1Host = ee.ece.utah.edu 2Command = ./talldp >>talldp.lst-intel-ia32-freebsd-CC-O3 2>&1 3uname -a = FreeBSD ee.ece.utah.edu 4.4-RELEASE FreeBSD 4.4-RELEASE #0: Tue Oct i386 unknown unknown FreeBSD 4Make flags = -i NAME=intel-ia32-freebsd-CC-O3 CC=CC CFLAGS=-O3 5Date = Tue May 28 14:59:21 MDT 2002 6---------------------------------------- 7 8ibeta............ 2 9it............... 53 10irnd............. 5 11ngrd............. 0 12machep........... -52 13negep............ -53 14iexp............. 11 15minexp........... -1022 16maxexp........... 1024 17eps.............. 2.22044604925031308e-16 18epsneg........... 1.11022302462515654e-16 19xmin............. 2.22507385850720138e-308 20xmax............. 1.79769313486231571e+308 211TEST OF ALOG(X) VS T.S. EXPANSION OF ALOG(1+Y) 22 23 24 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 25 (1-EPS,1+EPS), WHERE EPS = 7.6294e-06 26 27 28 ALOG(X) WAS LARGER 0 TIMES, 29 AGREED 2000 TIMES, AND 30 WAS SMALLER 0 TIMES. 31 32 33 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 34 35 36 THE MAXIMUM RELATIVE ERROR OF 0.0000e+00 = 2 **-999.00 37 OCCURRED FOR X = 0.000000e+00 38 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 39 40 41 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0000e+00 = 2 **-999.00 42 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 43 44 451TEST OF ALOG(X) VS ALOG(17X/16)-ALOG(17/16) 46 47 48 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 49 ( 7.0711e-01, 9.3750e-01) 50 51 52 ALOG(X) WAS LARGER 0 TIMES, 53 AGREED 1718 TIMES, AND 54 WAS SMALLER 282 TIMES. 55 56 57 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 58 59 60 THE MAXIMUM RELATIVE ERROR OF 2.2185e-16 = 2 ** -52.00 61 OCCURRED FOR X = 7.786299e-01 62 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.00 63 64 65 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 6.8010e-17 = 2 ** -53.71 66 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 67 68 691TEST OF ALOG10(X) VS ALOG10(11X/10)-ALOG10(11/10) 70 71 72 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 73 ( 3.1623e-01, 9.0000e-01) 74 75 76 ALOG10(X) WAS LARGER 0 TIMES, 77 AGREED 1002 TIMES, AND 78 WAS SMALLER 998 TIMES. 79 80 81 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 82 83 84 THE MAXIMUM RELATIVE ERROR OF 4.5325e-16 = 2 ** -50.97 85 OCCURRED FOR X = 8.996477e-01 86 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 2.03 87 88 89 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.3742e-16 = 2 ** -52.69 90 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.31 91 92 931TEST OF ALOG(X*X) VS 2 * LOG(X) 94 95 96 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 97 ( 1.6000e+01, 2.4000e+02) 98 99 100 ALOG(X) WAS LARGER 63 TIMES, 101 AGREED 1937 TIMES, AND 102 WAS SMALLER 0 TIMES. 103 104 105 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 106 107 108 THE MAXIMUM RELATIVE ERROR OF 2.2042e-16 = 2 ** -52.01 109 OCCURRED FOR X = 5.622823e+01 110 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99 111 112 113 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 2.9630e-17 = 2 ** -54.91 114 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 115 116 1171SPECIAL TESTS 118 119 120 THE IDENTITY ALOG(X) = -ALOG(1/X) WILL BE TESTED. 121 122 X F(X) + F(1/X) 123 124 1.5983318e+01 1.0473393e-16 125 126 1.5339606e+01 -6.9822620e-17 127 128 1.5347572e+01 1.0603497e-16 129 130 1.5813231e+01 7.0256301e-17 131 132 1.5740176e+01 -8.1315163e-17 133 134 135 136 TEST OF SPECIAL ARGUMENTS 137 138 139 ALOG(1.0) = 0.0000000e+00 140 141 142 ALOG(XMIN) = ALOG( 2.2250739e-308) = -7.0839642e+02 143 144 145 ALOG(XMAX) = ALOG( 1.7976931e+308) = 7.0978271e+02 146 147 1481TEST OF ERROR RETURNS 149 150 151 ALOG WILL BE CALLED WITH THE ARGUMENT -2.0000e+00 152 THIS SHOULD TRIGGER AN ERROR MESSAGE 153 154 155 ALOG RETURNED THE VALUE NaN 156 157 158 ALOG WILL BE CALLED WITH THE ARGUMENT 0.0000e+00 159 THIS SHOULD TRIGGER AN ERROR MESSAGE 160 161 162 ALOG RETURNED THE VALUE -Inf 163 164 165 166 THIS CONCLUDES THE TESTS 1671TEST OF ASIN(X) VS TAYLOR SERIES 168 169 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 170 ( -1.2500e-01, 1.2500e-01) 171 172 173 ASIN(X) WAS LARGER 416 TIMES, 174 AGREED 1185 TIMES, AND 175 WAS SMALLER 399 TIMES. 176 177 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 178 179 THE MAXIMUM RELATIVE ERROR OF 2.5819e-16 = 2 ** -51.78 180 OCCURRED FOR X = -1.072935e-01 181 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.22 182 183 184 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.0032e-16 = 2 ** -53.15 185 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 186 187 1881TEST OF ACOS(X) VS TAYLOR SERIES 189 190 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 191 ( -1.2500e-01, 1.2500e-01) 192 193 194 ACOS(X) WAS LARGER 494 TIMES, 195 AGREED 1054 TIMES, AND 196 WAS SMALLER 452 TIMES. 197 198 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 199 200 THE MAXIMUM RELATIVE ERROR OF 1.5360e-16 = 2 ** -52.53 201 OCCURRED FOR X = 1.248467e-01 202 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.47 203 204 205 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 9.7674e-17 = 2 ** -53.18 206 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 207 208 2091TEST OF ASIN(X) VS TAYLOR SERIES 210 211 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 212 ( 7.5000e-01, 1.0000e+00) 213 214 215 ASIN(X) WAS LARGER 365 TIMES, 216 AGREED 1277 TIMES, AND 217 WAS SMALLER 358 TIMES. 218 219 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 220 221 THE MAXIMUM RELATIVE ERROR OF 2.2191e-16 = 2 ** -52.00 222 OCCURRED FOR X = 8.418029e-01 223 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.00 224 225 226 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.0044e-16 = 2 ** -53.14 227 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 228 229 2301TEST OF ACOS(X) VS TAYLOR SERIES 231 232 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 233 ( 7.5000e-01, 1.0000e+00) 234 235 236 ACOS(X) WAS LARGER 429 TIMES, 237 AGREED 1116 TIMES, AND 238 WAS SMALLER 455 TIMES. 239 240 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 241 242 THE MAXIMUM RELATIVE ERROR OF 4.2522e-16 = 2 ** -51.06 243 OCCURRED FOR X = 8.667282e-01 244 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.94 245 246 247 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.1398e-16 = 2 ** -52.96 248 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.04 249 250 2511TEST OF ACOS(X) VS TAYLOR SERIES 252 253 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 254 ( -1.0000e+00, -7.5000e-01) 255 256 257 ACOS(X) WAS LARGER 409 TIMES, 258 AGREED 1163 TIMES, AND 259 WAS SMALLER 428 TIMES. 260 261 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 262 263 THE MAXIMUM RELATIVE ERROR OF 1.8358e-16 = 2 ** -52.27 264 OCCURRED FOR X = -7.501318e-01 265 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.73 266 267 268 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.0794e-16 = 2 ** -53.04 269 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 270 271 2721SPECIAL TESTS 273 274 THE IDENTITY ASIN(-X) = -ASIN(X) WILL BE TESTED. 275 276 X F(X) + F(-X) 277 -5.0384110e-01 0.0000000e+00 278 279 -5.1721352e-01 0.0000000e+00 280 281 -4.6127087e-01 0.0000000e+00 282 283 -3.5739680e-01 0.0000000e+00 284 285 -3.2497569e-01 0.0000000e+00 286 287 THE IDENTITY ASIN(X) = X , X SMALL, WILL BE TESTED. 288 289 X X - F(X) 290 8.2729394e-17 -9.1842784e-33 291 292 4.1364697e-17 0.0000000e+00 293 294 2.0682348e-17 0.0000000e+00 295 296 1.0341174e-17 0.0000000e+00 297 298 5.1705871e-18 0.0000000e+00 299 300 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. 301 302 ASIN(1.821832e-231) =1.821832e-231 303 3041TEST OF ERROR RETURNS 305 306 307 ASIN WILL BE CALLED WITH THE ARGUMENT 1.2000e+00 308 THIS SHOULD TRIGGER AN ERROR MESSAGE 309 310 311 ASIN RETURNED THE VALUE NaN 312 313 314 THIS CONCLUDES THE TESTS 3151TEST OF ATAN(X) VS TRUNCATED TAYLOR SERIES 316 317 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 318 ( -6.2500e-02, 6.2500e-02) 319 320 321 ATAN(X) WAS LARGER 0 TIMES, 322 AGREED 1999 TIMES, AND 323 WAS SMALLER 1 TIMES. 324 325 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 326 327 THE MAXIMUM RELATIVE ERROR OF 1.1856e-16 = 2 ** -52.91 328 OCCURRED FOR X = -5.859376e-02 329 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.09 330 331 332 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 2.6511e-18 = 2 ** -58.39 333 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 334 335 3361TEST OF ATAN(X) VS ATAN(1/16) + ATAN((X-1/16)/(1+X/16)) 337 338 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 339 ( 6.2500e-02, 2.6795e-01) 340 341 342 ATAN(X) WAS LARGER 265 TIMES, 343 AGREED 1509 TIMES, AND 344 WAS SMALLER 226 TIMES. 345 346 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 347 348 THE MAXIMUM RELATIVE ERROR OF 2.2199e-16 = 2 ** -52.00 349 OCCURRED FOR X = 1.256840e-01 350 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.00 351 352 353 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 7.9412e-17 = 2 ** -53.48 354 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 355 356 3571TEST OF 2*ATAN(X) VS ATAN(2X/(1-X*X)) 358 359 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 360 ( 2.6795e-01, 4.1421e-01) 361 362 363 ATAN(X) WAS LARGER 269 TIMES, 364 AGREED 1416 TIMES, AND 365 WAS SMALLER 315 TIMES. 366 367 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 368 369 THE MAXIMUM RELATIVE ERROR OF 2.1197e-16 = 2 ** -52.07 370 OCCURRED FOR X = 2.680413e-01 371 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.93 372 373 374 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 9.3466e-17 = 2 ** -53.25 375 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 376 377 3781TEST OF 2*ATAN(X) VS ATAN(2X/(1-X*X)) 379 380 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 381 ( 4.1421e-01, 1.0000e+00) 382 383 384 ATAN(X) WAS LARGER 137 TIMES, 385 AGREED 1717 TIMES, AND 386 WAS SMALLER 146 TIMES. 387 388 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 389 390 THE MAXIMUM RELATIVE ERROR OF 2.2064e-16 = 2 ** -52.01 391 OCCURRED FOR X = 5.504280e-01 392 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99 393 394 395 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 5.7452e-17 = 2 ** -53.95 396 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 397 398 3991SPECIAL TESTS 400 401 THE IDENTITY ATAN(-X) = -ATAN(X) WILL BE TESTED. 402 403 404 X F(X) + F(-X) 405 406 2.4582943e+00 0.0000000e+00 407 408 8.4901561e-01 0.0000000e+00 409 410 8.6893012e-01 0.0000000e+00 411 412 2.0330784e+00 0.0000000e+00 413 414 1.8504397e+00 0.0000000e+00 415 416 THE IDENTITY ATAN(X) = X , X SMALL, WILL BE TESTED. 417 418 419 X X - F(X) 420 421 6.9279836e-17 0.0000000e+00 422 423 3.4639918e-17 0.0000000e+00 424 425 1.7319959e-17 0.0000000e+00 426 427 8.6599794e-18 0.0000000e+00 428 429 4.3299897e-18 0.0000000e+00 430 431 THE IDENTITY ATAN(X/Y) = ATAN2(X,Y) WILL BE TESTED 432 THE FIRST COLUMN OF RESULTS SHOULD BE 0, THE SECOND +-PI 433 434 X Y F1(X/Y)-F2(X,Y)F1(X/Y)-F2(X/(-Y)) 435 -9.1978515e-01 5.8925193e-01 -9.3241387e-18 3.1415927e+00 436 437 -1.7546973e+00 2.1346841e-01 -4.0115480e-18 3.1415927e+00 438 439 -2.2456381e-01 2.9761609e-01 -1.3931998e-17 3.1415927e+00 440 441 -9.9445784e-01 8.9905633e-01 2.6020852e-17 3.1415927e+00 442 443 1.0204660e+00 6.9518594e-01 -7.0473141e-19 -3.1415927e+00 444 445 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. 446 447 ATAN(1.821832e-231) =1.821832e-231 4481TEST OF ERROR RETURNS 449 450 451 ATAN WILL BE CALLED WITH THE ARGUMENT 1.7976931e+308 452 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 453 454 455 ATAN(1.797693e+308) = 1.570796e+00 456 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 457 1.0000000e+00 0.0000000e+00 458 459 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 460 461 462 ATAN2( 1.000000e+00 0.000000e+00) = 1.570796e+00 463 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 464 2.2250739e-308 1.7976931e+308 465 466 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 467 468 469 ATAN2(2.225074e-3081.797693e+308) = 0.000000e+00 470 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 471 1.7976931e+308 2.2250739e-308 472 473 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 474 475 476 ATAN2(1.797693e+3082.225074e-308) = 1.570796e+00 477 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 478 0.0000000e+00 0.0000000e+00 479 480 THIS SHOULD TRIGGER AN ERROR MESSAGE 481 482 483 ATAN2( 0.000000e+00 0.000000e+00) = 0.000000e+00 484 THIS CONCLUDES THE TESTS 4851TEST OF EXP(X- 0.0625) VS EXP(X)/EXP( 0.0625) 486 487 488 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 489 ( -2.8407e-01, 3.4657e-01) 490 491 492 EXP(X-V) WAS LARGER 258 TIMES, 493 AGREED 1484 TIMES, AND 494 WAS SMALLER 258 TIMES. 495 496 497 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 498 499 500 THE MAXIMUM RELATIVE ERROR OF 2.2196e-16 = 2 ** -52.00 501 OCCURRED FOR X = 6.288667e-02 502 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.00 503 504 505 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.0711e-17 = 2 ** -53.46 506 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 507 508 5091TEST OF EXP(X- 2.8125) VS EXP(X)/EXP( 2.8125) 510 511 512 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 513 ( -3.4657e+00, -6.7027e+02) 514 515 516 EXP(X-V) WAS LARGER 295 TIMES, 517 AGREED 1487 TIMES, AND 518 WAS SMALLER 218 TIMES. 519 520 521 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 522 523 524 THE MAXIMUM RELATIVE ERROR OF 2.3097e-16 = 2 ** -51.94 525 OCCURRED FOR X = -4.505452e+02 526 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.06 527 528 529 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.2787e-17 = 2 ** -53.42 530 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 531 532 5331TEST OF EXP(X- 2.8125) VS EXP(X)/EXP( 2.8125) 534 535 536 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 537 ( 6.9315e+00, 7.0968e+02) 538 539 540 EXP(X-V) WAS LARGER 304 TIMES, 541 AGREED 1456 TIMES, AND 542 WAS SMALLER 240 TIMES. 543 544 545 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 546 547 548 THE MAXIMUM RELATIVE ERROR OF 2.2146e-16 = 2 ** -52.00 549 OCCURRED FOR X = 2.731425e+02 550 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.00 551 552 553 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.3696e-17 = 2 ** -53.41 554 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 555 556 5571SPECIAL TESTS 558 559 560 THE IDENTITY EXP(X)*EXP(-X) = 1.0 WILL BE TESTED. 561 562 X F(X)*F(-X) - 1 563 564 7.8325859e-01 0.0000000e+00 565 566 4.1536184e-01 0.0000000e+00 567 568 2.8620958e-02 0.0000000e+00 569 570 1.2024206e+00 0.0000000e+00 571 572 1.8213778e+00 0.0000000e+00 573 574 575 576 TEST OF SPECIAL ARGUMENTS 577 578 579 EXP(0.0) - 1.0E0 = 0.0000000e+00 580 581 EXP(-7.080000e+02) =3.307553e-308 582 583 EXP( 7.090000e+02) =8.218407e+307 584 585 IF EXP( 3.545000e+02) = 9.065543e+153 IS NOT ABOUT 586 EXP( 1.772500e+02)**2 =9.065543e+153 THERE IS AN ARG RED ERROR 5871TEST OF ERROR RETURNS 588 589 590 EXP WILL BE CALLED WITH THE ARGUMENT -6.7039e+153 591 THIS SHOULD TRIGGER AN ERROR MESSAGE 592 593 594 EXP RETURNED THE VALUE 0.0000e+00 595 596 597 598 EXP WILL BE CALLED WITH THE ARGUMENT 6.7039e+153 599 THIS SHOULD TRIGGER AN ERROR MESSAGE 600 601 602 EXP RETURNED THE VALUE Inf 603 604 605 606 THIS CONCLUDES THE TESTS 6071TEST OF X**1.0 VS X 608 609 610 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 611 ( 5.0000e-01, 1.0000e+00) 612 613 614 X**1.0 WAS LARGER 0 TIMES, 615 AGREED 0 TIMES, AND 616 WAS SMALLER 2000 TIMES. 617 618 619 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 620 621 622 THE MAXIMUM RELATIVE ERROR OF 0.0000e+00 = 2 ** -999.00 623 OCCURRED FOR X = 0.000000e+00 624 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 625 626 627 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0000e+00 = 2 **-999.00 628 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 629 630 6311TEST OF XSQ**1.5 VS XSQ*X 632 633 634 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 635 ( 5.0000e-01, 1.0000e+00) 636 637 638 X**1.5 WAS LARGER 141 TIMES, 639 AGREED 0 TIMES, AND 640 WAS SMALLER 1859 TIMES. 641 642 643 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 644 645 646 THE MAXIMUM RELATIVE ERROR OF 2.2131e-16 = 2 ** -52.00 647 OCCURRED FOR X = 5.005552e-01 648 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.00 649 650 651 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 6.2277e-17 = 2 ** -53.83 652 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 653 654 6551TEST OF XSQ**1.5 VS XSQ*X 656 657 658 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 659 ( 1.0000e+00, 5.6438e+102) 660 661 662 X**1.5 WAS LARGER 158 TIMES, 663 AGREED 0 TIMES, AND 664 WAS SMALLER 1842 TIMES. 665 666 667 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 668 669 670 THE MAXIMUM RELATIVE ERROR OF 2.2011e-16 = 2 ** -52.01 671 OCCURRED FOR X = 8.914343e+101 672 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99 673 674 675 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 6.5334e-17 = 2 ** -53.76 676 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 677 678 6791TEST OF X**Y VS XSQ**(Y/2) 680 681 682 2000 RANDOM ARGUMENTS WERE TESTED FROM THE REGION 683 X IN ( 1.0000e-02, 1.0000e+01), Y IN ( -1.5413e+02, 1.5413e+02) 684 685 686 X**Y WAS LARGER 944 TIMES, 687 AGREED 0 TIMES, AND 688 WAS SMALLER 1056 TIMES. 689 690 691 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 692 693 694 THE MAXIMUM RELATIVE ERROR OF 8.2124e-15 = 2 ** -46.79 695 OCCURRED FOR X = 5.686868e+00 Y = 1.504408e+02 696 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 6.21 697 698 699 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 2.0843e-15 = 2 ** -48.77 700 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 4.23 701 702 7031SPECIAL TESTS 704 705 706 THE IDENTITY X ** Y = (1/X) ** (-Y) WILL BE TESTED. 707 708 X Y (X**Y-(1/X)**(-Y)) / X**Y 709 710 6.0384110e+00 6.1721352e+00 -4.4054454e-16 711 712 5.6127087e+00 4.5739680e+00 -1.7024686e-16 713 714 4.2497569e+00 8.4516013e+00 0.0000000e+00 715 716 2.2708162e+00 7.5027289e+00 -2.4175382e-16 717 718 6.1387364e+00 3.7554795e+00 -2.4953170e-16 719 7201TEST OF ERROR RETURNS 721 722 723 ( 2.0000000e+00) ** (-1.0220000e+03) WILL BE COMPUTED. 724 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 725 726 727 THE VALUE RETURNED IS 2.2251e-308 728 729 730 731 ( 2.0000000e+00) ** ( 1.0230000e+03) WILL BE COMPUTED. 732 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 733 734 735 THE VALUE RETURNED IS 8.9885e+307 736 737 738 739 ( 0.0000000e+00) ** ( 2.0000000e+00) WILL BE COMPUTED. 740 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 741 742 743 THE VALUE RETURNED IS 0.0000e+00 744 745 746 747 (-2.0000000e+00) ** ( 0.0000000e+00) WILL BE COMPUTED. 748 THIS SHOULD TRIGGER AN ERROR MESSAGE 749 750 751 THE VALUE RETURNED IS 1.0000e+00 752 753 754 755 (-2.0000000e+00) ** ( 2.0000000e+00) WILL BE COMPUTED. 756 THIS SHOULD TRIGGER AN ERROR MESSAGE 757 758 759 THE VALUE RETURNED IS 4.0000e+00 760 761 762 763 ( 0.0000000e+00) ** ( 0.0000000e+00) WILL BE COMPUTED. 764 THIS SHOULD TRIGGER AN ERROR MESSAGE 765 766 767 THE VALUE RETURNED IS 1.0000e+00 768 769 770 771 THIS CONCLUDES THE TESTS 7721TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3 773 774 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 775 ( 0.0000e+00, 1.5708e+00) 776 777 778 SIN(X) WAS LARGER 404 TIMES, 779 AGREED 1203 TIMES, AND 780 WAS SMALLER 393 TIMES. 781 782 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 783 784 THE MAXIMUM RELATIVE ERROR OF 2.4822e-16 = 2 ** -51.84 785 OCCURRED FOR X = 1.120528e-01 786 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.16 787 788 789 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 9.0431e-17 = 2 ** -53.30 790 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 791 792 7931TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3 794 795 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 796 ( 1.8850e+01, 2.0420e+01) 797 798 799 SIN(X) WAS LARGER 384 TIMES, 800 AGREED 1266 TIMES, AND 801 WAS SMALLER 350 TIMES. 802 803 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 804 805 THE MAXIMUM RELATIVE ERROR OF 2.6086e-16 = 2 ** -51.77 806 OCCURRED FOR X = 1.886286e+01 807 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.23 808 809 810 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.5273e-17 = 2 ** -53.38 811 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 812 813 8141TEST OF COS(X) VS 4*COS(X/3)**3-3*COS(X/3) 815 816 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 817 ( 2.1991e+01, 2.3562e+01) 818 819 820 COS(X) WAS LARGER 398 TIMES, 821 AGREED 1234 TIMES, AND 822 WAS SMALLER 368 TIMES. 823 824 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 825 826 THE MAXIMUM RELATIVE ERROR OF 2.8652e-16 = 2 ** -51.63 827 OCCURRED FOR X = 2.346492e+01 828 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.37 829 830 831 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.8469e-17 = 2 ** -53.33 832 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 833 834 8351SPECIAL TESTS 836 837 IF 1.000000e+00 IS NOT ALMOST 1.0E0, SIN HAS THE WRONG PERIOD. 838 839 THE IDENTITY SIN(-X) = -SIN(X) WILL BE TESTED. 840 X F(X) + F(-X) 841 7.3820383e+00 0.0000000e+00 842 843 3.9146931e+00 0.0000000e+00 844 845 2.6974617e-01 0.0000000e+00 846 847 1.1332547e+01 0.0000000e+00 848 849 1.7166081e+01 0.0000000e+00 850 851 THE IDENTITY SIN(X) = X , X SMALL, WILL BE TESTED. 852 X X - F(X) 853 854 5.7051156e-17 0.0000000e+00 855 856 2.8525578e-17 0.0000000e+00 857 858 1.4262789e-17 0.0000000e+00 859 860 7.1313945e-18 0.0000000e+00 861 862 3.5656973e-18 0.0000000e+00 863 864 THE IDENTITY COS(-X) = COS(X) WILL BE TESTED. 865 X F(X) - F(-X) 866 4.4566459e+00 0.0000000e+00 867 868 4.8316547e+00 0.0000000e+00 869 870 2.1326225e+00 0.0000000e+00 871 872 1.5061690e+01 0.0000000e+00 873 874 2.2071794e+00 0.0000000e+00 875 876 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. 877 878 879 SIN(1.821832e-231) = 1.821832e-231 880 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE 881 FOR LARGE ARGUMENTS. THE ARGUMENTS ARE CONSECUTIVE. 882 883 SIN( 9.490627e+07) = 9.419571e-01 884 885 SIN( 9.490627e+07) = 9.419571e-01 886 887 SIN( 9.490627e+07) = 9.419570e-01 8881TEST OF ERROR RETURNS 889 890 891 SIN WILL BE CALLED WITH THE ARGUMENT 9.0072e+15 892 THIS SHOULD TRIGGER AN ERROR MESSAGE 893 894 895 SIN RETURNED THE VALUE -8.4893e-01 896 897 898 899 THIS CONCLUDES THE TESTS 9001TEST OF SINH(X) VS T.S. EXPANSION OF SINH(X) 901 902 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 903 ( 0.0000e+00, 5.0000e-01) 904 905 906 SINH(X) WAS LARGER 272 TIMES, 907 AGREED 1441 TIMES, AND 908 WAS SMALLER 287 TIMES. 909 910 911 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 912 913 914 THE MAXIMUM RELATIVE ERROR OF 2.2125e-16 = 2 ** -52.01 915 OCCURRED FOR X = 6.268396e-02 916 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99 917 918 919 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.2273e-17 = 2 ** -53.43 920 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 921 922 9231TEST OF COSH(X) VS T.S. EXPANSION OF COSH(X) 924 925 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 926 ( 0.0000e+00, 5.0000e-01) 927 928 929 COSH(X) WAS LARGER 40 TIMES, 930 AGREED 1908 TIMES, AND 931 WAS SMALLER 52 TIMES. 932 933 934 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 935 936 937 THE MAXIMUM RELATIVE ERROR OF 2.2036e-16 = 2 ** -52.01 938 OCCURRED FOR X = 1.236239e-01 939 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99 940 941 942 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 4.3957e-17 = 2 ** -54.34 943 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 944 945 9461TEST OF SINH(X) VS C*(SINH(X+1)+SINH(X-1)) 947 948 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 949 ( 3.0000e+00, 7.0978e+02) 950 951 952 SINH(X) WAS LARGER 996 TIMES, 953 AGREED 954 TIMES, AND 954 WAS SMALLER 50 TIMES. 955 956 957 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 958 959 960 THE MAXIMUM RELATIVE ERROR OF 3.3802e-16 = 2 ** -51.39 961 OCCURRED FOR X = 6.234122e+02 962 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.61 963 964 965 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.2498e-16 = 2 ** -52.83 966 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.17 967 968 9691TEST OF COSH(X) VS C*(COSH(X+1)+COSH(X-1)) 970 971 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 972 ( 3.0000e+00, 7.0978e+02) 973 974 975 COSH(X) WAS LARGER 984 TIMES, 976 AGREED 967 TIMES, AND 977 WAS SMALLER 49 TIMES. 978 979 980 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 981 982 983 THE MAXIMUM RELATIVE ERROR OF 3.4980e-16 = 2 ** -51.34 984 OCCURRED FOR X = 1.146079e+02 985 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.66 986 987 988 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.2337e-16 = 2 ** -52.85 989 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.15 990 991 9921SPECIAL TESTS 993 994 THE IDENTITY SINH(-X) = -SINH(X) WILL BE TESTED. 995 996 X F(X) + F(-X) 997 998 1.4749766e+00 0.0000000e+00 999 1000 5.0940937e-01 0.0000000e+00 1001 1002 5.2135807e-01 0.0000000e+00 1003 1004 1.2198471e+00 0.0000000e+00 1005 1006 1.1102638e+00 0.0000000e+00 1007 1008 THE IDENTITY SINH(X) = X , X SMALL, WILL BE TESTED. 1009 1010 X X - F(X) 1011 1012 6.9279836e-17 0.0000000e+00 1013 1014 3.4639918e-17 0.0000000e+00 1015 1016 1.7319959e-17 0.0000000e+00 1017 1018 8.6599794e-18 0.0000000e+00 1019 1020 4.3299897e-18 0.0000000e+00 1021 1022 THE IDENTITY COSH(-X) = COSH(X) WILL BE TESTED. 1023 1024 X F(X) - F(-X) 1025 1026 8.1016114e-01 0.0000000e+00 1027 1028 1.7677558e+00 0.0000000e+00 1029 1030 1.8397699e-01 0.0000000e+00 1031 1032 6.4040522e-01 0.0000000e+00 1033 1034 1.3315771e+00 0.0000000e+00 1035 1036 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. 1037 1038 SINH(1.821832e-231) =1.821832e-231 1039 10401TEST OF ERROR RETURNS 1041 1042 1043 SINH WILL BE CALLED WITH THE ARGUMENT 7.0991e+02 1044 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 1045 1046 1047 SINH RETURNED THE VALUE 1.0185e+308 1048 1049 1050 1051SINH WILL BE CALLED WITH THE ARGUMENT 9.0072e+15 1052 THIS SHOULD TRIGGER AN ERROR MESSAGE 1053 1054 1055 SINH RETURNED THE VALUE Inf 1056 1057 1058 1059 THIS CONCLUDES THE TESTS 1060 10611TEST OF SQRT(X*X) - X 1062 1063 1064 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1065 ( 7.0711e-01, 1.0000e+00) 1066 1067 1068 SQRT(X) WAS LARGER 0 TIMES, 1069 AGREED 2000 TIMES, AND 1070 WAS SMALLER 0 TIMES. 1071 1072 1073 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1074 1075 1076 THE MAXIMUM RELATIVE ERROR OF 0.0000e+00 = 2 **-999.00 1077 OCCURRED FOR X = 0.000000e+00 1078 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1079 1080 1081 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0000e+00 = 2 **-999.00 1082 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1083 1084 10851TEST OF SQRT(X*X) - X 1086 1087 1088 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1089 ( 1.0000e+00, 1.4142e+00) 1090 1091 1092 SQRT(X) WAS LARGER 0 TIMES, 1093 AGREED 2000 TIMES, AND 1094 WAS SMALLER 0 TIMES. 1095 1096 1097 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1098 1099 1100 THE MAXIMUM RELATIVE ERROR OF 0.0000e+00 = 2 **-999.00 1101 OCCURRED FOR X = 0.000000e+00 1102 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1103 1104 1105 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0000e+00 = 2 **-999.00 1106 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1107 1108 11091TEST OF SPECIAL ARGUMENTS 1110 1111 1112 SQRT(XMIN) = SQRT( 2.2250739e-308) = 1.4916681e-154 1113 1114 1115 SQRT(1-EPSNEG) = SQRT(1- 1.1102230e-16) = 1.0000000e+00 1116 1117 1118 SQRT(1.0) = SQRT( 1.0000000e+00) = 1.0000000e+00 1119 1120 1121 SQRT(1+EPS) = SQRT(1+ 2.2204460e-16) = 1.0000000e+00 1122 1123 1124 SQRT(XMAX) = SQRT( 1.7976931e+308) = 1.3407808e+154 1125 1126 11271TEST OF ERROR RETURNS 1128 1129 1130 SQRT WILL BE CALLED WITH THE ARGUMENT 0.0000e+00 1131 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 1132 1133 1134 SQRT RETURNED THE VALUE 0.0000e+00 1135 1136 1137 1138SQRT WILL BE CALLED WITH THE ARGUMENT -1.0000e+00 1139 THIS SHOULD TRIGGER AN ERROR MESSAGE 1140 1141 1142 SQRT RETURNED THE VALUE NaN 1143 1144 1145 1146 THIS CONCLUDES THE TESTS 11471TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2) 1148 1149 1150 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1151 ( 0.0000e+00, 7.8540e-01) 1152 1153 1154 TAN(X) WAS LARGER 467 TIMES, 1155 AGREED 1097 TIMES, AND 1156 WAS SMALLER 436 TIMES. 1157 1158 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1159 1160 1161 THE MAXIMUM RELATIVE ERROR OF 3.9035e-16 = 2 ** -51.19 1162 OCCURRED FOR X = 2.771006e-01 1163 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.81 1164 1165 1166 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.0950e-16 = 2 ** -53.02 1167 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1168 1169 11701TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2) 1171 1172 1173 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1174 ( 2.7489e+00, 3.5343e+00) 1175 1176 1177 TAN(X) WAS LARGER 364 TIMES, 1178 AGREED 1293 TIMES, AND 1179 WAS SMALLER 343 TIMES. 1180 1181 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1182 1183 1184 THE MAXIMUM RELATIVE ERROR OF 2.7828e-16 = 2 ** -51.67 1185 OCCURRED FOR X = 3.191421e+00 1186 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.33 1187 1188 1189 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 9.6273e-17 = 2 ** -53.21 1190 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1191 1192 11931TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2) 1194 1195 1196 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1197 ( 1.8850e+01, 1.9635e+01) 1198 1199 1200 TAN(X) WAS LARGER 445 TIMES, 1201 AGREED 1074 TIMES, AND 1202 WAS SMALLER 481 TIMES. 1203 1204 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1205 1206 1207 THE MAXIMUM RELATIVE ERROR OF 4.3423e-16 = 2 ** -51.03 1208 OCCURRED FOR X = 1.903901e+01 1209 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.97 1210 1211 1212 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.1360e-16 = 2 ** -52.97 1213 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.03 1214 1215 12161TEST OF COT(X) VS (COT(X/2)**2-1)/(2*COT(X/2)) 1217 1218 1219 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1220 ( 1.8850e+01, 1.9635e+01) 1221 1222 1223 COT(X) WAS LARGER 381 TIMES, 1224 AGREED 1223 TIMES, AND 1225 WAS SMALLER 396 TIMES. 1226 1227 1228 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1229 1230 1231 THE MAXIMUM RELATIVE ERROR OF 3.2058e-16 = 2 ** -51.47 1232 OCCURRED FOR X = 1.947482e+01 1233 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.53 1234 1235 1236 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.0360e-16 = 2 ** -53.10 1237 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1238 1239 12401SPECIAL TESTS 1241 1242 1243 THE IDENTITY TAN(-X) = -TAN(X) WILL BE TESTED. 1244 1245 X F(X) + F(-X) 1246 1247 9.2675513e+00 0.0000000e+00 1248 1249 3.2007135e+00 0.0000000e+00 1250 1251 3.2757894e+00 0.0000000e+00 1252 1253 7.6645251e+00 0.0000000e+00 1254 1255 6.9759933e+00 0.0000000e+00 1256 1257 THE IDENTITY TAN(X) = X , X SMALL, WILL BE TESTED. 1258 1259 X X - F(X) 1260 1261 6.9279836e-17 0.0000000e+00 1262 1263 3.4639918e-17 0.0000000e+00 1264 1265 1.7319959e-17 0.0000000e+00 1266 1267 8.6599794e-18 0.0000000e+00 1268 1269 4.3299897e-18 0.0000000e+00 1270 1271 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. 1272 1273 TAN(1.821832e-231) =1.821832e-231 1274 1275 THE RELATIVE ERROR IN TAN(11) IS 5.4049159e-17 = 2 ** -54.04 WHERE 1276 1277 TAN( 1.100000e+01) =-2.259508e+02 1278 1279 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1280 1281 12821TEST OF ERROR RETURNS 1283 1284 1285 TAN WILL BE CALLED WITH THE ARGUMENT 6.7109e+07 1286 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE 1287 1288 1289 TAN RETURNED THE VALUE -4.6381e-01 1290 1291 1292 1293 1294TAN WILL BE CALLED WITH THE ARGUMENT 9.0072e+15 1295 THIS SHOULD TRIGGER AN ERROR MESSAGE 1296 1297 1298 TAN RETURNED THE VALUE 1.6063e+00 1299 1300 1301 1302 THIS CONCLUDES THE TESTS 13031TEST OF TANH(X) VS (TANH(X-1/8)+TANH(1/8))/(1+TANH(X-1/8)TANH(1/8)) 1304 1305 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1306 ( 1.2500e-01, 5.4931e-01) 1307 1308 1309 TANH(X) WAS LARGER 620 TIMES, 1310 AGREED 863 TIMES, AND 1311 WAS SMALLER 517 TIMES. 1312 1313 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1314 1315 THE MAXIMUM RELATIVE ERROR OF 4.4440e-16 = 2 ** -51.00 1316 OCCURRED FOR X = 5.488338e-01 1317 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 2.00 1318 1319 1320 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 1.4005e-16 = 2 ** -52.66 1321 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.34 1322 1323 13241TEST OF TANH(X) VS (TANH(X-1/8)+TANH(1/8))/(1+TANH(X-1/8)TANH(1/8)) 1325 1326 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL 1327 ( 6.7431e-01, 1.9408e+01) 1328 1329 1330 TANH(X) WAS LARGER 579 TIMES, 1331 AGREED 941 TIMES, AND 1332 WAS SMALLER 480 TIMES. 1333 1334 THERE ARE 53 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER 1335 1336 THE MAXIMUM RELATIVE ERROR OF 3.6158e-16 = 2 ** -51.30 1337 OCCURRED FOR X = 7.154747e-01 1338 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.70 1339 1340 1341 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 9.2767e-17 = 2 ** -53.26 1342 THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.00 1343 1344 13451SPECIAL TESTS 1346 1347 THE IDENTITY TANH(-X) = -TANH(X) WILL BE TESTED. 1348 1349 1350 X F(X) + F(-X) 1351 1352 5.5568571e-02 0.0000000e+00 1353 1354 2.5889429e-01 0.0000000e+00 1355 1356 2.2333500e-01 0.0000000e+00 1357 1358 6.0939174e-01 0.0000000e+00 1359 1360 7.4587289e-01 0.0000000e+00 1361 1362 THE IDENTITY TANH(X) = X , X SMALL, WILL BE TESTED. 1363 1364 1365 X X - F(X) 1366 1367 2.9291640e-17 0.0000000e+00 1368 1369 1.4645820e-17 0.0000000e+00 1370 1371 7.3229100e-18 0.0000000e+00 1372 1373 3.6614550e-18 0.0000000e+00 1374 1375 1.8307275e-18 0.0000000e+00 1376 1377 THE IDENTITY TANH(X) = 1 , X LARGE, WILL BE TESTED. 1378 1379 1380 X 1 - F(X) 1381 1382 1.9408121e+01 0.0000000e+00 1383 1384 2.3408121e+01 0.0000000e+00 1385 1386 2.7408121e+01 0.0000000e+00 1387 1388 3.1408121e+01 0.0000000e+00 1389 1390 3.5408121e+01 0.0000000e+00 1391 1392 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. 1393 1394 TANH(1.821832e-231) =1.821832e-231 1395 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 1.7976931e+308 1396 TANH(1.797693e+308) = 1.000000e+00 1397 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 2.2250739e-308 1398 TANH(2.225074e-308) =2.225074e-308 1399 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 0.0000000e+00 1400 TANH( 0.000000e+00) = 0.000000e+00 1401 THIS CONCLUDES THE TESTS 1402