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/bits"
12	"strings"
13	"testing"
14)
15
16func TestMaxBase(t *testing.T) {
17	if MaxBase != len(digits) {
18		t.Fatalf("%d != %d", MaxBase, len(digits))
19	}
20}
21
22// log2 computes the integer binary logarithm of x.
23// The result is the integer n for which 2^n <= x < 2^(n+1).
24// If x == 0, the result is -1.
25func log2(x Word) int {
26	return bits.Len(uint(x)) - 1
27}
28
29func itoa(x nat, base int) []byte {
30	// special cases
31	switch {
32	case base < 2:
33		panic("illegal base")
34	case len(x) == 0:
35		return []byte("0")
36	}
37
38	// allocate buffer for conversion
39	i := x.bitLen()/log2(Word(base)) + 1 // +1: round up
40	s := make([]byte, i)
41
42	// don't destroy x
43	q := nat(nil).set(x)
44
45	// convert
46	for len(q) > 0 {
47		i--
48		var r Word
49		q, r = q.divW(q, Word(base))
50		s[i] = digits[r]
51	}
52
53	return s[i:]
54}
55
56var strTests = []struct {
57	x nat    // nat value to be converted
58	b int    // conversion base
59	s string // expected result
60}{
61	{nil, 2, "0"},
62	{nat{1}, 2, "1"},
63	{nat{0xc5}, 2, "11000101"},
64	{nat{03271}, 8, "3271"},
65	{nat{10}, 10, "10"},
66	{nat{1234567890}, 10, "1234567890"},
67	{nat{0xdeadbeef}, 16, "deadbeef"},
68	{nat{0x229be7}, 17, "1a2b3c"},
69	{nat{0x309663e6}, 32, "o9cov6"},
70	{nat{0x309663e6}, 62, "TakXI"},
71}
72
73func TestString(t *testing.T) {
74	// test invalid base explicitly
75	var panicStr string
76	func() {
77		defer func() {
78			panicStr = recover().(string)
79		}()
80		natOne.utoa(1)
81	}()
82	if panicStr != "invalid base" {
83		t.Errorf("expected panic for invalid base")
84	}
85
86	for _, a := range strTests {
87		s := string(a.x.utoa(a.b))
88		if s != a.s {
89			t.Errorf("string%+v\n\tgot s = %s; want %s", a, s, a.s)
90		}
91
92		x, b, _, err := nat(nil).scan(strings.NewReader(a.s), a.b, false)
93		if x.cmp(a.x) != 0 {
94			t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
95		}
96		if b != a.b {
97			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.b)
98		}
99		if err != nil {
100			t.Errorf("scan%+v\n\tgot error = %s", a, err)
101		}
102	}
103}
104
105var natScanTests = []struct {
106	s     string // string to be scanned
107	base  int    // input base
108	frac  bool   // fraction ok
109	x     nat    // expected nat
110	b     int    // expected base
111	count int    // expected digit count
112	err   error  // expected error
113	next  rune   // next character (or 0, if at EOF)
114}{
115	// invalid: no digits
116	{"", 0, false, nil, 10, 0, errNoDigits, 0},
117	{"_", 0, false, nil, 10, 0, errNoDigits, 0},
118	{"?", 0, false, nil, 10, 0, errNoDigits, '?'},
119	{"?", 10, false, nil, 10, 0, errNoDigits, '?'},
120	{"", 10, false, nil, 10, 0, errNoDigits, 0},
121	{"", 36, false, nil, 36, 0, errNoDigits, 0},
122	{"", 62, false, nil, 62, 0, errNoDigits, 0},
123	{"0b", 0, false, nil, 2, 0, errNoDigits, 0},
124	{"0o", 0, false, nil, 8, 0, errNoDigits, 0},
125	{"0x", 0, false, nil, 16, 0, errNoDigits, 0},
126	{"0x_", 0, false, nil, 16, 0, errNoDigits, 0},
127	{"0b2", 0, false, nil, 2, 0, errNoDigits, '2'},
128	{"0B2", 0, false, nil, 2, 0, errNoDigits, '2'},
129	{"0o8", 0, false, nil, 8, 0, errNoDigits, '8'},
130	{"0O8", 0, false, nil, 8, 0, errNoDigits, '8'},
131	{"0xg", 0, false, nil, 16, 0, errNoDigits, 'g'},
132	{"0Xg", 0, false, nil, 16, 0, errNoDigits, 'g'},
133	{"345", 2, false, nil, 2, 0, errNoDigits, '3'},
134
135	// invalid: incorrect use of decimal point
136	{"._", 0, true, nil, 10, 0, errNoDigits, 0},
137	{".0", 0, false, nil, 10, 0, errNoDigits, '.'},
138	{".0", 10, false, nil, 10, 0, errNoDigits, '.'},
139	{".", 0, true, nil, 10, 0, errNoDigits, 0},
140	{"0x.", 0, true, nil, 16, 0, errNoDigits, 0},
141	{"0x.g", 0, true, nil, 16, 0, errNoDigits, 'g'},
142	{"0x.0", 0, false, nil, 16, 0, errNoDigits, '.'},
143
144	// invalid: incorrect use of separators
145	{"_0", 0, false, nil, 10, 1, errInvalSep, 0},
146	{"0_", 0, false, nil, 10, 1, errInvalSep, 0},
147	{"0__0", 0, false, nil, 8, 1, errInvalSep, 0},
148	{"0x___0", 0, false, nil, 16, 1, errInvalSep, 0},
149	{"0_x", 0, false, nil, 10, 1, errInvalSep, 'x'},
150	{"0_8", 0, false, nil, 10, 1, errInvalSep, '8'},
151	{"123_.", 0, true, nat{123}, 10, 0, errInvalSep, 0},
152	{"._123", 0, true, nat{123}, 10, -3, errInvalSep, 0},
153	{"0b__1000", 0, false, nat{0x8}, 2, 4, errInvalSep, 0},
154	{"0o60___0", 0, false, nat{0600}, 8, 3, errInvalSep, 0},
155	{"0466_", 0, false, nat{0466}, 8, 3, errInvalSep, 0},
156	{"01234567_8", 0, false, nat{01234567}, 8, 7, errInvalSep, '8'},
157	{"1_.", 0, true, nat{1}, 10, 0, errInvalSep, 0},
158	{"0._1", 0, true, nat{1}, 10, -1, errInvalSep, 0},
159	{"2.7_", 0, true, nat{27}, 10, -1, errInvalSep, 0},
160	{"0x1.0_", 0, true, nat{0x10}, 16, -1, errInvalSep, 0},
161
162	// valid: separators are not accepted for base != 0
163	{"0_", 10, false, nil, 10, 1, nil, '_'},
164	{"1__0", 10, false, nat{1}, 10, 1, nil, '_'},
165	{"0__8", 10, false, nil, 10, 1, nil, '_'},
166	{"xy_z_", 36, false, nat{33*36 + 34}, 36, 2, nil, '_'},
167
168	// valid, no decimal point
169	{"0", 0, false, nil, 10, 1, nil, 0},
170	{"0", 36, false, nil, 36, 1, nil, 0},
171	{"0", 62, false, nil, 62, 1, nil, 0},
172	{"1", 0, false, nat{1}, 10, 1, nil, 0},
173	{"1", 10, false, nat{1}, 10, 1, nil, 0},
174	{"0 ", 0, false, nil, 10, 1, nil, ' '},
175	{"00 ", 0, false, nil, 8, 1, nil, ' '}, // octal 0
176	{"0b1", 0, false, nat{1}, 2, 1, nil, 0},
177	{"0B11000101", 0, false, nat{0xc5}, 2, 8, nil, 0},
178	{"0B110001012", 0, false, nat{0xc5}, 2, 8, nil, '2'},
179	{"07", 0, false, nat{7}, 8, 1, nil, 0},
180	{"08", 0, false, nil, 10, 1, nil, '8'},
181	{"08", 10, false, nat{8}, 10, 2, nil, 0},
182	{"018", 0, false, nat{1}, 8, 1, nil, '8'},
183	{"0o7", 0, false, nat{7}, 8, 1, nil, 0},
184	{"0o18", 0, false, nat{1}, 8, 1, nil, '8'},
185	{"0O17", 0, false, nat{017}, 8, 2, nil, 0},
186	{"03271", 0, false, nat{03271}, 8, 4, nil, 0},
187	{"10ab", 0, false, nat{10}, 10, 2, nil, 'a'},
188	{"1234567890", 0, false, nat{1234567890}, 10, 10, nil, 0},
189	{"A", 36, false, nat{10}, 36, 1, nil, 0},
190	{"A", 37, false, nat{36}, 37, 1, nil, 0},
191	{"xyz", 36, false, nat{(33*36+34)*36 + 35}, 36, 3, nil, 0},
192	{"XYZ?", 36, false, nat{(33*36+34)*36 + 35}, 36, 3, nil, '?'},
193	{"XYZ?", 62, false, nat{(59*62+60)*62 + 61}, 62, 3, nil, '?'},
194	{"0x", 16, false, nil, 16, 1, nil, 'x'},
195	{"0xdeadbeef", 0, false, nat{0xdeadbeef}, 16, 8, nil, 0},
196	{"0XDEADBEEF", 0, false, nat{0xdeadbeef}, 16, 8, nil, 0},
197
198	// valid, with decimal point
199	{"0.", 0, false, nil, 10, 1, nil, '.'},
200	{"0.", 10, true, nil, 10, 0, nil, 0},
201	{"0.1.2", 10, true, nat{1}, 10, -1, nil, '.'},
202	{".000", 10, true, nil, 10, -3, nil, 0},
203	{"12.3", 10, true, nat{123}, 10, -1, nil, 0},
204	{"012.345", 10, true, nat{12345}, 10, -3, nil, 0},
205	{"0.1", 0, true, nat{1}, 10, -1, nil, 0},
206	{"0.1", 2, true, nat{1}, 2, -1, nil, 0},
207	{"0.12", 2, true, nat{1}, 2, -1, nil, '2'},
208	{"0b0.1", 0, true, nat{1}, 2, -1, nil, 0},
209	{"0B0.12", 0, true, nat{1}, 2, -1, nil, '2'},
210	{"0o0.7", 0, true, nat{7}, 8, -1, nil, 0},
211	{"0O0.78", 0, true, nat{7}, 8, -1, nil, '8'},
212	{"0xdead.beef", 0, true, nat{0xdeadbeef}, 16, -4, nil, 0},
213
214	// valid, with separators
215	{"1_000", 0, false, nat{1000}, 10, 4, nil, 0},
216	{"0_466", 0, false, nat{0466}, 8, 3, nil, 0},
217	{"0o_600", 0, false, nat{0600}, 8, 3, nil, 0},
218	{"0x_f0_0d", 0, false, nat{0xf00d}, 16, 4, nil, 0},
219	{"0b1000_0001", 0, false, nat{0x81}, 2, 8, nil, 0},
220	{"1_000.000_1", 0, true, nat{10000001}, 10, -4, nil, 0},
221	{"0x_f00d.1e", 0, true, nat{0xf00d1e}, 16, -2, nil, 0},
222	{"0x_f00d.1E2", 0, true, nat{0xf00d1e2}, 16, -3, nil, 0},
223	{"0x_f00d.1eg", 0, true, nat{0xf00d1e}, 16, -2, nil, 'g'},
224}
225
226func TestScanBase(t *testing.T) {
227	for _, a := range natScanTests {
228		r := strings.NewReader(a.s)
229		x, b, count, err := nat(nil).scan(r, a.base, a.frac)
230		if err != a.err {
231			t.Errorf("scan%+v\n\tgot error = %v; want %v", a, err, a.err)
232		}
233		if x.cmp(a.x) != 0 {
234			t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
235		}
236		if b != a.b {
237			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.base)
238		}
239		if count != a.count {
240			t.Errorf("scan%+v\n\tgot count = %d; want %d", a, count, a.count)
241		}
242		next, _, err := r.ReadRune()
243		if err == io.EOF {
244			next = 0
245			err = nil
246		}
247		if err == nil && next != a.next {
248			t.Errorf("scan%+v\n\tgot next = %q; want %q", a, next, a.next)
249		}
250	}
251}
252
253var pi = "3" +
254	"14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651" +
255	"32823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461" +
256	"28475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920" +
257	"96282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179" +
258	"31051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798" +
259	"60943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901" +
260	"22495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837" +
261	"29780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083" +
262	"81420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909" +
263	"21642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151" +
264	"55748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035" +
265	"63707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104" +
266	"75216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992" +
267	"45863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818" +
268	"34797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548" +
269	"16136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179" +
270	"04946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886" +
271	"26945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645" +
272	"99581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745" +
273	"53050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382" +
274	"68683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244" +
275	"13654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767" +
276	"88952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288" +
277	"79710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821" +
278	"68299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610" +
279	"21359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435" +
280	"06430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675" +
281	"14269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672" +
282	"21825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539" +
283	"05796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007" +
284	"23055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816" +
285	"90915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398" +
286	"31501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064" +
287	"20467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325" +
288	"97463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100" +
289	"44929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915" +
290	"44110104468232527162010526522721116603966655730925471105578537634668206531098965269186205647693125705863566201" +
291	"85581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318" +
292	"58676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797" +
293	"27082668306343285878569830523580893306575740679545716377525420211495576158140025012622859413021647155097925923" +
294	"09907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111" +
295	"79042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043" +
296	"06332175182979866223717215916077166925474873898665494945011465406284336639379003976926567214638530673609657120" +
297	"91807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862" +
298	"94726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939" +
299	"78054193414473774418426312986080998886874132604721569516239658645730216315981931951673538129741677294786724229" +
300	"24654366800980676928238280689964004824354037014163149658979409243237896907069779422362508221688957383798623001" +
301	"59377647165122893578601588161755782973523344604281512627203734314653197777416031990665541876397929334419521541" +
302	"34189948544473456738316249934191318148092777710386387734317720754565453220777092120190516609628049092636019759" +
303	"88281613323166636528619326686336062735676303544776280350450777235547105859548702790814356240145171806246436267" +
304	"94561275318134078330336254232783944975382437205835311477119926063813346776879695970309833913077109870408591337"
305
306// Test case for BenchmarkScanPi.
307func TestScanPi(t *testing.T) {
308	var x nat
309	z, _, _, err := x.scan(strings.NewReader(pi), 10, false)
310	if err != nil {
311		t.Errorf("scanning pi: %s", err)
312	}
313	if s := string(z.utoa(10)); s != pi {
314		t.Errorf("scanning pi: got %s", s)
315	}
316}
317
318func TestScanPiParallel(t *testing.T) {
319	const n = 2
320	c := make(chan int)
321	for i := 0; i < n; i++ {
322		go func() {
323			TestScanPi(t)
324			c <- 0
325		}()
326	}
327	for i := 0; i < n; i++ {
328		<-c
329	}
330}
331
332func BenchmarkScanPi(b *testing.B) {
333	for i := 0; i < b.N; i++ {
334		var x nat
335		x.scan(strings.NewReader(pi), 10, false)
336	}
337}
338
339func BenchmarkStringPiParallel(b *testing.B) {
340	var x nat
341	x, _, _, _ = x.scan(strings.NewReader(pi), 0, false)
342	if string(x.utoa(10)) != pi {
343		panic("benchmark incorrect: conversion failed")
344	}
345	b.RunParallel(func(pb *testing.PB) {
346		for pb.Next() {
347			x.utoa(10)
348		}
349	})
350}
351
352func BenchmarkScan(b *testing.B) {
353	const x = 10
354	for _, base := range []int{2, 8, 10, 16} {
355		for _, y := range []Word{10, 100, 1000, 10000, 100000} {
356			if isRaceBuilder && y > 1000 {
357				continue
358			}
359			b.Run(fmt.Sprintf("%d/Base%d", y, base), func(b *testing.B) {
360				b.StopTimer()
361				var z nat
362				z = z.expWW(x, y)
363
364				s := z.utoa(base)
365				if t := itoa(z, base); !bytes.Equal(s, t) {
366					b.Fatalf("scanning: got %s; want %s", s, t)
367				}
368				b.StartTimer()
369
370				for i := 0; i < b.N; i++ {
371					z.scan(bytes.NewReader(s), base, false)
372				}
373			})
374		}
375	}
376}
377
378func BenchmarkString(b *testing.B) {
379	const x = 10
380	for _, base := range []int{2, 8, 10, 16} {
381		for _, y := range []Word{10, 100, 1000, 10000, 100000} {
382			if isRaceBuilder && y > 1000 {
383				continue
384			}
385			b.Run(fmt.Sprintf("%d/Base%d", y, base), func(b *testing.B) {
386				b.StopTimer()
387				var z nat
388				z = z.expWW(x, y)
389				z.utoa(base) // warm divisor cache
390				b.StartTimer()
391
392				for i := 0; i < b.N; i++ {
393					_ = z.utoa(base)
394				}
395			})
396		}
397	}
398}
399
400func BenchmarkLeafSize(b *testing.B) {
401	for n := 0; n <= 16; n++ {
402		b.Run(fmt.Sprint(n), func(b *testing.B) { LeafSizeHelper(b, 10, n) })
403	}
404	// Try some large lengths
405	for _, n := range []int{32, 64} {
406		b.Run(fmt.Sprint(n), func(b *testing.B) { LeafSizeHelper(b, 10, n) })
407	}
408}
409
410func LeafSizeHelper(b *testing.B, base, size int) {
411	b.StopTimer()
412	originalLeafSize := leafSize
413	resetTable(cacheBase10.table[:])
414	leafSize = size
415	b.StartTimer()
416
417	for d := 1; d <= 10000; d *= 10 {
418		b.StopTimer()
419		var z nat
420		z = z.expWW(Word(base), Word(d)) // build target number
421		_ = z.utoa(base)                 // warm divisor cache
422		b.StartTimer()
423
424		for i := 0; i < b.N; i++ {
425			_ = z.utoa(base)
426		}
427	}
428
429	b.StopTimer()
430	resetTable(cacheBase10.table[:])
431	leafSize = originalLeafSize
432	b.StartTimer()
433}
434
435func resetTable(table []divisor) {
436	if table != nil && table[0].bbb != nil {
437		for i := 0; i < len(table); i++ {
438			table[i].bbb = nil
439			table[i].nbits = 0
440			table[i].ndigits = 0
441		}
442	}
443}
444
445func TestStringPowers(t *testing.T) {
446	var p Word
447	for b := 2; b <= 16; b++ {
448		for p = 0; p <= 512; p++ {
449			if testing.Short() && p > 10 {
450				break
451			}
452			x := nat(nil).expWW(Word(b), p)
453			xs := x.utoa(b)
454			xs2 := itoa(x, b)
455			if !bytes.Equal(xs, xs2) {
456				t.Errorf("failed at %d ** %d in base %d: %s != %s", b, p, b, xs, xs2)
457			}
458		}
459		if b >= 3 && testing.Short() {
460			break
461		}
462	}
463}
464