1 // Copyright 2015 The Go Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package big 6 7 import ( 8 "bytes" 9 "fmt" 10 "math" 11 "strconv" 12 "strings" 13 "testing" 14 ) 15 16 type StringTest struct { 17 in, out string 18 ok bool 19 } 20 21 var setStringTests = []StringTest{ 22 {"0", "0", true}, 23 {"-0", "0", true}, 24 {"1", "1", true}, 25 {"-1", "-1", true}, 26 {"1.", "1", true}, 27 {"1e0", "1", true}, 28 {"1.e1", "10", true}, 29 {in: "1e"}, 30 {in: "1.e"}, 31 {in: "1e+14e-5"}, 32 {in: "1e4.5"}, 33 {in: "r"}, 34 {in: "a/b"}, 35 {in: "a.b"}, 36 {"-0.1", "-1/10", true}, 37 {"-.1", "-1/10", true}, 38 {"2/4", "1/2", true}, 39 {".25", "1/4", true}, 40 {"-1/5", "-1/5", true}, 41 {"8129567.7690E14", "812956776900000000000", true}, 42 {"78189e+4", "781890000", true}, 43 {"553019.8935e+8", "55301989350000", true}, 44 {"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true}, 45 {"9877861857500000E-7", "3951144743/4", true}, 46 {"2169378.417e-3", "2169378417/1000000", true}, 47 {"884243222337379604041632732738665534", "884243222337379604041632732738665534", true}, 48 {"53/70893980658822810696", "53/70893980658822810696", true}, 49 {"106/141787961317645621392", "53/70893980658822810696", true}, 50 {"204211327800791583.81095", "4084226556015831676219/20000", true}, 51 {"0e9999999999", "0", true}, // issue #16176 52 {in: "1/0"}, 53 {in: "4/3/2"}, // issue 17001 54 {in: "4/3/"}, 55 {in: "4/3."}, 56 {in: "4/"}, 57 } 58 59 // These are not supported by fmt.Fscanf. 60 var setStringTests2 = []StringTest{ 61 {"0x10", "16", true}, 62 {"-010/1", "-8", true}, // TODO(gri) should we even permit octal here? 63 {"-010.", "-10", true}, 64 {"0x10/0x20", "1/2", true}, 65 {"0b1000/3", "8/3", true}, 66 {in: "4/3x"}, 67 // TODO(gri) add more tests 68 } 69 70 func TestRatSetString(t *testing.T) { 71 var tests []StringTest 72 tests = append(tests, setStringTests...) 73 tests = append(tests, setStringTests2...) 74 75 for i, test := range tests { 76 x, ok := new(Rat).SetString(test.in) 77 78 if ok { 79 if !test.ok { 80 t.Errorf("#%d SetString(%q) expected failure", i, test.in) 81 } else if x.RatString() != test.out { 82 t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out) 83 } 84 } else if x != nil { 85 t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x) 86 } 87 } 88 } 89 90 func TestRatScan(t *testing.T) { 91 var buf bytes.Buffer 92 for i, test := range setStringTests { 93 x := new(Rat) 94 buf.Reset() 95 buf.WriteString(test.in) 96 97 _, err := fmt.Fscanf(&buf, "%v", x) 98 if err == nil != test.ok { 99 if test.ok { 100 t.Errorf("#%d (%s) error: %s", i, test.in, err) 101 } else { 102 t.Errorf("#%d (%s) expected error", i, test.in) 103 } 104 continue 105 } 106 if err == nil && x.RatString() != test.out { 107 t.Errorf("#%d got %s want %s", i, x.RatString(), test.out) 108 } 109 } 110 } 111 112 var floatStringTests = []struct { 113 in string 114 prec int 115 out string 116 }{ 117 {"0", 0, "0"}, 118 {"0", 4, "0.0000"}, 119 {"1", 0, "1"}, 120 {"1", 2, "1.00"}, 121 {"-1", 0, "-1"}, 122 {"0.05", 1, "0.1"}, 123 {"-0.05", 1, "-0.1"}, 124 {".25", 2, "0.25"}, 125 {".25", 1, "0.3"}, 126 {".25", 3, "0.250"}, 127 {"-1/3", 3, "-0.333"}, 128 {"-2/3", 4, "-0.6667"}, 129 {"0.96", 1, "1.0"}, 130 {"0.999", 2, "1.00"}, 131 {"0.9", 0, "1"}, 132 {".25", -1, "0"}, 133 {".55", -1, "1"}, 134 } 135 136 func TestFloatString(t *testing.T) { 137 for i, test := range floatStringTests { 138 x, _ := new(Rat).SetString(test.in) 139 140 if x.FloatString(test.prec) != test.out { 141 t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out) 142 } 143 } 144 } 145 146 // Test inputs to Rat.SetString. The prefix "long:" causes the test 147 // to be skipped except in -long mode. (The threshold is about 500us.) 148 var float64inputs = []string{ 149 // Constants plundered from strconv/testfp.txt. 150 151 // Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP 152 "5e+125", 153 "69e+267", 154 "999e-026", 155 "7861e-034", 156 "75569e-254", 157 "928609e-261", 158 "9210917e+080", 159 "84863171e+114", 160 "653777767e+273", 161 "5232604057e-298", 162 "27235667517e-109", 163 "653532977297e-123", 164 "3142213164987e-294", 165 "46202199371337e-072", 166 "231010996856685e-073", 167 "9324754620109615e+212", 168 "78459735791271921e+049", 169 "272104041512242479e+200", 170 "6802601037806061975e+198", 171 "20505426358836677347e-221", 172 "836168422905420598437e-234", 173 "4891559871276714924261e+222", 174 175 // Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP 176 "9e-265", 177 "85e-037", 178 "623e+100", 179 "3571e+263", 180 "81661e+153", 181 "920657e-023", 182 "4603285e-024", 183 "87575437e-309", 184 "245540327e+122", 185 "6138508175e+120", 186 "83356057653e+193", 187 "619534293513e+124", 188 "2335141086879e+218", 189 "36167929443327e-159", 190 "609610927149051e-255", 191 "3743626360493413e-165", 192 "94080055902682397e-242", 193 "899810892172646163e+283", 194 "7120190517612959703e+120", 195 "25188282901709339043e-252", 196 "308984926168550152811e-052", 197 "6372891218502368041059e+064", 198 199 // Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP 200 "5e-20", 201 "67e+14", 202 "985e+15", 203 "7693e-42", 204 "55895e-16", 205 "996622e-44", 206 "7038531e-32", 207 "60419369e-46", 208 "702990899e-20", 209 "6930161142e-48", 210 "25933168707e+13", 211 "596428896559e+20", 212 213 // Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP 214 "3e-23", 215 "57e+18", 216 "789e-35", 217 "2539e-18", 218 "76173e+28", 219 "887745e-11", 220 "5382571e-37", 221 "82381273e-35", 222 "750486563e-38", 223 "3752432815e-39", 224 "75224575729e-45", 225 "459926601011e+15", 226 227 // Constants plundered from strconv/atof_test.go. 228 229 "0", 230 "1", 231 "+1", 232 "1e23", 233 "1E23", 234 "100000000000000000000000", 235 "1e-100", 236 "123456700", 237 "99999999999999974834176", 238 "100000000000000000000001", 239 "100000000000000008388608", 240 "100000000000000016777215", 241 "100000000000000016777216", 242 "-1", 243 "-0.1", 244 "-0", // NB: exception made for this input 245 "1e-20", 246 "625e-3", 247 248 // largest float64 249 "1.7976931348623157e308", 250 "-1.7976931348623157e308", 251 // next float64 - too large 252 "1.7976931348623159e308", 253 "-1.7976931348623159e308", 254 // the border is ...158079 255 // borderline - okay 256 "1.7976931348623158e308", 257 "-1.7976931348623158e308", 258 // borderline - too large 259 "1.797693134862315808e308", 260 "-1.797693134862315808e308", 261 262 // a little too large 263 "1e308", 264 "2e308", 265 "1e309", 266 267 // way too large 268 "1e310", 269 "-1e310", 270 "1e400", 271 "-1e400", 272 "long:1e400000", 273 "long:-1e400000", 274 275 // denormalized 276 "1e-305", 277 "1e-306", 278 "1e-307", 279 "1e-308", 280 "1e-309", 281 "1e-310", 282 "1e-322", 283 // smallest denormal 284 "5e-324", 285 "4e-324", 286 "3e-324", 287 // too small 288 "2e-324", 289 // way too small 290 "1e-350", 291 "long:1e-400000", 292 // way too small, negative 293 "-1e-350", 294 "long:-1e-400000", 295 296 // try to overflow exponent 297 // [Disabled: too slow and memory-hungry with rationals.] 298 // "1e-4294967296", 299 // "1e+4294967296", 300 // "1e-18446744073709551616", 301 // "1e+18446744073709551616", 302 303 // http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/ 304 "2.2250738585072012e-308", 305 // http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/ 306 "2.2250738585072011e-308", 307 308 // A very large number (initially wrongly parsed by the fast algorithm). 309 "4.630813248087435e+307", 310 311 // A different kind of very large number. 312 "22.222222222222222", 313 "long:2." + strings.Repeat("2", 4000) + "e+1", 314 315 // Exactly halfway between 1 and math.Nextafter(1, 2). 316 // Round to even (down). 317 "1.00000000000000011102230246251565404236316680908203125", 318 // Slightly lower; still round down. 319 "1.00000000000000011102230246251565404236316680908203124", 320 // Slightly higher; round up. 321 "1.00000000000000011102230246251565404236316680908203126", 322 // Slightly higher, but you have to read all the way to the end. 323 "long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1", 324 325 // Smallest denormal, 2^(-1022-52) 326 "4.940656458412465441765687928682213723651e-324", 327 // Half of smallest denormal, 2^(-1022-53) 328 "2.470328229206232720882843964341106861825e-324", 329 // A little more than the exact half of smallest denormal 330 // 2^-1075 + 2^-1100. (Rounds to 1p-1074.) 331 "2.470328302827751011111470718709768633275e-324", 332 // The exact halfway between smallest normal and largest denormal: 333 // 2^-1022 - 2^-1075. (Rounds to 2^-1022.) 334 "2.225073858507201136057409796709131975935e-308", 335 336 "1152921504606846975", // 1<<60 - 1 337 "-1152921504606846975", // -(1<<60 - 1) 338 "1152921504606846977", // 1<<60 + 1 339 "-1152921504606846977", // -(1<<60 + 1) 340 341 "1/3", 342 } 343 344 // isFinite reports whether f represents a finite rational value. 345 // It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0). 346 func isFinite(f float64) bool { 347 return math.Abs(f) <= math.MaxFloat64 348 } 349 350 func TestFloat32SpecialCases(t *testing.T) { 351 for _, input := range float64inputs { 352 if strings.HasPrefix(input, "long:") { 353 if !*long { 354 continue 355 } 356 input = input[len("long:"):] 357 } 358 359 r, ok := new(Rat).SetString(input) 360 if !ok { 361 t.Errorf("Rat.SetString(%q) failed", input) 362 continue 363 } 364 f, exact := r.Float32() 365 366 // 1. Check string -> Rat -> float32 conversions are 367 // consistent with strconv.ParseFloat. 368 // Skip this check if the input uses "a/b" rational syntax. 369 if !strings.Contains(input, "/") { 370 e64, _ := strconv.ParseFloat(input, 32) 371 e := float32(e64) 372 373 // Careful: negative Rats too small for 374 // float64 become -0, but Rat obviously cannot 375 // preserve the sign from SetString("-0"). 376 switch { 377 case math.Float32bits(e) == math.Float32bits(f): 378 // Ok: bitwise equal. 379 case f == 0 && r.Num().BitLen() == 0: 380 // Ok: Rat(0) is equivalent to both +/- float64(0). 381 default: 382 t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e) 383 } 384 } 385 386 if !isFinite(float64(f)) { 387 continue 388 } 389 390 // 2. Check f is best approximation to r. 391 if !checkIsBestApprox32(t, f, r) { 392 // Append context information. 393 t.Errorf("(input was %q)", input) 394 } 395 396 // 3. Check f->R->f roundtrip is non-lossy. 397 checkNonLossyRoundtrip32(t, f) 398 399 // 4. Check exactness using slow algorithm. 400 if wasExact := new(Rat).SetFloat64(float64(f)).Cmp(r) == 0; wasExact != exact { 401 t.Errorf("Rat.SetString(%q).Float32().exact = %t, want %t", input, exact, wasExact) 402 } 403 } 404 } 405 406 func TestFloat64SpecialCases(t *testing.T) { 407 for _, input := range float64inputs { 408 if strings.HasPrefix(input, "long:") { 409 if !*long { 410 continue 411 } 412 input = input[len("long:"):] 413 } 414 415 r, ok := new(Rat).SetString(input) 416 if !ok { 417 t.Errorf("Rat.SetString(%q) failed", input) 418 continue 419 } 420 f, exact := r.Float64() 421 422 // 1. Check string -> Rat -> float64 conversions are 423 // consistent with strconv.ParseFloat. 424 // Skip this check if the input uses "a/b" rational syntax. 425 if !strings.Contains(input, "/") { 426 e, _ := strconv.ParseFloat(input, 64) 427 428 // Careful: negative Rats too small for 429 // float64 become -0, but Rat obviously cannot 430 // preserve the sign from SetString("-0"). 431 switch { 432 case math.Float64bits(e) == math.Float64bits(f): 433 // Ok: bitwise equal. 434 case f == 0 && r.Num().BitLen() == 0: 435 // Ok: Rat(0) is equivalent to both +/- float64(0). 436 default: 437 t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e) 438 } 439 } 440 441 if !isFinite(f) { 442 continue 443 } 444 445 // 2. Check f is best approximation to r. 446 if !checkIsBestApprox64(t, f, r) { 447 // Append context information. 448 t.Errorf("(input was %q)", input) 449 } 450 451 // 3. Check f->R->f roundtrip is non-lossy. 452 checkNonLossyRoundtrip64(t, f) 453 454 // 4. Check exactness using slow algorithm. 455 if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact { 456 t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact) 457 } 458 } 459 } 460
