------------------------------------------------------------------------
-- maxmag.decTest -- decimal maximum by magnitude                     --
-- 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

-- we assume that base comparison is tested in compare.decTest, so
-- these mainly cover special cases and rounding

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

-- sanity checks
mxgx001 maxmag  -2  -2  -> -2
mxgx002 maxmag  -2  -1  -> -2
mxgx003 maxmag  -2   0  -> -2
mxgx004 maxmag  -2   1  -> -2
mxgx005 maxmag  -2   2  ->  2
mxgx006 maxmag  -1  -2  -> -2
mxgx007 maxmag  -1  -1  -> -1
mxgx008 maxmag  -1   0  -> -1
mxgx009 maxmag  -1   1  ->  1
mxgx010 maxmag  -1   2  ->  2
mxgx011 maxmag   0  -2  -> -2
mxgx012 maxmag   0  -1  -> -1
mxgx013 maxmag   0   0  ->  0
mxgx014 maxmag   0   1  ->  1
mxgx015 maxmag   0   2  ->  2
mxgx016 maxmag   1  -2  -> -2
mxgx017 maxmag   1  -1  ->  1
mxgx018 maxmag   1   0  ->  1
mxgx019 maxmag   1   1  ->  1
mxgx020 maxmag   1   2  ->  2
mxgx021 maxmag   2  -2  ->  2
mxgx022 maxmag   2  -1  ->  2
mxgx023 maxmag   2   0  ->  2
mxgx025 maxmag   2   1  ->  2
mxgx026 maxmag   2   2  ->  2

-- extended zeros
mxgx030 maxmag   0     0   ->  0
mxgx031 maxmag   0    -0   ->  0
mxgx032 maxmag   0    -0.0 ->  0
mxgx033 maxmag   0     0.0 ->  0
mxgx034 maxmag  -0     0   ->  0    -- note: -0 = 0, but 0 chosen
mxgx035 maxmag  -0    -0   -> -0
mxgx036 maxmag  -0    -0.0 -> -0.0
mxgx037 maxmag  -0     0.0 ->  0.0
mxgx038 maxmag   0.0   0   ->  0
mxgx039 maxmag   0.0  -0   ->  0.0
mxgx040 maxmag   0.0  -0.0 ->  0.0
mxgx041 maxmag   0.0   0.0 ->  0.0
mxgx042 maxmag  -0.0   0   ->  0
mxgx043 maxmag  -0.0  -0   -> -0.0
mxgx044 maxmag  -0.0  -0.0 -> -0.0
mxgx045 maxmag  -0.0   0.0 ->  0.0

mxgx050 maxmag  -0E1   0E1 ->  0E+1
mxgx051 maxmag  -0E2   0E2 ->  0E+2
mxgx052 maxmag  -0E2   0E1 ->  0E+1
mxgx053 maxmag  -0E1   0E2 ->  0E+2
mxgx054 maxmag   0E1  -0E1 ->  0E+1
mxgx055 maxmag   0E2  -0E2 ->  0E+2
mxgx056 maxmag   0E2  -0E1 ->  0E+2
mxgx057 maxmag   0E1  -0E2 ->  0E+1

mxgx058 maxmag   0E1   0E1 ->  0E+1
mxgx059 maxmag   0E2   0E2 ->  0E+2
mxgx060 maxmag   0E2   0E1 ->  0E+2
mxgx061 maxmag   0E1   0E2 ->  0E+2
mxgx062 maxmag  -0E1  -0E1 -> -0E+1
mxgx063 maxmag  -0E2  -0E2 -> -0E+2
mxgx064 maxmag  -0E2  -0E1 -> -0E+1
mxgx065 maxmag  -0E1  -0E2 -> -0E+1

-- Specials
precision: 9
mxgx090 maxmag  Inf  -Inf   ->  Infinity
mxgx091 maxmag  Inf  -1000  ->  Infinity
mxgx092 maxmag  Inf  -1     ->  Infinity
mxgx093 maxmag  Inf  -0     ->  Infinity
mxgx094 maxmag  Inf   0     ->  Infinity
mxgx095 maxmag  Inf   1     ->  Infinity
mxgx096 maxmag  Inf   1000  ->  Infinity
mxgx097 maxmag  Inf   Inf   ->  Infinity
mxgx098 maxmag -1000  Inf   ->  Infinity
mxgx099 maxmag -Inf   Inf   ->  Infinity
mxgx100 maxmag -1     Inf   ->  Infinity
mxgx101 maxmag -0     Inf   ->  Infinity
mxgx102 maxmag  0     Inf   ->  Infinity
mxgx103 maxmag  1     Inf   ->  Infinity
mxgx104 maxmag  1000  Inf   ->  Infinity
mxgx105 maxmag  Inf   Inf   ->  Infinity

mxgx120 maxmag -Inf  -Inf   -> -Infinity
mxgx121 maxmag -Inf  -1000  -> -Infinity
mxgx122 maxmag -Inf  -1     -> -Infinity
mxgx123 maxmag -Inf  -0     -> -Infinity
mxgx124 maxmag -Inf   0     -> -Infinity
mxgx125 maxmag -Inf   1     -> -Infinity
mxgx126 maxmag -Inf   1000  -> -Infinity
mxgx127 maxmag -Inf   Inf   ->  Infinity
mxgx128 maxmag -Inf  -Inf   -> -Infinity
mxgx129 maxmag -1000 -Inf   -> -Infinity
mxgx130 maxmag -1    -Inf   -> -Infinity
mxgx131 maxmag -0    -Inf   -> -Infinity
mxgx132 maxmag  0    -Inf   -> -Infinity
mxgx133 maxmag  1    -Inf   -> -Infinity
mxgx134 maxmag  1000 -Inf   -> -Infinity
mxgx135 maxmag  Inf  -Inf   ->  Infinity

-- 2004.08.02 754r chooses number over NaN in mixed cases
mxgx141 maxmag  NaN -Inf    -> -Infinity
mxgx142 maxmag  NaN -1000   -> -1000
mxgx143 maxmag  NaN -1      -> -1
mxgx144 maxmag  NaN -0      -> -0
mxgx145 maxmag  NaN  0      ->  0
mxgx146 maxmag  NaN  1      ->  1
mxgx147 maxmag  NaN  1000   ->  1000
mxgx148 maxmag  NaN  Inf    ->  Infinity
mxgx149 maxmag  NaN  NaN    ->  NaN
mxgx150 maxmag -Inf  NaN    -> -Infinity
mxgx151 maxmag -1000 NaN    -> -1000
mxgx152 maxmag -1    NaN    -> -1
mxgx153 maxmag -0    NaN    -> -0
mxgx154 maxmag  0    NaN    ->  0
mxgx155 maxmag  1    NaN    ->  1
mxgx156 maxmag  1000 NaN    ->  1000
mxgx157 maxmag  Inf  NaN    ->  Infinity

mxgx161 maxmag  sNaN -Inf   ->  NaN  Invalid_operation
mxgx162 maxmag  sNaN -1000  ->  NaN  Invalid_operation
mxgx163 maxmag  sNaN -1     ->  NaN  Invalid_operation
mxgx164 maxmag  sNaN -0     ->  NaN  Invalid_operation
mxgx165 maxmag  sNaN  0     ->  NaN  Invalid_operation
mxgx166 maxmag  sNaN  1     ->  NaN  Invalid_operation
mxgx167 maxmag  sNaN  1000  ->  NaN  Invalid_operation
mxgx168 maxmag  sNaN  NaN   ->  NaN  Invalid_operation
mxgx169 maxmag  sNaN sNaN   ->  NaN  Invalid_operation
mxgx170 maxmag  NaN  sNaN   ->  NaN  Invalid_operation
mxgx171 maxmag -Inf  sNaN   ->  NaN  Invalid_operation
mxgx172 maxmag -1000 sNaN   ->  NaN  Invalid_operation
mxgx173 maxmag -1    sNaN   ->  NaN  Invalid_operation
mxgx174 maxmag -0    sNaN   ->  NaN  Invalid_operation
mxgx175 maxmag  0    sNaN   ->  NaN  Invalid_operation
mxgx176 maxmag  1    sNaN   ->  NaN  Invalid_operation
mxgx177 maxmag  1000 sNaN   ->  NaN  Invalid_operation
mxgx178 maxmag  Inf  sNaN   ->  NaN  Invalid_operation
mxgx179 maxmag  NaN  sNaN   ->  NaN  Invalid_operation

-- propagating NaNs
mxgx181 maxmag  NaN9  -Inf   -> -Infinity
mxgx182 maxmag  NaN8     9   ->  9
mxgx183 maxmag -NaN7   Inf   ->  Infinity

mxgx184 maxmag -NaN1   NaN11 -> -NaN1
mxgx185 maxmag  NaN2   NaN12 ->  NaN2
mxgx186 maxmag -NaN13 -NaN7  -> -NaN13
mxgx187 maxmag  NaN14 -NaN5  ->  NaN14

mxgx188 maxmag -Inf    NaN4  -> -Infinity
mxgx189 maxmag -9     -NaN3  -> -9
mxgx190 maxmag  Inf    NaN2  ->  Infinity

mxgx191 maxmag  sNaN99 -Inf    ->  NaN99 Invalid_operation
mxgx192 maxmag  sNaN98 -1      ->  NaN98 Invalid_operation
mxgx193 maxmag -sNaN97  NaN    -> -NaN97 Invalid_operation
mxgx194 maxmag  sNaN96 sNaN94  ->  NaN96 Invalid_operation
mxgx195 maxmag  NaN95  sNaN93  ->  NaN93 Invalid_operation
mxgx196 maxmag -Inf    sNaN92  ->  NaN92 Invalid_operation
mxgx197 maxmag  0      sNaN91  ->  NaN91 Invalid_operation
mxgx198 maxmag  Inf   -sNaN90  -> -NaN90 Invalid_operation
mxgx199 maxmag  NaN    sNaN89  ->  NaN89 Invalid_operation

-- rounding checks
maxexponent: 999
minexponent: -999
precision: 9
mxgx201 maxmag 12345678000 1  -> 1.23456780E+10 Rounded
mxgx202 maxmag 1 12345678000  -> 1.23456780E+10 Rounded
mxgx203 maxmag 1234567800  1  -> 1.23456780E+9 Rounded
mxgx204 maxmag 1 1234567800   -> 1.23456780E+9 Rounded
mxgx205 maxmag 1234567890  1  -> 1.23456789E+9 Rounded
mxgx206 maxmag 1 1234567890   -> 1.23456789E+9 Rounded
mxgx207 maxmag 1234567891  1  -> 1.23456789E+9 Inexact Rounded
mxgx208 maxmag 1 1234567891   -> 1.23456789E+9 Inexact Rounded
mxgx209 maxmag 12345678901 1  -> 1.23456789E+10 Inexact Rounded
mxgx210 maxmag 1 12345678901  -> 1.23456789E+10 Inexact Rounded
mxgx211 maxmag 1234567896  1  -> 1.23456790E+9 Inexact Rounded
mxgx212 maxmag 1 1234567896   -> 1.23456790E+9 Inexact Rounded
mxgx213 maxmag -1234567891  1 -> -1.23456789E+9   Inexact Rounded
mxgx214 maxmag 1 -1234567891  -> -1.23456789E+9   Inexact Rounded
mxgx215 maxmag -12345678901 1 -> -1.23456789E+10  Inexact Rounded
mxgx216 maxmag 1 -12345678901 -> -1.23456789E+10  Inexact Rounded
mxgx217 maxmag -1234567896  1 -> -1.23456790E+9   Inexact Rounded
mxgx218 maxmag 1 -1234567896  -> -1.23456790E+9   Inexact Rounded

precision: 15
mxgx221 maxmag 12345678000 1  -> 12345678000
mxgx222 maxmag 1 12345678000  -> 12345678000
mxgx223 maxmag 1234567800  1  -> 1234567800
mxgx224 maxmag 1 1234567800   -> 1234567800
mxgx225 maxmag 1234567890  1  -> 1234567890
mxgx226 maxmag 1 1234567890   -> 1234567890
mxgx227 maxmag 1234567891  1  -> 1234567891
mxgx228 maxmag 1 1234567891   -> 1234567891
mxgx229 maxmag 12345678901 1  -> 12345678901
mxgx230 maxmag 1 12345678901  -> 12345678901
mxgx231 maxmag 1234567896  1  -> 1234567896
mxgx232 maxmag 1 1234567896   -> 1234567896
mxgx233 maxmag -1234567891  1 -> -1234567891
mxgx234 maxmag 1 -1234567891  -> -1234567891
mxgx235 maxmag -12345678901 1 -> -12345678901
mxgx236 maxmag 1 -12345678901 -> -12345678901
mxgx237 maxmag -1234567896  1 -> -1234567896
mxgx238 maxmag 1 -1234567896  -> -1234567896

-- from examples
mxgx280 maxmag '3'   '2'  ->  '3'
mxgx281 maxmag '-10' '3'  ->  '-10'
mxgx282 maxmag '1.0' '1'  ->  '1'
mxgx283 maxmag '1' '1.0'  ->  '1'
mxgx284 maxmag '7' 'NaN'  ->  '7'

-- overflow and underflow tests ...
maxExponent: 999999999
minexponent: -999999999
mxgx330 maxmag +1.23456789012345E-0 9E+999999999 ->  9E+999999999
mxgx331 maxmag 9E+999999999 +1.23456789012345E-0 ->  9E+999999999
mxgx332 maxmag +0.100 9E-999999999               ->  0.100
mxgx333 maxmag 9E-999999999 +0.100               ->  0.100
mxgx335 maxmag -1.23456789012345E-0 9E+999999999 ->  9E+999999999
mxgx336 maxmag 9E+999999999 -1.23456789012345E-0 ->  9E+999999999
mxgx337 maxmag -0.100 9E-999999999               ->  -0.100
mxgx338 maxmag 9E-999999999 -0.100               ->  -0.100

mxgx339 maxmag 1e-599999999 1e-400000001   ->  1E-400000001
mxgx340 maxmag 1e-599999999 1e-400000000   ->  1E-400000000
mxgx341 maxmag 1e-600000000 1e-400000000   ->  1E-400000000
mxgx342 maxmag 9e-999999998 0.01           ->  0.01
mxgx343 maxmag 9e-999999998 0.1            ->  0.1
mxgx344 maxmag 0.01 9e-999999998           ->  0.01
mxgx345 maxmag 1e599999999 1e400000001     ->  1E+599999999
mxgx346 maxmag 1e599999999 1e400000000     ->  1E+599999999
mxgx347 maxmag 1e600000000 1e400000000     ->  1E+600000000
mxgx348 maxmag 9e999999998 100             ->  9E+999999998
mxgx349 maxmag 9e999999998 10              ->  9E+999999998
mxgx350 maxmag 100  9e999999998            ->  9E+999999998
-- signs
mxgx351 maxmag  1e+777777777  1e+411111111 ->  1E+777777777
mxgx352 maxmag  1e+777777777 -1e+411111111 ->  1E+777777777
mxgx353 maxmag -1e+777777777  1e+411111111 -> -1E+777777777
mxgx354 maxmag -1e+777777777 -1e+411111111 -> -1E+777777777
mxgx355 maxmag  1e-777777777  1e-411111111 ->  1E-411111111
mxgx356 maxmag  1e-777777777 -1e-411111111 -> -1E-411111111
mxgx357 maxmag -1e-777777777  1e-411111111 ->  1E-411111111
mxgx358 maxmag -1e-777777777 -1e-411111111 -> -1E-411111111

-- expanded list from min/max 754r purple prose
-- [explicit tests for exponent ordering]
mxgx401 maxmag  Inf    1.1     ->  Infinity
mxgx402 maxmag  1.1    1       ->  1.1
mxgx403 maxmag  1      1.0     ->  1
mxgx404 maxmag  1.0    0.1     ->  1.0
mxgx405 maxmag  0.1    0.10    ->  0.1
mxgx406 maxmag  0.10   0.100   ->  0.10
mxgx407 maxmag  0.10   0       ->  0.10
mxgx408 maxmag  0      0.0     ->  0
mxgx409 maxmag  0.0   -0       ->  0.0
mxgx410 maxmag  0.0   -0.0     ->  0.0
mxgx411 maxmag  0.00  -0.0     ->  0.00
mxgx412 maxmag  0.0   -0.00    ->  0.0
mxgx413 maxmag  0     -0.0     ->  0
mxgx414 maxmag  0     -0       ->  0
mxgx415 maxmag -0.0   -0       -> -0.0
mxgx416 maxmag -0     -0.100   -> -0.100
mxgx417 maxmag -0.100 -0.10    -> -0.100
mxgx418 maxmag -0.10  -0.1     -> -0.10
mxgx419 maxmag -0.1   -1.0     -> -1.0
mxgx420 maxmag -1.0   -1       -> -1.0
mxgx421 maxmag -1     -1.1     -> -1.1
mxgx423 maxmag -1.1   -Inf     -> -Infinity
-- same with operands reversed
mxgx431 maxmag  1.1    Inf     ->  Infinity
mxgx432 maxmag  1      1.1     ->  1.1
mxgx433 maxmag  1.0    1       ->  1
mxgx434 maxmag  0.1    1.0     ->  1.0
mxgx435 maxmag  0.10   0.1     ->  0.1
mxgx436 maxmag  0.100  0.10    ->  0.10
mxgx437 maxmag  0      0.10    ->  0.10
mxgx438 maxmag  0.0    0       ->  0
mxgx439 maxmag -0      0.0     ->  0.0
mxgx440 maxmag -0.0    0.0     ->  0.0
mxgx441 maxmag -0.0    0.00    ->  0.00
mxgx442 maxmag -0.00   0.0     ->  0.0
mxgx443 maxmag -0.0    0       ->  0
mxgx444 maxmag -0      0       ->  0
mxgx445 maxmag -0     -0.0     -> -0.0
mxgx446 maxmag -0.100 -0       -> -0.100
mxgx447 maxmag -0.10  -0.100   -> -0.100
mxgx448 maxmag -0.1   -0.10    -> -0.10
mxgx449 maxmag -1.0   -0.1     -> -1.0
mxgx450 maxmag -1     -1.0     -> -1.0
mxgx451 maxmag -1.1   -1       -> -1.1
mxgx453 maxmag -Inf   -1.1     -> -Infinity
-- largies
mxgx460 maxmag  1000   1E+3    ->  1E+3
mxgx461 maxmag  1E+3   1000    ->  1E+3
mxgx462 maxmag  1000  -1E+3    ->  1000
mxgx463 maxmag  1E+3  -1000    ->  1E+3
mxgx464 maxmag -1000   1E+3    ->  1E+3
mxgx465 maxmag -1E+3   1000    ->  1000
mxgx466 maxmag -1000  -1E+3    -> -1000
mxgx467 maxmag -1E+3  -1000    -> -1000

-- rounding (results treated as though plus)
maxexponent: 999999999
minexponent: -999999999
precision: 3

mxgx470 maxmag  1      .5     ->  1
mxgx471 maxmag  10     5      ->  10
mxgx472 maxmag  100    50     ->  100
mxgx473 maxmag  1000   500    ->  1.00E+3 Rounded
mxgx474 maxmag  10000  5000   ->  1.00E+4 Rounded
mxgx475 maxmag  6      .5     ->  6
mxgx476 maxmag  66     5      ->  66
mxgx477 maxmag  666    50     ->  666
mxgx478 maxmag  6666   500    ->  6.67E+3 Rounded Inexact
mxgx479 maxmag  66666  5000   ->  6.67E+4 Rounded Inexact
mxgx480 maxmag  33333  5000   ->  3.33E+4 Rounded Inexact
mxgx481 maxmag  .5     1      ->  1
mxgx482 maxmag  .5     10     ->  10
mxgx483 maxmag  .5     100    ->  100
mxgx484 maxmag  .5     1000   ->  1.00E+3 Rounded
mxgx485 maxmag  .5     10000  ->  1.00E+4 Rounded
mxgx486 maxmag  .5     6      ->  6
mxgx487 maxmag  .5     66     ->  66
mxgx488 maxmag  .5     666    ->  666
mxgx489 maxmag  .5     6666   ->  6.67E+3 Rounded Inexact
mxgx490 maxmag  .5     66666  ->  6.67E+4 Rounded Inexact
mxgx491 maxmag  .5     33333  ->  3.33E+4 Rounded Inexact

-- overflow tests
maxexponent: 999999999
minexponent: -999999999
precision: 3
mxgx500 maxmag 9.999E+999999999  0 ->  Infinity Inexact Overflow Rounded
mxgx501 maxmag -9.999E+999999999 0 -> -Infinity Inexact Overflow Rounded

-- subnormals and underflow
precision: 3
maxexponent: 999
minexponent: -999
mxgx510 maxmag  1.00E-999       0  ->   1.00E-999
mxgx511 maxmag  0.1E-999        0  ->   1E-1000   Subnormal
mxgx512 maxmag  0.10E-999       0  ->   1.0E-1000 Subnormal
mxgx513 maxmag  0.100E-999      0  ->   1.0E-1000 Subnormal Rounded
mxgx514 maxmag  0.01E-999       0  ->   1E-1001   Subnormal
-- next is rounded to Nmin
mxgx515 maxmag  0.999E-999      0  ->   1.00E-999 Inexact Rounded Subnormal Underflow
mxgx516 maxmag  0.099E-999      0  ->   1.0E-1000 Inexact Rounded Subnormal Underflow
mxgx517 maxmag  0.009E-999      0  ->   1E-1001   Inexact Rounded Subnormal Underflow
mxgx518 maxmag  0.001E-999      0  ->   0E-1001   Inexact Rounded Subnormal Underflow Clamped
mxgx519 maxmag  0.0009E-999     0  ->   0E-1001   Inexact Rounded Subnormal Underflow Clamped
mxgx520 maxmag  0.0001E-999     0  ->   0E-1001   Inexact Rounded Subnormal Underflow Clamped

mxgx530 maxmag -1.00E-999       0  ->  -1.00E-999
mxgx531 maxmag -0.1E-999        0  ->  -1E-1000   Subnormal
mxgx532 maxmag -0.10E-999       0  ->  -1.0E-1000 Subnormal
mxgx533 maxmag -0.100E-999      0  ->  -1.0E-1000 Subnormal Rounded
mxgx534 maxmag -0.01E-999       0  ->  -1E-1001   Subnormal
-- next is rounded to -Nmin
mxgx535 maxmag -0.999E-999      0  ->  -1.00E-999 Inexact Rounded Subnormal Underflow
mxgx536 maxmag -0.099E-999      0  ->  -1.0E-1000 Inexact Rounded Subnormal Underflow
mxgx537 maxmag -0.009E-999      0  ->  -1E-1001   Inexact Rounded Subnormal Underflow
mxgx538 maxmag -0.001E-999      0  ->  -0E-1001   Inexact Rounded Subnormal Underflow Clamped
mxgx539 maxmag -0.0009E-999     0  ->  -0E-1001   Inexact Rounded Subnormal Underflow Clamped
mxgx540 maxmag -0.0001E-999     0  ->  -0E-1001   Inexact Rounded Subnormal Underflow Clamped

-- Null tests
mxgx900 maxmag 10  #  -> NaN Invalid_operation
mxgx901 maxmag  # 10  -> NaN Invalid_operation