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
5package big
6
7import (
8	"bytes"
9	"fmt"
10	"io"
11	"math"
12	"reflect"
13	"strconv"
14	"strings"
15	"testing"
16)
17
18var exponentTests = []struct {
19	s       string // string to be scanned
20	base2ok bool   // true if 'p'/'P' exponents are accepted
21	sepOk   bool   // true if '_' separators are accepted
22	x       int64  // expected exponent
23	b       int    // expected exponent base
24	err     error  // expected error
25	next    rune   // next character (or 0, if at EOF)
26}{
27	// valid, without separators
28	{"", false, false, 0, 10, nil, 0},
29	{"1", false, false, 0, 10, nil, '1'},
30	{"e0", false, false, 0, 10, nil, 0},
31	{"E1", false, false, 1, 10, nil, 0},
32	{"e+10", false, false, 10, 10, nil, 0},
33	{"e-10", false, false, -10, 10, nil, 0},
34	{"e123456789a", false, false, 123456789, 10, nil, 'a'},
35	{"p", false, false, 0, 10, nil, 'p'},
36	{"P+100", false, false, 0, 10, nil, 'P'},
37	{"p0", true, false, 0, 2, nil, 0},
38	{"P-123", true, false, -123, 2, nil, 0},
39	{"p+0a", true, false, 0, 2, nil, 'a'},
40	{"p+123__", true, false, 123, 2, nil, '_'}, // '_' is not part of the number anymore
41
42	// valid, with separators
43	{"e+1_0", false, true, 10, 10, nil, 0},
44	{"e-1_0", false, true, -10, 10, nil, 0},
45	{"e123_456_789a", false, true, 123456789, 10, nil, 'a'},
46	{"P+1_00", false, true, 0, 10, nil, 'P'},
47	{"p-1_2_3", true, true, -123, 2, nil, 0},
48
49	// invalid: no digits
50	{"e", false, false, 0, 10, errNoDigits, 0},
51	{"ef", false, false, 0, 10, errNoDigits, 'f'},
52	{"e+", false, false, 0, 10, errNoDigits, 0},
53	{"E-x", false, false, 0, 10, errNoDigits, 'x'},
54	{"p", true, false, 0, 2, errNoDigits, 0},
55	{"P-", true, false, 0, 2, errNoDigits, 0},
56	{"p+e", true, false, 0, 2, errNoDigits, 'e'},
57	{"e+_x", false, true, 0, 10, errNoDigits, 'x'},
58
59	// invalid: incorrect use of separator
60	{"e0_", false, true, 0, 10, errInvalSep, 0},
61	{"e_0", false, true, 0, 10, errInvalSep, 0},
62	{"e-1_2__3", false, true, -123, 10, errInvalSep, 0},
63}
64
65func TestScanExponent(t *testing.T) {
66	for _, a := range exponentTests {
67		r := strings.NewReader(a.s)
68		x, b, err := scanExponent(r, a.base2ok, a.sepOk)
69		if err != a.err {
70			t.Errorf("scanExponent%+v\n\tgot error = %v; want %v", a, err, a.err)
71		}
72		if x != a.x {
73			t.Errorf("scanExponent%+v\n\tgot z = %v; want %v", a, x, a.x)
74		}
75		if b != a.b {
76			t.Errorf("scanExponent%+v\n\tgot b = %d; want %d", a, b, a.b)
77		}
78		next, _, err := r.ReadRune()
79		if err == io.EOF {
80			next = 0
81			err = nil
82		}
83		if err == nil && next != a.next {
84			t.Errorf("scanExponent%+v\n\tgot next = %q; want %q", a, next, a.next)
85		}
86	}
87}
88
89type StringTest struct {
90	in, out string
91	ok      bool
92}
93
94var setStringTests = []StringTest{
95	// invalid
96	{in: "1e"},
97	{in: "1.e"},
98	{in: "1e+14e-5"},
99	{in: "1e4.5"},
100	{in: "r"},
101	{in: "a/b"},
102	{in: "a.b"},
103	{in: "1/0"},
104	{in: "4/3/2"}, // issue 17001
105	{in: "4/3/"},
106	{in: "4/3."},
107	{in: "4/"},
108	{in: "13e-9223372036854775808"}, // CVE-2022-23772
109
110	// valid
111	{"0", "0", true},
112	{"-0", "0", true},
113	{"1", "1", true},
114	{"-1", "-1", true},
115	{"1.", "1", true},
116	{"1e0", "1", true},
117	{"1.e1", "10", true},
118	{"-0.1", "-1/10", true},
119	{"-.1", "-1/10", true},
120	{"2/4", "1/2", true},
121	{".25", "1/4", true},
122	{"-1/5", "-1/5", true},
123	{"8129567.7690E14", "812956776900000000000", true},
124	{"78189e+4", "781890000", true},
125	{"553019.8935e+8", "55301989350000", true},
126	{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
127	{"9877861857500000E-7", "3951144743/4", true},
128	{"2169378.417e-3", "2169378417/1000000", true},
129	{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
130	{"53/70893980658822810696", "53/70893980658822810696", true},
131	{"106/141787961317645621392", "53/70893980658822810696", true},
132	{"204211327800791583.81095", "4084226556015831676219/20000", true},
133	{"0e9999999999", "0", true}, // issue #16176
134}
135
136// These are not supported by fmt.Fscanf.
137var setStringTests2 = []StringTest{
138	// invalid
139	{in: "4/3x"},
140	{in: "0/-1"},
141	{in: "-1/-1"},
142
143	// invalid with separators
144	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
145	{in: "10_/1"},
146	{in: "_10/1"},
147	{in: "1/1__0"},
148
149	// valid
150	{"0b1000/3", "8/3", true},
151	{"0B1000/0x8", "1", true},
152	{"-010/1", "-8", true}, // 0-prefix indicates octal in this case
153	{"-010.0", "-10", true},
154	{"-0o10/1", "-8", true},
155	{"0x10/1", "16", true},
156	{"0x10/0x20", "1/2", true},
157
158	{"0010", "10", true}, // 0-prefix is ignored in this case (not a fraction)
159	{"0x10.0", "16", true},
160	{"0x1.8", "3/2", true},
161	{"0X1.8p4", "24", true},
162	{"0x1.1E2", "2289/2048", true}, // E is part of hex mantissa, not exponent
163	{"0b1.1E2", "150", true},
164	{"0B1.1P3", "12", true},
165	{"0o10e-2", "2/25", true},
166	{"0O10p-3", "1", true},
167
168	// valid with separators
169	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
170	{"0b_1000/3", "8/3", true},
171	{"0B_10_00/0x8", "1", true},
172	{"0xdead/0B1101_1110_1010_1101", "1", true},
173	{"0B1101_1110_1010_1101/0XD_E_A_D", "1", true},
174	{"1_000.0", "1000", true},
175
176	{"0x_10.0", "16", true},
177	{"0x1_0.0", "16", true},
178	{"0x1.8_0", "3/2", true},
179	{"0X1.8p0_4", "24", true},
180	{"0b1.1_0E2", "150", true},
181	{"0o1_0e-2", "2/25", true},
182	{"0O_10p-3", "1", true},
183}
184
185func TestRatSetString(t *testing.T) {
186	var tests []StringTest
187	tests = append(tests, setStringTests...)
188	tests = append(tests, setStringTests2...)
189
190	for i, test := range tests {
191		x, ok := new(Rat).SetString(test.in)
192
193		if ok {
194			if !test.ok {
195				t.Errorf("#%d SetString(%q) expected failure", i, test.in)
196			} else if x.RatString() != test.out {
197				t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
198			}
199		} else {
200			if test.ok {
201				t.Errorf("#%d SetString(%q) expected success", i, test.in)
202			} else if x != nil {
203				t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
204			}
205		}
206	}
207}
208
209func TestRatSetStringZero(t *testing.T) {
210	got, _ := new(Rat).SetString("0")
211	want := new(Rat).SetInt64(0)
212	if !reflect.DeepEqual(got, want) {
213		t.Errorf("got %#+v, want %#+v", got, want)
214	}
215}
216
217func TestRatScan(t *testing.T) {
218	var buf bytes.Buffer
219	for i, test := range setStringTests {
220		x := new(Rat)
221		buf.Reset()
222		buf.WriteString(test.in)
223
224		_, err := fmt.Fscanf(&buf, "%v", x)
225		if err == nil != test.ok {
226			if test.ok {
227				t.Errorf("#%d (%s) error: %s", i, test.in, err)
228			} else {
229				t.Errorf("#%d (%s) expected error", i, test.in)
230			}
231			continue
232		}
233		if err == nil && x.RatString() != test.out {
234			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
235		}
236	}
237}
238
239var floatStringTests = []struct {
240	in   string
241	prec int
242	out  string
243}{
244	{"0", 0, "0"},
245	{"0", 4, "0.0000"},
246	{"1", 0, "1"},
247	{"1", 2, "1.00"},
248	{"-1", 0, "-1"},
249	{"0.05", 1, "0.1"},
250	{"-0.05", 1, "-0.1"},
251	{".25", 2, "0.25"},
252	{".25", 1, "0.3"},
253	{".25", 3, "0.250"},
254	{"-1/3", 3, "-0.333"},
255	{"-2/3", 4, "-0.6667"},
256	{"0.96", 1, "1.0"},
257	{"0.999", 2, "1.00"},
258	{"0.9", 0, "1"},
259	{".25", -1, "0"},
260	{".55", -1, "1"},
261}
262
263func TestFloatString(t *testing.T) {
264	for i, test := range floatStringTests {
265		x, _ := new(Rat).SetString(test.in)
266
267		if x.FloatString(test.prec) != test.out {
268			t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
269		}
270	}
271}
272
273// Test inputs to Rat.SetString. The prefix "long:" causes the test
274// to be skipped except in -long mode.  (The threshold is about 500us.)
275var float64inputs = []string{
276	// Constants plundered from strconv/testfp.txt.
277
278	// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
279	"5e+125",
280	"69e+267",
281	"999e-026",
282	"7861e-034",
283	"75569e-254",
284	"928609e-261",
285	"9210917e+080",
286	"84863171e+114",
287	"653777767e+273",
288	"5232604057e-298",
289	"27235667517e-109",
290	"653532977297e-123",
291	"3142213164987e-294",
292	"46202199371337e-072",
293	"231010996856685e-073",
294	"9324754620109615e+212",
295	"78459735791271921e+049",
296	"272104041512242479e+200",
297	"6802601037806061975e+198",
298	"20505426358836677347e-221",
299	"836168422905420598437e-234",
300	"4891559871276714924261e+222",
301
302	// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
303	"9e-265",
304	"85e-037",
305	"623e+100",
306	"3571e+263",
307	"81661e+153",
308	"920657e-023",
309	"4603285e-024",
310	"87575437e-309",
311	"245540327e+122",
312	"6138508175e+120",
313	"83356057653e+193",
314	"619534293513e+124",
315	"2335141086879e+218",
316	"36167929443327e-159",
317	"609610927149051e-255",
318	"3743626360493413e-165",
319	"94080055902682397e-242",
320	"899810892172646163e+283",
321	"7120190517612959703e+120",
322	"25188282901709339043e-252",
323	"308984926168550152811e-052",
324	"6372891218502368041059e+064",
325
326	// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
327	"5e-20",
328	"67e+14",
329	"985e+15",
330	"7693e-42",
331	"55895e-16",
332	"996622e-44",
333	"7038531e-32",
334	"60419369e-46",
335	"702990899e-20",
336	"6930161142e-48",
337	"25933168707e+13",
338	"596428896559e+20",
339
340	// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
341	"3e-23",
342	"57e+18",
343	"789e-35",
344	"2539e-18",
345	"76173e+28",
346	"887745e-11",
347	"5382571e-37",
348	"82381273e-35",
349	"750486563e-38",
350	"3752432815e-39",
351	"75224575729e-45",
352	"459926601011e+15",
353
354	// Constants plundered from strconv/atof_test.go.
355
356	"0",
357	"1",
358	"+1",
359	"1e23",
360	"1E23",
361	"100000000000000000000000",
362	"1e-100",
363	"123456700",
364	"99999999999999974834176",
365	"100000000000000000000001",
366	"100000000000000008388608",
367	"100000000000000016777215",
368	"100000000000000016777216",
369	"-1",
370	"-0.1",
371	"-0", // NB: exception made for this input
372	"1e-20",
373	"625e-3",
374
375	// largest float64
376	"1.7976931348623157e308",
377	"-1.7976931348623157e308",
378	// next float64 - too large
379	"1.7976931348623159e308",
380	"-1.7976931348623159e308",
381	// the border is ...158079
382	// borderline - okay
383	"1.7976931348623158e308",
384	"-1.7976931348623158e308",
385	// borderline - too large
386	"1.797693134862315808e308",
387	"-1.797693134862315808e308",
388
389	// a little too large
390	"1e308",
391	"2e308",
392	"1e309",
393
394	// way too large
395	"1e310",
396	"-1e310",
397	"1e400",
398	"-1e400",
399	"long:1e400000",
400	"long:-1e400000",
401
402	// denormalized
403	"1e-305",
404	"1e-306",
405	"1e-307",
406	"1e-308",
407	"1e-309",
408	"1e-310",
409	"1e-322",
410	// smallest denormal
411	"5e-324",
412	"4e-324",
413	"3e-324",
414	// too small
415	"2e-324",
416	// way too small
417	"1e-350",
418	"long:1e-400000",
419	// way too small, negative
420	"-1e-350",
421	"long:-1e-400000",
422
423	// try to overflow exponent
424	// [Disabled: too slow and memory-hungry with rationals.]
425	// "1e-4294967296",
426	// "1e+4294967296",
427	// "1e-18446744073709551616",
428	// "1e+18446744073709551616",
429
430	// https://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
431	"2.2250738585072012e-308",
432	// https://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
433	"2.2250738585072011e-308",
434
435	// A very large number (initially wrongly parsed by the fast algorithm).
436	"4.630813248087435e+307",
437
438	// A different kind of very large number.
439	"22.222222222222222",
440	"long:2." + strings.Repeat("2", 4000) + "e+1",
441
442	// Exactly halfway between 1 and math.Nextafter(1, 2).
443	// Round to even (down).
444	"1.00000000000000011102230246251565404236316680908203125",
445	// Slightly lower; still round down.
446	"1.00000000000000011102230246251565404236316680908203124",
447	// Slightly higher; round up.
448	"1.00000000000000011102230246251565404236316680908203126",
449	// Slightly higher, but you have to read all the way to the end.
450	"long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",
451
452	// Smallest denormal, 2^(-1022-52)
453	"4.940656458412465441765687928682213723651e-324",
454	// Half of smallest denormal, 2^(-1022-53)
455	"2.470328229206232720882843964341106861825e-324",
456	// A little more than the exact half of smallest denormal
457	// 2^-1075 + 2^-1100.  (Rounds to 1p-1074.)
458	"2.470328302827751011111470718709768633275e-324",
459	// The exact halfway between smallest normal and largest denormal:
460	// 2^-1022 - 2^-1075.  (Rounds to 2^-1022.)
461	"2.225073858507201136057409796709131975935e-308",
462
463	"1152921504606846975",  //   1<<60 - 1
464	"-1152921504606846975", // -(1<<60 - 1)
465	"1152921504606846977",  //   1<<60 + 1
466	"-1152921504606846977", // -(1<<60 + 1)
467
468	"1/3",
469}
470
471// isFinite reports whether f represents a finite rational value.
472// It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0).
473func isFinite(f float64) bool {
474	return math.Abs(f) <= math.MaxFloat64
475}
476
477func TestFloat32SpecialCases(t *testing.T) {
478	for _, input := range float64inputs {
479		if strings.HasPrefix(input, "long:") {
480			if !*long {
481				continue
482			}
483			input = input[len("long:"):]
484		}
485
486		r, ok := new(Rat).SetString(input)
487		if !ok {
488			t.Errorf("Rat.SetString(%q) failed", input)
489			continue
490		}
491		f, exact := r.Float32()
492
493		// 1. Check string -> Rat -> float32 conversions are
494		// consistent with strconv.ParseFloat.
495		// Skip this check if the input uses "a/b" rational syntax.
496		if !strings.Contains(input, "/") {
497			e64, _ := strconv.ParseFloat(input, 32)
498			e := float32(e64)
499
500			// Careful: negative Rats too small for
501			// float64 become -0, but Rat obviously cannot
502			// preserve the sign from SetString("-0").
503			switch {
504			case math.Float32bits(e) == math.Float32bits(f):
505				// Ok: bitwise equal.
506			case f == 0 && r.Num().BitLen() == 0:
507				// Ok: Rat(0) is equivalent to both +/- float64(0).
508			default:
509				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
510			}
511		}
512
513		if !isFinite(float64(f)) {
514			continue
515		}
516
517		// 2. Check f is best approximation to r.
518		if !checkIsBestApprox32(t, f, r) {
519			// Append context information.
520			t.Errorf("(input was %q)", input)
521		}
522
523		// 3. Check f->R->f roundtrip is non-lossy.
524		checkNonLossyRoundtrip32(t, f)
525
526		// 4. Check exactness using slow algorithm.
527		if wasExact := new(Rat).SetFloat64(float64(f)).Cmp(r) == 0; wasExact != exact {
528			t.Errorf("Rat.SetString(%q).Float32().exact = %t, want %t", input, exact, wasExact)
529		}
530	}
531}
532
533func TestFloat64SpecialCases(t *testing.T) {
534	for _, input := range float64inputs {
535		if strings.HasPrefix(input, "long:") {
536			if !*long {
537				continue
538			}
539			input = input[len("long:"):]
540		}
541
542		r, ok := new(Rat).SetString(input)
543		if !ok {
544			t.Errorf("Rat.SetString(%q) failed", input)
545			continue
546		}
547		f, exact := r.Float64()
548
549		// 1. Check string -> Rat -> float64 conversions are
550		// consistent with strconv.ParseFloat.
551		// Skip this check if the input uses "a/b" rational syntax.
552		if !strings.Contains(input, "/") {
553			e, _ := strconv.ParseFloat(input, 64)
554
555			// Careful: negative Rats too small for
556			// float64 become -0, but Rat obviously cannot
557			// preserve the sign from SetString("-0").
558			switch {
559			case math.Float64bits(e) == math.Float64bits(f):
560				// Ok: bitwise equal.
561			case f == 0 && r.Num().BitLen() == 0:
562				// Ok: Rat(0) is equivalent to both +/- float64(0).
563			default:
564				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
565			}
566		}
567
568		if !isFinite(f) {
569			continue
570		}
571
572		// 2. Check f is best approximation to r.
573		if !checkIsBestApprox64(t, f, r) {
574			// Append context information.
575			t.Errorf("(input was %q)", input)
576		}
577
578		// 3. Check f->R->f roundtrip is non-lossy.
579		checkNonLossyRoundtrip64(t, f)
580
581		// 4. Check exactness using slow algorithm.
582		if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
583			t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
584		}
585	}
586}
587
588func TestIssue31184(t *testing.T) {
589	var x Rat
590	for _, want := range []string{
591		"-213.090",
592		"8.192",
593		"16.000",
594	} {
595		x.SetString(want)
596		got := x.FloatString(3)
597		if got != want {
598			t.Errorf("got %s, want %s", got, want)
599		}
600	}
601}
602
603func TestIssue45910(t *testing.T) {
604	var x Rat
605	for _, test := range []struct {
606		input string
607		want  bool
608	}{
609		{"1e-1000001", false},
610		{"1e-1000000", true},
611		{"1e+1000000", true},
612		{"1e+1000001", false},
613
614		{"0p1000000000000", true},
615		{"1p-10000001", false},
616		{"1p-10000000", true},
617		{"1p+10000000", true},
618		{"1p+10000001", false},
619		{"1.770p02041010010011001001", false}, // test case from issue
620	} {
621		_, got := x.SetString(test.input)
622		if got != test.want {
623			t.Errorf("SetString(%s) got ok = %v; want %v", test.input, got, test.want)
624		}
625	}
626}
627func TestFloatPrec(t *testing.T) {
628	var tests = []struct {
629		f    string
630		prec int
631		ok   bool
632		fdec string
633	}{
634		// examples from the issue #50489
635		{"10/100", 1, true, "0.1"},
636		{"3/100", 2, true, "0.03"},
637		{"10", 0, true, "10"},
638
639		// more examples
640		{"zero", 0, true, "0"},      // test uninitialized zero value for Rat
641		{"0", 0, true, "0"},         // 0
642		{"1", 0, true, "1"},         // 1
643		{"1/2", 1, true, "0.5"},     // 0.5
644		{"1/3", 0, false, "0"},      // 0.(3)
645		{"1/4", 2, true, "0.25"},    // 0.25
646		{"1/5", 1, true, "0.2"},     // 0.2
647		{"1/6", 1, false, "0.2"},    // 0.1(6)
648		{"1/7", 0, false, "0"},      // 0.(142857)
649		{"1/8", 3, true, "0.125"},   // 0.125
650		{"1/9", 0, false, "0"},      // 0.(1)
651		{"1/10", 1, true, "0.1"},    // 0.1
652		{"1/11", 0, false, "0"},     // 0.(09)
653		{"1/12", 2, false, "0.08"},  // 0.08(3)
654		{"1/13", 0, false, "0"},     // 0.(076923)
655		{"1/14", 1, false, "0.1"},   // 0.0(714285)
656		{"1/15", 1, false, "0.1"},   // 0.0(6)
657		{"1/16", 4, true, "0.0625"}, // 0.0625
658
659		{"10/2", 0, true, "5"},                    // 5
660		{"10/3", 0, false, "3"},                   // 3.(3)
661		{"10/6", 0, false, "2"},                   // 1.(6)
662		{"1/10000000", 7, true, "0.0000001"},      // 0.0000001
663		{"1/3125", 5, true, "0.00032"},            // "0.00032"
664		{"1/1024", 10, true, "0.0009765625"},      // 0.0009765625
665		{"1/304000", 7, false, "0.0000033"},       // 0.0000032(894736842105263157)
666		{"1/48828125", 11, true, "0.00000002048"}, // 0.00000002048
667	}
668
669	for _, test := range tests {
670		var f Rat
671
672		// check uninitialized zero value
673		if test.f != "zero" {
674			_, ok := f.SetString(test.f)
675			if !ok {
676				t.Fatalf("invalid test case: f = %s", test.f)
677			}
678		}
679
680		// results for f and -f must be the same
681		fdec := test.fdec
682		for i := 0; i < 2; i++ {
683			prec, ok := f.FloatPrec()
684			if prec != test.prec || ok != test.ok {
685				t.Errorf("%s: FloatPrec(%s): got prec, ok = %d, %v; want %d, %v", test.f, &f, prec, ok, test.prec, test.ok)
686			}
687			s := f.FloatString(test.prec)
688			if s != fdec {
689				t.Errorf("%s: FloatString(%s, %d): got %s; want %s", test.f, &f, prec, s, fdec)
690			}
691			// proceed with -f but don't add a "-" before a "0"
692			if f.Sign() > 0 {
693				f.Neg(&f)
694				fdec = "-" + fdec
695			}
696		}
697	}
698}
699
700func BenchmarkFloatPrecExact(b *testing.B) {
701	for _, n := range []int{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6} {
702		// d := 5^n
703		d := NewInt(5)
704		p := NewInt(int64(n))
705		d.Exp(d, p, nil)
706
707		// r := 1/d
708		var r Rat
709		r.SetFrac(NewInt(1), d)
710
711		b.Run(fmt.Sprint(n), func(b *testing.B) {
712			for i := 0; i < b.N; i++ {
713				prec, ok := r.FloatPrec()
714				if prec != n || !ok {
715					b.Fatalf("got exact, ok = %d, %v; want %d, %v", prec, ok, uint64(n), true)
716				}
717			}
718		})
719	}
720}
721
722func BenchmarkFloatPrecMixed(b *testing.B) {
723	for _, n := range []int{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6} {
724		// d := (3·5·7·11)^n
725		d := NewInt(3 * 5 * 7 * 11)
726		p := NewInt(int64(n))
727		d.Exp(d, p, nil)
728
729		// r := 1/d
730		var r Rat
731		r.SetFrac(NewInt(1), d)
732
733		b.Run(fmt.Sprint(n), func(b *testing.B) {
734			for i := 0; i < b.N; i++ {
735				prec, ok := r.FloatPrec()
736				if prec != n || ok {
737					b.Fatalf("got exact, ok = %d, %v; want %d, %v", prec, ok, uint64(n), false)
738				}
739			}
740		})
741	}
742}
743
744func BenchmarkFloatPrecInexact(b *testing.B) {
745	for _, n := range []int{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6} {
746		// d := 5^n + 1
747		d := NewInt(5)
748		p := NewInt(int64(n))
749		d.Exp(d, p, nil)
750		d.Add(d, NewInt(1))
751
752		// r := 1/d
753		var r Rat
754		r.SetFrac(NewInt(1), d)
755
756		b.Run(fmt.Sprint(n), func(b *testing.B) {
757			for i := 0; i < b.N; i++ {
758				_, ok := r.FloatPrec()
759				if ok {
760					b.Fatalf("got unexpected ok")
761				}
762			}
763		})
764	}
765}
766