------------------------------------------------------------------------
-- remainder0.decTest -- decimal remainder (simplified)               --
-- 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: 2.58

extended:    0
precision:   9
rounding:    half_up
maxExponent: 999
minexponent: -999

rem001 remainder  1     1    ->  0
rem002 remainder  2     1    ->  0
rem003 remainder  1     2    ->  1
rem004 remainder  2     2    ->  0
rem005 remainder  0     1    ->  0
rem006 remainder  0     2    ->  0
rem007 remainder  1     3    ->  1
rem008 remainder  2     3    ->  2
rem009 remainder  3     3    ->  0

rem010 remainder  2.4   1    ->  0.4
rem011 remainder  2.4   -1   ->  0.4
rem012 remainder  -2.4  1    ->  -0.4
rem013 remainder  -2.4  -1   ->  -0.4
rem014 remainder  2.40  1    ->  0.40
rem015 remainder  2.400 1    ->  0.400
rem016 remainder  2.4   2    ->  0.4
rem017 remainder  2.400 2    ->  0.400
rem018 remainder  2.    2    ->  0
rem019 remainder  20    20   ->  0

rem020 remainder  187   187    ->  0
rem021 remainder  5     2      ->  1
rem022 remainder  5     2.0    ->  1.0
rem023 remainder  5     2.000  ->  1.000
rem024 remainder  5     0.200  ->  0
rem025 remainder  5     0.200  ->  0

rem030 remainder  1     2      ->  1
rem031 remainder  1     4      ->  1
rem032 remainder  1     8      ->  1
rem033 remainder  1     16     ->  1
rem034 remainder  1     32     ->  1
rem035 remainder  1     64     ->  1
rem040 remainder  1    -2      ->  1
rem041 remainder  1    -4      ->  1
rem042 remainder  1    -8      ->  1
rem043 remainder  1    -16     ->  1
rem044 remainder  1    -32     ->  1
rem045 remainder  1    -64     ->  1
rem050 remainder -1     2      ->  -1
rem051 remainder -1     4      ->  -1
rem052 remainder -1     8      ->  -1
rem053 remainder -1     16     ->  -1
rem054 remainder -1     32     ->  -1
rem055 remainder -1     64     ->  -1
rem060 remainder -1    -2      ->  -1
rem061 remainder -1    -4      ->  -1
rem062 remainder -1    -8      ->  -1
rem063 remainder -1    -16     ->  -1
rem064 remainder -1    -32     ->  -1
rem065 remainder -1    -64     ->  -1

rem070 remainder  999999999     1  -> 0
rem071 remainder  999999999.4   1  -> 0 Inexact Lost_digits Rounded
rem072 remainder  999999999.5   1  -> ? Division_impossible Inexact Lost_digits Rounded
rem073 remainder  999999999.9   1  -> ? Division_impossible Inexact Lost_digits Rounded
rem074 remainder  999999999.999 1  -> ? Division_impossible Inexact Lost_digits Rounded
precision: 6
rem080 remainder  999999999     1  -> ? Division_impossible Inexact Lost_digits Rounded
rem081 remainder  99999999      1  -> ? Division_impossible Inexact Lost_digits Rounded
rem082 remainder  9999999       1  -> ? Division_impossible Inexact Lost_digits Rounded
rem083 remainder  999999        1  -> 0
rem084 remainder  99999         1  -> 0
rem085 remainder  9999          1  -> 0
rem086 remainder  999           1  -> 0
rem087 remainder  99            1  -> 0
rem088 remainder  9             1  -> 0

precision: 9
rem090 remainder  0.            1  -> 0
rem091 remainder  .0            1  -> 0
rem092 remainder  0.00          1  -> 0
rem093 remainder  0.00E+9       1  -> 0
rem094 remainder  0.0000E-50    1  -> 0

rem100 remainder  1  1   -> 0
rem101 remainder  1  2   -> 1
rem102 remainder  1  3   -> 1
rem103 remainder  1  4   -> 1
rem104 remainder  1  5   -> 1
rem105 remainder  1  6   -> 1
rem106 remainder  1  7   -> 1
rem107 remainder  1  8   -> 1
rem108 remainder  1  9   -> 1
rem109 remainder  1  10  -> 1
rem110 remainder  1  1   -> 0
rem111 remainder  2  1   -> 0
rem112 remainder  3  1   -> 0
rem113 remainder  4  1   -> 0
rem114 remainder  5  1   -> 0
rem115 remainder  6  1   -> 0
rem116 remainder  7  1   -> 0
rem117 remainder  8  1   -> 0
rem118 remainder  9  1   -> 0
rem119 remainder  10 1   -> 0

-- Various flavours of remainder by 0
maxexponent: 999999999
minexponent: -999999999
rem201 remainder  0      0   -> ? Division_undefined
rem202 remainder  0.0E5  0   -> ? Division_undefined
rem203 remainder  0.000  0   -> ? Division_undefined
rem204 remainder  0.0001 0   -> ? Invalid_operation
rem205 remainder  0.01   0   -> ? Invalid_operation
rem206 remainder  0.1    0   -> ? Invalid_operation
rem207 remainder  1      0   -> ? Invalid_operation
rem208 remainder  1      0.0 -> ? Invalid_operation
rem209 remainder 10      0.0 -> ? Invalid_operation
rem210 remainder 1E+100  0.0 -> ? Invalid_operation
rem211 remainder 1E+1000 0   -> ? Invalid_operation

-- some differences from remainderNear
rem231 remainder   0.4  1.020 ->  0.400
rem232 remainder   0.50 1.020 ->  0.500
rem233 remainder   0.51 1.020 ->  0.510
rem234 remainder   0.52 1.020 ->  0.520
rem235 remainder   0.6  1.020 ->  0.600

-- test some cases that are close to exponent overflow
maxexponent: 999999999
minexponent: -999999999
rem270 remainder 1 1e999999999    -> 1
rem271 remainder 1 0.9e999999999  -> 1
rem272 remainder 1 0.99e999999999 -> 1
rem273 remainder 1 0.999999999e999999999 -> 1
rem274 remainder 9e999999999          1 -> ? Division_impossible
rem275 remainder 9.9e999999999        1 -> ? Division_impossible
rem276 remainder 9.99e999999999       1 -> ? Division_impossible
rem277 remainder 9.99999999e999999999 1 -> ? Division_impossible

rem280 remainder 0.1 9e-999999999       -> ? Division_impossible
rem281 remainder 0.1 99e-999999999      -> ? Division_impossible
rem282 remainder 0.1 999e-999999999     -> ? Division_impossible

rem283 remainder 0.1 9e-999999998       -> ? Division_impossible
rem284 remainder 0.1 99e-999999998      -> ? Division_impossible
rem285 remainder 0.1 999e-999999998     -> ? Division_impossible
rem286 remainder 0.1 999e-999999997     -> ? Division_impossible
rem287 remainder 0.1 9999e-999999997    -> ? Division_impossible
rem288 remainder 0.1 99999e-999999997   -> ? Division_impossible

-- rem3xx are from DiagBigDecimal
rem301 remainder   1    3     ->  1
rem302 remainder   5    5     ->  0
rem303 remainder   13   10    ->  3
rem304 remainder   13   50    ->  13
rem305 remainder   13   100   ->  13
rem306 remainder   13   1000  ->  13
rem307 remainder   .13    1   ->  0.13
rem308 remainder   0.133  1   ->  0.133
rem309 remainder   0.1033 1   ->  0.1033
rem310 remainder   1.033  1   ->  0.033
rem311 remainder   10.33  1   ->  0.33
rem312 remainder   10.33 10   ->  0.33
rem313 remainder   103.3  1   ->  0.3
rem314 remainder   133   10   ->  3
rem315 remainder   1033  10   ->  3
rem316 remainder   1033  50   ->  33
rem317 remainder   101.0  3   ->  2.0
rem318 remainder   102.0  3   ->  0
rem319 remainder   103.0  3   ->  1.0
rem320 remainder   2.40   1   ->  0.40
rem321 remainder   2.400  1   ->  0.400
rem322 remainder   2.4    1   ->  0.4
rem323 remainder   2.4    2   ->  0.4
rem324 remainder   2.400  2   ->  0.400
rem325 remainder   1   0.3    ->  0.1
rem326 remainder   1   0.30   ->  0.10
rem327 remainder   1   0.300  ->  0.100
rem328 remainder   1   0.3000 ->  0.1000
rem329 remainder   1.0    0.3 ->  0.1
rem330 remainder   1.00   0.3 ->  0.10
rem331 remainder   1.000  0.3 ->  0.100
rem332 remainder   1.0000 0.3 ->  0.1000
rem333 remainder   0.5  2     ->  0.5
rem334 remainder   0.5  2.1   ->  0.5
rem335 remainder   0.5  2.01  ->  0.50
rem336 remainder   0.5  2.001 ->  0.500
rem337 remainder   0.50 2     ->  0.50
rem338 remainder   0.50 2.01  ->  0.50
rem339 remainder   0.50 2.001 ->  0.500

rem340 remainder   0.5   0.5000001    ->  0.5000000
rem341 remainder   0.5   0.50000001    ->  0.50000000
rem342 remainder   0.5   0.500000001    ->  0.500000000
rem343 remainder   0.5   0.5000000001    ->  0 Inexact Lost_digits Rounded
rem344 remainder   0.5   0.50000000001    ->  0 Inexact Lost_digits Rounded
rem345 remainder   0.5   0.4999999    ->  1E-7
rem346 remainder   0.5   0.49999999    ->  1E-8
rem347 remainder   0.5   0.499999999    ->  1E-9
rem348 remainder   0.5   0.4999999999    ->  0 Inexact Lost_digits Rounded
rem349 remainder   0.5   0.49999999999    ->  0 Inexact Lost_digits Rounded

rem350 remainder   0.03  7  ->  0.03
rem351 remainder   5   2    ->  1
rem352 remainder   4.1   2    ->  0.1
rem353 remainder   4.01   2    ->  0.01
rem354 remainder   4.001   2    ->  0.001
rem355 remainder   4.0001   2    ->  0.0001
rem356 remainder   4.00001   2    ->  0.00001
rem357 remainder   4.000001   2    ->  0.000001
rem358 remainder   4.0000001   2    ->  1E-7

rem360 remainder   1.2   0.7345 ->  0.4655
rem361 remainder   0.8   12     ->  0.8
rem362 remainder   0.8   0.2    ->  0
rem363 remainder   0.8   0.3    ->  0.2
rem364 remainder   0.800   12   ->  0.800
rem365 remainder   0.800   1.7  ->  0.800
rem366 remainder   2.400   2    ->  0.400

precision: 6
rem371 remainder   2.400  2        ->  0.400
precision: 3
-- lostDigits in the next one
rem372 remainder   12345678900000 12e+12 -> 3E+11 Inexact Lost_digits Rounded

precision: 5
rem381 remainder 12345  1         ->  0
rem382 remainder 12345  1.0001    ->  0.7657
rem383 remainder 12345  1.001     ->  0.668
rem384 remainder 12345  1.01      ->  0.78
rem385 remainder 12345  1.1       ->  0.8
rem386 remainder 12355  4         ->  3
rem387 remainder 12345  4         ->  1
rem388 remainder 12355  4.0001    ->  2.6912
rem389 remainder 12345  4.0001    ->  0.6914
rem390 remainder 12345  4.9       ->  1.9
rem391 remainder 12345  4.99      ->  4.73
rem392 remainder 12345  4.999     ->  2.469
rem393 remainder 12345  4.9999    ->  0.2469
rem394 remainder 12345  5         ->  0
rem395 remainder 12345  5.0001    ->  4.7532
rem396 remainder 12345  5.001     ->  2.532
rem397 remainder 12345  5.01      ->  0.36
rem398 remainder 12345  5.1       ->  3.0

precision: 9
-- some nasty division-by-1 cases [some similar above]
rem401 remainder   0.5         1   ->  0.5
rem402 remainder   0.55        1   ->  0.55
rem403 remainder   0.555       1   ->  0.555
rem404 remainder   0.5555      1   ->  0.5555
rem405 remainder   0.55555     1   ->  0.55555
rem406 remainder   0.555555    1   ->  0.555555
rem407 remainder   0.5555555   1   ->  0.5555555
rem408 remainder   0.55555555  1   ->  0.55555555
rem409 remainder   0.555555555 1   ->  0.555555555

-- overflow and underflow tests [from divide]
precision: 9
maxexponent: 999999999
minexponent: -999999999
rem430 remainder +1.23456789012345E-0 9E+999999999 -> 1.23456789 Inexact Lost_digits Rounded
rem431 remainder 9E+999999999 +0.23456789012345E-0 -> ? Division_impossible Inexact Lost_digits Rounded
rem432 remainder +0.100 9E+999999999               -> 0.100
rem433 remainder 9E-999999999 +9.100               -> 9E-999999999
rem435 remainder -1.23456789012345E-0 9E+999999999 -> -1.23456789 Inexact Lost_digits Rounded
rem436 remainder 9E+999999999 -0.83456789012345E-0 -> ? Division_impossible Inexact Lost_digits Rounded
rem437 remainder -0.100 9E+999999999               -> -0.100
rem438 remainder 9E-999999999 -9.100               -> 9E-999999999

-- lostDigits checks
maxexponent: 999
minexponent: -999
precision: 9
rem501 remainder 12345678000 100 -> 0 Rounded
rem502 remainder 1 12345678000   -> 1 Rounded
rem503 remainder 1234567800  10  -> 0 Rounded
rem504 remainder 1 1234567800    -> 1 Rounded
rem505 remainder 1234567890  10  -> 0 Rounded
rem506 remainder 1 1234567890    -> 1 Rounded
rem507 remainder 1234567891  10  -> 0 Inexact Lost_digits Rounded
rem508 remainder 1 1234567891    -> 1 Inexact Lost_digits Rounded
rem509 remainder 12345678901 100 -> 0 Inexact Lost_digits Rounded
rem510 remainder 1 12345678901   -> 1 Inexact Lost_digits Rounded
rem511 remainder 1234567896  10  -> 0 Inexact Lost_digits Rounded
rem512 remainder 1 1234567896    -> 1 Inexact Lost_digits Rounded

precision: 15
-- still checking for [no] lostDigits
rem541 remainder 12345678000 100 -> 0
rem542 remainder 1 12345678000   -> 1
rem543 remainder 1234567800  10  -> 0
rem544 remainder 1 1234567800    -> 1
rem545 remainder 1234567890  10  -> 0
rem546 remainder 1 1234567890    -> 1
rem547 remainder 1234567891  10  -> 1
rem548 remainder 1 1234567891    -> 1
rem549 remainder 12345678901 100 -> 1
rem550 remainder 1 12345678901   -> 1
rem551 remainder 1234567896  10  -> 6
rem552 remainder 1 1234567896    -> 1

-- Null tests
rem900 remainder 10  # -> ? Invalid_operation
rem901 remainder  # 10 -> ? Invalid_operation

