1 /* $NetBSD: lfpfunc.c,v 1.1.1.3 2015/10/23 17:47:45 christos Exp $ */ 2 3 #include "config.h" 4 5 #include "ntp_stdlib.h" 6 #include "ntp_fp.h" 7 8 #include "unity.h" 9 10 #include <float.h> 11 #include <math.h> 12 13 14 /* replaced TEST_ASSERT_EQUAL_MEMORY(&a, &b, sizeof(a)) with TEST_ASSERT_EQUAL_l_fp(a, b). 15 It's safer this way, because structs can be compared even if they aren't initiated 16 with memset (due to padding bytes). 17 */ 18 #define TEST_ASSERT_EQUAL_l_fp(a, b) { \ 19 TEST_ASSERT_EQUAL_MESSAGE(a.l_i, b.l_i, "Field l_i"); \ 20 TEST_ASSERT_EQUAL_UINT_MESSAGE(a.l_uf, b.l_uf, "Field l_uf"); \ 21 } 22 23 24 25 typedef int bool; // typedef enum { FALSE, TRUE } boolean; -> can't use this because TRUE and FALSE are already defined 26 27 28 typedef struct { 29 uint32_t h, l; 30 } lfp_hl; 31 32 33 int l_fp_scmp(const l_fp first, const l_fp second); 34 int l_fp_ucmp(const l_fp first, l_fp second ); 35 l_fp l_fp_init(int32 i, u_int32 f); 36 l_fp l_fp_add(const l_fp first, const l_fp second); 37 l_fp l_fp_subtract(const l_fp first, const l_fp second); 38 l_fp l_fp_negate(const l_fp first); 39 l_fp l_fp_abs(const l_fp first); 40 int l_fp_signum(const l_fp first); 41 double l_fp_convert_to_double(const l_fp first); 42 l_fp l_fp_init_from_double( double rhs); 43 void l_fp_swap(l_fp * first, l_fp *second); 44 bool l_isgt(const l_fp first, const l_fp second); 45 bool l_isgtu(const l_fp first, const l_fp second); 46 bool l_ishis(const l_fp first, const l_fp second); 47 bool l_isgeq(const l_fp first, const l_fp second); 48 bool l_isequ(const l_fp first, const l_fp second); 49 double eps(double d); 50 51 52 void test_AdditionLR(void); 53 void test_AdditionRL(void); 54 void test_SubtractionLR(void); 55 void test_SubtractionRL(void); 56 void test_Negation(void); 57 void test_Absolute(void); 58 void test_FDF_RoundTrip(void); 59 void test_SignedRelOps(void); 60 void test_UnsignedRelOps(void); 61 62 63 64 static int cmp_work(u_int32 a[3], u_int32 b[3]); 65 66 //---------------------------------------------------------------------- 67 // reference comparision 68 // This is implementad as a full signed MP-subtract in 3 limbs, where 69 // the operands are zero or sign extended before the subtraction is 70 // executed. 71 //---------------------------------------------------------------------- 72 73 int 74 l_fp_scmp(const l_fp first, const l_fp second) 75 { 76 u_int32 a[3], b[3]; 77 78 const l_fp op1 = first; 79 const l_fp op2 = second; 80 81 a[0] = op1.l_uf; a[1] = op1.l_ui; a[2] = 0; 82 b[0] = op2.l_uf; b[1] = op2.l_ui; b[2] = 0; 83 84 a[2] -= (op1.l_i < 0); 85 b[2] -= (op2.l_i < 0); 86 87 return cmp_work(a,b); 88 } 89 90 int 91 l_fp_ucmp(const l_fp first, l_fp second ) 92 { 93 u_int32 a[3], b[3]; 94 const l_fp op1 = first; 95 const l_fp op2 = second; 96 97 a[0] = op1.l_uf; a[1] = op1.l_ui; a[2] = 0; 98 b[0] = op2.l_uf; b[1] = op2.l_ui; b[2] = 0; 99 100 return cmp_work(a,b); 101 } 102 103 // maybe rename it to lf_cmp_work 104 int 105 cmp_work(u_int32 a[3], u_int32 b[3]) 106 { 107 u_int32 cy, idx, tmp; 108 for (cy = idx = 0; idx < 3; ++idx) { 109 tmp = a[idx]; cy = (a[idx] -= cy ) > tmp; 110 tmp = a[idx]; cy |= (a[idx] -= b[idx]) > tmp; 111 } 112 if (a[2]) 113 return -1; 114 return a[0] || a[1]; 115 } 116 117 118 //---------------------------------------------------------------------- 119 // imlementation of the LFP stuff 120 // This should be easy enough... 121 //---------------------------------------------------------------------- 122 123 l_fp 124 l_fp_init(int32 i, u_int32 f) 125 { 126 l_fp temp; 127 temp.l_i = i; 128 temp.l_uf = f; 129 130 return temp; 131 } 132 133 l_fp 134 l_fp_add(const l_fp first, const l_fp second) 135 { 136 l_fp temp = first; 137 L_ADD(&temp, &second); 138 139 return temp; 140 } 141 142 l_fp 143 l_fp_subtract(const l_fp first, const l_fp second) 144 { 145 l_fp temp = first; 146 L_SUB(&temp, &second); 147 148 return temp; 149 } 150 151 l_fp 152 l_fp_negate(const l_fp first) 153 { 154 l_fp temp = first; 155 L_NEG(&temp); 156 157 return temp; 158 } 159 160 l_fp 161 l_fp_abs(const l_fp first) 162 { 163 l_fp temp = first; 164 if (L_ISNEG(&temp)) 165 L_NEG(&temp); 166 return temp; 167 } 168 169 int 170 l_fp_signum(const l_fp first) 171 { 172 if (first.l_ui & 0x80000000u) 173 return -1; 174 return (first.l_ui || first.l_uf); 175 } 176 177 double 178 l_fp_convert_to_double(const l_fp first) 179 { 180 double res; 181 LFPTOD(&first, res); 182 return res; 183 } 184 185 l_fp 186 l_fp_init_from_double( double rhs) 187 { 188 l_fp temp; 189 DTOLFP(rhs, &temp); 190 return temp; 191 } 192 193 void 194 l_fp_swap(l_fp * first, l_fp *second){ 195 l_fp temp = *second; 196 197 *second = *first; 198 *first = temp; 199 } 200 201 //---------------------------------------------------------------------- 202 // testing the relational macros works better with proper predicate 203 // formatting functions; it slows down the tests a bit, but makes for 204 // readable failure messages. 205 //---------------------------------------------------------------------- 206 207 208 bool 209 l_isgt (const l_fp first, const l_fp second) { 210 return L_ISGT(&first, &second); 211 } 212 213 bool 214 l_isgtu(const l_fp first, const l_fp second) { 215 return L_ISGTU(&first, &second); 216 } 217 218 bool 219 l_ishis(const l_fp first, const l_fp second) { 220 return L_ISHIS(&first, &second); 221 } 222 223 bool 224 l_isgeq(const l_fp first, const l_fp second) { 225 return L_ISGEQ(&first, &second); 226 } 227 228 bool 229 l_isequ(const l_fp first, const l_fp second) { 230 return L_ISEQU(&first, &second); 231 } 232 233 234 //---------------------------------------------------------------------- 235 // test data table for add/sub and compare 236 //---------------------------------------------------------------------- 237 238 239 static const lfp_hl addsub_tab[][3] = { 240 // trivial idendity: 241 {{0 ,0 }, { 0,0 }, { 0,0}}, 242 // with carry from fraction and sign change: 243 {{-1,0x80000000}, { 0,0x80000000}, { 0,0}}, 244 // without carry from fraction 245 {{ 1,0x40000000}, { 1,0x40000000}, { 2,0x80000000}}, 246 // with carry from fraction: 247 {{ 1,0xC0000000}, { 1,0xC0000000}, { 3,0x80000000}}, 248 // with carry from fraction and sign change: 249 {{0x7FFFFFFF, 0x7FFFFFFF}, {0x7FFFFFFF,0x7FFFFFFF}, {0xFFFFFFFE,0xFFFFFFFE}}, 250 // two tests w/o carry (used for l_fp<-->double): 251 {{0x55555555,0xAAAAAAAA}, {0x11111111,0x11111111}, {0x66666666,0xBBBBBBBB}}, 252 {{0x55555555,0x55555555}, {0x11111111,0x11111111}, {0x66666666,0x66666666}}, 253 // wide-range test, triggers compare trouble 254 {{0x80000000,0x00000001}, {0xFFFFFFFF,0xFFFFFFFE}, {0x7FFFFFFF,0xFFFFFFFF}} 255 }; 256 static const size_t addsub_cnt = (sizeof(addsub_tab)/sizeof(addsub_tab[0])); 257 static const size_t addsub_tot = (sizeof(addsub_tab)/sizeof(addsub_tab[0][0])); 258 259 260 261 //---------------------------------------------------------------------- 262 // epsilon estimation for the precision of a conversion double --> l_fp 263 // 264 // The error estimation limit is as follows: 265 // * The 'l_fp' fixed point fraction has 32 bits precision, so we allow 266 // for the LSB to toggle by clamping the epsilon to be at least 2^(-31) 267 // 268 // * The double mantissa has a precsion 54 bits, so the other minimum is 269 // dval * (2^(-53)) 270 // 271 // The maximum of those two boundaries is used for the check. 272 // 273 // Note: once there are more than 54 bits between the highest and lowest 274 // '1'-bit of the l_fp value, the roundtrip *will* create truncation 275 // errors. This is an inherent property caused by the 54-bit mantissa of 276 // the 'double' type. 277 double 278 eps(double d) 279 { 280 return fmax(ldexp(1.0, -31), ldexp(fabs(d), -53)); 281 } 282 283 //---------------------------------------------------------------------- 284 // test addition 285 //---------------------------------------------------------------------- 286 void 287 test_AdditionLR(void) { 288 289 size_t idx = 0; 290 for (idx = 0; idx < addsub_cnt; ++idx) { 291 l_fp op1 = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 292 l_fp op2 = l_fp_init(addsub_tab[idx][1].h, addsub_tab[idx][1].l); 293 l_fp exp = l_fp_init(addsub_tab[idx][2].h, addsub_tab[idx][2].l); 294 l_fp res = l_fp_add(op1, op2); 295 296 TEST_ASSERT_EQUAL_l_fp(exp, res); 297 } 298 } 299 300 void 301 test_AdditionRL(void) { 302 size_t idx = 0; 303 for (idx = 0; idx < addsub_cnt; ++idx) { 304 l_fp op2 = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 305 l_fp op1 = l_fp_init(addsub_tab[idx][1].h, addsub_tab[idx][1].l); 306 l_fp exp = l_fp_init(addsub_tab[idx][2].h, addsub_tab[idx][2].l); 307 l_fp res = l_fp_add(op1, op2); 308 309 TEST_ASSERT_EQUAL_l_fp(exp, res); 310 } 311 } 312 313 314 315 //---------------------------------------------------------------------- 316 // test subtraction 317 //---------------------------------------------------------------------- 318 void 319 test_SubtractionLR(void) { 320 size_t idx = 0; 321 for (idx = 0; idx < addsub_cnt; ++idx) { 322 l_fp op2 = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 323 l_fp exp = l_fp_init(addsub_tab[idx][1].h, addsub_tab[idx][1].l); 324 l_fp op1 = l_fp_init(addsub_tab[idx][2].h, addsub_tab[idx][2].l); 325 l_fp res = l_fp_subtract(op1, op2); 326 327 TEST_ASSERT_EQUAL_l_fp(exp, res); 328 } 329 } 330 331 void 332 test_SubtractionRL(void) { 333 size_t idx = 0; 334 for (idx = 0; idx < addsub_cnt; ++idx) { 335 l_fp exp = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 336 l_fp op2 = l_fp_init(addsub_tab[idx][1].h, addsub_tab[idx][1].l); 337 l_fp op1 = l_fp_init(addsub_tab[idx][2].h, addsub_tab[idx][2].l); 338 l_fp res = l_fp_subtract(op1, op2); 339 340 TEST_ASSERT_EQUAL_l_fp(exp, res); 341 } 342 } 343 344 //---------------------------------------------------------------------- 345 // test negation 346 //---------------------------------------------------------------------- 347 348 void 349 test_Negation(void) { 350 351 size_t idx = 0; 352 for (idx = 0; idx < addsub_cnt; ++idx) { 353 l_fp op1 = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 354 l_fp op2 = l_fp_negate(op1); 355 l_fp sum = l_fp_add(op1, op2); 356 357 l_fp zero = l_fp_init(0, 0); 358 359 TEST_ASSERT_EQUAL_l_fp(zero, sum); 360 } 361 } 362 363 364 365 //---------------------------------------------------------------------- 366 // test absolute value 367 //---------------------------------------------------------------------- 368 void 369 test_Absolute(void) { 370 size_t idx = 0; 371 for (idx = 0; idx < addsub_cnt; ++idx) { 372 l_fp op1 = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 373 l_fp op2 = l_fp_abs(op1); 374 375 TEST_ASSERT_TRUE(l_fp_signum(op2) >= 0); 376 377 if (l_fp_signum(op1) >= 0) 378 op1 = l_fp_subtract(op1, op2); 379 else 380 op1 = l_fp_add(op1, op2); 381 382 l_fp zero = l_fp_init(0, 0); 383 384 TEST_ASSERT_EQUAL_l_fp(zero, op1); 385 } 386 387 // There is one special case we have to check: the minimum 388 // value cannot be negated, or, to be more precise, the 389 // negation reproduces the original pattern. 390 l_fp minVal = l_fp_init(0x80000000, 0x00000000); 391 l_fp minAbs = l_fp_abs(minVal); 392 TEST_ASSERT_EQUAL(-1, l_fp_signum(minVal)); 393 394 TEST_ASSERT_EQUAL_l_fp(minVal, minAbs); 395 } 396 397 398 //---------------------------------------------------------------------- 399 // fp -> double -> fp rountrip test 400 //---------------------------------------------------------------------- 401 void 402 test_FDF_RoundTrip(void) { 403 // since a l_fp has 64 bits in it's mantissa and a double has 404 // only 54 bits available (including the hidden '1') we have to 405 // make a few concessions on the roundtrip precision. The 'eps()' 406 // function makes an educated guess about the avilable precision 407 // and checks the difference in the two 'l_fp' values against 408 // that limit. 409 size_t idx = 0; 410 for (idx = 0; idx < addsub_cnt; ++idx) { 411 l_fp op1 = l_fp_init(addsub_tab[idx][0].h, addsub_tab[idx][0].l); 412 double op2 = l_fp_convert_to_double(op1); 413 l_fp op3 = l_fp_init_from_double(op2); 414 415 l_fp temp = l_fp_subtract(op1, op3); 416 double d = l_fp_convert_to_double(temp); 417 TEST_ASSERT_DOUBLE_WITHIN(eps(op2), 0.0, fabs(d)); 418 } 419 } 420 421 422 //---------------------------------------------------------------------- 423 // test the compare stuff 424 // 425 // This uses the local compare and checks if the operations using the 426 // macros in 'ntp_fp.h' produce mathing results. 427 // ---------------------------------------------------------------------- 428 void 429 test_SignedRelOps(void) { 430 const lfp_hl * tv = (&addsub_tab[0][0]); 431 size_t lc ; 432 for (lc = addsub_tot - 1; lc; --lc, ++tv) { 433 l_fp op1 = l_fp_init(tv[0].h, tv[0].l); 434 l_fp op2 = l_fp_init(tv[1].h, tv[1].l); 435 int cmp = l_fp_scmp(op1, op2); 436 437 switch (cmp) { 438 case -1: 439 //printf("op1:%d %d, op2:%d %d\n",op1.l_uf,op1.l_ui,op2.l_uf,op2.l_ui); 440 l_fp_swap(&op1, &op2); 441 //printf("op1:%d %d, op2:%d %d\n",op1.l_uf,op1.l_ui,op2.l_uf,op2.l_ui); 442 case 1: 443 TEST_ASSERT_TRUE (l_isgt(op1, op2)); 444 TEST_ASSERT_FALSE(l_isgt(op2, op1)); 445 446 TEST_ASSERT_TRUE (l_isgeq(op1, op2)); 447 TEST_ASSERT_FALSE(l_isgeq(op2, op1)); 448 449 TEST_ASSERT_FALSE(l_isequ(op1, op2)); 450 TEST_ASSERT_FALSE(l_isequ(op2, op1)); 451 break; 452 case 0: 453 TEST_ASSERT_FALSE(l_isgt(op1, op2)); 454 TEST_ASSERT_FALSE(l_isgt(op2, op1)); 455 456 TEST_ASSERT_TRUE (l_isgeq(op1, op2)); 457 TEST_ASSERT_TRUE (l_isgeq(op2, op1)); 458 459 TEST_ASSERT_TRUE (l_isequ(op1, op2)); 460 TEST_ASSERT_TRUE (l_isequ(op2, op1)); 461 break; 462 default: 463 TEST_FAIL_MESSAGE("unexpected UCMP result: " ); 464 } 465 } 466 } 467 468 void 469 test_UnsignedRelOps(void) { 470 const lfp_hl * tv =(&addsub_tab[0][0]); 471 size_t lc; 472 for (lc = addsub_tot - 1; lc; --lc, ++tv) { 473 l_fp op1 = l_fp_init(tv[0].h, tv[0].l); 474 l_fp op2 = l_fp_init(tv[1].h, tv[1].l); 475 int cmp = l_fp_ucmp(op1, op2); 476 477 switch (cmp) { 478 case -1: 479 //printf("op1:%d %d, op2:%d %d\n",op1.l_uf,op1.l_ui,op2.l_uf,op2.l_ui); 480 l_fp_swap(&op1, &op2); 481 //printf("op1:%d %d, op2:%d %d\n",op1.l_uf,op1.l_ui,op2.l_uf,op2.l_ui); 482 case 1: 483 TEST_ASSERT_TRUE (l_isgtu(op1, op2)); 484 TEST_ASSERT_FALSE(l_isgtu(op2, op1)); 485 486 TEST_ASSERT_TRUE (l_ishis(op1, op2)); 487 TEST_ASSERT_FALSE(l_ishis(op2, op1)); 488 break; 489 case 0: 490 TEST_ASSERT_FALSE(l_isgtu(op1, op2)); 491 TEST_ASSERT_FALSE(l_isgtu(op2, op1)); 492 493 TEST_ASSERT_TRUE (l_ishis(op1, op2)); 494 TEST_ASSERT_TRUE (l_ishis(op2, op1)); 495 break; 496 default: 497 TEST_FAIL_MESSAGE("unexpected UCMP result: " ); 498 } 499 } 500 } 501 /* 502 */ 503 504 //---------------------------------------------------------------------- 505 // that's all folks... but feel free to add things! 506 //---------------------------------------------------------------------- 507