1 ------------------------------------------------------------------------ 2 -- dqMultiply.decTest -- decQuad 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 (a] uk.ibm.com -- 19 ------------------------------------------------------------------------ 20 version: 2.59 21 22 -- This set of tests are for decQuads only; all arguments are 23 -- representable in a decQuad 24 extended: 1 25 clamp: 1 26 precision: 34 27 maxExponent: 6144 28 minExponent: -6143 29 rounding: half_even 30 31 -- sanity checks 32 dqmul000 multiply 2 2 -> 4 33 dqmul001 multiply 2 3 -> 6 34 dqmul002 multiply 5 1 -> 5 35 dqmul003 multiply 5 2 -> 10 36 dqmul004 multiply 1.20 2 -> 2.40 37 dqmul005 multiply 1.20 0 -> 0.00 38 dqmul006 multiply 1.20 -2 -> -2.40 39 dqmul007 multiply -1.20 2 -> -2.40 40 dqmul008 multiply -1.20 0 -> -0.00 41 dqmul009 multiply -1.20 -2 -> 2.40 42 dqmul010 multiply 5.09 7.1 -> 36.139 43 dqmul011 multiply 2.5 4 -> 10.0 44 dqmul012 multiply 2.50 4 -> 10.00 45 dqmul013 multiply 1.23456789 1.0000000000000000000000000000 -> 1.234567890000000000000000000000000 Rounded 46 dqmul015 multiply 2.50 4 -> 10.00 47 dqmul016 multiply 9.99999999999999999 9.99999999999999999 -> 99.99999999999999980000000000000000 Inexact Rounded 48 dqmul017 multiply 9.99999999999999999 -9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded 49 dqmul018 multiply -9.99999999999999999 9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded 50 dqmul019 multiply -9.99999999999999999 -9.99999999999999999 -> 99.99999999999999980000000000000000 Inexact Rounded 51 52 -- zeros, etc. 53 dqmul021 multiply 0 0 -> 0 54 dqmul022 multiply 0 -0 -> -0 55 dqmul023 multiply -0 0 -> -0 56 dqmul024 multiply -0 -0 -> 0 57 dqmul025 multiply -0.0 -0.0 -> 0.00 58 dqmul026 multiply -0.0 -0.0 -> 0.00 59 dqmul027 multiply -0.0 -0.0 -> 0.00 60 dqmul028 multiply -0.0 -0.0 -> 0.00 61 dqmul030 multiply 5.00 1E-3 -> 0.00500 62 dqmul031 multiply 00.00 0.000 -> 0.00000 63 dqmul032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0 64 dqmul033 multiply 0E-3 00.00 -> 0.00000 -- lhs is 0 65 dqmul034 multiply -5.00 1E-3 -> -0.00500 66 dqmul035 multiply -00.00 0.000 -> -0.00000 67 dqmul036 multiply -00.00 0E-3 -> -0.00000 -- rhs is 0 68 dqmul037 multiply -0E-3 00.00 -> -0.00000 -- lhs is 0 69 dqmul038 multiply 5.00 -1E-3 -> -0.00500 70 dqmul039 multiply 00.00 -0.000 -> -0.00000 71 dqmul040 multiply 00.00 -0E-3 -> -0.00000 -- rhs is 0 72 dqmul041 multiply 0E-3 -00.00 -> -0.00000 -- lhs is 0 73 dqmul042 multiply -5.00 -1E-3 -> 0.00500 74 dqmul043 multiply -00.00 -0.000 -> 0.00000 75 dqmul044 multiply -00.00 -0E-3 -> 0.00000 -- rhs is 0 76 dqmul045 multiply -0E-3 -00.00 -> 0.00000 -- lhs is 0 77 78 -- examples from decarith 79 dqmul050 multiply 1.20 3 -> 3.60 80 dqmul051 multiply 7 3 -> 21 81 dqmul052 multiply 0.9 0.8 -> 0.72 82 dqmul053 multiply 0.9 -0 -> -0.0 83 dqmul054 multiply 654321 654321 -> 428135971041 84 85 dqmul060 multiply 123.45 1e7 -> 1.2345E+9 86 dqmul061 multiply 123.45 1e8 -> 1.2345E+10 87 dqmul062 multiply 123.45 1e+9 -> 1.2345E+11 88 dqmul063 multiply 123.45 1e10 -> 1.2345E+12 89 dqmul064 multiply 123.45 1e11 -> 1.2345E+13 90 dqmul065 multiply 123.45 1e12 -> 1.2345E+14 91 dqmul066 multiply 123.45 1e13 -> 1.2345E+15 92 93 94 -- test some intermediate lengths 95 -- 1234567890123456 96 dqmul080 multiply 0.1 1230123456456789 -> 123012345645678.9 97 dqmul084 multiply 0.1 1230123456456789 -> 123012345645678.9 98 dqmul090 multiply 1230123456456789 0.1 -> 123012345645678.9 99 dqmul094 multiply 1230123456456789 0.1 -> 123012345645678.9 100 101 -- test some more edge cases and carries 102 dqmul101 multiply 9 9 -> 81 103 dqmul102 multiply 9 90 -> 810 104 dqmul103 multiply 9 900 -> 8100 105 dqmul104 multiply 9 9000 -> 81000 106 dqmul105 multiply 9 90000 -> 810000 107 dqmul106 multiply 9 900000 -> 8100000 108 dqmul107 multiply 9 9000000 -> 81000000 109 dqmul108 multiply 9 90000000 -> 810000000 110 dqmul109 multiply 9 900000000 -> 8100000000 111 dqmul110 multiply 9 9000000000 -> 81000000000 112 dqmul111 multiply 9 90000000000 -> 810000000000 113 dqmul112 multiply 9 900000000000 -> 8100000000000 114 dqmul113 multiply 9 9000000000000 -> 81000000000000 115 dqmul114 multiply 9 90000000000000 -> 810000000000000 116 dqmul115 multiply 9 900000000000000 -> 8100000000000000 117 --dqmul116 multiply 9 9000000000000000 -> 81000000000000000 118 --dqmul117 multiply 9 90000000000000000 -> 810000000000000000 119 --dqmul118 multiply 9 900000000000000000 -> 8100000000000000000 120 --dqmul119 multiply 9 9000000000000000000 -> 81000000000000000000 121 --dqmul120 multiply 9 90000000000000000000 -> 810000000000000000000 122 --dqmul121 multiply 9 900000000000000000000 -> 8100000000000000000000 123 --dqmul122 multiply 9 9000000000000000000000 -> 81000000000000000000000 124 --dqmul123 multiply 9 90000000000000000000000 -> 810000000000000000000000 125 -- test some more edge cases without carries 126 dqmul131 multiply 3 3 -> 9 127 dqmul132 multiply 3 30 -> 90 128 dqmul133 multiply 3 300 -> 900 129 dqmul134 multiply 3 3000 -> 9000 130 dqmul135 multiply 3 30000 -> 90000 131 dqmul136 multiply 3 300000 -> 900000 132 dqmul137 multiply 3 3000000 -> 9000000 133 dqmul138 multiply 3 30000000 -> 90000000 134 dqmul139 multiply 3 300000000 -> 900000000 135 dqmul140 multiply 3 3000000000 -> 9000000000 136 dqmul141 multiply 3 30000000000 -> 90000000000 137 dqmul142 multiply 3 300000000000 -> 900000000000 138 dqmul143 multiply 3 3000000000000 -> 9000000000000 139 dqmul144 multiply 3 30000000000000 -> 90000000000000 140 dqmul145 multiply 3 300000000000000 -> 900000000000000 141 dqmul146 multiply 3 3000000000000000 -> 9000000000000000 142 dqmul147 multiply 3 30000000000000000 -> 90000000000000000 143 dqmul148 multiply 3 300000000000000000 -> 900000000000000000 144 dqmul149 multiply 3 3000000000000000000 -> 9000000000000000000 145 dqmul150 multiply 3 30000000000000000000 -> 90000000000000000000 146 dqmul151 multiply 3 300000000000000000000 -> 900000000000000000000 147 dqmul152 multiply 3 3000000000000000000000 -> 9000000000000000000000 148 dqmul153 multiply 3 30000000000000000000000 -> 90000000000000000000000 149 150 dqmul263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928296 Inexact Rounded 151 152 -- test some edge cases with exact rounding 153 dqmul301 multiply 900000000000000000 9 -> 8100000000000000000 154 dqmul302 multiply 900000000000000000 90 -> 81000000000000000000 155 dqmul303 multiply 900000000000000000 900 -> 810000000000000000000 156 dqmul304 multiply 900000000000000000 9000 -> 8100000000000000000000 157 dqmul305 multiply 900000000000000000 90000 -> 81000000000000000000000 158 dqmul306 multiply 900000000000000000 900000 -> 810000000000000000000000 159 dqmul307 multiply 900000000000000000 9000000 -> 8100000000000000000000000 160 dqmul308 multiply 900000000000000000 90000000 -> 81000000000000000000000000 161 dqmul309 multiply 900000000000000000 900000000 -> 810000000000000000000000000 162 dqmul310 multiply 900000000000000000 9000000000 -> 8100000000000000000000000000 163 dqmul311 multiply 900000000000000000 90000000000 -> 81000000000000000000000000000 164 dqmul312 multiply 900000000000000000 900000000000 -> 810000000000000000000000000000 165 dqmul313 multiply 900000000000000000 9000000000000 -> 8100000000000000000000000000000 166 dqmul314 multiply 900000000000000000 90000000000000 -> 81000000000000000000000000000000 167 dqmul315 multiply 900000000000000000 900000000000000 -> 810000000000000000000000000000000 168 dqmul316 multiply 900000000000000000 9000000000000000 -> 8100000000000000000000000000000000 169 dqmul317 multiply 9000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+34 Rounded 170 dqmul318 multiply 90000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+35 Rounded 171 dqmul319 multiply 900000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+36 Rounded 172 dqmul320 multiply 9000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+37 Rounded 173 dqmul321 multiply 90000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+38 Rounded 174 dqmul322 multiply 900000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+39 Rounded 175 dqmul323 multiply 9000000000000000000000000 9000000000000000 -> 8.100000000000000000000000000000000E+40 Rounded 176 177 -- tryzeros cases 178 dqmul504 multiply 0E-4260 1000E-4260 -> 0E-6176 Clamped 179 dqmul505 multiply 100E+4260 0E+4260 -> 0E+6111 Clamped 180 181 -- mixed with zeros 182 dqmul541 multiply 0 -1 -> -0 183 dqmul542 multiply -0 -1 -> 0 184 dqmul543 multiply 0 1 -> 0 185 dqmul544 multiply -0 1 -> -0 186 dqmul545 multiply -1 0 -> -0 187 dqmul546 multiply -1 -0 -> 0 188 dqmul547 multiply 1 0 -> 0 189 dqmul548 multiply 1 -0 -> -0 190 191 dqmul551 multiply 0.0 -1 -> -0.0 192 dqmul552 multiply -0.0 -1 -> 0.0 193 dqmul553 multiply 0.0 1 -> 0.0 194 dqmul554 multiply -0.0 1 -> -0.0 195 dqmul555 multiply -1.0 0 -> -0.0 196 dqmul556 multiply -1.0 -0 -> 0.0 197 dqmul557 multiply 1.0 0 -> 0.0 198 dqmul558 multiply 1.0 -0 -> -0.0 199 200 dqmul561 multiply 0 -1.0 -> -0.0 201 dqmul562 multiply -0 -1.0 -> 0.0 202 dqmul563 multiply 0 1.0 -> 0.0 203 dqmul564 multiply -0 1.0 -> -0.0 204 dqmul565 multiply -1 0.0 -> -0.0 205 dqmul566 multiply -1 -0.0 -> 0.0 206 dqmul567 multiply 1 0.0 -> 0.0 207 dqmul568 multiply 1 -0.0 -> -0.0 208 209 dqmul571 multiply 0.0 -1.0 -> -0.00 210 dqmul572 multiply -0.0 -1.0 -> 0.00 211 dqmul573 multiply 0.0 1.0 -> 0.00 212 dqmul574 multiply -0.0 1.0 -> -0.00 213 dqmul575 multiply -1.0 0.0 -> -0.00 214 dqmul576 multiply -1.0 -0.0 -> 0.00 215 dqmul577 multiply 1.0 0.0 -> 0.00 216 dqmul578 multiply 1.0 -0.0 -> -0.00 217 218 219 -- Specials 220 dqmul580 multiply Inf -Inf -> -Infinity 221 dqmul581 multiply Inf -1000 -> -Infinity 222 dqmul582 multiply Inf -1 -> -Infinity 223 dqmul583 multiply Inf -0 -> NaN Invalid_operation 224 dqmul584 multiply Inf 0 -> NaN Invalid_operation 225 dqmul585 multiply Inf 1 -> Infinity 226 dqmul586 multiply Inf 1000 -> Infinity 227 dqmul587 multiply Inf Inf -> Infinity 228 dqmul588 multiply -1000 Inf -> -Infinity 229 dqmul589 multiply -Inf Inf -> -Infinity 230 dqmul590 multiply -1 Inf -> -Infinity 231 dqmul591 multiply -0 Inf -> NaN Invalid_operation 232 dqmul592 multiply 0 Inf -> NaN Invalid_operation 233 dqmul593 multiply 1 Inf -> Infinity 234 dqmul594 multiply 1000 Inf -> Infinity 235 dqmul595 multiply Inf Inf -> Infinity 236 237 dqmul600 multiply -Inf -Inf -> Infinity 238 dqmul601 multiply -Inf -1000 -> Infinity 239 dqmul602 multiply -Inf -1 -> Infinity 240 dqmul603 multiply -Inf -0 -> NaN Invalid_operation 241 dqmul604 multiply -Inf 0 -> NaN Invalid_operation 242 dqmul605 multiply -Inf 1 -> -Infinity 243 dqmul606 multiply -Inf 1000 -> -Infinity 244 dqmul607 multiply -Inf Inf -> -Infinity 245 dqmul608 multiply -1000 Inf -> -Infinity 246 dqmul609 multiply -Inf -Inf -> Infinity 247 dqmul610 multiply -1 -Inf -> Infinity 248 dqmul611 multiply -0 -Inf -> NaN Invalid_operation 249 dqmul612 multiply 0 -Inf -> NaN Invalid_operation 250 dqmul613 multiply 1 -Inf -> -Infinity 251 dqmul614 multiply 1000 -Inf -> -Infinity 252 dqmul615 multiply Inf -Inf -> -Infinity 253 254 dqmul621 multiply NaN -Inf -> NaN 255 dqmul622 multiply NaN -1000 -> NaN 256 dqmul623 multiply NaN -1 -> NaN 257 dqmul624 multiply NaN -0 -> NaN 258 dqmul625 multiply NaN 0 -> NaN 259 dqmul626 multiply NaN 1 -> NaN 260 dqmul627 multiply NaN 1000 -> NaN 261 dqmul628 multiply NaN Inf -> NaN 262 dqmul629 multiply NaN NaN -> NaN 263 dqmul630 multiply -Inf NaN -> NaN 264 dqmul631 multiply -1000 NaN -> NaN 265 dqmul632 multiply -1 NaN -> NaN 266 dqmul633 multiply -0 NaN -> NaN 267 dqmul634 multiply 0 NaN -> NaN 268 dqmul635 multiply 1 NaN -> NaN 269 dqmul636 multiply 1000 NaN -> NaN 270 dqmul637 multiply Inf NaN -> NaN 271 272 dqmul641 multiply sNaN -Inf -> NaN Invalid_operation 273 dqmul642 multiply sNaN -1000 -> NaN Invalid_operation 274 dqmul643 multiply sNaN -1 -> NaN Invalid_operation 275 dqmul644 multiply sNaN -0 -> NaN Invalid_operation 276 dqmul645 multiply sNaN 0 -> NaN Invalid_operation 277 dqmul646 multiply sNaN 1 -> NaN Invalid_operation 278 dqmul647 multiply sNaN 1000 -> NaN Invalid_operation 279 dqmul648 multiply sNaN NaN -> NaN Invalid_operation 280 dqmul649 multiply sNaN sNaN -> NaN Invalid_operation 281 dqmul650 multiply NaN sNaN -> NaN Invalid_operation 282 dqmul651 multiply -Inf sNaN -> NaN Invalid_operation 283 dqmul652 multiply -1000 sNaN -> NaN Invalid_operation 284 dqmul653 multiply -1 sNaN -> NaN Invalid_operation 285 dqmul654 multiply -0 sNaN -> NaN Invalid_operation 286 dqmul655 multiply 0 sNaN -> NaN Invalid_operation 287 dqmul656 multiply 1 sNaN -> NaN Invalid_operation 288 dqmul657 multiply 1000 sNaN -> NaN Invalid_operation 289 dqmul658 multiply Inf sNaN -> NaN Invalid_operation 290 dqmul659 multiply NaN sNaN -> NaN Invalid_operation 291 292 -- propagating NaNs 293 dqmul661 multiply NaN9 -Inf -> NaN9 294 dqmul662 multiply NaN8 999 -> NaN8 295 dqmul663 multiply NaN71 Inf -> NaN71 296 dqmul664 multiply NaN6 NaN5 -> NaN6 297 dqmul665 multiply -Inf NaN4 -> NaN4 298 dqmul666 multiply -999 NaN33 -> NaN33 299 dqmul667 multiply Inf NaN2 -> NaN2 300 301 dqmul671 multiply sNaN99 -Inf -> NaN99 Invalid_operation 302 dqmul672 multiply sNaN98 -11 -> NaN98 Invalid_operation 303 dqmul673 multiply sNaN97 NaN -> NaN97 Invalid_operation 304 dqmul674 multiply sNaN16 sNaN94 -> NaN16 Invalid_operation 305 dqmul675 multiply NaN95 sNaN93 -> NaN93 Invalid_operation 306 dqmul676 multiply -Inf sNaN92 -> NaN92 Invalid_operation 307 dqmul677 multiply 088 sNaN91 -> NaN91 Invalid_operation 308 dqmul678 multiply Inf sNaN90 -> NaN90 Invalid_operation 309 dqmul679 multiply NaN sNaN89 -> NaN89 Invalid_operation 310 311 dqmul681 multiply -NaN9 -Inf -> -NaN9 312 dqmul682 multiply -NaN8 999 -> -NaN8 313 dqmul683 multiply -NaN71 Inf -> -NaN71 314 dqmul684 multiply -NaN6 -NaN5 -> -NaN6 315 dqmul685 multiply -Inf -NaN4 -> -NaN4 316 dqmul686 multiply -999 -NaN33 -> -NaN33 317 dqmul687 multiply Inf -NaN2 -> -NaN2 318 319 dqmul691 multiply -sNaN99 -Inf -> -NaN99 Invalid_operation 320 dqmul692 multiply -sNaN98 -11 -> -NaN98 Invalid_operation 321 dqmul693 multiply -sNaN97 NaN -> -NaN97 Invalid_operation 322 dqmul694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation 323 dqmul695 multiply -NaN95 -sNaN93 -> -NaN93 Invalid_operation 324 dqmul696 multiply -Inf -sNaN92 -> -NaN92 Invalid_operation 325 dqmul697 multiply 088 -sNaN91 -> -NaN91 Invalid_operation 326 dqmul698 multiply Inf -sNaN90 -> -NaN90 Invalid_operation 327 dqmul699 multiply -NaN -sNaN89 -> -NaN89 Invalid_operation 328 329 dqmul701 multiply -NaN -Inf -> -NaN 330 dqmul702 multiply -NaN 999 -> -NaN 331 dqmul703 multiply -NaN Inf -> -NaN 332 dqmul704 multiply -NaN -NaN -> -NaN 333 dqmul705 multiply -Inf -NaN0 -> -NaN 334 dqmul706 multiply -999 -NaN -> -NaN 335 dqmul707 multiply Inf -NaN -> -NaN 336 337 dqmul711 multiply -sNaN -Inf -> -NaN Invalid_operation 338 dqmul712 multiply -sNaN -11 -> -NaN Invalid_operation 339 dqmul713 multiply -sNaN00 NaN -> -NaN Invalid_operation 340 dqmul714 multiply -sNaN -sNaN -> -NaN Invalid_operation 341 dqmul715 multiply -NaN -sNaN -> -NaN Invalid_operation 342 dqmul716 multiply -Inf -sNaN -> -NaN Invalid_operation 343 dqmul717 multiply 088 -sNaN -> -NaN Invalid_operation 344 dqmul718 multiply Inf -sNaN -> -NaN Invalid_operation 345 dqmul719 multiply -NaN -sNaN -> -NaN Invalid_operation 346 347 -- overflow and underflow tests .. note subnormal results 348 -- signs 349 dqmul751 multiply 1e+4277 1e+3311 -> Infinity Overflow Inexact Rounded 350 dqmul752 multiply 1e+4277 -1e+3311 -> -Infinity Overflow Inexact Rounded 351 dqmul753 multiply -1e+4277 1e+3311 -> -Infinity Overflow Inexact Rounded 352 dqmul754 multiply -1e+4277 -1e+3311 -> Infinity Overflow Inexact Rounded 353 dqmul755 multiply 1e-4277 1e-3311 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 354 dqmul756 multiply 1e-4277 -1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped 355 dqmul757 multiply -1e-4277 1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped 356 dqmul758 multiply -1e-4277 -1e-3311 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 357 358 -- 'subnormal' boundary (all hard underflow or overflow in base arithemtic) 359 dqmul760 multiply 1e-6069 1e-101 -> 1E-6170 Subnormal 360 dqmul761 multiply 1e-6069 1e-102 -> 1E-6171 Subnormal 361 dqmul762 multiply 1e-6069 1e-103 -> 1E-6172 Subnormal 362 dqmul763 multiply 1e-6069 1e-104 -> 1E-6173 Subnormal 363 dqmul764 multiply 1e-6069 1e-105 -> 1E-6174 Subnormal 364 dqmul765 multiply 1e-6069 1e-106 -> 1E-6175 Subnormal 365 dqmul766 multiply 1e-6069 1e-107 -> 1E-6176 Subnormal 366 dqmul767 multiply 1e-6069 1e-108 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 367 dqmul768 multiply 1e-6069 1e-109 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 368 dqmul769 multiply 1e-6069 1e-110 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 369 -- [no equivalent of 'subnormal' for overflow] 370 dqmul770 multiply 1e+40 1e+6101 -> 1.000000000000000000000000000000E+6141 Clamped 371 dqmul771 multiply 1e+40 1e+6102 -> 1.0000000000000000000000000000000E+6142 Clamped 372 dqmul772 multiply 1e+40 1e+6103 -> 1.00000000000000000000000000000000E+6143 Clamped 373 dqmul773 multiply 1e+40 1e+6104 -> 1.000000000000000000000000000000000E+6144 Clamped 374 dqmul774 multiply 1e+40 1e+6105 -> Infinity Overflow Inexact Rounded 375 dqmul775 multiply 1e+40 1e+6106 -> Infinity Overflow Inexact Rounded 376 dqmul776 multiply 1e+40 1e+6107 -> Infinity Overflow Inexact Rounded 377 dqmul777 multiply 1e+40 1e+6108 -> Infinity Overflow Inexact Rounded 378 dqmul778 multiply 1e+40 1e+6109 -> Infinity Overflow Inexact Rounded 379 dqmul779 multiply 1e+40 1e+6110 -> Infinity Overflow Inexact Rounded 380 381 dqmul801 multiply 1.0000E-6172 1 -> 1.0000E-6172 Subnormal 382 dqmul802 multiply 1.000E-6172 1e-1 -> 1.000E-6173 Subnormal 383 dqmul803 multiply 1.00E-6172 1e-2 -> 1.00E-6174 Subnormal 384 dqmul804 multiply 1.0E-6172 1e-3 -> 1.0E-6175 Subnormal 385 dqmul805 multiply 1.0E-6172 1e-4 -> 1E-6176 Subnormal Rounded 386 dqmul806 multiply 1.3E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded 387 dqmul807 multiply 1.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 388 dqmul808 multiply 1.7E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 389 dqmul809 multiply 2.3E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 390 dqmul810 multiply 2.5E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 391 dqmul811 multiply 2.7E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded 392 dqmul812 multiply 1.49E-6172 1e-4 -> 1E-6176 Underflow Subnormal Inexact Rounded 393 dqmul813 multiply 1.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 394 dqmul814 multiply 1.51E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 395 dqmul815 multiply 2.49E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 396 dqmul816 multiply 2.50E-6172 1e-4 -> 2E-6176 Underflow Subnormal Inexact Rounded 397 dqmul817 multiply 2.51E-6172 1e-4 -> 3E-6176 Underflow Subnormal Inexact Rounded 398 399 dqmul818 multiply 1E-6172 1e-4 -> 1E-6176 Subnormal 400 dqmul819 multiply 3E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 401 dqmul820 multiply 5E-6172 1e-5 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 402 dqmul821 multiply 7E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded 403 dqmul822 multiply 9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded 404 dqmul823 multiply 9.9E-6172 1e-5 -> 1E-6176 Underflow Subnormal Inexact Rounded 405 406 dqmul824 multiply 1E-6172 -1e-4 -> -1E-6176 Subnormal 407 dqmul825 multiply 3E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped 408 dqmul826 multiply -5E-6172 1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped 409 dqmul827 multiply 7E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded 410 dqmul828 multiply -9E-6172 1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded 411 dqmul829 multiply 9.9E-6172 -1e-5 -> -1E-6176 Underflow Subnormal Inexact Rounded 412 dqmul830 multiply 3.0E-6172 -1e-5 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped 413 414 dqmul831 multiply 1.0E-5977 1e-200 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped 415 dqmul832 multiply 1.0E-5977 1e-199 -> 1E-6176 Subnormal Rounded 416 dqmul833 multiply 1.0E-5977 1e-198 -> 1.0E-6175 Subnormal 417 dqmul834 multiply 2.0E-5977 2e-198 -> 4.0E-6175 Subnormal 418 dqmul835 multiply 4.0E-5977 4e-198 -> 1.60E-6174 Subnormal 419 dqmul836 multiply 10.0E-5977 10e-198 -> 1.000E-6173 Subnormal 420 dqmul837 multiply 30.0E-5977 30e-198 -> 9.000E-6173 Subnormal 421 dqmul838 multiply 40.0E-5982 40e-166 -> 1.6000E-6145 Subnormal 422 dqmul839 multiply 40.0E-5982 40e-165 -> 1.6000E-6144 Subnormal 423 dqmul840 multiply 40.0E-5982 40e-164 -> 1.6000E-6143 424 425 -- Long operand overflow may be a different path 426 dqmul870 multiply 100 9.999E+6143 -> Infinity Inexact Overflow Rounded 427 dqmul871 multiply 100 -9.999E+6143 -> -Infinity Inexact Overflow Rounded 428 dqmul872 multiply 9.999E+6143 100 -> Infinity Inexact Overflow Rounded 429 dqmul873 multiply -9.999E+6143 100 -> -Infinity Inexact Overflow Rounded 430 431 -- check for double-rounded subnormals 432 dqmul881 multiply 1.2347E-6133 1.2347E-40 -> 1.524E-6173 Inexact Rounded Subnormal Underflow 433 dqmul882 multiply 1.234E-6133 1.234E-40 -> 1.523E-6173 Inexact Rounded Subnormal Underflow 434 dqmul883 multiply 1.23E-6133 1.23E-40 -> 1.513E-6173 Inexact Rounded Subnormal Underflow 435 dqmul884 multiply 1.2E-6133 1.2E-40 -> 1.44E-6173 Subnormal 436 dqmul885 multiply 1.2E-6133 1.2E-41 -> 1.44E-6174 Subnormal 437 dqmul886 multiply 1.2E-6133 1.2E-42 -> 1.4E-6175 Subnormal Inexact Rounded Underflow 438 dqmul887 multiply 1.2E-6133 1.3E-42 -> 1.6E-6175 Subnormal Inexact Rounded Underflow 439 dqmul888 multiply 1.3E-6133 1.3E-42 -> 1.7E-6175 Subnormal Inexact Rounded Underflow 440 dqmul889 multiply 1.3E-6133 1.3E-43 -> 2E-6176 Subnormal Inexact Rounded Underflow 441 dqmul890 multiply 1.3E-6134 1.3E-43 -> 0E-6176 Clamped Subnormal Inexact Rounded Underflow 442 443 dqmul891 multiply 1.2345E-39 1.234E-6133 -> 1.5234E-6172 Inexact Rounded Subnormal Underflow 444 dqmul892 multiply 1.23456E-39 1.234E-6133 -> 1.5234E-6172 Inexact Rounded Subnormal Underflow 445 dqmul893 multiply 1.2345E-40 1.234E-6133 -> 1.523E-6173 Inexact Rounded Subnormal Underflow 446 dqmul894 multiply 1.23456E-40 1.234E-6133 -> 1.523E-6173 Inexact Rounded Subnormal Underflow 447 dqmul895 multiply 1.2345E-41 1.234E-6133 -> 1.52E-6174 Inexact Rounded Subnormal Underflow 448 dqmul896 multiply 1.23456E-41 1.234E-6133 -> 1.52E-6174 Inexact Rounded Subnormal Underflow 449 450 -- Now explore the case where we get a normal result with Underflow 451 -- prove operands are exact 452 dqmul906 multiply 9.999999999999999999999999999999999E-6143 1 -> 9.999999999999999999999999999999999E-6143 453 dqmul907 multiply 1 0.09999999999999999999999999999999999 -> 0.09999999999999999999999999999999999 454 -- the next rounds to Nmin 455 dqmul908 multiply 9.999999999999999999999999999999999E-6143 0.09999999999999999999999999999999999 -> 1.000000000000000000000000000000000E-6143 Underflow Inexact Subnormal Rounded 456 457 -- hugest 458 dqmul909 multiply 9999999999999999999999999999999999 9999999999999999999999999999999999 -> 9.999999999999999999999999999999998E+67 Inexact Rounded 459 -- VG case 460 dqmul910 multiply 8.81125000000001349436E-1548 8.000000000000000000E-1550 -> 7.049000000000010795488000000000000E-3097 Rounded 461 462 -- Examples from SQL proposal (Krishna Kulkarni) 463 precision: 34 464 rounding: half_up 465 maxExponent: 6144 466 minExponent: -6143 467 dqmul911 multiply 130E-2 120E-2 -> 1.5600 468 dqmul912 multiply 130E-2 12E-1 -> 1.560 469 dqmul913 multiply 130E-2 1E0 -> 1.30 470 dqmul914 multiply 1E2 1E4 -> 1E+6 471 472 -- power-of-ten edge cases 473 dqmul1001 multiply 1 10 -> 10 474 dqmul1002 multiply 1 100 -> 100 475 dqmul1003 multiply 1 1000 -> 1000 476 dqmul1004 multiply 1 10000 -> 10000 477 dqmul1005 multiply 1 100000 -> 100000 478 dqmul1006 multiply 1 1000000 -> 1000000 479 dqmul1007 multiply 1 10000000 -> 10000000 480 dqmul1008 multiply 1 100000000 -> 100000000 481 dqmul1009 multiply 1 1000000000 -> 1000000000 482 dqmul1010 multiply 1 10000000000 -> 10000000000 483 dqmul1011 multiply 1 100000000000 -> 100000000000 484 dqmul1012 multiply 1 1000000000000 -> 1000000000000 485 dqmul1013 multiply 1 10000000000000 -> 10000000000000 486 dqmul1014 multiply 1 100000000000000 -> 100000000000000 487 dqmul1015 multiply 1 1000000000000000 -> 1000000000000000 488 489 dqmul1016 multiply 1 1000000000000000000 -> 1000000000000000000 490 dqmul1017 multiply 1 100000000000000000000000000 -> 100000000000000000000000000 491 dqmul1018 multiply 1 1000000000000000000000000000 -> 1000000000000000000000000000 492 dqmul1019 multiply 1 10000000000000000000000000000 -> 10000000000000000000000000000 493 dqmul1020 multiply 1 1000000000000000000000000000000000 -> 1000000000000000000000000000000000 494 495 dqmul1021 multiply 10 1 -> 10 496 dqmul1022 multiply 10 10 -> 100 497 dqmul1023 multiply 10 100 -> 1000 498 dqmul1024 multiply 10 1000 -> 10000 499 dqmul1025 multiply 10 10000 -> 100000 500 dqmul1026 multiply 10 100000 -> 1000000 501 dqmul1027 multiply 10 1000000 -> 10000000 502 dqmul1028 multiply 10 10000000 -> 100000000 503 dqmul1029 multiply 10 100000000 -> 1000000000 504 dqmul1030 multiply 10 1000000000 -> 10000000000 505 dqmul1031 multiply 10 10000000000 -> 100000000000 506 dqmul1032 multiply 10 100000000000 -> 1000000000000 507 dqmul1033 multiply 10 1000000000000 -> 10000000000000 508 dqmul1034 multiply 10 10000000000000 -> 100000000000000 509 dqmul1035 multiply 10 100000000000000 -> 1000000000000000 510 511 dqmul1036 multiply 10 100000000000000000 -> 1000000000000000000 512 dqmul1037 multiply 10 10000000000000000000000000 -> 100000000000000000000000000 513 dqmul1038 multiply 10 100000000000000000000000000 -> 1000000000000000000000000000 514 dqmul1039 multiply 10 1000000000000000000000000000 -> 10000000000000000000000000000 515 dqmul1040 multiply 10 100000000000000000000000000000000 -> 1000000000000000000000000000000000 516 517 dqmul1041 multiply 100 0.1 -> 10.0 518 dqmul1042 multiply 100 1 -> 100 519 dqmul1043 multiply 100 10 -> 1000 520 dqmul1044 multiply 100 100 -> 10000 521 dqmul1045 multiply 100 1000 -> 100000 522 dqmul1046 multiply 100 10000 -> 1000000 523 dqmul1047 multiply 100 100000 -> 10000000 524 dqmul1048 multiply 100 1000000 -> 100000000 525 dqmul1049 multiply 100 10000000 -> 1000000000 526 dqmul1050 multiply 100 100000000 -> 10000000000 527 dqmul1051 multiply 100 1000000000 -> 100000000000 528 dqmul1052 multiply 100 10000000000 -> 1000000000000 529 dqmul1053 multiply 100 100000000000 -> 10000000000000 530 dqmul1054 multiply 100 1000000000000 -> 100000000000000 531 dqmul1055 multiply 100 10000000000000 -> 1000000000000000 532 533 dqmul1056 multiply 100 10000000000000000 -> 1000000000000000000 534 dqmul1057 multiply 100 1000000000000000000000000 -> 100000000000000000000000000 535 dqmul1058 multiply 100 10000000000000000000000000 -> 1000000000000000000000000000 536 dqmul1059 multiply 100 100000000000000000000000000 -> 10000000000000000000000000000 537 dqmul1060 multiply 100 10000000000000000000000000000000 -> 1000000000000000000000000000000000 538 539 dqmul1061 multiply 1000 0.01 -> 10.00 540 dqmul1062 multiply 1000 0.1 -> 100.0 541 dqmul1063 multiply 1000 1 -> 1000 542 dqmul1064 multiply 1000 10 -> 10000 543 dqmul1065 multiply 1000 100 -> 100000 544 dqmul1066 multiply 1000 1000 -> 1000000 545 dqmul1067 multiply 1000 10000 -> 10000000 546 dqmul1068 multiply 1000 100000 -> 100000000 547 dqmul1069 multiply 1000 1000000 -> 1000000000 548 dqmul1070 multiply 1000 10000000 -> 10000000000 549 dqmul1071 multiply 1000 100000000 -> 100000000000 550 dqmul1072 multiply 1000 1000000000 -> 1000000000000 551 dqmul1073 multiply 1000 10000000000 -> 10000000000000 552 dqmul1074 multiply 1000 100000000000 -> 100000000000000 553 dqmul1075 multiply 1000 1000000000000 -> 1000000000000000 554 555 dqmul1076 multiply 1000 1000000000000000 -> 1000000000000000000 556 dqmul1077 multiply 1000 100000000000000000000000 -> 100000000000000000000000000 557 dqmul1078 multiply 1000 1000000000000000000000000 -> 1000000000000000000000000000 558 dqmul1079 multiply 1000 10000000000000000000000000 -> 10000000000000000000000000000 559 dqmul1080 multiply 1000 1000000000000000000000000000000 -> 1000000000000000000000000000000000 560 561 dqmul1081 multiply 10000 0.001 -> 10.000 562 dqmul1082 multiply 10000 0.01 -> 100.00 563 dqmul1083 multiply 10000 0.1 -> 1000.0 564 dqmul1084 multiply 10000 1 -> 10000 565 dqmul1085 multiply 10000 10 -> 100000 566 dqmul1086 multiply 10000 100 -> 1000000 567 dqmul1087 multiply 10000 1000 -> 10000000 568 dqmul1088 multiply 10000 10000 -> 100000000 569 dqmul1089 multiply 10000 100000 -> 1000000000 570 dqmul1090 multiply 10000 1000000 -> 10000000000 571 dqmul1091 multiply 10000 10000000 -> 100000000000 572 dqmul1092 multiply 10000 100000000 -> 1000000000000 573 dqmul1093 multiply 10000 1000000000 -> 10000000000000 574 dqmul1094 multiply 10000 10000000000 -> 100000000000000 575 dqmul1095 multiply 10000 100000000000 -> 1000000000000000 576 577 dqmul1096 multiply 10000 100000000000000 -> 1000000000000000000 578 dqmul1097 multiply 10000 10000000000000000000000 -> 100000000000000000000000000 579 dqmul1098 multiply 10000 100000000000000000000000 -> 1000000000000000000000000000 580 dqmul1099 multiply 10000 1000000000000000000000000 -> 10000000000000000000000000000 581 dqmul1100 multiply 10000 100000000000000000000000000000 -> 1000000000000000000000000000000000 582 583 dqmul1107 multiply 10000 99999999999 -> 999999999990000 584 dqmul1108 multiply 10000 99999999999 -> 999999999990000 585 586 -- Null tests 587 dqmul9990 multiply 10 # -> NaN Invalid_operation 588 dqmul9991 multiply # 10 -> NaN Invalid_operation 589 590
