AppPkg/Applications/Python/Python-2.7.2/Lib/test/decimaltestdata/remainderNear.decTest

   1 ------------------------------------------------------------------------
   2 -- remainderNear.decTest -- decimal remainder-near (IEEE remainder)   --
   3 -- Copyright (c) IBM Corporation, 1981, 2008.  All rights reserved.   --
   4 ------------------------------------------------------------------------
   5 -- Please see the document "General Decimal Arithmetic Testcases"     --
   6 -- at http://www2.hursley.ibm.com/decimal for the description of      --
   7 -- these testcases.                                                   --
   8 --                                                                    --
   9 -- These testcases are experimental ('beta' versions), and they       --
  10 -- may contain errors.  They are offered on an as-is basis.  In       --
  11 -- particular, achieving the same results as the tests here is not    --
  12 -- a guarantee that an implementation complies with any Standard      --
  13 -- or specification.  The tests are not exhaustive.                   --
  14 --                                                                    --
  15 -- Please send comments, suggestions, and corrections to the author:  --
  16 --   Mike Cowlishaw, IBM Fellow                                       --
  17 --   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         --
  18 --   mfc@uk.ibm.com                                                   --
  19 ------------------------------------------------------------------------
  20 version: 2.59
  21
  22 extended:    1
  23 precision:   9
  24 rounding:    half_up
  25 maxExponent: 384
  26 minexponent: -383
  27
  28 rmnx001 remaindernear  1     1    ->  0
  29 rmnx002 remaindernear  2     1    ->  0
  30 rmnx003 remaindernear  1     2    ->  1
  31 rmnx004 remaindernear  2     2    ->  0
  32 rmnx005 remaindernear  0     1    ->  0
  33 rmnx006 remaindernear  0     2    ->  0
  34 rmnx007 remaindernear  1     3    ->  1
  35 rmnx008 remaindernear  2     3    -> -1
  36 rmnx009 remaindernear  3     3    ->  0
  37
  38 rmnx010 remaindernear  2.4   1    ->  0.4
  39 rmnx011 remaindernear  2.4   -1   ->  0.4
  40 rmnx012 remaindernear  -2.4  1    ->  -0.4
  41 rmnx013 remaindernear  -2.4  -1   ->  -0.4
  42 rmnx014 remaindernear  2.40  1    ->  0.40
  43 rmnx015 remaindernear  2.400 1    ->  0.400
  44 rmnx016 remaindernear  2.4   2    ->  0.4
  45 rmnx017 remaindernear  2.400 2    ->  0.400
  46 rmnx018 remaindernear  2.    2    ->  0
  47 rmnx019 remaindernear  20    20   ->  0
  48
  49 rmnx020 remaindernear  187   187    ->  0
  50 rmnx021 remaindernear  5     2      ->  1
  51 rmnx022 remaindernear  5     2.0    ->  1.0
  52 rmnx023 remaindernear  5     2.000  ->  1.000
  53 rmnx024 remaindernear  5     0.200  ->  0.000
  54 rmnx025 remaindernear  5     0.200  ->  0.000
  55
  56 rmnx030 remaindernear  1     2      ->  1
  57 rmnx031 remaindernear  1     4      ->  1
  58 rmnx032 remaindernear  1     8      ->  1
  59 rmnx033 remaindernear  1     16     ->  1
  60 rmnx034 remaindernear  1     32     ->  1
  61 rmnx035 remaindernear  1     64     ->  1
  62 rmnx040 remaindernear  1    -2      ->  1
  63 rmnx041 remaindernear  1    -4      ->  1
  64 rmnx042 remaindernear  1    -8      ->  1
  65 rmnx043 remaindernear  1    -16     ->  1
  66 rmnx044 remaindernear  1    -32     ->  1
  67 rmnx045 remaindernear  1    -64     ->  1
  68 rmnx050 remaindernear -1     2      ->  -1
  69 rmnx051 remaindernear -1     4      ->  -1
  70 rmnx052 remaindernear -1     8      ->  -1
  71 rmnx053 remaindernear -1     16     ->  -1
  72 rmnx054 remaindernear -1     32     ->  -1
  73 rmnx055 remaindernear -1     64     ->  -1
  74 rmnx060 remaindernear -1    -2      ->  -1
  75 rmnx061 remaindernear -1    -4      ->  -1
  76 rmnx062 remaindernear -1    -8      ->  -1
  77 rmnx063 remaindernear -1    -16     ->  -1
  78 rmnx064 remaindernear -1    -32     ->  -1
  79 rmnx065 remaindernear -1    -64     ->  -1
  80
  81 rmnx066 remaindernear  999999997     1  -> 0
  82 rmnx067 remaindernear  999999997.4   1  -> 0.4
  83 rmnx068 remaindernear  999999997.5   1  -> -0.5
  84 rmnx069 remaindernear  999999997.9   1  -> -0.1
  85 rmnx070 remaindernear  999999997.999 1  -> -0.001
  86
  87 rmnx071 remaindernear  999999998     1  -> 0
  88 rmnx072 remaindernear  999999998.4   1  -> 0.4
  89 rmnx073 remaindernear  999999998.5   1  -> 0.5
  90 rmnx074 remaindernear  999999998.9   1  -> -0.1
  91 rmnx075 remaindernear  999999998.999 1  -> -0.001
  92
  93 rmnx076 remaindernear  999999999     1  -> 0
  94 rmnx077 remaindernear  999999999.4   1  -> 0.4
  95 rmnx078 remaindernear  999999999.5   1  -> NaN Division_impossible
  96 rmnx079 remaindernear  999999999.9   1  -> NaN Division_impossible
  97 rmnx080 remaindernear  999999999.999 1  -> NaN Division_impossible
  98
  99 precision: 6
 100 rmnx081 remaindernear  999999999     1  -> NaN Division_impossible
 101 rmnx082 remaindernear  99999999      1  -> NaN Division_impossible
 102 rmnx083 remaindernear  9999999       1  -> NaN Division_impossible
 103 rmnx084 remaindernear  999999        1  -> 0
 104 rmnx085 remaindernear  99999         1  -> 0
 105 rmnx086 remaindernear  9999          1  -> 0
 106 rmnx087 remaindernear  999           1  -> 0
 107 rmnx088 remaindernear  99            1  -> 0
 108 rmnx089 remaindernear  9             1  -> 0
 109
 110 precision: 9
 111 rmnx090 remaindernear  0.            1  -> 0
 112 rmnx091 remaindernear  .0            1  -> 0.0
 113 rmnx092 remaindernear  0.00          1  -> 0.00
 114 rmnx093 remaindernear  0.00E+9       1  -> 0
 115 rmnx094 remaindernear  0.0000E-50    1  -> 0E-54
 116
 117
 118 -- Various flavours of remaindernear by 0
 119 precision: 9
 120 maxexponent: 999999999
 121 minexponent: -999999999
 122 rmnx101 remaindernear  0       0   -> NaN Division_undefined
 123 rmnx102 remaindernear  0      -0   -> NaN Division_undefined
 124 rmnx103 remaindernear -0       0   -> NaN Division_undefined
 125 rmnx104 remaindernear -0      -0   -> NaN Division_undefined
 126 rmnx105 remaindernear  0.0E5   0   -> NaN Division_undefined
 127 rmnx106 remaindernear  0.000   0   -> NaN Division_undefined
 128 -- [Some think this next group should be Division_by_zero exception,
 129 -- but IEEE 854 is explicit that it is Invalid operation .. for
 130 -- remaindernear-near, anyway]
 131 rmnx107 remaindernear  0.0001  0   -> NaN Invalid_operation
 132 rmnx108 remaindernear  0.01    0   -> NaN Invalid_operation
 133 rmnx109 remaindernear  0.1     0   -> NaN Invalid_operation
 134 rmnx110 remaindernear  1       0   -> NaN Invalid_operation
 135 rmnx111 remaindernear  1       0.0 -> NaN Invalid_operation
 136 rmnx112 remaindernear 10       0.0 -> NaN Invalid_operation
 137 rmnx113 remaindernear 1E+100   0.0 -> NaN Invalid_operation
 138 rmnx114 remaindernear 1E+1000  0   -> NaN Invalid_operation
 139 rmnx115 remaindernear  0.0001 -0   -> NaN Invalid_operation
 140 rmnx116 remaindernear  0.01   -0   -> NaN Invalid_operation
 141 rmnx119 remaindernear  0.1    -0   -> NaN Invalid_operation
 142 rmnx120 remaindernear  1      -0   -> NaN Invalid_operation
 143 rmnx121 remaindernear  1      -0.0 -> NaN Invalid_operation
 144 rmnx122 remaindernear 10      -0.0 -> NaN Invalid_operation
 145 rmnx123 remaindernear 1E+100  -0.0 -> NaN Invalid_operation
 146 rmnx124 remaindernear 1E+1000 -0   -> NaN Invalid_operation
 147 -- and zeros on left
 148 rmnx130 remaindernear  0      1   ->  0
 149 rmnx131 remaindernear  0     -1   ->  0
 150 rmnx132 remaindernear  0.0    1   ->  0.0
 151 rmnx133 remaindernear  0.0   -1   ->  0.0
 152 rmnx134 remaindernear -0      1   -> -0
 153 rmnx135 remaindernear -0     -1   -> -0
 154 rmnx136 remaindernear -0.0    1   -> -0.0
 155 rmnx137 remaindernear -0.0   -1   -> -0.0
 156
 157 -- 0.5ers
 158 rmmx143 remaindernear   0.5  2     ->  0.5
 159 rmmx144 remaindernear   0.5  2.1   ->  0.5
 160 rmmx145 remaindernear   0.5  2.01  ->  0.50
 161 rmmx146 remaindernear   0.5  2.001 ->  0.500
 162 rmmx147 remaindernear   0.50 2     ->  0.50
 163 rmmx148 remaindernear   0.50 2.01  ->  0.50
 164 rmmx149 remaindernear   0.50 2.001 ->  0.500
 165
 166 -- some differences from remainder
 167 rmnx150 remaindernear   0.4  1.020 ->  0.400
 168 rmnx151 remaindernear   0.50 1.020 ->  0.500
 169 rmnx152 remaindernear   0.51 1.020 ->  0.510
 170 rmnx153 remaindernear   0.52 1.020 -> -0.500
 171 rmnx154 remaindernear   0.6  1.020 -> -0.420
 172 rmnx155 remaindernear   0.49 1     ->  0.49
 173 rmnx156 remaindernear   0.50 1     ->  0.50
 174 rmnx157 remaindernear   1.50 1     -> -0.50
 175 rmnx158 remaindernear   2.50 1     ->  0.50
 176 rmnx159 remaindernear   9.50 1     -> -0.50
 177 rmnx160 remaindernear   0.51 1     -> -0.49
 178
 179 -- the nasty division-by-1 cases
 180 rmnx161 remaindernear   0.4         1   ->  0.4
 181 rmnx162 remaindernear   0.45        1   ->  0.45
 182 rmnx163 remaindernear   0.455       1   ->  0.455
 183 rmnx164 remaindernear   0.4555      1   ->  0.4555
 184 rmnx165 remaindernear   0.45555     1   ->  0.45555
 185 rmnx166 remaindernear   0.455555    1   ->  0.455555
 186 rmnx167 remaindernear   0.4555555   1   ->  0.4555555
 187 rmnx168 remaindernear   0.45555555  1   ->  0.45555555
 188 rmnx169 remaindernear   0.455555555 1   ->  0.455555555
 189 -- with spill...
 190 rmnx171 remaindernear   0.5         1   ->  0.5
 191 rmnx172 remaindernear   0.55        1   -> -0.45
 192 rmnx173 remaindernear   0.555       1   -> -0.445
 193 rmnx174 remaindernear   0.5555      1   -> -0.4445
 194 rmnx175 remaindernear   0.55555     1   -> -0.44445
 195 rmnx176 remaindernear   0.555555    1   -> -0.444445
 196 rmnx177 remaindernear   0.5555555   1   -> -0.4444445
 197 rmnx178 remaindernear   0.55555555  1   -> -0.44444445
 198 rmnx179 remaindernear   0.555555555 1   -> -0.444444445
 199
 200 -- progression
 201 rmnx180 remaindernear  1  1   -> 0
 202 rmnx181 remaindernear  1  2   -> 1
 203 rmnx182 remaindernear  1  3   -> 1
 204 rmnx183 remaindernear  1  4   -> 1
 205 rmnx184 remaindernear  1  5   -> 1
 206 rmnx185 remaindernear  1  6   -> 1
 207 rmnx186 remaindernear  1  7   -> 1
 208 rmnx187 remaindernear  1  8   -> 1
 209 rmnx188 remaindernear  1  9   -> 1
 210 rmnx189 remaindernear  1  10  -> 1
 211 rmnx190 remaindernear  1  1   -> 0
 212 rmnx191 remaindernear  2  1   -> 0
 213 rmnx192 remaindernear  3  1   -> 0
 214 rmnx193 remaindernear  4  1   -> 0
 215 rmnx194 remaindernear  5  1   -> 0
 216 rmnx195 remaindernear  6  1   -> 0
 217 rmnx196 remaindernear  7  1   -> 0
 218 rmnx197 remaindernear  8  1   -> 0
 219 rmnx198 remaindernear  9  1   -> 0
 220 rmnx199 remaindernear  10 1   -> 0
 221
 222
 223 -- Various flavours of remaindernear by 0
 224 maxexponent: 999999999
 225 minexponent: -999999999
 226 rmnx201 remaindernear  0      0   -> NaN Division_undefined
 227 rmnx202 remaindernear  0.0E5  0   -> NaN Division_undefined
 228 rmnx203 remaindernear  0.000  0   -> NaN Division_undefined
 229 rmnx204 remaindernear  0.0001 0   -> NaN Invalid_operation
 230 rmnx205 remaindernear  0.01   0   -> NaN Invalid_operation
 231 rmnx206 remaindernear  0.1    0   -> NaN Invalid_operation
 232 rmnx207 remaindernear  1      0   -> NaN Invalid_operation
 233 rmnx208 remaindernear  1      0.0 -> NaN Invalid_operation
 234 rmnx209 remaindernear 10      0.0 -> NaN Invalid_operation
 235 rmnx210 remaindernear 1E+100  0.0 -> NaN Invalid_operation
 236 rmnx211 remaindernear 1E+1000 0   -> NaN Invalid_operation
 237
 238 -- tests from the extended specification
 239 rmnx221 remaindernear 2.1     3   -> -0.9
 240 rmnx222 remaindernear  10     6   -> -2
 241 rmnx223 remaindernear  10     3   ->  1
 242 rmnx224 remaindernear -10     3   -> -1
 243 rmnx225 remaindernear  10.2   1   -> 0.2
 244 rmnx226 remaindernear  10     0.3 -> 0.1
 245 rmnx227 remaindernear   3.6   1.3 -> -0.3
 246
 247 -- some differences from remainder
 248 rmnx231 remaindernear   0.4  1.020 ->  0.400
 249 rmnx232 remaindernear   0.50 1.020 ->  0.500
 250 rmnx233 remaindernear   0.51 1.020 ->  0.510
 251 rmnx234 remaindernear   0.52 1.020 -> -0.500
 252 rmnx235 remaindernear   0.6  1.020 -> -0.420
 253
 254 -- test some cases that are close to exponent overflow
 255 maxexponent: 999999999
 256 minexponent: -999999999
 257 rmnx270 remaindernear 1 1e999999999    -> 1
 258 rmnx271 remaindernear 1 0.9e999999999  -> 1
 259 rmnx272 remaindernear 1 0.99e999999999 -> 1
 260 rmnx273 remaindernear 1 0.999999999e999999999 -> 1
 261 rmnx274 remaindernear 9e999999999          1 -> NaN Division_impossible
 262 rmnx275 remaindernear 9.9e999999999        1 -> NaN Division_impossible
 263 rmnx276 remaindernear 9.99e999999999       1 -> NaN Division_impossible
 264 rmnx277 remaindernear 9.99999999e999999999 1 -> NaN Division_impossible
 265
 266 rmnx280 remaindernear 0.1 9e-999999999       -> NaN Division_impossible
 267 rmnx281 remaindernear 0.1 99e-999999999      -> NaN Division_impossible
 268 rmnx282 remaindernear 0.1 999e-999999999     -> NaN Division_impossible
 269
 270 rmnx283 remaindernear 0.1 9e-999999998       -> NaN Division_impossible
 271 rmnx284 remaindernear 0.1 99e-999999998      -> NaN Division_impossible
 272 rmnx285 remaindernear 0.1 999e-999999998     -> NaN Division_impossible
 273 rmnx286 remaindernear 0.1 999e-999999997     -> NaN Division_impossible
 274 rmnx287 remaindernear 0.1 9999e-999999997    -> NaN Division_impossible
 275 rmnx288 remaindernear 0.1 99999e-999999997   -> NaN Division_impossible
 276
 277 -- rmnx3xx are from DiagBigDecimal
 278 rmnx301 remaindernear   1    3     ->  1
 279 rmnx302 remaindernear   5    5     ->  0
 280 rmnx303 remaindernear   13   10    ->  3
 281 rmnx304 remaindernear   13   50    ->  13
 282 rmnx305 remaindernear   13   100   ->  13
 283 rmnx306 remaindernear   13   1000  ->  13
 284 rmnx307 remaindernear   .13    1   ->  0.13
 285 rmnx308 remaindernear   0.133  1   ->  0.133
 286 rmnx309 remaindernear   0.1033 1   ->  0.1033
 287 rmnx310 remaindernear   1.033  1   ->  0.033
 288 rmnx311 remaindernear   10.33  1   ->  0.33
 289 rmnx312 remaindernear   10.33 10   ->  0.33
 290 rmnx313 remaindernear   103.3  1   ->  0.3
 291 rmnx314 remaindernear   133   10   ->  3
 292 rmnx315 remaindernear   1033  10   ->  3
 293 rmnx316 remaindernear   1033  50   -> -17
 294 rmnx317 remaindernear   101.0  3   -> -1.0
 295 rmnx318 remaindernear   102.0  3   ->  0.0
 296 rmnx319 remaindernear   103.0  3   ->  1.0
 297 rmnx320 remaindernear   2.40   1   ->  0.40
 298 rmnx321 remaindernear   2.400  1   ->  0.400
 299 rmnx322 remaindernear   2.4    1   ->  0.4
 300 rmnx323 remaindernear   2.4    2   ->  0.4
 301 rmnx324 remaindernear   2.400  2   ->  0.400
 302 rmnx325 remaindernear   1   0.3    ->  0.1
 303 rmnx326 remaindernear   1   0.30   ->  0.10
 304 rmnx327 remaindernear   1   0.300  ->  0.100
 305 rmnx328 remaindernear   1   0.3000 ->  0.1000
 306 rmnx329 remaindernear   1.0    0.3 ->  0.1
 307 rmnx330 remaindernear   1.00   0.3 ->  0.10
 308 rmnx331 remaindernear   1.000  0.3 ->  0.100
 309 rmnx332 remaindernear   1.0000 0.3 ->  0.1000
 310 rmnx333 remaindernear   0.5  2     ->  0.5
 311 rmnx334 remaindernear   0.5  2.1   ->  0.5
 312 rmnx335 remaindernear   0.5  2.01  ->  0.50
 313 rmnx336 remaindernear   0.5  2.001 ->  0.500
 314 rmnx337 remaindernear   0.50 2     ->  0.50
 315 rmnx338 remaindernear   0.50 2.01  ->  0.50
 316 rmnx339 remaindernear   0.50 2.001 ->  0.500
 317
 318 rmnx340 remaindernear   0.5   0.5000001    ->  -1E-7
 319 rmnx341 remaindernear   0.5   0.50000001    ->  -1E-8
 320 rmnx342 remaindernear   0.5   0.500000001    ->  -1E-9
 321 rmnx343 remaindernear   0.5   0.5000000001    ->  -1E-10
 322 rmnx344 remaindernear   0.5   0.50000000001    ->  -1E-11
 323 rmnx345 remaindernear   0.5   0.4999999    ->  1E-7
 324 rmnx346 remaindernear   0.5   0.49999999    ->  1E-8
 325 rmnx347 remaindernear   0.5   0.499999999    ->  1E-9
 326 rmnx348 remaindernear   0.5   0.4999999999    ->  1E-10
 327 rmnx349 remaindernear   0.5   0.49999999999    ->  1E-11
 328
 329 rmnx350 remaindernear   0.03  7  ->  0.03
 330 rmnx351 remaindernear   5   2    ->  1
 331 rmnx352 remaindernear   4.1   2    ->  0.1
 332 rmnx353 remaindernear   4.01   2    ->  0.01
 333 rmnx354 remaindernear   4.001   2    ->  0.001
 334 rmnx355 remaindernear   4.0001   2    ->  0.0001
 335 rmnx356 remaindernear   4.00001   2    ->  0.00001
 336 rmnx357 remaindernear   4.000001   2    ->  0.000001
 337 rmnx358 remaindernear   4.0000001   2    ->  1E-7
 338
 339 rmnx360 remaindernear   1.2   0.7345 -> -0.2690
 340 rmnx361 remaindernear   0.8   12     ->  0.8
 341 rmnx362 remaindernear   0.8   0.2    ->  0.0
 342 rmnx363 remaindernear   0.8   0.3    -> -0.1
 343 rmnx364 remaindernear   0.800   12   ->  0.800
 344 rmnx365 remaindernear   0.800   1.7  ->  0.800
 345 rmnx366 remaindernear   2.400   2    ->  0.400
 346
 347 precision: 6
 348 rmnx371 remaindernear   2.400  2        ->  0.400
 349 precision: 3
 350 rmnx372 remaindernear   12345678900000 12e+12 -> 3.46E+11 Inexact Rounded
 351
 352 precision: 5
 353 rmnx381 remaindernear 12345  1         ->  0
 354 rmnx382 remaindernear 12345  1.0001    -> -0.2344
 355 rmnx383 remaindernear 12345  1.001     -> -0.333
 356 rmnx384 remaindernear 12345  1.01      -> -0.23
 357 rmnx385 remaindernear 12345  1.1       -> -0.3
 358 rmnx386 remaindernear 12355  4         -> -1
 359 rmnx387 remaindernear 12345  4         ->  1
 360 rmnx388 remaindernear 12355  4.0001    -> -1.3089
 361 rmnx389 remaindernear 12345  4.0001    ->  0.6914
 362 rmnx390 remaindernear 12345  4.9       ->  1.9
 363 rmnx391 remaindernear 12345  4.99      -> -0.26
 364 rmnx392 remaindernear 12345  4.999     ->  2.469
 365 rmnx393 remaindernear 12345  4.9999    ->  0.2469
 366 rmnx394 remaindernear 12345  5         ->  0
 367 rmnx395 remaindernear 12345  5.0001    -> -0.2469
 368 rmnx396 remaindernear 12345  5.001     -> -2.469
 369 rmnx397 remaindernear 12345  5.01      ->  0.36
 370 rmnx398 remaindernear 12345  5.1       -> -2.1
 371
 372 precision: 9
 373 -- some nasty division-by-1 cases [some similar above]
 374 rmnx401 remaindernear   0.4         1   ->  0.4
 375 rmnx402 remaindernear   0.45        1   ->  0.45
 376 rmnx403 remaindernear   0.455       1   ->  0.455
 377 rmnx404 remaindernear   0.4555      1   ->  0.4555
 378 rmnx405 remaindernear   0.45555     1   ->  0.45555
 379 rmnx406 remaindernear   0.455555    1   ->  0.455555
 380 rmnx407 remaindernear   0.4555555   1   ->  0.4555555
 381 rmnx408 remaindernear   0.45555555  1   ->  0.45555555
 382 rmnx409 remaindernear   0.455555555 1   ->  0.455555555
 383
 384 -- some tricky LHSs
 385 rmnx420 remaindernear   99999999.999999999   1E+8   -> -1E-9
 386 rmnx421 remaindernear  999999999.999999999   1E+9   -> -1E-9
 387 precision: 9
 388 rmnx430 remaindernear   0.455555555 1   ->  0.455555555
 389 precision: 8
 390 rmnx431 remaindernear   0.455555555 1   ->  0.45555556 Inexact Rounded
 391 precision: 7
 392 rmnx432 remaindernear   0.455555555 1   ->  0.4555556  Inexact Rounded
 393 precision: 6
 394 rmnx433 remaindernear   0.455555555 1   ->  0.455556   Inexact Rounded
 395 precision: 5
 396 rmnx434 remaindernear   0.455555555 1   ->  0.45556    Inexact Rounded
 397 precision: 4
 398 rmnx435 remaindernear   0.455555555 1   ->  0.4556     Inexact Rounded
 399 precision: 3
 400 rmnx436 remaindernear   0.455555555 1   ->  0.456      Inexact Rounded
 401 precision: 2
 402 rmnx437 remaindernear   0.455555555 1   ->  0.46       Inexact Rounded
 403 precision: 1
 404 rmnx438 remaindernear   0.455555555 1   ->  0.5        Inexact Rounded
 405
 406 -- early tests; from text descriptions
 407 precision: 9
 408 rmnx601 remaindernear  10   6  -> -2
 409 rmnx602 remaindernear -10   6  -> 2
 410 rmnx603 remaindernear  11   3  -> -1
 411 rmnx604 remaindernear  11   5  -> 1
 412 rmnx605 remaindernear   7.7 8  -> -0.3
 413 rmnx606 remaindernear  31.5 3  -> 1.5    -- i=10
 414 rmnx607 remaindernear  34.5 3  -> -1.5   -- i=11
 415
 416 -- zero signs
 417 rmnx650 remaindernear  1  1 ->  0
 418 rmnx651 remaindernear -1  1 -> -0
 419 rmnx652 remaindernear  1 -1 ->  0
 420 rmnx653 remaindernear -1 -1 -> -0
 421 rmnx654 remaindernear  0  1 ->  0
 422 rmnx655 remaindernear -0  1 -> -0
 423 rmnx656 remaindernear  0 -1 ->  0
 424 rmnx657 remaindernear -0 -1 -> -0
 425 rmnx658 remaindernear  0.00  1  ->  0.00
 426 rmnx659 remaindernear -0.00  1  -> -0.00
 427
 428 -- Specials
 429 rmnx680 remaindernear  Inf  -Inf   ->  NaN Invalid_operation
 430 rmnx681 remaindernear  Inf  -1000  ->  NaN Invalid_operation
 431 rmnx682 remaindernear  Inf  -1     ->  NaN Invalid_operation
 432 rmnx683 remaindernear  Inf   0     ->  NaN Invalid_operation
 433 rmnx684 remaindernear  Inf  -0     ->  NaN Invalid_operation
 434 rmnx685 remaindernear  Inf   1     ->  NaN Invalid_operation
 435 rmnx686 remaindernear  Inf   1000  ->  NaN Invalid_operation
 436 rmnx687 remaindernear  Inf   Inf   ->  NaN Invalid_operation
 437 rmnx688 remaindernear -1000  Inf   -> -1000
 438 rmnx689 remaindernear -Inf   Inf   ->  NaN Invalid_operation
 439 rmnx691 remaindernear -1     Inf   -> -1
 440 rmnx692 remaindernear  0     Inf   ->  0
 441 rmnx693 remaindernear -0     Inf   -> -0
 442 rmnx694 remaindernear  1     Inf   ->  1
 443 rmnx695 remaindernear  1000  Inf   ->  1000
 444 rmnx696 remaindernear  Inf   Inf   ->  NaN Invalid_operation
 445
 446 rmnx700 remaindernear -Inf  -Inf   ->  NaN Invalid_operation
 447 rmnx701 remaindernear -Inf  -1000  ->  NaN Invalid_operation
 448 rmnx702 remaindernear -Inf  -1     ->  NaN Invalid_operation
 449 rmnx703 remaindernear -Inf  -0     ->  NaN Invalid_operation
 450 rmnx704 remaindernear -Inf   0     ->  NaN Invalid_operation
 451 rmnx705 remaindernear -Inf   1     ->  NaN Invalid_operation
 452 rmnx706 remaindernear -Inf   1000  ->  NaN Invalid_operation
 453 rmnx707 remaindernear -Inf   Inf   ->  NaN Invalid_operation
 454 rmnx708 remaindernear -Inf  -Inf   ->  NaN Invalid_operation
 455 rmnx709 remaindernear -1000  Inf   -> -1000
 456 rmnx710 remaindernear -1    -Inf   -> -1
 457 rmnx711 remaindernear -0    -Inf   -> -0
 458 rmnx712 remaindernear  0    -Inf   ->  0
 459 rmnx713 remaindernear  1    -Inf   ->  1
 460 rmnx714 remaindernear  1000 -Inf   ->  1000
 461 rmnx715 remaindernear  Inf  -Inf   ->  NaN Invalid_operation
 462
 463 rmnx721 remaindernear  NaN -Inf    ->  NaN
 464 rmnx722 remaindernear  NaN -1000   ->  NaN
 465 rmnx723 remaindernear  NaN -1      ->  NaN
 466 rmnx724 remaindernear  NaN -0      ->  NaN
 467 rmnx725 remaindernear  NaN  0      ->  NaN
 468 rmnx726 remaindernear  NaN  1      ->  NaN
 469 rmnx727 remaindernear  NaN  1000   ->  NaN
 470 rmnx728 remaindernear  NaN  Inf    ->  NaN
 471 rmnx729 remaindernear  NaN  NaN    ->  NaN
 472 rmnx730 remaindernear -Inf  NaN    ->  NaN
 473 rmnx731 remaindernear -1000 NaN    ->  NaN
 474 rmnx732 remaindernear -1   -NaN    -> -NaN
 475 rmnx733 remaindernear -0    NaN    ->  NaN
 476 rmnx734 remaindernear  0    NaN    ->  NaN
 477 rmnx735 remaindernear  1    NaN    ->  NaN
 478 rmnx736 remaindernear  1000 NaN    ->  NaN
 479 rmnx737 remaindernear  Inf  NaN    ->  NaN
 480
 481 rmnx741 remaindernear  sNaN -Inf   ->  NaN  Invalid_operation
 482 rmnx742 remaindernear  sNaN -1000  ->  NaN  Invalid_operation
 483 rmnx743 remaindernear -sNaN -1     -> -NaN  Invalid_operation
 484 rmnx744 remaindernear  sNaN -0     ->  NaN  Invalid_operation
 485 rmnx745 remaindernear  sNaN  0     ->  NaN  Invalid_operation
 486 rmnx746 remaindernear  sNaN  1     ->  NaN  Invalid_operation
 487 rmnx747 remaindernear  sNaN  1000  ->  NaN  Invalid_operation
 488 rmnx749 remaindernear  sNaN  NaN   ->  NaN  Invalid_operation
 489 rmnx750 remaindernear  sNaN sNaN   ->  NaN  Invalid_operation
 490 rmnx751 remaindernear  NaN  sNaN   ->  NaN  Invalid_operation
 491 rmnx752 remaindernear -Inf  sNaN   ->  NaN  Invalid_operation
 492 rmnx753 remaindernear -1000 sNaN   ->  NaN  Invalid_operation
 493 rmnx754 remaindernear -1    sNaN   ->  NaN  Invalid_operation
 494 rmnx755 remaindernear -0   -sNaN   -> -NaN  Invalid_operation
 495 rmnx756 remaindernear  0    sNaN   ->  NaN  Invalid_operation
 496 rmnx757 remaindernear  1    sNaN   ->  NaN  Invalid_operation
 497 rmnx758 remaindernear  1000 sNaN   ->  NaN  Invalid_operation
 498 rmnx759 remaindernear  Inf  sNaN   ->  NaN  Invalid_operation
 499 rmnx760 remaindernear  NaN  sNaN   ->  NaN  Invalid_operation
 500
 501 -- propaging NaNs
 502 rmnx761 remaindernear  NaN1   NaN7   ->  NaN1
 503 rmnx762 remaindernear sNaN2   NaN8   ->  NaN2 Invalid_operation
 504 rmnx763 remaindernear  NaN3 -sNaN9   -> -NaN9 Invalid_operation
 505 rmnx764 remaindernear sNaN4  sNaN10  ->  NaN4 Invalid_operation
 506 rmnx765 remaindernear    15   NaN11  ->  NaN11
 507 rmnx766 remaindernear  NaN6   NaN12  ->  NaN6
 508 rmnx767 remaindernear  Inf   -NaN13  -> -NaN13
 509 rmnx768 remaindernear  NaN14  -Inf   ->  NaN14
 510 rmnx769 remaindernear    0    NaN15  ->  NaN15
 511 rmnx770 remaindernear -NaN16   -0    -> -NaN16
 512
 513 -- test some cases that are close to exponent overflow
 514 maxexponent: 999999999
 515 minexponent: -999999999
 516 rmnx780 remaindernear 1 1e999999999    -> 1
 517 rmnx781 remaindernear 1 0.9e999999999  -> 1
 518 rmnx782 remaindernear 1 0.99e999999999 -> 1
 519 rmnx783 remaindernear 1 0.999999999e999999999 -> 1
 520 rmnx784 remaindernear 9e999999999          1 -> NaN Division_impossible
 521 rmnx785 remaindernear 9.9e999999999        1 -> NaN Division_impossible
 522 rmnx786 remaindernear 9.99e999999999       1 -> NaN Division_impossible
 523 rmnx787 remaindernear 9.99999999e999999999 1 -> NaN Division_impossible
 524
 525
 526 -- overflow and underflow tests [from divide]
 527 precision: 9
 528 maxexponent: 999999999
 529 minexponent: -999999999
 530 rmnx790 remaindernear +1.23456789012345E-0 9E+999999999 -> 1.23456789 Inexact Rounded
 531 rmnx791 remaindernear 9E+999999999 +0.23456789012345E-0 -> NaN Division_impossible
 532 rmnx792 remaindernear +0.100 9E+999999999               -> 0.100
 533 rmnx793 remaindernear 9E-999999999 +9.100               -> 9E-999999999
 534 rmnx795 remaindernear -1.23456789012345E-0 9E+999999999 -> -1.23456789 Inexact Rounded
 535 rmnx796 remaindernear 9E+999999999 -0.83456789012345E-0 -> NaN Division_impossible
 536 rmnx797 remaindernear -0.100 9E+999999999               -> -0.100
 537 rmnx798 remaindernear 9E-999999999 -9.100               -> 9E-999999999
 538
 539 -- long operands checks
 540 maxexponent: 999
 541 minexponent: -999
 542 precision: 9
 543 rmnx801 remaindernear 12345678000 100 -> 0
 544 rmnx802 remaindernear 1 12345678000   -> 1
 545 rmnx803 remaindernear 1234567800  10  -> 0
 546 rmnx804 remaindernear 1 1234567800    -> 1
 547 rmnx805 remaindernear 1234567890  10  -> 0
 548 rmnx806 remaindernear 1 1234567890    -> 1
 549 rmnx807 remaindernear 1234567891  10  -> 1
 550 rmnx808 remaindernear 1 1234567891    -> 1
 551 rmnx809 remaindernear 12345678901 100 -> 1
 552 rmnx810 remaindernear 1 12345678901   -> 1
 553 rmnx811 remaindernear 1234567896  10  -> -4
 554 rmnx812 remaindernear 1 1234567896    -> 1
 555
 556 precision: 15
 557 rmnx841 remaindernear 12345678000 100 -> 0
 558 rmnx842 remaindernear 1 12345678000   -> 1
 559 rmnx843 remaindernear 1234567800  10  -> 0
 560 rmnx844 remaindernear 1 1234567800    -> 1
 561 rmnx845 remaindernear 1234567890  10  -> 0
 562 rmnx846 remaindernear 1 1234567890    -> 1
 563 rmnx847 remaindernear 1234567891  10  -> 1
 564 rmnx848 remaindernear 1 1234567891    -> 1
 565 rmnx849 remaindernear 12345678901 100 -> 1
 566 rmnx850 remaindernear 1 12345678901   -> 1
 567 rmnx851 remaindernear 1234567896  10  -> -4
 568 rmnx852 remaindernear 1 1234567896    -> 1
 569
 570 -- Null tests
 571 rmnx900 remaindernear 10  # -> NaN Invalid_operation
 572 rmnx901 remaindernear  # 10 -> NaN Invalid_operation