1------------------------------------------------------------------------ 2-- multiply.decTest -- decimal multiplication -- 3-- Copyright (c) IBM Corporation, 1981, 2008. All rights reserved. -- 4------------------------------------------------------------------------ 5-- Please see the document "General Decimal Arithmetic Testcases" -- 6-- at http://www2.hursley.ibm.com/decimal for the description of -- 7-- these testcases. -- 8-- -- 9-- These testcases are experimental ('beta' versions), and they -- 10-- may contain errors. They are offered on an as-is basis. In -- 11-- particular, achieving the same results as the tests here is not -- 12-- a guarantee that an implementation complies with any Standard -- 13-- or specification. The tests are not exhaustive. -- 14-- -- 15-- Please send comments, suggestions, and corrections to the author: -- 16-- Mike Cowlishaw, IBM Fellow -- 17-- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK -- 18-- mfc@uk.ibm.com -- 19------------------------------------------------------------------------ 20version: 2.59 21 22extended: 1 23precision: 9 24rounding: half_up 25maxExponent: 384 26minexponent: -383 27 28-- sanity checks (as base, above) 29mulx000 multiply 2 2 -> 4 30mulx001 multiply 2 3 -> 6 31mulx002 multiply 5 1 -> 5 32mulx003 multiply 5 2 -> 10 33mulx004 multiply 1.20 2 -> 2.40 34mulx005 multiply 1.20 0 -> 0.00 35mulx006 multiply 1.20 -2 -> -2.40 36mulx007 multiply -1.20 2 -> -2.40 37mulx008 multiply -1.20 0 -> -0.00 38mulx009 multiply -1.20 -2 -> 2.40 39mulx010 multiply 5.09 7.1 -> 36.139 40mulx011 multiply 2.5 4 -> 10.0 41mulx012 multiply 2.50 4 -> 10.00 42mulx013 multiply 1.23456789 1.00000000 -> 1.23456789 Rounded 43mulx014 multiply 9.999999999 9.999999999 -> 100.000000 Inexact Rounded 44mulx015 multiply 2.50 4 -> 10.00 45precision: 6 46mulx016 multiply 2.50 4 -> 10.00 47mulx017 multiply 9.999999999 9.999999999 -> 100.000 Inexact Rounded 48mulx018 multiply 9.999999999 -9.999999999 -> -100.000 Inexact Rounded 49mulx019 multiply -9.999999999 9.999999999 -> -100.000 Inexact Rounded 50mulx020 multiply -9.999999999 -9.999999999 -> 100.000 Inexact Rounded 51 52-- 1999.12.21: next one is an edge case if intermediate longs are used 53precision: 15 54mulx059 multiply 999999999999 9765625 -> 9.76562499999023E+18 Inexact Rounded 55precision: 30 56mulx160 multiply 999999999999 9765625 -> 9765624999990234375 57precision: 9 58----- 59 60-- zeros, etc. 61mulx021 multiply 0 0 -> 0 62mulx022 multiply 0 -0 -> -0 63mulx023 multiply -0 0 -> -0 64mulx024 multiply -0 -0 -> 0 65mulx025 multiply -0.0 -0.0 -> 0.00 66mulx026 multiply -0.0 -0.0 -> 0.00 67mulx027 multiply -0.0 -0.0 -> 0.00 68mulx028 multiply -0.0 -0.0 -> 0.00 69mulx030 multiply 5.00 1E-3 -> 0.00500 70mulx031 multiply 00.00 0.000 -> 0.00000 71mulx032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0 72mulx033 multiply 0E-3 00.00 -> 0.00000 -- lhs is 0 73mulx034 multiply -5.00 1E-3 -> -0.00500 74mulx035 multiply -00.00 0.000 -> -0.00000 75mulx036 multiply -00.00 0E-3 -> -0.00000 -- rhs is 0 76mulx037 multiply -0E-3 00.00 -> -0.00000 -- lhs is 0 77mulx038 multiply 5.00 -1E-3 -> -0.00500 78mulx039 multiply 00.00 -0.000 -> -0.00000 79mulx040 multiply 00.00 -0E-3 -> -0.00000 -- rhs is 0 80mulx041 multiply 0E-3 -00.00 -> -0.00000 -- lhs is 0 81mulx042 multiply -5.00 -1E-3 -> 0.00500 82mulx043 multiply -00.00 -0.000 -> 0.00000 83mulx044 multiply -00.00 -0E-3 -> 0.00000 -- rhs is 0 84mulx045 multiply -0E-3 -00.00 -> 0.00000 -- lhs is 0 85 86-- examples from decarith 87mulx050 multiply 1.20 3 -> 3.60 88mulx051 multiply 7 3 -> 21 89mulx052 multiply 0.9 0.8 -> 0.72 90mulx053 multiply 0.9 -0 -> -0.0 91mulx054 multiply 654321 654321 -> 4.28135971E+11 Inexact Rounded 92 93mulx060 multiply 123.45 1e7 -> 1.2345E+9 94mulx061 multiply 123.45 1e8 -> 1.2345E+10 95mulx062 multiply 123.45 1e+9 -> 1.2345E+11 96mulx063 multiply 123.45 1e10 -> 1.2345E+12 97mulx064 multiply 123.45 1e11 -> 1.2345E+13 98mulx065 multiply 123.45 1e12 -> 1.2345E+14 99mulx066 multiply 123.45 1e13 -> 1.2345E+15 100 101 102-- test some intermediate lengths 103precision: 9 104mulx080 multiply 0.1 123456789 -> 12345678.9 105mulx081 multiply 0.1 1234567891 -> 123456789 Inexact Rounded 106mulx082 multiply 0.1 12345678912 -> 1.23456789E+9 Inexact Rounded 107mulx083 multiply 0.1 12345678912345 -> 1.23456789E+12 Inexact Rounded 108mulx084 multiply 0.1 123456789 -> 12345678.9 109precision: 8 110mulx085 multiply 0.1 12345678912 -> 1.2345679E+9 Inexact Rounded 111mulx086 multiply 0.1 12345678912345 -> 1.2345679E+12 Inexact Rounded 112precision: 7 113mulx087 multiply 0.1 12345678912 -> 1.234568E+9 Inexact Rounded 114mulx088 multiply 0.1 12345678912345 -> 1.234568E+12 Inexact Rounded 115 116precision: 9 117mulx090 multiply 123456789 0.1 -> 12345678.9 118mulx091 multiply 1234567891 0.1 -> 123456789 Inexact Rounded 119mulx092 multiply 12345678912 0.1 -> 1.23456789E+9 Inexact Rounded 120mulx093 multiply 12345678912345 0.1 -> 1.23456789E+12 Inexact Rounded 121mulx094 multiply 123456789 0.1 -> 12345678.9 122precision: 8 123mulx095 multiply 12345678912 0.1 -> 1.2345679E+9 Inexact Rounded 124mulx096 multiply 12345678912345 0.1 -> 1.2345679E+12 Inexact Rounded 125precision: 7 126mulx097 multiply 12345678912 0.1 -> 1.234568E+9 Inexact Rounded 127mulx098 multiply 12345678912345 0.1 -> 1.234568E+12 Inexact Rounded 128 129-- test some more edge cases and carries 130maxexponent: 9999 131minexponent: -9999 132precision: 33 133mulx101 multiply 9 9 -> 81 134mulx102 multiply 9 90 -> 810 135mulx103 multiply 9 900 -> 8100 136mulx104 multiply 9 9000 -> 81000 137mulx105 multiply 9 90000 -> 810000 138mulx106 multiply 9 900000 -> 8100000 139mulx107 multiply 9 9000000 -> 81000000 140mulx108 multiply 9 90000000 -> 810000000 141mulx109 multiply 9 900000000 -> 8100000000 142mulx110 multiply 9 9000000000 -> 81000000000 143mulx111 multiply 9 90000000000 -> 810000000000 144mulx112 multiply 9 900000000000 -> 8100000000000 145mulx113 multiply 9 9000000000000 -> 81000000000000 146mulx114 multiply 9 90000000000000 -> 810000000000000 147mulx115 multiply 9 900000000000000 -> 8100000000000000 148mulx116 multiply 9 9000000000000000 -> 81000000000000000 149mulx117 multiply 9 90000000000000000 -> 810000000000000000 150mulx118 multiply 9 900000000000000000 -> 8100000000000000000 151mulx119 multiply 9 9000000000000000000 -> 81000000000000000000 152mulx120 multiply 9 90000000000000000000 -> 810000000000000000000 153mulx121 multiply 9 900000000000000000000 -> 8100000000000000000000 154mulx122 multiply 9 9000000000000000000000 -> 81000000000000000000000 155mulx123 multiply 9 90000000000000000000000 -> 810000000000000000000000 156-- test some more edge cases without carries 157mulx131 multiply 3 3 -> 9 158mulx132 multiply 3 30 -> 90 159mulx133 multiply 3 300 -> 900 160mulx134 multiply 3 3000 -> 9000 161mulx135 multiply 3 30000 -> 90000 162mulx136 multiply 3 300000 -> 900000 163mulx137 multiply 3 3000000 -> 9000000 164mulx138 multiply 3 30000000 -> 90000000 165mulx139 multiply 3 300000000 -> 900000000 166mulx140 multiply 3 3000000000 -> 9000000000 167mulx141 multiply 3 30000000000 -> 90000000000 168mulx142 multiply 3 300000000000 -> 900000000000 169mulx143 multiply 3 3000000000000 -> 9000000000000 170mulx144 multiply 3 30000000000000 -> 90000000000000 171mulx145 multiply 3 300000000000000 -> 900000000000000 172mulx146 multiply 3 3000000000000000 -> 9000000000000000 173mulx147 multiply 3 30000000000000000 -> 90000000000000000 174mulx148 multiply 3 300000000000000000 -> 900000000000000000 175mulx149 multiply 3 3000000000000000000 -> 9000000000000000000 176mulx150 multiply 3 30000000000000000000 -> 90000000000000000000 177mulx151 multiply 3 300000000000000000000 -> 900000000000000000000 178mulx152 multiply 3 3000000000000000000000 -> 9000000000000000000000 179mulx153 multiply 3 30000000000000000000000 -> 90000000000000000000000 180 181maxexponent: 999999999 182minexponent: -999999999 183precision: 9 184-- test some cases that are close to exponent overflow/underflow 185mulx170 multiply 1 9e999999999 -> 9E+999999999 186mulx171 multiply 1 9.9e999999999 -> 9.9E+999999999 187mulx172 multiply 1 9.99e999999999 -> 9.99E+999999999 188mulx173 multiply 9e999999999 1 -> 9E+999999999 189mulx174 multiply 9.9e999999999 1 -> 9.9E+999999999 190mulx176 multiply 9.99e999999999 1 -> 9.99E+999999999 191mulx177 multiply 1 9.99999999e999999999 -> 9.99999999E+999999999 192mulx178 multiply 9.99999999e999999999 1 -> 9.99999999E+999999999 193 194mulx180 multiply 0.1 9e-999999998 -> 9E-999999999 195mulx181 multiply 0.1 99e-999999998 -> 9.9E-999999998 196mulx182 multiply 0.1 999e-999999998 -> 9.99E-999999997 197 198mulx183 multiply 0.1 9e-999999998 -> 9E-999999999 199mulx184 multiply 0.1 99e-999999998 -> 9.9E-999999998 200mulx185 multiply 0.1 999e-999999998 -> 9.99E-999999997 201mulx186 multiply 0.1 999e-999999997 -> 9.99E-999999996 202mulx187 multiply 0.1 9999e-999999997 -> 9.999E-999999995 203mulx188 multiply 0.1 99999e-999999997 -> 9.9999E-999999994 204 205mulx190 multiply 1 9e-999999998 -> 9E-999999998 206mulx191 multiply 1 99e-999999998 -> 9.9E-999999997 207mulx192 multiply 1 999e-999999998 -> 9.99E-999999996 208mulx193 multiply 9e-999999998 1 -> 9E-999999998 209mulx194 multiply 99e-999999998 1 -> 9.9E-999999997 210mulx195 multiply 999e-999999998 1 -> 9.99E-999999996 211 212mulx196 multiply 1e-599999999 1e-400000000 -> 1E-999999999 213mulx197 multiply 1e-600000000 1e-399999999 -> 1E-999999999 214mulx198 multiply 1.2e-599999999 1.2e-400000000 -> 1.44E-999999999 215mulx199 multiply 1.2e-600000000 1.2e-399999999 -> 1.44E-999999999 216 217mulx201 multiply 1e599999999 1e400000000 -> 1E+999999999 218mulx202 multiply 1e600000000 1e399999999 -> 1E+999999999 219mulx203 multiply 1.2e599999999 1.2e400000000 -> 1.44E+999999999 220mulx204 multiply 1.2e600000000 1.2e399999999 -> 1.44E+999999999 221 222-- long operand triangle 223precision: 33 224mulx246 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511992830 Inexact Rounded 225precision: 32 226mulx247 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199283 Inexact Rounded 227precision: 31 228mulx248 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928 Inexact Rounded 229precision: 30 230mulx249 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511993 Inexact Rounded 231precision: 29 232mulx250 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199 Inexact Rounded 233precision: 28 234mulx251 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165120 Inexact Rounded 235precision: 27 236mulx252 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916512 Inexact Rounded 237precision: 26 238mulx253 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651 Inexact Rounded 239precision: 25 240mulx254 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165 Inexact Rounded 241precision: 24 242mulx255 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671917 Inexact Rounded 243precision: 23 244mulx256 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967192 Inexact Rounded 245precision: 22 246mulx257 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719 Inexact Rounded 247precision: 21 248mulx258 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369672 Inexact Rounded 249precision: 20 250mulx259 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967 Inexact Rounded 251precision: 19 252mulx260 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933697 Inexact Rounded 253precision: 18 254mulx261 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193370 Inexact Rounded 255precision: 17 256mulx262 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119337 Inexact Rounded 257precision: 16 258mulx263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011934 Inexact Rounded 259precision: 15 260mulx264 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193 Inexact Rounded 261precision: 14 262mulx265 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119 Inexact Rounded 263precision: 13 264mulx266 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908012 Inexact Rounded 265precision: 12 266mulx267 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801 Inexact Rounded 267precision: 11 268mulx268 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080 Inexact Rounded 269precision: 10 270mulx269 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908 Inexact Rounded 271precision: 9 272mulx270 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.291 Inexact Rounded 273precision: 8 274mulx271 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29 Inexact Rounded 275precision: 7 276mulx272 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.3 Inexact Rounded 277precision: 6 278mulx273 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433 Inexact Rounded 279precision: 5 280mulx274 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.4543E+5 Inexact Rounded 281precision: 4 282mulx275 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.454E+5 Inexact Rounded 283precision: 3 284mulx276 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.45E+5 Inexact Rounded 285precision: 2 286mulx277 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.5E+5 Inexact Rounded 287precision: 1 288mulx278 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1E+5 Inexact Rounded 289 290-- test some edge cases with exact rounding 291maxexponent: 9999 292minexponent: -9999 293precision: 9 294mulx301 multiply 9 9 -> 81 295mulx302 multiply 9 90 -> 810 296mulx303 multiply 9 900 -> 8100 297mulx304 multiply 9 9000 -> 81000 298mulx305 multiply 9 90000 -> 810000 299mulx306 multiply 9 900000 -> 8100000 300mulx307 multiply 9 9000000 -> 81000000 301mulx308 multiply 9 90000000 -> 810000000 302mulx309 multiply 9 900000000 -> 8.10000000E+9 Rounded 303mulx310 multiply 9 9000000000 -> 8.10000000E+10 Rounded 304mulx311 multiply 9 90000000000 -> 8.10000000E+11 Rounded 305mulx312 multiply 9 900000000000 -> 8.10000000E+12 Rounded 306mulx313 multiply 9 9000000000000 -> 8.10000000E+13 Rounded 307mulx314 multiply 9 90000000000000 -> 8.10000000E+14 Rounded 308mulx315 multiply 9 900000000000000 -> 8.10000000E+15 Rounded 309mulx316 multiply 9 9000000000000000 -> 8.10000000E+16 Rounded 310mulx317 multiply 9 90000000000000000 -> 8.10000000E+17 Rounded 311mulx318 multiply 9 900000000000000000 -> 8.10000000E+18 Rounded 312mulx319 multiply 9 9000000000000000000 -> 8.10000000E+19 Rounded 313mulx320 multiply 9 90000000000000000000 -> 8.10000000E+20 Rounded 314mulx321 multiply 9 900000000000000000000 -> 8.10000000E+21 Rounded 315mulx322 multiply 9 9000000000000000000000 -> 8.10000000E+22 Rounded 316mulx323 multiply 9 90000000000000000000000 -> 8.10000000E+23 Rounded 317 318-- fastpath breakers 319precision: 29 320mulx330 multiply 1.491824697641270317824852952837224 1.105170918075647624811707826490246514675628614562883537345747603 -> 1.6487212707001281468486507878 Inexact Rounded 321precision: 55 322mulx331 multiply 0.8958341352965282506768545828765117803873717284891040428 0.8958341352965282506768545828765117803873717284891040428 -> 0.8025187979624784829842553829934069955890983696752228299 Inexact Rounded 323 324 325-- tryzeros cases 326precision: 7 327rounding: half_up 328maxExponent: 92 329minexponent: -92 330mulx504 multiply 0E-60 1000E-60 -> 0E-98 Clamped 331mulx505 multiply 100E+60 0E+60 -> 0E+92 Clamped 332 333-- mixed with zeros 334maxexponent: 999999999 335minexponent: -999999999 336precision: 9 337mulx541 multiply 0 -1 -> -0 338mulx542 multiply -0 -1 -> 0 339mulx543 multiply 0 1 -> 0 340mulx544 multiply -0 1 -> -0 341mulx545 multiply -1 0 -> -0 342mulx546 multiply -1 -0 -> 0 343mulx547 multiply 1 0 -> 0 344mulx548 multiply 1 -0 -> -0 345 346mulx551 multiply 0.0 -1 -> -0.0 347mulx552 multiply -0.0 -1 -> 0.0 348mulx553 multiply 0.0 1 -> 0.0 349mulx554 multiply -0.0 1 -> -0.0 350mulx555 multiply -1.0 0 -> -0.0 351mulx556 multiply -1.0 -0 -> 0.0 352mulx557 multiply 1.0 0 -> 0.0 353mulx558 multiply 1.0 -0 -> -0.0 354 355mulx561 multiply 0 -1.0 -> -0.0 356mulx562 multiply -0 -1.0 -> 0.0 357mulx563 multiply 0 1.0 -> 0.0 358mulx564 multiply -0 1.0 -> -0.0 359mulx565 multiply -1 0.0 -> -0.0 360mulx566 multiply -1 -0.0 -> 0.0 361mulx567 multiply 1 0.0 -> 0.0 362mulx568 multiply 1 -0.0 -> -0.0 363 364mulx571 multiply 0.0 -1.0 -> -0.00 365mulx572 multiply -0.0 -1.0 -> 0.00 366mulx573 multiply 0.0 1.0 -> 0.00 367mulx574 multiply -0.0 1.0 -> -0.00 368mulx575 multiply -1.0 0.0 -> -0.00 369mulx576 multiply -1.0 -0.0 -> 0.00 370mulx577 multiply 1.0 0.0 -> 0.00 371mulx578 multiply 1.0 -0.0 -> -0.00 372 373 374-- Specials 375mulx580 multiply Inf -Inf -> -Infinity 376mulx581 multiply Inf -1000 -> -Infinity 377mulx582 multiply Inf -1 -> -Infinity 378mulx583 multiply Inf -0 -> NaN Invalid_operation 379mulx584 multiply Inf 0 -> NaN Invalid_operation 380mulx585 multiply Inf 1 -> Infinity 381mulx586 multiply Inf 1000 -> Infinity 382mulx587 multiply Inf Inf -> Infinity 383mulx588 multiply -1000 Inf -> -Infinity 384mulx589 multiply -Inf Inf -> -Infinity 385mulx590 multiply -1 Inf -> -Infinity 386mulx591 multiply -0 Inf -> NaN Invalid_operation 387mulx592 multiply 0 Inf -> NaN Invalid_operation 388mulx593 multiply 1 Inf -> Infinity 389mulx594 multiply 1000 Inf -> Infinity 390mulx595 multiply Inf Inf -> Infinity 391 392mulx600 multiply -Inf -Inf -> Infinity 393mulx601 multiply -Inf -1000 -> Infinity 394mulx602 multiply -Inf -1 -> Infinity 395mulx603 multiply -Inf -0 -> NaN Invalid_operation 396mulx604 multiply -Inf 0 -> NaN Invalid_operation 397mulx605 multiply -Inf 1 -> -Infinity 398mulx606 multiply -Inf 1000 -> -Infinity 399mulx607 multiply -Inf Inf -> -Infinity 400mulx608 multiply -1000 Inf -> -Infinity 401mulx609 multiply -Inf -Inf -> Infinity 402mulx610 multiply -1 -Inf -> Infinity 403mulx611 multiply -0 -Inf -> NaN Invalid_operation 404mulx612 multiply 0 -Inf -> NaN Invalid_operation 405mulx613 multiply 1 -Inf -> -Infinity 406mulx614 multiply 1000 -Inf -> -Infinity 407mulx615 multiply Inf -Inf -> -Infinity 408 409mulx621 multiply NaN -Inf -> NaN 410mulx622 multiply NaN -1000 -> NaN 411mulx623 multiply NaN -1 -> NaN 412mulx624 multiply NaN -0 -> NaN 413mulx625 multiply NaN 0 -> NaN 414mulx626 multiply NaN 1 -> NaN 415mulx627 multiply NaN 1000 -> NaN 416mulx628 multiply NaN Inf -> NaN 417mulx629 multiply NaN NaN -> NaN 418mulx630 multiply -Inf NaN -> NaN 419mulx631 multiply -1000 NaN -> NaN 420mulx632 multiply -1 NaN -> NaN 421mulx633 multiply -0 NaN -> NaN 422mulx634 multiply 0 NaN -> NaN 423mulx635 multiply 1 NaN -> NaN 424mulx636 multiply 1000 NaN -> NaN 425mulx637 multiply Inf NaN -> NaN 426 427mulx641 multiply sNaN -Inf -> NaN Invalid_operation 428mulx642 multiply sNaN -1000 -> NaN Invalid_operation 429mulx643 multiply sNaN -1 -> NaN Invalid_operation 430mulx644 multiply sNaN -0 -> NaN Invalid_operation 431mulx645 multiply sNaN 0 -> NaN Invalid_operation 432mulx646 multiply sNaN 1 -> NaN Invalid_operation 433mulx647 multiply sNaN 1000 -> NaN Invalid_operation 434mulx648 multiply sNaN NaN -> NaN Invalid_operation 435mulx649 multiply sNaN sNaN -> NaN Invalid_operation 436mulx650 multiply NaN sNaN -> NaN Invalid_operation 437mulx651 multiply -Inf sNaN -> NaN Invalid_operation 438mulx652 multiply -1000 sNaN -> NaN Invalid_operation 439mulx653 multiply -1 sNaN -> NaN Invalid_operation 440mulx654 multiply -0 sNaN -> NaN Invalid_operation 441mulx655 multiply 0 sNaN -> NaN Invalid_operation 442mulx656 multiply 1 sNaN -> NaN Invalid_operation 443mulx657 multiply 1000 sNaN -> NaN Invalid_operation 444mulx658 multiply Inf sNaN -> NaN Invalid_operation 445mulx659 multiply NaN sNaN -> NaN Invalid_operation 446 447-- propagating NaNs 448mulx661 multiply NaN9 -Inf -> NaN9 449mulx662 multiply NaN8 999 -> NaN8 450mulx663 multiply NaN71 Inf -> NaN71 451mulx664 multiply NaN6 NaN5 -> NaN6 452mulx665 multiply -Inf NaN4 -> NaN4 453mulx666 multiply -999 NaN33 -> NaN33 454mulx667 multiply Inf NaN2 -> NaN2 455 456mulx671 multiply sNaN99 -Inf -> NaN99 Invalid_operation 457mulx672 multiply sNaN98 -11 -> NaN98 Invalid_operation 458mulx673 multiply sNaN97 NaN -> NaN97 Invalid_operation 459mulx674 multiply sNaN16 sNaN94 -> NaN16 Invalid_operation 460mulx675 multiply NaN95 sNaN93 -> NaN93 Invalid_operation 461mulx676 multiply -Inf sNaN92 -> NaN92 Invalid_operation 462mulx677 multiply 088 sNaN91 -> NaN91 Invalid_operation 463mulx678 multiply Inf sNaN90 -> NaN90 Invalid_operation 464mulx679 multiply NaN sNaN89 -> NaN89 Invalid_operation 465 466mulx681 multiply -NaN9 -Inf -> -NaN9 467mulx682 multiply -NaN8 999 -> -NaN8 468mulx683 multiply -NaN71 Inf -> -NaN71 469mulx684 multiply -NaN6 -NaN5 -> -NaN6 470mulx685 multiply -Inf -NaN4 -> -NaN4 471mulx686 multiply -999 -NaN33 -> -NaN33 472mulx687 multiply Inf -NaN2 -> -NaN2 473 474mulx691 multiply -sNaN99 -Inf -> -NaN99 Invalid_operation 475mulx692 multiply -sNaN98 -11 -> -NaN98 Invalid_operation 476mulx693 multiply -sNaN97 NaN -> -NaN97 Invalid_operation 477mulx694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation 478mulx695 multiply -NaN95 -sNaN93 -> -NaN93 Invalid_operation 479mulx696 multiply -Inf -sNaN92 -> -NaN92 Invalid_operation 480mulx697 multiply 088 -sNaN91 -> -NaN91 Invalid_operation 481mulx698 multiply Inf -sNaN90 -> -NaN90 Invalid_operation 482mulx699 multiply -NaN -sNaN89 -> -NaN89 Invalid_operation 483 484mulx701 multiply -NaN -Inf -> -NaN 485mulx702 multiply -NaN 999 -> -NaN 486mulx703 multiply -NaN Inf -> -NaN 487mulx704 multiply -NaN -NaN -> -NaN 488mulx705 multiply -Inf -NaN0 -> -NaN 489mulx706 multiply -999 -NaN -> -NaN 490mulx707 multiply Inf -NaN -> -NaN 491 492mulx711 multiply -sNaN -Inf -> -NaN Invalid_operation 493mulx712 multiply -sNaN -11 -> -NaN Invalid_operation 494mulx713 multiply -sNaN00 NaN -> -NaN Invalid_operation 495mulx714 multiply -sNaN -sNaN -> -NaN Invalid_operation 496mulx715 multiply -NaN -sNaN -> -NaN Invalid_operation 497mulx716 multiply -Inf -sNaN -> -NaN Invalid_operation 498mulx717 multiply 088 -sNaN -> -NaN Invalid_operation 499mulx718 multiply Inf -sNaN -> -NaN Invalid_operation 500mulx719 multiply -NaN -sNaN -> -NaN Invalid_operation 501 502-- overflow and underflow tests .. note subnormal results 503maxexponent: 999999999 504minexponent: -999999999 505mulx730 multiply +1.23456789012345E-0 9E+999999999 -> Infinity Inexact Overflow Rounded 506mulx731 multiply 9E+999999999 +1.23456789012345E-0 -> Infinity Inexact Overflow Rounded 507mulx732 multiply +0.100 9E-999999999 -> 9.00E-1000000000 Subnormal 508mulx733 multiply 9E-999999999 +0.100 -> 9.00E-1000000000 Subnormal 509mulx735 multiply -1.23456789012345E-0 9E+999999999 -> -Infinity Inexact Overflow Rounded 510mulx736 multiply 9E+999999999 -1.23456789012345E-0 -> -Infinity Inexact Overflow Rounded 511mulx737 multiply -0.100 9E-999999999 -> -9.00E-1000000000 Subnormal 512mulx738 multiply 9E-999999999 -0.100 -> -9.00E-1000000000 Subnormal 513 514mulx739 multiply 1e-599999999 1e-400000001 -> 1E-1000000000 Subnormal 515mulx740 multiply 1e-599999999 1e-400000000 -> 1E-999999999 516mulx741 multiply 1e-600000000 1e-400000000 -> 1E-1000000000 Subnormal 517mulx742 multiply 9e-999999998 0.01 -> 9E-1000000000 Subnormal 518mulx743 multiply 9e-999999998 0.1 -> 9E-999999999 519mulx744 multiply 0.01 9e-999999998 -> 9E-1000000000 Subnormal 520mulx745 multiply 1e599999999 1e400000001 -> Infinity Overflow Inexact Rounded 521mulx746 multiply 1e599999999 1e400000000 -> 1E+999999999 522mulx747 multiply 1e600000000 1e400000000 -> Infinity Overflow Inexact Rounded 523mulx748 multiply 9e999999998 100 -> Infinity Overflow Inexact Rounded 524mulx749 multiply 9e999999998 10 -> 9.0E+999999999 525mulx750 multiply 100 9e999999998 -> Infinity Overflow Inexact Rounded 526-- signs 527mulx751 multiply 1e+777777777 1e+411111111 -> Infinity Overflow Inexact Rounded 528mulx752 multiply 1e+777777777 -1e+411111111 -> -Infinity Overflow Inexact Rounded 529mulx753 multiply -1e+777777777 1e+411111111 -> -Infinity Overflow Inexact Rounded 530mulx754 multiply -1e+777777777 -1e+411111111 -> Infinity Overflow Inexact Rounded 531mulx755 multiply 1e-777777777 1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 532mulx756 multiply 1e-777777777 -1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 533mulx757 multiply -1e-777777777 1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 534mulx758 multiply -1e-777777777 -1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 535 536-- 'subnormal' boundary (all hard underflow or overflow in base arithmetic) 537precision: 9 538mulx760 multiply 1e-600000000 1e-400000001 -> 1E-1000000001 Subnormal 539mulx761 multiply 1e-600000000 1e-400000002 -> 1E-1000000002 Subnormal 540mulx762 multiply 1e-600000000 1e-400000003 -> 1E-1000000003 Subnormal 541mulx763 multiply 1e-600000000 1e-400000004 -> 1E-1000000004 Subnormal 542mulx764 multiply 1e-600000000 1e-400000005 -> 1E-1000000005 Subnormal 543mulx765 multiply 1e-600000000 1e-400000006 -> 1E-1000000006 Subnormal 544mulx766 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal 545mulx767 multiply 1e-600000000 1e-400000008 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 546mulx768 multiply 1e-600000000 1e-400000009 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 547mulx769 multiply 1e-600000000 1e-400000010 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 548-- [no equivalent of 'subnormal' for overflow] 549mulx770 multiply 1e+600000000 1e+400000001 -> Infinity Overflow Inexact Rounded 550mulx771 multiply 1e+600000000 1e+400000002 -> Infinity Overflow Inexact Rounded 551mulx772 multiply 1e+600000000 1e+400000003 -> Infinity Overflow Inexact Rounded 552mulx773 multiply 1e+600000000 1e+400000004 -> Infinity Overflow Inexact Rounded 553mulx774 multiply 1e+600000000 1e+400000005 -> Infinity Overflow Inexact Rounded 554mulx775 multiply 1e+600000000 1e+400000006 -> Infinity Overflow Inexact Rounded 555mulx776 multiply 1e+600000000 1e+400000007 -> Infinity Overflow Inexact Rounded 556mulx777 multiply 1e+600000000 1e+400000008 -> Infinity Overflow Inexact Rounded 557mulx778 multiply 1e+600000000 1e+400000009 -> Infinity Overflow Inexact Rounded 558mulx779 multiply 1e+600000000 1e+400000010 -> Infinity Overflow Inexact Rounded 559 560-- 'subnormal' test edge condition at higher precisions 561precision: 99 562mulx780 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal 563mulx781 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal 564mulx782 multiply 1e-600000000 1e-400000097 -> 1E-1000000097 Subnormal 565mulx783 multiply 1e-600000000 1e-400000098 -> 0E-1000000097 Underflow Subnormal Inexact Rounded Clamped 566precision: 999 567mulx784 multiply 1e-600000000 1e-400000997 -> 1E-1000000997 Subnormal 568mulx785 multiply 1e-600000000 1e-400000998 -> 0E-1000000997 Underflow Subnormal Inexact Rounded Clamped 569 570-- following testcases [through mulx800] not yet run against code 571precision: 9999 572mulx786 multiply 1e-600000000 1e-400009997 -> 1E-1000009997 Subnormal 573mulx787 multiply 1e-600000000 1e-400009998 -> 0E-1000009997 Underflow Subnormal Inexact Rounded Clamped 574precision: 99999 575mulx788 multiply 1e-600000000 1e-400099997 -> 1E-1000099997 Subnormal 576mulx789 multiply 1e-600000000 1e-400099998 -> 0E-1000099997 Underflow Subnormal Inexact Rounded Clamped 577precision: 999999 578mulx790 multiply 1e-600000000 1e-400999997 -> 1E-1000999997 Subnormal 579mulx791 multiply 1e-600000000 1e-400999998 -> 0E-1000999997 Underflow Subnormal Inexact Rounded Clamped 580precision: 9999999 581mulx792 multiply 1e-600000000 1e-409999997 -> 1E-1009999997 Subnormal 582mulx793 multiply 1e-600000000 1e-409999998 -> 0E-1009999997 Underflow Subnormal Inexact Rounded Clamped 583precision: 99999999 584mulx794 multiply 1e-600000000 1e-499999997 -> 1E-1099999997 Subnormal 585mulx795 multiply 1e-600000000 1e-499999998 -> 0E-1099999997 Underflow Subnormal Inexact Rounded Clamped 586precision: 999999999 587mulx796 multiply 1e-999999999 1e-999999997 -> 1E-1999999996 Subnormal 588mulx797 multiply 1e-999999999 1e-999999998 -> 1E-1999999997 Subnormal 589mulx798 multiply 1e-999999999 1e-999999999 -> 0E-1999999997 Underflow Subnormal Inexact Rounded Clamped 590mulx799 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal 591mulx800 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal 592 593-- test subnormals rounding 594precision: 5 595maxExponent: 999 596minexponent: -999 597rounding: half_even 598 599mulx801 multiply 1.0000E-999 1 -> 1.0000E-999 600mulx802 multiply 1.000E-999 1e-1 -> 1.000E-1000 Subnormal 601mulx803 multiply 1.00E-999 1e-2 -> 1.00E-1001 Subnormal 602mulx804 multiply 1.0E-999 1e-3 -> 1.0E-1002 Subnormal 603mulx805 multiply 1.0E-999 1e-4 -> 1E-1003 Subnormal Rounded 604mulx806 multiply 1.3E-999 1e-4 -> 1E-1003 Underflow Subnormal Inexact Rounded 605mulx807 multiply 1.5E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 606mulx808 multiply 1.7E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 607mulx809 multiply 2.3E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 608mulx810 multiply 2.5E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 609mulx811 multiply 2.7E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded 610mulx812 multiply 1.49E-999 1e-4 -> 1E-1003 Underflow Subnormal Inexact Rounded 611mulx813 multiply 1.50E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 612mulx814 multiply 1.51E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 613mulx815 multiply 2.49E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 614mulx816 multiply 2.50E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 615mulx817 multiply 2.51E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded 616 617mulx818 multiply 1E-999 1e-4 -> 1E-1003 Subnormal 618mulx819 multiply 3E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 619mulx820 multiply 5E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 620mulx821 multiply 7E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded 621mulx822 multiply 9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded 622mulx823 multiply 9.9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded 623 624mulx824 multiply 1E-999 -1e-4 -> -1E-1003 Subnormal 625mulx825 multiply 3E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped 626mulx826 multiply -5E-999 1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped 627mulx827 multiply 7E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded 628mulx828 multiply -9E-999 1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded 629mulx829 multiply 9.9E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded 630mulx830 multiply 3.0E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped 631 632mulx831 multiply 1.0E-501 1e-501 -> 1.0E-1002 Subnormal 633mulx832 multiply 2.0E-501 2e-501 -> 4.0E-1002 Subnormal 634mulx833 multiply 4.0E-501 4e-501 -> 1.60E-1001 Subnormal 635mulx834 multiply 10.0E-501 10e-501 -> 1.000E-1000 Subnormal 636mulx835 multiply 30.0E-501 30e-501 -> 9.000E-1000 Subnormal 637mulx836 multiply 40.0E-501 40e-501 -> 1.6000E-999 638 639-- squares 640mulx840 multiply 1E-502 1e-502 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 641mulx841 multiply 1E-501 1e-501 -> 1E-1002 Subnormal 642mulx842 multiply 2E-501 2e-501 -> 4E-1002 Subnormal 643mulx843 multiply 4E-501 4e-501 -> 1.6E-1001 Subnormal 644mulx844 multiply 10E-501 10e-501 -> 1.00E-1000 Subnormal 645mulx845 multiply 30E-501 30e-501 -> 9.00E-1000 Subnormal 646mulx846 multiply 40E-501 40e-501 -> 1.600E-999 647 648-- cubes 649mulx850 multiply 1E-670 1e-335 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 650mulx851 multiply 1E-668 1e-334 -> 1E-1002 Subnormal 651mulx852 multiply 4E-668 2e-334 -> 8E-1002 Subnormal 652mulx853 multiply 9E-668 3e-334 -> 2.7E-1001 Subnormal 653mulx854 multiply 16E-668 4e-334 -> 6.4E-1001 Subnormal 654mulx855 multiply 25E-668 5e-334 -> 1.25E-1000 Subnormal 655mulx856 multiply 10E-668 100e-334 -> 1.000E-999 656 657-- test derived from result of 0.099 ** 999 at 15 digits with unlimited exponent 658precision: 19 659mulx860 multiply 6636851557994578716E-520 6636851557994578716E-520 -> 4.40477986028551E-1003 Underflow Subnormal Inexact Rounded 660 661-- Long operand overflow may be a different path 662precision: 3 663maxExponent: 999999999 664minexponent: -999999999 665mulx870 multiply 1 9.999E+999999999 -> Infinity Inexact Overflow Rounded 666mulx871 multiply 1 -9.999E+999999999 -> -Infinity Inexact Overflow Rounded 667mulx872 multiply 9.999E+999999999 1 -> Infinity Inexact Overflow Rounded 668mulx873 multiply -9.999E+999999999 1 -> -Infinity Inexact Overflow Rounded 669 670-- check for double-rounded subnormals 671precision: 5 672maxexponent: 79 673minexponent: -79 674mulx881 multiply 1.2347E-40 1.2347E-40 -> 1.524E-80 Inexact Rounded Subnormal Underflow 675mulx882 multiply 1.234E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow 676mulx883 multiply 1.23E-40 1.23E-40 -> 1.513E-80 Inexact Rounded Subnormal Underflow 677mulx884 multiply 1.2E-40 1.2E-40 -> 1.44E-80 Subnormal 678mulx885 multiply 1.2E-40 1.2E-41 -> 1.44E-81 Subnormal 679mulx886 multiply 1.2E-40 1.2E-42 -> 1.4E-82 Subnormal Inexact Rounded Underflow 680mulx887 multiply 1.2E-40 1.3E-42 -> 1.6E-82 Subnormal Inexact Rounded Underflow 681mulx888 multiply 1.3E-40 1.3E-42 -> 1.7E-82 Subnormal Inexact Rounded Underflow 682mulx889 multiply 1.3E-40 1.3E-43 -> 2E-83 Subnormal Inexact Rounded Underflow 683mulx890 multiply 1.3E-41 1.3E-43 -> 0E-83 Clamped Subnormal Inexact Rounded Underflow 684 685mulx891 multiply 1.2345E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded 686mulx892 multiply 1.23456E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded 687mulx893 multiply 1.2345E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow 688mulx894 multiply 1.23456E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow 689mulx895 multiply 1.2345E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow 690mulx896 multiply 1.23456E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow 691 692-- Now explore the case where we get a normal result with Underflow 693precision: 16 694rounding: half_up 695maxExponent: 384 696minExponent: -383 697 698mulx900 multiply 0.3000000000E-191 0.3000000000E-191 -> 9.00000000000000E-384 Subnormal Rounded 699mulx901 multiply 0.3000000001E-191 0.3000000001E-191 -> 9.00000000600000E-384 Underflow Inexact Subnormal Rounded 700mulx902 multiply 9.999999999999999E-383 0.0999999999999 -> 9.99999999999000E-384 Underflow Inexact Subnormal Rounded 701mulx903 multiply 9.999999999999999E-383 0.09999999999999 -> 9.99999999999900E-384 Underflow Inexact Subnormal Rounded 702mulx904 multiply 9.999999999999999E-383 0.099999999999999 -> 9.99999999999990E-384 Underflow Inexact Subnormal Rounded 703mulx905 multiply 9.999999999999999E-383 0.0999999999999999 -> 9.99999999999999E-384 Underflow Inexact Subnormal Rounded 704-- prove operands are exact 705mulx906 multiply 9.999999999999999E-383 1 -> 9.999999999999999E-383 706mulx907 multiply 1 0.09999999999999999 -> 0.09999999999999999 707-- the next rounds to Nmin 708mulx908 multiply 9.999999999999999E-383 0.09999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 709mulx909 multiply 9.999999999999999E-383 0.099999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 710mulx910 multiply 9.999999999999999E-383 0.0999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 711mulx911 multiply 9.999999999999999E-383 0.09999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 712 713 714-- Examples from SQL proposal (Krishna Kulkarni) 715precision: 34 716rounding: half_up 717maxExponent: 6144 718minExponent: -6143 719mulx1001 multiply 130E-2 120E-2 -> 1.5600 720mulx1002 multiply 130E-2 12E-1 -> 1.560 721mulx1003 multiply 130E-2 1E0 -> 1.30 722mulx1004 multiply 1E2 1E4 -> 1E+6 723 724-- payload decapitate 725precision: 5 726mulx1010 multiply 11 -sNaN1234567890 -> -NaN67890 Invalid_operation 727 728-- Null tests 729mulx990 multiply 10 # -> NaN Invalid_operation 730mulx991 multiply # 10 -> NaN Invalid_operation 731 732