1 /*- 2 * Copyright (c) 2008-2010 David Schultz <das@FreeBSD.org> 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24 * SUCH DAMAGE. 25 */ 26 27 /* 28 * Tests for corner cases in log*(). 29 */ 30 31 #include <sys/cdefs.h> 32 __FBSDID("$FreeBSD$"); 33 34 #include <sys/param.h> 35 #include <assert.h> 36 #include <fenv.h> 37 #include <float.h> 38 #include <math.h> 39 #include <stdio.h> 40 41 #ifdef __i386__ 42 #include <ieeefp.h> 43 #endif 44 45 #include "test-utils.h" 46 47 #pragma STDC FENV_ACCESS ON 48 49 /* 50 * Test that a function returns the correct value and sets the 51 * exception flags correctly. The exceptmask specifies which 52 * exceptions we should check. We need to be lenient for several 53 * reasoons, but mainly because on some architectures it's impossible 54 * to raise FE_OVERFLOW without raising FE_INEXACT. 55 * 56 * These are macros instead of functions so that assert provides more 57 * meaningful error messages. 58 * 59 * XXX The volatile here is to avoid gcc's bogus constant folding and work 60 * around the lack of support for the FENV_ACCESS pragma. 61 */ 62 #define test(func, x, result, exceptmask, excepts) do { \ 63 volatile long double _d = x; \ 64 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 65 assert(fpequal((func)(_d), (result))); \ 66 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \ 67 } while (0) 68 69 #define test(func, x, result, exceptmask, excepts) do { \ 70 volatile long double _d = x; \ 71 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 72 assert(fpequal((func)(_d), (result))); \ 73 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \ 74 } while (0) 75 76 #define test_tol(func, z, result, tol) do { \ 77 volatile long double _d = z; \ 78 debug(" testing %6s(%15La) ~= % .36Le\n", #func, _d, result); \ 79 assert(fpequal_tol((func)(_d), (result), (tol), CS_BOTH)); \ 80 } while (0) 81 82 /* Test all the functions that compute log(x). */ 83 #define testall0(x, result, exceptmask, excepts) do { \ 84 test(log, x, result, exceptmask, excepts); \ 85 test(logf, x, result, exceptmask, excepts); \ 86 test(logl, x, result, exceptmask, excepts); \ 87 test(log2, x, result, exceptmask, excepts); \ 88 test(log2f, x, result, exceptmask, excepts); \ 89 test(log2l, x, result, exceptmask, excepts); \ 90 test(log10, x, result, exceptmask, excepts); \ 91 test(log10f, x, result, exceptmask, excepts); \ 92 test(log10l, x, result, exceptmask, excepts); \ 93 } while (0) 94 95 /* Test all the functions that compute log(1+x). */ 96 #define testall1(x, result, exceptmask, excepts) do { \ 97 test(log1p, x, result, exceptmask, excepts); \ 98 test(log1pf, x, result, exceptmask, excepts); \ 99 test(log1pl, x, result, exceptmask, excepts); \ 100 } while (0) 101 102 static void 103 run_generic_tests(void) 104 { 105 106 /* log(1) == 0, no exceptions raised */ 107 testall0(1.0, 0.0, ALL_STD_EXCEPT, 0); 108 testall1(0.0, 0.0, ALL_STD_EXCEPT, 0); 109 testall1(-0.0, -0.0, ALL_STD_EXCEPT, 0); 110 111 /* log(NaN) == NaN, no exceptions raised */ 112 testall0(NAN, NAN, ALL_STD_EXCEPT, 0); 113 testall1(NAN, NAN, ALL_STD_EXCEPT, 0); 114 115 /* log(Inf) == Inf, no exceptions raised */ 116 testall0(INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 117 testall1(INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 118 119 /* log(x) == NaN for x < 0, invalid exception raised */ 120 testall0(-INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 121 testall1(-INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 122 testall0(-1.0, NAN, ALL_STD_EXCEPT, FE_INVALID); 123 testall1(-1.5, NAN, ALL_STD_EXCEPT, FE_INVALID); 124 125 /* log(0) == -Inf, divide-by-zero exception */ 126 testall0(0.0, -INFINITY, ALL_STD_EXCEPT & ~FE_INEXACT, FE_DIVBYZERO); 127 testall0(-0.0, -INFINITY, ALL_STD_EXCEPT & ~FE_INEXACT, FE_DIVBYZERO); 128 testall1(-1.0, -INFINITY, ALL_STD_EXCEPT & ~FE_INEXACT, FE_DIVBYZERO); 129 } 130 131 static void 132 run_log2_tests(void) 133 { 134 unsigned i; 135 136 /* 137 * We should insist that log2() return exactly the correct 138 * result and not raise an inexact exception for powers of 2. 139 */ 140 assert(feclearexcept(FE_ALL_EXCEPT) == 0); 141 for (i = FLT_MIN_EXP - FLT_MANT_DIG; i < FLT_MAX_EXP; i++) { 142 assert(log2f(ldexpf(1.0, i)) == i); 143 assert(fetestexcept(ALL_STD_EXCEPT) == 0); 144 } 145 for (i = DBL_MIN_EXP - DBL_MANT_DIG; i < DBL_MAX_EXP; i++) { 146 assert(log2(ldexp(1.0, i)) == i); 147 assert(fetestexcept(ALL_STD_EXCEPT) == 0); 148 } 149 for (i = LDBL_MIN_EXP - LDBL_MANT_DIG; i < LDBL_MAX_EXP; i++) { 150 assert(log2l(ldexpl(1.0, i)) == i); 151 #if 0 152 /* XXX This test does not pass yet. */ 153 assert(fetestexcept(ALL_STD_EXCEPT) == 0); 154 #endif 155 } 156 } 157 158 static void 159 run_roundingmode_tests(void) 160 { 161 162 /* 163 * Corner cases in other rounding modes. 164 */ 165 fesetround(FE_DOWNWARD); 166 /* These are still positive per IEEE 754R */ 167 #if 0 168 testall0(1.0, 0.0, ALL_STD_EXCEPT, 0); 169 #else 170 /* logl, log2l, and log10l don't pass yet. */ 171 test(log, 1.0, 0.0, ALL_STD_EXCEPT, 0); 172 test(logf, 1.0, 0.0, ALL_STD_EXCEPT, 0); 173 test(log2, 1.0, 0.0, ALL_STD_EXCEPT, 0); 174 test(log2f, 1.0, 0.0, ALL_STD_EXCEPT, 0); 175 test(log10, 1.0, 0.0, ALL_STD_EXCEPT, 0); 176 test(log10f, 1.0, 0.0, ALL_STD_EXCEPT, 0); 177 #endif 178 testall1(0.0, 0.0, ALL_STD_EXCEPT, 0); 179 fesetround(FE_TOWARDZERO); 180 testall0(1.0, 0.0, ALL_STD_EXCEPT, 0); 181 testall1(0.0, 0.0, ALL_STD_EXCEPT, 0); 182 183 fesetround(FE_UPWARD); 184 testall0(1.0, 0.0, ALL_STD_EXCEPT, 0); 185 testall1(0.0, 0.0, ALL_STD_EXCEPT, 0); 186 /* log1p(-0.0) == -0.0 even when rounding upwards */ 187 testall1(-0.0, -0.0, ALL_STD_EXCEPT, 0); 188 189 fesetround(FE_TONEAREST); 190 } 191 192 static void 193 run_accuracy_tests(void) 194 { 195 static const struct { 196 float x; 197 long double log2x; 198 long double logex; 199 long double log10x; 200 } tests[] = { 201 { 0x1p-120 + 0x1p-140, 202 -1.19999998624139449158861798943319717e2L, 203 -8.31776607135195754708796206665656732e1L, 204 -3.61235990655024477716980559136055915e1L, 205 }, 206 { 1.0 - 0x1p-20, 207 -1.37586186296463416424364914705656460e-6L, 208 -9.53674771153890007250243736279163253e-7L, 209 -4.14175690642480911859354110516159131e-7L, }, 210 { 1.0 + 0x1p-20, 211 1.37586055084113820105668028340371476e-6L, 212 9.53673861659188233908415514963336144e-7L, 213 4.14175295653950611453333571759200697e-7L }, 214 { 19.75, 215 4.30378074817710292442728634194115348e0L, 216 2.98315349134713087533848129856505779e0L, 217 1.29556709996247903756734359702926363e0L }, 218 { 19.75 * 0x1p100, 219 1.043037807481771029244272863419411534e2L, 220 7.229787154734166181706169344438271459e1L, 221 3.139856666636059855894123306947856631e1L }, 222 }; 223 unsigned i; 224 225 for (i = 0; i < nitems(tests); i++) { 226 test_tol(log2, tests[i].x, tests[i].log2x, DBL_ULP()); 227 test_tol(log2f, tests[i].x, tests[i].log2x, FLT_ULP()); 228 test_tol(log2l, tests[i].x, tests[i].log2x, LDBL_ULP()); 229 test_tol(log, tests[i].x, tests[i].logex, DBL_ULP()); 230 test_tol(logf, tests[i].x, tests[i].logex, FLT_ULP()); 231 test_tol(logl, tests[i].x, tests[i].logex, LDBL_ULP()); 232 test_tol(log10, tests[i].x, tests[i].log10x, DBL_ULP()); 233 test_tol(log10f, tests[i].x, tests[i].log10x, FLT_ULP()); 234 test_tol(log10l, tests[i].x, tests[i].log10x, LDBL_ULP()); 235 if (tests[i].x >= 0.5) { 236 test_tol(log1p, tests[i].x - 1, tests[i].logex, 237 DBL_ULP()); 238 test_tol(log1pf, tests[i].x - 1, tests[i].logex, 239 FLT_ULP()); 240 test_tol(log1pl, tests[i].x - 1, tests[i].logex, 241 LDBL_ULP()); 242 } 243 } 244 } 245 246 static void 247 run_log1p_accuracy_tests(void) 248 { 249 250 test_tol(log1pf, 0x0.333333p0F, 251 1.82321546859847114303367992804596800640e-1L, FLT_ULP()); 252 test_tol(log1p, 0x0.3333333333333p0, 253 1.82321556793954589204283870982629267635e-1L, DBL_ULP()); 254 test_tol(log1pl, 0x0.33333333333333332p0L, 255 1.82321556793954626202683007050468762914e-1L, LDBL_ULP()); 256 257 test_tol(log1pf, -0x0.333333p0F, 258 -2.23143536413048672940940199918017467652e-1L, FLT_ULP()); 259 test_tol(log1p, -0x0.3333333333333p0, 260 -2.23143551314209700255143859052009022937e-1L, DBL_ULP()); 261 test_tol(log1pl, -0x0.33333333333333332p0L, 262 -2.23143551314209755752742563153765697950e-1L, LDBL_ULP()); 263 } 264 265 int 266 main(void) 267 { 268 269 printf("1..5\n"); 270 271 run_generic_tests(); 272 printf("ok 1 - logarithm\n"); 273 274 run_log2_tests(); 275 printf("ok 2 - logarithm\n"); 276 277 run_roundingmode_tests(); 278 printf("ok 3 - logarithm\n"); 279 280 run_accuracy_tests(); 281 printf("ok 4 - logarithm\n"); 282 283 run_log1p_accuracy_tests(); 284 printf("ok 5 - logarithm\n"); 285 286 return (0); 287 } 288