90000000000000 -> 1230
ddrem933 remainder 123e1       9000000000000 -> 1230
ddrem934 remainder 123e1        900000000000 -> 1230
ddrem935 remainder 123e1         90000000000 -> 1230
ddrem936 remainder 123e1          9000000000 -> 1230
ddrem937 remainder 123e1           900000000 -> 1230
ddrem939 remainder 123e1            90000000 -> 1230
ddrem940 remainder 123e1             9000000 -> 1230
ddrem941 remainder 123e1              900000 -> 1230
ddrem942 remainder 123e1               90000 -> 1230
ddrem943 remainder 123e1                9000 -> 1230
ddrem944 remainder 123e1                 900 ->  330
ddrem945 remainder 123e1                  90 ->   60
ddrem946 remainder 123e1                   9 ->    6

ddrem950 remainder 123e1   1000000000000000 -> 1230
ddrem961 remainder 123e1   2999999999999999 -> 1230
ddrem962 remainder 123e1   3999999999999999 -> 1230
ddrem963 remainder 123e1   4999999999999999 -> 1230
ddrem964 remainder 123e1   5999999999999999 -> 1230
ddrem965 remainder 123e1   6999999999999999 -> 1230
ddrem966 remainder 123e1   7999999999999999 -> 1230
ddrem967 remainder 123e1   8999999999999999 -> 1230
ddrem968 remainder 123e1   9999999999999999 -> 1230
ddrem969 remainder 123e1   9876543210987654 -> 1230

ddrem980 remainder 123e1 1000E299 -> 1.23E+3  -- 123E+1 internally

-- overflow and underflow tests [from divide]
ddrem1051 remainder  1e+277  1e-311 ->  NaN Division_impossible
ddrem1052 remainder  1e+277 -1e-311 ->  NaN Division_impossible
ddrem1053 remainder -1e+277  1e-311 ->  NaN Division_impossible
ddrem1054 remainder -1e+277 -1e-311 ->  NaN Division_impossible
ddrem1055 remainder  1e-277  1e+311 ->  1E-277
ddrem1056 remainder  1e-277 -1e+311 ->  1E-277
ddrem1057 remainder -1e-277  1e+311 -> -1E-277
ddrem1058 remainder -1e-277 -1e+311 -> -1E-277

-- destructive subtract
ddrem1101 remainder  1234567890123456  1.000000000000001  ->  0.765432109876546
ddrem1102 remainder  1234567890123456   1.00000000000001  ->   0.65432109876557
ddrem1103 remainder  1234567890123456    1.0000000000001  ->    0.5432109876668
ddrem1104 remainder  1234567890123455  4.000000000000001  ->  2.691358027469137
ddrem1105 remainder  1234567890123456  4.000000000000001  ->  3.691358027469137
ddrem1106 remainder  1234567890123456    4.9999999999999  ->    0.6913578024696
ddrem1107 remainder  1234567890123456   4.99999999999999  ->   3.46913578024691
ddrem1108 remainder  1234567890123456  4.999999999999999  ->  1.246913578024691
ddrem1109 remainder  1234567890123456  5.000000000000001  ->  0.753086421975309
ddrem1110 remainder  1234567890123456   5.00000000000001  ->   3.53086421975310
ddrem1111 remainder  1234567890123456    5.0000000000001  ->    1.3086421975314

-- Null tests
ddrem1000 remainder 10  # -> NaN Invalid_operation
ddrem1001 remainder  # 10 -> NaN Invalid_operation