remaindernear.dectest

eda is an estimation of distributions algorithm

------------------------------------------------------------------------
-- remainderNear.decTest -- decimal remainder-near (IEEE remainder)   --
-- Copyright (c) IBM Corporation, 1981, 2002.  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         --
--   [e-mail]                                                   --
------------------------------------------------------------------------
version: 2.15

extended:    1
precision:   9
rounding:    half_up
maxExponent: 999

rmnx001 remaindernear  1     1    ->  0
rmnx002 remaindernear  2     1    ->  0
rmnx003 remaindernear  1     2    ->  1
rmnx004 remaindernear  2     2    ->  0
rmnx005 remaindernear  0     1    ->  0
rmnx006 remaindernear  0     2    ->  0
rmnx007 remaindernear  1     3    ->  1
rmnx008 remaindernear  2     3    -> -1
rmnx009 remaindernear  3     3    ->  0

rmnx010 remaindernear  2.4   1    ->  0.4
rmnx011 remaindernear  2.4   -1   ->  0.4
rmnx012 remaindernear  -2.4  1    ->  -0.4
rmnx013 remaindernear  -2.4  -1   ->  -0.4
rmnx014 remaindernear  2.40  1    ->  0.40
rmnx015 remaindernear  2.400 1    ->  0.400
rmnx016 remaindernear  2.4   2    ->  0.4
rmnx017 remaindernear  2.400 2    ->  0.400
rmnx018 remaindernear  2.    2    ->  0
rmnx019 remaindernear  20    20   ->  0

rmnx020 remaindernear  187   187    ->  0
rmnx021 remaindernear  5     2      ->  1
rmnx022 remaindernear  5     2.0    ->  1.0
rmnx023 remaindernear  5     2.000  ->  1.000
rmnx024 remaindernear  5     0.200  ->  0
rmnx025 remaindernear  5     0.200  ->  0

rmnx030 remaindernear  1     2      ->  1
rmnx031 remaindernear  1     4      ->  1
rmnx032 remaindernear  1     8      ->  1
rmnx033 remaindernear  1     16     ->  1
rmnx034 remaindernear  1     32     ->  1
rmnx035 remaindernear  1     64     ->  1
rmnx040 remaindernear  1    -2      ->  1
rmnx041 remaindernear  1    -4      ->  1
rmnx042 remaindernear  1    -8      ->  1
rmnx043 remaindernear  1    -16     ->  1
rmnx044 remaindernear  1    -32     ->  1
rmnx045 remaindernear  1    -64     ->  1
rmnx050 remaindernear -1     2      ->  -1
rmnx051 remaindernear -1     4      ->  -1
rmnx052 remaindernear -1     8      ->  -1
rmnx053 remaindernear -1     16     ->  -1
rmnx054 remaindernear -1     32     ->  -1
rmnx055 remaindernear -1     64     ->  -1
rmnx060 remaindernear -1    -2      ->  -1
rmnx061 remaindernear -1    -4      ->  -1
rmnx062 remaindernear -1    -8      ->  -1
rmnx063 remaindernear -1    -16     ->  -1
rmnx064 remaindernear -1    -32     ->  -1
rmnx065 remaindernear -1    -64     ->  -1

rmnx066 remaindernear  999999997     1  -> 0
rmnx067 remaindernear  999999997.4   1  -> 0.4
rmnx068 remaindernear  999999997.5   1  -> -0.5
rmnx069 remaindernear  999999997.9   1  -> -0.1
rmnx070 remaindernear  999999997.999 1  -> -0.001

rmnx071 remaindernear  999999998     1  -> 0
rmnx072 remaindernear  999999998.4   1  -> 0.4
rmnx073 remaindernear  999999998.5   1  -> 0.5
rmnx074 remaindernear  999999998.9   1  -> -0.1
rmnx075 remaindernear  999999998.999 1  -> -0.001

rmnx076 remaindernear  999999999     1  -> 0
rmnx077 remaindernear  999999999.4   1  -> 0.4
rmnx078 remaindernear  999999999.5   1  -> NaN Division_impossible
rmnx079 remaindernear  999999999.9   1  -> NaN Division_impossible
rmnx080 remaindernear  999999999.999 1  -> NaN Division_impossible

precision: 6
rmnx081 remaindernear  999999999     1  -> NaN Division_impossible
rmnx082 remaindernear  99999999      1  -> NaN Division_impossible
rmnx083 remaindernear  9999999       1  -> NaN Division_impossible
rmnx084 remaindernear  999999        1  -> 0
rmnx085 remaindernear  99999         1  -> 0
rmnx086 remaindernear  9999          1  -> 0
rmnx087 remaindernear  999           1  -> 0
rmnx088 remaindernear  99            1  -> 0
rmnx089 remaindernear  9             1  -> 0

precision: 9
rmnx090 remaindernear  0.            1  -> 0
rmnx091 remaindernear  .0            1  -> 0.0
rmnx092 remaindernear  0.00          1  -> 0.00
rmnx093 remaindernear  0.00E+9       1  -> 0
rmnx094 remaindernear  0.0000E-50    1  -> 0E-54


-- Various flavours of remaindernear by 0
precision: 9
maxexponent: 999999999
rmnx101 remaindernear  0       0   -> NaN Division_undefined
rmnx102 remaindernear  0      -0   -> NaN Division_undefined
rmnx103 remaindernear -0       0   -> NaN Division_undefined
rmnx104 remaindernear -0      -0   -> NaN Division_undefined
rmnx105 remaindernear  0.0E5   0   -> NaN Division_undefined
rmnx106 remaindernear  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
-- remaindernear-near, anyway]
rmnx107 remaindernear  0.0001  0   -> NaN Invalid_operation
rmnx108 remaindernear  0.01    0   -> NaN Invalid_operation
rmnx109 remaindernear  0.1     0   -> NaN Invalid_operation
rmnx110 remaindernear  1       0   -> NaN Invalid_operation
rmnx111 remaindernear  1       0.0 -> NaN Invalid_operation
rmnx112 remaindernear 10       0.0 -> NaN Invalid_operation
rmnx113 remaindernear 1E+100   0.0 -> NaN Invalid_operation
rmnx114 remaindernear 1E+1000  0   -> NaN Invalid_operation
rmnx115 remaindernear  0.0001 -0   -> NaN Invalid_operation
rmnx116 remaindernear  0.01   -0   -> NaN Invalid_operation
rmnx119 remaindernear  0.1    -0   -> NaN Invalid_operation
rmnx120 remaindernear  1      -0   -> NaN Invalid_operation
rmnx121 remaindernear  1      -0.0 -> NaN Invalid_operation
rmnx122 remaindernear 10      -0.0 -> NaN Invalid_operation
rmnx123 remaindernear 1E+100  -0.0 -> NaN Invalid_operation
rmnx124 remaindernear 1E+1000 -0   -> NaN Invalid_operation
-- and zeros on left
rmnx130 remaindernear  0      1   ->  0
rmnx131 remaindernear  0     -1   ->  0
rmnx132 remaindernear  0.0    1   ->  0.0
rmnx133 remaindernear  0.0   -1   ->  0.0
rmnx134 remaindernear -0      1   -> -0
rmnx135 remaindernear -0     -1   -> -0
rmnx136 remaindernear -0.0    1   -> -0.0
rmnx137 remaindernear -0.0   -1   -> -0.0

-- 0.5ers
rmmx143 remaindernear   0.5  2     ->  0.5
rmmx144 remaindernear   0.5  2.1   ->  0.5
rmmx145 remaindernear   0.5  2.01  ->  0.5
rmmx146 remaindernear   0.5  2.001 ->  0.5
rmmx147 remaindernear   0.50 2     ->  0.50
rmmx148 remaindernear   0.50 2.01  ->  0.50
rmmx149 remaindernear   0.50 2.001 ->  0.50

-- some differences from remainder
rmnx150 remaindernear   0.4  1.020 ->  0.4
rmnx151 remaindernear   0.50 1.020 ->  0.50
rmnx152 remaindernear   0.51 1.020 ->  0.51
rmnx153 remaindernear   0.52 1.020 -> -0.500
rmnx154 remaindernear   0.6  1.020 -> -0.420
rmnx155 remaindernear   0.49 1     ->  0.49
rmnx156 remaindernear   0.50 1     ->  0.50
rmnx157 remaindernear   1.50 1     -> -0.50
rmnx158 remaindernear   2.50 1     ->  0.50
rmnx159 remaindernear   9.50 1     -> -0.50
rmnx160 remaindernear   0.51 1     -> -0.49

-- the nasty division-by-1 cases
rmnx161 remaindernear   0.4         1   ->  0.4
rmnx162 remaindernear   0.45        1   ->  0.45
rmnx163 remaindernear   0.455       1   ->  0.455
rmnx164 remaindernear   0.4555      1   ->  0.4555
rmnx165 remaindernear   0.45555     1   ->  0.45555
rmnx166 remaindernear   0.455555    1   ->  0.455555
rmnx167 remaindernear   0.4555555   1   ->  0.4555555
rmnx168 remaindernear   0.45555555  1   ->  0.45555555
rmnx169 remaindernear   0.455555555 1   ->  0.455555555
-- with spill...
rmnx171 remaindernear   0.5         1   ->  0.5
rmnx172 remaindernear   0.55        1   -> -0.45
rmnx173 remaindernear   0.555       1   -> -0.445
rmnx174 remaindernear   0.5555      1   -> -0.4445
rmnx175 remaindernear   0.55555     1   -> -0.44445
rmnx176 remaindernear   0.555555    1   -> -0.444445
rmnx177 remaindernear   0.5555555   1   -> -0.4444445
rmnx178 remaindernear   0.55555555  1   -> -0.44444445
rmnx179 remaindernear   0.555555555 1   -> -0.444444445

-- progression
rmnx180 remaindernear  1  1   -> 0
rmnx181 remaindernear  1  2   -> 1
rmnx182 remaindernear  1  3   -> 1
rmnx183 remaindernear  1  4   -> 1
rmnx184 remaindernear  1  5   -> 1
rmnx185 remaindernear  1  6   -> 1
rmnx186 remaindernear  1  7   -> 1
rmnx187 remaindernear  1  8   -> 1
rmnx188 remaindernear  1  9   -> 1
rmnx189 remaindernear  1  10  -> 1
rmnx190 remaindernear  1  1   -> 0
rmnx191 remaindernear  2  1   -> 0
rmnx192 remaindernear  3  1   -> 0
rmnx193 remaindernear  4  1   -> 0
rmnx194 remaindernear  5  1   -> 0
rmnx195 remaindernear  6  1   -> 0
rmnx196 remaindernear  7  1   -> 0
rmnx197 remaindernear  8  1   -> 0
rmnx198 remaindernear  9  1   -> 0
rmnx199 remaindernear  10 1   -> 0


-- Various flavours of remaindernear by 0
maxexponent: 999999999
rmnx201 remaindernear  0      0   -> NaN Division_undefined
rmnx202 remaindernear  0.0E5  0   -> NaN Division_undefined
rmnx203 remaindernear  0.000  0   -> NaN Division_undefined
rmnx204 remaindernear  0.0001 0   -> NaN Invalid_operation
rmnx205 remaindernear  0.01   0   -> NaN Invalid_operation
rmnx206 remaindernear  0.1    0   -> NaN Invalid_operation
rmnx207 remaindernear  1      0   -> NaN Invalid_operation
rmnx208 remaindernear  1      0.0 -> NaN Invalid_operation
rmnx209 remaindernear 10      0.0 -> NaN Invalid_operation
rmnx210 remaindernear 1E+100  0.0 -> NaN Invalid_operation
rmnx211 remaindernear 1E+1000 0   -> NaN Invalid_operation

-- tests from the extended specification
rmnx221 remaindernear 2.1     3   -> -0.9
rmnx222 remaindernear  10     6   -> -2
rmnx223 remaindernear  10     3   ->  1
rmnx224 remaindernear -10     3   -> -1
rmnx225 remaindernear  10.2   1   -> 0.2
rmnx226 remaindernear  10     0.3 -> 0.1
rmnx227 remaindernear   3.6   1.3 -> -0.3

-- some differences from remainder
rmnx231 remaindernear   0.4  1.020 ->  0.4
rmnx232 remaindernear   0.50 1.020 ->  0.50
rmnx233 remaindernear   0.51 1.020 ->  0.51
rmnx234 remaindernear   0.52 1.020 -> -0.500
rmnx235 remaindernear   0.6  1.020 -> -0.420

-- test some cases that are close to exponent overflow
maxexponent: 999999999
rmnx270 remaindernear 1 1e999999999    -> 1
rmnx271 remaindernear 1 0.9e999999999  -> 1
rmnx272 remaindernear 1 0.99e999999999 -> 1
rmnx273 remaindernear 1 0.999999999e999999999 -> 1
rmnx274 remaindernear 9e999999999          1 -> NaN Division_impossible
rmnx275 remaindernear 9.9e999999999        1 -> NaN Division_impossible
rmnx276 remaindernear 9.99e999999999       1 -> NaN Division_impossible
rmnx277 remaindernear 9.99999999e999999999 1 -> NaN Division_impossible

rmnx280 remaindernear 0.1 9e-999999999       -> NaN Division_impossible
rmnx281 remaindernear 0.1 99e-999999999      -> NaN Division_impossible
rmnx282 remaindernear 0.1 999e-999999999     -> NaN Division_impossible

rmnx283 remaindernear 0.1 9e-999999998       -> NaN Division_impossible
rmnx284 remaindernear 0.1 99e-999999998      -> NaN Division_impossible
rmnx285 remaindernear 0.1 999e-999999998     -> NaN Division_impossible
rmnx286 remaindernear 0.1 999e-999999997     -> NaN Division_impossible
rmnx287 remaindernear 0.1 9999e-999999997    -> NaN Division_impossible
rmnx288 remaindernear 0.1 99999e-999999997   -> NaN Division_impossible