1 ------------------------------------------------------------------------ 2 -- rounding.decTest -- decimal rounding modes testcases -- 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 -- These tests require that implementations take account of residues in 23 -- order to get correct results for some rounding modes. Rather than 24 -- single rounding tests we therefore need tests for most operators. 25 -- [We do assume add/minus/plus/subtract are common paths, however, as 26 -- is rounding of negatives (if the latter works for addition, assume it 27 -- works for the others, too).] 28 -- 29 -- Round-for-reround (05UP) is tested as a separate block, mostly for 30 -- 'historical' reasons. 31 -- 32 -- Underflow Subnormal and overflow behaviours are tested under the 33 -- individual operators. 34 35 extended: 1 36 precision: 5 -- for easier visual inspection 37 maxExponent: 999 38 minexponent: -999 39 40 -- Addition operators ------------------------------------------------- 41 rounding: down 42 43 radx100 add 12345 -0.1 -> 12344 Inexact Rounded 44 radx101 add 12345 -0.01 -> 12344 Inexact Rounded 45 radx102 add 12345 -0.001 -> 12344 Inexact Rounded 46 radx103 add 12345 -0.00001 -> 12344 Inexact Rounded 47 radx104 add 12345 -0.000001 -> 12344 Inexact Rounded 48 radx105 add 12345 -0.0000001 -> 12344 Inexact Rounded 49 radx106 add 12345 0 -> 12345 50 radx107 add 12345 0.0000001 -> 12345 Inexact Rounded 51 radx108 add 12345 0.000001 -> 12345 Inexact Rounded 52 radx109 add 12345 0.00001 -> 12345 Inexact Rounded 53 radx110 add 12345 0.0001 -> 12345 Inexact Rounded 54 radx111 add 12345 0.001 -> 12345 Inexact Rounded 55 radx112 add 12345 0.01 -> 12345 Inexact Rounded 56 radx113 add 12345 0.1 -> 12345 Inexact Rounded 57 58 radx115 add 12346 0.49999 -> 12346 Inexact Rounded 59 radx116 add 12346 0.5 -> 12346 Inexact Rounded 60 radx117 add 12346 0.50001 -> 12346 Inexact Rounded 61 62 radx120 add 12345 0.4 -> 12345 Inexact Rounded 63 radx121 add 12345 0.49 -> 12345 Inexact Rounded 64 radx122 add 12345 0.499 -> 12345 Inexact Rounded 65 radx123 add 12345 0.49999 -> 12345 Inexact Rounded 66 radx124 add 12345 0.5 -> 12345 Inexact Rounded 67 radx125 add 12345 0.50001 -> 12345 Inexact Rounded 68 radx126 add 12345 0.5001 -> 12345 Inexact Rounded 69 radx127 add 12345 0.501 -> 12345 Inexact Rounded 70 radx128 add 12345 0.51 -> 12345 Inexact Rounded 71 radx129 add 12345 0.6 -> 12345 Inexact Rounded 72 73 rounding: half_down 74 75 radx140 add 12345 -0.1 -> 12345 Inexact Rounded 76 radx141 add 12345 -0.01 -> 12345 Inexact Rounded 77 radx142 add 12345 -0.001 -> 12345 Inexact Rounded 78 radx143 add 12345 -0.00001 -> 12345 Inexact Rounded 79 radx144 add 12345 -0.000001 -> 12345 Inexact Rounded 80 radx145 add 12345 -0.0000001 -> 12345 Inexact Rounded 81 radx146 add 12345 0 -> 12345 82 radx147 add 12345 0.0000001 -> 12345 Inexact Rounded 83 radx148 add 12345 0.000001 -> 12345 Inexact Rounded 84 radx149 add 12345 0.00001 -> 12345 Inexact Rounded 85 radx150 add 12345 0.0001 -> 12345 Inexact Rounded 86 radx151 add 12345 0.001 -> 12345 Inexact Rounded 87 radx152 add 12345 0.01 -> 12345 Inexact Rounded 88 radx153 add 12345 0.1 -> 12345 Inexact Rounded 89 90 radx155 add 12346 0.49999 -> 12346 Inexact Rounded 91 radx156 add 12346 0.5 -> 12346 Inexact Rounded 92 radx157 add 12346 0.50001 -> 12347 Inexact Rounded 93 94 radx160 add 12345 0.4 -> 12345 Inexact Rounded 95 radx161 add 12345 0.49 -> 12345 Inexact Rounded 96 radx162 add 12345 0.499 -> 12345 Inexact Rounded 97 radx163 add 12345 0.49999 -> 12345 Inexact Rounded 98 radx164 add 12345 0.5 -> 12345 Inexact Rounded 99 radx165 add 12345 0.50001 -> 12346 Inexact Rounded 100 radx166 add 12345 0.5001 -> 12346 Inexact Rounded 101 radx167 add 12345 0.501 -> 12346 Inexact Rounded 102 radx168 add 12345 0.51 -> 12346 Inexact Rounded 103 radx169 add 12345 0.6 -> 12346 Inexact Rounded 104 105 rounding: half_even 106 107 radx170 add 12345 -0.1 -> 12345 Inexact Rounded 108 radx171 add 12345 -0.01 -> 12345 Inexact Rounded 109 radx172 add 12345 -0.001 -> 12345 Inexact Rounded 110 radx173 add 12345 -0.00001 -> 12345 Inexact Rounded 111 radx174 add 12345 -0.000001 -> 12345 Inexact Rounded 112 radx175 add 12345 -0.0000001 -> 12345 Inexact Rounded 113 radx176 add 12345 0 -> 12345 114 radx177 add 12345 0.0000001 -> 12345 Inexact Rounded 115 radx178 add 12345 0.000001 -> 12345 Inexact Rounded 116 radx179 add 12345 0.00001 -> 12345 Inexact Rounded 117 radx180 add 12345 0.0001 -> 12345 Inexact Rounded 118 radx181 add 12345 0.001 -> 12345 Inexact Rounded 119 radx182 add 12345 0.01 -> 12345 Inexact Rounded 120 radx183 add 12345 0.1 -> 12345 Inexact Rounded 121 122 radx185 add 12346 0.49999 -> 12346 Inexact Rounded 123 radx186 add 12346 0.5 -> 12346 Inexact Rounded 124 radx187 add 12346 0.50001 -> 12347 Inexact Rounded 125 126 radx190 add 12345 0.4 -> 12345 Inexact Rounded 127 radx191 add 12345 0.49 -> 12345 Inexact Rounded 128 radx192 add 12345 0.499 -> 12345 Inexact Rounded 129 radx193 add 12345 0.49999 -> 12345 Inexact Rounded 130 radx194 add 12345 0.5 -> 12346 Inexact Rounded 131 radx195 add 12345 0.50001 -> 12346 Inexact Rounded 132 radx196 add 12345 0.5001 -> 12346 Inexact Rounded 133 radx197 add 12345 0.501 -> 12346 Inexact Rounded 134 radx198 add 12345 0.51 -> 12346 Inexact Rounded 135 radx199 add 12345 0.6 -> 12346 Inexact Rounded 136 137 rounding: half_up 138 139 radx200 add 12345 -0.1 -> 12345 Inexact Rounded 140 radx201 add 12345 -0.01 -> 12345 Inexact Rounded 141 radx202 add 12345 -0.001 -> 12345 Inexact Rounded 142 radx203 add 12345 -0.00001 -> 12345 Inexact Rounded 143 radx204 add 12345 -0.000001 -> 12345 Inexact Rounded 144 radx205 add 12345 -0.0000001 -> 12345 Inexact Rounded 145 radx206 add 12345 0 -> 12345 146 radx207 add 12345 0.0000001 -> 12345 Inexact Rounded 147 radx208 add 12345 0.000001 -> 12345 Inexact Rounded 148 radx209 add 12345 0.00001 -> 12345 Inexact Rounded 149 radx210 add 12345 0.0001 -> 12345 Inexact Rounded 150 radx211 add 12345 0.001 -> 12345 Inexact Rounded 151 radx212 add 12345 0.01 -> 12345 Inexact Rounded 152 radx213 add 12345 0.1 -> 12345 Inexact Rounded 153 154 radx215 add 12346 0.49999 -> 12346 Inexact Rounded 155 radx216 add 12346 0.5 -> 12347 Inexact Rounded 156 radx217 add 12346 0.50001 -> 12347 Inexact Rounded 157 158 radx220 add 12345 0.4 -> 12345 Inexact Rounded 159 radx221 add 12345 0.49 -> 12345 Inexact Rounded 160 radx222 add 12345 0.499 -> 12345 Inexact Rounded 161 radx223 add 12345 0.49999 -> 12345 Inexact Rounded 162 radx224 add 12345 0.5 -> 12346 Inexact Rounded 163 radx225 add 12345 0.50001 -> 12346 Inexact Rounded 164 radx226 add 12345 0.5001 -> 12346 Inexact Rounded 165 radx227 add 12345 0.501 -> 12346 Inexact Rounded 166 radx228 add 12345 0.51 -> 12346 Inexact Rounded 167 radx229 add 12345 0.6 -> 12346 Inexact Rounded 168 169 rounding: up 170 171 radx230 add 12345 -0.1 -> 12345 Inexact Rounded 172 radx231 add 12345 -0.01 -> 12345 Inexact Rounded 173 radx232 add 12345 -0.001 -> 12345 Inexact Rounded 174 radx233 add 12345 -0.00001 -> 12345 Inexact Rounded 175 radx234 add 12345 -0.000001 -> 12345 Inexact Rounded 176 radx235 add 12345 -0.0000001 -> 12345 Inexact Rounded 177 radx236 add 12345 0 -> 12345 178 radx237 add 12345 0.0000001 -> 12346 Inexact Rounded 179 radx238 add 12345 0.000001 -> 12346 Inexact Rounded 180 radx239 add 12345 0.00001 -> 12346 Inexact Rounded 181 radx240 add 12345 0.0001 -> 12346 Inexact Rounded 182 radx241 add 12345 0.001 -> 12346 Inexact Rounded 183 radx242 add 12345 0.01 -> 12346 Inexact Rounded 184 radx243 add 12345 0.1 -> 12346 Inexact Rounded 185 186 radx245 add 12346 0.49999 -> 12347 Inexact Rounded 187 radx246 add 12346 0.5 -> 12347 Inexact Rounded 188 radx247 add 12346 0.50001 -> 12347 Inexact Rounded 189 190 radx250 add 12345 0.4 -> 12346 Inexact Rounded 191 radx251 add 12345 0.49 -> 12346 Inexact Rounded 192 radx252 add 12345 0.499 -> 12346 Inexact Rounded 193 radx253 add 12345 0.49999 -> 12346 Inexact Rounded 194 radx254 add 12345 0.5 -> 12346 Inexact Rounded 195 radx255 add 12345 0.50001 -> 12346 Inexact Rounded 196 radx256 add 12345 0.5001 -> 12346 Inexact Rounded 197 radx257 add 12345 0.501 -> 12346 Inexact Rounded 198 radx258 add 12345 0.51 -> 12346 Inexact Rounded 199 radx259 add 12345 0.6 -> 12346 Inexact Rounded 200 201 rounding: floor 202 203 radx300 add 12345 -0.1 -> 12344 Inexact Rounded 204 radx301 add 12345 -0.01 -> 12344 Inexact Rounded 205 radx302 add 12345 -0.001 -> 12344 Inexact Rounded 206 radx303 add 12345 -0.00001 -> 12344 Inexact Rounded 207 radx304 add 12345 -0.000001 -> 12344 Inexact Rounded 208 radx305 add 12345 -0.0000001 -> 12344 Inexact Rounded 209 radx306 add 12345 0 -> 12345 210 radx307 add 12345 0.0000001 -> 12345 Inexact Rounded 211 radx308 add 12345 0.000001 -> 12345 Inexact Rounded 212 radx309 add 12345 0.00001 -> 12345 Inexact Rounded 213 radx310 add 12345 0.0001 -> 12345 Inexact Rounded 214 radx311 add 12345 0.001 -> 12345 Inexact Rounded 215 radx312 add 12345 0.01 -> 12345 Inexact Rounded 216 radx313 add 12345 0.1 -> 12345 Inexact Rounded 217 218 radx315 add 12346 0.49999 -> 12346 Inexact Rounded 219 radx316 add 12346 0.5 -> 12346 Inexact Rounded 220 radx317 add 12346 0.50001 -> 12346 Inexact Rounded 221 222 radx320 add 12345 0.4 -> 12345 Inexact Rounded 223 radx321 add 12345 0.49 -> 12345 Inexact Rounded 224 radx322 add 12345 0.499 -> 12345 Inexact Rounded 225 radx323 add 12345 0.49999 -> 12345 Inexact Rounded 226 radx324 add 12345 0.5 -> 12345 Inexact Rounded 227 radx325 add 12345 0.50001 -> 12345 Inexact Rounded 228 radx326 add 12345 0.5001 -> 12345 Inexact Rounded 229 radx327 add 12345 0.501 -> 12345 Inexact Rounded 230 radx328 add 12345 0.51 -> 12345 Inexact Rounded 231 radx329 add 12345 0.6 -> 12345 Inexact Rounded 232 233 rounding: ceiling 234 235 radx330 add 12345 -0.1 -> 12345 Inexact Rounded 236 radx331 add 12345 -0.01 -> 12345 Inexact Rounded 237 radx332 add 12345 -0.001 -> 12345 Inexact Rounded 238 radx333 add 12345 -0.00001 -> 12345 Inexact Rounded 239 radx334 add 12345 -0.000001 -> 12345 Inexact Rounded 240 radx335 add 12345 -0.0000001 -> 12345 Inexact Rounded 241 radx336 add 12345 0 -> 12345 242 radx337 add 12345 0.0000001 -> 12346 Inexact Rounded 243 radx338 add 12345 0.000001 -> 12346 Inexact Rounded 244 radx339 add 12345 0.00001 -> 12346 Inexact Rounded 245 radx340 add 12345 0.0001 -> 12346 Inexact Rounded 246 radx341 add 12345 0.001 -> 12346 Inexact Rounded 247 radx342 add 12345 0.01 -> 12346 Inexact Rounded 248 radx343 add 12345 0.1 -> 12346 Inexact Rounded 249 250 radx345 add 12346 0.49999 -> 12347 Inexact Rounded 251 radx346 add 12346 0.5 -> 12347 Inexact Rounded 252 radx347 add 12346 0.50001 -> 12347 Inexact Rounded 253 254 radx350 add 12345 0.4 -> 12346 Inexact Rounded 255 radx351 add 12345 0.49 -> 12346 Inexact Rounded 256 radx352 add 12345 0.499 -> 12346 Inexact Rounded 257 radx353 add 12345 0.49999 -> 12346 Inexact Rounded 258 radx354 add 12345 0.5 -> 12346 Inexact Rounded 259 radx355 add 12345 0.50001 -> 12346 Inexact Rounded 260 radx356 add 12345 0.5001 -> 12346 Inexact Rounded 261 radx357 add 12345 0.501 -> 12346 Inexact Rounded 262 radx358 add 12345 0.51 -> 12346 Inexact Rounded 263 radx359 add 12345 0.6 -> 12346 Inexact Rounded 264 265 -- negatives... 266 267 rounding: down 268 269 rsux100 add -12345 -0.1 -> -12345 Inexact Rounded 270 rsux101 add -12345 -0.01 -> -12345 Inexact Rounded 271 rsux102 add -12345 -0.001 -> -12345 Inexact Rounded 272 rsux103 add -12345 -0.00001 -> -12345 Inexact Rounded 273 rsux104 add -12345 -0.000001 -> -12345 Inexact Rounded 274 rsux105 add -12345 -0.0000001 -> -12345 Inexact Rounded 275 rsux106 add -12345 0 -> -12345 276 rsux107 add -12345 0.0000001 -> -12344 Inexact Rounded 277 rsux108 add -12345 0.000001 -> -12344 Inexact Rounded 278 rsux109 add -12345 0.00001 -> -12344 Inexact Rounded 279 rsux110 add -12345 0.0001 -> -12344 Inexact Rounded 280 rsux111 add -12345 0.001 -> -12344 Inexact Rounded 281 rsux112 add -12345 0.01 -> -12344 Inexact Rounded 282 rsux113 add -12345 0.1 -> -12344 Inexact Rounded 283 284 rsux115 add -12346 0.49999 -> -12345 Inexact Rounded 285 rsux116 add -12346 0.5 -> -12345 Inexact Rounded 286 rsux117 add -12346 0.50001 -> -12345 Inexact Rounded 287 288 rsux120 add -12345 0.4 -> -12344 Inexact Rounded 289 rsux121 add -12345 0.49 -> -12344 Inexact Rounded 290 rsux122 add -12345 0.499 -> -12344 Inexact Rounded 291 rsux123 add -12345 0.49999 -> -12344 Inexact Rounded 292 rsux124 add -12345 0.5 -> -12344 Inexact Rounded 293 rsux125 add -12345 0.50001 -> -12344 Inexact Rounded 294 rsux126 add -12345 0.5001 -> -12344 Inexact Rounded 295 rsux127 add -12345 0.501 -> -12344 Inexact Rounded 296 rsux128 add -12345 0.51 -> -12344 Inexact Rounded 297 rsux129 add -12345 0.6 -> -12344 Inexact Rounded 298 299 rounding: half_down 300 301 rsux140 add -12345 -0.1 -> -12345 Inexact Rounded 302 rsux141 add -12345 -0.01 -> -12345 Inexact Rounded 303 rsux142 add -12345 -0.001 -> -12345 Inexact Rounded 304 rsux143 add -12345 -0.00001 -> -12345 Inexact Rounded 305 rsux144 add -12345 -0.000001 -> -12345 Inexact Rounded 306 rsux145 add -12345 -0.0000001 -> -12345 Inexact Rounded 307 rsux146 add -12345 0 -> -12345 308 rsux147 add -12345 0.0000001 -> -12345 Inexact Rounded 309 rsux148 add -12345 0.000001 -> -12345 Inexact Rounded 310 rsux149 add -12345 0.00001 -> -12345 Inexact Rounded 311 rsux150 add -12345 0.0001 -> -12345 Inexact Rounded 312 rsux151 add -12345 0.001 -> -12345 Inexact Rounded 313 rsux152 add -12345 0.01 -> -12345 Inexact Rounded 314 rsux153 add -12345 0.1 -> -12345 Inexact Rounded 315 316 rsux155 add -12346 0.49999 -> -12346 Inexact Rounded 317 rsux156 add -12346 0.5 -> -12345 Inexact Rounded 318 rsux157 add -12346 0.50001 -> -12345 Inexact Rounded 319 320 rsux160 add -12345 0.4 -> -12345 Inexact Rounded 321 rsux161 add -12345 0.49 -> -12345 Inexact Rounded 322 rsux162 add -12345 0.499 -> -12345 Inexact Rounded 323 rsux163 add -12345 0.49999 -> -12345 Inexact Rounded 324 rsux164 add -12345 0.5 -> -12344 Inexact Rounded 325 rsux165 add -12345 0.50001 -> -12344 Inexact Rounded 326 rsux166 add -12345 0.5001 -> -12344 Inexact Rounded 327 rsux167 add -12345 0.501 -> -12344 Inexact Rounded 328 rsux168 add -12345 0.51 -> -12344 Inexact Rounded 329 rsux169 add -12345 0.6 -> -12344 Inexact Rounded 330 331 rounding: half_even 332 333 rsux170 add -12345 -0.1 -> -12345 Inexact Rounded 334 rsux171 add -12345 -0.01 -> -12345 Inexact Rounded 335 rsux172 add -12345 -0.001 -> -12345 Inexact Rounded 336 rsux173 add -12345 -0.00001 -> -12345 Inexact Rounded 337 rsux174 add -12345 -0.000001 -> -12345 Inexact Rounded 338 rsux175 add -12345 -0.0000001 -> -12345 Inexact Rounded 339 rsux176 add -12345 0 -> -12345 340 rsux177 add -12345 0.0000001 -> -12345 Inexact Rounded 341 rsux178 add -12345 0.000001 -> -12345 Inexact Rounded 342 rsux179 add -12345 0.00001 -> -12345 Inexact Rounded 343 rsux180 add -12345 0.0001 -> -12345 Inexact Rounded 344 rsux181 add -12345 0.001 -> -12345 Inexact Rounded 345 rsux182 add -12345 0.01 -> -12345 Inexact Rounded 346 rsux183 add -12345 0.1 -> -12345 Inexact Rounded 347 348 rsux185 add -12346 0.49999 -> -12346 Inexact Rounded 349 rsux186 add -12346 0.5 -> -12346 Inexact Rounded 350 rsux187 add -12346 0.50001 -> -12345 Inexact Rounded 351 352 rsux190 add -12345 0.4 -> -12345 Inexact Rounded 353 rsux191 add -12345 0.49 -> -12345 Inexact Rounded 354 rsux192 add -12345 0.499 -> -12345 Inexact Rounded 355 rsux193 add -12345 0.49999 -> -12345 Inexact Rounded 356 rsux194 add -12345 0.5 -> -12344 Inexact Rounded 357 rsux195 add -12345 0.50001 -> -12344 Inexact Rounded 358 rsux196 add -12345 0.5001 -> -12344 Inexact Rounded 359 rsux197 add -12345 0.501 -> -12344 Inexact Rounded 360 rsux198 add -12345 0.51 -> -12344 Inexact Rounded 361 rsux199 add -12345 0.6 -> -12344 Inexact Rounded 362 363 rounding: half_up 364 365 rsux200 add -12345 -0.1 -> -12345 Inexact Rounded 366 rsux201 add -12345 -0.01 -> -12345 Inexact Rounded 367 rsux202 add -12345 -0.001 -> -12345 Inexact Rounded 368 rsux203 add -12345 -0.00001 -> -12345 Inexact Rounded 369 rsux204 add -12345 -0.000001 -> -12345 Inexact Rounded 370 rsux205 add -12345 -0.0000001 -> -12345 Inexact Rounded 371 rsux206 add -12345 0 -> -12345 372 rsux207 add -12345 0.0000001 -> -12345 Inexact Rounded 373 rsux208 add -12345 0.000001 -> -12345 Inexact Rounded 374 rsux209 add -12345 0.00001 -> -12345 Inexact Rounded 375 rsux210 add -12345 0.0001 -> -12345 Inexact Rounded 376 rsux211 add -12345 0.001 -> -12345 Inexact Rounded 377 rsux212 add -12345 0.01 -> -12345 Inexact Rounded 378 rsux213 add -12345 0.1 -> -12345 Inexact Rounded 379 380 rsux215 add -12346 0.49999 -> -12346 Inexact Rounded 381 rsux216 add -12346 0.5 -> -12346 Inexact Rounded 382 rsux217 add -12346 0.50001 -> -12345 Inexact Rounded 383 384 rsux220 add -12345 0.4 -> -12345 Inexact Rounded 385 rsux221 add -12345 0.49 -> -12345 Inexact Rounded 386 rsux222 add -12345 0.499 -> -12345 Inexact Rounded 387 rsux223 add -12345 0.49999 -> -12345 Inexact Rounded 388 rsux224 add -12345 0.5 -> -12345 Inexact Rounded 389 rsux225 add -12345 0.50001 -> -12344 Inexact Rounded 390 rsux226 add -12345 0.5001 -> -12344 Inexact Rounded 391 rsux227 add -12345 0.501 -> -12344 Inexact Rounded 392 rsux228 add -12345 0.51 -> -12344 Inexact Rounded 393 rsux229 add -12345 0.6 -> -12344 Inexact Rounded 394 395 rounding: up 396 397 rsux230 add -12345 -0.1 -> -12346 Inexact Rounded 398 rsux231 add -12345 -0.01 -> -12346 Inexact Rounded 399 rsux232 add -12345 -0.001 -> -12346 Inexact Rounded 400 rsux233 add -12345 -0.00001 -> -12346 Inexact Rounded 401 rsux234 add -12345 -0.000001 -> -12346 Inexact Rounded 402 rsux235 add -12345 -0.0000001 -> -12346 Inexact Rounded 403 rsux236 add -12345 0 -> -12345 404 rsux237 add -12345 0.0000001 -> -12345 Inexact Rounded 405 rsux238 add -12345 0.000001 -> -12345 Inexact Rounded 406 rsux239 add -12345 0.00001 -> -12345 Inexact Rounded 407 rsux240 add -12345 0.0001 -> -12345 Inexact Rounded 408 rsux241 add -12345 0.001 -> -12345 Inexact Rounded 409 rsux242 add -12345 0.01 -> -12345 Inexact Rounded 410 rsux243 add -12345 0.1 -> -12345 Inexact Rounded 411 412 rsux245 add -12346 0.49999 -> -12346 Inexact Rounded 413 rsux246 add -12346 0.5 -> -12346 Inexact Rounded 414 rsux247 add -12346 0.50001 -> -12346 Inexact Rounded 415 416 rsux250 add -12345 0.4 -> -12345 Inexact Rounded 417 rsux251 add -12345 0.49 -> -12345 Inexact Rounded 418 rsux252 add -12345 0.499 -> -12345 Inexact Rounded 419 rsux253 add -12345 0.49999 -> -12345 Inexact Rounded 420 rsux254 add -12345 0.5 -> -12345 Inexact Rounded 421 rsux255 add -12345 0.50001 -> -12345 Inexact Rounded 422 rsux256 add -12345 0.5001 -> -12345 Inexact Rounded 423 rsux257 add -12345 0.501 -> -12345 Inexact Rounded 424 rsux258 add -12345 0.51 -> -12345 Inexact Rounded 425 rsux259 add -12345 0.6 -> -12345 Inexact Rounded 426 427 rounding: floor 428 429 rsux300 add -12345 -0.1 -> -12346 Inexact Rounded 430 rsux301 add -12345 -0.01 -> -12346 Inexact Rounded 431 rsux302 add -12345 -0.001 -> -12346 Inexact Rounded 432 rsux303 add -12345 -0.00001 -> -12346 Inexact Rounded 433 rsux304 add -12345 -0.000001 -> -12346 Inexact Rounded 434 rsux305 add -12345 -0.0000001 -> -12346 Inexact Rounded 435 rsux306 add -12345 0 -> -12345 436 rsux307 add -12345 0.0000001 -> -12345 Inexact Rounded 437 rsux308 add -12345 0.000001 -> -12345 Inexact Rounded 438 rsux309 add -12345 0.00001 -> -12345 Inexact Rounded 439 rsux310 add -12345 0.0001 -> -12345 Inexact Rounded 440 rsux311 add -12345 0.001 -> -12345 Inexact Rounded 441 rsux312 add -12345 0.01 -> -12345 Inexact Rounded 442 rsux313 add -12345 0.1 -> -12345 Inexact Rounded 443 444 rsux315 add -12346 0.49999 -> -12346 Inexact Rounded 445 rsux316 add -12346 0.5 -> -12346 Inexact Rounded 446 rsux317 add -12346 0.50001 -> -12346 Inexact Rounded 447 448 rsux320 add -12345 0.4 -> -12345 Inexact Rounded 449 rsux321 add -12345 0.49 -> -12345 Inexact Rounded 450 rsux322 add -12345 0.499 -> -12345 Inexact Rounded 451 rsux323 add -12345 0.49999 -> -12345 Inexact Rounded 452 rsux324 add -12345 0.5 -> -12345 Inexact Rounded 453 rsux325 add -12345 0.50001 -> -12345 Inexact Rounded 454 rsux326 add -12345 0.5001 -> -12345 Inexact Rounded 455 rsux327 add -12345 0.501 -> -12345 Inexact Rounded 456 rsux328 add -12345 0.51 -> -12345 Inexact Rounded 457 rsux329 add -12345 0.6 -> -12345 Inexact Rounded 458 459 rounding: ceiling 460 461 rsux330 add -12345 -0.1 -> -12345 Inexact Rounded 462 rsux331 add -12345 -0.01 -> -12345 Inexact Rounded 463 rsux332 add -12345 -0.001 -> -12345 Inexact Rounded 464 rsux333 add -12345 -0.00001 -> -12345 Inexact Rounded 465 rsux334 add -12345 -0.000001 -> -12345 Inexact Rounded 466 rsux335 add -12345 -0.0000001 -> -12345 Inexact Rounded 467 rsux336 add -12345 0 -> -12345 468 rsux337 add -12345 0.0000001 -> -12344 Inexact Rounded 469 rsux338 add -12345 0.000001 -> -12344 Inexact Rounded 470 rsux339 add -12345 0.00001 -> -12344 Inexact Rounded 471 rsux340 add -12345 0.0001 -> -12344 Inexact Rounded 472 rsux341 add -12345 0.001 -> -12344 Inexact Rounded 473 rsux342 add -12345 0.01 -> -12344 Inexact Rounded 474 rsux343 add -12345 0.1 -> -12344 Inexact Rounded 475 476 rsux345 add -12346 0.49999 -> -12345 Inexact Rounded 477 rsux346 add -12346 0.5 -> -12345 Inexact Rounded 478 rsux347 add -12346 0.50001 -> -12345 Inexact Rounded 479 480 rsux350 add -12345 0.4 -> -12344 Inexact Rounded 481 rsux351 add -12345 0.49 -> -12344 Inexact Rounded 482 rsux352 add -12345 0.499 -> -12344 Inexact Rounded 483 rsux353 add -12345 0.49999 -> -12344 Inexact Rounded 484 rsux354 add -12345 0.5 -> -12344 Inexact Rounded 485 rsux355 add -12345 0.50001 -> -12344 Inexact Rounded 486 rsux356 add -12345 0.5001 -> -12344 Inexact Rounded 487 rsux357 add -12345 0.501 -> -12344 Inexact Rounded 488 rsux358 add -12345 0.51 -> -12344 Inexact Rounded 489 rsux359 add -12345 0.6 -> -12344 Inexact Rounded 490 491 -- Check cancellation subtractions 492 -- (The IEEE 854 'curious rule' in $6.3) 493 494 rounding: down 495 rzex001 add 0 0 -> 0 496 rzex002 add 0 -0 -> 0 497 rzex003 add -0 0 -> 0 498 rzex004 add -0 -0 -> -0 499 rzex005 add 1 -1 -> 0 500 rzex006 add -1 1 -> 0 501 rzex007 add 1.5 -1.5 -> 0.0 502 rzex008 add -1.5 1.5 -> 0.0 503 rzex009 add 2 -2 -> 0 504 rzex010 add -2 2 -> 0 505 506 rounding: up 507 rzex011 add 0 0 -> 0 508 rzex012 add 0 -0 -> 0 509 rzex013 add -0 0 -> 0 510 rzex014 add -0 -0 -> -0 511 rzex015 add 1 -1 -> 0 512 rzex016 add -1 1 -> 0 513 rzex017 add 1.5 -1.5 -> 0.0 514 rzex018 add -1.5 1.5 -> 0.0 515 rzex019 add 2 -2 -> 0 516 rzex020 add -2 2 -> 0 517 518 rounding: half_up 519 rzex021 add 0 0 -> 0 520 rzex022 add 0 -0 -> 0 521 rzex023 add -0 0 -> 0 522 rzex024 add -0 -0 -> -0 523 rzex025 add 1 -1 -> 0 524 rzex026 add -1 1 -> 0 525 rzex027 add 1.5 -1.5 -> 0.0 526 rzex028 add -1.5 1.5 -> 0.0 527 rzex029 add 2 -2 -> 0 528 rzex030 add -2 2 -> 0 529 530 rounding: half_down 531 rzex031 add 0 0 -> 0 532 rzex032 add 0 -0 -> 0 533 rzex033 add -0 0 -> 0 534 rzex034 add -0 -0 -> -0 535 rzex035 add 1 -1 -> 0 536 rzex036 add -1 1 -> 0 537 rzex037 add 1.5 -1.5 -> 0.0 538 rzex038 add -1.5 1.5 -> 0.0 539 rzex039 add 2 -2 -> 0 540 rzex040 add -2 2 -> 0 541 542 rounding: half_even 543 rzex041 add 0 0 -> 0 544 rzex042 add 0 -0 -> 0 545 rzex043 add -0 0 -> 0 546 rzex044 add -0 -0 -> -0 547 rzex045 add 1 -1 -> 0 548 rzex046 add -1 1 -> 0 549 rzex047 add 1.5 -1.5 -> 0.0 550 rzex048 add -1.5 1.5 -> 0.0 551 rzex049 add 2 -2 -> 0 552 rzex050 add -2 2 -> 0 553 554 rounding: floor 555 rzex051 add 0 0 -> 0 556 rzex052 add 0 -0 -> -0 -- here are two 'curious' 557 rzex053 add -0 0 -> -0 -- 558 rzex054 add -0 -0 -> -0 559 rzex055 add 1 -1 -> -0 -- here are the rest 560 rzex056 add -1 1 -> -0 -- .. 561 rzex057 add 1.5 -1.5 -> -0.0 -- .. 562 rzex058 add -1.5 1.5 -> -0.0 -- .. 563 rzex059 add 2 -2 -> -0 -- .. 564 rzex060 add -2 2 -> -0 -- .. 565 566 rounding: ceiling 567 rzex061 add 0 0 -> 0 568 rzex062 add 0 -0 -> 0 569 rzex063 add -0 0 -> 0 570 rzex064 add -0 -0 -> -0 571 rzex065 add 1 -1 -> 0 572 rzex066 add -1 1 -> 0 573 rzex067 add 1.5 -1.5 -> 0.0 574 rzex068 add -1.5 1.5 -> 0.0 575 rzex069 add 2 -2 -> 0 576 rzex070 add -2 2 -> 0 577 578 579 -- Division operators ------------------------------------------------- 580 581 rounding: down 582 rdvx101 divide 12345 1 -> 12345 583 rdvx102 divide 12345 1.0001 -> 12343 Inexact Rounded 584 rdvx103 divide 12345 1.001 -> 12332 Inexact Rounded 585 rdvx104 divide 12345 1.01 -> 12222 Inexact Rounded 586 rdvx105 divide 12345 1.1 -> 11222 Inexact Rounded 587 rdvx106 divide 12355 4 -> 3088.7 Inexact Rounded 588 rdvx107 divide 12345 4 -> 3086.2 Inexact Rounded 589 rdvx108 divide 12355 4.0001 -> 3088.6 Inexact Rounded 590 rdvx109 divide 12345 4.0001 -> 3086.1 Inexact Rounded 591 rdvx110 divide 12345 4.9 -> 2519.3 Inexact Rounded 592 rdvx111 divide 12345 4.99 -> 2473.9 Inexact Rounded 593 rdvx112 divide 12345 4.999 -> 2469.4 Inexact Rounded 594 rdvx113 divide 12345 4.9999 -> 2469.0 Inexact Rounded 595 rdvx114 divide 12345 5 -> 2469 596 rdvx115 divide 12345 5.0001 -> 2468.9 Inexact Rounded 597 rdvx116 divide 12345 5.001 -> 2468.5 Inexact Rounded 598 rdvx117 divide 12345 5.01 -> 2464.0 Inexact Rounded 599 rdvx118 divide 12345 5.1 -> 2420.5 Inexact Rounded 600 601 rounding: half_down 602 rdvx201 divide 12345 1 -> 12345 603 rdvx202 divide 12345 1.0001 -> 12344 Inexact Rounded 604 rdvx203 divide 12345 1.001 -> 12333 Inexact Rounded 605 rdvx204 divide 12345 1.01 -> 12223 Inexact Rounded 606 rdvx205 divide 12345 1.1 -> 11223 Inexact Rounded 607 rdvx206 divide 12355 4 -> 3088.7 Inexact Rounded 608 rdvx207 divide 12345 4 -> 3086.2 Inexact Rounded 609 rdvx208 divide 12355 4.0001 -> 3088.7 Inexact Rounded 610 rdvx209 divide 12345 4.0001 -> 3086.2 Inexact Rounded 611 rdvx210 divide 12345 4.9 -> 2519.4 Inexact Rounded 612 rdvx211 divide 12345 4.99 -> 2473.9 Inexact Rounded 613 rdvx212 divide 12345 4.999 -> 2469.5 Inexact Rounded 614 rdvx213 divide 12345 4.9999 -> 2469.0 Inexact Rounded 615 rdvx214 divide 12345 5 -> 2469 616 rdvx215 divide 12345 5.0001 -> 2469.0 Inexact Rounded 617 rdvx216 divide 12345 5.001 -> 2468.5 Inexact Rounded 618 rdvx217 divide 12345 5.01 -> 2464.1 Inexact Rounded 619 rdvx218 divide 12345 5.1 -> 2420.6 Inexact Rounded 620 621 rounding: half_even 622 rdvx301 divide 12345 1 -> 12345 623 rdvx302 divide 12345 1.0001 -> 12344 Inexact Rounded 624 rdvx303 divide 12345 1.001 -> 12333 Inexact Rounded 625 rdvx304 divide 12345 1.01 -> 12223 Inexact Rounded 626 rdvx305 divide 12345 1.1 -> 11223 Inexact Rounded 627 rdvx306 divide 12355 4 -> 3088.8 Inexact Rounded 628 rdvx307 divide 12345 4 -> 3086.2 Inexact Rounded 629 rdvx308 divide 12355 4.0001 -> 3088.7 Inexact Rounded 630 rdvx309 divide 12345 4.0001 -> 3086.2 Inexact Rounded 631 rdvx310 divide 12345 4.9 -> 2519.4 Inexact Rounded 632 rdvx311 divide 12345 4.99 -> 2473.9 Inexact Rounded 633 rdvx312 divide 12345 4.999 -> 2469.5 Inexact Rounded 634 rdvx313 divide 12345 4.9999 -> 2469.0 Inexact Rounded 635 rdvx314 divide 12345 5 -> 2469 636 rdvx315 divide 12345 5.0001 -> 2469.0 Inexact Rounded 637 rdvx316 divide 12345 5.001 -> 2468.5 Inexact Rounded 638 rdvx317 divide 12345 5.01 -> 2464.1 Inexact Rounded 639 rdvx318 divide 12345 5.1 -> 2420.6 Inexact Rounded 640 641 rounding: half_up 642 rdvx401 divide 12345 1 -> 12345 643 rdvx402 divide 12345 1.0001 -> 12344 Inexact Rounded 644 rdvx403 divide 12345 1.001 -> 12333 Inexact Rounded 645 rdvx404 divide 12345 1.01 -> 12223 Inexact Rounded 646 rdvx405 divide 12345 1.1 -> 11223 Inexact Rounded 647 rdvx406 divide 12355 4 -> 3088.8 Inexact Rounded 648 rdvx407 divide 12345 4 -> 3086.3 Inexact Rounded 649 rdvx408 divide 12355 4.0001 -> 3088.7 Inexact Rounded 650 rdvx409 divide 12345 4.0001 -> 3086.2 Inexact Rounded 651 rdvx410 divide 12345 4.9 -> 2519.4 Inexact Rounded 652 rdvx411 divide 12345 4.99 -> 2473.9 Inexact Rounded 653 rdvx412 divide 12345 4.999 -> 2469.5 Inexact Rounded 654 rdvx413 divide 12345 4.9999 -> 2469.0 Inexact Rounded 655 rdvx414 divide 12345 5 -> 2469 656 rdvx415 divide 12345 5.0001 -> 2469.0 Inexact Rounded 657 rdvx416 divide 12345 5.001 -> 2468.5 Inexact Rounded 658 rdvx417 divide 12345 5.01 -> 2464.1 Inexact Rounded 659 rdvx418 divide 12345 5.1 -> 2420.6 Inexact Rounded 660 661 rounding: up 662 rdvx501 divide 12345 1 -> 12345 663 rdvx502 divide 12345 1.0001 -> 12344 Inexact Rounded 664 rdvx503 divide 12345 1.001 -> 12333 Inexact Rounded 665 rdvx504 divide 12345 1.01 -> 12223 Inexact Rounded 666 rdvx505 divide 12345 1.1 -> 11223 Inexact Rounded 667 rdvx506 divide 12355 4 -> 3088.8 Inexact Rounded 668 rdvx507 divide 12345 4 -> 3086.3 Inexact Rounded 669 rdvx508 divide 12355 4.0001 -> 3088.7 Inexact Rounded 670 rdvx509 divide 12345 4.0001 -> 3086.2 Inexact Rounded 671 rdvx510 divide 12345 4.9 -> 2519.4 Inexact Rounded 672 rdvx511 divide 12345 4.99 -> 2474.0 Inexact Rounded 673 rdvx512 divide 12345 4.999 -> 2469.5 Inexact Rounded 674 rdvx513 divide 12345 4.9999 -> 2469.1 Inexact Rounded 675 rdvx514 divide 12345 5 -> 2469 676 rdvx515 divide 12345 5.0001 -> 2469.0 Inexact Rounded 677 rdvx516 divide 12345 5.001 -> 2468.6 Inexact Rounded 678 rdvx517 divide 12345 5.01 -> 2464.1 Inexact Rounded 679 rdvx518 divide 12345 5.1 -> 2420.6 Inexact Rounded 680 681 rounding: floor 682 rdvx601 divide 12345 1 -> 12345 683 rdvx602 divide 12345 1.0001 -> 12343 Inexact Rounded 684 rdvx603 divide 12345 1.001 -> 12332 Inexact Rounded 685 rdvx604 divide 12345 1.01 -> 12222 Inexact Rounded 686 rdvx605 divide 12345 1.1 -> 11222 Inexact Rounded 687 rdvx606 divide 12355 4 -> 3088.7 Inexact Rounded 688 rdvx607 divide 12345 4 -> 3086.2 Inexact Rounded 689 rdvx608 divide 12355 4.0001 -> 3088.6 Inexact Rounded 690 rdvx609 divide 12345 4.0001 -> 3086.1 Inexact Rounded 691 rdvx610 divide 12345 4.9 -> 2519.3 Inexact Rounded 692 rdvx611 divide 12345 4.99 -> 2473.9 Inexact Rounded 693 rdvx612 divide 12345 4.999 -> 2469.4 Inexact Rounded 694 rdvx613 divide 12345 4.9999 -> 2469.0 Inexact Rounded 695 rdvx614 divide 12345 5 -> 2469 696 rdvx615 divide 12345 5.0001 -> 2468.9 Inexact Rounded 697 rdvx616 divide 12345 5.001 -> 2468.5 Inexact Rounded 698 rdvx617 divide 12345 5.01 -> 2464.0 Inexact Rounded 699 rdvx618 divide 12345 5.1 -> 2420.5 Inexact Rounded 700 701 rounding: ceiling 702 rdvx701 divide 12345 1 -> 12345 703 rdvx702 divide 12345 1.0001 -> 12344 Inexact Rounded 704 rdvx703 divide 12345 1.001 -> 12333 Inexact Rounded 705 rdvx704 divide 12345 1.01 -> 12223 Inexact Rounded 706 rdvx705 divide 12345 1.1 -> 11223 Inexact Rounded 707 rdvx706 divide 12355 4 -> 3088.8 Inexact Rounded 708 rdvx707 divide 12345 4 -> 3086.3 Inexact Rounded 709 rdvx708 divide 12355 4.0001 -> 3088.7 Inexact Rounded 710 rdvx709 divide 12345 4.0001 -> 3086.2 Inexact Rounded 711 rdvx710 divide 12345 4.9 -> 2519.4 Inexact Rounded 712 rdvx711 divide 12345 4.99 -> 2474.0 Inexact Rounded 713 rdvx712 divide 12345 4.999 -> 2469.5 Inexact Rounded 714 rdvx713 divide 12345 4.9999 -> 2469.1 Inexact Rounded 715 rdvx714 divide 12345 5 -> 2469 716 rdvx715 divide 12345 5.0001 -> 2469.0 Inexact Rounded 717 rdvx716 divide 12345 5.001 -> 2468.6 Inexact Rounded 718 rdvx717 divide 12345 5.01 -> 2464.1 Inexact Rounded 719 rdvx718 divide 12345 5.1 -> 2420.6 Inexact Rounded 720 721 -- [divideInteger and remainder unaffected] 722 723 -- Multiplication operator -------------------------------------------- 724 725 rounding: down 726 rmux101 multiply 12345 1 -> 12345 727 rmux102 multiply 12345 1.0001 -> 12346 Inexact Rounded 728 rmux103 multiply 12345 1.001 -> 12357 Inexact Rounded 729 rmux104 multiply 12345 1.01 -> 12468 Inexact Rounded 730 rmux105 multiply 12345 1.1 -> 13579 Inexact Rounded 731 rmux106 multiply 12345 4 -> 49380 732 rmux107 multiply 12345 4.0001 -> 49381 Inexact Rounded 733 rmux108 multiply 12345 4.9 -> 60490 Inexact Rounded 734 rmux109 multiply 12345 4.99 -> 61601 Inexact Rounded 735 rmux110 multiply 12345 4.999 -> 61712 Inexact Rounded 736 rmux111 multiply 12345 4.9999 -> 61723 Inexact Rounded 737 rmux112 multiply 12345 5 -> 61725 738 rmux113 multiply 12345 5.0001 -> 61726 Inexact Rounded 739 rmux114 multiply 12345 5.001 -> 61737 Inexact Rounded 740 rmux115 multiply 12345 5.01 -> 61848 Inexact Rounded 741 rmux116 multiply 12345 12 -> 1.4814E+5 Rounded 742 rmux117 multiply 12345 13 -> 1.6048E+5 Inexact Rounded 743 rmux118 multiply 12355 12 -> 1.4826E+5 Rounded 744 rmux119 multiply 12355 13 -> 1.6061E+5 Inexact Rounded 745 746 rounding: half_down 747 rmux201 multiply 12345 1 -> 12345 748 rmux202 multiply 12345 1.0001 -> 12346 Inexact Rounded 749 rmux203 multiply 12345 1.001 -> 12357 Inexact Rounded 750 rmux204 multiply 12345 1.01 -> 12468 Inexact Rounded 751 rmux205 multiply 12345 1.1 -> 13579 Inexact Rounded 752 rmux206 multiply 12345 4 -> 49380 753 rmux207 multiply 12345 4.0001 -> 49381 Inexact Rounded 754 rmux208 multiply 12345 4.9 -> 60490 Inexact Rounded 755 rmux209 multiply 12345 4.99 -> 61602 Inexact Rounded 756 rmux210 multiply 12345 4.999 -> 61713 Inexact Rounded 757 rmux211 multiply 12345 4.9999 -> 61724 Inexact Rounded 758 rmux212 multiply 12345 5 -> 61725 759 rmux213 multiply 12345 5.0001 -> 61726 Inexact Rounded 760 rmux214 multiply 12345 5.001 -> 61737 Inexact Rounded 761 rmux215 multiply 12345 5.01 -> 61848 Inexact Rounded 762 rmux216 multiply 12345 12 -> 1.4814E+5 Rounded 763 rmux217 multiply 12345 13 -> 1.6048E+5 Inexact Rounded 764 rmux218 multiply 12355 12 -> 1.4826E+5 Rounded 765 rmux219 multiply 12355 13 -> 1.6061E+5 Inexact Rounded 766 767 rounding: half_even 768 rmux301 multiply 12345 1 -> 12345 769 rmux302 multiply 12345 1.0001 -> 12346 Inexact Rounded 770 rmux303 multiply 12345 1.001 -> 12357 Inexact Rounded 771 rmux304 multiply 12345 1.01 -> 12468 Inexact Rounded 772 rmux305 multiply 12345 1.1 -> 13580 Inexact Rounded 773 rmux306 multiply 12345 4 -> 49380 774 rmux307 multiply 12345 4.0001 -> 49381 Inexact Rounded 775 rmux308 multiply 12345 4.9 -> 60490 Inexact Rounded 776 rmux309 multiply 12345 4.99 -> 61602 Inexact Rounded 777 rmux310 multiply 12345 4.999 -> 61713 Inexact Rounded 778 rmux311 multiply 12345 4.9999 -> 61724 Inexact Rounded 779 rmux312 multiply 12345 5 -> 61725 780 rmux313 multiply 12345 5.0001 -> 61726 Inexact Rounded 781 rmux314 multiply 12345 5.001 -> 61737 Inexact Rounded 782 rmux315 multiply 12345 5.01 -> 61848 Inexact Rounded 783 rmux316 multiply 12345 12 -> 1.4814E+5 Rounded 784 rmux317 multiply 12345 13 -> 1.6048E+5 Inexact Rounded 785 rmux318 multiply 12355 12 -> 1.4826E+5 Rounded 786 rmux319 multiply 12355 13 -> 1.6062E+5 Inexact Rounded 787 788 rounding: half_up 789 rmux401 multiply 12345 1 -> 12345 790 rmux402 multiply 12345 1.0001 -> 12346 Inexact Rounded 791 rmux403 multiply 12345 1.001 -> 12357 Inexact Rounded 792 rmux404 multiply 12345 1.01 -> 12468 Inexact Rounded 793 rmux405 multiply 12345 1.1 -> 13580 Inexact Rounded 794 rmux406 multiply 12345 4 -> 49380 795 rmux407 multiply 12345 4.0001 -> 49381 Inexact Rounded 796 rmux408 multiply 12345 4.9 -> 60491 Inexact Rounded 797 rmux409 multiply 12345 4.99 -> 61602 Inexact Rounded 798 rmux410 multiply 12345 4.999 -> 61713 Inexact Rounded 799 rmux411 multiply 12345 4.9999 -> 61724 Inexact Rounded 800 rmux412 multiply 12345 5 -> 61725 801 rmux413 multiply 12345 5.0001 -> 61726 Inexact Rounded 802 rmux414 multiply 12345 5.001 -> 61737 Inexact Rounded 803 rmux415 multiply 12345 5.01 -> 61848 Inexact Rounded 804 rmux416 multiply 12345 12 -> 1.4814E+5 Rounded 805 rmux417 multiply 12345 13 -> 1.6049E+5 Inexact Rounded 806 rmux418 multiply 12355 12 -> 1.4826E+5 Rounded 807 rmux419 multiply 12355 13 -> 1.6062E+5 Inexact Rounded 808 809 rounding: up 810 rmux501 multiply 12345 1 -> 12345 811 rmux502 multiply 12345 1.0001 -> 12347 Inexact Rounded 812 rmux503 multiply 12345 1.001 -> 12358 Inexact Rounded 813 rmux504 multiply 12345 1.01 -> 12469 Inexact Rounded 814 rmux505 multiply 12345 1.1 -> 13580 Inexact Rounded 815 rmux506 multiply 12345 4 -> 49380 816 rmux507 multiply 12345 4.0001 -> 49382 Inexact Rounded 817 rmux508 multiply 12345 4.9 -> 60491 Inexact Rounded 818 rmux509 multiply 12345 4.99 -> 61602 Inexact Rounded 819 rmux510 multiply 12345 4.999 -> 61713 Inexact Rounded 820 rmux511 multiply 12345 4.9999 -> 61724 Inexact Rounded 821 rmux512 multiply 12345 5 -> 61725 822 rmux513 multiply 12345 5.0001 -> 61727 Inexact Rounded 823 rmux514 multiply 12345 5.001 -> 61738 Inexact Rounded 824 rmux515 multiply 12345 5.01 -> 61849 Inexact Rounded 825 rmux516 multiply 12345 12 -> 1.4814E+5 Rounded 826 rmux517 multiply 12345 13 -> 1.6049E+5 Inexact Rounded 827 rmux518 multiply 12355 12 -> 1.4826E+5 Rounded 828 rmux519 multiply 12355 13 -> 1.6062E+5 Inexact Rounded 829 -- [rmux516 & rmux518] can surprise 830 831 rounding: floor 832 rmux601 multiply 12345 1 -> 12345 833 rmux602 multiply 12345 1.0001 -> 12346 Inexact Rounded 834 rmux603 multiply 12345 1.001 -> 12357 Inexact Rounded 835 rmux604 multiply 12345 1.01 -> 12468 Inexact Rounded 836 rmux605 multiply 12345 1.1 -> 13579 Inexact Rounded 837 rmux606 multiply 12345 4 -> 49380 838 rmux607 multiply 12345 4.0001 -> 49381 Inexact Rounded 839 rmux608 multiply 12345 4.9 -> 60490 Inexact Rounded 840 rmux609 multiply 12345 4.99 -> 61601 Inexact Rounded 841 rmux610 multiply 12345 4.999 -> 61712 Inexact Rounded 842 rmux611 multiply 12345 4.9999 -> 61723 Inexact Rounded 843 rmux612 multiply 12345 5 -> 61725 844 rmux613 multiply 12345 5.0001 -> 61726 Inexact Rounded 845 rmux614 multiply 12345 5.001 -> 61737 Inexact Rounded 846 rmux615 multiply 12345 5.01 -> 61848 Inexact Rounded 847 rmux616 multiply 12345 12 -> 1.4814E+5 Rounded 848 rmux617 multiply 12345 13 -> 1.6048E+5 Inexact Rounded 849 rmux618 multiply 12355 12 -> 1.4826E+5 Rounded 850 rmux619 multiply 12355 13 -> 1.6061E+5 Inexact Rounded 851 852 rounding: ceiling 853 rmux701 multiply 12345 1 -> 12345 854 rmux702 multiply 12345 1.0001 -> 12347 Inexact Rounded 855 rmux703 multiply 12345 1.001 -> 12358 Inexact Rounded 856 rmux704 multiply 12345 1.01 -> 12469 Inexact Rounded 857 rmux705 multiply 12345 1.1 -> 13580 Inexact Rounded 858 rmux706 multiply 12345 4 -> 49380 859 rmux707 multiply 12345 4.0001 -> 49382 Inexact Rounded 860 rmux708 multiply 12345 4.9 -> 60491 Inexact Rounded 861 rmux709 multiply 12345 4.99 -> 61602 Inexact Rounded 862 rmux710 multiply 12345 4.999 -> 61713 Inexact Rounded 863 rmux711 multiply 12345 4.9999 -> 61724 Inexact Rounded 864 rmux712 multiply 12345 5 -> 61725 865 rmux713 multiply 12345 5.0001 -> 61727 Inexact Rounded 866 rmux714 multiply 12345 5.001 -> 61738 Inexact Rounded 867 rmux715 multiply 12345 5.01 -> 61849 Inexact Rounded 868 rmux716 multiply 12345 12 -> 1.4814E+5 Rounded 869 rmux717 multiply 12345 13 -> 1.6049E+5 Inexact Rounded 870 rmux718 multiply 12355 12 -> 1.4826E+5 Rounded 871 rmux719 multiply 12355 13 -> 1.6062E+5 Inexact Rounded 872 873 -- Power operator ----------------------------------------------------- 874 875 rounding: down 876 rpox101 power 12345 -5 -> 3.4877E-21 Inexact Rounded 877 rpox102 power 12345 -4 -> 4.3056E-17 Inexact Rounded 878 rpox103 power 12345 -3 -> 5.3152E-13 Inexact Rounded 879 rpox104 power 12345 -2 -> 6.5617E-9 Inexact Rounded 880 rpox105 power 12345 -1 -> 0.000081004 Inexact Rounded 881 rpox106 power 12345 0 -> 1 882 rpox107 power 12345 1 -> 12345 883 rpox108 power 12345 2 -> 1.5239E+8 Inexact Rounded 884 rpox109 power 12345 3 -> 1.8813E+12 Inexact Rounded 885 rpox110 power 12345 4 -> 2.3225E+16 Inexact Rounded 886 rpox111 power 12345 5 -> 2.8671E+20 Inexact Rounded 887 rpox112 power 415 2 -> 1.7222E+5 Inexact Rounded 888 rpox113 power 75 3 -> 4.2187E+5 Inexact Rounded 889 890 rounding: half_down 891 rpox201 power 12345 -5 -> 3.4877E-21 Inexact Rounded 892 rpox202 power 12345 -4 -> 4.3056E-17 Inexact Rounded 893 rpox203 power 12345 -3 -> 5.3153E-13 Inexact Rounded 894 rpox204 power 12345 -2 -> 6.5617E-9 Inexact Rounded 895 rpox205 power 12345 -1 -> 0.000081004 Inexact Rounded 896 rpox206 power 12345 0 -> 1 897 rpox207 power 12345 1 -> 12345 898 rpox208 power 12345 2 -> 1.5240E+8 Inexact Rounded 899 rpox209 power 12345 3 -> 1.8814E+12 Inexact Rounded 900 rpox210 power 12345 4 -> 2.3225E+16 Inexact Rounded 901 rpox211 power 12345 5 -> 2.8672E+20 Inexact Rounded 902 rpox212 power 415 2 -> 1.7222E+5 Inexact Rounded 903 rpox213 power 75 3 -> 4.2187E+5 Inexact Rounded 904 905 rounding: half_even 906 rpox301 power 12345 -5 -> 3.4877E-21 Inexact Rounded 907 rpox302 power 12345 -4 -> 4.3056E-17 Inexact Rounded 908 rpox303 power 12345 -3 -> 5.3153E-13 Inexact Rounded 909 rpox304 power 12345 -2 -> 6.5617E-9 Inexact Rounded 910 rpox305 power 12345 -1 -> 0.000081004 Inexact Rounded 911 rpox306 power 12345 0 -> 1 912 rpox307 power 12345 1 -> 12345 913 rpox308 power 12345 2 -> 1.5240E+8 Inexact Rounded 914 rpox309 power 12345 3 -> 1.8814E+12 Inexact Rounded 915 rpox310 power 12345 4 -> 2.3225E+16 Inexact Rounded 916 rpox311 power 12345 5 -> 2.8672E+20 Inexact Rounded 917 rpox312 power 415 2 -> 1.7222E+5 Inexact Rounded 918 rpox313 power 75 3 -> 4.2188E+5 Inexact Rounded 919 920 rounding: half_up 921 rpox401 power 12345 -5 -> 3.4877E-21 Inexact Rounded 922 rpox402 power 12345 -4 -> 4.3056E-17 Inexact Rounded 923 rpox403 power 12345 -3 -> 5.3153E-13 Inexact Rounded 924 rpox404 power 12345 -2 -> 6.5617E-9 Inexact Rounded 925 rpox405 power 12345 -1 -> 0.000081004 Inexact Rounded 926 rpox406 power 12345 0 -> 1 927 rpox407 power 12345 1 -> 12345 928 rpox408 power 12345 2 -> 1.5240E+8 Inexact Rounded 929 rpox409 power 12345 3 -> 1.8814E+12 Inexact Rounded 930 rpox410 power 12345 4 -> 2.3225E+16 Inexact Rounded 931 rpox411 power 12345 5 -> 2.8672E+20 Inexact Rounded 932 rpox412 power 415 2 -> 1.7223E+5 Inexact Rounded 933 rpox413 power 75 3 -> 4.2188E+5 Inexact Rounded 934 935 rounding: up 936 rpox501 power 12345 -5 -> 3.4878E-21 Inexact Rounded 937 rpox502 power 12345 -4 -> 4.3057E-17 Inexact Rounded 938 rpox503 power 12345 -3 -> 5.3153E-13 Inexact Rounded 939 rpox504 power 12345 -2 -> 6.5618E-9 Inexact Rounded 940 rpox505 power 12345 -1 -> 0.000081005 Inexact Rounded 941 rpox506 power 12345 0 -> 1 942 rpox507 power 12345 1 -> 12345 943 rpox508 power 12345 2 -> 1.5240E+8 Inexact Rounded 944 rpox509 power 12345 3 -> 1.8814E+12 Inexact Rounded 945 rpox510 power 12345 4 -> 2.3226E+16 Inexact Rounded 946 rpox511 power 12345 5 -> 2.8672E+20 Inexact Rounded 947 rpox512 power 415 2 -> 1.7223E+5 Inexact Rounded 948 rpox513 power 75 3 -> 4.2188E+5 Inexact Rounded 949 950 rounding: floor 951 rpox601 power 12345 -5 -> 3.4877E-21 Inexact Rounded 952 rpox602 power 12345 -4 -> 4.3056E-17 Inexact Rounded 953 rpox603 power 12345 -3 -> 5.3152E-13 Inexact Rounded 954 rpox604 power 12345 -2 -> 6.5617E-9 Inexact Rounded 955 rpox605 power 12345 -1 -> 0.000081004 Inexact Rounded 956 rpox606 power 12345 0 -> 1 957 rpox607 power 12345 1 -> 12345 958 rpox608 power 12345 2 -> 1.5239E+8 Inexact Rounded 959 rpox609 power 12345 3 -> 1.8813E+12 Inexact Rounded 960 rpox610 power 12345 4 -> 2.3225E+16 Inexact Rounded 961 rpox611 power 12345 5 -> 2.8671E+20 Inexact Rounded 962 rpox612 power 415 2 -> 1.7222E+5 Inexact Rounded 963 rpox613 power 75 3 -> 4.2187E+5 Inexact Rounded 964 965 rounding: ceiling 966 rpox701 power 12345 -5 -> 3.4878E-21 Inexact Rounded 967 rpox702 power 12345 -4 -> 4.3057E-17 Inexact Rounded 968 rpox703 power 12345 -3 -> 5.3153E-13 Inexact Rounded 969 rpox704 power 12345 -2 -> 6.5618E-9 Inexact Rounded 970 rpox705 power 12345 -1 -> 0.000081005 Inexact Rounded 971 rpox706 power 12345 0 -> 1 972 rpox707 power 12345 1 -> 12345 973 rpox708 power 12345 2 -> 1.5240E+8 Inexact Rounded 974 rpox709 power 12345 3 -> 1.8814E+12 Inexact Rounded 975 rpox710 power 12345 4 -> 2.3226E+16 Inexact Rounded 976 rpox711 power 12345 5 -> 2.8672E+20 Inexact Rounded 977 rpox712 power 415 2 -> 1.7223E+5 Inexact Rounded 978 rpox713 power 75 3 -> 4.2188E+5 Inexact Rounded 979 980 -- Underflow Subnormal and overflow values vary with rounding mode and sign 981 maxexponent: 999999999 982 minexponent: -999999999 983 rounding: down 984 rovx100 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded 985 rovx101 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded 986 rovx102 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 987 rovx104 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 988 989 rounding: up 990 rovx110 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded 991 rovx111 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded 992 rovx112 divide 1E-9 9E+999999999 -> 1E-1000000003 Underflow Subnormal Inexact Rounded 993 rovx114 divide -1E-9 9E+999999999 -> -1E-1000000003 Underflow Subnormal Inexact Rounded 994 995 rounding: ceiling 996 rovx120 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded 997 rovx121 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded 998 rovx122 divide 1E-9 9E+999999999 -> 1E-1000000003 Underflow Subnormal Inexact Rounded 999 rovx124 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1000 1001 rounding: floor 1002 rovx130 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded 1003 rovx131 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded 1004 rovx132 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1005 rovx134 divide -1E-9 9E+999999999 -> -1E-1000000003 Underflow Subnormal Inexact Rounded 1006 1007 rounding: half_up 1008 rovx140 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded 1009 rovx141 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded 1010 rovx142 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1011 rovx144 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1012 1013 rounding: half_even 1014 rovx150 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded 1015 rovx151 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded 1016 rovx152 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1017 rovx154 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1018 1019 rounding: half_down 1020 rovx160 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded 1021 rovx161 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded 1022 rovx162 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1023 rovx164 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded Clamped 1024 1025 -- check maximum finite value over a range of precisions 1026 rounding: down 1027 precision: 1 1028 rovx200 multiply 10 9E+999999999 -> 9E+999999999 Overflow Inexact Rounded 1029 rovx201 multiply -10 9E+999999999 -> -9E+999999999 Overflow Inexact Rounded 1030 precision: 2 1031 rovx210 multiply 10 9E+999999999 -> 9.9E+999999999 Overflow Inexact Rounded 1032 rovx211 multiply -10 9E+999999999 -> -9.9E+999999999 Overflow Inexact Rounded 1033 precision: 3 1034 rovx220 multiply 10 9E+999999999 -> 9.99E+999999999 Overflow Inexact Rounded 1035 rovx221 multiply -10 9E+999999999 -> -9.99E+999999999 Overflow Inexact Rounded 1036 precision: 4 1037 rovx230 multiply 10 9E+999999999 -> 9.999E+999999999 Overflow Inexact Rounded 1038 rovx231 multiply -10 9E+999999999 -> -9.999E+999999999 Overflow Inexact Rounded 1039 precision: 5 1040 rovx240 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded 1041 rovx241 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded 1042 precision: 6 1043 rovx250 multiply 10 9E+999999999 -> 9.99999E+999999999 Overflow Inexact Rounded 1044 rovx251 multiply -10 9E+999999999 -> -9.99999E+999999999 Overflow Inexact Rounded 1045 precision: 7 1046 rovx260 multiply 10 9E+999999999 -> 9.999999E+999999999 Overflow Inexact Rounded 1047 rovx261 multiply -10 9E+999999999 -> -9.999999E+999999999 Overflow Inexact Rounded 1048 precision: 8 1049 rovx270 multiply 10 9E+999999999 -> 9.9999999E+999999999 Overflow Inexact Rounded 1050 rovx271 multiply -10 9E+999999999 -> -9.9999999E+999999999 Overflow Inexact Rounded 1051 precision: 9 1052 rovx280 multiply 10 9E+999999999 -> 9.99999999E+999999999 Overflow Inexact Rounded 1053 rovx281 multiply -10 9E+999999999 -> -9.99999999E+999999999 Overflow Inexact Rounded 1054 precision: 10 1055 rovx290 multiply 10 9E+999999999 -> 9.999999999E+999999999 Overflow Inexact Rounded 1056 rovx291 multiply -10 9E+999999999 -> -9.999999999E+999999999 Overflow Inexact Rounded 1057 1058 -- reprise rounding mode effect (using multiplies so precision directive used) 1059 precision: 9 1060 maxexponent: 999999999 1061 rounding: half_up 1062 rmex400 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded 1063 rmex401 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded 1064 rounding: half_down 1065 rmex402 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded 1066 rmex403 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded 1067 rounding: half_even 1068 rmex404 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded 1069 rmex405 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded 1070 rounding: floor 1071 rmex406 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded 1072 rmex407 multiply 9.999E+999999999 10 -> 9.99999999E+999999999 Overflow Inexact Rounded 1073 rounding: ceiling 1074 rmex408 multiply -9.999E+999999999 10 -> -9.99999999E+999999999 Overflow Inexact Rounded 1075 rmex409 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded 1076 rounding: up 1077 rmex410 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded 1078 rmex411 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded 1079 rounding: down 1080 rmex412 multiply -9.999E+999999999 10 -> -9.99999999E+999999999 Overflow Inexact Rounded 1081 rmex413 multiply 9.999E+999999999 10 -> 9.99999999E+999999999 Overflow Inexact Rounded 1082 1083 ----- Round-for-reround ----- 1084 rounding: 05up 1085 precision: 5 -- for easier visual inspection 1086 maxExponent: 999 1087 minexponent: -999 1088 1089 -- basic rounding; really is just 0 and 5 up 1090 r05up001 add 12340 0.001 -> 12341 Inexact Rounded 1091 r05up002 add 12341 0.001 -> 12341 Inexact Rounded 1092 r05up003 add 12342 0.001 -> 12342 Inexact Rounded 1093 r05up004 add 12343 0.001 -> 12343 Inexact Rounded 1094 r05up005 add 12344 0.001 -> 12344 Inexact Rounded 1095 r05up006 add 12345 0.001 -> 12346 Inexact Rounded 1096 r05up007 add 12346 0.001 -> 12346 Inexact Rounded 1097 r05up008 add 12347 0.001 -> 12347 Inexact Rounded 1098 r05up009 add 12348 0.001 -> 12348 Inexact Rounded 1099 r05up010 add 12349 0.001 -> 12349 Inexact Rounded 1100 1101 r05up011 add 12340 0.000 -> 12340 Rounded 1102 r05up012 add 12341 0.000 -> 12341 Rounded 1103 r05up013 add 12342 0.000 -> 12342 Rounded 1104 r05up014 add 12343 0.000 -> 12343 Rounded 1105 r05up015 add 12344 0.000 -> 12344 Rounded 1106 r05up016 add 12345 0.000 -> 12345 Rounded 1107 r05up017 add 12346 0.000 -> 12346 Rounded 1108 r05up018 add 12347 0.000 -> 12347 Rounded 1109 r05up019 add 12348 0.000 -> 12348 Rounded 1110 r05up020 add 12349 0.000 -> 12349 Rounded 1111 1112 r05up021 add 12340 0.901 -> 12341 Inexact Rounded 1113 r05up022 add 12341 0.901 -> 12341 Inexact Rounded 1114 r05up023 add 12342 0.901 -> 12342 Inexact Rounded 1115 r05up024 add 12343 0.901 -> 12343 Inexact Rounded 1116 r05up025 add 12344 0.901 -> 12344 Inexact Rounded 1117 r05up026 add 12345 0.901 -> 12346 Inexact Rounded 1118 r05up027 add 12346 0.901 -> 12346 Inexact Rounded 1119 r05up028 add 12347 0.901 -> 12347 Inexact Rounded 1120 r05up029 add 12348 0.901 -> 12348 Inexact Rounded 1121 r05up030 add 12349 0.901 -> 12349 Inexact Rounded 1122 1123 r05up031 add -12340 -0.001 -> -12341 Inexact Rounded 1124 r05up032 add -12341 -0.001 -> -12341 Inexact Rounded 1125 r05up033 add -12342 -0.001 -> -12342 Inexact Rounded 1126 r05up034 add -12343 -0.001 -> -12343 Inexact Rounded 1127 r05up035 add -12344 -0.001 -> -12344 Inexact Rounded 1128 r05up036 add -12345 -0.001 -> -12346 Inexact Rounded 1129 r05up037 add -12346 -0.001 -> -12346 Inexact Rounded 1130 r05up038 add -12347 -0.001 -> -12347 Inexact Rounded 1131 r05up039 add -12348 -0.001 -> -12348 Inexact Rounded 1132 r05up040 add -12349 -0.001 -> -12349 Inexact Rounded 1133 1134 r05up041 add -12340 0.001 -> -12339 Inexact Rounded 1135 r05up042 add -12341 0.001 -> -12341 Inexact Rounded 1136 r05up043 add -12342 0.001 -> -12341 Inexact Rounded 1137 r05up044 add -12343 0.001 -> -12342 Inexact Rounded 1138 r05up045 add -12344 0.001 -> -12343 Inexact Rounded 1139 r05up046 add -12345 0.001 -> -12344 Inexact Rounded 1140 r05up047 add -12346 0.001 -> -12346 Inexact Rounded 1141 r05up048 add -12347 0.001 -> -12346 Inexact Rounded 1142 r05up049 add -12348 0.001 -> -12347 Inexact Rounded 1143 r05up050 add -12349 0.001 -> -12348 Inexact Rounded 1144 1145 -- Addition operators ------------------------------------------------- 1146 -- [The first few of these check negative residue possibilities; these 1147 -- cases may be implemented as a negative residue in fastpaths] 1148 1149 r0adx100 add 12345 -0.1 -> 12344 Inexact Rounded 1150 r0adx101 add 12345 -0.01 -> 12344 Inexact Rounded 1151 r0adx102 add 12345 -0.001 -> 12344 Inexact Rounded 1152 r0adx103 add 12345 -0.00001 -> 12344 Inexact Rounded 1153 r0adx104 add 12345 -0.000001 -> 12344 Inexact Rounded 1154 r0adx105 add 12345 -0.0000001 -> 12344 Inexact Rounded 1155 r0adx106 add 12345 0 -> 12345 1156 r0adx107 add 12345 0.0000001 -> 12346 Inexact Rounded 1157 r0adx108 add 12345 0.000001 -> 12346 Inexact Rounded 1158 r0adx109 add 12345 0.00001 -> 12346 Inexact Rounded 1159 r0adx110 add 12345 0.0001 -> 12346 Inexact Rounded 1160 r0adx111 add 12345 0.001 -> 12346 Inexact Rounded 1161 r0adx112 add 12345 0.01 -> 12346 Inexact Rounded 1162 r0adx113 add 12345 0.1 -> 12346 Inexact Rounded 1163 1164 r0adx115 add 12346 0.49999 -> 12346 Inexact Rounded 1165 r0adx116 add 12346 0.5 -> 12346 Inexact Rounded 1166 r0adx117 add 12346 0.50001 -> 12346 Inexact Rounded 1167 1168 r0adx120 add 12345 0.4 -> 12346 Inexact Rounded 1169 r0adx121 add 12345 0.49 -> 12346 Inexact Rounded 1170 r0adx122 add 12345 0.499 -> 12346 Inexact Rounded 1171 r0adx123 add 12345 0.49999 -> 12346 Inexact Rounded 1172 r0adx124 add 12345 0.5 -> 12346 Inexact Rounded 1173 r0adx125 add 12345 0.50001 -> 12346 Inexact Rounded 1174 r0adx126 add 12345 0.5001 -> 12346 Inexact Rounded 1175 r0adx127 add 12345 0.501 -> 12346 Inexact Rounded 1176 r0adx128 add 12345 0.51 -> 12346 Inexact Rounded 1177 r0adx129 add 12345 0.6 -> 12346 Inexact Rounded 1178 1179 -- negatives... 1180 1181 r0sux100 add -12345 -0.1 -> -12346 Inexact Rounded 1182 r0sux101 add -12345 -0.01 -> -12346 Inexact Rounded 1183 r0sux102 add -12345 -0.001 -> -12346 Inexact Rounded 1184 r0sux103 add -12345 -0.00001 -> -12346 Inexact Rounded 1185 r0sux104 add -12345 -0.000001 -> -12346 Inexact Rounded 1186 r0sux105 add -12345 -0.0000001 -> -12346 Inexact Rounded 1187 r0sux106 add -12345 0 -> -12345 1188 r0sux107 add -12345 0.0000001 -> -12344 Inexact Rounded 1189 r0sux108 add -12345 0.000001 -> -12344 Inexact Rounded 1190 r0sux109 add -12345 0.00001 -> -12344 Inexact Rounded 1191 r0sux110 add -12345 0.0001 -> -12344 Inexact Rounded 1192 r0sux111 add -12345 0.001 -> -12344 Inexact Rounded 1193 r0sux112 add -12345 0.01 -> -12344 Inexact Rounded 1194 r0sux113 add -12345 0.1 -> -12344 Inexact Rounded 1195 1196 r0sux115 add -12346 0.49999 -> -12346 Inexact Rounded 1197 r0sux116 add -12346 0.5 -> -12346 Inexact Rounded 1198 r0sux117 add -12346 0.50001 -> -12346 Inexact Rounded 1199 1200 r0sux120 add -12345 0.4 -> -12344 Inexact Rounded 1201 r0sux121 add -12345 0.49 -> -12344 Inexact Rounded 1202 r0sux122 add -12345 0.499 -> -12344 Inexact Rounded 1203 r0sux123 add -12345 0.49999 -> -12344 Inexact Rounded 1204 r0sux124 add -12345 0.5 -> -12344 Inexact Rounded 1205 r0sux125 add -12345 0.50001 -> -12344 Inexact Rounded 1206 r0sux126 add -12345 0.5001 -> -12344 Inexact Rounded 1207 r0sux127 add -12345 0.501 -> -12344 Inexact Rounded 1208 r0sux128 add -12345 0.51 -> -12344 Inexact Rounded 1209 r0sux129 add -12345 0.6 -> -12344 Inexact Rounded 1210 1211 -- Check cancellation subtractions 1212 -- (The IEEE 854 'curious rule' in $6.3) 1213 1214 r0zex001 add 0 0 -> 0 1215 r0zex002 add 0 -0 -> 0 1216 r0zex003 add -0 0 -> 0 1217 r0zex004 add -0 -0 -> -0 1218 r0zex005 add 1 -1 -> 0 1219 r0zex006 add -1 1 -> 0 1220 r0zex007 add 1.5 -1.5 -> 0.0 1221 r0zex008 add -1.5 1.5 -> 0.0 1222 r0zex009 add 2 -2 -> 0 1223 r0zex010 add -2 2 -> 0 1224 1225 1226 -- Division operators ------------------------------------------------- 1227 1228 r0dvx101 divide 12345 1 -> 12345 1229 r0dvx102 divide 12345 1.0001 -> 12343 Inexact Rounded 1230 r0dvx103 divide 12345 1.001 -> 12332 Inexact Rounded 1231 r0dvx104 divide 12345 1.01 -> 12222 Inexact Rounded 1232 r0dvx105 divide 12345 1.1 -> 11222 Inexact Rounded 1233 r0dvx106 divide 12355 4 -> 3088.7 Inexact Rounded 1234 r0dvx107 divide 12345 4 -> 3086.2 Inexact Rounded 1235 r0dvx108 divide 12355 4.0001 -> 3088.6 Inexact Rounded 1236 r0dvx109 divide 12345 4.0001 -> 3086.1 Inexact Rounded 1237 r0dvx110 divide 12345 4.9 -> 2519.3 Inexact Rounded 1238 r0dvx111 divide 12345 4.99 -> 2473.9 Inexact Rounded 1239 r0dvx112 divide 12345 4.999 -> 2469.4 Inexact Rounded 1240 r0dvx113 divide 12345 4.9999 -> 2469.1 Inexact Rounded 1241 r0dvx114 divide 12345 5 -> 2469 1242 r0dvx115 divide 12345 5.0001 -> 2468.9 Inexact Rounded 1243 r0dvx116 divide 12345 5.001 -> 2468.6 Inexact Rounded 1244 r0dvx117 divide 12345 5.01 -> 2464.1 Inexact Rounded 1245 r0dvx118 divide 12345 5.1 -> 2420.6 Inexact Rounded 1246 1247 -- [divideInteger and remainder unaffected] 1248 1249 -- Multiplication operator -------------------------------------------- 1250 1251 r0mux101 multiply 12345 1 -> 12345 1252 r0mux102 multiply 12345 1.0001 -> 12346 Inexact Rounded 1253 r0mux103 multiply 12345 1.001 -> 12357 Inexact Rounded 1254 r0mux104 multiply 12345 1.01 -> 12468 Inexact Rounded 1255 r0mux105 multiply 12345 1.1 -> 13579 Inexact Rounded 1256 r0mux106 multiply 12345 4 -> 49380 1257 r0mux107 multiply 12345 4.0001 -> 49381 Inexact Rounded 1258 r0mux108 multiply 12345 4.9 -> 60491 Inexact Rounded 1259 r0mux109 multiply 12345 4.99 -> 61601 Inexact Rounded 1260 r0mux110 multiply 12345 4.999 -> 61712 Inexact Rounded 1261 r0mux111 multiply 12345 4.9999 -> 61723 Inexact Rounded 1262 r0mux112 multiply 12345 5 -> 61725 1263 r0mux113 multiply 12345 5.0001 -> 61726 Inexact Rounded 1264 r0mux114 multiply 12345 5.001 -> 61737 Inexact Rounded 1265 r0mux115 multiply 12345 5.01 -> 61848 Inexact Rounded 1266 r0mux116 multiply 12345 12 -> 1.4814E+5 Rounded 1267 r0mux117 multiply 12345 13 -> 1.6048E+5 Inexact Rounded 1268 r0mux118 multiply 12355 12 -> 1.4826E+5 Rounded 1269 r0mux119 multiply 12355 13 -> 1.6061E+5 Inexact Rounded 1270 1271 1272 -- Power operator ----------------------------------------------------- 1273 1274 r0pox101 power 12345 -5 -> 3.4877E-21 Inexact Rounded 1275 r0pox102 power 12345 -4 -> 4.3056E-17 Inexact Rounded 1276 r0pox103 power 12345 -3 -> 5.3152E-13 Inexact Rounded 1277 r0pox104 power 12345 -2 -> 6.5617E-9 Inexact Rounded 1278 r0pox105 power 12345 -1 -> 0.000081004 Inexact Rounded 1279 r0pox106 power 12345 0 -> 1 1280 r0pox107 power 12345 1 -> 12345 1281 r0pox108 power 12345 2 -> 1.5239E+8 Inexact Rounded 1282 r0pox109 power 12345 3 -> 1.8813E+12 Inexact Rounded 1283 r0pox110 power 12345 4 -> 2.3226E+16 Inexact Rounded 1284 r0pox111 power 12345 5 -> 2.8671E+20 Inexact Rounded 1285 r0pox112 power 415 2 -> 1.7222E+5 Inexact Rounded 1286 r0pox113 power 75 3 -> 4.2187E+5 Inexact Rounded 1287 1288 1289 -- Underflow Subnormal and overflow values vary with rounding mode and sign 1290 maxexponent: 999999999 1291 minexponent: -999999999 1292 -- [round down gives Nmax on first two and .0E... on the next two] 1293 r0ovx100 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded 1294 r0ovx101 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded 1295 r0ovx102 divide 1E-9 9E+999999999 -> 1E-1000000003 Underflow Subnormal Inexact Rounded 1296 r0ovx104 divide -1E-9 9E+999999999 -> -1E-1000000003 Underflow Subnormal Inexact Rounded 1297 1298 -- reprise rounding mode effect (using multiplies so precision directive used) 1299 precision: 9 1300 maxexponent: 999999999 1301 r0mex412 multiply -9.999E+999999999 10 -> -9.99999999E+999999999 Overflow Inexact Rounded 1302 r0mex413 multiply 9.999E+999999999 10 -> 9.99999999E+999999999 Overflow Inexact Rounded 1303 1304
