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✏️ ddAdd.decTest
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------------------------------------------------------------------------ -- ddAdd.decTest -- decDouble addition -- -- 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 -- This set of tests are for decDoubles only; all arguments are -- representable in a decDouble precision: 16 maxExponent: 384 minExponent: -383 extended: 1 clamp: 1 rounding: half_even -- [first group are 'quick confidence check'] ddadd001 add 1 1 -> 2 ddadd002 add 2 3 -> 5 ddadd003 add '5.75' '3.3' -> 9.05 ddadd004 add '5' '-3' -> 2 ddadd005 add '-5' '-3' -> -8 ddadd006 add '-7' '2.5' -> -4.5 ddadd007 add '0.7' '0.3' -> 1.0 ddadd008 add '1.25' '1.25' -> 2.50 ddadd009 add '1.23456789' '1.00000000' -> '2.23456789' ddadd010 add '1.23456789' '1.00000011' -> '2.23456800' -- 1234567890123456 1234567890123456 ddadd011 add '0.4444444444444446' '0.5555555555555555' -> '1.000000000000000' Inexact Rounded ddadd012 add '0.4444444444444445' '0.5555555555555555' -> '1.000000000000000' Rounded ddadd013 add '0.4444444444444444' '0.5555555555555555' -> '0.9999999999999999' ddadd014 add '4444444444444444' '0.49' -> '4444444444444444' Inexact Rounded ddadd015 add '4444444444444444' '0.499' -> '4444444444444444' Inexact Rounded ddadd016 add '4444444444444444' '0.4999' -> '4444444444444444' Inexact Rounded ddadd017 add '4444444444444444' '0.5000' -> '4444444444444444' Inexact Rounded ddadd018 add '4444444444444444' '0.5001' -> '4444444444444445' Inexact Rounded ddadd019 add '4444444444444444' '0.501' -> '4444444444444445' Inexact Rounded ddadd020 add '4444444444444444' '0.51' -> '4444444444444445' Inexact Rounded ddadd021 add 0 1 -> 1 ddadd022 add 1 1 -> 2 ddadd023 add 2 1 -> 3 ddadd024 add 3 1 -> 4 ddadd025 add 4 1 -> 5 ddadd026 add 5 1 -> 6 ddadd027 add 6 1 -> 7 ddadd028 add 7 1 -> 8 ddadd029 add 8 1 -> 9 ddadd030 add 9 1 -> 10 -- some carrying effects ddadd031 add '0.9998' '0.0000' -> '0.9998' ddadd032 add '0.9998' '0.0001' -> '0.9999' ddadd033 add '0.9998' '0.0002' -> '1.0000' ddadd034 add '0.9998' '0.0003' -> '1.0001' ddadd035 add '70' '10000e+16' -> '1.000000000000000E+20' Inexact Rounded ddadd036 add '700' '10000e+16' -> '1.000000000000000E+20' Inexact Rounded ddadd037 add '7000' '10000e+16' -> '1.000000000000000E+20' Inexact Rounded ddadd038 add '70000' '10000e+16' -> '1.000000000000001E+20' Inexact Rounded ddadd039 add '700000' '10000e+16' -> '1.000000000000007E+20' Rounded -- symmetry: ddadd040 add '10000e+16' '70' -> '1.000000000000000E+20' Inexact Rounded ddadd041 add '10000e+16' '700' -> '1.000000000000000E+20' Inexact Rounded ddadd042 add '10000e+16' '7000' -> '1.000000000000000E+20' Inexact Rounded ddadd044 add '10000e+16' '70000' -> '1.000000000000001E+20' Inexact Rounded ddadd045 add '10000e+16' '700000' -> '1.000000000000007E+20' Rounded -- same, without rounding ddadd046 add '10000e+9' '7' -> '10000000000007' ddadd047 add '10000e+9' '70' -> '10000000000070' ddadd048 add '10000e+9' '700' -> '10000000000700' ddadd049 add '10000e+9' '7000' -> '10000000007000' ddadd050 add '10000e+9' '70000' -> '10000000070000' ddadd051 add '10000e+9' '700000' -> '10000000700000' ddadd052 add '10000e+9' '7000000' -> '10000007000000' -- examples from decarith ddadd053 add '12' '7.00' -> '19.00' ddadd054 add '1.3' '-1.07' -> '0.23' ddadd055 add '1.3' '-1.30' -> '0.00' ddadd056 add '1.3' '-2.07' -> '-0.77' ddadd057 add '1E+2' '1E+4' -> '1.01E+4' -- leading zero preservation ddadd061 add 1 '0.0001' -> '1.0001' ddadd062 add 1 '0.00001' -> '1.00001' ddadd063 add 1 '0.000001' -> '1.000001' ddadd064 add 1 '0.0000001' -> '1.0000001' ddadd065 add 1 '0.00000001' -> '1.00000001' -- some funny zeros [in case of bad signum] ddadd070 add 1 0 -> 1 ddadd071 add 1 0. -> 1 ddadd072 add 1 .0 -> 1.0 ddadd073 add 1 0.0 -> 1.0 ddadd074 add 1 0.00 -> 1.00 ddadd075 add 0 1 -> 1 ddadd076 add 0. 1 -> 1 ddadd077 add .0 1 -> 1.0 ddadd078 add 0.0 1 -> 1.0 ddadd079 add 0.00 1 -> 1.00 -- some carries ddadd080 add 999999998 1 -> 999999999 ddadd081 add 999999999 1 -> 1000000000 ddadd082 add 99999999 1 -> 100000000 ddadd083 add 9999999 1 -> 10000000 ddadd084 add 999999 1 -> 1000000 ddadd085 add 99999 1 -> 100000 ddadd086 add 9999 1 -> 10000 ddadd087 add 999 1 -> 1000 ddadd088 add 99 1 -> 100 ddadd089 add 9 1 -> 10 -- more LHS swaps ddadd090 add '-56267E-10' 0 -> '-0.0000056267' ddadd091 add '-56267E-6' 0 -> '-0.056267' ddadd092 add '-56267E-5' 0 -> '-0.56267' ddadd093 add '-56267E-4' 0 -> '-5.6267' ddadd094 add '-56267E-3' 0 -> '-56.267' ddadd095 add '-56267E-2' 0 -> '-562.67' ddadd096 add '-56267E-1' 0 -> '-5626.7' ddadd097 add '-56267E-0' 0 -> '-56267' ddadd098 add '-5E-10' 0 -> '-5E-10' ddadd099 add '-5E-7' 0 -> '-5E-7' ddadd100 add '-5E-6' 0 -> '-0.000005' ddadd101 add '-5E-5' 0 -> '-0.00005' ddadd102 add '-5E-4' 0 -> '-0.0005' ddadd103 add '-5E-1' 0 -> '-0.5' ddadd104 add '-5E0' 0 -> '-5' ddadd105 add '-5E1' 0 -> '-50' ddadd106 add '-5E5' 0 -> '-500000' ddadd107 add '-5E15' 0 -> '-5000000000000000' ddadd108 add '-5E16' 0 -> '-5.000000000000000E+16' Rounded ddadd109 add '-5E17' 0 -> '-5.000000000000000E+17' Rounded ddadd110 add '-5E18' 0 -> '-5.000000000000000E+18' Rounded ddadd111 add '-5E100' 0 -> '-5.000000000000000E+100' Rounded -- more RHS swaps ddadd113 add 0 '-56267E-10' -> '-0.0000056267' ddadd114 add 0 '-56267E-6' -> '-0.056267' ddadd116 add 0 '-56267E-5' -> '-0.56267' ddadd117 add 0 '-56267E-4' -> '-5.6267' ddadd119 add 0 '-56267E-3' -> '-56.267' ddadd120 add 0 '-56267E-2' -> '-562.67' ddadd121 add 0 '-56267E-1' -> '-5626.7' ddadd122 add 0 '-56267E-0' -> '-56267' ddadd123 add 0 '-5E-10' -> '-5E-10' ddadd124 add 0 '-5E-7' -> '-5E-7' ddadd125 add 0 '-5E-6' -> '-0.000005' ddadd126 add 0 '-5E-5' -> '-0.00005' ddadd127 add 0 '-5E-4' -> '-0.0005' ddadd128 add 0 '-5E-1' -> '-0.5' ddadd129 add 0 '-5E0' -> '-5' ddadd130 add 0 '-5E1' -> '-50' ddadd131 add 0 '-5E5' -> '-500000' ddadd132 add 0 '-5E15' -> '-5000000000000000' ddadd133 add 0 '-5E16' -> '-5.000000000000000E+16' Rounded ddadd134 add 0 '-5E17' -> '-5.000000000000000E+17' Rounded ddadd135 add 0 '-5E18' -> '-5.000000000000000E+18' Rounded ddadd136 add 0 '-5E100' -> '-5.000000000000000E+100' Rounded -- related ddadd137 add 1 '0E-19' -> '1.000000000000000' Rounded ddadd138 add -1 '0E-19' -> '-1.000000000000000' Rounded ddadd139 add '0E-19' 1 -> '1.000000000000000' Rounded ddadd140 add '0E-19' -1 -> '-1.000000000000000' Rounded ddadd141 add 1E+11 0.0000 -> '100000000000.0000' ddadd142 add 1E+11 0.00000 -> '100000000000.0000' Rounded ddadd143 add 0.000 1E+12 -> '1000000000000.000' ddadd144 add 0.0000 1E+12 -> '1000000000000.000' Rounded -- [some of the next group are really constructor tests] ddadd146 add '00.0' 0 -> '0.0' ddadd147 add '0.00' 0 -> '0.00' ddadd148 add 0 '0.00' -> '0.00' ddadd149 add 0 '00.0' -> '0.0' ddadd150 add '00.0' '0.00' -> '0.00' ddadd151 add '0.00' '00.0' -> '0.00' ddadd152 add '3' '.3' -> '3.3' ddadd153 add '3.' '.3' -> '3.3' ddadd154 add '3.0' '.3' -> '3.3' ddadd155 add '3.00' '.3' -> '3.30' ddadd156 add '3' '3' -> '6' ddadd157 add '3' '+3' -> '6' ddadd158 add '3' '-3' -> '0' ddadd159 add '0.3' '-0.3' -> '0.0' ddadd160 add '0.03' '-0.03' -> '0.00' -- try borderline precision, with carries, etc. ddadd161 add '1E+12' '-1' -> '999999999999' ddadd162 add '1E+12' '1.11' -> '1000000000001.11' ddadd163 add '1.11' '1E+12' -> '1000000000001.11' ddadd164 add '-1' '1E+12' -> '999999999999' ddadd165 add '7E+12' '-1' -> '6999999999999' ddadd166 add '7E+12' '1.11' -> '7000000000001.11' ddadd167 add '1.11' '7E+12' -> '7000000000001.11' ddadd168 add '-1' '7E+12' -> '6999999999999' rounding: half_up -- 1.234567890123456 1234567890123456 1 234567890123456 ddadd170 add '4.444444444444444' '0.5555555555555567' -> '5.000000000000001' Inexact Rounded ddadd171 add '4.444444444444444' '0.5555555555555566' -> '5.000000000000001' Inexact Rounded ddadd172 add '4.444444444444444' '0.5555555555555565' -> '5.000000000000001' Inexact Rounded ddadd173 add '4.444444444444444' '0.5555555555555564' -> '5.000000000000000' Inexact Rounded ddadd174 add '4.444444444444444' '0.5555555555555553' -> '4.999999999999999' Inexact Rounded ddadd175 add '4.444444444444444' '0.5555555555555552' -> '4.999999999999999' Inexact Rounded ddadd176 add '4.444444444444444' '0.5555555555555551' -> '4.999999999999999' Inexact Rounded ddadd177 add '4.444444444444444' '0.5555555555555550' -> '4.999999999999999' Rounded ddadd178 add '4.444444444444444' '0.5555555555555545' -> '4.999999999999999' Inexact Rounded ddadd179 add '4.444444444444444' '0.5555555555555544' -> '4.999999999999998' Inexact Rounded ddadd180 add '4.444444444444444' '0.5555555555555543' -> '4.999999999999998' Inexact Rounded ddadd181 add '4.444444444444444' '0.5555555555555542' -> '4.999999999999998' Inexact Rounded ddadd182 add '4.444444444444444' '0.5555555555555541' -> '4.999999999999998' Inexact Rounded ddadd183 add '4.444444444444444' '0.5555555555555540' -> '4.999999999999998' Rounded -- and some more, including residue effects and different roundings rounding: half_up ddadd200 add '1234560123456789' 0 -> '1234560123456789' ddadd201 add '1234560123456789' 0.000000001 -> '1234560123456789' Inexact Rounded ddadd202 add '1234560123456789' 0.000001 -> '1234560123456789' Inexact Rounded ddadd203 add '1234560123456789' 0.1 -> '1234560123456789' Inexact Rounded ddadd204 add '1234560123456789' 0.4 -> '1234560123456789' Inexact Rounded ddadd205 add '1234560123456789' 0.49 -> '1234560123456789' Inexact Rounded ddadd206 add '1234560123456789' 0.499999 -> '1234560123456789' Inexact Rounded ddadd207 add '1234560123456789' 0.499999999 -> '1234560123456789' Inexact Rounded ddadd208 add '1234560123456789' 0.5 -> '1234560123456790' Inexact Rounded ddadd209 add '1234560123456789' 0.500000001 -> '1234560123456790' Inexact Rounded ddadd210 add '1234560123456789' 0.500001 -> '1234560123456790' Inexact Rounded ddadd211 add '1234560123456789' 0.51 -> '1234560123456790' Inexact Rounded ddadd212 add '1234560123456789' 0.6 -> '1234560123456790' Inexact Rounded ddadd213 add '1234560123456789' 0.9 -> '1234560123456790' Inexact Rounded ddadd214 add '1234560123456789' 0.99999 -> '1234560123456790' Inexact Rounded ddadd215 add '1234560123456789' 0.999999999 -> '1234560123456790' Inexact Rounded ddadd216 add '1234560123456789' 1 -> '1234560123456790' ddadd217 add '1234560123456789' 1.000000001 -> '1234560123456790' Inexact Rounded ddadd218 add '1234560123456789' 1.00001 -> '1234560123456790' Inexact Rounded ddadd219 add '1234560123456789' 1.1 -> '1234560123456790' Inexact Rounded rounding: half_even ddadd220 add '1234560123456789' 0 -> '1234560123456789' ddadd221 add '1234560123456789' 0.000000001 -> '1234560123456789' Inexact Rounded ddadd222 add '1234560123456789' 0.000001 -> '1234560123456789' Inexact Rounded ddadd223 add '1234560123456789' 0.1 -> '1234560123456789' Inexact Rounded ddadd224 add '1234560123456789' 0.4 -> '1234560123456789' Inexact Rounded ddadd225 add '1234560123456789' 0.49 -> '1234560123456789' Inexact Rounded ddadd226 add '1234560123456789' 0.499999 -> '1234560123456789' Inexact Rounded ddadd227 add '1234560123456789' 0.499999999 -> '1234560123456789' Inexact Rounded ddadd228 add '1234560123456789' 0.5 -> '1234560123456790' Inexact Rounded ddadd229 add '1234560123456789' 0.500000001 -> '1234560123456790' Inexact Rounded ddadd230 add '1234560123456789' 0.500001 -> '1234560123456790' Inexact Rounded ddadd231 add '1234560123456789' 0.51 -> '1234560123456790' Inexact Rounded ddadd232 add '1234560123456789' 0.6 -> '1234560123456790' Inexact Rounded ddadd233 add '1234560123456789' 0.9 -> '1234560123456790' Inexact Rounded ddadd234 add '1234560123456789' 0.99999 -> '1234560123456790' Inexact Rounded ddadd235 add '1234560123456789' 0.999999999 -> '1234560123456790' Inexact Rounded ddadd236 add '1234560123456789' 1 -> '1234560123456790' ddadd237 add '1234560123456789' 1.00000001 -> '1234560123456790' Inexact Rounded ddadd238 add '1234560123456789' 1.00001 -> '1234560123456790' Inexact Rounded ddadd239 add '1234560123456789' 1.1 -> '1234560123456790' Inexact Rounded -- critical few with even bottom digit... ddadd240 add '1234560123456788' 0.499999999 -> '1234560123456788' Inexact Rounded ddadd241 add '1234560123456788' 0.5 -> '1234560123456788' Inexact Rounded ddadd242 add '1234560123456788' 0.500000001 -> '1234560123456789' Inexact Rounded rounding: down ddadd250 add '1234560123456789' 0 -> '1234560123456789' ddadd251 add '1234560123456789' 0.000000001 -> '1234560123456789' Inexact Rounded ddadd252 add '1234560123456789' 0.000001 -> '1234560123456789' Inexact Rounded ddadd253 add '1234560123456789' 0.1 -> '1234560123456789' Inexact Rounded ddadd254 add '1234560123456789' 0.4 -> '1234560123456789' Inexact Rounded ddadd255 add '1234560123456789' 0.49 -> '1234560123456789' Inexact Rounded ddadd256 add '1234560123456789' 0.499999 -> '1234560123456789' Inexact Rounded ddadd257 add '1234560123456789' 0.499999999 -> '1234560123456789' Inexact Rounded ddadd258 add '1234560123456789' 0.5 -> '1234560123456789' Inexact Rounded ddadd259 add '1234560123456789' 0.500000001 -> '1234560123456789' Inexact Rounded ddadd260 add '1234560123456789' 0.500001 -> '1234560123456789' Inexact Rounded ddadd261 add '1234560123456789' 0.51 -> '1234560123456789' Inexact Rounded ddadd262 add '1234560123456789' 0.6 -> '1234560123456789' Inexact Rounded ddadd263 add '1234560123456789' 0.9 -> '1234560123456789' Inexact Rounded ddadd264 add '1234560123456789' 0.99999 -> '1234560123456789' Inexact Rounded ddadd265 add '1234560123456789' 0.999999999 -> '1234560123456789' Inexact Rounded ddadd266 add '1234560123456789' 1 -> '1234560123456790' ddadd267 add '1234560123456789' 1.00000001 -> '1234560123456790' Inexact Rounded ddadd268 add '1234560123456789' 1.00001 -> '1234560123456790' Inexact Rounded ddadd269 add '1234560123456789' 1.1 -> '1234560123456790' Inexact Rounded -- 1 in last place tests rounding: half_up ddadd301 add -1 1 -> 0 ddadd302 add 0 1 -> 1 ddadd303 add 1 1 -> 2 ddadd304 add 12 1 -> 13 ddadd305 add 98 1 -> 99 ddadd306 add 99 1 -> 100 ddadd307 add 100 1 -> 101 ddadd308 add 101 1 -> 102 ddadd309 add -1 -1 -> -2 ddadd310 add 0 -1 -> -1 ddadd311 add 1 -1 -> 0 ddadd312 add 12 -1 -> 11 ddadd313 add 98 -1 -> 97 ddadd314 add 99 -1 -> 98 ddadd315 add 100 -1 -> 99 ddadd316 add 101 -1 -> 100 ddadd321 add -0.01 0.01 -> 0.00 ddadd322 add 0.00 0.01 -> 0.01 ddadd323 add 0.01 0.01 -> 0.02 ddadd324 add 0.12 0.01 -> 0.13 ddadd325 add 0.98 0.01 -> 0.99 ddadd326 add 0.99 0.01 -> 1.00 ddadd327 add 1.00 0.01 -> 1.01 ddadd328 add 1.01 0.01 -> 1.02 ddadd329 add -0.01 -0.01 -> -0.02 ddadd330 add 0.00 -0.01 -> -0.01 ddadd331 add 0.01 -0.01 -> 0.00 ddadd332 add 0.12 -0.01 -> 0.11 ddadd333 add 0.98 -0.01 -> 0.97 ddadd334 add 0.99 -0.01 -> 0.98 ddadd335 add 1.00 -0.01 -> 0.99 ddadd336 add 1.01 -0.01 -> 1.00 -- some more cases where adding 0 affects the coefficient ddadd340 add 1E+3 0 -> 1000 ddadd341 add 1E+15 0 -> 1000000000000000 ddadd342 add 1E+16 0 -> 1.000000000000000E+16 Rounded ddadd343 add 1E+20 0 -> 1.000000000000000E+20 Rounded -- which simply follow from these cases ... ddadd344 add 1E+3 1 -> 1001 ddadd345 add 1E+15 1 -> 1000000000000001 ddadd346 add 1E+16 1 -> 1.000000000000000E+16 Inexact Rounded ddadd347 add 1E+20 1 -> 1.000000000000000E+20 Inexact Rounded ddadd348 add 1E+3 7 -> 1007 ddadd349 add 1E+15 7 -> 1000000000000007 ddadd350 add 1E+16 7 -> 1.000000000000001E+16 Inexact Rounded ddadd351 add 1E+20 7 -> 1.000000000000000E+20 Inexact Rounded -- tryzeros cases rounding: half_up ddadd360 add 0E+50 10000E+1 -> 1.0000E+5 ddadd361 add 0E-50 10000E+1 -> 100000.0000000000 Rounded ddadd362 add 10000E+1 0E-50 -> 100000.0000000000 Rounded ddadd363 add 10000E+1 10000E-50 -> 100000.0000000000 Rounded Inexact ddadd364 add 9.999999999999999E+384 -9.999999999999999E+384 -> 0E+369 -- a curiosity from JSR 13 testing rounding: half_down ddadd370 add 999999999999999 815 -> 1000000000000814 ddadd371 add 9999999999999999 815 -> 1.000000000000081E+16 Rounded Inexact rounding: half_up ddadd372 add 999999999999999 815 -> 1000000000000814 ddadd373 add 9999999999999999 815 -> 1.000000000000081E+16 Rounded Inexact rounding: half_even ddadd374 add 999999999999999 815 -> 1000000000000814 ddadd375 add 9999999999999999 815 -> 1.000000000000081E+16 Rounded Inexact -- operands folded ddadd380 add 1E+384 1E+384 -> 2.000000000000000E+384 Clamped ddadd381 add 1E+380 1E+380 -> 2.00000000000E+380 Clamped ddadd382 add 1E+376 1E+376 -> 2.0000000E+376 Clamped ddadd383 add 1E+372 1E+372 -> 2.000E+372 Clamped ddadd384 add 1E+370 1E+370 -> 2.0E+370 Clamped ddadd385 add 1E+369 1E+369 -> 2E+369 ddadd386 add 1E+368 1E+368 -> 2E+368 -- ulp replacement tests ddadd400 add 1 77e-14 -> 1.00000000000077 ddadd401 add 1 77e-15 -> 1.000000000000077 ddadd402 add 1 77e-16 -> 1.000000000000008 Inexact Rounded ddadd403 add 1 77e-17 -> 1.000000000000001 Inexact Rounded ddadd404 add 1 77e-18 -> 1.000000000000000 Inexact Rounded ddadd405 add 1 77e-19 -> 1.000000000000000 Inexact Rounded ddadd406 add 1 77e-299 -> 1.000000000000000 Inexact Rounded ddadd410 add 10 77e-14 -> 10.00000000000077 ddadd411 add 10 77e-15 -> 10.00000000000008 Inexact Rounded ddadd412 add 10 77e-16 -> 10.00000000000001 Inexact Rounded ddadd413 add 10 77e-17 -> 10.00000000000000 Inexact Rounded ddadd414 add 10 77e-18 -> 10.00000000000000 Inexact Rounded ddadd415 add 10 77e-19 -> 10.00000000000000 Inexact Rounded ddadd416 add 10 77e-299 -> 10.00000000000000 Inexact Rounded ddadd420 add 77e-14 1 -> 1.00000000000077 ddadd421 add 77e-15 1 -> 1.000000000000077 ddadd422 add 77e-16 1 -> 1.000000000000008 Inexact Rounded ddadd423 add 77e-17 1 -> 1.000000000000001 Inexact Rounded ddadd424 add 77e-18 1 -> 1.000000000000000 Inexact Rounded ddadd425 add 77e-19 1 -> 1.000000000000000 Inexact Rounded ddadd426 add 77e-299 1 -> 1.000000000000000 Inexact Rounded ddadd430 add 77e-14 10 -> 10.00000000000077 ddadd431 add 77e-15 10 -> 10.00000000000008 Inexact Rounded ddadd432 add 77e-16 10 -> 10.00000000000001 Inexact Rounded ddadd433 add 77e-17 10 -> 10.00000000000000 Inexact Rounded ddadd434 add 77e-18 10 -> 10.00000000000000 Inexact Rounded ddadd435 add 77e-19 10 -> 10.00000000000000 Inexact Rounded ddadd436 add 77e-299 10 -> 10.00000000000000 Inexact Rounded -- fastpath boundary (more in dqadd) -- 1234567890123456 ddadd539 add '4444444444444444' '3333333333333333' -> '7777777777777777' ddadd540 add '4444444444444444' '4444444444444444' -> '8888888888888888' ddadd541 add '4444444444444444' '5555555555555555' -> '9999999999999999' ddadd542 add '3333333333333333' '4444444444444444' -> '7777777777777777' ddadd543 add '4444444444444444' '4444444444444444' -> '8888888888888888' ddadd544 add '5555555555555555' '4444444444444444' -> '9999999999999999' ddadd545 add '3000004000000000' '3000000000000040' -> '6000004000000040' ddadd546 add '3000000400000000' '4000000000000400' -> '7000000400000400' ddadd547 add '3000000040000000' '5000000000004000' -> '8000000040004000' ddadd548 add '4000000004000000' '3000000000040000' -> '7000000004040000' ddadd549 add '4000000000400000' '4000000000400000' -> '8000000000800000' ddadd550 add '4000000000040000' '5000000004000000' -> '9000000004040000' ddadd551 add '5000000000004000' '3000000040000000' -> '8000000040004000' ddadd552 add '5000000000000400' '4000000400000000' -> '9000000400000400' ddadd553 add '5000000000000040' '5000004000000000' -> 1.000000400000004E+16 Rounded -- check propagation ddadd554 add '8999999999999999' '0000000000000001' -> 9000000000000000 ddadd555 add '0000000000000001' '8999999999999999' -> 9000000000000000 ddadd556 add '0999999999999999' '0000000000000001' -> 1000000000000000 ddadd557 add '0000000000000001' '0999999999999999' -> 1000000000000000 ddadd558 add '4444444444444444' '4555555555555556' -> 9000000000000000 ddadd559 add '4555555555555556' '4444444444444444' -> 9000000000000000 -- negative ulps ddadd6440 add 1 -77e-14 -> 0.99999999999923 ddadd6441 add 1 -77e-15 -> 0.999999999999923 ddadd6442 add 1 -77e-16 -> 0.9999999999999923 ddadd6443 add 1 -77e-17 -> 0.9999999999999992 Inexact Rounded ddadd6444 add 1 -77e-18 -> 0.9999999999999999 Inexact Rounded ddadd6445 add 1 -77e-19 -> 1.000000000000000 Inexact Rounded ddadd6446 add 1 -77e-99 -> 1.000000000000000 Inexact Rounded ddadd6450 add 10 -77e-14 -> 9.99999999999923 ddadd6451 add 10 -77e-15 -> 9.999999999999923 ddadd6452 add 10 -77e-16 -> 9.999999999999992 Inexact Rounded ddadd6453 add 10 -77e-17 -> 9.999999999999999 Inexact Rounded ddadd6454 add 10 -77e-18 -> 10.00000000000000 Inexact Rounded ddadd6455 add 10 -77e-19 -> 10.00000000000000 Inexact Rounded ddadd6456 add 10 -77e-99 -> 10.00000000000000 Inexact Rounded ddadd6460 add -77e-14 1 -> 0.99999999999923 ddadd6461 add -77e-15 1 -> 0.999999999999923 ddadd6462 add -77e-16 1 -> 0.9999999999999923 ddadd6463 add -77e-17 1 -> 0.9999999999999992 Inexact Rounded ddadd6464 add -77e-18 1 -> 0.9999999999999999 Inexact Rounded ddadd6465 add -77e-19 1 -> 1.000000000000000 Inexact Rounded ddadd6466 add -77e-99 1 -> 1.000000000000000 Inexact Rounded ddadd6470 add -77e-14 10 -> 9.99999999999923 ddadd6471 add -77e-15 10 -> 9.999999999999923 ddadd6472 add -77e-16 10 -> 9.999999999999992 Inexact Rounded ddadd6473 add -77e-17 10 -> 9.999999999999999 Inexact Rounded ddadd6474 add -77e-18 10 -> 10.00000000000000 Inexact Rounded ddadd6475 add -77e-19 10 -> 10.00000000000000 Inexact Rounded ddadd6476 add -77e-99 10 -> 10.00000000000000 Inexact Rounded -- negative ulps ddadd6480 add -1 77e-14 -> -0.99999999999923 ddadd6481 add -1 77e-15 -> -0.999999999999923 ddadd6482 add -1 77e-16 -> -0.9999999999999923 ddadd6483 add -1 77e-17 -> -0.9999999999999992 Inexact Rounded ddadd6484 add -1 77e-18 -> -0.9999999999999999 Inexact Rounded ddadd6485 add -1 77e-19 -> -1.000000000000000 Inexact Rounded ddadd6486 add -1 77e-99 -> -1.000000000000000 Inexact Rounded ddadd6490 add -10 77e-14 -> -9.99999999999923 ddadd6491 add -10 77e-15 -> -9.999999999999923 ddadd6492 add -10 77e-16 -> -9.999999999999992 Inexact Rounded ddadd6493 add -10 77e-17 -> -9.999999999999999 Inexact Rounded ddadd6494 add -10 77e-18 -> -10.00000000000000 Inexact Rounded ddadd6495 add -10 77e-19 -> -10.00000000000000 Inexact Rounded ddadd6496 add -10 77e-99 -> -10.00000000000000 Inexact Rounded ddadd6500 add 77e-14 -1 -> -0.99999999999923 ddadd6501 add 77e-15 -1 -> -0.999999999999923 ddadd6502 add 77e-16 -1 -> -0.9999999999999923 ddadd6503 add 77e-17 -1 -> -0.9999999999999992 Inexact Rounded ddadd6504 add 77e-18 -1 -> -0.9999999999999999 Inexact Rounded ddadd6505 add 77e-19 -1 -> -1.000000000000000 Inexact Rounded ddadd6506 add 77e-99 -1 -> -1.000000000000000 Inexact Rounded ddadd6510 add 77e-14 -10 -> -9.99999999999923 ddadd6511 add 77e-15 -10 -> -9.999999999999923 ddadd6512 add 77e-16 -10 -> -9.999999999999992 Inexact Rounded ddadd6513 add 77e-17 -10 -> -9.999999999999999 Inexact Rounded ddadd6514 add 77e-18 -10 -> -10.00000000000000 Inexact Rounded ddadd6515 add 77e-19 -10 -> -10.00000000000000 Inexact Rounded ddadd6516 add 77e-99 -10 -> -10.00000000000000 Inexact Rounded -- and some more residue effects and different roundings rounding: half_up ddadd6540 add '6543210123456789' 0 -> '6543210123456789' ddadd6541 add '6543210123456789' 0.000000001 -> '6543210123456789' Inexact Rounded ddadd6542 add '6543210123456789' 0.000001 -> '6543210123456789' Inexact Rounded ddadd6543 add '6543210123456789' 0.1 -> '6543210123456789' Inexact Rounded ddadd6544 add '6543210123456789' 0.4 -> '6543210123456789' Inexact Rounded ddadd6545 add '6543210123456789' 0.49 -> '6543210123456789' Inexact Rounded ddadd6546 add '6543210123456789' 0.499999 -> '6543210123456789' Inexact Rounded ddadd6547 add '6543210123456789' 0.499999999 -> '6543210123456789' Inexact Rounded ddadd6548 add '6543210123456789' 0.5 -> '6543210123456790' Inexact Rounded ddadd6549 add '6543210123456789' 0.500000001 -> '6543210123456790' Inexact Rounded ddadd6550 add '6543210123456789' 0.500001 -> '6543210123456790' Inexact Rounded ddadd6551 add '6543210123456789' 0.51 -> '6543210123456790' Inexact Rounded ddadd6552 add '6543210123456789' 0.6 -> '6543210123456790' Inexact Rounded ddadd6553 add '6543210123456789' 0.9 -> '6543210123456790' Inexact Rounded ddadd6554 add '6543210123456789' 0.99999 -> '6543210123456790' Inexact Rounded ddadd6555 add '6543210123456789' 0.999999999 -> '6543210123456790' Inexact Rounded ddadd6556 add '6543210123456789' 1 -> '6543210123456790' ddadd6557 add '6543210123456789' 1.000000001 -> '6543210123456790' Inexact Rounded ddadd6558 add '6543210123456789' 1.00001 -> '6543210123456790' Inexact Rounded ddadd6559 add '6543210123456789' 1.1 -> '6543210123456790' Inexact Rounded rounding: half_even ddadd6560 add '6543210123456789' 0 -> '6543210123456789' ddadd6561 add '6543210123456789' 0.000000001 -> '6543210123456789' Inexact Rounded ddadd6562 add '6543210123456789' 0.000001 -> '6543210123456789' Inexact Rounded ddadd6563 add '6543210123456789' 0.1 -> '6543210123456789' Inexact Rounded ddadd6564 add '6543210123456789' 0.4 -> '6543210123456789' Inexact Rounded ddadd6565 add '6543210123456789' 0.49 -> '6543210123456789' Inexact Rounded ddadd6566 add '6543210123456789' 0.499999 -> '6543210123456789' Inexact Rounded ddadd6567 add '6543210123456789' 0.499999999 -> '6543210123456789' Inexact Rounded ddadd6568 add '6543210123456789' 0.5 -> '6543210123456790' Inexact Rounded ddadd6569 add '6543210123456789' 0.500000001 -> '6543210123456790' Inexact Rounded ddadd6570 add '6543210123456789' 0.500001 -> '6543210123456790' Inexact Rounded ddadd6571 add '6543210123456789' 0.51 -> '6543210123456790' Inexact Rounded ddadd6572 add '6543210123456789' 0.6 -> '6543210123456790' Inexact Rounded ddadd6573 add '6543210123456789' 0.9 -> '6543210123456790' Inexact Rounded ddadd6574 add '6543210123456789' 0.99999 -> '6543210123456790' Inexact Rounded ddadd6575 add '6543210123456789' 0.999999999 -> '6543210123456790' Inexact Rounded ddadd6576 add '6543210123456789' 1 -> '6543210123456790' ddadd6577 add '6543210123456789' 1.00000001 -> '6543210123456790' Inexact Rounded ddadd6578 add '6543210123456789' 1.00001 -> '6543210123456790' Inexact Rounded ddadd6579 add '6543210123456789' 1.1 -> '6543210123456790' Inexact Rounded -- critical few with even bottom digit... ddadd7540 add '6543210123456788' 0.499999999 -> '6543210123456788' Inexact Rounded ddadd7541 add '6543210123456788' 0.5 -> '6543210123456788' Inexact Rounded ddadd7542 add '6543210123456788' 0.500000001 -> '6543210123456789' Inexact Rounded rounding: down ddadd7550 add '6543210123456789' 0 -> '6543210123456789' ddadd7551 add '6543210123456789' 0.000000001 -> '6543210123456789' Inexact Rounded ddadd7552 add '6543210123456789' 0.000001 -> '6543210123456789' Inexact Rounded ddadd7553 add '6543210123456789' 0.1 -> '6543210123456789' Inexact Rounded ddadd7554 add '6543210123456789' 0.4 -> '6543210123456789' Inexact Rounded ddadd7555 add '6543210123456789' 0.49 -> '6543210123456789' Inexact Rounded ddadd7556 add '6543210123456789' 0.499999 -> '6543210123456789' Inexact Rounded ddadd7557 add '6543210123456789' 0.499999999 -> '6543210123456789' Inexact Rounded ddadd7558 add '6543210123456789' 0.5 -> '6543210123456789' Inexact Rounded ddadd7559 add '6543210123456789' 0.500000001 -> '6543210123456789' Inexact Rounded ddadd7560 add '6543210123456789' 0.500001 -> '6543210123456789' Inexact Rounded ddadd7561 add '6543210123456789' 0.51 -> '6543210123456789' Inexact Rounded ddadd7562 add '6543210123456789' 0.6 -> '6543210123456789' Inexact Rounded ddadd7563 add '6543210123456789' 0.9 -> '6543210123456789' Inexact Rounded ddadd7564 add '6543210123456789' 0.99999 -> '6543210123456789' Inexact Rounded ddadd7565 add '6543210123456789' 0.999999999 -> '6543210123456789' Inexact Rounded ddadd7566 add '6543210123456789' 1 -> '6543210123456790' ddadd7567 add '6543210123456789' 1.00000001 -> '6543210123456790' Inexact Rounded ddadd7568 add '6543210123456789' 1.00001 -> '6543210123456790' Inexact Rounded ddadd7569 add '6543210123456789' 1.1 -> '6543210123456790' Inexact Rounded -- verify a query rounding: down ddadd7661 add 1e-398 9.000000000000000E+384 -> 9.000000000000000E+384 Inexact Rounded ddadd7662 add 0 9.000000000000000E+384 -> 9.000000000000000E+384 Rounded ddadd7663 add 1e-388 9.000000000000000E+374 -> 9.000000000000000E+374 Inexact Rounded ddadd7664 add 0 9.000000000000000E+374 -> 9.000000000000000E+374 Rounded -- more zeros, etc. rounding: half_even ddadd7701 add 5.00 1.00E-3 -> 5.00100 ddadd7702 add 00.00 0.000 -> 0.000 ddadd7703 add 00.00 0E-3 -> 0.000 ddadd7704 add 0E-3 00.00 -> 0.000 ddadd7710 add 0E+3 00.00 -> 0.00 ddadd7711 add 0E+3 00.0 -> 0.0 ddadd7712 add 0E+3 00. -> 0 ddadd7713 add 0E+3 00.E+1 -> 0E+1 ddadd7714 add 0E+3 00.E+2 -> 0E+2 ddadd7715 add 0E+3 00.E+3 -> 0E+3 ddadd7716 add 0E+3 00.E+4 -> 0E+3 ddadd7717 add 0E+3 00.E+5 -> 0E+3 ddadd7718 add 0E+3 -00.0 -> 0.0 ddadd7719 add 0E+3 -00. -> 0 ddadd7731 add 0E+3 -00.E+1 -> 0E+1 ddadd7720 add 00.00 0E+3 -> 0.00 ddadd7721 add 00.0 0E+3 -> 0.0 ddadd7722 add 00. 0E+3 -> 0 ddadd7723 add 00.E+1 0E+3 -> 0E+1 ddadd7724 add 00.E+2 0E+3 -> 0E+2 ddadd7725 add 00.E+3 0E+3 -> 0E+3 ddadd7726 add 00.E+4 0E+3 -> 0E+3 ddadd7727 add 00.E+5 0E+3 -> 0E+3 ddadd7728 add -00.00 0E+3 -> 0.00 ddadd7729 add -00.0 0E+3 -> 0.0 ddadd7730 add -00. 0E+3 -> 0 ddadd7732 add 0 0 -> 0 ddadd7733 add 0 -0 -> 0 ddadd7734 add -0 0 -> 0 ddadd7735 add -0 -0 -> -0 -- IEEE 854 special case ddadd7736 add 1 -1 -> 0 ddadd7737 add -1 -1 -> -2 ddadd7738 add 1 1 -> 2 ddadd7739 add -1 1 -> 0 ddadd7741 add 0 -1 -> -1 ddadd7742 add -0 -1 -> -1 ddadd7743 add 0 1 -> 1 ddadd7744 add -0 1 -> 1 ddadd7745 add -1 0 -> -1 ddadd7746 add -1 -0 -> -1 ddadd7747 add 1 0 -> 1 ddadd7748 add 1 -0 -> 1 ddadd7751 add 0.0 -1 -> -1.0 ddadd7752 add -0.0 -1 -> -1.0 ddadd7753 add 0.0 1 -> 1.0 ddadd7754 add -0.0 1 -> 1.0 ddadd7755 add -1.0 0 -> -1.0 ddadd7756 add -1.0 -0 -> -1.0 ddadd7757 add 1.0 0 -> 1.0 ddadd7758 add 1.0 -0 -> 1.0 ddadd7761 add 0 -1.0 -> -1.0 ddadd7762 add -0 -1.0 -> -1.0 ddadd7763 add 0 1.0 -> 1.0 ddadd7764 add -0 1.0 -> 1.0 ddadd7765 add -1 0.0 -> -1.0 ddadd7766 add -1 -0.0 -> -1.0 ddadd7767 add 1 0.0 -> 1.0 ddadd7768 add 1 -0.0 -> 1.0 ddadd7771 add 0.0 -1.0 -> -1.0 ddadd7772 add -0.0 -1.0 -> -1.0 ddadd7773 add 0.0 1.0 -> 1.0 ddadd7774 add -0.0 1.0 -> 1.0 ddadd7775 add -1.0 0.0 -> -1.0 ddadd7776 add -1.0 -0.0 -> -1.0 ddadd7777 add 1.0 0.0 -> 1.0 ddadd7778 add 1.0 -0.0 -> 1.0 -- Specials ddadd7780 add -Inf -Inf -> -Infinity ddadd7781 add -Inf -1000 -> -Infinity ddadd7782 add -Inf -1 -> -Infinity ddadd7783 add -Inf -0 -> -Infinity ddadd7784 add -Inf 0 -> -Infinity ddadd7785 add -Inf 1 -> -Infinity ddadd7786 add -Inf 1000 -> -Infinity ddadd7787 add -1000 -Inf -> -Infinity ddadd7788 add -Inf -Inf -> -Infinity ddadd7789 add -1 -Inf -> -Infinity ddadd7790 add -0 -Inf -> -Infinity ddadd7791 add 0 -Inf -> -Infinity ddadd7792 add 1 -Inf -> -Infinity ddadd7793 add 1000 -Inf -> -Infinity ddadd7794 add Inf -Inf -> NaN Invalid_operation ddadd7800 add Inf -Inf -> NaN Invalid_operation ddadd7801 add Inf -1000 -> Infinity ddadd7802 add Inf -1 -> Infinity ddadd7803 add Inf -0 -> Infinity ddadd7804 add Inf 0 -> Infinity ddadd7805 add Inf 1 -> Infinity ddadd7806 add Inf 1000 -> Infinity ddadd7807 add Inf Inf -> Infinity ddadd7808 add -1000 Inf -> Infinity ddadd7809 add -Inf Inf -> NaN Invalid_operation ddadd7810 add -1 Inf -> Infinity ddadd7811 add -0 Inf -> Infinity ddadd7812 add 0 Inf -> Infinity ddadd7813 add 1 Inf -> Infinity ddadd7814 add 1000 Inf -> Infinity ddadd7815 add Inf Inf -> Infinity ddadd7821 add NaN -Inf -> NaN ddadd7822 add NaN -1000 -> NaN ddadd7823 add NaN -1 -> NaN ddadd7824 add NaN -0 -> NaN ddadd7825 add NaN 0 -> NaN ddadd7826 add NaN 1 -> NaN ddadd7827 add NaN 1000 -> NaN ddadd7828 add NaN Inf -> NaN ddadd7829 add NaN NaN -> NaN ddadd7830 add -Inf NaN -> NaN ddadd7831 add -1000 NaN -> NaN ddadd7832 add -1 NaN -> NaN ddadd7833 add -0 NaN -> NaN ddadd7834 add 0 NaN -> NaN ddadd7835 add 1 NaN -> NaN ddadd7836 add 1000 NaN -> NaN ddadd7837 add Inf NaN -> NaN ddadd7841 add sNaN -Inf -> NaN Invalid_operation ddadd7842 add sNaN -1000 -> NaN Invalid_operation ddadd7843 add sNaN -1 -> NaN Invalid_operation ddadd7844 add sNaN -0 -> NaN Invalid_operation ddadd7845 add sNaN 0 -> NaN Invalid_operation ddadd7846 add sNaN 1 -> NaN Invalid_operation ddadd7847 add sNaN 1000 -> NaN Invalid_operation ddadd7848 add sNaN NaN -> NaN Invalid_operation ddadd7849 add sNaN sNaN -> NaN Invalid_operation ddadd7850 add NaN sNaN -> NaN Invalid_operation ddadd7851 add -Inf sNaN -> NaN Invalid_operation ddadd7852 add -1000 sNaN -> NaN Invalid_operation ddadd7853 add -1 sNaN -> NaN Invalid_operation ddadd7854 add -0 sNaN -> NaN Invalid_operation ddadd7855 add 0 sNaN -> NaN Invalid_operation ddadd7856 add 1 sNaN -> NaN Invalid_operation ddadd7857 add 1000 sNaN -> NaN Invalid_operation ddadd7858 add Inf sNaN -> NaN Invalid_operation ddadd7859 add NaN sNaN -> NaN Invalid_operation -- propagating NaNs ddadd7861 add NaN1 -Inf -> NaN1 ddadd7862 add +NaN2 -1000 -> NaN2 ddadd7863 add NaN3 1000 -> NaN3 ddadd7864 add NaN4 Inf -> NaN4 ddadd7865 add NaN5 +NaN6 -> NaN5 ddadd7866 add -Inf NaN7 -> NaN7 ddadd7867 add -1000 NaN8 -> NaN8 ddadd7868 add 1000 NaN9 -> NaN9 ddadd7869 add Inf +NaN10 -> NaN10 ddadd7871 add sNaN11 -Inf -> NaN11 Invalid_operation ddadd7872 add sNaN12 -1000 -> NaN12 Invalid_operation ddadd7873 add sNaN13 1000 -> NaN13 Invalid_operation ddadd7874 add sNaN14 NaN17 -> NaN14 Invalid_operation ddadd7875 add sNaN15 sNaN18 -> NaN15 Invalid_operation ddadd7876 add NaN16 sNaN19 -> NaN19 Invalid_operation ddadd7877 add -Inf +sNaN20 -> NaN20 Invalid_operation ddadd7878 add -1000 sNaN21 -> NaN21 Invalid_operation ddadd7879 add 1000 sNaN22 -> NaN22 Invalid_operation ddadd7880 add Inf sNaN23 -> NaN23 Invalid_operation ddadd7881 add +NaN25 +sNaN24 -> NaN24 Invalid_operation ddadd7882 add -NaN26 NaN28 -> -NaN26 ddadd7883 add -sNaN27 sNaN29 -> -NaN27 Invalid_operation ddadd7884 add 1000 -NaN30 -> -NaN30 ddadd7885 add 1000 -sNaN31 -> -NaN31 Invalid_operation -- Here we explore near the boundary of rounding a subnormal to Nmin ddadd7575 add 1E-383 -1E-398 -> 9.99999999999999E-384 Subnormal ddadd7576 add -1E-383 +1E-398 -> -9.99999999999999E-384 Subnormal -- and another curious case ddadd7577 add 7.000000000000E-385 -1.00000E-391 -> 6.999999000000E-385 Subnormal -- check overflow edge case -- 1234567890123456 ddadd7972 apply 9.999999999999999E+384 -> 9.999999999999999E+384 ddadd7973 add 9.999999999999999E+384 1 -> 9.999999999999999E+384 Inexact Rounded ddadd7974 add 9999999999999999E+369 1 -> 9.999999999999999E+384 Inexact Rounded ddadd7975 add 9999999999999999E+369 1E+369 -> Infinity Overflow Inexact Rounded ddadd7976 add 9999999999999999E+369 9E+368 -> Infinity Overflow Inexact Rounded ddadd7977 add 9999999999999999E+369 8E+368 -> Infinity Overflow Inexact Rounded ddadd7978 add 9999999999999999E+369 7E+368 -> Infinity Overflow Inexact Rounded ddadd7979 add 9999999999999999E+369 6E+368 -> Infinity Overflow Inexact Rounded ddadd7980 add 9999999999999999E+369 5E+368 -> Infinity Overflow Inexact Rounded ddadd7981 add 9999999999999999E+369 4E+368 -> 9.999999999999999E+384 Inexact Rounded ddadd7982 add 9999999999999999E+369 3E+368 -> 9.999999999999999E+384 Inexact Rounded ddadd7983 add 9999999999999999E+369 2E+368 -> 9.999999999999999E+384 Inexact Rounded ddadd7984 add 9999999999999999E+369 1E+368 -> 9.999999999999999E+384 Inexact Rounded ddadd7985 apply -9.999999999999999E+384 -> -9.999999999999999E+384 ddadd7986 add -9.999999999999999E+384 -1 -> -9.999999999999999E+384 Inexact Rounded ddadd7987 add -9999999999999999E+369 -1 -> -9.999999999999999E+384 Inexact Rounded ddadd7988 add -9999999999999999E+369 -1E+369 -> -Infinity Overflow Inexact Rounded ddadd7989 add -9999999999999999E+369 -9E+368 -> -Infinity Overflow Inexact Rounded ddadd7990 add -9999999999999999E+369 -8E+368 -> -Infinity Overflow Inexact Rounded ddadd7991 add -9999999999999999E+369 -7E+368 -> -Infinity Overflow Inexact Rounded ddadd7992 add -9999999999999999E+369 -6E+368 -> -Infinity Overflow Inexact Rounded ddadd7993 add -9999999999999999E+369 -5E+368 -> -Infinity Overflow Inexact Rounded ddadd7994 add -9999999999999999E+369 -4E+368 -> -9.999999999999999E+384 Inexact Rounded ddadd7995 add -9999999999999999E+369 -3E+368 -> -9.999999999999999E+384 Inexact Rounded ddadd7996 add -9999999999999999E+369 -2E+368 -> -9.999999999999999E+384 Inexact Rounded ddadd7997 add -9999999999999999E+369 -1E+368 -> -9.999999999999999E+384 Inexact Rounded -- And for round down full and subnormal results rounding: down ddadd71100 add 1e+2 -1e-383 -> 99.99999999999999 Rounded Inexact ddadd71101 add 1e+1 -1e-383 -> 9.999999999999999 Rounded Inexact ddadd71103 add +1 -1e-383 -> 0.9999999999999999 Rounded Inexact ddadd71104 add 1e-1 -1e-383 -> 0.09999999999999999 Rounded Inexact ddadd71105 add 1e-2 -1e-383 -> 0.009999999999999999 Rounded Inexact ddadd71106 add 1e-3 -1e-383 -> 0.0009999999999999999 Rounded Inexact ddadd71107 add 1e-4 -1e-383 -> 0.00009999999999999999 Rounded Inexact ddadd71108 add 1e-5 -1e-383 -> 0.000009999999999999999 Rounded Inexact ddadd71109 add 1e-6 -1e-383 -> 9.999999999999999E-7 Rounded Inexact rounding: ceiling ddadd71110 add -1e+2 +1e-383 -> -99.99999999999999 Rounded Inexact ddadd71111 add -1e+1 +1e-383 -> -9.999999999999999 Rounded Inexact ddadd71113 add -1 +1e-383 -> -0.9999999999999999 Rounded Inexact ddadd71114 add -1e-1 +1e-383 -> -0.09999999999999999 Rounded Inexact ddadd71115 add -1e-2 +1e-383 -> -0.009999999999999999 Rounded Inexact ddadd71116 add -1e-3 +1e-383 -> -0.0009999999999999999 Rounded Inexact ddadd71117 add -1e-4 +1e-383 -> -0.00009999999999999999 Rounded Inexact ddadd71118 add -1e-5 +1e-383 -> -0.000009999999999999999 Rounded Inexact ddadd71119 add -1e-6 +1e-383 -> -9.999999999999999E-7 Rounded Inexact -- tests based on Gunnar Degnbol's edge case rounding: half_even ddadd71300 add 1E16 -0.5 -> 1.000000000000000E+16 Inexact Rounded ddadd71310 add 1E16 -0.51 -> 9999999999999999 Inexact Rounded ddadd71311 add 1E16 -0.501 -> 9999999999999999 Inexact Rounded ddadd71312 add 1E16 -0.5001 -> 9999999999999999 Inexact Rounded ddadd71313 add 1E16 -0.50001 -> 9999999999999999 Inexact Rounded ddadd71314 add 1E16 -0.500001 -> 9999999999999999 Inexact Rounded ddadd71315 add 1E16 -0.5000001 -> 9999999999999999 Inexact Rounded ddadd71316 add 1E16 -0.50000001 -> 9999999999999999 Inexact Rounded ddadd71317 add 1E16 -0.500000001 -> 9999999999999999 Inexact Rounded ddadd71318 add 1E16 -0.5000000001 -> 9999999999999999 Inexact Rounded ddadd71319 add 1E16 -0.50000000001 -> 9999999999999999 Inexact Rounded ddadd71320 add 1E16 -0.500000000001 -> 9999999999999999 Inexact Rounded ddadd71321 add 1E16 -0.5000000000001 -> 9999999999999999 Inexact Rounded ddadd71322 add 1E16 -0.50000000000001 -> 9999999999999999 Inexact Rounded ddadd71323 add 1E16 -0.500000000000001 -> 9999999999999999 Inexact Rounded ddadd71324 add 1E16 -0.5000000000000001 -> 9999999999999999 Inexact Rounded ddadd71325 add 1E16 -0.5000000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71326 add 1E16 -0.500000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71327 add 1E16 -0.50000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71328 add 1E16 -0.5000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71329 add 1E16 -0.500000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71330 add 1E16 -0.50000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71331 add 1E16 -0.5000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71332 add 1E16 -0.500000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71333 add 1E16 -0.50000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71334 add 1E16 -0.5000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71335 add 1E16 -0.500000 -> 1.000000000000000E+16 Inexact Rounded ddadd71336 add 1E16 -0.50000 -> 1.000000000000000E+16 Inexact Rounded ddadd71337 add 1E16 -0.5000 -> 1.000000000000000E+16 Inexact Rounded ddadd71338 add 1E16 -0.500 -> 1.000000000000000E+16 Inexact Rounded ddadd71339 add 1E16 -0.50 -> 1.000000000000000E+16 Inexact Rounded ddadd71340 add 1E16 -5000000.000010001 -> 9999999995000000 Inexact Rounded ddadd71341 add 1E16 -5000000.000000001 -> 9999999995000000 Inexact Rounded ddadd71349 add 9999999999999999 0.4 -> 9999999999999999 Inexact Rounded ddadd71350 add 9999999999999999 0.49 -> 9999999999999999 Inexact Rounded ddadd71351 add 9999999999999999 0.499 -> 9999999999999999 Inexact Rounded ddadd71352 add 9999999999999999 0.4999 -> 9999999999999999 Inexact Rounded ddadd71353 add 9999999999999999 0.49999 -> 9999999999999999 Inexact Rounded ddadd71354 add 9999999999999999 0.499999 -> 9999999999999999 Inexact Rounded ddadd71355 add 9999999999999999 0.4999999 -> 9999999999999999 Inexact Rounded ddadd71356 add 9999999999999999 0.49999999 -> 9999999999999999 Inexact Rounded ddadd71357 add 9999999999999999 0.499999999 -> 9999999999999999 Inexact Rounded ddadd71358 add 9999999999999999 0.4999999999 -> 9999999999999999 Inexact Rounded ddadd71359 add 9999999999999999 0.49999999999 -> 9999999999999999 Inexact Rounded ddadd71360 add 9999999999999999 0.499999999999 -> 9999999999999999 Inexact Rounded ddadd71361 add 9999999999999999 0.4999999999999 -> 9999999999999999 Inexact Rounded ddadd71362 add 9999999999999999 0.49999999999999 -> 9999999999999999 Inexact Rounded ddadd71363 add 9999999999999999 0.499999999999999 -> 9999999999999999 Inexact Rounded ddadd71364 add 9999999999999999 0.4999999999999999 -> 9999999999999999 Inexact Rounded ddadd71365 add 9999999999999999 0.5000000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71367 add 9999999999999999 0.500000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71368 add 9999999999999999 0.50000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71369 add 9999999999999999 0.5000000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71370 add 9999999999999999 0.500000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71371 add 9999999999999999 0.50000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71372 add 9999999999999999 0.5000000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71373 add 9999999999999999 0.500000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71374 add 9999999999999999 0.50000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71375 add 9999999999999999 0.5000000 -> 1.000000000000000E+16 Inexact Rounded ddadd71376 add 9999999999999999 0.500000 -> 1.000000000000000E+16 Inexact Rounded ddadd71377 add 9999999999999999 0.50000 -> 1.000000000000000E+16 Inexact Rounded ddadd71378 add 9999999999999999 0.5000 -> 1.000000000000000E+16 Inexact Rounded ddadd71379 add 9999999999999999 0.500 -> 1.000000000000000E+16 Inexact Rounded ddadd71380 add 9999999999999999 0.50 -> 1.000000000000000E+16 Inexact Rounded ddadd71381 add 9999999999999999 0.5 -> 1.000000000000000E+16 Inexact Rounded ddadd71382 add 9999999999999999 0.5000000000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71383 add 9999999999999999 0.500000000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71384 add 9999999999999999 0.50000000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71385 add 9999999999999999 0.5000000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71386 add 9999999999999999 0.500000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71387 add 9999999999999999 0.50000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71388 add 9999999999999999 0.5000000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71389 add 9999999999999999 0.500000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71390 add 9999999999999999 0.50000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71391 add 9999999999999999 0.5000001 -> 1.000000000000000E+16 Inexact Rounded ddadd71392 add 9999999999999999 0.500001 -> 1.000000000000000E+16 Inexact Rounded ddadd71393 add 9999999999999999 0.50001 -> 1.000000000000000E+16 Inexact Rounded ddadd71394 add 9999999999999999 0.5001 -> 1.000000000000000E+16 Inexact Rounded ddadd71395 add 9999999999999999 0.501 -> 1.000000000000000E+16 Inexact Rounded ddadd71396 add 9999999999999999 0.51 -> 1.000000000000000E+16 Inexact Rounded -- More GD edge cases, where difference between the unadjusted -- exponents is larger than the maximum precision and one side is 0 ddadd71420 add 0 1.123456789012345 -> 1.123456789012345 ddadd71421 add 0 1.123456789012345E-1 -> 0.1123456789012345 ddadd71422 add 0 1.123456789012345E-2 -> 0.01123456789012345 ddadd71423 add 0 1.123456789012345E-3 -> 0.001123456789012345 ddadd71424 add 0 1.123456789012345E-4 -> 0.0001123456789012345 ddadd71425 add 0 1.123456789012345E-5 -> 0.00001123456789012345 ddadd71426 add 0 1.123456789012345E-6 -> 0.000001123456789012345 ddadd71427 add 0 1.123456789012345E-7 -> 1.123456789012345E-7 ddadd71428 add 0 1.123456789012345E-8 -> 1.123456789012345E-8 ddadd71429 add 0 1.123456789012345E-9 -> 1.123456789012345E-9 ddadd71430 add 0 1.123456789012345E-10 -> 1.123456789012345E-10 ddadd71431 add 0 1.123456789012345E-11 -> 1.123456789012345E-11 ddadd71432 add 0 1.123456789012345E-12 -> 1.123456789012345E-12 ddadd71433 add 0 1.123456789012345E-13 -> 1.123456789012345E-13 ddadd71434 add 0 1.123456789012345E-14 -> 1.123456789012345E-14 ddadd71435 add 0 1.123456789012345E-15 -> 1.123456789012345E-15 ddadd71436 add 0 1.123456789012345E-16 -> 1.123456789012345E-16 ddadd71437 add 0 1.123456789012345E-17 -> 1.123456789012345E-17 ddadd71438 add 0 1.123456789012345E-18 -> 1.123456789012345E-18 ddadd71439 add 0 1.123456789012345E-19 -> 1.123456789012345E-19 -- same, reversed 0 ddadd71440 add 1.123456789012345 0 -> 1.123456789012345 ddadd71441 add 1.123456789012345E-1 0 -> 0.1123456789012345 ddadd71442 add 1.123456789012345E-2 0 -> 0.01123456789012345 ddadd71443 add 1.123456789012345E-3 0 -> 0.001123456789012345 ddadd71444 add 1.123456789012345E-4 0 -> 0.0001123456789012345 ddadd71445 add 1.123456789012345E-5 0 -> 0.00001123456789012345 ddadd71446 add 1.123456789012345E-6 0 -> 0.000001123456789012345 ddadd71447 add 1.123456789012345E-7 0 -> 1.123456789012345E-7 ddadd71448 add 1.123456789012345E-8 0 -> 1.123456789012345E-8 ddadd71449 add 1.123456789012345E-9 0 -> 1.123456789012345E-9 ddadd71450 add 1.123456789012345E-10 0 -> 1.123456789012345E-10 ddadd71451 add 1.123456789012345E-11 0 -> 1.123456789012345E-11 ddadd71452 add 1.123456789012345E-12 0 -> 1.123456789012345E-12 ddadd71453 add 1.123456789012345E-13 0 -> 1.123456789012345E-13 ddadd71454 add 1.123456789012345E-14 0 -> 1.123456789012345E-14 ddadd71455 add 1.123456789012345E-15 0 -> 1.123456789012345E-15 ddadd71456 add 1.123456789012345E-16 0 -> 1.123456789012345E-16 ddadd71457 add 1.123456789012345E-17 0 -> 1.123456789012345E-17 ddadd71458 add 1.123456789012345E-18 0 -> 1.123456789012345E-18 ddadd71459 add 1.123456789012345E-19 0 -> 1.123456789012345E-19 -- same, Es on the 0 ddadd71460 add 1.123456789012345 0E-0 -> 1.123456789012345 ddadd71461 add 1.123456789012345 0E-1 -> 1.123456789012345 ddadd71462 add 1.123456789012345 0E-2 -> 1.123456789012345 ddadd71463 add 1.123456789012345 0E-3 -> 1.123456789012345 ddadd71464 add 1.123456789012345 0E-4 -> 1.123456789012345 ddadd71465 add 1.123456789012345 0E-5 -> 1.123456789012345 ddadd71466 add 1.123456789012345 0E-6 -> 1.123456789012345 ddadd71467 add 1.123456789012345 0E-7 -> 1.123456789012345 ddadd71468 add 1.123456789012345 0E-8 -> 1.123456789012345 ddadd71469 add 1.123456789012345 0E-9 -> 1.123456789012345 ddadd71470 add 1.123456789012345 0E-10 -> 1.123456789012345 ddadd71471 add 1.123456789012345 0E-11 -> 1.123456789012345 ddadd71472 add 1.123456789012345 0E-12 -> 1.123456789012345 ddadd71473 add 1.123456789012345 0E-13 -> 1.123456789012345 ddadd71474 add 1.123456789012345 0E-14 -> 1.123456789012345 ddadd71475 add 1.123456789012345 0E-15 -> 1.123456789012345 -- next four flag Rounded because the 0 extends the result ddadd71476 add 1.123456789012345 0E-16 -> 1.123456789012345 Rounded ddadd71477 add 1.123456789012345 0E-17 -> 1.123456789012345 Rounded ddadd71478 add 1.123456789012345 0E-18 -> 1.123456789012345 Rounded ddadd71479 add 1.123456789012345 0E-19 -> 1.123456789012345 Rounded -- sum of two opposite-sign operands is exactly 0 and floor => -0 rounding: half_up -- exact zeros from zeros ddadd71500 add 0 0E-19 -> 0E-19 ddadd71501 add -0 0E-19 -> 0E-19 ddadd71502 add 0 -0E-19 -> 0E-19 ddadd71503 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71511 add -11 11 -> 0 ddadd71512 add 11 -11 -> 0 rounding: half_down -- exact zeros from zeros ddadd71520 add 0 0E-19 -> 0E-19 ddadd71521 add -0 0E-19 -> 0E-19 ddadd71522 add 0 -0E-19 -> 0E-19 ddadd71523 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71531 add -11 11 -> 0 ddadd71532 add 11 -11 -> 0 rounding: half_even -- exact zeros from zeros ddadd71540 add 0 0E-19 -> 0E-19 ddadd71541 add -0 0E-19 -> 0E-19 ddadd71542 add 0 -0E-19 -> 0E-19 ddadd71543 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71551 add -11 11 -> 0 ddadd71552 add 11 -11 -> 0 rounding: up -- exact zeros from zeros ddadd71560 add 0 0E-19 -> 0E-19 ddadd71561 add -0 0E-19 -> 0E-19 ddadd71562 add 0 -0E-19 -> 0E-19 ddadd71563 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71571 add -11 11 -> 0 ddadd71572 add 11 -11 -> 0 rounding: down -- exact zeros from zeros ddadd71580 add 0 0E-19 -> 0E-19 ddadd71581 add -0 0E-19 -> 0E-19 ddadd71582 add 0 -0E-19 -> 0E-19 ddadd71583 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71591 add -11 11 -> 0 ddadd71592 add 11 -11 -> 0 rounding: ceiling -- exact zeros from zeros ddadd71600 add 0 0E-19 -> 0E-19 ddadd71601 add -0 0E-19 -> 0E-19 ddadd71602 add 0 -0E-19 -> 0E-19 ddadd71603 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71611 add -11 11 -> 0 ddadd71612 add 11 -11 -> 0 -- and the extra-special ugly case; unusual minuses marked by -- * rounding: floor -- exact zeros from zeros ddadd71620 add 0 0E-19 -> 0E-19 ddadd71621 add -0 0E-19 -> -0E-19 -- * ddadd71622 add 0 -0E-19 -> -0E-19 -- * ddadd71623 add -0 -0E-19 -> -0E-19 -- exact zeros from non-zeros ddadd71631 add -11 11 -> -0 -- * ddadd71632 add 11 -11 -> -0 -- * -- Examples from SQL proposal (Krishna Kulkarni) ddadd71701 add 130E-2 120E-2 -> 2.50 ddadd71702 add 130E-2 12E-1 -> 2.50 ddadd71703 add 130E-2 1E0 -> 2.30 ddadd71704 add 1E2 1E4 -> 1.01E+4 ddadd71705 add 130E-2 -120E-2 -> 0.10 ddadd71706 add 130E-2 -12E-1 -> 0.10 ddadd71707 add 130E-2 -1E0 -> 0.30 ddadd71708 add 1E2 -1E4 -> -9.9E+3 -- query from Vincent Kulandaisamy rounding: ceiling ddadd71801 add 7.8822773805862E+277 -5.1757503820663E-21 -> 7.882277380586200E+277 Inexact Rounded ddadd71802 add 7.882277380586200E+277 12.341 -> 7.882277380586201E+277 Inexact Rounded ddadd71803 add 7.882277380586201E+277 2.7270545046613E-31 -> 7.882277380586202E+277 Inexact Rounded ddadd71811 add 12.341 -5.1757503820663E-21 -> 12.34100000000000 Inexact Rounded ddadd71812 add 12.34100000000000 2.7270545046613E-31 -> 12.34100000000001 Inexact Rounded ddadd71813 add 12.34100000000001 7.8822773805862E+277 -> 7.882277380586201E+277 Inexact Rounded -- Gappy coefficients; check residue handling even with full coefficient gap rounding: half_even ddadd75001 add 1234567890123456 1 -> 1234567890123457 ddadd75002 add 1234567890123456 0.6 -> 1234567890123457 Inexact Rounded ddadd75003 add 1234567890123456 0.06 -> 1234567890123456 Inexact Rounded ddadd75004 add 1234567890123456 6E-3 -> 1234567890123456 Inexact Rounded ddadd75005 add 1234567890123456 6E-4 -> 1234567890123456 Inexact Rounded ddadd75006 add 1234567890123456 6E-5 -> 1234567890123456 Inexact Rounded ddadd75007 add 1234567890123456 6E-6 -> 1234567890123456 Inexact Rounded ddadd75008 add 1234567890123456 6E-7 -> 1234567890123456 Inexact Rounded ddadd75009 add 1234567890123456 6E-8 -> 1234567890123456 Inexact Rounded ddadd75010 add 1234567890123456 6E-9 -> 1234567890123456 Inexact Rounded ddadd75011 add 1234567890123456 6E-10 -> 1234567890123456 Inexact Rounded ddadd75012 add 1234567890123456 6E-11 -> 1234567890123456 Inexact Rounded ddadd75013 add 1234567890123456 6E-12 -> 1234567890123456 Inexact Rounded ddadd75014 add 1234567890123456 6E-13 -> 1234567890123456 Inexact Rounded ddadd75015 add 1234567890123456 6E-14 -> 1234567890123456 Inexact Rounded ddadd75016 add 1234567890123456 6E-15 -> 1234567890123456 Inexact Rounded ddadd75017 add 1234567890123456 6E-16 -> 1234567890123456 Inexact Rounded ddadd75018 add 1234567890123456 6E-17 -> 1234567890123456 Inexact Rounded ddadd75019 add 1234567890123456 6E-18 -> 1234567890123456 Inexact Rounded ddadd75020 add 1234567890123456 6E-19 -> 1234567890123456 Inexact Rounded ddadd75021 add 1234567890123456 6E-20 -> 1234567890123456 Inexact Rounded -- widening second argument at gap ddadd75030 add 12345678 1 -> 12345679 ddadd75031 add 12345678 0.1 -> 12345678.1 ddadd75032 add 12345678 0.12 -> 12345678.12 ddadd75033 add 12345678 0.123 -> 12345678.123 ddadd75034 add 12345678 0.1234 -> 12345678.1234 ddadd75035 add 12345678 0.12345 -> 12345678.12345 ddadd75036 add 12345678 0.123456 -> 12345678.123456 ddadd75037 add 12345678 0.1234567 -> 12345678.1234567 ddadd75038 add 12345678 0.12345678 -> 12345678.12345678 ddadd75039 add 12345678 0.123456789 -> 12345678.12345679 Inexact Rounded ddadd75040 add 12345678 0.123456785 -> 12345678.12345678 Inexact Rounded ddadd75041 add 12345678 0.1234567850 -> 12345678.12345678 Inexact Rounded ddadd75042 add 12345678 0.1234567851 -> 12345678.12345679 Inexact Rounded ddadd75043 add 12345678 0.12345678501 -> 12345678.12345679 Inexact Rounded ddadd75044 add 12345678 0.123456785001 -> 12345678.12345679 Inexact Rounded ddadd75045 add 12345678 0.1234567850001 -> 12345678.12345679 Inexact Rounded ddadd75046 add 12345678 0.12345678500001 -> 12345678.12345679 Inexact Rounded ddadd75047 add 12345678 0.123456785000001 -> 12345678.12345679 Inexact Rounded ddadd75048 add 12345678 0.1234567850000001 -> 12345678.12345679 Inexact Rounded ddadd75049 add 12345678 0.1234567850000000 -> 12345678.12345678 Inexact Rounded -- 90123456 rounding: half_even ddadd75050 add 12345678 0.0234567750000000 -> 12345678.02345678 Inexact Rounded ddadd75051 add 12345678 0.0034567750000000 -> 12345678.00345678 Inexact Rounded ddadd75052 add 12345678 0.0004567750000000 -> 12345678.00045678 Inexact Rounded ddadd75053 add 12345678 0.0000567750000000 -> 12345678.00005678 Inexact Rounded ddadd75054 add 12345678 0.0000067750000000 -> 12345678.00000678 Inexact Rounded ddadd75055 add 12345678 0.0000007750000000 -> 12345678.00000078 Inexact Rounded ddadd75056 add 12345678 0.0000000750000000 -> 12345678.00000008 Inexact Rounded ddadd75057 add 12345678 0.0000000050000000 -> 12345678.00000000 Inexact Rounded ddadd75060 add 12345678 0.0234567750000001 -> 12345678.02345678 Inexact Rounded ddadd75061 add 12345678 0.0034567750000001 -> 12345678.00345678 Inexact Rounded ddadd75062 add 12345678 0.0004567750000001 -> 12345678.00045678 Inexact Rounded ddadd75063 add 12345678 0.0000567750000001 -> 12345678.00005678 Inexact Rounded ddadd75064 add 12345678 0.0000067750000001 -> 12345678.00000678 Inexact Rounded ddadd75065 add 12345678 0.0000007750000001 -> 12345678.00000078 Inexact Rounded ddadd75066 add 12345678 0.0000000750000001 -> 12345678.00000008 Inexact Rounded ddadd75067 add 12345678 0.0000000050000001 -> 12345678.00000001 Inexact Rounded -- far-out residues (full coefficient gap is 16+15 digits) rounding: up ddadd75070 add 12345678 1E-8 -> 12345678.00000001 ddadd75071 add 12345678 1E-9 -> 12345678.00000001 Inexact Rounded ddadd75072 add 12345678 1E-10 -> 12345678.00000001 Inexact Rounded ddadd75073 add 12345678 1E-11 -> 12345678.00000001 Inexact Rounded ddadd75074 add 12345678 1E-12 -> 12345678.00000001 Inexact Rounded ddadd75075 add 12345678 1E-13 -> 12345678.00000001 Inexact Rounded ddadd75076 add 12345678 1E-14 -> 12345678.00000001 Inexact Rounded ddadd75077 add 12345678 1E-15 -> 12345678.00000001 Inexact Rounded ddadd75078 add 12345678 1E-16 -> 12345678.00000001 Inexact Rounded ddadd75079 add 12345678 1E-17 -> 12345678.00000001 Inexact Rounded ddadd75080 add 12345678 1E-18 -> 12345678.00000001 Inexact Rounded ddadd75081 add 12345678 1E-19 -> 12345678.00000001 Inexact Rounded ddadd75082 add 12345678 1E-20 -> 12345678.00000001 Inexact Rounded ddadd75083 add 12345678 1E-25 -> 12345678.00000001 Inexact Rounded ddadd75084 add 12345678 1E-30 -> 12345678.00000001 Inexact Rounded ddadd75085 add 12345678 1E-31 -> 12345678.00000001 Inexact Rounded ddadd75086 add 12345678 1E-32 -> 12345678.00000001 Inexact Rounded ddadd75087 add 12345678 1E-33 -> 12345678.00000001 Inexact Rounded ddadd75088 add 12345678 1E-34 -> 12345678.00000001 Inexact Rounded ddadd75089 add 12345678 1E-35 -> 12345678.00000001 Inexact Rounded -- Punit's ddadd75100 add 1.000 -200.000 -> -199.000 -- Rounding swathe rounding: half_even ddadd81100 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81101 add .2301 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81102 add .2310 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81103 add .2350 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81104 add .2351 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81105 add .2450 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81106 add .2451 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81107 add .2360 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81108 add .2370 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81109 add .2399 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81120 add 9999999999999999E+369 9E+369 -> Infinity Overflow Inexact Rounded ddadd81121 add -9999999999999999E+369 -9E+369 -> -Infinity Overflow Inexact Rounded rounding: half_up ddadd81200 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81201 add .2301 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81202 add .2310 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81203 add .2350 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81204 add .2351 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81205 add .2450 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81206 add .2451 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81207 add .2360 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81208 add .2370 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81209 add .2399 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81220 add 9999999999999999E+369 9E+369 -> Infinity Overflow Inexact Rounded ddadd81221 add -9999999999999999E+369 -9E+369 -> -Infinity Overflow Inexact Rounded rounding: half_down ddadd81300 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81301 add .2301 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81302 add .2310 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81303 add .2350 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81304 add .2351 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81305 add .2450 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81306 add .2451 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81307 add .2360 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81308 add .2370 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81309 add .2399 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81320 add 9999999999999999E+369 9E+369 -> Infinity Overflow Inexact Rounded ddadd81321 add -9999999999999999E+369 -9E+369 -> -Infinity Overflow Inexact Rounded rounding: up ddadd81400 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81401 add .2301 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81402 add .2310 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81403 add .2350 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81404 add .2351 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81405 add .2450 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81406 add .2451 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81407 add .2360 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81408 add .2370 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81409 add .2399 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81411 add -.2399 -12345678901234.00 -> -12345678901234.24 Inexact Rounded ddadd81420 add 9999999999999999E+369 9E+369 -> Infinity Overflow Inexact Rounded ddadd81421 add -9999999999999999E+369 -9E+369 -> -Infinity Overflow Inexact Rounded rounding: down ddadd81500 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81501 add .2301 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81502 add .2310 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81503 add .2350 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81504 add .2351 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81505 add .2450 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81506 add .2451 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81507 add .2360 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81508 add .2370 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81509 add .2399 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81511 add -.2399 -12345678901234.00 -> -12345678901234.23 Inexact Rounded ddadd81520 add 9999999999999999E+369 9E+369 -> 9.999999999999999E+384 Overflow Inexact Rounded ddadd81521 add -9999999999999999E+369 -9E+369 -> -9.999999999999999E+384 Overflow Inexact Rounded rounding: ceiling ddadd81600 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81601 add .2301 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81602 add .2310 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81603 add .2350 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81604 add .2351 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81605 add .2450 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81606 add .2451 12345678901234.00 -> 12345678901234.25 Inexact Rounded ddadd81607 add .2360 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81608 add .2370 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81609 add .2399 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81611 add -.2399 -12345678901234.00 -> -12345678901234.23 Inexact Rounded ddadd81620 add 9999999999999999E+369 9E+369 -> Infinity Overflow Inexact Rounded ddadd81621 add -9999999999999999E+369 -9E+369 -> -9.999999999999999E+384 Overflow Inexact Rounded rounding: floor ddadd81700 add .2300 12345678901234.00 -> 12345678901234.23 Rounded ddadd81701 add .2301 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81702 add .2310 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81703 add .2350 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81704 add .2351 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81705 add .2450 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81706 add .2451 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd81707 add .2360 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81708 add .2370 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81709 add .2399 12345678901234.00 -> 12345678901234.23 Inexact Rounded ddadd81711 add -.2399 -12345678901234.00 -> -12345678901234.24 Inexact Rounded ddadd81720 add 9999999999999999E+369 9E+369 -> 9.999999999999999E+384 Overflow Inexact Rounded ddadd81721 add -9999999999999999E+369 -9E+369 -> -Infinity Overflow Inexact Rounded rounding: 05up ddadd81800 add .2000 12345678901234.00 -> 12345678901234.20 Rounded ddadd81801 add .2001 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81802 add .2010 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81803 add .2050 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81804 add .2051 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81807 add .2060 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81808 add .2070 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81809 add .2099 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81811 add -.2099 -12345678901234.00 -> -12345678901234.21 Inexact Rounded ddadd81820 add 9999999999999999E+369 9E+369 -> 9.999999999999999E+384 Overflow Inexact Rounded ddadd81821 add -9999999999999999E+369 -9E+369 -> -9.999999999999999E+384 Overflow Inexact Rounded ddadd81900 add .2100 12345678901234.00 -> 12345678901234.21 Rounded ddadd81901 add .2101 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81902 add .2110 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81903 add .2150 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81904 add .2151 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81907 add .2160 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81908 add .2170 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81909 add .2199 12345678901234.00 -> 12345678901234.21 Inexact Rounded ddadd81911 add -.2199 -12345678901234.00 -> -12345678901234.21 Inexact Rounded ddadd82000 add .2400 12345678901234.00 -> 12345678901234.24 Rounded ddadd82001 add .2401 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82002 add .2410 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82003 add .2450 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82004 add .2451 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82007 add .2460 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82008 add .2470 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82009 add .2499 12345678901234.00 -> 12345678901234.24 Inexact Rounded ddadd82011 add -.2499 -12345678901234.00 -> -12345678901234.24 Inexact Rounded ddadd82100 add .2500 12345678901234.00 -> 12345678901234.25 Rounded ddadd82101 add .2501 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82102 add .2510 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82103 add .2550 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82104 add .2551 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82107 add .2560 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82108 add .2570 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82109 add .2599 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82111 add -.2599 -12345678901234.00 -> -12345678901234.26 Inexact Rounded ddadd82200 add .2600 12345678901234.00 -> 12345678901234.26 Rounded ddadd82201 add .2601 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82202 add .2610 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82203 add .2650 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82204 add .2651 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82207 add .2660 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82208 add .2670 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82209 add .2699 12345678901234.00 -> 12345678901234.26 Inexact Rounded ddadd82211 add -.2699 -12345678901234.00 -> -12345678901234.26 Inexact Rounded ddadd82300 add .2900 12345678901234.00 -> 12345678901234.29 Rounded ddadd82301 add .2901 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82302 add .2910 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82303 add .2950 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82304 add .2951 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82307 add .2960 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82308 add .2970 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82309 add .2999 12345678901234.00 -> 12345678901234.29 Inexact Rounded ddadd82311 add -.2999 -12345678901234.00 -> -12345678901234.29 Inexact Rounded -- Null tests ddadd9990 add 10 # -> NaN Invalid_operation ddadd9991 add # 10 -> NaN Invalid_operation
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