1------------------------------------------------------------------------ 2-- multiply.decTest -- decimal multiplication -- 3-- Copyright (c) Mike Cowlishaw, 1981, 2010. All rights reserved. -- 4-- Parts copyright (c) IBM Corporation, 1981, 2008. -- 5------------------------------------------------------------------------ 6-- Please see the document "General Decimal Arithmetic Testcases" -- 7-- at http://speleotrove.com/decimal for the description of -- 8-- these testcases. -- 9-- -- 10-- These testcases are experimental ('beta' versions), and they -- 11-- may contain errors. They are offered on an as-is basis. In -- 12-- particular, achieving the same results as the tests here is not -- 13-- a guarantee that an implementation complies with any Standard -- 14-- or specification. The tests are not exhaustive. -- 15-- -- 16-- Please send comments, suggestions, and corrections to the author: -- 17-- Mike Cowlishaw, mfc@speleotrove.com -- 18------------------------------------------------------------------------ 19version: 2.62 20 21extended: 1 22precision: 9 23rounding: half_up 24maxExponent: 384 25minexponent: -383 26 27-- sanity checks (as base, above) 28mulx000 multiply 2 2 -> 4 29mulx001 multiply 2 3 -> 6 30mulx002 multiply 5 1 -> 5 31mulx003 multiply 5 2 -> 10 32mulx004 multiply 1.20 2 -> 2.40 33mulx005 multiply 1.20 0 -> 0.00 34mulx006 multiply 1.20 -2 -> -2.40 35mulx007 multiply -1.20 2 -> -2.40 36mulx008 multiply -1.20 0 -> -0.00 37mulx009 multiply -1.20 -2 -> 2.40 38mulx010 multiply 5.09 7.1 -> 36.139 39mulx011 multiply 2.5 4 -> 10.0 40mulx012 multiply 2.50 4 -> 10.00 41mulx013 multiply 1.23456789 1.00000000 -> 1.23456789 Rounded 42mulx014 multiply 9.999999999 9.999999999 -> 100.000000 Inexact Rounded 43mulx015 multiply 2.50 4 -> 10.00 44precision: 6 45mulx016 multiply 2.50 4 -> 10.00 46mulx017 multiply 9.999999999 9.999999999 -> 100.000 Inexact Rounded 47mulx018 multiply 9.999999999 -9.999999999 -> -100.000 Inexact Rounded 48mulx019 multiply -9.999999999 9.999999999 -> -100.000 Inexact Rounded 49mulx020 multiply -9.999999999 -9.999999999 -> 100.000 Inexact Rounded 50 51-- 1999.12.21: next one is a edge case if intermediate longs are used 52precision: 15 53mulx059 multiply 999999999999 9765625 -> 9.76562499999023E+18 Inexact Rounded 54precision: 30 55mulx160 multiply 999999999999 9765625 -> 9765624999990234375 56precision: 9 57----- 58 59-- zeros, etc. 60mulx021 multiply 0 0 -> 0 61mulx022 multiply 0 -0 -> -0 62mulx023 multiply -0 0 -> -0 63mulx024 multiply -0 -0 -> 0 64mulx025 multiply -0.0 -0.0 -> 0.00 65mulx026 multiply -0.0 -0.0 -> 0.00 66mulx027 multiply -0.0 -0.0 -> 0.00 67mulx028 multiply -0.0 -0.0 -> 0.00 68mulx030 multiply 5.00 1E-3 -> 0.00500 69mulx031 multiply 00.00 0.000 -> 0.00000 70mulx032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0 71mulx033 multiply 0E-3 00.00 -> 0.00000 -- lhs is 0 72mulx034 multiply -5.00 1E-3 -> -0.00500 73mulx035 multiply -00.00 0.000 -> -0.00000 74mulx036 multiply -00.00 0E-3 -> -0.00000 -- rhs is 0 75mulx037 multiply -0E-3 00.00 -> -0.00000 -- lhs is 0 76mulx038 multiply 5.00 -1E-3 -> -0.00500 77mulx039 multiply 00.00 -0.000 -> -0.00000 78mulx040 multiply 00.00 -0E-3 -> -0.00000 -- rhs is 0 79mulx041 multiply 0E-3 -00.00 -> -0.00000 -- lhs is 0 80mulx042 multiply -5.00 -1E-3 -> 0.00500 81mulx043 multiply -00.00 -0.000 -> 0.00000 82mulx044 multiply -00.00 -0E-3 -> 0.00000 -- rhs is 0 83mulx045 multiply -0E-3 -00.00 -> 0.00000 -- lhs is 0 84 85-- examples from decarith 86mulx050 multiply 1.20 3 -> 3.60 87mulx051 multiply 7 3 -> 21 88mulx052 multiply 0.9 0.8 -> 0.72 89mulx053 multiply 0.9 -0 -> -0.0 90mulx054 multiply 654321 654321 -> 4.28135971E+11 Inexact Rounded 91 92mulx060 multiply 123.45 1e7 -> 1.2345E+9 93mulx061 multiply 123.45 1e8 -> 1.2345E+10 94mulx062 multiply 123.45 1e+9 -> 1.2345E+11 95mulx063 multiply 123.45 1e10 -> 1.2345E+12 96mulx064 multiply 123.45 1e11 -> 1.2345E+13 97mulx065 multiply 123.45 1e12 -> 1.2345E+14 98mulx066 multiply 123.45 1e13 -> 1.2345E+15 99 100 101-- test some intermediate lengths 102precision: 9 103mulx080 multiply 0.1 123456789 -> 12345678.9 104mulx081 multiply 0.1 1234567891 -> 123456789 Inexact Rounded 105mulx082 multiply 0.1 12345678912 -> 1.23456789E+9 Inexact Rounded 106mulx083 multiply 0.1 12345678912345 -> 1.23456789E+12 Inexact Rounded 107mulx084 multiply 0.1 123456789 -> 12345678.9 108precision: 8 109mulx085 multiply 0.1 12345678912 -> 1.2345679E+9 Inexact Rounded 110mulx086 multiply 0.1 12345678912345 -> 1.2345679E+12 Inexact Rounded 111precision: 7 112mulx087 multiply 0.1 12345678912 -> 1.234568E+9 Inexact Rounded 113mulx088 multiply 0.1 12345678912345 -> 1.234568E+12 Inexact Rounded 114 115precision: 9 116mulx090 multiply 123456789 0.1 -> 12345678.9 117mulx091 multiply 1234567891 0.1 -> 123456789 Inexact Rounded 118mulx092 multiply 12345678912 0.1 -> 1.23456789E+9 Inexact Rounded 119mulx093 multiply 12345678912345 0.1 -> 1.23456789E+12 Inexact Rounded 120mulx094 multiply 123456789 0.1 -> 12345678.9 121precision: 8 122mulx095 multiply 12345678912 0.1 -> 1.2345679E+9 Inexact Rounded 123mulx096 multiply 12345678912345 0.1 -> 1.2345679E+12 Inexact Rounded 124precision: 7 125mulx097 multiply 12345678912 0.1 -> 1.234568E+9 Inexact Rounded 126mulx098 multiply 12345678912345 0.1 -> 1.234568E+12 Inexact Rounded 127 128-- test some more edge cases and carries 129maxexponent: 9999 130minexponent: -9999 131precision: 33 132mulx101 multiply 9 9 -> 81 133mulx102 multiply 9 90 -> 810 134mulx103 multiply 9 900 -> 8100 135mulx104 multiply 9 9000 -> 81000 136mulx105 multiply 9 90000 -> 810000 137mulx106 multiply 9 900000 -> 8100000 138mulx107 multiply 9 9000000 -> 81000000 139mulx108 multiply 9 90000000 -> 810000000 140mulx109 multiply 9 900000000 -> 8100000000 141mulx110 multiply 9 9000000000 -> 81000000000 142mulx111 multiply 9 90000000000 -> 810000000000 143mulx112 multiply 9 900000000000 -> 8100000000000 144mulx113 multiply 9 9000000000000 -> 81000000000000 145mulx114 multiply 9 90000000000000 -> 810000000000000 146mulx115 multiply 9 900000000000000 -> 8100000000000000 147mulx116 multiply 9 9000000000000000 -> 81000000000000000 148mulx117 multiply 9 90000000000000000 -> 810000000000000000 149mulx118 multiply 9 900000000000000000 -> 8100000000000000000 150mulx119 multiply 9 9000000000000000000 -> 81000000000000000000 151mulx120 multiply 9 90000000000000000000 -> 810000000000000000000 152mulx121 multiply 9 900000000000000000000 -> 8100000000000000000000 153mulx122 multiply 9 9000000000000000000000 -> 81000000000000000000000 154mulx123 multiply 9 90000000000000000000000 -> 810000000000000000000000 155-- test some more edge cases without carries 156mulx131 multiply 3 3 -> 9 157mulx132 multiply 3 30 -> 90 158mulx133 multiply 3 300 -> 900 159mulx134 multiply 3 3000 -> 9000 160mulx135 multiply 3 30000 -> 90000 161mulx136 multiply 3 300000 -> 900000 162mulx137 multiply 3 3000000 -> 9000000 163mulx138 multiply 3 30000000 -> 90000000 164mulx139 multiply 3 300000000 -> 900000000 165mulx140 multiply 3 3000000000 -> 9000000000 166mulx141 multiply 3 30000000000 -> 90000000000 167mulx142 multiply 3 300000000000 -> 900000000000 168mulx143 multiply 3 3000000000000 -> 9000000000000 169mulx144 multiply 3 30000000000000 -> 90000000000000 170mulx145 multiply 3 300000000000000 -> 900000000000000 171mulx146 multiply 3 3000000000000000 -> 9000000000000000 172mulx147 multiply 3 30000000000000000 -> 90000000000000000 173mulx148 multiply 3 300000000000000000 -> 900000000000000000 174mulx149 multiply 3 3000000000000000000 -> 9000000000000000000 175mulx150 multiply 3 30000000000000000000 -> 90000000000000000000 176mulx151 multiply 3 300000000000000000000 -> 900000000000000000000 177mulx152 multiply 3 3000000000000000000000 -> 9000000000000000000000 178mulx153 multiply 3 30000000000000000000000 -> 90000000000000000000000 179 180maxexponent: 999999999 181minexponent: -999999999 182precision: 9 183-- test some cases that are close to exponent overflow/underflow 184mulx170 multiply 1 9e999999999 -> 9E+999999999 185mulx171 multiply 1 9.9e999999999 -> 9.9E+999999999 186mulx172 multiply 1 9.99e999999999 -> 9.99E+999999999 187mulx173 multiply 9e999999999 1 -> 9E+999999999 188mulx174 multiply 9.9e999999999 1 -> 9.9E+999999999 189mulx176 multiply 9.99e999999999 1 -> 9.99E+999999999 190mulx177 multiply 1 9.99999999e999999999 -> 9.99999999E+999999999 191mulx178 multiply 9.99999999e999999999 1 -> 9.99999999E+999999999 192 193mulx180 multiply 0.1 9e-999999998 -> 9E-999999999 194mulx181 multiply 0.1 99e-999999998 -> 9.9E-999999998 195mulx182 multiply 0.1 999e-999999998 -> 9.99E-999999997 196 197mulx183 multiply 0.1 9e-999999998 -> 9E-999999999 198mulx184 multiply 0.1 99e-999999998 -> 9.9E-999999998 199mulx185 multiply 0.1 999e-999999998 -> 9.99E-999999997 200mulx186 multiply 0.1 999e-999999997 -> 9.99E-999999996 201mulx187 multiply 0.1 9999e-999999997 -> 9.999E-999999995 202mulx188 multiply 0.1 99999e-999999997 -> 9.9999E-999999994 203 204mulx190 multiply 1 9e-999999998 -> 9E-999999998 205mulx191 multiply 1 99e-999999998 -> 9.9E-999999997 206mulx192 multiply 1 999e-999999998 -> 9.99E-999999996 207mulx193 multiply 9e-999999998 1 -> 9E-999999998 208mulx194 multiply 99e-999999998 1 -> 9.9E-999999997 209mulx195 multiply 999e-999999998 1 -> 9.99E-999999996 210 211mulx196 multiply 1e-599999999 1e-400000000 -> 1E-999999999 212mulx197 multiply 1e-600000000 1e-399999999 -> 1E-999999999 213mulx198 multiply 1.2e-599999999 1.2e-400000000 -> 1.44E-999999999 214mulx199 multiply 1.2e-600000000 1.2e-399999999 -> 1.44E-999999999 215 216mulx201 multiply 1e599999999 1e400000000 -> 1E+999999999 217mulx202 multiply 1e600000000 1e399999999 -> 1E+999999999 218mulx203 multiply 1.2e599999999 1.2e400000000 -> 1.44E+999999999 219mulx204 multiply 1.2e600000000 1.2e399999999 -> 1.44E+999999999 220 221-- long operand triangle 222precision: 33 223mulx246 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511992830 Inexact Rounded 224precision: 32 225mulx247 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199283 Inexact Rounded 226precision: 31 227mulx248 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928 Inexact Rounded 228precision: 30 229mulx249 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511993 Inexact Rounded 230precision: 29 231mulx250 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199 Inexact Rounded 232precision: 28 233mulx251 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165120 Inexact Rounded 234precision: 27 235mulx252 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916512 Inexact Rounded 236precision: 26 237mulx253 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651 Inexact Rounded 238precision: 25 239mulx254 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165 Inexact Rounded 240precision: 24 241mulx255 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671917 Inexact Rounded 242precision: 23 243mulx256 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967192 Inexact Rounded 244precision: 22 245mulx257 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719 Inexact Rounded 246precision: 21 247mulx258 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369672 Inexact Rounded 248precision: 20 249mulx259 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967 Inexact Rounded 250precision: 19 251mulx260 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933697 Inexact Rounded 252precision: 18 253mulx261 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193370 Inexact Rounded 254precision: 17 255mulx262 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119337 Inexact Rounded 256precision: 16 257mulx263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011934 Inexact Rounded 258precision: 15 259mulx264 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193 Inexact Rounded 260precision: 14 261mulx265 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119 Inexact Rounded 262precision: 13 263mulx266 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908012 Inexact Rounded 264precision: 12 265mulx267 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801 Inexact Rounded 266precision: 11 267mulx268 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080 Inexact Rounded 268precision: 10 269mulx269 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908 Inexact Rounded 270precision: 9 271mulx270 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.291 Inexact Rounded 272precision: 8 273mulx271 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29 Inexact Rounded 274precision: 7 275mulx272 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.3 Inexact Rounded 276precision: 6 277mulx273 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433 Inexact Rounded 278precision: 5 279mulx274 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.4543E+5 Inexact Rounded 280precision: 4 281mulx275 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.454E+5 Inexact Rounded 282precision: 3 283mulx276 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.45E+5 Inexact Rounded 284precision: 2 285mulx277 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.5E+5 Inexact Rounded 286precision: 1 287mulx278 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1E+5 Inexact Rounded 288 289-- test some edge cases with exact rounding 290maxexponent: 9999 291minexponent: -9999 292precision: 9 293mulx301 multiply 9 9 -> 81 294mulx302 multiply 9 90 -> 810 295mulx303 multiply 9 900 -> 8100 296mulx304 multiply 9 9000 -> 81000 297mulx305 multiply 9 90000 -> 810000 298mulx306 multiply 9 900000 -> 8100000 299mulx307 multiply 9 9000000 -> 81000000 300mulx308 multiply 9 90000000 -> 810000000 301mulx309 multiply 9 900000000 -> 8.10000000E+9 Rounded 302mulx310 multiply 9 9000000000 -> 8.10000000E+10 Rounded 303mulx311 multiply 9 90000000000 -> 8.10000000E+11 Rounded 304mulx312 multiply 9 900000000000 -> 8.10000000E+12 Rounded 305mulx313 multiply 9 9000000000000 -> 8.10000000E+13 Rounded 306mulx314 multiply 9 90000000000000 -> 8.10000000E+14 Rounded 307mulx315 multiply 9 900000000000000 -> 8.10000000E+15 Rounded 308mulx316 multiply 9 9000000000000000 -> 8.10000000E+16 Rounded 309mulx317 multiply 9 90000000000000000 -> 8.10000000E+17 Rounded 310mulx318 multiply 9 900000000000000000 -> 8.10000000E+18 Rounded 311mulx319 multiply 9 9000000000000000000 -> 8.10000000E+19 Rounded 312mulx320 multiply 9 90000000000000000000 -> 8.10000000E+20 Rounded 313mulx321 multiply 9 900000000000000000000 -> 8.10000000E+21 Rounded 314mulx322 multiply 9 9000000000000000000000 -> 8.10000000E+22 Rounded 315mulx323 multiply 9 90000000000000000000000 -> 8.10000000E+23 Rounded 316 317-- fastpath breakers 318precision: 29 319mulx330 multiply 1.491824697641270317824852952837224 1.105170918075647624811707826490246514675628614562883537345747603 -> 1.6487212707001281468486507878 Inexact Rounded 320precision: 55 321mulx331 multiply 0.8958341352965282506768545828765117803873717284891040428 0.8958341352965282506768545828765117803873717284891040428 -> 0.8025187979624784829842553829934069955890983696752228299 Inexact Rounded 322 323 324-- tryzeros cases 325precision: 7 326rounding: half_up 327maxExponent: 92 328minexponent: -92 329mulx504 multiply 0E-60 1000E-60 -> 0E-98 Clamped 330mulx505 multiply 100E+60 0E+60 -> 0E+92 Clamped 331 332-- mixed with zeros 333maxexponent: 999999999 334minexponent: -999999999 335precision: 9 336mulx541 multiply 0 -1 -> -0 337mulx542 multiply -0 -1 -> 0 338mulx543 multiply 0 1 -> 0 339mulx544 multiply -0 1 -> -0 340mulx545 multiply -1 0 -> -0 341mulx546 multiply -1 -0 -> 0 342mulx547 multiply 1 0 -> 0 343mulx548 multiply 1 -0 -> -0 344 345mulx551 multiply 0.0 -1 -> -0.0 346mulx552 multiply -0.0 -1 -> 0.0 347mulx553 multiply 0.0 1 -> 0.0 348mulx554 multiply -0.0 1 -> -0.0 349mulx555 multiply -1.0 0 -> -0.0 350mulx556 multiply -1.0 -0 -> 0.0 351mulx557 multiply 1.0 0 -> 0.0 352mulx558 multiply 1.0 -0 -> -0.0 353 354mulx561 multiply 0 -1.0 -> -0.0 355mulx562 multiply -0 -1.0 -> 0.0 356mulx563 multiply 0 1.0 -> 0.0 357mulx564 multiply -0 1.0 -> -0.0 358mulx565 multiply -1 0.0 -> -0.0 359mulx566 multiply -1 -0.0 -> 0.0 360mulx567 multiply 1 0.0 -> 0.0 361mulx568 multiply 1 -0.0 -> -0.0 362 363mulx571 multiply 0.0 -1.0 -> -0.00 364mulx572 multiply -0.0 -1.0 -> 0.00 365mulx573 multiply 0.0 1.0 -> 0.00 366mulx574 multiply -0.0 1.0 -> -0.00 367mulx575 multiply -1.0 0.0 -> -0.00 368mulx576 multiply -1.0 -0.0 -> 0.00 369mulx577 multiply 1.0 0.0 -> 0.00 370mulx578 multiply 1.0 -0.0 -> -0.00 371 372 373-- Specials 374mulx580 multiply Inf -Inf -> -Infinity 375mulx581 multiply Inf -1000 -> -Infinity 376mulx582 multiply Inf -1 -> -Infinity 377mulx583 multiply Inf -0 -> NaN Invalid_operation 378mulx584 multiply Inf 0 -> NaN Invalid_operation 379mulx585 multiply Inf 1 -> Infinity 380mulx586 multiply Inf 1000 -> Infinity 381mulx587 multiply Inf Inf -> Infinity 382mulx588 multiply -1000 Inf -> -Infinity 383mulx589 multiply -Inf Inf -> -Infinity 384mulx590 multiply -1 Inf -> -Infinity 385mulx591 multiply -0 Inf -> NaN Invalid_operation 386mulx592 multiply 0 Inf -> NaN Invalid_operation 387mulx593 multiply 1 Inf -> Infinity 388mulx594 multiply 1000 Inf -> Infinity 389mulx595 multiply Inf Inf -> Infinity 390 391mulx600 multiply -Inf -Inf -> Infinity 392mulx601 multiply -Inf -1000 -> Infinity 393mulx602 multiply -Inf -1 -> Infinity 394mulx603 multiply -Inf -0 -> NaN Invalid_operation 395mulx604 multiply -Inf 0 -> NaN Invalid_operation 396mulx605 multiply -Inf 1 -> -Infinity 397mulx606 multiply -Inf 1000 -> -Infinity 398mulx607 multiply -Inf Inf -> -Infinity 399mulx608 multiply -1000 Inf -> -Infinity 400mulx609 multiply -Inf -Inf -> Infinity 401mulx610 multiply -1 -Inf -> Infinity 402mulx611 multiply -0 -Inf -> NaN Invalid_operation 403mulx612 multiply 0 -Inf -> NaN Invalid_operation 404mulx613 multiply 1 -Inf -> -Infinity 405mulx614 multiply 1000 -Inf -> -Infinity 406mulx615 multiply Inf -Inf -> -Infinity 407 408mulx621 multiply NaN -Inf -> NaN 409mulx622 multiply NaN -1000 -> NaN 410mulx623 multiply NaN -1 -> NaN 411mulx624 multiply NaN -0 -> NaN 412mulx625 multiply NaN 0 -> NaN 413mulx626 multiply NaN 1 -> NaN 414mulx627 multiply NaN 1000 -> NaN 415mulx628 multiply NaN Inf -> NaN 416mulx629 multiply NaN NaN -> NaN 417mulx630 multiply -Inf NaN -> NaN 418mulx631 multiply -1000 NaN -> NaN 419mulx632 multiply -1 NaN -> NaN 420mulx633 multiply -0 NaN -> NaN 421mulx634 multiply 0 NaN -> NaN 422mulx635 multiply 1 NaN -> NaN 423mulx636 multiply 1000 NaN -> NaN 424mulx637 multiply Inf NaN -> NaN 425 426mulx641 multiply sNaN -Inf -> NaN Invalid_operation 427mulx642 multiply sNaN -1000 -> NaN Invalid_operation 428mulx643 multiply sNaN -1 -> NaN Invalid_operation 429mulx644 multiply sNaN -0 -> NaN Invalid_operation 430mulx645 multiply sNaN 0 -> NaN Invalid_operation 431mulx646 multiply sNaN 1 -> NaN Invalid_operation 432mulx647 multiply sNaN 1000 -> NaN Invalid_operation 433mulx648 multiply sNaN NaN -> NaN Invalid_operation 434mulx649 multiply sNaN sNaN -> NaN Invalid_operation 435mulx650 multiply NaN sNaN -> NaN Invalid_operation 436mulx651 multiply -Inf sNaN -> NaN Invalid_operation 437mulx652 multiply -1000 sNaN -> NaN Invalid_operation 438mulx653 multiply -1 sNaN -> NaN Invalid_operation 439mulx654 multiply -0 sNaN -> NaN Invalid_operation 440mulx655 multiply 0 sNaN -> NaN Invalid_operation 441mulx656 multiply 1 sNaN -> NaN Invalid_operation 442mulx657 multiply 1000 sNaN -> NaN Invalid_operation 443mulx658 multiply Inf sNaN -> NaN Invalid_operation 444mulx659 multiply NaN sNaN -> NaN Invalid_operation 445 446-- propagating NaNs 447mulx661 multiply NaN9 -Inf -> NaN9 448mulx662 multiply NaN8 999 -> NaN8 449mulx663 multiply NaN71 Inf -> NaN71 450mulx664 multiply NaN6 NaN5 -> NaN6 451mulx665 multiply -Inf NaN4 -> NaN4 452mulx666 multiply -999 NaN33 -> NaN33 453mulx667 multiply Inf NaN2 -> NaN2 454 455mulx671 multiply sNaN99 -Inf -> NaN99 Invalid_operation 456mulx672 multiply sNaN98 -11 -> NaN98 Invalid_operation 457mulx673 multiply sNaN97 NaN -> NaN97 Invalid_operation 458mulx674 multiply sNaN16 sNaN94 -> NaN16 Invalid_operation 459mulx675 multiply NaN95 sNaN93 -> NaN93 Invalid_operation 460mulx676 multiply -Inf sNaN92 -> NaN92 Invalid_operation 461mulx677 multiply 088 sNaN91 -> NaN91 Invalid_operation 462mulx678 multiply Inf sNaN90 -> NaN90 Invalid_operation 463mulx679 multiply NaN sNaN89 -> NaN89 Invalid_operation 464 465mulx681 multiply -NaN9 -Inf -> -NaN9 466mulx682 multiply -NaN8 999 -> -NaN8 467mulx683 multiply -NaN71 Inf -> -NaN71 468mulx684 multiply -NaN6 -NaN5 -> -NaN6 469mulx685 multiply -Inf -NaN4 -> -NaN4 470mulx686 multiply -999 -NaN33 -> -NaN33 471mulx687 multiply Inf -NaN2 -> -NaN2 472 473mulx691 multiply -sNaN99 -Inf -> -NaN99 Invalid_operation 474mulx692 multiply -sNaN98 -11 -> -NaN98 Invalid_operation 475mulx693 multiply -sNaN97 NaN -> -NaN97 Invalid_operation 476mulx694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation 477mulx695 multiply -NaN95 -sNaN93 -> -NaN93 Invalid_operation 478mulx696 multiply -Inf -sNaN92 -> -NaN92 Invalid_operation 479mulx697 multiply 088 -sNaN91 -> -NaN91 Invalid_operation 480mulx698 multiply Inf -sNaN90 -> -NaN90 Invalid_operation 481mulx699 multiply -NaN -sNaN89 -> -NaN89 Invalid_operation 482 483mulx701 multiply -NaN -Inf -> -NaN 484mulx702 multiply -NaN 999 -> -NaN 485mulx703 multiply -NaN Inf -> -NaN 486mulx704 multiply -NaN -NaN -> -NaN 487mulx705 multiply -Inf -NaN0 -> -NaN 488mulx706 multiply -999 -NaN -> -NaN 489mulx707 multiply Inf -NaN -> -NaN 490 491mulx711 multiply -sNaN -Inf -> -NaN Invalid_operation 492mulx712 multiply -sNaN -11 -> -NaN Invalid_operation 493mulx713 multiply -sNaN00 NaN -> -NaN Invalid_operation 494mulx714 multiply -sNaN -sNaN -> -NaN Invalid_operation 495mulx715 multiply -NaN -sNaN -> -NaN Invalid_operation 496mulx716 multiply -Inf -sNaN -> -NaN Invalid_operation 497mulx717 multiply 088 -sNaN -> -NaN Invalid_operation 498mulx718 multiply Inf -sNaN -> -NaN Invalid_operation 499mulx719 multiply -NaN -sNaN -> -NaN Invalid_operation 500 501-- overflow and underflow tests .. note subnormal results 502maxexponent: 999999999 503minexponent: -999999999 504mulx730 multiply +1.23456789012345E-0 9E+999999999 -> Infinity Inexact Overflow Rounded 505mulx731 multiply 9E+999999999 +1.23456789012345E-0 -> Infinity Inexact Overflow Rounded 506mulx732 multiply +0.100 9E-999999999 -> 9.00E-1000000000 Subnormal 507mulx733 multiply 9E-999999999 +0.100 -> 9.00E-1000000000 Subnormal 508mulx735 multiply -1.23456789012345E-0 9E+999999999 -> -Infinity Inexact Overflow Rounded 509mulx736 multiply 9E+999999999 -1.23456789012345E-0 -> -Infinity Inexact Overflow Rounded 510mulx737 multiply -0.100 9E-999999999 -> -9.00E-1000000000 Subnormal 511mulx738 multiply 9E-999999999 -0.100 -> -9.00E-1000000000 Subnormal 512 513mulx739 multiply 1e-599999999 1e-400000001 -> 1E-1000000000 Subnormal 514mulx740 multiply 1e-599999999 1e-400000000 -> 1E-999999999 515mulx741 multiply 1e-600000000 1e-400000000 -> 1E-1000000000 Subnormal 516mulx742 multiply 9e-999999998 0.01 -> 9E-1000000000 Subnormal 517mulx743 multiply 9e-999999998 0.1 -> 9E-999999999 518mulx744 multiply 0.01 9e-999999998 -> 9E-1000000000 Subnormal 519mulx745 multiply 1e599999999 1e400000001 -> Infinity Overflow Inexact Rounded 520mulx746 multiply 1e599999999 1e400000000 -> 1E+999999999 521mulx747 multiply 1e600000000 1e400000000 -> Infinity Overflow Inexact Rounded 522mulx748 multiply 9e999999998 100 -> Infinity Overflow Inexact Rounded 523mulx749 multiply 9e999999998 10 -> 9.0E+999999999 524mulx750 multiply 100 9e999999998 -> Infinity Overflow Inexact Rounded 525-- signs 526mulx751 multiply 1e+777777777 1e+411111111 -> Infinity Overflow Inexact Rounded 527mulx752 multiply 1e+777777777 -1e+411111111 -> -Infinity Overflow Inexact Rounded 528mulx753 multiply -1e+777777777 1e+411111111 -> -Infinity Overflow Inexact Rounded 529mulx754 multiply -1e+777777777 -1e+411111111 -> Infinity Overflow Inexact Rounded 530mulx755 multiply 1e-777777777 1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 531mulx756 multiply 1e-777777777 -1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 532mulx757 multiply -1e-777777777 1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 533mulx758 multiply -1e-777777777 -1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 534 535-- 'subnormal' boundary (all hard underflow or overflow in base arithemtic) 536precision: 9 537mulx760 multiply 1e-600000000 1e-400000001 -> 1E-1000000001 Subnormal 538mulx761 multiply 1e-600000000 1e-400000002 -> 1E-1000000002 Subnormal 539mulx762 multiply 1e-600000000 1e-400000003 -> 1E-1000000003 Subnormal 540mulx763 multiply 1e-600000000 1e-400000004 -> 1E-1000000004 Subnormal 541mulx764 multiply 1e-600000000 1e-400000005 -> 1E-1000000005 Subnormal 542mulx765 multiply 1e-600000000 1e-400000006 -> 1E-1000000006 Subnormal 543mulx766 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal 544mulx767 multiply 1e-600000000 1e-400000008 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 545mulx768 multiply 1e-600000000 1e-400000009 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 546mulx769 multiply 1e-600000000 1e-400000010 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped 547-- [no equivalent of 'subnormal' for overflow] 548mulx770 multiply 1e+600000000 1e+400000001 -> Infinity Overflow Inexact Rounded 549mulx771 multiply 1e+600000000 1e+400000002 -> Infinity Overflow Inexact Rounded 550mulx772 multiply 1e+600000000 1e+400000003 -> Infinity Overflow Inexact Rounded 551mulx773 multiply 1e+600000000 1e+400000004 -> Infinity Overflow Inexact Rounded 552mulx774 multiply 1e+600000000 1e+400000005 -> Infinity Overflow Inexact Rounded 553mulx775 multiply 1e+600000000 1e+400000006 -> Infinity Overflow Inexact Rounded 554mulx776 multiply 1e+600000000 1e+400000007 -> Infinity Overflow Inexact Rounded 555mulx777 multiply 1e+600000000 1e+400000008 -> Infinity Overflow Inexact Rounded 556mulx778 multiply 1e+600000000 1e+400000009 -> Infinity Overflow Inexact Rounded 557mulx779 multiply 1e+600000000 1e+400000010 -> Infinity Overflow Inexact Rounded 558 559-- 'subnormal' test edge condition at higher precisions 560precision: 99 561mulx780 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal 562mulx781 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal 563mulx782 multiply 1e-600000000 1e-400000097 -> 1E-1000000097 Subnormal 564mulx783 multiply 1e-600000000 1e-400000098 -> 0E-1000000097 Underflow Subnormal Inexact Rounded Clamped 565precision: 999 566mulx784 multiply 1e-600000000 1e-400000997 -> 1E-1000000997 Subnormal 567mulx785 multiply 1e-600000000 1e-400000998 -> 0E-1000000997 Underflow Subnormal Inexact Rounded Clamped 568 569-- following testcases [through mulx800] not yet run against code 570precision: 9999 571mulx786 multiply 1e-600000000 1e-400009997 -> 1E-1000009997 Subnormal 572mulx787 multiply 1e-600000000 1e-400009998 -> 0E-1000009997 Underflow Subnormal Inexact Rounded Clamped 573precision: 99999 574mulx788 multiply 1e-600000000 1e-400099997 -> 1E-1000099997 Subnormal 575mulx789 multiply 1e-600000000 1e-400099998 -> 0E-1000099997 Underflow Subnormal Inexact Rounded Clamped 576precision: 999999 577mulx790 multiply 1e-600000000 1e-400999997 -> 1E-1000999997 Subnormal 578mulx791 multiply 1e-600000000 1e-400999998 -> 0E-1000999997 Underflow Subnormal Inexact Rounded Clamped 579precision: 9999999 580mulx792 multiply 1e-600000000 1e-409999997 -> 1E-1009999997 Subnormal 581mulx793 multiply 1e-600000000 1e-409999998 -> 0E-1009999997 Underflow Subnormal Inexact Rounded Clamped 582precision: 99999999 583mulx794 multiply 1e-600000000 1e-499999997 -> 1E-1099999997 Subnormal 584mulx795 multiply 1e-600000000 1e-499999998 -> 0E-1099999997 Underflow Subnormal Inexact Rounded Clamped 585precision: 999999999 586mulx796 multiply 1e-999999999 1e-999999997 -> 1E-1999999996 Subnormal 587mulx797 multiply 1e-999999999 1e-999999998 -> 1E-1999999997 Subnormal 588mulx798 multiply 1e-999999999 1e-999999999 -> 0E-1999999997 Underflow Subnormal Inexact Rounded Clamped 589mulx799 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal 590mulx800 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal 591 592-- test subnormals rounding 593precision: 5 594maxExponent: 999 595minexponent: -999 596rounding: half_even 597 598mulx801 multiply 1.0000E-999 1 -> 1.0000E-999 599mulx802 multiply 1.000E-999 1e-1 -> 1.000E-1000 Subnormal 600mulx803 multiply 1.00E-999 1e-2 -> 1.00E-1001 Subnormal 601mulx804 multiply 1.0E-999 1e-3 -> 1.0E-1002 Subnormal 602mulx805 multiply 1.0E-999 1e-4 -> 1E-1003 Subnormal Rounded 603mulx806 multiply 1.3E-999 1e-4 -> 1E-1003 Underflow Subnormal Inexact Rounded 604mulx807 multiply 1.5E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 605mulx808 multiply 1.7E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 606mulx809 multiply 2.3E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 607mulx810 multiply 2.5E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 608mulx811 multiply 2.7E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded 609mulx812 multiply 1.49E-999 1e-4 -> 1E-1003 Underflow Subnormal Inexact Rounded 610mulx813 multiply 1.50E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 611mulx814 multiply 1.51E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 612mulx815 multiply 2.49E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 613mulx816 multiply 2.50E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded 614mulx817 multiply 2.51E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded 615 616mulx818 multiply 1E-999 1e-4 -> 1E-1003 Subnormal 617mulx819 multiply 3E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 618mulx820 multiply 5E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 619mulx821 multiply 7E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded 620mulx822 multiply 9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded 621mulx823 multiply 9.9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded 622 623mulx824 multiply 1E-999 -1e-4 -> -1E-1003 Subnormal 624mulx825 multiply 3E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped 625mulx826 multiply -5E-999 1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped 626mulx827 multiply 7E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded 627mulx828 multiply -9E-999 1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded 628mulx829 multiply 9.9E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded 629mulx830 multiply 3.0E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped 630 631mulx831 multiply 1.0E-501 1e-501 -> 1.0E-1002 Subnormal 632mulx832 multiply 2.0E-501 2e-501 -> 4.0E-1002 Subnormal 633mulx833 multiply 4.0E-501 4e-501 -> 1.60E-1001 Subnormal 634mulx834 multiply 10.0E-501 10e-501 -> 1.000E-1000 Subnormal 635mulx835 multiply 30.0E-501 30e-501 -> 9.000E-1000 Subnormal 636mulx836 multiply 40.0E-501 40e-501 -> 1.6000E-999 637 638-- squares 639mulx840 multiply 1E-502 1e-502 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 640mulx841 multiply 1E-501 1e-501 -> 1E-1002 Subnormal 641mulx842 multiply 2E-501 2e-501 -> 4E-1002 Subnormal 642mulx843 multiply 4E-501 4e-501 -> 1.6E-1001 Subnormal 643mulx844 multiply 10E-501 10e-501 -> 1.00E-1000 Subnormal 644mulx845 multiply 30E-501 30e-501 -> 9.00E-1000 Subnormal 645mulx846 multiply 40E-501 40e-501 -> 1.600E-999 646 647-- cubes 648mulx850 multiply 1E-670 1e-335 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped 649mulx851 multiply 1E-668 1e-334 -> 1E-1002 Subnormal 650mulx852 multiply 4E-668 2e-334 -> 8E-1002 Subnormal 651mulx853 multiply 9E-668 3e-334 -> 2.7E-1001 Subnormal 652mulx854 multiply 16E-668 4e-334 -> 6.4E-1001 Subnormal 653mulx855 multiply 25E-668 5e-334 -> 1.25E-1000 Subnormal 654mulx856 multiply 10E-668 100e-334 -> 1.000E-999 655 656-- test derived from result of 0.099 ** 999 at 15 digits with unlimited exponent 657precision: 19 658mulx860 multiply 6636851557994578716E-520 6636851557994578716E-520 -> 4.40477986028551E-1003 Underflow Subnormal Inexact Rounded 659 660-- Long operand overflow may be a different path 661precision: 3 662maxExponent: 999999999 663minexponent: -999999999 664mulx870 multiply 1 9.999E+999999999 -> Infinity Inexact Overflow Rounded 665mulx871 multiply 1 -9.999E+999999999 -> -Infinity Inexact Overflow Rounded 666mulx872 multiply 9.999E+999999999 1 -> Infinity Inexact Overflow Rounded 667mulx873 multiply -9.999E+999999999 1 -> -Infinity Inexact Overflow Rounded 668 669-- check for double-rounded subnormals 670precision: 5 671maxexponent: 79 672minexponent: -79 673mulx881 multiply 1.2347E-40 1.2347E-40 -> 1.524E-80 Inexact Rounded Subnormal Underflow 674mulx882 multiply 1.234E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow 675mulx883 multiply 1.23E-40 1.23E-40 -> 1.513E-80 Inexact Rounded Subnormal Underflow 676mulx884 multiply 1.2E-40 1.2E-40 -> 1.44E-80 Subnormal 677mulx885 multiply 1.2E-40 1.2E-41 -> 1.44E-81 Subnormal 678mulx886 multiply 1.2E-40 1.2E-42 -> 1.4E-82 Subnormal Inexact Rounded Underflow 679mulx887 multiply 1.2E-40 1.3E-42 -> 1.6E-82 Subnormal Inexact Rounded Underflow 680mulx888 multiply 1.3E-40 1.3E-42 -> 1.7E-82 Subnormal Inexact Rounded Underflow 681mulx889 multiply 1.3E-40 1.3E-43 -> 2E-83 Subnormal Inexact Rounded Underflow 682mulx890 multiply 1.3E-41 1.3E-43 -> 0E-83 Clamped Subnormal Inexact Rounded Underflow 683 684mulx891 multiply 1.2345E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded 685mulx892 multiply 1.23456E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded 686mulx893 multiply 1.2345E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow 687mulx894 multiply 1.23456E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow 688mulx895 multiply 1.2345E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow 689mulx896 multiply 1.23456E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow 690 691-- Now explore the case where we get a normal result with Underflow 692precision: 16 693rounding: half_up 694maxExponent: 384 695minExponent: -383 696 697mulx900 multiply 0.3000000000E-191 0.3000000000E-191 -> 9.00000000000000E-384 Subnormal Rounded 698mulx901 multiply 0.3000000001E-191 0.3000000001E-191 -> 9.00000000600000E-384 Underflow Inexact Subnormal Rounded 699mulx902 multiply 9.999999999999999E-383 0.0999999999999 -> 9.99999999999000E-384 Underflow Inexact Subnormal Rounded 700mulx903 multiply 9.999999999999999E-383 0.09999999999999 -> 9.99999999999900E-384 Underflow Inexact Subnormal Rounded 701mulx904 multiply 9.999999999999999E-383 0.099999999999999 -> 9.99999999999990E-384 Underflow Inexact Subnormal Rounded 702mulx905 multiply 9.999999999999999E-383 0.0999999999999999 -> 9.99999999999999E-384 Underflow Inexact Subnormal Rounded 703-- prove operands are exact 704mulx906 multiply 9.999999999999999E-383 1 -> 9.999999999999999E-383 705mulx907 multiply 1 0.09999999999999999 -> 0.09999999999999999 706-- the next rounds to Nmin 707mulx908 multiply 9.999999999999999E-383 0.09999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 708mulx909 multiply 9.999999999999999E-383 0.099999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 709mulx910 multiply 9.999999999999999E-383 0.0999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 710mulx911 multiply 9.999999999999999E-383 0.09999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded 711 712 713-- Examples from SQL proposal (Krishna Kulkarni) 714precision: 34 715rounding: half_up 716maxExponent: 6144 717minExponent: -6143 718mulx1001 multiply 130E-2 120E-2 -> 1.5600 719mulx1002 multiply 130E-2 12E-1 -> 1.560 720mulx1003 multiply 130E-2 1E0 -> 1.30 721mulx1004 multiply 1E2 1E4 -> 1E+6 722 723-- payload decapitate 724precision: 5 725mulx1010 multiply 11 -sNaN1234567890 -> -NaN67890 Invalid_operation 726 727-- Null tests 728mulx990 multiply 10 # -> NaN Invalid_operation 729mulx991 multiply # 10 -> NaN Invalid_operation 730 731