1// Copyright 2009 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	"encoding/hex"
10	"fmt"
11	"math/rand"
12	"strconv"
13	"strings"
14	"testing"
15	"testing/quick"
16)
17
18func isNormalized(x *Int) bool {
19	if len(x.abs) == 0 {
20		return !x.neg
21	}
22	// len(x.abs) > 0
23	return x.abs[len(x.abs)-1] != 0
24}
25
26type funZZ func(z, x, y *Int) *Int
27type argZZ struct {
28	z, x, y *Int
29}
30
31var sumZZ = []argZZ{
32	{NewInt(0), NewInt(0), NewInt(0)},
33	{NewInt(1), NewInt(1), NewInt(0)},
34	{NewInt(1111111110), NewInt(123456789), NewInt(987654321)},
35	{NewInt(-1), NewInt(-1), NewInt(0)},
36	{NewInt(864197532), NewInt(-123456789), NewInt(987654321)},
37	{NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)},
38}
39
40var prodZZ = []argZZ{
41	{NewInt(0), NewInt(0), NewInt(0)},
42	{NewInt(0), NewInt(1), NewInt(0)},
43	{NewInt(1), NewInt(1), NewInt(1)},
44	{NewInt(-991 * 991), NewInt(991), NewInt(-991)},
45	// TODO(gri) add larger products
46}
47
48func TestSignZ(t *testing.T) {
49	var zero Int
50	for _, a := range sumZZ {
51		s := a.z.Sign()
52		e := a.z.Cmp(&zero)
53		if s != e {
54			t.Errorf("got %d; want %d for z = %v", s, e, a.z)
55		}
56	}
57}
58
59func TestSetZ(t *testing.T) {
60	for _, a := range sumZZ {
61		var z Int
62		z.Set(a.z)
63		if !isNormalized(&z) {
64			t.Errorf("%v is not normalized", z)
65		}
66		if (&z).Cmp(a.z) != 0 {
67			t.Errorf("got z = %v; want %v", z, a.z)
68		}
69	}
70}
71
72func TestAbsZ(t *testing.T) {
73	var zero Int
74	for _, a := range sumZZ {
75		var z Int
76		z.Abs(a.z)
77		var e Int
78		e.Set(a.z)
79		if e.Cmp(&zero) < 0 {
80			e.Sub(&zero, &e)
81		}
82		if z.Cmp(&e) != 0 {
83			t.Errorf("got z = %v; want %v", z, e)
84		}
85	}
86}
87
88func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) {
89	var z Int
90	f(&z, a.x, a.y)
91	if !isNormalized(&z) {
92		t.Errorf("%s%v is not normalized", msg, z)
93	}
94	if (&z).Cmp(a.z) != 0 {
95		t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z)
96	}
97}
98
99func TestSumZZ(t *testing.T) {
100	AddZZ := func(z, x, y *Int) *Int { return z.Add(x, y) }
101	SubZZ := func(z, x, y *Int) *Int { return z.Sub(x, y) }
102	for _, a := range sumZZ {
103		arg := a
104		testFunZZ(t, "AddZZ", AddZZ, arg)
105
106		arg = argZZ{a.z, a.y, a.x}
107		testFunZZ(t, "AddZZ symmetric", AddZZ, arg)
108
109		arg = argZZ{a.x, a.z, a.y}
110		testFunZZ(t, "SubZZ", SubZZ, arg)
111
112		arg = argZZ{a.y, a.z, a.x}
113		testFunZZ(t, "SubZZ symmetric", SubZZ, arg)
114	}
115}
116
117func TestProdZZ(t *testing.T) {
118	MulZZ := func(z, x, y *Int) *Int { return z.Mul(x, y) }
119	for _, a := range prodZZ {
120		arg := a
121		testFunZZ(t, "MulZZ", MulZZ, arg)
122
123		arg = argZZ{a.z, a.y, a.x}
124		testFunZZ(t, "MulZZ symmetric", MulZZ, arg)
125	}
126}
127
128// mulBytes returns x*y via grade school multiplication. Both inputs
129// and the result are assumed to be in big-endian representation (to
130// match the semantics of Int.Bytes and Int.SetBytes).
131func mulBytes(x, y []byte) []byte {
132	z := make([]byte, len(x)+len(y))
133
134	// multiply
135	k0 := len(z) - 1
136	for j := len(y) - 1; j >= 0; j-- {
137		d := int(y[j])
138		if d != 0 {
139			k := k0
140			carry := 0
141			for i := len(x) - 1; i >= 0; i-- {
142				t := int(z[k]) + int(x[i])*d + carry
143				z[k], carry = byte(t), t>>8
144				k--
145			}
146			z[k] = byte(carry)
147		}
148		k0--
149	}
150
151	// normalize (remove leading 0's)
152	i := 0
153	for i < len(z) && z[i] == 0 {
154		i++
155	}
156
157	return z[i:]
158}
159
160func checkMul(a, b []byte) bool {
161	var x, y, z1 Int
162	x.SetBytes(a)
163	y.SetBytes(b)
164	z1.Mul(&x, &y)
165
166	var z2 Int
167	z2.SetBytes(mulBytes(a, b))
168
169	return z1.Cmp(&z2) == 0
170}
171
172func TestMul(t *testing.T) {
173	if err := quick.Check(checkMul, nil); err != nil {
174		t.Error(err)
175	}
176}
177
178var mulRangesZ = []struct {
179	a, b int64
180	prod string
181}{
182	// entirely positive ranges are covered by mulRangesN
183	{-1, 1, "0"},
184	{-2, -1, "2"},
185	{-3, -2, "6"},
186	{-3, -1, "-6"},
187	{1, 3, "6"},
188	{-10, -10, "-10"},
189	{0, -1, "1"},                      // empty range
190	{-1, -100, "1"},                   // empty range
191	{-1, 1, "0"},                      // range includes 0
192	{-1e9, 0, "0"},                    // range includes 0
193	{-1e9, 1e9, "0"},                  // range includes 0
194	{-10, -1, "3628800"},              // 10!
195	{-20, -2, "-2432902008176640000"}, // -20!
196	{-99, -1,
197		"-933262154439441526816992388562667004907159682643816214685929" +
198			"638952175999932299156089414639761565182862536979208272237582" +
199			"511852109168640000000000000000000000", // -99!
200	},
201}
202
203func TestMulRangeZ(t *testing.T) {
204	var tmp Int
205	// test entirely positive ranges
206	for i, r := range mulRangesN {
207		prod := tmp.MulRange(int64(r.a), int64(r.b)).String()
208		if prod != r.prod {
209			t.Errorf("#%da: got %s; want %s", i, prod, r.prod)
210		}
211	}
212	// test other ranges
213	for i, r := range mulRangesZ {
214		prod := tmp.MulRange(r.a, r.b).String()
215		if prod != r.prod {
216			t.Errorf("#%db: got %s; want %s", i, prod, r.prod)
217		}
218	}
219}
220
221func TestBinomial(t *testing.T) {
222	var z Int
223	for _, test := range []struct {
224		n, k int64
225		want string
226	}{
227		{0, 0, "1"},
228		{0, 1, "0"},
229		{1, 0, "1"},
230		{1, 1, "1"},
231		{1, 10, "0"},
232		{4, 0, "1"},
233		{4, 1, "4"},
234		{4, 2, "6"},
235		{4, 3, "4"},
236		{4, 4, "1"},
237		{10, 1, "10"},
238		{10, 9, "10"},
239		{10, 5, "252"},
240		{11, 5, "462"},
241		{11, 6, "462"},
242		{100, 10, "17310309456440"},
243		{100, 90, "17310309456440"},
244		{1000, 10, "263409560461970212832400"},
245		{1000, 990, "263409560461970212832400"},
246	} {
247		if got := z.Binomial(test.n, test.k).String(); got != test.want {
248			t.Errorf("Binomial(%d, %d) = %s; want %s", test.n, test.k, got, test.want)
249		}
250	}
251}
252
253func BenchmarkBinomial(b *testing.B) {
254	var z Int
255	for i := b.N - 1; i >= 0; i-- {
256		z.Binomial(1000, 990)
257	}
258}
259
260// Examples from the Go Language Spec, section "Arithmetic operators"
261var divisionSignsTests = []struct {
262	x, y int64
263	q, r int64 // T-division
264	d, m int64 // Euclidean division
265}{
266	{5, 3, 1, 2, 1, 2},
267	{-5, 3, -1, -2, -2, 1},
268	{5, -3, -1, 2, -1, 2},
269	{-5, -3, 1, -2, 2, 1},
270	{1, 2, 0, 1, 0, 1},
271	{8, 4, 2, 0, 2, 0},
272}
273
274func TestDivisionSigns(t *testing.T) {
275	for i, test := range divisionSignsTests {
276		x := NewInt(test.x)
277		y := NewInt(test.y)
278		q := NewInt(test.q)
279		r := NewInt(test.r)
280		d := NewInt(test.d)
281		m := NewInt(test.m)
282
283		q1 := new(Int).Quo(x, y)
284		r1 := new(Int).Rem(x, y)
285		if !isNormalized(q1) {
286			t.Errorf("#%d Quo: %v is not normalized", i, *q1)
287		}
288		if !isNormalized(r1) {
289			t.Errorf("#%d Rem: %v is not normalized", i, *r1)
290		}
291		if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 {
292			t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r)
293		}
294
295		q2, r2 := new(Int).QuoRem(x, y, new(Int))
296		if !isNormalized(q2) {
297			t.Errorf("#%d Quo: %v is not normalized", i, *q2)
298		}
299		if !isNormalized(r2) {
300			t.Errorf("#%d Rem: %v is not normalized", i, *r2)
301		}
302		if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 {
303			t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r)
304		}
305
306		d1 := new(Int).Div(x, y)
307		m1 := new(Int).Mod(x, y)
308		if !isNormalized(d1) {
309			t.Errorf("#%d Div: %v is not normalized", i, *d1)
310		}
311		if !isNormalized(m1) {
312			t.Errorf("#%d Mod: %v is not normalized", i, *m1)
313		}
314		if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 {
315			t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m)
316		}
317
318		d2, m2 := new(Int).DivMod(x, y, new(Int))
319		if !isNormalized(d2) {
320			t.Errorf("#%d Div: %v is not normalized", i, *d2)
321		}
322		if !isNormalized(m2) {
323			t.Errorf("#%d Mod: %v is not normalized", i, *m2)
324		}
325		if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 {
326			t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m)
327		}
328	}
329}
330
331func norm(x nat) nat {
332	i := len(x)
333	for i > 0 && x[i-1] == 0 {
334		i--
335	}
336	return x[:i]
337}
338
339func TestBits(t *testing.T) {
340	for _, test := range []nat{
341		nil,
342		{0},
343		{1},
344		{0, 1, 2, 3, 4},
345		{4, 3, 2, 1, 0},
346		{4, 3, 2, 1, 0, 0, 0, 0},
347	} {
348		var z Int
349		z.neg = true
350		got := z.SetBits(test)
351		want := norm(test)
352		if got.abs.cmp(want) != 0 {
353			t.Errorf("SetBits(%v) = %v; want %v", test, got.abs, want)
354		}
355
356		if got.neg {
357			t.Errorf("SetBits(%v): got negative result", test)
358		}
359
360		bits := nat(z.Bits())
361		if bits.cmp(want) != 0 {
362			t.Errorf("%v.Bits() = %v; want %v", z.abs, bits, want)
363		}
364	}
365}
366
367func checkSetBytes(b []byte) bool {
368	hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes())
369	hex2 := hex.EncodeToString(b)
370
371	for len(hex1) < len(hex2) {
372		hex1 = "0" + hex1
373	}
374
375	for len(hex1) > len(hex2) {
376		hex2 = "0" + hex2
377	}
378
379	return hex1 == hex2
380}
381
382func TestSetBytes(t *testing.T) {
383	if err := quick.Check(checkSetBytes, nil); err != nil {
384		t.Error(err)
385	}
386}
387
388func checkBytes(b []byte) bool {
389	// trim leading zero bytes since Bytes() won't return them
390	// (was issue 12231)
391	for len(b) > 0 && b[0] == 0 {
392		b = b[1:]
393	}
394	b2 := new(Int).SetBytes(b).Bytes()
395	return bytes.Equal(b, b2)
396}
397
398func TestBytes(t *testing.T) {
399	if err := quick.Check(checkBytes, nil); err != nil {
400		t.Error(err)
401	}
402}
403
404func checkQuo(x, y []byte) bool {
405	u := new(Int).SetBytes(x)
406	v := new(Int).SetBytes(y)
407
408	if len(v.abs) == 0 {
409		return true
410	}
411
412	r := new(Int)
413	q, r := new(Int).QuoRem(u, v, r)
414
415	if r.Cmp(v) >= 0 {
416		return false
417	}
418
419	uprime := new(Int).Set(q)
420	uprime.Mul(uprime, v)
421	uprime.Add(uprime, r)
422
423	return uprime.Cmp(u) == 0
424}
425
426var quoTests = []struct {
427	x, y string
428	q, r string
429}{
430	{
431		"476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
432		"9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
433		"50911",
434		"1",
435	},
436	{
437		"11510768301994997771168",
438		"1328165573307167369775",
439		"8",
440		"885443715537658812968",
441	},
442}
443
444func TestQuo(t *testing.T) {
445	if err := quick.Check(checkQuo, nil); err != nil {
446		t.Error(err)
447	}
448
449	for i, test := range quoTests {
450		x, _ := new(Int).SetString(test.x, 10)
451		y, _ := new(Int).SetString(test.y, 10)
452		expectedQ, _ := new(Int).SetString(test.q, 10)
453		expectedR, _ := new(Int).SetString(test.r, 10)
454
455		r := new(Int)
456		q, r := new(Int).QuoRem(x, y, r)
457
458		if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
459			t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
460		}
461	}
462}
463
464func TestQuoStepD6(t *testing.T) {
465	// See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises
466	// a code path which only triggers 1 in 10^{-19} cases.
467
468	u := &Int{false, nat{0, 0, 1 + 1<<(_W-1), _M ^ (1 << (_W - 1))}}
469	v := &Int{false, nat{5, 2 + 1<<(_W-1), 1 << (_W - 1)}}
470
471	r := new(Int)
472	q, r := new(Int).QuoRem(u, v, r)
473	const expectedQ64 = "18446744073709551613"
474	const expectedR64 = "3138550867693340382088035895064302439801311770021610913807"
475	const expectedQ32 = "4294967293"
476	const expectedR32 = "39614081266355540837921718287"
477	if q.String() != expectedQ64 && q.String() != expectedQ32 ||
478		r.String() != expectedR64 && r.String() != expectedR32 {
479		t.Errorf("got (%s, %s) want (%s, %s) or (%s, %s)", q, r, expectedQ64, expectedR64, expectedQ32, expectedR32)
480	}
481}
482
483func BenchmarkQuoRem(b *testing.B) {
484	x, _ := new(Int).SetString("153980389784927331788354528594524332344709972855165340650588877572729725338415474372475094155672066328274535240275856844648695200875763869073572078279316458648124537905600131008790701752441155668003033945258023841165089852359980273279085783159654751552359397986180318708491098942831252291841441726305535546071", 0)
485	y, _ := new(Int).SetString("7746362281539803897849273317883545285945243323447099728551653406505888775727297253384154743724750941556720663282745352402758568446486952008757638690735720782793164586481245379056001310087907017524411556680030339452580238411650898523599802732790857831596547515523593979861803187084910989428312522918414417263055355460715745539358014631136245887418412633787074173796862711588221766398229333338511838891484974940633857861775630560092874987828057333663969469797013996401149696897591265769095952887917296740109742927689053276850469671231961384715398038978492733178835452859452433234470997285516534065058887757272972533841547437247509415567206632827453524027585684464869520087576386907357207827931645864812453790560013100879070175244115566800303394525802384116508985235998027327908578315965475155235939798618031870849109894283125229184144172630553554607112725169432413343763989564437170644270643461665184965150423819594083121075825", 0)
486	q := new(Int)
487	r := new(Int)
488
489	b.ResetTimer()
490	for i := 0; i < b.N; i++ {
491		q.QuoRem(y, x, r)
492	}
493}
494
495var bitLenTests = []struct {
496	in  string
497	out int
498}{
499	{"-1", 1},
500	{"0", 0},
501	{"1", 1},
502	{"2", 2},
503	{"4", 3},
504	{"0xabc", 12},
505	{"0x8000", 16},
506	{"0x80000000", 32},
507	{"0x800000000000", 48},
508	{"0x8000000000000000", 64},
509	{"0x80000000000000000000", 80},
510	{"-0x4000000000000000000000", 87},
511}
512
513func TestBitLen(t *testing.T) {
514	for i, test := range bitLenTests {
515		x, ok := new(Int).SetString(test.in, 0)
516		if !ok {
517			t.Errorf("#%d test input invalid: %s", i, test.in)
518			continue
519		}
520
521		if n := x.BitLen(); n != test.out {
522			t.Errorf("#%d got %d want %d", i, n, test.out)
523		}
524	}
525}
526
527var expTests = []struct {
528	x, y, m string
529	out     string
530}{
531	// y <= 0
532	{"0", "0", "", "1"},
533	{"1", "0", "", "1"},
534	{"-10", "0", "", "1"},
535	{"1234", "-1", "", "1"},
536
537	// m == 1
538	{"0", "0", "1", "0"},
539	{"1", "0", "1", "0"},
540	{"-10", "0", "1", "0"},
541	{"1234", "-1", "1", "0"},
542
543	// misc
544	{"5", "1", "3", "2"},
545	{"5", "-7", "", "1"},
546	{"-5", "-7", "", "1"},
547	{"5", "0", "", "1"},
548	{"-5", "0", "", "1"},
549	{"5", "1", "", "5"},
550	{"-5", "1", "", "-5"},
551	{"-5", "1", "7", "2"},
552	{"-2", "3", "2", "0"},
553	{"5", "2", "", "25"},
554	{"1", "65537", "2", "1"},
555	{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
556	{"0x8000000000000000", "2", "6719", "4944"},
557	{"0x8000000000000000", "3", "6719", "5447"},
558	{"0x8000000000000000", "1000", "6719", "1603"},
559	{"0x8000000000000000", "1000000", "6719", "3199"},
560	{"0x8000000000000000", "-1000000", "6719", "1"},
561
562	{"0xffffffffffffffffffffffffffffffff", "0x12345678123456781234567812345678123456789", "0x01112222333344445555666677778889", "0x36168FA1DB3AAE6C8CE647E137F97A"},
563
564	{
565		"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
566		"298472983472983471903246121093472394872319615612417471234712061",
567		"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
568		"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
569	},
570	// test case for issue 8822
571	{
572		"11001289118363089646017359372117963499250546375269047542777928006103246876688756735760905680604646624353196869572752623285140408755420374049317646428185270079555372763503115646054602867593662923894140940837479507194934267532831694565516466765025434902348314525627418515646588160955862839022051353653052947073136084780742729727874803457643848197499548297570026926927502505634297079527299004267769780768565695459945235586892627059178884998772989397505061206395455591503771677500931269477503508150175717121828518985901959919560700853226255420793148986854391552859459511723547532575574664944815966793196961286234040892865",
573		"0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
574		"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
575		"21484252197776302499639938883777710321993113097987201050501182909581359357618579566746556372589385361683610524730509041328855066514963385522570894839035884713051640171474186548713546686476761306436434146475140156284389181808675016576845833340494848283681088886584219750554408060556769486628029028720727393293111678826356480455433909233520504112074401376133077150471237549474149190242010469539006449596611576612573955754349042329130631128234637924786466585703488460540228477440853493392086251021228087076124706778899179648655221663765993962724699135217212118535057766739392069738618682722216712319320435674779146070442",
576	},
577	{
578		"-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
579		"0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
580		"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
581		"21484252197776302499639938883777710321993113097987201050501182909581359357618579566746556372589385361683610524730509041328855066514963385522570894839035884713051640171474186548713546686476761306436434146475140156284389181808675016576845833340494848283681088886584219750554408060556769486628029028720727393293111678826356480455433909233520504112074401376133077150471237549474149190242010469539006449596611576612573955754349042329130631128234637924786466585703488460540228477440853493392086251021228087076124706778899179648655221663765993962724699135217212118535057766739392069738618682722216712319320435674779146070442",
582	},
583
584	// test cases for issue 13907
585	{"0xffffffff00000001", "0xffffffff00000001", "0xffffffff00000001", "0"},
586	{"0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0"},
587	{"0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0"},
588	{"0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0"},
589
590	{
591		"2",
592		"0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
593		"0xAC6BDB41324A9A9BF166DE5E1389582FAF72B6651987EE07FC3192943DB56050A37329CBB4A099ED8193E0757767A13DD52312AB4B03310DCD7F48A9DA04FD50E8083969EDB767B0CF6095179A163AB3661A05FBD5FAAAE82918A9962F0B93B855F97993EC975EEAA80D740ADBF4FF747359D041D5C33EA71D281E446B14773BCA97B43A23FB801676BD207A436C6481F1D2B9078717461A5B9D32E688F87748544523B524B0D57D5EA77A2775D2ECFA032CFBDBF52FB3786160279004E57AE6AF874E7303CE53299CCC041C7BC308D82A5698F3A8D0C38271AE35F8E9DBFBB694B5C803D89F7AE435DE236D525F54759B65E372FCD68EF20FA7111F9E4AFF73", // odd
594		"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
595	},
596	{
597		"2",
598		"0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
599		"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even
600		"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
601	},
602}
603
604func TestExp(t *testing.T) {
605	for i, test := range expTests {
606		x, ok1 := new(Int).SetString(test.x, 0)
607		y, ok2 := new(Int).SetString(test.y, 0)
608		out, ok3 := new(Int).SetString(test.out, 0)
609
610		var ok4 bool
611		var m *Int
612
613		if len(test.m) == 0 {
614			m, ok4 = nil, true
615		} else {
616			m, ok4 = new(Int).SetString(test.m, 0)
617		}
618
619		if !ok1 || !ok2 || !ok3 || !ok4 {
620			t.Errorf("#%d: error in input", i)
621			continue
622		}
623
624		z1 := new(Int).Exp(x, y, m)
625		if !isNormalized(z1) {
626			t.Errorf("#%d: %v is not normalized", i, *z1)
627		}
628		if z1.Cmp(out) != 0 {
629			t.Errorf("#%d: got %x want %x", i, z1, out)
630		}
631
632		if m == nil {
633			// The result should be the same as for m == 0;
634			// specifically, there should be no div-zero panic.
635			m = &Int{abs: nat{}} // m != nil && len(m.abs) == 0
636			z2 := new(Int).Exp(x, y, m)
637			if z2.Cmp(z1) != 0 {
638				t.Errorf("#%d: got %x want %x", i, z2, z1)
639			}
640		}
641	}
642}
643
644func BenchmarkExp(b *testing.B) {
645	x, _ := new(Int).SetString("11001289118363089646017359372117963499250546375269047542777928006103246876688756735760905680604646624353196869572752623285140408755420374049317646428185270079555372763503115646054602867593662923894140940837479507194934267532831694565516466765025434902348314525627418515646588160955862839022051353653052947073136084780742729727874803457643848197499548297570026926927502505634297079527299004267769780768565695459945235586892627059178884998772989397505061206395455591503771677500931269477503508150175717121828518985901959919560700853226255420793148986854391552859459511723547532575574664944815966793196961286234040892865", 0)
646	y, _ := new(Int).SetString("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
647	n, _ := new(Int).SetString("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
648	out := new(Int)
649	for i := 0; i < b.N; i++ {
650		out.Exp(x, y, n)
651	}
652}
653
654func BenchmarkExp2(b *testing.B) {
655	x, _ := new(Int).SetString("2", 0)
656	y, _ := new(Int).SetString("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
657	n, _ := new(Int).SetString("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
658	out := new(Int)
659	for i := 0; i < b.N; i++ {
660		out.Exp(x, y, n)
661	}
662}
663
664func checkGcd(aBytes, bBytes []byte) bool {
665	x := new(Int)
666	y := new(Int)
667	a := new(Int).SetBytes(aBytes)
668	b := new(Int).SetBytes(bBytes)
669
670	d := new(Int).GCD(x, y, a, b)
671	x.Mul(x, a)
672	y.Mul(y, b)
673	x.Add(x, y)
674
675	return x.Cmp(d) == 0
676}
677
678// euclidGCD is a reference implementation of Euclid's GCD
679// algorithm for testing against optimized algorithms.
680// Requirements: a, b > 0
681func euclidGCD(a, b *Int) *Int {
682
683	A := new(Int).Set(a)
684	B := new(Int).Set(b)
685	t := new(Int)
686
687	for len(B.abs) > 0 {
688		// A, B = B, A % B
689		t.Rem(A, B)
690		A, B, t = B, t, A
691	}
692	return A
693}
694
695func checkLehmerGcd(aBytes, bBytes []byte) bool {
696	a := new(Int).SetBytes(aBytes)
697	b := new(Int).SetBytes(bBytes)
698
699	if a.Sign() <= 0 || b.Sign() <= 0 {
700		return true // can only test positive arguments
701	}
702
703	d := new(Int).lehmerGCD(a, b)
704	d0 := euclidGCD(a, b)
705
706	return d.Cmp(d0) == 0
707}
708
709var gcdTests = []struct {
710	d, x, y, a, b string
711}{
712	// a <= 0 || b <= 0
713	{"0", "0", "0", "0", "0"},
714	{"0", "0", "0", "0", "7"},
715	{"0", "0", "0", "11", "0"},
716	{"0", "0", "0", "-77", "35"},
717	{"0", "0", "0", "64515", "-24310"},
718	{"0", "0", "0", "-64515", "-24310"},
719
720	{"1", "-9", "47", "120", "23"},
721	{"7", "1", "-2", "77", "35"},
722	{"935", "-3", "8", "64515", "24310"},
723	{"935000000000000000", "-3", "8", "64515000000000000000", "24310000000000000000"},
724	{"1", "-221", "22059940471369027483332068679400581064239780177629666810348940098015901108344", "98920366548084643601728869055592650835572950932266967461790948584315647051443", "991"},
725
726	// test early exit (after one Euclidean iteration) in binaryGCD
727	{"1", "", "", "1", "98920366548084643601728869055592650835572950932266967461790948584315647051443"},
728}
729
730func testGcd(t *testing.T, d, x, y, a, b *Int) {
731	var X *Int
732	if x != nil {
733		X = new(Int)
734	}
735	var Y *Int
736	if y != nil {
737		Y = new(Int)
738	}
739
740	D := new(Int).GCD(X, Y, a, b)
741	if D.Cmp(d) != 0 {
742		t.Errorf("GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, D, d)
743	}
744	if x != nil && X.Cmp(x) != 0 {
745		t.Errorf("GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, X, x)
746	}
747	if y != nil && Y.Cmp(y) != 0 {
748		t.Errorf("GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, Y, y)
749	}
750
751	// check results in presence of aliasing (issue #11284)
752	a2 := new(Int).Set(a)
753	b2 := new(Int).Set(b)
754	a2.GCD(X, Y, a2, b2) // result is same as 1st argument
755	if a2.Cmp(d) != 0 {
756		t.Errorf("aliased z = a GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, a2, d)
757	}
758
759	a2 = new(Int).Set(a)
760	b2 = new(Int).Set(b)
761	b2.GCD(X, Y, a2, b2) // result is same as 2nd argument
762	if b2.Cmp(d) != 0 {
763		t.Errorf("aliased z = b GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, b2, d)
764	}
765}
766
767func TestGcd(t *testing.T) {
768	for _, test := range gcdTests {
769		d, _ := new(Int).SetString(test.d, 0)
770		x, _ := new(Int).SetString(test.x, 0)
771		y, _ := new(Int).SetString(test.y, 0)
772		a, _ := new(Int).SetString(test.a, 0)
773		b, _ := new(Int).SetString(test.b, 0)
774
775		testGcd(t, d, nil, nil, a, b)
776		testGcd(t, d, x, nil, a, b)
777		testGcd(t, d, nil, y, a, b)
778		testGcd(t, d, x, y, a, b)
779	}
780
781	if err := quick.Check(checkGcd, nil); err != nil {
782		t.Error(err)
783	}
784
785	if err := quick.Check(checkLehmerGcd, nil); err != nil {
786		t.Error(err)
787	}
788}
789
790type intShiftTest struct {
791	in    string
792	shift uint
793	out   string
794}
795
796var rshTests = []intShiftTest{
797	{"0", 0, "0"},
798	{"-0", 0, "0"},
799	{"0", 1, "0"},
800	{"0", 2, "0"},
801	{"1", 0, "1"},
802	{"1", 1, "0"},
803	{"1", 2, "0"},
804	{"2", 0, "2"},
805	{"2", 1, "1"},
806	{"-1", 0, "-1"},
807	{"-1", 1, "-1"},
808	{"-1", 10, "-1"},
809	{"-100", 2, "-25"},
810	{"-100", 3, "-13"},
811	{"-100", 100, "-1"},
812	{"4294967296", 0, "4294967296"},
813	{"4294967296", 1, "2147483648"},
814	{"4294967296", 2, "1073741824"},
815	{"18446744073709551616", 0, "18446744073709551616"},
816	{"18446744073709551616", 1, "9223372036854775808"},
817	{"18446744073709551616", 2, "4611686018427387904"},
818	{"18446744073709551616", 64, "1"},
819	{"340282366920938463463374607431768211456", 64, "18446744073709551616"},
820	{"340282366920938463463374607431768211456", 128, "1"},
821}
822
823func TestRsh(t *testing.T) {
824	for i, test := range rshTests {
825		in, _ := new(Int).SetString(test.in, 10)
826		expected, _ := new(Int).SetString(test.out, 10)
827		out := new(Int).Rsh(in, test.shift)
828
829		if !isNormalized(out) {
830			t.Errorf("#%d: %v is not normalized", i, *out)
831		}
832		if out.Cmp(expected) != 0 {
833			t.Errorf("#%d: got %s want %s", i, out, expected)
834		}
835	}
836}
837
838func TestRshSelf(t *testing.T) {
839	for i, test := range rshTests {
840		z, _ := new(Int).SetString(test.in, 10)
841		expected, _ := new(Int).SetString(test.out, 10)
842		z.Rsh(z, test.shift)
843
844		if !isNormalized(z) {
845			t.Errorf("#%d: %v is not normalized", i, *z)
846		}
847		if z.Cmp(expected) != 0 {
848			t.Errorf("#%d: got %s want %s", i, z, expected)
849		}
850	}
851}
852
853var lshTests = []intShiftTest{
854	{"0", 0, "0"},
855	{"0", 1, "0"},
856	{"0", 2, "0"},
857	{"1", 0, "1"},
858	{"1", 1, "2"},
859	{"1", 2, "4"},
860	{"2", 0, "2"},
861	{"2", 1, "4"},
862	{"2", 2, "8"},
863	{"-87", 1, "-174"},
864	{"4294967296", 0, "4294967296"},
865	{"4294967296", 1, "8589934592"},
866	{"4294967296", 2, "17179869184"},
867	{"18446744073709551616", 0, "18446744073709551616"},
868	{"9223372036854775808", 1, "18446744073709551616"},
869	{"4611686018427387904", 2, "18446744073709551616"},
870	{"1", 64, "18446744073709551616"},
871	{"18446744073709551616", 64, "340282366920938463463374607431768211456"},
872	{"1", 128, "340282366920938463463374607431768211456"},
873}
874
875func TestLsh(t *testing.T) {
876	for i, test := range lshTests {
877		in, _ := new(Int).SetString(test.in, 10)
878		expected, _ := new(Int).SetString(test.out, 10)
879		out := new(Int).Lsh(in, test.shift)
880
881		if !isNormalized(out) {
882			t.Errorf("#%d: %v is not normalized", i, *out)
883		}
884		if out.Cmp(expected) != 0 {
885			t.Errorf("#%d: got %s want %s", i, out, expected)
886		}
887	}
888}
889
890func TestLshSelf(t *testing.T) {
891	for i, test := range lshTests {
892		z, _ := new(Int).SetString(test.in, 10)
893		expected, _ := new(Int).SetString(test.out, 10)
894		z.Lsh(z, test.shift)
895
896		if !isNormalized(z) {
897			t.Errorf("#%d: %v is not normalized", i, *z)
898		}
899		if z.Cmp(expected) != 0 {
900			t.Errorf("#%d: got %s want %s", i, z, expected)
901		}
902	}
903}
904
905func TestLshRsh(t *testing.T) {
906	for i, test := range rshTests {
907		in, _ := new(Int).SetString(test.in, 10)
908		out := new(Int).Lsh(in, test.shift)
909		out = out.Rsh(out, test.shift)
910
911		if !isNormalized(out) {
912			t.Errorf("#%d: %v is not normalized", i, *out)
913		}
914		if in.Cmp(out) != 0 {
915			t.Errorf("#%d: got %s want %s", i, out, in)
916		}
917	}
918	for i, test := range lshTests {
919		in, _ := new(Int).SetString(test.in, 10)
920		out := new(Int).Lsh(in, test.shift)
921		out.Rsh(out, test.shift)
922
923		if !isNormalized(out) {
924			t.Errorf("#%d: %v is not normalized", i, *out)
925		}
926		if in.Cmp(out) != 0 {
927			t.Errorf("#%d: got %s want %s", i, out, in)
928		}
929	}
930}
931
932// Entries must be sorted by value in ascending order.
933var cmpAbsTests = []string{
934	"0",
935	"1",
936	"2",
937	"10",
938	"10000000",
939	"2783678367462374683678456387645876387564783686583485",
940	"2783678367462374683678456387645876387564783686583486",
941	"32957394867987420967976567076075976570670947609750670956097509670576075067076027578341538",
942}
943
944func TestCmpAbs(t *testing.T) {
945	values := make([]*Int, len(cmpAbsTests))
946	var prev *Int
947	for i, s := range cmpAbsTests {
948		x, ok := new(Int).SetString(s, 0)
949		if !ok {
950			t.Fatalf("SetString(%s, 0) failed", s)
951		}
952		if prev != nil && prev.Cmp(x) >= 0 {
953			t.Fatal("cmpAbsTests entries not sorted in ascending order")
954		}
955		values[i] = x
956		prev = x
957	}
958
959	for i, x := range values {
960		for j, y := range values {
961			// try all combinations of signs for x, y
962			for k := 0; k < 4; k++ {
963				var a, b Int
964				a.Set(x)
965				b.Set(y)
966				if k&1 != 0 {
967					a.Neg(&a)
968				}
969				if k&2 != 0 {
970					b.Neg(&b)
971				}
972
973				got := a.CmpAbs(&b)
974				want := 0
975				switch {
976				case i > j:
977					want = 1
978				case i < j:
979					want = -1
980				}
981				if got != want {
982					t.Errorf("absCmp |%s|, |%s|: got %d; want %d", &a, &b, got, want)
983				}
984			}
985		}
986	}
987}
988
989var int64Tests = []string{
990	// int64
991	"0",
992	"1",
993	"-1",
994	"4294967295",
995	"-4294967295",
996	"4294967296",
997	"-4294967296",
998	"9223372036854775807",
999	"-9223372036854775807",
1000	"-9223372036854775808",
1001
1002	// not int64
1003	"0x8000000000000000",
1004	"-0x8000000000000001",
1005	"38579843757496759476987459679745",
1006	"-38579843757496759476987459679745",
1007}
1008
1009func TestInt64(t *testing.T) {
1010	for _, s := range int64Tests {
1011		var x Int
1012		_, ok := x.SetString(s, 0)
1013		if !ok {
1014			t.Errorf("SetString(%s, 0) failed", s)
1015			continue
1016		}
1017
1018		want, err := strconv.ParseInt(s, 0, 64)
1019		if err != nil {
1020			if err.(*strconv.NumError).Err == strconv.ErrRange {
1021				if x.IsInt64() {
1022					t.Errorf("IsInt64(%s) succeeded unexpectedly", s)
1023				}
1024			} else {
1025				t.Errorf("ParseInt(%s) failed", s)
1026			}
1027			continue
1028		}
1029
1030		if !x.IsInt64() {
1031			t.Errorf("IsInt64(%s) failed unexpectedly", s)
1032		}
1033
1034		got := x.Int64()
1035		if got != want {
1036			t.Errorf("Int64(%s) = %d; want %d", s, got, want)
1037		}
1038	}
1039}
1040
1041var uint64Tests = []string{
1042	// uint64
1043	"0",
1044	"1",
1045	"4294967295",
1046	"4294967296",
1047	"8589934591",
1048	"8589934592",
1049	"9223372036854775807",
1050	"9223372036854775808",
1051	"0x08000000000000000",
1052
1053	// not uint64
1054	"0x10000000000000000",
1055	"-0x08000000000000000",
1056	"-1",
1057}
1058
1059func TestUint64(t *testing.T) {
1060	for _, s := range uint64Tests {
1061		var x Int
1062		_, ok := x.SetString(s, 0)
1063		if !ok {
1064			t.Errorf("SetString(%s, 0) failed", s)
1065			continue
1066		}
1067
1068		want, err := strconv.ParseUint(s, 0, 64)
1069		if err != nil {
1070			// check for sign explicitly (ErrRange doesn't cover signed input)
1071			if s[0] == '-' || err.(*strconv.NumError).Err == strconv.ErrRange {
1072				if x.IsUint64() {
1073					t.Errorf("IsUint64(%s) succeeded unexpectedly", s)
1074				}
1075			} else {
1076				t.Errorf("ParseUint(%s) failed", s)
1077			}
1078			continue
1079		}
1080
1081		if !x.IsUint64() {
1082			t.Errorf("IsUint64(%s) failed unexpectedly", s)
1083		}
1084
1085		got := x.Uint64()
1086		if got != want {
1087			t.Errorf("Uint64(%s) = %d; want %d", s, got, want)
1088		}
1089	}
1090}
1091
1092var bitwiseTests = []struct {
1093	x, y                 string
1094	and, or, xor, andNot string
1095}{
1096	{"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"},
1097	{"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
1098	{"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
1099	{"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
1100	{"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"},
1101	{"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
1102	{"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
1103	{"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
1104	{"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"},
1105	{"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"},
1106	{"0xff", "-0x0a", "0xf6", "-0x01", "-0xf7", "0x09"},
1107	{"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"},
1108	{"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"},
1109	{"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"},
1110	{
1111		"0x1000009dc6e3d9822cba04129bcbe3401",
1112		"0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1113		"0x1000001186210100001000009048c2001",
1114		"0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
1115		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
1116		"0x8c40c2d8822caa04120b8321400",
1117	},
1118	{
1119		"0x1000009dc6e3d9822cba04129bcbe3401",
1120		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1121		"0x8c40c2d8822caa04120b8321401",
1122		"-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd",
1123		"-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe",
1124		"0x1000001186210100001000009048c2000",
1125	},
1126	{
1127		"-0x1000009dc6e3d9822cba04129bcbe3401",
1128		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1129		"-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
1130		"-0x1000001186210100001000009048c2001",
1131		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
1132		"0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc",
1133	},
1134}
1135
1136type bitFun func(z, x, y *Int) *Int
1137
1138func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
1139	expected := new(Int)
1140	expected.SetString(exp, 0)
1141
1142	out := f(new(Int), x, y)
1143	if out.Cmp(expected) != 0 {
1144		t.Errorf("%s: got %s want %s", msg, out, expected)
1145	}
1146}
1147
1148func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
1149	self := new(Int)
1150	self.Set(x)
1151	expected := new(Int)
1152	expected.SetString(exp, 0)
1153
1154	self = f(self, self, y)
1155	if self.Cmp(expected) != 0 {
1156		t.Errorf("%s: got %s want %s", msg, self, expected)
1157	}
1158}
1159
1160func altBit(x *Int, i int) uint {
1161	z := new(Int).Rsh(x, uint(i))
1162	z = z.And(z, NewInt(1))
1163	if z.Cmp(new(Int)) != 0 {
1164		return 1
1165	}
1166	return 0
1167}
1168
1169func altSetBit(z *Int, x *Int, i int, b uint) *Int {
1170	one := NewInt(1)
1171	m := one.Lsh(one, uint(i))
1172	switch b {
1173	case 1:
1174		return z.Or(x, m)
1175	case 0:
1176		return z.AndNot(x, m)
1177	}
1178	panic("set bit is not 0 or 1")
1179}
1180
1181func testBitset(t *testing.T, x *Int) {
1182	n := x.BitLen()
1183	z := new(Int).Set(x)
1184	z1 := new(Int).Set(x)
1185	for i := 0; i < n+10; i++ {
1186		old := z.Bit(i)
1187		old1 := altBit(z1, i)
1188		if old != old1 {
1189			t.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1, i, old, old1)
1190		}
1191		z := new(Int).SetBit(z, i, 1)
1192		z1 := altSetBit(new(Int), z1, i, 1)
1193		if z.Bit(i) == 0 {
1194			t.Errorf("bitset: bit %d of %s got 0 want 1", i, x)
1195		}
1196		if z.Cmp(z1) != 0 {
1197			t.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z, z1)
1198		}
1199		z.SetBit(z, i, 0)
1200		altSetBit(z1, z1, i, 0)
1201		if z.Bit(i) != 0 {
1202			t.Errorf("bitset: bit %d of %s got 1 want 0", i, x)
1203		}
1204		if z.Cmp(z1) != 0 {
1205			t.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z, z1)
1206		}
1207		altSetBit(z1, z1, i, old)
1208		z.SetBit(z, i, old)
1209		if z.Cmp(z1) != 0 {
1210			t.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z, z1)
1211		}
1212	}
1213	if z.Cmp(x) != 0 {
1214		t.Errorf("bitset: got %s want %s", z, x)
1215	}
1216}
1217
1218var bitsetTests = []struct {
1219	x string
1220	i int
1221	b uint
1222}{
1223	{"0", 0, 0},
1224	{"0", 200, 0},
1225	{"1", 0, 1},
1226	{"1", 1, 0},
1227	{"-1", 0, 1},
1228	{"-1", 200, 1},
1229	{"0x2000000000000000000000000000", 108, 0},
1230	{"0x2000000000000000000000000000", 109, 1},
1231	{"0x2000000000000000000000000000", 110, 0},
1232	{"-0x2000000000000000000000000001", 108, 1},
1233	{"-0x2000000000000000000000000001", 109, 0},
1234	{"-0x2000000000000000000000000001", 110, 1},
1235}
1236
1237func TestBitSet(t *testing.T) {
1238	for _, test := range bitwiseTests {
1239		x := new(Int)
1240		x.SetString(test.x, 0)
1241		testBitset(t, x)
1242		x = new(Int)
1243		x.SetString(test.y, 0)
1244		testBitset(t, x)
1245	}
1246	for i, test := range bitsetTests {
1247		x := new(Int)
1248		x.SetString(test.x, 0)
1249		b := x.Bit(test.i)
1250		if b != test.b {
1251			t.Errorf("#%d got %v want %v", i, b, test.b)
1252		}
1253	}
1254	z := NewInt(1)
1255	z.SetBit(NewInt(0), 2, 1)
1256	if z.Cmp(NewInt(4)) != 0 {
1257		t.Errorf("destination leaked into result; got %s want 4", z)
1258	}
1259}
1260
1261func BenchmarkBitset(b *testing.B) {
1262	z := new(Int)
1263	z.SetBit(z, 512, 1)
1264	b.ResetTimer()
1265	b.StartTimer()
1266	for i := b.N - 1; i >= 0; i-- {
1267		z.SetBit(z, i&512, 1)
1268	}
1269}
1270
1271func BenchmarkBitsetNeg(b *testing.B) {
1272	z := NewInt(-1)
1273	z.SetBit(z, 512, 0)
1274	b.ResetTimer()
1275	b.StartTimer()
1276	for i := b.N - 1; i >= 0; i-- {
1277		z.SetBit(z, i&512, 0)
1278	}
1279}
1280
1281func BenchmarkBitsetOrig(b *testing.B) {
1282	z := new(Int)
1283	altSetBit(z, z, 512, 1)
1284	b.ResetTimer()
1285	b.StartTimer()
1286	for i := b.N - 1; i >= 0; i-- {
1287		altSetBit(z, z, i&512, 1)
1288	}
1289}
1290
1291func BenchmarkBitsetNegOrig(b *testing.B) {
1292	z := NewInt(-1)
1293	altSetBit(z, z, 512, 0)
1294	b.ResetTimer()
1295	b.StartTimer()
1296	for i := b.N - 1; i >= 0; i-- {
1297		altSetBit(z, z, i&512, 0)
1298	}
1299}
1300
1301// tri generates the trinomial 2**(n*2) - 2**n - 1, which is always 3 mod 4 and
1302// 7 mod 8, so that 2 is always a quadratic residue.
1303func tri(n uint) *Int {
1304	x := NewInt(1)
1305	x.Lsh(x, n)
1306	x2 := new(Int).Lsh(x, n)
1307	x2.Sub(x2, x)
1308	x2.Sub(x2, intOne)
1309	return x2
1310}
1311
1312func BenchmarkModSqrt225_Tonelli(b *testing.B) {
1313	p := tri(225)
1314	x := NewInt(2)
1315	for i := 0; i < b.N; i++ {
1316		x.SetUint64(2)
1317		x.modSqrtTonelliShanks(x, p)
1318	}
1319}
1320
1321func BenchmarkModSqrt224_3Mod4(b *testing.B) {
1322	p := tri(225)
1323	x := new(Int).SetUint64(2)
1324	for i := 0; i < b.N; i++ {
1325		x.SetUint64(2)
1326		x.modSqrt3Mod4Prime(x, p)
1327	}
1328}
1329
1330func BenchmarkModSqrt5430_Tonelli(b *testing.B) {
1331	if isRaceBuilder {
1332		b.Skip("skipping on race builder")
1333	}
1334	p := tri(5430)
1335	x := new(Int).SetUint64(2)
1336	for i := 0; i < b.N; i++ {
1337		x.SetUint64(2)
1338		x.modSqrtTonelliShanks(x, p)
1339	}
1340}
1341
1342func BenchmarkModSqrt5430_3Mod4(b *testing.B) {
1343	if isRaceBuilder {
1344		b.Skip("skipping on race builder")
1345	}
1346	p := tri(5430)
1347	x := new(Int).SetUint64(2)
1348	for i := 0; i < b.N; i++ {
1349		x.SetUint64(2)
1350		x.modSqrt3Mod4Prime(x, p)
1351	}
1352}
1353
1354func TestBitwise(t *testing.T) {
1355	x := new(Int)
1356	y := new(Int)
1357	for _, test := range bitwiseTests {
1358		x.SetString(test.x, 0)
1359		y.SetString(test.y, 0)
1360
1361		testBitFun(t, "and", (*Int).And, x, y, test.and)
1362		testBitFunSelf(t, "and", (*Int).And, x, y, test.and)
1363		testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot)
1364		testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot)
1365		testBitFun(t, "or", (*Int).Or, x, y, test.or)
1366		testBitFunSelf(t, "or", (*Int).Or, x, y, test.or)
1367		testBitFun(t, "xor", (*Int).Xor, x, y, test.xor)
1368		testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor)
1369	}
1370}
1371
1372var notTests = []struct {
1373	in  string
1374	out string
1375}{
1376	{"0", "-1"},
1377	{"1", "-2"},
1378	{"7", "-8"},
1379	{"0", "-1"},
1380	{"-81910", "81909"},
1381	{
1382		"298472983472983471903246121093472394872319615612417471234712061",
1383		"-298472983472983471903246121093472394872319615612417471234712062",
1384	},
1385}
1386
1387func TestNot(t *testing.T) {
1388	in := new(Int)
1389	out := new(Int)
1390	expected := new(Int)
1391	for i, test := range notTests {
1392		in.SetString(test.in, 10)
1393		expected.SetString(test.out, 10)
1394		out = out.Not(in)
1395		if out.Cmp(expected) != 0 {
1396			t.Errorf("#%d: got %s want %s", i, out, expected)
1397		}
1398		out = out.Not(out)
1399		if out.Cmp(in) != 0 {
1400			t.Errorf("#%d: got %s want %s", i, out, in)
1401		}
1402	}
1403}
1404
1405var modInverseTests = []struct {
1406	element string
1407	modulus string
1408}{
1409	{"1234567", "458948883992"},
1410	{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
1411	{"-10", "13"}, // issue #16984
1412}
1413
1414func TestModInverse(t *testing.T) {
1415	var element, modulus, gcd, inverse Int
1416	one := NewInt(1)
1417	for i, test := range modInverseTests {
1418		(&element).SetString(test.element, 10)
1419		(&modulus).SetString(test.modulus, 10)
1420		(&inverse).ModInverse(&element, &modulus)
1421		(&inverse).Mul(&inverse, &element)
1422		(&inverse).Mod(&inverse, &modulus)
1423		if (&inverse).Cmp(one) != 0 {
1424			t.Errorf("#%d: failed (e·e^(-1)=%s)", i, &inverse)
1425		}
1426	}
1427	// exhaustive test for small values
1428	for n := 2; n < 100; n++ {
1429		(&modulus).SetInt64(int64(n))
1430		for x := 1; x < n; x++ {
1431			(&element).SetInt64(int64(x))
1432			(&gcd).GCD(nil, nil, &element, &modulus)
1433			if (&gcd).Cmp(one) != 0 {
1434				continue
1435			}
1436			(&inverse).ModInverse(&element, &modulus)
1437			(&inverse).Mul(&inverse, &element)
1438			(&inverse).Mod(&inverse, &modulus)
1439			if (&inverse).Cmp(one) != 0 {
1440				t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
1441			}
1442		}
1443	}
1444}
1445
1446// testModSqrt is a helper for TestModSqrt,
1447// which checks that ModSqrt can compute a square-root of elt^2.
1448func testModSqrt(t *testing.T, elt, mod, sq, sqrt *Int) bool {
1449	var sqChk, sqrtChk, sqrtsq Int
1450	sq.Mul(elt, elt)
1451	sq.Mod(sq, mod)
1452	z := sqrt.ModSqrt(sq, mod)
1453	if z != sqrt {
1454		t.Errorf("ModSqrt returned wrong value %s", z)
1455	}
1456
1457	// test ModSqrt arguments outside the range [0,mod)
1458	sqChk.Add(sq, mod)
1459	z = sqrtChk.ModSqrt(&sqChk, mod)
1460	if z != &sqrtChk || z.Cmp(sqrt) != 0 {
1461		t.Errorf("ModSqrt returned inconsistent value %s", z)
1462	}
1463	sqChk.Sub(sq, mod)
1464	z = sqrtChk.ModSqrt(&sqChk, mod)
1465	if z != &sqrtChk || z.Cmp(sqrt) != 0 {
1466		t.Errorf("ModSqrt returned inconsistent value %s", z)
1467	}
1468
1469	// test x aliasing z
1470	z = sqrtChk.ModSqrt(sqrtChk.Set(sq), mod)
1471	if z != &sqrtChk || z.Cmp(sqrt) != 0 {
1472		t.Errorf("ModSqrt returned inconsistent value %s", z)
1473	}
1474
1475	// make sure we actually got a square root
1476	if sqrt.Cmp(elt) == 0 {
1477		return true // we found the "desired" square root
1478	}
1479	sqrtsq.Mul(sqrt, sqrt) // make sure we found the "other" one
1480	sqrtsq.Mod(&sqrtsq, mod)
1481	return sq.Cmp(&sqrtsq) == 0
1482}
1483
1484func TestModSqrt(t *testing.T) {
1485	var elt, mod, modx4, sq, sqrt Int
1486	r := rand.New(rand.NewSource(9))
1487	for i, s := range primes[1:] { // skip 2, use only odd primes
1488		mod.SetString(s, 10)
1489		modx4.Lsh(&mod, 2)
1490
1491		// test a few random elements per prime
1492		for x := 1; x < 5; x++ {
1493			elt.Rand(r, &modx4)
1494			elt.Sub(&elt, &mod) // test range [-mod, 3*mod)
1495			if !testModSqrt(t, &elt, &mod, &sq, &sqrt) {
1496				t.Errorf("#%d: failed (sqrt(e) = %s)", i, &sqrt)
1497			}
1498		}
1499
1500		if testing.Short() && i > 2 {
1501			break
1502		}
1503	}
1504
1505	if testing.Short() {
1506		return
1507	}
1508
1509	// exhaustive test for small values
1510	for n := 3; n < 100; n++ {
1511		mod.SetInt64(int64(n))
1512		if !mod.ProbablyPrime(10) {
1513			continue
1514		}
1515		isSquare := make([]bool, n)
1516
1517		// test all the squares
1518		for x := 1; x < n; x++ {
1519			elt.SetInt64(int64(x))
1520			if !testModSqrt(t, &elt, &mod, &sq, &sqrt) {
1521				t.Errorf("#%d: failed (sqrt(%d,%d) = %s)", x, &elt, &mod, &sqrt)
1522			}
1523			isSquare[sq.Uint64()] = true
1524		}
1525
1526		// test all non-squares
1527		for x := 1; x < n; x++ {
1528			sq.SetInt64(int64(x))
1529			z := sqrt.ModSqrt(&sq, &mod)
1530			if !isSquare[x] && z != nil {
1531				t.Errorf("#%d: failed (sqrt(%d,%d) = nil)", x, &sqrt, &mod)
1532			}
1533		}
1534	}
1535}
1536
1537func TestJacobi(t *testing.T) {
1538	testCases := []struct {
1539		x, y   int64
1540		result int
1541	}{
1542		{0, 1, 1},
1543		{0, -1, 1},
1544		{1, 1, 1},
1545		{1, -1, 1},
1546		{0, 5, 0},
1547		{1, 5, 1},
1548		{2, 5, -1},
1549		{-2, 5, -1},
1550		{2, -5, -1},
1551		{-2, -5, 1},
1552		{3, 5, -1},
1553		{5, 5, 0},
1554		{-5, 5, 0},
1555		{6, 5, 1},
1556		{6, -5, 1},
1557		{-6, 5, 1},
1558		{-6, -5, -1},
1559	}
1560
1561	var x, y Int
1562
1563	for i, test := range testCases {
1564		x.SetInt64(test.x)
1565		y.SetInt64(test.y)
1566		expected := test.result
1567		actual := Jacobi(&x, &y)
1568		if actual != expected {
1569			t.Errorf("#%d: Jacobi(%d, %d) = %d, but expected %d", i, test.x, test.y, actual, expected)
1570		}
1571	}
1572}
1573
1574func TestJacobiPanic(t *testing.T) {
1575	const failureMsg = "test failure"
1576	defer func() {
1577		msg := recover()
1578		if msg == nil || msg == failureMsg {
1579			panic(msg)
1580		}
1581		t.Log(msg)
1582	}()
1583	x := NewInt(1)
1584	y := NewInt(2)
1585	// Jacobi should panic when the second argument is even.
1586	Jacobi(x, y)
1587	panic(failureMsg)
1588}
1589
1590func TestIssue2607(t *testing.T) {
1591	// This code sequence used to hang.
1592	n := NewInt(10)
1593	n.Rand(rand.New(rand.NewSource(9)), n)
1594}
1595
1596func TestSqrt(t *testing.T) {
1597	root := 0
1598	r := new(Int)
1599	for i := 0; i < 10000; i++ {
1600		if (root+1)*(root+1) <= i {
1601			root++
1602		}
1603		n := NewInt(int64(i))
1604		r.SetInt64(-2)
1605		r.Sqrt(n)
1606		if r.Cmp(NewInt(int64(root))) != 0 {
1607			t.Errorf("Sqrt(%v) = %v, want %v", n, r, root)
1608		}
1609	}
1610
1611	for i := 0; i < 1000; i += 10 {
1612		n, _ := new(Int).SetString("1"+strings.Repeat("0", i), 10)
1613		r := new(Int).Sqrt(n)
1614		root, _ := new(Int).SetString("1"+strings.Repeat("0", i/2), 10)
1615		if r.Cmp(root) != 0 {
1616			t.Errorf("Sqrt(1e%d) = %v, want 1e%d", i, r, i/2)
1617		}
1618	}
1619
1620	// Test aliasing.
1621	r.SetInt64(100)
1622	r.Sqrt(r)
1623	if r.Int64() != 10 {
1624		t.Errorf("Sqrt(100) = %v, want 10 (aliased output)", r.Int64())
1625	}
1626}
1627
1628// We can't test this together with the other Exp tests above because
1629// it requires a different receiver setup.
1630func TestIssue22830(t *testing.T) {
1631	one := new(Int).SetInt64(1)
1632	base, _ := new(Int).SetString("84555555300000000000", 10)
1633	mod, _ := new(Int).SetString("66666670001111111111", 10)
1634	want, _ := new(Int).SetString("17888885298888888889", 10)
1635
1636	var tests = []int64{
1637		0, 1, -1,
1638	}
1639
1640	for _, n := range tests {
1641		m := NewInt(n)
1642		if got := m.Exp(base, one, mod); got.Cmp(want) != 0 {
1643			t.Errorf("(%v).Exp(%s, 1, %s) = %s, want %s", n, base, mod, got, want)
1644		}
1645	}
1646}
1647
1648func BenchmarkSqrt(b *testing.B) {
1649	n, _ := new(Int).SetString("1"+strings.Repeat("0", 1001), 10)
1650	b.ResetTimer()
1651	t := new(Int)
1652	for i := 0; i < b.N; i++ {
1653		t.Sqrt(n)
1654	}
1655}
1656
1657func benchmarkIntSqr(b *testing.B, nwords int) {
1658	x := new(Int)
1659	x.abs = rndNat(nwords)
1660	t := new(Int)
1661	b.ResetTimer()
1662	for i := 0; i < b.N; i++ {
1663		t.Mul(x, x)
1664	}
1665}
1666
1667func BenchmarkIntSqr(b *testing.B) {
1668	for _, n := range sqrBenchSizes {
1669		if isRaceBuilder && n > 1e3 {
1670			continue
1671		}
1672		b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
1673			benchmarkIntSqr(b, n)
1674		})
1675	}
1676}
1677