diff options
Diffstat (limited to 'Lib/test/decimaltestdata/add.decTest')
| -rw-r--r-- | Lib/test/decimaltestdata/add.decTest | 1624 |
1 files changed, 1601 insertions, 23 deletions
diff --git a/Lib/test/decimaltestdata/add.decTest b/Lib/test/decimaltestdata/add.decTest index 2d3efab..3460aa4 100644 --- a/Lib/test/decimaltestdata/add.decTest +++ b/Lib/test/decimaltestdata/add.decTest @@ -1,6 +1,6 @@ ------------------------------------------------------------------------- +------/cancell---------------------------------------------------------- -- add.decTest -- decimal addition -- --- Copyright (c) IBM Corporation, 1981, 2004. All rights reserved. -- +-- Copyright (c) IBM Corporation, 1981, 2007. All rights reserved. -- ------------------------------------------------------------------------ -- Please see the document "General Decimal Arithmetic Testcases" -- -- at http://www2.hursley.ibm.com/decimal for the description of -- @@ -17,7 +17,7 @@ -- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK -- -- mfc@uk.ibm.com -- ------------------------------------------------------------------------ -version: 2.39 +version: 2.56 precision: 9 rounding: half_up @@ -86,6 +86,7 @@ addx048 add '10000e+9' '700' -> '10000000000700' addx049 add '10000e+9' '7000' -> '10000000007000' addx050 add '10000e+9' '70000' -> '10000000070000' addx051 add '10000e+9' '700000' -> '10000000700000' +addx052 add '10000e+9' '7000000' -> '10000007000000' -- examples from decarith addx053 add '12' '7.00' -> '19.00' @@ -216,7 +217,7 @@ addx166 add '7E+12' '1.11' -> '7000000000001.11' addx167 add '1.11' '7E+12' -> '7000000000001.11' addx168 add '-1' '7E+12' -> '6999999999999' --- 123456789012345 123456789012345 1 23456789012345 +-- 123456789012345 123456789012345 1 23456789012345 addx170 add '0.444444444444444' '0.555555555555563' -> '1.00000000000001' Inexact Rounded addx171 add '0.444444444444444' '0.555555555555562' -> '1.00000000000001' Inexact Rounded addx172 add '0.444444444444444' '0.555555555555561' -> '1.00000000000001' Inexact Rounded @@ -396,6 +397,7 @@ minexponent: -92 addx361 add 0E+50 10000E+1 -> 1.0000E+5 addx362 add 10000E+1 0E-50 -> 100000.0 Rounded addx363 add 10000E+1 10000E-50 -> 100000.0 Rounded Inexact +addx364 add 9.999999E+92 -9.999999E+92 -> 0E+86 -- a curiosity from JSR 13 testing rounding: half_down @@ -568,7 +570,7 @@ minExponent: -393 rounding: down addx561 add 1e-398 9.000000000000000E+384 -> 9.000000000000000E+384 Inexact Rounded addx562 add 0 9.000000000000000E+384 -> 9.000000000000000E+384 Rounded --- and using decimal64 bounds... +-- and using decimal64 bounds (see also ddadd.decTest) precision: 16 maxExponent: +384 minExponent: -383 @@ -576,6 +578,7 @@ rounding: down addx563 add 1e-388 9.000000000000000E+374 -> 9.000000000000000E+374 Inexact Rounded addx564 add 0 9.000000000000000E+374 -> 9.000000000000000E+374 Rounded + -- some more residue effects with extreme rounding precision: 9 rounding: half_up @@ -955,26 +958,26 @@ addx911 add 0.1E-999 0 -> 1E-1000 Subnormal addx912 add 0.10E-999 0 -> 1.0E-1000 Subnormal addx913 add 0.100E-999 0 -> 1.0E-1000 Subnormal Rounded addx914 add 0.01E-999 0 -> 1E-1001 Subnormal --- next is rounded to Emin +-- next is rounded to Nmin addx915 add 0.999E-999 0 -> 1.00E-999 Inexact Rounded Subnormal Underflow addx916 add 0.099E-999 0 -> 1.0E-1000 Inexact Rounded Subnormal Underflow addx917 add 0.009E-999 0 -> 1E-1001 Inexact Rounded Subnormal Underflow -addx918 add 0.001E-999 0 -> 0E-1001 Inexact Rounded Subnormal Underflow -addx919 add 0.0009E-999 0 -> 0E-1001 Inexact Rounded Subnormal Underflow -addx920 add 0.0001E-999 0 -> 0E-1001 Inexact Rounded Subnormal Underflow +addx918 add 0.001E-999 0 -> 0E-1001 Inexact Rounded Subnormal Underflow Clamped +addx919 add 0.0009E-999 0 -> 0E-1001 Inexact Rounded Subnormal Underflow Clamped +addx920 add 0.0001E-999 0 -> 0E-1001 Inexact Rounded Subnormal Underflow Clamped addx930 add -1.00E-999 0 -> -1.00E-999 addx931 add -0.1E-999 0 -> -1E-1000 Subnormal addx932 add -0.10E-999 0 -> -1.0E-1000 Subnormal addx933 add -0.100E-999 0 -> -1.0E-1000 Subnormal Rounded addx934 add -0.01E-999 0 -> -1E-1001 Subnormal --- next is rounded to Emin +-- next is rounded to Nmin addx935 add -0.999E-999 0 -> -1.00E-999 Inexact Rounded Subnormal Underflow addx936 add -0.099E-999 0 -> -1.0E-1000 Inexact Rounded Subnormal Underflow addx937 add -0.009E-999 0 -> -1E-1001 Inexact Rounded Subnormal Underflow -addx938 add -0.001E-999 0 -> -0E-1001 Inexact Rounded Subnormal Underflow -addx939 add -0.0009E-999 0 -> -0E-1001 Inexact Rounded Subnormal Underflow -addx940 add -0.0001E-999 0 -> -0E-1001 Inexact Rounded Subnormal Underflow +addx938 add -0.001E-999 0 -> -0E-1001 Inexact Rounded Subnormal Underflow Clamped +addx939 add -0.0009E-999 0 -> -0E-1001 Inexact Rounded Subnormal Underflow Clamped +addx940 add -0.0001E-999 0 -> -0E-1001 Inexact Rounded Subnormal Underflow Clamped -- some non-zero subnormal adds addx950 add 1.00E-999 0.1E-999 -> 1.10E-999 @@ -995,12 +998,43 @@ addx963 add 0.10E-999 -0.1E-999 -> 0E-1001 addx964 add 0.100E-999 -0.1E-999 -> 0E-1001 Clamped addx965 add 0.01E-999 -0.1E-999 -> -9E-1001 Subnormal addx966 add 0.999E-999 -0.1E-999 -> 9.0E-1000 Inexact Rounded Subnormal Underflow -addx967 add 0.099E-999 -0.1E-999 -> -0E-1001 Inexact Rounded Subnormal Underflow +addx967 add 0.099E-999 -0.1E-999 -> -0E-1001 Inexact Rounded Subnormal Underflow Clamped addx968 add 0.009E-999 -0.1E-999 -> -9E-1001 Inexact Rounded Subnormal Underflow addx969 add 0.001E-999 -0.1E-999 -> -1.0E-1000 Inexact Rounded Subnormal Underflow addx970 add 0.0009E-999 -0.1E-999 -> -1.0E-1000 Inexact Rounded Subnormal Underflow addx971 add 0.0001E-999 -0.1E-999 -> -1.0E-1000 Inexact Rounded Subnormal Underflow +-- some 'real' numbers +maxExponent: 384 +minExponent: -383 +precision: 8 +addx566 add 99999061735E-394 0E-394 -> 9.999906E-384 Inexact Rounded Underflow Subnormal +precision: 7 +addx567 add 99999061735E-394 0E-394 -> 9.99991E-384 Inexact Rounded Underflow Subnormal +precision: 6 +addx568 add 99999061735E-394 0E-394 -> 9.9999E-384 Inexact Rounded Underflow Subnormal + +-- now the case where we can get underflow but the result is normal +-- [note this can't happen if the operands are also bounded, as we +-- cannot represent 1E-399, for example] +precision: 16 +rounding: half_up +maxExponent: 384 +minExponent: -383 + +addx571 add 1E-383 0 -> 1E-383 +addx572 add 1E-384 0 -> 1E-384 Subnormal +addx573 add 1E-383 1E-384 -> 1.1E-383 +addx574 subtract 1E-383 1E-384 -> 9E-384 Subnormal + +-- Here we explore the boundary of rounding a subnormal to Nmin +addx575 subtract 1E-383 1E-398 -> 9.99999999999999E-384 Subnormal +addx576 subtract 1E-383 1E-398 -> 9.99999999999999E-384 Subnormal +addx577 subtract 1E-383 1E-399 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +addx578 subtract 1E-383 1E-400 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +addx579 subtract 1E-383 1E-401 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +addx580 subtract 1E-383 1E-402 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded + -- check overflow edge case precision: 7 rounding: half_up @@ -1106,22 +1140,1566 @@ addx1138 add 10000E-101 -1e-200 -> 9.999E-98 Subnormal Inexact Rounded U addx1139 add 1000E-101 -1e-200 -> 9.99E-99 Subnormal Inexact Rounded Underflow addx1140 add 100E-101 -1e-200 -> 9.9E-100 Subnormal Inexact Rounded Underflow addx1141 add 10E-101 -1e-200 -> 9E-101 Subnormal Inexact Rounded Underflow -addx1142 add 1E-101 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow -addx1143 add 0E-101 -1e-200 -> -0E-101 Subnormal Inexact Rounded Underflow -addx1144 add 1E-102 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow +addx1142 add 1E-101 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow Clamped +addx1143 add 0E-101 -1e-200 -> -0E-101 Subnormal Inexact Rounded Underflow Clamped +addx1144 add 1E-102 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow Clamped addx1151 add 10000E-102 -1e-200 -> 9.99E-99 Subnormal Inexact Rounded Underflow addx1152 add 1000E-102 -1e-200 -> 9.9E-100 Subnormal Inexact Rounded Underflow addx1153 add 100E-102 -1e-200 -> 9E-101 Subnormal Inexact Rounded Underflow -addx1154 add 10E-102 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow -addx1155 add 1E-102 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow -addx1156 add 0E-102 -1e-200 -> -0E-101 Subnormal Inexact Rounded Underflow -addx1157 add 1E-103 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow +addx1154 add 10E-102 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow Clamped +addx1155 add 1E-102 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow Clamped +addx1156 add 0E-102 -1e-200 -> -0E-101 Subnormal Inexact Rounded Underflow Clamped +addx1157 add 1E-103 -1e-200 -> 0E-101 Subnormal Inexact Rounded Underflow Clamped + +addx1160 add 100E-105 -1e-101 -> -0E-101 Subnormal Inexact Rounded Underflow Clamped +addx1161 add 100E-105 -1e-201 -> 0E-101 Subnormal Inexact Rounded Underflow Clamped + +-- tests based on Gunnar Degnbol's edge case +precision: 15 +rounding: half_up +maxExponent: 384 +minexponent: -383 + +addx1200 add 1E15 -0.5 -> 1.00000000000000E+15 Inexact Rounded +addx1201 add 1E15 -0.50 -> 1.00000000000000E+15 Inexact Rounded +addx1210 add 1E15 -0.51 -> 999999999999999 Inexact Rounded +addx1211 add 1E15 -0.501 -> 999999999999999 Inexact Rounded +addx1212 add 1E15 -0.5001 -> 999999999999999 Inexact Rounded +addx1213 add 1E15 -0.50001 -> 999999999999999 Inexact Rounded +addx1214 add 1E15 -0.500001 -> 999999999999999 Inexact Rounded +addx1215 add 1E15 -0.5000001 -> 999999999999999 Inexact Rounded +addx1216 add 1E15 -0.50000001 -> 999999999999999 Inexact Rounded +addx1217 add 1E15 -0.500000001 -> 999999999999999 Inexact Rounded +addx1218 add 1E15 -0.5000000001 -> 999999999999999 Inexact Rounded +addx1219 add 1E15 -0.50000000001 -> 999999999999999 Inexact Rounded +addx1220 add 1E15 -0.500000000001 -> 999999999999999 Inexact Rounded +addx1221 add 1E15 -0.5000000000001 -> 999999999999999 Inexact Rounded +addx1222 add 1E15 -0.50000000000001 -> 999999999999999 Inexact Rounded +addx1223 add 1E15 -0.500000000000001 -> 999999999999999 Inexact Rounded +addx1224 add 1E15 -0.5000000000000001 -> 999999999999999 Inexact Rounded +addx1225 add 1E15 -0.5000000000000000 -> 1.00000000000000E+15 Inexact Rounded +addx1230 add 1E15 -5000000.000000001 -> 999999995000000 Inexact Rounded + +precision: 16 + +addx1300 add 1E16 -0.5 -> 1.000000000000000E+16 Inexact Rounded +addx1310 add 1E16 -0.51 -> 9999999999999999 Inexact Rounded +addx1311 add 1E16 -0.501 -> 9999999999999999 Inexact Rounded +addx1312 add 1E16 -0.5001 -> 9999999999999999 Inexact Rounded +addx1313 add 1E16 -0.50001 -> 9999999999999999 Inexact Rounded +addx1314 add 1E16 -0.500001 -> 9999999999999999 Inexact Rounded +addx1315 add 1E16 -0.5000001 -> 9999999999999999 Inexact Rounded +addx1316 add 1E16 -0.50000001 -> 9999999999999999 Inexact Rounded +addx1317 add 1E16 -0.500000001 -> 9999999999999999 Inexact Rounded +addx1318 add 1E16 -0.5000000001 -> 9999999999999999 Inexact Rounded +addx1319 add 1E16 -0.50000000001 -> 9999999999999999 Inexact Rounded +addx1320 add 1E16 -0.500000000001 -> 9999999999999999 Inexact Rounded +addx1321 add 1E16 -0.5000000000001 -> 9999999999999999 Inexact Rounded +addx1322 add 1E16 -0.50000000000001 -> 9999999999999999 Inexact Rounded +addx1323 add 1E16 -0.500000000000001 -> 9999999999999999 Inexact Rounded +addx1324 add 1E16 -0.5000000000000001 -> 9999999999999999 Inexact Rounded +addx1325 add 1E16 -0.5000000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1326 add 1E16 -0.500000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1327 add 1E16 -0.50000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1328 add 1E16 -0.5000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1329 add 1E16 -0.500000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1330 add 1E16 -0.50000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1331 add 1E16 -0.5000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1332 add 1E16 -0.500000000 -> 1.000000000000000E+16 Inexact Rounded +addx1333 add 1E16 -0.50000000 -> 1.000000000000000E+16 Inexact Rounded +addx1334 add 1E16 -0.5000000 -> 1.000000000000000E+16 Inexact Rounded +addx1335 add 1E16 -0.500000 -> 1.000000000000000E+16 Inexact Rounded +addx1336 add 1E16 -0.50000 -> 1.000000000000000E+16 Inexact Rounded +addx1337 add 1E16 -0.5000 -> 1.000000000000000E+16 Inexact Rounded +addx1338 add 1E16 -0.500 -> 1.000000000000000E+16 Inexact Rounded +addx1339 add 1E16 -0.50 -> 1.000000000000000E+16 Inexact Rounded + +addx1340 add 1E16 -5000000.000010001 -> 9999999995000000 Inexact Rounded +addx1341 add 1E16 -5000000.000000001 -> 9999999995000000 Inexact Rounded + +addx1349 add 9999999999999999 0.4 -> 9999999999999999 Inexact Rounded +addx1350 add 9999999999999999 0.49 -> 9999999999999999 Inexact Rounded +addx1351 add 9999999999999999 0.499 -> 9999999999999999 Inexact Rounded +addx1352 add 9999999999999999 0.4999 -> 9999999999999999 Inexact Rounded +addx1353 add 9999999999999999 0.49999 -> 9999999999999999 Inexact Rounded +addx1354 add 9999999999999999 0.499999 -> 9999999999999999 Inexact Rounded +addx1355 add 9999999999999999 0.4999999 -> 9999999999999999 Inexact Rounded +addx1356 add 9999999999999999 0.49999999 -> 9999999999999999 Inexact Rounded +addx1357 add 9999999999999999 0.499999999 -> 9999999999999999 Inexact Rounded +addx1358 add 9999999999999999 0.4999999999 -> 9999999999999999 Inexact Rounded +addx1359 add 9999999999999999 0.49999999999 -> 9999999999999999 Inexact Rounded +addx1360 add 9999999999999999 0.499999999999 -> 9999999999999999 Inexact Rounded +addx1361 add 9999999999999999 0.4999999999999 -> 9999999999999999 Inexact Rounded +addx1362 add 9999999999999999 0.49999999999999 -> 9999999999999999 Inexact Rounded +addx1363 add 9999999999999999 0.499999999999999 -> 9999999999999999 Inexact Rounded +addx1364 add 9999999999999999 0.4999999999999999 -> 9999999999999999 Inexact Rounded +addx1365 add 9999999999999999 0.5000000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1367 add 9999999999999999 0.500000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1368 add 9999999999999999 0.50000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1369 add 9999999999999999 0.5000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1370 add 9999999999999999 0.500000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1371 add 9999999999999999 0.50000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1372 add 9999999999999999 0.5000000000 -> 1.000000000000000E+16 Inexact Rounded +addx1373 add 9999999999999999 0.500000000 -> 1.000000000000000E+16 Inexact Rounded +addx1374 add 9999999999999999 0.50000000 -> 1.000000000000000E+16 Inexact Rounded +addx1375 add 9999999999999999 0.5000000 -> 1.000000000000000E+16 Inexact Rounded +addx1376 add 9999999999999999 0.500000 -> 1.000000000000000E+16 Inexact Rounded +addx1377 add 9999999999999999 0.50000 -> 1.000000000000000E+16 Inexact Rounded +addx1378 add 9999999999999999 0.5000 -> 1.000000000000000E+16 Inexact Rounded +addx1379 add 9999999999999999 0.500 -> 1.000000000000000E+16 Inexact Rounded +addx1380 add 9999999999999999 0.50 -> 1.000000000000000E+16 Inexact Rounded +addx1381 add 9999999999999999 0.5 -> 1.000000000000000E+16 Inexact Rounded +addx1382 add 9999999999999999 0.5000000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1383 add 9999999999999999 0.500000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1384 add 9999999999999999 0.50000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1385 add 9999999999999999 0.5000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1386 add 9999999999999999 0.500000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1387 add 9999999999999999 0.50000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1388 add 9999999999999999 0.5000000001 -> 1.000000000000000E+16 Inexact Rounded +addx1389 add 9999999999999999 0.500000001 -> 1.000000000000000E+16 Inexact Rounded +addx1390 add 9999999999999999 0.50000001 -> 1.000000000000000E+16 Inexact Rounded +addx1391 add 9999999999999999 0.5000001 -> 1.000000000000000E+16 Inexact Rounded +addx1392 add 9999999999999999 0.500001 -> 1.000000000000000E+16 Inexact Rounded +addx1393 add 9999999999999999 0.50001 -> 1.000000000000000E+16 Inexact Rounded +addx1394 add 9999999999999999 0.5001 -> 1.000000000000000E+16 Inexact Rounded +addx1395 add 9999999999999999 0.501 -> 1.000000000000000E+16 Inexact Rounded +addx1396 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 +precision: 15 +rounding: half_up +maxExponent: 384 +minexponent: -383 + +addx1400 add 0 1.23456789012345 -> 1.23456789012345 +addx1401 add 0 1.23456789012345E-1 -> 0.123456789012345 +addx1402 add 0 1.23456789012345E-2 -> 0.0123456789012345 +addx1403 add 0 1.23456789012345E-3 -> 0.00123456789012345 +addx1404 add 0 1.23456789012345E-4 -> 0.000123456789012345 +addx1405 add 0 1.23456789012345E-5 -> 0.0000123456789012345 +addx1406 add 0 1.23456789012345E-6 -> 0.00000123456789012345 +addx1407 add 0 1.23456789012345E-7 -> 1.23456789012345E-7 +addx1408 add 0 1.23456789012345E-8 -> 1.23456789012345E-8 +addx1409 add 0 1.23456789012345E-9 -> 1.23456789012345E-9 +addx1410 add 0 1.23456789012345E-10 -> 1.23456789012345E-10 +addx1411 add 0 1.23456789012345E-11 -> 1.23456789012345E-11 +addx1412 add 0 1.23456789012345E-12 -> 1.23456789012345E-12 +addx1413 add 0 1.23456789012345E-13 -> 1.23456789012345E-13 +addx1414 add 0 1.23456789012345E-14 -> 1.23456789012345E-14 +addx1415 add 0 1.23456789012345E-15 -> 1.23456789012345E-15 +addx1416 add 0 1.23456789012345E-16 -> 1.23456789012345E-16 +addx1417 add 0 1.23456789012345E-17 -> 1.23456789012345E-17 +addx1418 add 0 1.23456789012345E-18 -> 1.23456789012345E-18 +addx1419 add 0 1.23456789012345E-19 -> 1.23456789012345E-19 + +-- same, precision 16.. +precision: 16 +addx1420 add 0 1.123456789012345 -> 1.123456789012345 +addx1421 add 0 1.123456789012345E-1 -> 0.1123456789012345 +addx1422 add 0 1.123456789012345E-2 -> 0.01123456789012345 +addx1423 add 0 1.123456789012345E-3 -> 0.001123456789012345 +addx1424 add 0 1.123456789012345E-4 -> 0.0001123456789012345 +addx1425 add 0 1.123456789012345E-5 -> 0.00001123456789012345 +addx1426 add 0 1.123456789012345E-6 -> 0.000001123456789012345 +addx1427 add 0 1.123456789012345E-7 -> 1.123456789012345E-7 +addx1428 add 0 1.123456789012345E-8 -> 1.123456789012345E-8 +addx1429 add 0 1.123456789012345E-9 -> 1.123456789012345E-9 +addx1430 add 0 1.123456789012345E-10 -> 1.123456789012345E-10 +addx1431 add 0 1.123456789012345E-11 -> 1.123456789012345E-11 +addx1432 add 0 1.123456789012345E-12 -> 1.123456789012345E-12 +addx1433 add 0 1.123456789012345E-13 -> 1.123456789012345E-13 +addx1434 add 0 1.123456789012345E-14 -> 1.123456789012345E-14 +addx1435 add 0 1.123456789012345E-15 -> 1.123456789012345E-15 +addx1436 add 0 1.123456789012345E-16 -> 1.123456789012345E-16 +addx1437 add 0 1.123456789012345E-17 -> 1.123456789012345E-17 +addx1438 add 0 1.123456789012345E-18 -> 1.123456789012345E-18 +addx1439 add 0 1.123456789012345E-19 -> 1.123456789012345E-19 + +-- same, reversed 0 +addx1440 add 1.123456789012345 0 -> 1.123456789012345 +addx1441 add 1.123456789012345E-1 0 -> 0.1123456789012345 +addx1442 add 1.123456789012345E-2 0 -> 0.01123456789012345 +addx1443 add 1.123456789012345E-3 0 -> 0.001123456789012345 +addx1444 add 1.123456789012345E-4 0 -> 0.0001123456789012345 +addx1445 add 1.123456789012345E-5 0 -> 0.00001123456789012345 +addx1446 add 1.123456789012345E-6 0 -> 0.000001123456789012345 +addx1447 add 1.123456789012345E-7 0 -> 1.123456789012345E-7 +addx1448 add 1.123456789012345E-8 0 -> 1.123456789012345E-8 +addx1449 add 1.123456789012345E-9 0 -> 1.123456789012345E-9 +addx1450 add 1.123456789012345E-10 0 -> 1.123456789012345E-10 +addx1451 add 1.123456789012345E-11 0 -> 1.123456789012345E-11 +addx1452 add 1.123456789012345E-12 0 -> 1.123456789012345E-12 +addx1453 add 1.123456789012345E-13 0 -> 1.123456789012345E-13 +addx1454 add 1.123456789012345E-14 0 -> 1.123456789012345E-14 +addx1455 add 1.123456789012345E-15 0 -> 1.123456789012345E-15 +addx1456 add 1.123456789012345E-16 0 -> 1.123456789012345E-16 +addx1457 add 1.123456789012345E-17 0 -> 1.123456789012345E-17 +addx1458 add 1.123456789012345E-18 0 -> 1.123456789012345E-18 +addx1459 add 1.123456789012345E-19 0 -> 1.123456789012345E-19 + +-- same, Es on the 0 +addx1460 add 1.123456789012345 0E-0 -> 1.123456789012345 +addx1461 add 1.123456789012345 0E-1 -> 1.123456789012345 +addx1462 add 1.123456789012345 0E-2 -> 1.123456789012345 +addx1463 add 1.123456789012345 0E-3 -> 1.123456789012345 +addx1464 add 1.123456789012345 0E-4 -> 1.123456789012345 +addx1465 add 1.123456789012345 0E-5 -> 1.123456789012345 +addx1466 add 1.123456789012345 0E-6 -> 1.123456789012345 +addx1467 add 1.123456789012345 0E-7 -> 1.123456789012345 +addx1468 add 1.123456789012345 0E-8 -> 1.123456789012345 +addx1469 add 1.123456789012345 0E-9 -> 1.123456789012345 +addx1470 add 1.123456789012345 0E-10 -> 1.123456789012345 +addx1471 add 1.123456789012345 0E-11 -> 1.123456789012345 +addx1472 add 1.123456789012345 0E-12 -> 1.123456789012345 +addx1473 add 1.123456789012345 0E-13 -> 1.123456789012345 +addx1474 add 1.123456789012345 0E-14 -> 1.123456789012345 +addx1475 add 1.123456789012345 0E-15 -> 1.123456789012345 +-- next four flag Rounded because the 0 extends the result +addx1476 add 1.123456789012345 0E-16 -> 1.123456789012345 Rounded +addx1477 add 1.123456789012345 0E-17 -> 1.123456789012345 Rounded +addx1478 add 1.123456789012345 0E-18 -> 1.123456789012345 Rounded +addx1479 add 1.123456789012345 0E-19 -> 1.123456789012345 Rounded + +-- sum of two opposite-sign operands is exactly 0 and floor => -0 +precision: 16 +maxExponent: 384 +minexponent: -383 + +rounding: half_up +-- exact zeros from zeros +addx1500 add 0 0E-19 -> 0E-19 +addx1501 add -0 0E-19 -> 0E-19 +addx1502 add 0 -0E-19 -> 0E-19 +addx1503 add -0 -0E-19 -> -0E-19 +addx1504 add 0E-400 0E-19 -> 0E-398 Clamped +addx1505 add -0E-400 0E-19 -> 0E-398 Clamped +addx1506 add 0E-400 -0E-19 -> 0E-398 Clamped +addx1507 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1511 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1512 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1513 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1514 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx1515 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1516 add -1E-401 1E-401 -> 0E-398 Clamped +addx1517 add 1E-401 -1E-401 -> 0E-398 Clamped +addx1518 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: half_down +-- exact zeros from zeros +addx1520 add 0 0E-19 -> 0E-19 +addx1521 add -0 0E-19 -> 0E-19 +addx1522 add 0 -0E-19 -> 0E-19 +addx1523 add -0 -0E-19 -> -0E-19 +addx1524 add 0E-400 0E-19 -> 0E-398 Clamped +addx1525 add -0E-400 0E-19 -> 0E-398 Clamped +addx1526 add 0E-400 -0E-19 -> 0E-398 Clamped +addx1527 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1531 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1532 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1533 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1534 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx1535 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1536 add -1E-401 1E-401 -> 0E-398 Clamped +addx1537 add 1E-401 -1E-401 -> 0E-398 Clamped +addx1538 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: half_even +-- exact zeros from zeros +addx1540 add 0 0E-19 -> 0E-19 +addx1541 add -0 0E-19 -> 0E-19 +addx1542 add 0 -0E-19 -> 0E-19 +addx1543 add -0 -0E-19 -> -0E-19 +addx1544 add 0E-400 0E-19 -> 0E-398 Clamped +addx1545 add -0E-400 0E-19 -> 0E-398 Clamped +addx1546 add 0E-400 -0E-19 -> 0E-398 Clamped +addx1547 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1551 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1552 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1553 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1554 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx1555 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1556 add -1E-401 1E-401 -> 0E-398 Clamped +addx1557 add 1E-401 -1E-401 -> 0E-398 Clamped +addx1558 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: up +-- exact zeros from zeros +addx1560 add 0 0E-19 -> 0E-19 +addx1561 add -0 0E-19 -> 0E-19 +addx1562 add 0 -0E-19 -> 0E-19 +addx1563 add -0 -0E-19 -> -0E-19 +addx1564 add 0E-400 0E-19 -> 0E-398 Clamped +addx1565 add -0E-400 0E-19 -> 0E-398 Clamped +addx1566 add 0E-400 -0E-19 -> 0E-398 Clamped +addx1567 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1571 add 1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx1572 add -1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx1573 add 1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +addx1574 add -1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +-- some exact zeros from non-zeros +addx1575 add 1E-401 1E-401 -> 1E-398 Subnormal Inexact Rounded Underflow +addx1576 add -1E-401 1E-401 -> 0E-398 Clamped +addx1577 add 1E-401 -1E-401 -> 0E-398 Clamped +addx1578 add -1E-401 -1E-401 -> -1E-398 Subnormal Inexact Rounded Underflow + +rounding: down +-- exact zeros from zeros +addx1580 add 0 0E-19 -> 0E-19 +addx1581 add -0 0E-19 -> 0E-19 +addx1582 add 0 -0E-19 -> 0E-19 +addx1583 add -0 -0E-19 -> -0E-19 +addx1584 add 0E-400 0E-19 -> 0E-398 Clamped +addx1585 add -0E-400 0E-19 -> 0E-398 Clamped +addx1586 add 0E-400 -0E-19 -> 0E-398 Clamped +addx1587 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1591 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1592 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1593 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1594 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx1595 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1596 add -1E-401 1E-401 -> 0E-398 Clamped +addx1597 add 1E-401 -1E-401 -> 0E-398 Clamped +addx1598 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: ceiling +-- exact zeros from zeros +addx1600 add 0 0E-19 -> 0E-19 +addx1601 add -0 0E-19 -> 0E-19 +addx1602 add 0 -0E-19 -> 0E-19 +addx1603 add -0 -0E-19 -> -0E-19 +addx1604 add 0E-400 0E-19 -> 0E-398 Clamped +addx1605 add -0E-400 0E-19 -> 0E-398 Clamped +addx1606 add 0E-400 -0E-19 -> 0E-398 Clamped +addx1607 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1611 add 1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx1612 add -1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx1613 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1614 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx1615 add 1E-401 1E-401 -> 1E-398 Subnormal Inexact Rounded Underflow +addx1616 add -1E-401 1E-401 -> 0E-398 Clamped +addx1617 add 1E-401 -1E-401 -> 0E-398 Clamped +addx1618 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +-- and the extra-special ugly case; unusual minuses marked by -- * +rounding: floor +-- exact zeros from zeros +addx1620 add 0 0E-19 -> 0E-19 +addx1621 add -0 0E-19 -> -0E-19 -- * +addx1622 add 0 -0E-19 -> -0E-19 -- * +addx1623 add -0 -0E-19 -> -0E-19 +addx1624 add 0E-400 0E-19 -> 0E-398 Clamped +addx1625 add -0E-400 0E-19 -> -0E-398 Clamped -- * +addx1626 add 0E-400 -0E-19 -> -0E-398 Clamped -- * +addx1627 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx1631 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1632 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1633 add 1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +addx1634 add -1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +-- some exact zeros from non-zeros +addx1635 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx1636 add -1E-401 1E-401 -> -0E-398 Clamped -- * +addx1637 add 1E-401 -1E-401 -> -0E-398 Clamped -- * +addx1638 add -1E-401 -1E-401 -> -1E-398 Subnormal Inexact Rounded Underflow + +-- BigDecimal problem testcases 2006.01.23 +precision: 16 +maxExponent: 384 +minexponent: -383 + +rounding: down +precision: 7 +addx1651 add 10001E+2 -2E+1 -> 1.00008E+6 +precision: 6 +addx1652 add 10001E+2 -2E+1 -> 1.00008E+6 +precision: 5 +addx1653 add 10001E+2 -2E+1 -> 1.0000E+6 Inexact Rounded +precision: 4 +addx1654 add 10001E+2 -2E+1 -> 1.000E+6 Inexact Rounded +precision: 3 +addx1655 add 10001E+2 -2E+1 -> 1.00E+6 Inexact Rounded +precision: 2 +addx1656 add 10001E+2 -2E+1 -> 1.0E+6 Inexact Rounded +precision: 1 +addx1657 add 10001E+2 -2E+1 -> 1E+6 Inexact Rounded + +rounding: half_even +precision: 7 +addx1661 add 10001E+2 -2E+1 -> 1.00008E+6 +precision: 6 +addx1662 add 10001E+2 -2E+1 -> 1.00008E+6 +precision: 5 +addx1663 add 10001E+2 -2E+1 -> 1.0001E+6 Inexact Rounded +precision: 4 +addx1664 add 10001E+2 -2E+1 -> 1.000E+6 Inexact Rounded +precision: 3 +addx1665 add 10001E+2 -2E+1 -> 1.00E+6 Inexact Rounded +precision: 2 +addx1666 add 10001E+2 -2E+1 -> 1.0E+6 Inexact Rounded +precision: 1 +addx1667 add 10001E+2 -2E+1 -> 1E+6 Inexact Rounded + +rounding: up +precision: 7 +addx1671 add 10001E+2 -2E+1 -> 1.00008E+6 +precision: 6 +addx1672 add 10001E+2 -2E+1 -> 1.00008E+6 +precision: 5 +addx1673 add 10001E+2 -2E+1 -> 1.0001E+6 Inexact Rounded +precision: 4 +addx1674 add 10001E+2 -2E+1 -> 1.001E+6 Inexact Rounded +precision: 3 +addx1675 add 10001E+2 -2E+1 -> 1.01E+6 Inexact Rounded +precision: 2 +addx1676 add 10001E+2 -2E+1 -> 1.1E+6 Inexact Rounded +precision: 1 +addx1677 add 10001E+2 -2E+1 -> 2E+6 Inexact Rounded + +precision: 34 +rounding: half_up +maxExponent: 6144 +minExponent: -6143 +-- Examples from SQL proposal (Krishna Kulkarni) +addx1701 add 130E-2 120E-2 -> 2.50 +addx1702 add 130E-2 12E-1 -> 2.50 +addx1703 add 130E-2 1E0 -> 2.30 +addx1704 add 1E2 1E4 -> 1.01E+4 +addx1705 subtract 130E-2 120E-2 -> 0.10 +addx1706 subtract 130E-2 12E-1 -> 0.10 +addx1707 subtract 130E-2 1E0 -> 0.30 +addx1708 subtract 1E2 1E4 -> -9.9E+3 + +------------------------------------------------------------------------ +-- Same as above, using decimal64 default parameters -- +------------------------------------------------------------------------ +precision: 16 +rounding: half_even +maxExponent: 384 +minexponent: -383 + +-- [first group are 'quick confidence check'] +addx6001 add 1 1 -> 2 +addx6002 add 2 3 -> 5 +addx6003 add '5.75' '3.3' -> 9.05 +addx6004 add '5' '-3' -> 2 +addx6005 add '-5' '-3' -> -8 +addx6006 add '-7' '2.5' -> -4.5 +addx6007 add '0.7' '0.3' -> 1.0 +addx6008 add '1.25' '1.25' -> 2.50 +addx6009 add '1.23456789' '1.00000000' -> '2.23456789' +addx6010 add '1.23456789' '1.00000011' -> '2.23456800' + +addx6011 add '0.44444444444444444' '0.55555555555555555' -> '1.000000000000000' Inexact Rounded +addx6012 add '0.44444444444444440' '0.55555555555555555' -> '1.000000000000000' Inexact Rounded +addx6013 add '0.44444444444444444' '0.55555555555555550' -> '0.9999999999999999' Inexact Rounded +addx6014 add '0.444444444444444449' '0' -> '0.4444444444444444' Inexact Rounded +addx6015 add '0.4444444444444444499' '0' -> '0.4444444444444444' Inexact Rounded +addx6016 add '0.44444444444444444999' '0' -> '0.4444444444444444' Inexact Rounded +addx6017 add '0.44444444444444445000' '0' -> '0.4444444444444444' Inexact Rounded +addx6018 add '0.44444444444444445001' '0' -> '0.4444444444444445' Inexact Rounded +addx6019 add '0.4444444444444444501' '0' -> '0.4444444444444445' Inexact Rounded +addx6020 add '0.444444444444444451' '0' -> '0.4444444444444445' Inexact Rounded + +addx6021 add 0 1 -> 1 +addx6022 add 1 1 -> 2 +addx6023 add 2 1 -> 3 +addx6024 add 3 1 -> 4 +addx6025 add 4 1 -> 5 +addx6026 add 5 1 -> 6 +addx6027 add 6 1 -> 7 +addx6028 add 7 1 -> 8 +addx6029 add 8 1 -> 9 +addx6030 add 9 1 -> 10 + +-- some carrying effects +addx6031 add '0.9998' '0.0000' -> '0.9998' +addx6032 add '0.9998' '0.0001' -> '0.9999' +addx6033 add '0.9998' '0.0002' -> '1.0000' +addx6034 add '0.9998' '0.0003' -> '1.0001' + +addx6035 add '70' '10000e+16' -> '1.000000000000000E+20' Inexact Rounded +addx6036 add '700' '10000e+16' -> '1.000000000000000E+20' Inexact Rounded +addx6037 add '7000' '10000e+16' -> '1.000000000000000E+20' Inexact Rounded +addx6038 add '70000' '10000e+16' -> '1.000000000000001E+20' Inexact Rounded +addx6039 add '700000' '10000e+16' -> '1.000000000000007E+20' Rounded + +-- symmetry: +addx6040 add '10000e+16' '70' -> '1.000000000000000E+20' Inexact Rounded +addx6041 add '10000e+16' '700' -> '1.000000000000000E+20' Inexact Rounded +addx6042 add '10000e+16' '7000' -> '1.000000000000000E+20' Inexact Rounded +addx6044 add '10000e+16' '70000' -> '1.000000000000001E+20' Inexact Rounded +addx6045 add '10000e+16' '700000' -> '1.000000000000007E+20' Rounded + +addx6046 add '10000e+9' '7' -> '10000000000007' +addx6047 add '10000e+9' '70' -> '10000000000070' +addx6048 add '10000e+9' '700' -> '10000000000700' +addx6049 add '10000e+9' '7000' -> '10000000007000' +addx6050 add '10000e+9' '70000' -> '10000000070000' +addx6051 add '10000e+9' '700000' -> '10000000700000' + +-- examples from decarith +addx6053 add '12' '7.00' -> '19.00' +addx6054 add '1.3' '-1.07' -> '0.23' +addx6055 add '1.3' '-1.30' -> '0.00' +addx6056 add '1.3' '-2.07' -> '-0.77' +addx6057 add '1E+2' '1E+4' -> '1.01E+4' + +-- from above +addx6061 add 1 '0.1' -> '1.1' +addx6062 add 1 '0.01' -> '1.01' +addx6063 add 1 '0.001' -> '1.001' +addx6064 add 1 '0.0001' -> '1.0001' +addx6065 add 1 '0.00001' -> '1.00001' +addx6066 add 1 '0.000001' -> '1.000001' +addx6067 add 1 '0.0000001' -> '1.0000001' +addx6068 add 1 '0.00000001' -> '1.00000001' + +-- cancellation to integer +addx6069 add 99999999999999123456789 -99999999999999E+9 -> 123456789 + +-- some funny zeros [in case of bad signum] +addx6070 add 1 0 -> 1 +addx6071 add 1 0. -> 1 +addx6072 add 1 .0 -> 1.0 +addx6073 add 1 0.0 -> 1.0 +addx6074 add 1 0.00 -> 1.00 +addx6075 add 0 1 -> 1 +addx6076 add 0. 1 -> 1 +addx6077 add .0 1 -> 1.0 +addx6078 add 0.0 1 -> 1.0 +addx6079 add 0.00 1 -> 1.00 + +-- some carries +addx6080 add 9999999999999998 1 -> 9999999999999999 +addx6081 add 9999999999999999 1 -> 1.000000000000000E+16 Rounded +addx6082 add 999999999999999 1 -> 1000000000000000 +addx6083 add 9999999999999 1 -> 10000000000000 +addx6084 add 99999999999 1 -> 100000000000 +addx6085 add 999999999 1 -> 1000000000 +addx6086 add 9999999 1 -> 10000000 +addx6087 add 99999 1 -> 100000 +addx6088 add 999 1 -> 1000 +addx6089 add 9 1 -> 10 + -addx1160 add 100E-105 -1e-101 -> -0E-101 Subnormal Inexact Rounded Underflow -addx1161 add 100E-105 -1e-201 -> 0E-101 Subnormal Inexact Rounded Underflow +-- more LHS swaps +addx6090 add '-56267E-10' 0 -> '-0.0000056267' +addx6091 add '-56267E-6' 0 -> '-0.056267' +addx6092 add '-56267E-5' 0 -> '-0.56267' +addx6093 add '-56267E-4' 0 -> '-5.6267' +addx6094 add '-56267E-3' 0 -> '-56.267' +addx6095 add '-56267E-2' 0 -> '-562.67' +addx6096 add '-56267E-1' 0 -> '-5626.7' +addx6097 add '-56267E-0' 0 -> '-56267' +addx6098 add '-5E-10' 0 -> '-5E-10' +addx6099 add '-5E-7' 0 -> '-5E-7' +addx6100 add '-5E-6' 0 -> '-0.000005' +addx6101 add '-5E-5' 0 -> '-0.00005' +addx6102 add '-5E-4' 0 -> '-0.0005' +addx6103 add '-5E-1' 0 -> '-0.5' +addx6104 add '-5E0' 0 -> '-5' +addx6105 add '-5E1' 0 -> '-50' +addx6106 add '-5E5' 0 -> '-500000' +addx6107 add '-5E15' 0 -> '-5000000000000000' +addx6108 add '-5E16' 0 -> '-5.000000000000000E+16' Rounded +addx6109 add '-5E17' 0 -> '-5.000000000000000E+17' Rounded +addx6110 add '-5E18' 0 -> '-5.000000000000000E+18' Rounded +addx6111 add '-5E100' 0 -> '-5.000000000000000E+100' Rounded + +-- more RHS swaps +addx6113 add 0 '-56267E-10' -> '-0.0000056267' +addx6114 add 0 '-56267E-6' -> '-0.056267' +addx6116 add 0 '-56267E-5' -> '-0.56267' +addx6117 add 0 '-56267E-4' -> '-5.6267' +addx6119 add 0 '-56267E-3' -> '-56.267' +addx6120 add 0 '-56267E-2' -> '-562.67' +addx6121 add 0 '-56267E-1' -> '-5626.7' +addx6122 add 0 '-56267E-0' -> '-56267' +addx6123 add 0 '-5E-10' -> '-5E-10' +addx6124 add 0 '-5E-7' -> '-5E-7' +addx6125 add 0 '-5E-6' -> '-0.000005' +addx6126 add 0 '-5E-5' -> '-0.00005' +addx6127 add 0 '-5E-4' -> '-0.0005' +addx6128 add 0 '-5E-1' -> '-0.5' +addx6129 add 0 '-5E0' -> '-5' +addx6130 add 0 '-5E1' -> '-50' +addx6131 add 0 '-5E5' -> '-500000' +addx6132 add 0 '-5E15' -> '-5000000000000000' +addx6133 add 0 '-5E16' -> '-5.000000000000000E+16' Rounded +addx6134 add 0 '-5E17' -> '-5.000000000000000E+17' Rounded +addx6135 add 0 '-5E18' -> '-5.000000000000000E+18' Rounded +addx6136 add 0 '-5E100' -> '-5.000000000000000E+100' Rounded + +-- related +addx6137 add 1 '0E-19' -> '1.000000000000000' Rounded +addx6138 add -1 '0E-19' -> '-1.000000000000000' Rounded +addx6139 add '0E-19' 1 -> '1.000000000000000' Rounded +addx6140 add '0E-19' -1 -> '-1.000000000000000' Rounded +addx6141 add 1E+11 0.0000 -> '100000000000.0000' +addx6142 add 1E+11 0.00000 -> '100000000000.0000' Rounded +addx6143 add 0.000 1E+12 -> '1000000000000.000' +addx6144 add 0.0000 1E+12 -> '1000000000000.000' Rounded + +-- [some of the next group are really constructor tests] +addx6146 add '00.0' 0 -> '0.0' +addx6147 add '0.00' 0 -> '0.00' +addx6148 add 0 '0.00' -> '0.00' +addx6149 add 0 '00.0' -> '0.0' +addx6150 add '00.0' '0.00' -> '0.00' +addx6151 add '0.00' '00.0' -> '0.00' +addx6152 add '3' '.3' -> '3.3' +addx6153 add '3.' '.3' -> '3.3' +addx6154 add '3.0' '.3' -> '3.3' +addx6155 add '3.00' '.3' -> '3.30' +addx6156 add '3' '3' -> '6' +addx6157 add '3' '+3' -> '6' +addx6158 add '3' '-3' -> '0' +addx6159 add '0.3' '-0.3' -> '0.0' +addx6160 add '0.03' '-0.03' -> '0.00' + +-- try borderline precision, with carries, etc. +addx6161 add '1E+13' '-1' -> '9999999999999' +addx6162 add '1E+13' '1.11' -> '10000000000001.11' +addx6163 add '1.11' '1E+13' -> '10000000000001.11' +addx6164 add '-1' '1E+13' -> '9999999999999' +addx6165 add '7E+13' '-1' -> '69999999999999' +addx6166 add '7E+13' '1.11' -> '70000000000001.11' +addx6167 add '1.11' '7E+13' -> '70000000000001.11' +addx6168 add '-1' '7E+13' -> '69999999999999' + +-- 1234567890123456 1234567890123456 1 234567890123456 +addx6170 add '0.4444444444444444' '0.5555555555555563' -> '1.000000000000001' Inexact Rounded +addx6171 add '0.4444444444444444' '0.5555555555555562' -> '1.000000000000001' Inexact Rounded +addx6172 add '0.4444444444444444' '0.5555555555555561' -> '1.000000000000000' Inexact Rounded +addx6173 add '0.4444444444444444' '0.5555555555555560' -> '1.000000000000000' Inexact Rounded +addx6174 add '0.4444444444444444' '0.5555555555555559' -> '1.000000000000000' Inexact Rounded +addx6175 add '0.4444444444444444' '0.5555555555555558' -> '1.000000000000000' Inexact Rounded +addx6176 add '0.4444444444444444' '0.5555555555555557' -> '1.000000000000000' Inexact Rounded +addx6177 add '0.4444444444444444' '0.5555555555555556' -> '1.000000000000000' Rounded +addx6178 add '0.4444444444444444' '0.5555555555555555' -> '0.9999999999999999' +addx6179 add '0.4444444444444444' '0.5555555555555554' -> '0.9999999999999998' +addx6180 add '0.4444444444444444' '0.5555555555555553' -> '0.9999999999999997' +addx6181 add '0.4444444444444444' '0.5555555555555552' -> '0.9999999999999996' +addx6182 add '0.4444444444444444' '0.5555555555555551' -> '0.9999999999999995' +addx6183 add '0.4444444444444444' '0.5555555555555550' -> '0.9999999999999994' + +-- and some more, including residue effects and different roundings +rounding: half_up +addx6200 add '6543210123456789' 0 -> '6543210123456789' +addx6201 add '6543210123456789' 0.000000001 -> '6543210123456789' Inexact Rounded +addx6202 add '6543210123456789' 0.000001 -> '6543210123456789' Inexact Rounded +addx6203 add '6543210123456789' 0.1 -> '6543210123456789' Inexact Rounded +addx6204 add '6543210123456789' 0.4 -> '6543210123456789' Inexact Rounded +addx6205 add '6543210123456789' 0.49 -> '6543210123456789' Inexact Rounded +addx6206 add '6543210123456789' 0.499999 -> '6543210123456789' Inexact Rounded +addx6207 add '6543210123456789' 0.499999999 -> '6543210123456789' Inexact Rounded +addx6208 add '6543210123456789' 0.5 -> '6543210123456790' Inexact Rounded +addx6209 add '6543210123456789' 0.500000001 -> '6543210123456790' Inexact Rounded +addx6210 add '6543210123456789' 0.500001 -> '6543210123456790' Inexact Rounded +addx6211 add '6543210123456789' 0.51 -> '6543210123456790' Inexact Rounded +addx6212 add '6543210123456789' 0.6 -> '6543210123456790' Inexact Rounded +addx6213 add '6543210123456789' 0.9 -> '6543210123456790' Inexact Rounded +addx6214 add '6543210123456789' 0.99999 -> '6543210123456790' Inexact Rounded +addx6215 add '6543210123456789' 0.999999999 -> '6543210123456790' Inexact Rounded +addx6216 add '6543210123456789' 1 -> '6543210123456790' +addx6217 add '6543210123456789' 1.000000001 -> '6543210123456790' Inexact Rounded +addx6218 add '6543210123456789' 1.00001 -> '6543210123456790' Inexact Rounded +addx6219 add '6543210123456789' 1.1 -> '6543210123456790' Inexact Rounded + +rounding: half_even +addx6220 add '6543210123456789' 0 -> '6543210123456789' +addx6221 add '6543210123456789' 0.000000001 -> '6543210123456789' Inexact Rounded +addx6222 add '6543210123456789' 0.000001 -> '6543210123456789' Inexact Rounded +addx6223 add '6543210123456789' 0.1 -> '6543210123456789' Inexact Rounded +addx6224 add '6543210123456789' 0.4 -> '6543210123456789' Inexact Rounded +addx6225 add '6543210123456789' 0.49 -> '6543210123456789' Inexact Rounded +addx6226 add '6543210123456789' 0.499999 -> '6543210123456789' Inexact Rounded +addx6227 add '6543210123456789' 0.499999999 -> '6543210123456789' Inexact Rounded +addx6228 add '6543210123456789' 0.5 -> '6543210123456790' Inexact Rounded +addx6229 add '6543210123456789' 0.500000001 -> '6543210123456790' Inexact Rounded +addx6230 add '6543210123456789' 0.500001 -> '6543210123456790' Inexact Rounded +addx6231 add '6543210123456789' 0.51 -> '6543210123456790' Inexact Rounded +addx6232 add '6543210123456789' 0.6 -> '6543210123456790' Inexact Rounded +addx6233 add '6543210123456789' 0.9 -> '6543210123456790' Inexact Rounded +addx6234 add '6543210123456789' 0.99999 -> '6543210123456790' Inexact Rounded +addx6235 add '6543210123456789' 0.999999999 -> '6543210123456790' Inexact Rounded +addx6236 add '6543210123456789' 1 -> '6543210123456790' +addx6237 add '6543210123456789' 1.00000001 -> '6543210123456790' Inexact Rounded +addx6238 add '6543210123456789' 1.00001 -> '6543210123456790' Inexact Rounded +addx6239 add '6543210123456789' 1.1 -> '6543210123456790' Inexact Rounded +-- critical few with even bottom digit... +addx6240 add '6543210123456788' 0.499999999 -> '6543210123456788' Inexact Rounded +addx6241 add '6543210123456788' 0.5 -> '6543210123456788' Inexact Rounded +addx6242 add '6543210123456788' 0.500000001 -> '6543210123456789' Inexact Rounded + +rounding: down +addx6250 add '6543210123456789' 0 -> '6543210123456789' +addx6251 add '6543210123456789' 0.000000001 -> '6543210123456789' Inexact Rounded +addx6252 add '6543210123456789' 0.000001 -> '6543210123456789' Inexact Rounded +addx6253 add '6543210123456789' 0.1 -> '6543210123456789' Inexact Rounded +addx6254 add '6543210123456789' 0.4 -> '6543210123456789' Inexact Rounded +addx6255 add '6543210123456789' 0.49 -> '6543210123456789' Inexact Rounded +addx6256 add '6543210123456789' 0.499999 -> '6543210123456789' Inexact Rounded +addx6257 add '6543210123456789' 0.499999999 -> '6543210123456789' Inexact Rounded +addx6258 add '6543210123456789' 0.5 -> '6543210123456789' Inexact Rounded +addx6259 add '6543210123456789' 0.500000001 -> '6543210123456789' Inexact Rounded +addx6260 add '6543210123456789' 0.500001 -> '6543210123456789' Inexact Rounded +addx6261 add '6543210123456789' 0.51 -> '6543210123456789' Inexact Rounded +addx6262 add '6543210123456789' 0.6 -> '6543210123456789' Inexact Rounded +addx6263 add '6543210123456789' 0.9 -> '6543210123456789' Inexact Rounded +addx6264 add '6543210123456789' 0.99999 -> '6543210123456789' Inexact Rounded +addx6265 add '6543210123456789' 0.999999999 -> '6543210123456789' Inexact Rounded +addx6266 add '6543210123456789' 1 -> '6543210123456790' +addx6267 add '6543210123456789' 1.00000001 -> '6543210123456790' Inexact Rounded +addx6268 add '6543210123456789' 1.00001 -> '6543210123456790' Inexact Rounded +addx6269 add '6543210123456789' 1.1 -> '6543210123456790' Inexact Rounded + +-- 1 in last place tests +rounding: half_even +addx6301 add -1 1 -> 0 +addx6302 add 0 1 -> 1 +addx6303 add 1 1 -> 2 +addx6304 add 12 1 -> 13 +addx6305 add 98 1 -> 99 +addx6306 add 99 1 -> 100 +addx6307 add 100 1 -> 101 +addx6308 add 101 1 -> 102 +addx6309 add -1 -1 -> -2 +addx6310 add 0 -1 -> -1 +addx6311 add 1 -1 -> 0 +addx6312 add 12 -1 -> 11 +addx6313 add 98 -1 -> 97 +addx6314 add 99 -1 -> 98 +addx6315 add 100 -1 -> 99 +addx6316 add 101 -1 -> 100 + +addx6321 add -0.01 0.01 -> 0.00 +addx6322 add 0.00 0.01 -> 0.01 +addx6323 add 0.01 0.01 -> 0.02 +addx6324 add 0.12 0.01 -> 0.13 +addx6325 add 0.98 0.01 -> 0.99 +addx6326 add 0.99 0.01 -> 1.00 +addx6327 add 1.00 0.01 -> 1.01 +addx6328 add 1.01 0.01 -> 1.02 +addx6329 add -0.01 -0.01 -> -0.02 +addx6330 add 0.00 -0.01 -> -0.01 +addx6331 add 0.01 -0.01 -> 0.00 +addx6332 add 0.12 -0.01 -> 0.11 +addx6333 add 0.98 -0.01 -> 0.97 +addx6334 add 0.99 -0.01 -> 0.98 +addx6335 add 1.00 -0.01 -> 0.99 +addx6336 add 1.01 -0.01 -> 1.00 + +-- some more cases where adding 0 affects the coefficient +addx6340 add 1E+3 0 -> 1000 +addx6341 add 1E+15 0 -> 1000000000000000 +addx6342 add 1E+16 0 -> 1.000000000000000E+16 Rounded +addx6343 add 1E+17 0 -> 1.000000000000000E+17 Rounded +-- which simply follow from these cases ... +addx6344 add 1E+3 1 -> 1001 +addx6345 add 1E+15 1 -> 1000000000000001 +addx6346 add 1E+16 1 -> 1.000000000000000E+16 Inexact Rounded +addx6347 add 1E+17 1 -> 1.000000000000000E+17 Inexact Rounded +addx6348 add 1E+3 7 -> 1007 +addx6349 add 1E+15 7 -> 1000000000000007 +addx6350 add 1E+16 7 -> 1.000000000000001E+16 Inexact Rounded +addx6351 add 1E+17 7 -> 1.000000000000000E+17 Inexact Rounded + +-- tryzeros cases +addx6361 add 0E+50 10000E+1 -> 1.0000E+5 +addx6362 add 10000E+1 0E-50 -> 100000.0000000000 Rounded +addx6363 add 10000E+1 10000E-50 -> 100000.0000000000 Rounded Inexact +addx6364 add 12.34 0e-398 -> 12.34000000000000 Rounded + +-- ulp replacement tests +addx6400 add 1 77e-14 -> 1.00000000000077 +addx6401 add 1 77e-15 -> 1.000000000000077 +addx6402 add 1 77e-16 -> 1.000000000000008 Inexact Rounded +addx6403 add 1 77e-17 -> 1.000000000000001 Inexact Rounded +addx6404 add 1 77e-18 -> 1.000000000000000 Inexact Rounded +addx6405 add 1 77e-19 -> 1.000000000000000 Inexact Rounded +addx6406 add 1 77e-99 -> 1.000000000000000 Inexact Rounded + +addx6410 add 10 77e-14 -> 10.00000000000077 +addx6411 add 10 77e-15 -> 10.00000000000008 Inexact Rounded +addx6412 add 10 77e-16 -> 10.00000000000001 Inexact Rounded +addx6413 add 10 77e-17 -> 10.00000000000000 Inexact Rounded +addx6414 add 10 77e-18 -> 10.00000000000000 Inexact Rounded +addx6415 add 10 77e-19 -> 10.00000000000000 Inexact Rounded +addx6416 add 10 77e-99 -> 10.00000000000000 Inexact Rounded + +addx6420 add 77e-14 1 -> 1.00000000000077 +addx6421 add 77e-15 1 -> 1.000000000000077 +addx6422 add 77e-16 1 -> 1.000000000000008 Inexact Rounded +addx6423 add 77e-17 1 -> 1.000000000000001 Inexact Rounded +addx6424 add 77e-18 1 -> 1.000000000000000 Inexact Rounded +addx6425 add 77e-19 1 -> 1.000000000000000 Inexact Rounded +addx6426 add 77e-99 1 -> 1.000000000000000 Inexact Rounded + +addx6430 add 77e-14 10 -> 10.00000000000077 +addx6431 add 77e-15 10 -> 10.00000000000008 Inexact Rounded +addx6432 add 77e-16 10 -> 10.00000000000001 Inexact Rounded +addx6433 add 77e-17 10 -> 10.00000000000000 Inexact Rounded +addx6434 add 77e-18 10 -> 10.00000000000000 Inexact Rounded +addx6435 add 77e-19 10 -> 10.00000000000000 Inexact Rounded +addx6436 add 77e-99 10 -> 10.00000000000000 Inexact Rounded + +-- negative ulps +addx6440 add 1 -77e-14 -> 0.99999999999923 +addx6441 add 1 -77e-15 -> 0.999999999999923 +addx6442 add 1 -77e-16 -> 0.9999999999999923 +addx6443 add 1 -77e-17 -> 0.9999999999999992 Inexact Rounded +addx6444 add 1 -77e-18 -> 0.9999999999999999 Inexact Rounded +addx6445 add 1 -77e-19 -> 1.000000000000000 Inexact Rounded +addx6446 add 1 -77e-99 -> 1.000000000000000 Inexact Rounded + +addx6450 add 10 -77e-14 -> 9.99999999999923 +addx6451 add 10 -77e-15 -> 9.999999999999923 +addx6452 add 10 -77e-16 -> 9.999999999999992 Inexact Rounded +addx6453 add 10 -77e-17 -> 9.999999999999999 Inexact Rounded +addx6454 add 10 -77e-18 -> 10.00000000000000 Inexact Rounded +addx6455 add 10 -77e-19 -> 10.00000000000000 Inexact Rounded +addx6456 add 10 -77e-99 -> 10.00000000000000 Inexact Rounded + +addx6460 add -77e-14 1 -> 0.99999999999923 +addx6461 add -77e-15 1 -> 0.999999999999923 +addx6462 add -77e-16 1 -> 0.9999999999999923 +addx6463 add -77e-17 1 -> 0.9999999999999992 Inexact Rounded +addx6464 add -77e-18 1 -> 0.9999999999999999 Inexact Rounded +addx6465 add -77e-19 1 -> 1.000000000000000 Inexact Rounded +addx6466 add -77e-99 1 -> 1.000000000000000 Inexact Rounded + +addx6470 add -77e-14 10 -> 9.99999999999923 +addx6471 add -77e-15 10 -> 9.999999999999923 +addx6472 add -77e-16 10 -> 9.999999999999992 Inexact Rounded +addx6473 add -77e-17 10 -> 9.999999999999999 Inexact Rounded +addx6474 add -77e-18 10 -> 10.00000000000000 Inexact Rounded +addx6475 add -77e-19 10 -> 10.00000000000000 Inexact Rounded +addx6476 add -77e-99 10 -> 10.00000000000000 Inexact Rounded + +-- negative ulps +addx6480 add -1 77e-14 -> -0.99999999999923 +addx6481 add -1 77e-15 -> -0.999999999999923 +addx6482 add -1 77e-16 -> -0.9999999999999923 +addx6483 add -1 77e-17 -> -0.9999999999999992 Inexact Rounded +addx6484 add -1 77e-18 -> -0.9999999999999999 Inexact Rounded +addx6485 add -1 77e-19 -> -1.000000000000000 Inexact Rounded +addx6486 add -1 77e-99 -> -1.000000000000000 Inexact Rounded + +addx6490 add -10 77e-14 -> -9.99999999999923 +addx6491 add -10 77e-15 -> -9.999999999999923 +addx6492 add -10 77e-16 -> -9.999999999999992 Inexact Rounded +addx6493 add -10 77e-17 -> -9.999999999999999 Inexact Rounded +addx6494 add -10 77e-18 -> -10.00000000000000 Inexact Rounded +addx6495 add -10 77e-19 -> -10.00000000000000 Inexact Rounded +addx6496 add -10 77e-99 -> -10.00000000000000 Inexact Rounded + +addx6500 add 77e-14 -1 -> -0.99999999999923 +addx6501 add 77e-15 -1 -> -0.999999999999923 +addx6502 add 77e-16 -1 -> -0.9999999999999923 +addx6503 add 77e-17 -1 -> -0.9999999999999992 Inexact Rounded +addx6504 add 77e-18 -1 -> -0.9999999999999999 Inexact Rounded +addx6505 add 77e-19 -1 -> -1.000000000000000 Inexact Rounded +addx6506 add 77e-99 -1 -> -1.000000000000000 Inexact Rounded + +addx6510 add 77e-14 -10 -> -9.99999999999923 +addx6511 add 77e-15 -10 -> -9.999999999999923 +addx6512 add 77e-16 -10 -> -9.999999999999992 Inexact Rounded +addx6513 add 77e-17 -10 -> -9.999999999999999 Inexact Rounded +addx6514 add 77e-18 -10 -> -10.00000000000000 Inexact Rounded +addx6515 add 77e-19 -10 -> -10.00000000000000 Inexact Rounded +addx6516 add 77e-99 -10 -> -10.00000000000000 Inexact Rounded +-- long operands +addx6521 add 101234562345678000 0 -> 1.012345623456780E+17 Rounded +addx6522 add 0 101234562345678000 -> 1.012345623456780E+17 Rounded +addx6523 add 10123456234567800 0 -> 1.012345623456780E+16 Rounded +addx6524 add 0 10123456234567800 -> 1.012345623456780E+16 Rounded +addx6525 add 10123456234567890 0 -> 1.012345623456789E+16 Rounded +addx6526 add 0 10123456234567890 -> 1.012345623456789E+16 Rounded +addx6527 add 10123456234567891 0 -> 1.012345623456789E+16 Inexact Rounded +addx6528 add 0 10123456234567891 -> 1.012345623456789E+16 Inexact Rounded +addx6529 add 101234562345678901 0 -> 1.012345623456789E+17 Inexact Rounded +addx6530 add 0 101234562345678901 -> 1.012345623456789E+17 Inexact Rounded +addx6531 add 10123456234567896 0 -> 1.012345623456790E+16 Inexact Rounded +addx6532 add 0 10123456234567896 -> 1.012345623456790E+16 Inexact Rounded + +-- verify a query +rounding: down +addx6561 add 1e-398 9.000000000000000E+384 -> 9.000000000000000E+384 Inexact Rounded +addx6562 add 0 9.000000000000000E+384 -> 9.000000000000000E+384 Rounded +-- and using decimal64 bounds... +rounding: down +addx6563 add 1e-388 9.000000000000000E+374 -> 9.000000000000000E+374 Inexact Rounded +addx6564 add 0 9.000000000000000E+374 -> 9.000000000000000E+374 Rounded + +-- more zeros, etc. +rounding: half_even + +addx6701 add 5.00 1.00E-3 -> 5.00100 +addx6702 add 00.00 0.000 -> 0.000 +addx6703 add 00.00 0E-3 -> 0.000 +addx6704 add 0E-3 00.00 -> 0.000 + +addx6710 add 0E+3 00.00 -> 0.00 +addx6711 add 0E+3 00.0 -> 0.0 +addx6712 add 0E+3 00. -> 0 +addx6713 add 0E+3 00.E+1 -> 0E+1 +addx6714 add 0E+3 00.E+2 -> 0E+2 +addx6715 add 0E+3 00.E+3 -> 0E+3 +addx6716 add 0E+3 00.E+4 -> 0E+3 +addx6717 add 0E+3 00.E+5 -> 0E+3 +addx6718 add 0E+3 -00.0 -> 0.0 +addx6719 add 0E+3 -00. -> 0 +addx6731 add 0E+3 -00.E+1 -> 0E+1 + +addx6720 add 00.00 0E+3 -> 0.00 +addx6721 add 00.0 0E+3 -> 0.0 +addx6722 add 00. 0E+3 -> 0 +addx6723 add 00.E+1 0E+3 -> 0E+1 +addx6724 add 00.E+2 0E+3 -> 0E+2 +addx6725 add 00.E+3 0E+3 -> 0E+3 +addx6726 add 00.E+4 0E+3 -> 0E+3 +addx6727 add 00.E+5 0E+3 -> 0E+3 +addx6728 add -00.00 0E+3 -> 0.00 +addx6729 add -00.0 0E+3 -> 0.0 +addx6730 add -00. 0E+3 -> 0 + +addx6732 add 0 0 -> 0 +addx6733 add 0 -0 -> 0 +addx6734 add -0 0 -> 0 +addx6735 add -0 -0 -> -0 -- IEEE 854 special case + +addx6736 add 1 -1 -> 0 +addx6737 add -1 -1 -> -2 +addx6738 add 1 1 -> 2 +addx6739 add -1 1 -> 0 + +addx6741 add 0 -1 -> -1 +addx6742 add -0 -1 -> -1 +addx6743 add 0 1 -> 1 +addx6744 add -0 1 -> 1 +addx6745 add -1 0 -> -1 +addx6746 add -1 -0 -> -1 +addx6747 add 1 0 -> 1 +addx6748 add 1 -0 -> 1 + +addx6751 add 0.0 -1 -> -1.0 +addx6752 add -0.0 -1 -> -1.0 +addx6753 add 0.0 1 -> 1.0 +addx6754 add -0.0 1 -> 1.0 +addx6755 add -1.0 0 -> -1.0 +addx6756 add -1.0 -0 -> -1.0 +addx6757 add 1.0 0 -> 1.0 +addx6758 add 1.0 -0 -> 1.0 + +addx6761 add 0 -1.0 -> -1.0 +addx6762 add -0 -1.0 -> -1.0 +addx6763 add 0 1.0 -> 1.0 +addx6764 add -0 1.0 -> 1.0 +addx6765 add -1 0.0 -> -1.0 +addx6766 add -1 -0.0 -> -1.0 +addx6767 add 1 0.0 -> 1.0 +addx6768 add 1 -0.0 -> 1.0 + +addx6771 add 0.0 -1.0 -> -1.0 +addx6772 add -0.0 -1.0 -> -1.0 +addx6773 add 0.0 1.0 -> 1.0 +addx6774 add -0.0 1.0 -> 1.0 +addx6775 add -1.0 0.0 -> -1.0 +addx6776 add -1.0 -0.0 -> -1.0 +addx6777 add 1.0 0.0 -> 1.0 +addx6778 add 1.0 -0.0 -> 1.0 + +-- Specials +addx6780 add -Inf -Inf -> -Infinity +addx6781 add -Inf -1000 -> -Infinity +addx6782 add -Inf -1 -> -Infinity +addx6783 add -Inf -0 -> -Infinity +addx6784 add -Inf 0 -> -Infinity +addx6785 add -Inf 1 -> -Infinity +addx6786 add -Inf 1000 -> -Infinity +addx6787 add -1000 -Inf -> -Infinity +addx6788 add -Inf -Inf -> -Infinity +addx6789 add -1 -Inf -> -Infinity +addx6790 add -0 -Inf -> -Infinity +addx6791 add 0 -Inf -> -Infinity +addx6792 add 1 -Inf -> -Infinity +addx6793 add 1000 -Inf -> -Infinity +addx6794 add Inf -Inf -> NaN Invalid_operation + +addx6800 add Inf -Inf -> NaN Invalid_operation +addx6801 add Inf -1000 -> Infinity +addx6802 add Inf -1 -> Infinity +addx6803 add Inf -0 -> Infinity +addx6804 add Inf 0 -> Infinity +addx6805 add Inf 1 -> Infinity +addx6806 add Inf 1000 -> Infinity +addx6807 add Inf Inf -> Infinity +addx6808 add -1000 Inf -> Infinity +addx6809 add -Inf Inf -> NaN Invalid_operation +addx6810 add -1 Inf -> Infinity +addx6811 add -0 Inf -> Infinity +addx6812 add 0 Inf -> Infinity +addx6813 add 1 Inf -> Infinity +addx6814 add 1000 Inf -> Infinity +addx6815 add Inf Inf -> Infinity + +addx6821 add NaN -Inf -> NaN +addx6822 add NaN -1000 -> NaN +addx6823 add NaN -1 -> NaN +addx6824 add NaN -0 -> NaN +addx6825 add NaN 0 -> NaN +addx6826 add NaN 1 -> NaN +addx6827 add NaN 1000 -> NaN +addx6828 add NaN Inf -> NaN +addx6829 add NaN NaN -> NaN +addx6830 add -Inf NaN -> NaN +addx6831 add -1000 NaN -> NaN +addx6832 add -1 NaN -> NaN +addx6833 add -0 NaN -> NaN +addx6834 add 0 NaN -> NaN +addx6835 add 1 NaN -> NaN +addx6836 add 1000 NaN -> NaN +addx6837 add Inf NaN -> NaN + +addx6841 add sNaN -Inf -> NaN Invalid_operation +addx6842 add sNaN -1000 -> NaN Invalid_operation +addx6843 add sNaN -1 -> NaN Invalid_operation +addx6844 add sNaN -0 -> NaN Invalid_operation +addx6845 add sNaN 0 -> NaN Invalid_operation +addx6846 add sNaN 1 -> NaN Invalid_operation +addx6847 add sNaN 1000 -> NaN Invalid_operation +addx6848 add sNaN NaN -> NaN Invalid_operation +addx6849 add sNaN sNaN -> NaN Invalid_operation +addx6850 add NaN sNaN -> NaN Invalid_operation +addx6851 add -Inf sNaN -> NaN Invalid_operation +addx6852 add -1000 sNaN -> NaN Invalid_operation +addx6853 add -1 sNaN -> NaN Invalid_operation +addx6854 add -0 sNaN -> NaN Invalid_operation +addx6855 add 0 sNaN -> NaN Invalid_operation +addx6856 add 1 sNaN -> NaN Invalid_operation +addx6857 add 1000 sNaN -> NaN Invalid_operation +addx6858 add Inf sNaN -> NaN Invalid_operation +addx6859 add NaN sNaN -> NaN Invalid_operation + +-- propagating NaNs +addx6861 add NaN1 -Inf -> NaN1 +addx6862 add +NaN2 -1000 -> NaN2 +addx6863 add NaN3 1000 -> NaN3 +addx6864 add NaN4 Inf -> NaN4 +addx6865 add NaN5 +NaN6 -> NaN5 +addx6866 add -Inf NaN7 -> NaN7 +addx6867 add -1000 NaN8 -> NaN8 +addx6868 add 1000 NaN9 -> NaN9 +addx6869 add Inf +NaN10 -> NaN10 +addx6871 add sNaN11 -Inf -> NaN11 Invalid_operation +addx6872 add sNaN12 -1000 -> NaN12 Invalid_operation +addx6873 add sNaN13 1000 -> NaN13 Invalid_operation +addx6874 add sNaN14 NaN17 -> NaN14 Invalid_operation +addx6875 add sNaN15 sNaN18 -> NaN15 Invalid_operation +addx6876 add NaN16 sNaN19 -> NaN19 Invalid_operation +addx6877 add -Inf +sNaN20 -> NaN20 Invalid_operation +addx6878 add -1000 sNaN21 -> NaN21 Invalid_operation +addx6879 add 1000 sNaN22 -> NaN22 Invalid_operation +addx6880 add Inf sNaN23 -> NaN23 Invalid_operation +addx6881 add +NaN25 +sNaN24 -> NaN24 Invalid_operation +addx6882 add -NaN26 NaN28 -> -NaN26 +addx6883 add -sNaN27 sNaN29 -> -NaN27 Invalid_operation +addx6884 add 1000 -NaN30 -> -NaN30 +addx6885 add 1000 -sNaN31 -> -NaN31 Invalid_operation + +-- now the case where we can get underflow but the result is normal +-- [note this can't happen if the operands are also bounded, as we +-- cannot represent 1E-399, for example] + +addx6571 add 1E-383 0 -> 1E-383 +addx6572 add 1E-384 0 -> 1E-384 Subnormal +addx6573 add 1E-383 1E-384 -> 1.1E-383 +addx6574 subtract 1E-383 1E-384 -> 9E-384 Subnormal + +-- Here we explore the boundary of rounding a subnormal to Nmin +addx6575 subtract 1E-383 1E-398 -> 9.99999999999999E-384 Subnormal +addx6576 subtract 1E-383 1E-398 -> 9.99999999999999E-384 Subnormal +addx6577 subtract 1E-383 1E-399 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +addx6578 subtract 1E-383 1E-400 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +addx6579 subtract 1E-383 1E-401 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +addx6580 subtract 1E-383 1E-402 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded + +-- check overflow edge case +-- 1234567890123456 +addx6972 apply 9.999999999999999E+384 -> 9.999999999999999E+384 +addx6973 add 9.999999999999999E+384 1 -> 9.999999999999999E+384 Inexact Rounded +addx6974 add 9999999999999999E+369 1 -> 9.999999999999999E+384 Inexact Rounded +addx6975 add 9999999999999999E+369 1E+369 -> Infinity Overflow Inexact Rounded +addx6976 add 9999999999999999E+369 9E+368 -> Infinity Overflow Inexact Rounded +addx6977 add 9999999999999999E+369 8E+368 -> Infinity Overflow Inexact Rounded +addx6978 add 9999999999999999E+369 7E+368 -> Infinity Overflow Inexact Rounded +addx6979 add 9999999999999999E+369 6E+368 -> Infinity Overflow Inexact Rounded +addx6980 add 9999999999999999E+369 5E+368 -> Infinity Overflow Inexact Rounded +addx6981 add 9999999999999999E+369 4E+368 -> 9.999999999999999E+384 Inexact Rounded +addx6982 add 9999999999999999E+369 3E+368 -> 9.999999999999999E+384 Inexact Rounded +addx6983 add 9999999999999999E+369 2E+368 -> 9.999999999999999E+384 Inexact Rounded +addx6984 add 9999999999999999E+369 1E+368 -> 9.999999999999999E+384 Inexact Rounded + +addx6985 apply -9.999999999999999E+384 -> -9.999999999999999E+384 +addx6986 add -9.999999999999999E+384 -1 -> -9.999999999999999E+384 Inexact Rounded +addx6987 add -9999999999999999E+369 -1 -> -9.999999999999999E+384 Inexact Rounded +addx6988 add -9999999999999999E+369 -1E+369 -> -Infinity Overflow Inexact Rounded +addx6989 add -9999999999999999E+369 -9E+368 -> -Infinity Overflow Inexact Rounded +addx6990 add -9999999999999999E+369 -8E+368 -> -Infinity Overflow Inexact Rounded +addx6991 add -9999999999999999E+369 -7E+368 -> -Infinity Overflow Inexact Rounded +addx6992 add -9999999999999999E+369 -6E+368 -> -Infinity Overflow Inexact Rounded +addx6993 add -9999999999999999E+369 -5E+368 -> -Infinity Overflow Inexact Rounded +addx6994 add -9999999999999999E+369 -4E+368 -> -9.999999999999999E+384 Inexact Rounded +addx6995 add -9999999999999999E+369 -3E+368 -> -9.999999999999999E+384 Inexact Rounded +addx6996 add -9999999999999999E+369 -2E+368 -> -9.999999999999999E+384 Inexact Rounded +addx6997 add -9999999999999999E+369 -1E+368 -> -9.999999999999999E+384 Inexact Rounded + +-- And for round down full and subnormal results +rounding: down +addx61100 add 1e+2 -1e-383 -> 99.99999999999999 Rounded Inexact +addx61101 add 1e+1 -1e-383 -> 9.999999999999999 Rounded Inexact +addx61103 add +1 -1e-383 -> 0.9999999999999999 Rounded Inexact +addx61104 add 1e-1 -1e-383 -> 0.09999999999999999 Rounded Inexact +addx61105 add 1e-2 -1e-383 -> 0.009999999999999999 Rounded Inexact +addx61106 add 1e-3 -1e-383 -> 0.0009999999999999999 Rounded Inexact +addx61107 add 1e-4 -1e-383 -> 0.00009999999999999999 Rounded Inexact +addx61108 add 1e-5 -1e-383 -> 0.000009999999999999999 Rounded Inexact +addx61109 add 1e-6 -1e-383 -> 9.999999999999999E-7 Rounded Inexact + +rounding: ceiling +addx61110 add -1e+2 +1e-383 -> -99.99999999999999 Rounded Inexact +addx61111 add -1e+1 +1e-383 -> -9.999999999999999 Rounded Inexact +addx61113 add -1 +1e-383 -> -0.9999999999999999 Rounded Inexact +addx61114 add -1e-1 +1e-383 -> -0.09999999999999999 Rounded Inexact +addx61115 add -1e-2 +1e-383 -> -0.009999999999999999 Rounded Inexact +addx61116 add -1e-3 +1e-383 -> -0.0009999999999999999 Rounded Inexact +addx61117 add -1e-4 +1e-383 -> -0.00009999999999999999 Rounded Inexact +addx61118 add -1e-5 +1e-383 -> -0.000009999999999999999 Rounded Inexact +addx61119 add -1e-6 +1e-383 -> -9.999999999999999E-7 Rounded Inexact + +-- tests based on Gunnar Degnbol's edge case +rounding: half_even + +addx61300 add 1E16 -0.5 -> 1.000000000000000E+16 Inexact Rounded +addx61310 add 1E16 -0.51 -> 9999999999999999 Inexact Rounded +addx61311 add 1E16 -0.501 -> 9999999999999999 Inexact Rounded +addx61312 add 1E16 -0.5001 -> 9999999999999999 Inexact Rounded +addx61313 add 1E16 -0.50001 -> 9999999999999999 Inexact Rounded +addx61314 add 1E16 -0.500001 -> 9999999999999999 Inexact Rounded +addx61315 add 1E16 -0.5000001 -> 9999999999999999 Inexact Rounded +addx61316 add 1E16 -0.50000001 -> 9999999999999999 Inexact Rounded +addx61317 add 1E16 -0.500000001 -> 9999999999999999 Inexact Rounded +addx61318 add 1E16 -0.5000000001 -> 9999999999999999 Inexact Rounded +addx61319 add 1E16 -0.50000000001 -> 9999999999999999 Inexact Rounded +addx61320 add 1E16 -0.500000000001 -> 9999999999999999 Inexact Rounded +addx61321 add 1E16 -0.5000000000001 -> 9999999999999999 Inexact Rounded +addx61322 add 1E16 -0.50000000000001 -> 9999999999999999 Inexact Rounded +addx61323 add 1E16 -0.500000000000001 -> 9999999999999999 Inexact Rounded +addx61324 add 1E16 -0.5000000000000001 -> 9999999999999999 Inexact Rounded +addx61325 add 1E16 -0.5000000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61326 add 1E16 -0.500000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61327 add 1E16 -0.50000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61328 add 1E16 -0.5000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61329 add 1E16 -0.500000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61330 add 1E16 -0.50000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61331 add 1E16 -0.5000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61332 add 1E16 -0.500000000 -> 1.000000000000000E+16 Inexact Rounded +addx61333 add 1E16 -0.50000000 -> 1.000000000000000E+16 Inexact Rounded +addx61334 add 1E16 -0.5000000 -> 1.000000000000000E+16 Inexact Rounded +addx61335 add 1E16 -0.500000 -> 1.000000000000000E+16 Inexact Rounded +addx61336 add 1E16 -0.50000 -> 1.000000000000000E+16 Inexact Rounded +addx61337 add 1E16 -0.5000 -> 1.000000000000000E+16 Inexact Rounded +addx61338 add 1E16 -0.500 -> 1.000000000000000E+16 Inexact Rounded +addx61339 add 1E16 -0.50 -> 1.000000000000000E+16 Inexact Rounded + +addx61340 add 1E16 -5000000.000010001 -> 9999999995000000 Inexact Rounded +addx61341 add 1E16 -5000000.000000001 -> 9999999995000000 Inexact Rounded + +addx61349 add 9999999999999999 0.4 -> 9999999999999999 Inexact Rounded +addx61350 add 9999999999999999 0.49 -> 9999999999999999 Inexact Rounded +addx61351 add 9999999999999999 0.499 -> 9999999999999999 Inexact Rounded +addx61352 add 9999999999999999 0.4999 -> 9999999999999999 Inexact Rounded +addx61353 add 9999999999999999 0.49999 -> 9999999999999999 Inexact Rounded +addx61354 add 9999999999999999 0.499999 -> 9999999999999999 Inexact Rounded +addx61355 add 9999999999999999 0.4999999 -> 9999999999999999 Inexact Rounded +addx61356 add 9999999999999999 0.49999999 -> 9999999999999999 Inexact Rounded +addx61357 add 9999999999999999 0.499999999 -> 9999999999999999 Inexact Rounded +addx61358 add 9999999999999999 0.4999999999 -> 9999999999999999 Inexact Rounded +addx61359 add 9999999999999999 0.49999999999 -> 9999999999999999 Inexact Rounded +addx61360 add 9999999999999999 0.499999999999 -> 9999999999999999 Inexact Rounded +addx61361 add 9999999999999999 0.4999999999999 -> 9999999999999999 Inexact Rounded +addx61362 add 9999999999999999 0.49999999999999 -> 9999999999999999 Inexact Rounded +addx61363 add 9999999999999999 0.499999999999999 -> 9999999999999999 Inexact Rounded +addx61364 add 9999999999999999 0.4999999999999999 -> 9999999999999999 Inexact Rounded +addx61365 add 9999999999999999 0.5000000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61367 add 9999999999999999 0.500000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61368 add 9999999999999999 0.50000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61369 add 9999999999999999 0.5000000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61370 add 9999999999999999 0.500000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61371 add 9999999999999999 0.50000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61372 add 9999999999999999 0.5000000000 -> 1.000000000000000E+16 Inexact Rounded +addx61373 add 9999999999999999 0.500000000 -> 1.000000000000000E+16 Inexact Rounded +addx61374 add 9999999999999999 0.50000000 -> 1.000000000000000E+16 Inexact Rounded +addx61375 add 9999999999999999 0.5000000 -> 1.000000000000000E+16 Inexact Rounded +addx61376 add 9999999999999999 0.500000 -> 1.000000000000000E+16 Inexact Rounded +addx61377 add 9999999999999999 0.50000 -> 1.000000000000000E+16 Inexact Rounded +addx61378 add 9999999999999999 0.5000 -> 1.000000000000000E+16 Inexact Rounded +addx61379 add 9999999999999999 0.500 -> 1.000000000000000E+16 Inexact Rounded +addx61380 add 9999999999999999 0.50 -> 1.000000000000000E+16 Inexact Rounded +addx61381 add 9999999999999999 0.5 -> 1.000000000000000E+16 Inexact Rounded +addx61382 add 9999999999999999 0.5000000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61383 add 9999999999999999 0.500000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61384 add 9999999999999999 0.50000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61385 add 9999999999999999 0.5000000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61386 add 9999999999999999 0.500000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61387 add 9999999999999999 0.50000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61388 add 9999999999999999 0.5000000001 -> 1.000000000000000E+16 Inexact Rounded +addx61389 add 9999999999999999 0.500000001 -> 1.000000000000000E+16 Inexact Rounded +addx61390 add 9999999999999999 0.50000001 -> 1.000000000000000E+16 Inexact Rounded +addx61391 add 9999999999999999 0.5000001 -> 1.000000000000000E+16 Inexact Rounded +addx61392 add 9999999999999999 0.500001 -> 1.000000000000000E+16 Inexact Rounded +addx61393 add 9999999999999999 0.50001 -> 1.000000000000000E+16 Inexact Rounded +addx61394 add 9999999999999999 0.5001 -> 1.000000000000000E+16 Inexact Rounded +addx61395 add 9999999999999999 0.501 -> 1.000000000000000E+16 Inexact Rounded +addx61396 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 +addx61420 add 0 1.123456789012345 -> 1.123456789012345 +addx61421 add 0 1.123456789012345E-1 -> 0.1123456789012345 +addx61422 add 0 1.123456789012345E-2 -> 0.01123456789012345 +addx61423 add 0 1.123456789012345E-3 -> 0.001123456789012345 +addx61424 add 0 1.123456789012345E-4 -> 0.0001123456789012345 +addx61425 add 0 1.123456789012345E-5 -> 0.00001123456789012345 +addx61426 add 0 1.123456789012345E-6 -> 0.000001123456789012345 +addx61427 add 0 1.123456789012345E-7 -> 1.123456789012345E-7 +addx61428 add 0 1.123456789012345E-8 -> 1.123456789012345E-8 +addx61429 add 0 1.123456789012345E-9 -> 1.123456789012345E-9 +addx61430 add 0 1.123456789012345E-10 -> 1.123456789012345E-10 +addx61431 add 0 1.123456789012345E-11 -> 1.123456789012345E-11 +addx61432 add 0 1.123456789012345E-12 -> 1.123456789012345E-12 +addx61433 add 0 1.123456789012345E-13 -> 1.123456789012345E-13 +addx61434 add 0 1.123456789012345E-14 -> 1.123456789012345E-14 +addx61435 add 0 1.123456789012345E-15 -> 1.123456789012345E-15 +addx61436 add 0 1.123456789012345E-16 -> 1.123456789012345E-16 +addx61437 add 0 1.123456789012345E-17 -> 1.123456789012345E-17 +addx61438 add 0 1.123456789012345E-18 -> 1.123456789012345E-18 +addx61439 add 0 1.123456789012345E-19 -> 1.123456789012345E-19 + +-- same, reversed 0 +addx61440 add 1.123456789012345 0 -> 1.123456789012345 +addx61441 add 1.123456789012345E-1 0 -> 0.1123456789012345 +addx61442 add 1.123456789012345E-2 0 -> 0.01123456789012345 +addx61443 add 1.123456789012345E-3 0 -> 0.001123456789012345 +addx61444 add 1.123456789012345E-4 0 -> 0.0001123456789012345 +addx61445 add 1.123456789012345E-5 0 -> 0.00001123456789012345 +addx61446 add 1.123456789012345E-6 0 -> 0.000001123456789012345 +addx61447 add 1.123456789012345E-7 0 -> 1.123456789012345E-7 +addx61448 add 1.123456789012345E-8 0 -> 1.123456789012345E-8 +addx61449 add 1.123456789012345E-9 0 -> 1.123456789012345E-9 +addx61450 add 1.123456789012345E-10 0 -> 1.123456789012345E-10 +addx61451 add 1.123456789012345E-11 0 -> 1.123456789012345E-11 +addx61452 add 1.123456789012345E-12 0 -> 1.123456789012345E-12 +addx61453 add 1.123456789012345E-13 0 -> 1.123456789012345E-13 +addx61454 add 1.123456789012345E-14 0 -> 1.123456789012345E-14 +addx61455 add 1.123456789012345E-15 0 -> 1.123456789012345E-15 +addx61456 add 1.123456789012345E-16 0 -> 1.123456789012345E-16 +addx61457 add 1.123456789012345E-17 0 -> 1.123456789012345E-17 +addx61458 add 1.123456789012345E-18 0 -> 1.123456789012345E-18 +addx61459 add 1.123456789012345E-19 0 -> 1.123456789012345E-19 + +-- same, Es on the 0 +addx61460 add 1.123456789012345 0E-0 -> 1.123456789012345 +addx61461 add 1.123456789012345 0E-1 -> 1.123456789012345 +addx61462 add 1.123456789012345 0E-2 -> 1.123456789012345 +addx61463 add 1.123456789012345 0E-3 -> 1.123456789012345 +addx61464 add 1.123456789012345 0E-4 -> 1.123456789012345 +addx61465 add 1.123456789012345 0E-5 -> 1.123456789012345 +addx61466 add 1.123456789012345 0E-6 -> 1.123456789012345 +addx61467 add 1.123456789012345 0E-7 -> 1.123456789012345 +addx61468 add 1.123456789012345 0E-8 -> 1.123456789012345 +addx61469 add 1.123456789012345 0E-9 -> 1.123456789012345 +addx61470 add 1.123456789012345 0E-10 -> 1.123456789012345 +addx61471 add 1.123456789012345 0E-11 -> 1.123456789012345 +addx61472 add 1.123456789012345 0E-12 -> 1.123456789012345 +addx61473 add 1.123456789012345 0E-13 -> 1.123456789012345 +addx61474 add 1.123456789012345 0E-14 -> 1.123456789012345 +addx61475 add 1.123456789012345 0E-15 -> 1.123456789012345 +-- next four flag Rounded because the 0 extends the result +addx61476 add 1.123456789012345 0E-16 -> 1.123456789012345 Rounded +addx61477 add 1.123456789012345 0E-17 -> 1.123456789012345 Rounded +addx61478 add 1.123456789012345 0E-18 -> 1.123456789012345 Rounded +addx61479 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 +addx61500 add 0 0E-19 -> 0E-19 +addx61501 add -0 0E-19 -> 0E-19 +addx61502 add 0 -0E-19 -> 0E-19 +addx61503 add -0 -0E-19 -> -0E-19 +addx61504 add 0E-400 0E-19 -> 0E-398 Clamped +addx61505 add -0E-400 0E-19 -> 0E-398 Clamped +addx61506 add 0E-400 -0E-19 -> 0E-398 Clamped +addx61507 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61511 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61512 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61513 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61514 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx61515 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61516 add -1E-401 1E-401 -> 0E-398 Clamped +addx61517 add 1E-401 -1E-401 -> 0E-398 Clamped +addx61518 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: half_down +-- exact zeros from zeros +addx61520 add 0 0E-19 -> 0E-19 +addx61521 add -0 0E-19 -> 0E-19 +addx61522 add 0 -0E-19 -> 0E-19 +addx61523 add -0 -0E-19 -> -0E-19 +addx61524 add 0E-400 0E-19 -> 0E-398 Clamped +addx61525 add -0E-400 0E-19 -> 0E-398 Clamped +addx61526 add 0E-400 -0E-19 -> 0E-398 Clamped +addx61527 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61531 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61532 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61533 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61534 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx61535 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61536 add -1E-401 1E-401 -> 0E-398 Clamped +addx61537 add 1E-401 -1E-401 -> 0E-398 Clamped +addx61538 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: half_even +-- exact zeros from zeros +addx61540 add 0 0E-19 -> 0E-19 +addx61541 add -0 0E-19 -> 0E-19 +addx61542 add 0 -0E-19 -> 0E-19 +addx61543 add -0 -0E-19 -> -0E-19 +addx61544 add 0E-400 0E-19 -> 0E-398 Clamped +addx61545 add -0E-400 0E-19 -> 0E-398 Clamped +addx61546 add 0E-400 -0E-19 -> 0E-398 Clamped +addx61547 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61551 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61552 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61553 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61554 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx61555 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61556 add -1E-401 1E-401 -> 0E-398 Clamped +addx61557 add 1E-401 -1E-401 -> 0E-398 Clamped +addx61558 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: up +-- exact zeros from zeros +addx61560 add 0 0E-19 -> 0E-19 +addx61561 add -0 0E-19 -> 0E-19 +addx61562 add 0 -0E-19 -> 0E-19 +addx61563 add -0 -0E-19 -> -0E-19 +addx61564 add 0E-400 0E-19 -> 0E-398 Clamped +addx61565 add -0E-400 0E-19 -> 0E-398 Clamped +addx61566 add 0E-400 -0E-19 -> 0E-398 Clamped +addx61567 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61571 add 1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx61572 add -1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx61573 add 1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +addx61574 add -1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +-- some exact zeros from non-zeros +addx61575 add 1E-401 1E-401 -> 1E-398 Subnormal Inexact Rounded Underflow +addx61576 add -1E-401 1E-401 -> 0E-398 Clamped +addx61577 add 1E-401 -1E-401 -> 0E-398 Clamped +addx61578 add -1E-401 -1E-401 -> -1E-398 Subnormal Inexact Rounded Underflow + +rounding: down +-- exact zeros from zeros +addx61580 add 0 0E-19 -> 0E-19 +addx61581 add -0 0E-19 -> 0E-19 +addx61582 add 0 -0E-19 -> 0E-19 +addx61583 add -0 -0E-19 -> -0E-19 +addx61584 add 0E-400 0E-19 -> 0E-398 Clamped +addx61585 add -0E-400 0E-19 -> 0E-398 Clamped +addx61586 add 0E-400 -0E-19 -> 0E-398 Clamped +addx61587 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61591 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61592 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61593 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61594 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx61595 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61596 add -1E-401 1E-401 -> 0E-398 Clamped +addx61597 add 1E-401 -1E-401 -> 0E-398 Clamped +addx61598 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +rounding: ceiling +-- exact zeros from zeros +addx61600 add 0 0E-19 -> 0E-19 +addx61601 add -0 0E-19 -> 0E-19 +addx61602 add 0 -0E-19 -> 0E-19 +addx61603 add -0 -0E-19 -> -0E-19 +addx61604 add 0E-400 0E-19 -> 0E-398 Clamped +addx61605 add -0E-400 0E-19 -> 0E-398 Clamped +addx61606 add 0E-400 -0E-19 -> 0E-398 Clamped +addx61607 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61611 add 1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx61612 add -1E-401 1E-400 -> 1E-398 Subnormal Inexact Rounded Underflow +addx61613 add 1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61614 add -1E-401 -1E-400 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped +-- some exact zeros from non-zeros +addx61615 add 1E-401 1E-401 -> 1E-398 Subnormal Inexact Rounded Underflow +addx61616 add -1E-401 1E-401 -> 0E-398 Clamped +addx61617 add 1E-401 -1E-401 -> 0E-398 Clamped +addx61618 add -1E-401 -1E-401 -> -0E-398 Subnormal Inexact Rounded Underflow Clamped + +-- and the extra-special ugly case; unusual minuses marked by -- * +rounding: floor +-- exact zeros from zeros +addx61620 add 0 0E-19 -> 0E-19 +addx61621 add -0 0E-19 -> -0E-19 -- * +addx61622 add 0 -0E-19 -> -0E-19 -- * +addx61623 add -0 -0E-19 -> -0E-19 +addx61624 add 0E-400 0E-19 -> 0E-398 Clamped +addx61625 add -0E-400 0E-19 -> -0E-398 Clamped -- * +addx61626 add 0E-400 -0E-19 -> -0E-398 Clamped -- * +addx61627 add -0E-400 -0E-19 -> -0E-398 Clamped +-- inexact zeros +addx61631 add 1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61632 add -1E-401 1E-400 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61633 add 1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +addx61634 add -1E-401 -1E-400 -> -1E-398 Subnormal Inexact Rounded Underflow +-- some exact zeros from non-zeros +addx61635 add 1E-401 1E-401 -> 0E-398 Subnormal Inexact Rounded Underflow Clamped +addx61636 add -1E-401 1E-401 -> -0E-398 Clamped -- * +addx61637 add 1E-401 -1E-401 -> -0E-398 Clamped -- * +addx61638 add -1E-401 -1E-401 -> -1E-398 Subnormal Inexact Rounded Underflow + +-- Examples from SQL proposal (Krishna Kulkarni) +addx61701 add 130E-2 120E-2 -> 2.50 +addx61702 add 130E-2 12E-1 -> 2.50 +addx61703 add 130E-2 1E0 -> 2.30 +addx61704 add 1E2 1E4 -> 1.01E+4 +addx61705 subtract 130E-2 120E-2 -> 0.10 +addx61706 subtract 130E-2 12E-1 -> 0.10 +addx61707 subtract 130E-2 1E0 -> 0.30 +addx61708 subtract 1E2 1E4 -> -9.9E+3 + +-- Gappy coefficients; check residue handling even with full coefficient gap +rounding: half_even + +addx62001 add 1234567890123456 1 -> 1234567890123457 +addx62002 add 1234567890123456 0.6 -> 1234567890123457 Inexact Rounded +addx62003 add 1234567890123456 0.06 -> 1234567890123456 Inexact Rounded +addx62004 add 1234567890123456 6E-3 -> 1234567890123456 Inexact Rounded +addx62005 add 1234567890123456 6E-4 -> 1234567890123456 Inexact Rounded +addx62006 add 1234567890123456 6E-5 -> 1234567890123456 Inexact Rounded +addx62007 add 1234567890123456 6E-6 -> 1234567890123456 Inexact Rounded +addx62008 add 1234567890123456 6E-7 -> 1234567890123456 Inexact Rounded +addx62009 add 1234567890123456 6E-8 -> 1234567890123456 Inexact Rounded +addx62010 add 1234567890123456 6E-9 -> 1234567890123456 Inexact Rounded +addx62011 add 1234567890123456 6E-10 -> 1234567890123456 Inexact Rounded +addx62012 add 1234567890123456 6E-11 -> 1234567890123456 Inexact Rounded +addx62013 add 1234567890123456 6E-12 -> 1234567890123456 Inexact Rounded +addx62014 add 1234567890123456 6E-13 -> 1234567890123456 Inexact Rounded +addx62015 add 1234567890123456 6E-14 -> 1234567890123456 Inexact Rounded +addx62016 add 1234567890123456 6E-15 -> 1234567890123456 Inexact Rounded +addx62017 add 1234567890123456 6E-16 -> 1234567890123456 Inexact Rounded +addx62018 add 1234567890123456 6E-17 -> 1234567890123456 Inexact Rounded +addx62019 add 1234567890123456 6E-18 -> 1234567890123456 Inexact Rounded +addx62020 add 1234567890123456 6E-19 -> 1234567890123456 Inexact Rounded +addx62021 add 1234567890123456 6E-20 -> 1234567890123456 Inexact Rounded + +-- widening second argument at gap +addx62030 add 12345678 1 -> 12345679 +addx62031 add 12345678 0.1 -> 12345678.1 +addx62032 add 12345678 0.12 -> 12345678.12 +addx62033 add 12345678 0.123 -> 12345678.123 +addx62034 add 12345678 0.1234 -> 12345678.1234 +addx62035 add 12345678 0.12345 -> 12345678.12345 +addx62036 add 12345678 0.123456 -> 12345678.123456 +addx62037 add 12345678 0.1234567 -> 12345678.1234567 +addx62038 add 12345678 0.12345678 -> 12345678.12345678 +addx62039 add 12345678 0.123456789 -> 12345678.12345679 Inexact Rounded +addx62040 add 12345678 0.123456785 -> 12345678.12345678 Inexact Rounded +addx62041 add 12345678 0.1234567850 -> 12345678.12345678 Inexact Rounded +addx62042 add 12345678 0.1234567851 -> 12345678.12345679 Inexact Rounded +addx62043 add 12345678 0.12345678501 -> 12345678.12345679 Inexact Rounded +addx62044 add 12345678 0.123456785001 -> 12345678.12345679 Inexact Rounded +addx62045 add 12345678 0.1234567850001 -> 12345678.12345679 Inexact Rounded +addx62046 add 12345678 0.12345678500001 -> 12345678.12345679 Inexact Rounded +addx62047 add 12345678 0.123456785000001 -> 12345678.12345679 Inexact Rounded +addx62048 add 12345678 0.1234567850000001 -> 12345678.12345679 Inexact Rounded +addx62049 add 12345678 0.1234567850000000 -> 12345678.12345678 Inexact Rounded +-- 90123456 +rounding: half_even +addx62050 add 12345678 0.0234567750000000 -> 12345678.02345678 Inexact Rounded +addx62051 add 12345678 0.0034567750000000 -> 12345678.00345678 Inexact Rounded +addx62052 add 12345678 0.0004567750000000 -> 12345678.00045678 Inexact Rounded +addx62053 add 12345678 0.0000567750000000 -> 12345678.00005678 Inexact Rounded +addx62054 add 12345678 0.0000067750000000 -> 12345678.00000678 Inexact Rounded +addx62055 add 12345678 0.0000007750000000 -> 12345678.00000078 Inexact Rounded +addx62056 add 12345678 0.0000000750000000 -> 12345678.00000008 Inexact Rounded +addx62057 add 12345678 0.0000000050000000 -> 12345678.00000000 Inexact Rounded +addx62060 add 12345678 0.0234567750000001 -> 12345678.02345678 Inexact Rounded +addx62061 add 12345678 0.0034567750000001 -> 12345678.00345678 Inexact Rounded +addx62062 add 12345678 0.0004567750000001 -> 12345678.00045678 Inexact Rounded +addx62063 add 12345678 0.0000567750000001 -> 12345678.00005678 Inexact Rounded +addx62064 add 12345678 0.0000067750000001 -> 12345678.00000678 Inexact Rounded +addx62065 add 12345678 0.0000007750000001 -> 12345678.00000078 Inexact Rounded +addx62066 add 12345678 0.0000000750000001 -> 12345678.00000008 Inexact Rounded +addx62067 add 12345678 0.0000000050000001 -> 12345678.00000001 Inexact Rounded +-- far-out residues (full coefficient gap is 16+15 digits) +rounding: up +addx62070 add 12345678 1E-8 -> 12345678.00000001 +addx62071 add 12345678 1E-9 -> 12345678.00000001 Inexact Rounded +addx62072 add 12345678 1E-10 -> 12345678.00000001 Inexact Rounded +addx62073 add 12345678 1E-11 -> 12345678.00000001 Inexact Rounded +addx62074 add 12345678 1E-12 -> 12345678.00000001 Inexact Rounded +addx62075 add 12345678 1E-13 -> 12345678.00000001 Inexact Rounded +addx62076 add 12345678 1E-14 -> 12345678.00000001 Inexact Rounded +addx62077 add 12345678 1E-15 -> 12345678.00000001 Inexact Rounded +addx62078 add 12345678 1E-16 -> 12345678.00000001 Inexact Rounded +addx62079 add 12345678 1E-17 -> 12345678.00000001 Inexact Rounded +addx62080 add 12345678 1E-18 -> 12345678.00000001 Inexact Rounded +addx62081 add 12345678 1E-19 -> 12345678.00000001 Inexact Rounded +addx62082 add 12345678 1E-20 -> 12345678.00000001 Inexact Rounded +addx62083 add 12345678 1E-25 -> 12345678.00000001 Inexact Rounded +addx62084 add 12345678 1E-30 -> 12345678.00000001 Inexact Rounded +addx62085 add 12345678 1E-31 -> 12345678.00000001 Inexact Rounded +addx62086 add 12345678 1E-32 -> 12345678.00000001 Inexact Rounded +addx62087 add 12345678 1E-33 -> 12345678.00000001 Inexact Rounded +addx62088 add 12345678 1E-34 -> 12345678.00000001 Inexact Rounded +addx62089 add 12345678 1E-35 -> 12345678.00000001 Inexact Rounded + +-- payload decapitate +precision: 5 +addx62100 add 11 sNaN123456789 -> NaN56789 Invalid_operation +addx62101 add -11 -sNaN123456789 -> -NaN56789 Invalid_operation +addx62102 add 11 NaN123456789 -> NaN56789 +addx62103 add -11 -NaN123456789 -> -NaN56789 + -- Null tests addx9990 add 10 # -> NaN Invalid_operation addx9991 add # 10 -> NaN Invalid_operation |