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