1 /* $NetBSD: t_exp.c,v 1.8 2014/10/07 16:53:44 gson Exp $ */ 2 3 /*- 4 * Copyright (c) 2011 The NetBSD Foundation, Inc. 5 * All rights reserved. 6 * 7 * This code is derived from software contributed to The NetBSD Foundation 8 * by Jukka Ruohonen. 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in the 17 * documentation and/or other materials provided with the distribution. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS 20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS 23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 29 * POSSIBILITY OF SUCH DAMAGE. 30 */ 31 32 #include <atf-c.h> 33 #include <math.h> 34 #include "t_libm.h" 35 36 /* y = exp(x) */ 37 static const struct { 38 double x; 39 double y; 40 double e; 41 } exp_values[] = { 42 { -10, 0.4539992976248485e-4, 1e-4, }, 43 { -5, 0.6737946999085467e-2, 1e-2, }, 44 { -1, 0.3678794411714423, 1e-1, }, 45 { -0.1, 0.9048374180359595, 1e-1, }, 46 { 0, 1.0000000000000000, 1, }, 47 { 0.1, 1.1051709180756477, 1, }, 48 { 1, 2.7182818284590452, 1, }, 49 { 5, 148.41315910257660, 1e2, }, 50 { 10, 22026.465794806718, 1e4, }, 51 }; 52 53 /* 54 * exp2/exp2f(3) 55 */ 56 ATF_LIBM_TEST(exp2_is_nan, "Test exp2(x) == NaN") 57 { 58 #ifdef T_LIBM_NAN 59 T_LIBM_CHECK_NAN(0, exp2, T_LIBM_NAN); 60 T_LIBM_CHECK_NAN(0, exp2f, T_LIBM_NAN); 61 #else 62 atf_tc_skip("no NaN on this machine"); 63 #endif 64 } 65 66 ATF_LIBM_TEST(exp2_is_plus_zero, "Test exp2(x) == +0.0") 67 { 68 #ifdef T_LIBM_MINUS_INF 69 T_LIBM_CHECK_PLUS_ZERO(0, exp2, T_LIBM_MINUS_INF); 70 T_LIBM_CHECK_PLUS_ZERO(0, exp2f, T_LIBM_MINUS_INF); 71 #else 72 atf_tc_skip("no +/-Inf on this machine"); 73 #endif 74 } 75 76 ATF_LIBM_TEST(exp2_powers, "Test exp2(x) is correct for some integer x") 77 { 78 static const struct { 79 double x; 80 double d_y; 81 double f_y; 82 } v[] = { 83 { +0.0, 1.0, 1.0 }, 84 { -0.0, 1.0, 1.0 }, 85 { 1, 0x1p1, 0x1p1 }, 86 { 2, 0x1p2, 0x1p2 }, 87 { 100, 0x1p100, 0x1p100 }, 88 { 125, 0x1p125, 0x1p125 }, 89 { 126, 0x1p126, 0x1p126 }, 90 #if __DBL_MAX_EXP__ > 129 91 { 127, 0x1p127, 0x1p127 }, 92 #endif 93 #ifdef T_LIBM_PLUS_INF 94 { 128, 0x1p128, T_LIBM_PLUS_INF }, 95 { 129, 0x1p129, T_LIBM_PLUS_INF }, 96 { 1000, 0x1p1000, T_LIBM_PLUS_INF }, 97 { 1020, 0x1p1020, T_LIBM_PLUS_INF }, 98 { 1023, 0x1p1023, T_LIBM_PLUS_INF }, 99 { 1024, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 100 { 1030, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 101 { 1050, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 102 { 2000, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 103 { 16383, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 104 { 16384, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 105 { 16385, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF }, 106 #endif 107 { -1, 0x1p-1, 0x1p-1 }, 108 { -2, 0x1p-2, 0x1p-2 }, 109 { -100, 0x1p-100, 0x1p-100 }, 110 { -127, 0x1p-127, 0x1p-127 }, 111 { -128, 0x1p-128, 0x1p-128 }, 112 #if __LDBL_MIN_EXP__ < -129 113 { -300, 0x1p-300, 0.0}, 114 { -400, 0x1p-400, 0.0}, 115 {-1000, 0x1p-1000, 0.0}, 116 {-1022, 0x1p-1022, 0.0}, 117 /* These should be denormal numbers */ 118 {-1023, 0x1p-1023, 0.0}, 119 {-1024, 0x1p-1024, 0.0}, 120 {-1040, 0x1p-1040, 0.0}, 121 {-1060, 0x1p-1060, 0.0}, 122 /* This is the smallest result gcc will allow */ 123 {-1074, 0x1p-1074, 0.0}, 124 #endif 125 {-1075, 0x0, 0.0}, 126 {-1080, 0x0, 0.0}, 127 {-2000, 0x0, 0.0}, 128 {-16382, 0x0, 0.0}, 129 {-16383, 0x0, 0.0}, 130 {-16384, 0x0, 0.0}, 131 }; 132 unsigned int i; 133 134 for (i = 0; i < __arraycount(v); i++) { 135 T_LIBM_CHECK(i, exp2, v[i].x, v[i].d_y, 0.0); 136 T_LIBM_CHECK(i, exp2f, v[i].x, v[i].f_y, 0.0); 137 } 138 } 139 140 ATF_LIBM_TEST(exp2_values, "Test exp2(x) is correct for some x") 141 { 142 static const struct { 143 double x; 144 double d_y; 145 float f_y; 146 double d_eps; 147 double f_eps; 148 } v[] = { 149 #if __DBL_MAX_EXP__ > 128 150 /* The largest double constant */ 151 { 0x1.fffffffffffffp9, 0x1.ffffffffffd3ap1023, 0.00, 152 0x1p969, 0.0 }, 153 /* The largest float constant */ 154 { 0x1.fffffep6, 0x1.ffff4ep+127, 0x1.ffff4ep+127, 6e30, 0.0 }, 155 #endif 156 #ifdef T_LIBM_PLUS_INF 157 { T_LIBM_PLUS_INF, T_LIBM_PLUS_INF, T_LIBM_PLUS_INF, 0.0, 0.0 }, 158 #endif 159 160 /* The few values from the old tests */ 161 /* Results from i386/amd64, d_eps needed on i386 */ 162 /* f_y values calculated using py-mpmath */ 163 { 1.1, 0x1.125fbee250664p+1, 0x1.125fc0p+1, 0x1p-52, 0x1.8p-22 }, 164 { 2.2, 0x1.2611186bae675p+2, 0x1.26111ap+2, 0x1p-51, 0x1.8p-21 }, 165 { 3.3, 0x1.3b2c47bff8328p+3, 0x1.3b2c48p+3, 0x1p-50, 0x1.8p-20 }, 166 { 4.4, 0x1.51cb453b9536ep+4, 0x1.51cb46p+4, 0x1p-49, 0x1.8p-19 }, 167 { 5.5, 0x1.6a09e667f3bcdp+5, 0x1.6a09e6p+5, 0x1p-48, 0x1.8p-18 }, 168 { 6.6, 0x1.8406003b2ae5bp+6, 0x1.8405fep+6, 0x1p-47, 0x1.8p-17 }, 169 { 7.7, 0x1.9fdf8bcce533ep+7, 0x1.9fdf88p+7, 0x1p-46, 0x1.8p-16 }, 170 { 8.8, 0x1.bdb8cdadbe124p+8, 0x1.bdb8d2p+8, 0x1p-45, 0x1.8p-15 }, 171 }; 172 unsigned int i; 173 174 for (i = 0; i < __arraycount(v); i++) { 175 T_LIBM_CHECK(i, exp2, v[i].x, v[i].d_y, v[i].d_eps); 176 if (i > 1) 177 T_LIBM_CHECK(i, exp2f, v[i].x, v[i].f_y, v[i].f_eps); 178 } 179 } 180 181 182 /* 183 * exp(3) 184 */ 185 ATF_TC(exp_nan); 186 ATF_TC_HEAD(exp_nan, tc) 187 { 188 atf_tc_set_md_var(tc, "descr", "Test exp(NaN) == NaN"); 189 } 190 191 ATF_TC_BODY(exp_nan, tc) 192 { 193 const double x = 0.0L / 0.0L; 194 195 if (isnan(exp(x)) == 0) 196 atf_tc_fail_nonfatal("exp(NaN) != NaN"); 197 } 198 199 ATF_TC(exp_inf_neg); 200 ATF_TC_HEAD(exp_inf_neg, tc) 201 { 202 atf_tc_set_md_var(tc, "descr", "Test exp(-Inf) == +0.0"); 203 } 204 205 ATF_TC_BODY(exp_inf_neg, tc) 206 { 207 const double x = -1.0L / 0.0L; 208 double y = exp(x); 209 210 if (fabs(y) > 0.0 || signbit(y) != 0) 211 atf_tc_fail_nonfatal("exp(-Inf) != +0.0"); 212 } 213 214 ATF_TC(exp_inf_pos); 215 ATF_TC_HEAD(exp_inf_pos, tc) 216 { 217 atf_tc_set_md_var(tc, "descr", "Test exp(+Inf) == +Inf"); 218 } 219 220 ATF_TC_BODY(exp_inf_pos, tc) 221 { 222 const double x = 1.0L / 0.0L; 223 double y = exp(x); 224 225 if (isinf(y) == 0 || signbit(y) != 0) 226 atf_tc_fail_nonfatal("exp(+Inf) != +Inf"); 227 } 228 229 ATF_TC(exp_product); 230 ATF_TC_HEAD(exp_product, tc) 231 { 232 atf_tc_set_md_var(tc, "descr", "Test some selected exp(x)"); 233 } 234 235 ATF_TC_BODY(exp_product, tc) 236 { 237 double eps; 238 double x; 239 double y; 240 size_t i; 241 242 for (i = 0; i < __arraycount(exp_values); i++) { 243 x = exp_values[i].x; 244 y = exp_values[i].y; 245 eps = 1e-15 * exp_values[i].e; 246 247 if (fabs(exp(x) - y) > eps) 248 atf_tc_fail_nonfatal("exp(%0.01f) != %18.18e", x, y); 249 } 250 } 251 252 ATF_TC(exp_zero_neg); 253 ATF_TC_HEAD(exp_zero_neg, tc) 254 { 255 atf_tc_set_md_var(tc, "descr", "Test exp(-0.0) == 1.0"); 256 } 257 258 ATF_TC_BODY(exp_zero_neg, tc) 259 { 260 const double x = -0.0L; 261 262 if (fabs(exp(x) - 1.0) > 0.0) 263 atf_tc_fail_nonfatal("exp(-0.0) != 1.0"); 264 } 265 266 ATF_TC(exp_zero_pos); 267 ATF_TC_HEAD(exp_zero_pos, tc) 268 { 269 atf_tc_set_md_var(tc, "descr", "Test exp(+0.0) == 1.0"); 270 } 271 272 ATF_TC_BODY(exp_zero_pos, tc) 273 { 274 const double x = 0.0L; 275 276 if (fabs(exp(x) - 1.0) > 0.0) 277 atf_tc_fail_nonfatal("exp(+0.0) != 1.0"); 278 } 279 280 /* 281 * expf(3) 282 */ 283 ATF_TC(expf_nan); 284 ATF_TC_HEAD(expf_nan, tc) 285 { 286 atf_tc_set_md_var(tc, "descr", "Test expf(NaN) == NaN"); 287 } 288 289 ATF_TC_BODY(expf_nan, tc) 290 { 291 const float x = 0.0L / 0.0L; 292 293 if (isnan(expf(x)) == 0) 294 atf_tc_fail_nonfatal("expf(NaN) != NaN"); 295 } 296 297 ATF_TC(expf_inf_neg); 298 ATF_TC_HEAD(expf_inf_neg, tc) 299 { 300 atf_tc_set_md_var(tc, "descr", "Test expf(-Inf) == +0.0"); 301 } 302 303 ATF_TC_BODY(expf_inf_neg, tc) 304 { 305 const float x = -1.0L / 0.0L; 306 float y = expf(x); 307 308 if (fabsf(y) > 0.0 || signbit(y) != 0) 309 atf_tc_fail_nonfatal("expf(-Inf) != +0.0"); 310 } 311 312 ATF_TC(expf_inf_pos); 313 ATF_TC_HEAD(expf_inf_pos, tc) 314 { 315 atf_tc_set_md_var(tc, "descr", "Test expf(+Inf) == +Inf"); 316 } 317 318 ATF_TC_BODY(expf_inf_pos, tc) 319 { 320 const float x = 1.0L / 0.0L; 321 float y = expf(x); 322 323 if (isinf(y) == 0 || signbit(y) != 0) 324 atf_tc_fail_nonfatal("expf(+Inf) != +Inf"); 325 } 326 327 ATF_TC(expf_product); 328 ATF_TC_HEAD(expf_product, tc) 329 { 330 atf_tc_set_md_var(tc, "descr", "Test some selected expf(x)"); 331 } 332 333 ATF_TC_BODY(expf_product, tc) 334 { 335 float eps; 336 float x; 337 float y; 338 size_t i; 339 340 for (i = 0; i < __arraycount(exp_values); i++) { 341 x = exp_values[i].x; 342 y = exp_values[i].y; 343 eps = 1e-6 * exp_values[i].e; 344 345 if (fabsf(expf(x) - y) > eps) 346 atf_tc_fail_nonfatal("expf(%0.01f) != %18.18e", x, y); 347 } 348 } 349 350 ATF_TC(expf_zero_neg); 351 ATF_TC_HEAD(expf_zero_neg, tc) 352 { 353 atf_tc_set_md_var(tc, "descr", "Test expf(-0.0) == 1.0"); 354 } 355 356 ATF_TC_BODY(expf_zero_neg, tc) 357 { 358 const float x = -0.0L; 359 360 if (fabsf(expf(x) - 1.0f) > 0.0) 361 atf_tc_fail_nonfatal("expf(-0.0) != 1.0"); 362 } 363 364 ATF_TC(expf_zero_pos); 365 ATF_TC_HEAD(expf_zero_pos, tc) 366 { 367 atf_tc_set_md_var(tc, "descr", "Test expf(+0.0) == 1.0"); 368 } 369 370 ATF_TC_BODY(expf_zero_pos, tc) 371 { 372 const float x = 0.0L; 373 374 if (fabsf(expf(x) - 1.0f) > 0.0) 375 atf_tc_fail_nonfatal("expf(+0.0) != 1.0"); 376 } 377 378 /* 379 * expm1(3) 380 */ 381 ATF_TC(expm1_nan); 382 ATF_TC_HEAD(expm1_nan, tc) 383 { 384 atf_tc_set_md_var(tc, "descr", "Test expm1(NaN) == NaN"); 385 } 386 387 ATF_TC_BODY(expm1_nan, tc) 388 { 389 const double x = 0.0L / 0.0L; 390 391 if (isnan(expm1(x)) == 0) 392 atf_tc_fail_nonfatal("expm1(NaN) != NaN"); 393 } 394 395 ATF_TC(expm1_inf_neg); 396 ATF_TC_HEAD(expm1_inf_neg, tc) 397 { 398 atf_tc_set_md_var(tc, "descr", "Test expm1(-Inf) == -1"); 399 } 400 401 ATF_TC_BODY(expm1_inf_neg, tc) 402 { 403 const double x = -1.0L / 0.0L; 404 405 if (expm1(x) != -1.0) 406 atf_tc_fail_nonfatal("expm1(-Inf) != -1.0"); 407 } 408 409 ATF_TC(expm1_inf_pos); 410 ATF_TC_HEAD(expm1_inf_pos, tc) 411 { 412 atf_tc_set_md_var(tc, "descr", "Test expm1(+Inf) == +Inf"); 413 } 414 415 ATF_TC_BODY(expm1_inf_pos, tc) 416 { 417 const double x = 1.0L / 0.0L; 418 double y = expm1(x); 419 420 if (isinf(y) == 0 || signbit(y) != 0) 421 atf_tc_fail_nonfatal("expm1(+Inf) != +Inf"); 422 } 423 424 ATF_TC(expm1_zero_neg); 425 ATF_TC_HEAD(expm1_zero_neg, tc) 426 { 427 atf_tc_set_md_var(tc, "descr", "Test expm1(-0.0) == -0.0"); 428 } 429 430 ATF_TC_BODY(expm1_zero_neg, tc) 431 { 432 const double x = -0.0L; 433 double y = expm1(x); 434 435 if (fabs(y) > 0.0 || signbit(y) == 0) 436 atf_tc_fail_nonfatal("expm1(-0.0) != -0.0"); 437 } 438 439 ATF_TC(expm1_zero_pos); 440 ATF_TC_HEAD(expm1_zero_pos, tc) 441 { 442 atf_tc_set_md_var(tc, "descr", "Test expm1(+0.0) == 1.0"); 443 } 444 445 ATF_TC_BODY(expm1_zero_pos, tc) 446 { 447 const double x = 0.0L; 448 double y = expm1(x); 449 450 if (fabs(y) > 0.0 || signbit(y) != 0) 451 atf_tc_fail_nonfatal("expm1(+0.0) != +0.0"); 452 } 453 454 /* 455 * expm1f(3) 456 */ 457 ATF_TC(expm1f_nan); 458 ATF_TC_HEAD(expm1f_nan, tc) 459 { 460 atf_tc_set_md_var(tc, "descr", "Test expm1f(NaN) == NaN"); 461 } 462 463 ATF_TC_BODY(expm1f_nan, tc) 464 { 465 const float x = 0.0L / 0.0L; 466 467 if (isnan(expm1f(x)) == 0) 468 atf_tc_fail_nonfatal("expm1f(NaN) != NaN"); 469 } 470 471 ATF_TC(expm1f_inf_neg); 472 ATF_TC_HEAD(expm1f_inf_neg, tc) 473 { 474 atf_tc_set_md_var(tc, "descr", "Test expm1f(-Inf) == -1"); 475 } 476 477 ATF_TC_BODY(expm1f_inf_neg, tc) 478 { 479 const float x = -1.0L / 0.0L; 480 481 if (expm1f(x) != -1.0) 482 atf_tc_fail_nonfatal("expm1f(-Inf) != -1.0"); 483 } 484 485 ATF_TC(expm1f_inf_pos); 486 ATF_TC_HEAD(expm1f_inf_pos, tc) 487 { 488 atf_tc_set_md_var(tc, "descr", "Test expm1f(+Inf) == +Inf"); 489 } 490 491 ATF_TC_BODY(expm1f_inf_pos, tc) 492 { 493 const float x = 1.0L / 0.0L; 494 float y = expm1f(x); 495 496 if (isinf(y) == 0 || signbit(y) != 0) 497 atf_tc_fail_nonfatal("expm1f(+Inf) != +Inf"); 498 } 499 500 ATF_TC(expm1f_zero_neg); 501 ATF_TC_HEAD(expm1f_zero_neg, tc) 502 { 503 atf_tc_set_md_var(tc, "descr", "Test expm1f(-0.0) == -0.0"); 504 } 505 506 ATF_TC_BODY(expm1f_zero_neg, tc) 507 { 508 const float x = -0.0L; 509 float y = expm1f(x); 510 511 if (fabsf(y) > 0.0 || signbit(y) == 0) 512 atf_tc_fail_nonfatal("expm1f(-0.0) != -0.0"); 513 } 514 515 ATF_TC(expm1f_zero_pos); 516 ATF_TC_HEAD(expm1f_zero_pos, tc) 517 { 518 atf_tc_set_md_var(tc, "descr", "Test expm1f(+0.0) == 1.0"); 519 } 520 521 ATF_TC_BODY(expm1f_zero_pos, tc) 522 { 523 const float x = 0.0L; 524 float y = expm1f(x); 525 526 if (fabsf(y) > 0.0 || signbit(y) != 0) 527 atf_tc_fail_nonfatal("expm1f(+0.0) != +0.0"); 528 } 529 530 ATF_TP_ADD_TCS(tp) 531 { 532 533 ATF_TP_ADD_TC(tp, exp2_is_nan); 534 ATF_TP_ADD_TC(tp, exp2_is_plus_zero); 535 ATF_TP_ADD_TC(tp, exp2_values); 536 ATF_TP_ADD_TC(tp, exp2_powers); 537 538 ATF_TP_ADD_TC(tp, exp_nan); 539 ATF_TP_ADD_TC(tp, exp_inf_neg); 540 ATF_TP_ADD_TC(tp, exp_inf_pos); 541 ATF_TP_ADD_TC(tp, exp_product); 542 ATF_TP_ADD_TC(tp, exp_zero_neg); 543 ATF_TP_ADD_TC(tp, exp_zero_pos); 544 545 ATF_TP_ADD_TC(tp, expf_nan); 546 ATF_TP_ADD_TC(tp, expf_inf_neg); 547 ATF_TP_ADD_TC(tp, expf_inf_pos); 548 ATF_TP_ADD_TC(tp, expf_product); 549 ATF_TP_ADD_TC(tp, expf_zero_neg); 550 ATF_TP_ADD_TC(tp, expf_zero_pos); 551 552 ATF_TP_ADD_TC(tp, expm1_nan); 553 ATF_TP_ADD_TC(tp, expm1_inf_neg); 554 ATF_TP_ADD_TC(tp, expm1_inf_pos); 555 ATF_TP_ADD_TC(tp, expm1_zero_neg); 556 ATF_TP_ADD_TC(tp, expm1_zero_pos); 557 558 ATF_TP_ADD_TC(tp, expm1f_nan); 559 ATF_TP_ADD_TC(tp, expm1f_inf_neg); 560 ATF_TP_ADD_TC(tp, expm1f_inf_pos); 561 ATF_TP_ADD_TC(tp, expm1f_zero_neg); 562 ATF_TP_ADD_TC(tp, expm1f_zero_pos); 563 564 return atf_no_error(); 565 } 566