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", "3663"}, // 3663 = ModInverse(3199, 6719) Issue #25865
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// euclidExtGCD is a reference implementation of Euclid's
679// extended GCD algorithm for testing against optimized algorithms.
680// Requirements: a, b > 0
681func euclidExtGCD(a, b *Int) (g, x, y *Int) {
682	A := new(Int).Set(a)
683	B := new(Int).Set(b)
684
685	// A = Ua*a + Va*b
686	// B = Ub*a + Vb*b
687	Ua := new(Int).SetInt64(1)
688	Va := new(Int)
689
690	Ub := new(Int)
691	Vb := new(Int).SetInt64(1)
692
693	q := new(Int)
694	temp := new(Int)
695
696	r := new(Int)
697	for len(B.abs) > 0 {
698		q, r = q.QuoRem(A, B, r)
699
700		A, B, r = B, r, A
701
702		// Ua, Ub = Ub, Ua-q*Ub
703		temp.Set(Ub)
704		Ub.Mul(Ub, q)
705		Ub.Sub(Ua, Ub)
706		Ua.Set(temp)
707
708		// Va, Vb = Vb, Va-q*Vb
709		temp.Set(Vb)
710		Vb.Mul(Vb, q)
711		Vb.Sub(Va, Vb)
712		Va.Set(temp)
713	}
714	return A, Ua, Va
715}
716
717func checkLehmerGcd(aBytes, bBytes []byte) bool {
718	a := new(Int).SetBytes(aBytes)
719	b := new(Int).SetBytes(bBytes)
720
721	if a.Sign() <= 0 || b.Sign() <= 0 {
722		return true // can only test positive arguments
723	}
724
725	d := new(Int).lehmerGCD(nil, nil, a, b)
726	d0, _, _ := euclidExtGCD(a, b)
727
728	return d.Cmp(d0) == 0
729}
730
731func checkLehmerExtGcd(aBytes, bBytes []byte) bool {
732	a := new(Int).SetBytes(aBytes)
733	b := new(Int).SetBytes(bBytes)
734	x := new(Int)
735	y := new(Int)
736
737	if a.Sign() <= 0 || b.Sign() <= 0 {
738		return true // can only test positive arguments
739	}
740
741	d := new(Int).lehmerGCD(x, y, a, b)
742	d0, x0, y0 := euclidExtGCD(a, b)
743
744	return d.Cmp(d0) == 0 && x.Cmp(x0) == 0 && y.Cmp(y0) == 0
745}
746
747var gcdTests = []struct {
748	d, x, y, a, b string
749}{
750	// a <= 0 || b <= 0
751	{"0", "0", "0", "0", "0"},
752	{"0", "0", "0", "0", "7"},
753	{"0", "0", "0", "11", "0"},
754	{"0", "0", "0", "-77", "35"},
755	{"0", "0", "0", "64515", "-24310"},
756	{"0", "0", "0", "-64515", "-24310"},
757
758	{"1", "-9", "47", "120", "23"},
759	{"7", "1", "-2", "77", "35"},
760	{"935", "-3", "8", "64515", "24310"},
761	{"935000000000000000", "-3", "8", "64515000000000000000", "24310000000000000000"},
762	{"1", "-221", "22059940471369027483332068679400581064239780177629666810348940098015901108344", "98920366548084643601728869055592650835572950932266967461790948584315647051443", "991"},
763
764	// test early exit (after one Euclidean iteration) in binaryGCD
765	{"1", "", "", "1", "98920366548084643601728869055592650835572950932266967461790948584315647051443"},
766}
767
768func testGcd(t *testing.T, d, x, y, a, b *Int) {
769	var X *Int
770	if x != nil {
771		X = new(Int)
772	}
773	var Y *Int
774	if y != nil {
775		Y = new(Int)
776	}
777
778	D := new(Int).GCD(X, Y, a, b)
779	if D.Cmp(d) != 0 {
780		t.Errorf("GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, D, d)
781	}
782	if x != nil && X.Cmp(x) != 0 {
783		t.Errorf("GCD(%s, %s, %s, %s): got x = %s, want %s", x, y, a, b, X, x)
784	}
785	if y != nil && Y.Cmp(y) != 0 {
786		t.Errorf("GCD(%s, %s, %s, %s): got y = %s, want %s", x, y, a, b, Y, y)
787	}
788
789	// check results in presence of aliasing (issue #11284)
790	a2 := new(Int).Set(a)
791	b2 := new(Int).Set(b)
792	a2.GCD(X, Y, a2, b2) // result is same as 1st argument
793	if a2.Cmp(d) != 0 {
794		t.Errorf("aliased z = a GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, a2, d)
795	}
796
797	a2 = new(Int).Set(a)
798	b2 = new(Int).Set(b)
799	b2.GCD(X, Y, a2, b2) // result is same as 2nd argument
800	if b2.Cmp(d) != 0 {
801		t.Errorf("aliased z = b GCD(%s, %s, %s, %s): got d = %s, want %s", x, y, a, b, b2, d)
802	}
803}
804
805func TestGcd(t *testing.T) {
806	for _, test := range gcdTests {
807		d, _ := new(Int).SetString(test.d, 0)
808		x, _ := new(Int).SetString(test.x, 0)
809		y, _ := new(Int).SetString(test.y, 0)
810		a, _ := new(Int).SetString(test.a, 0)
811		b, _ := new(Int).SetString(test.b, 0)
812
813		testGcd(t, d, nil, nil, a, b)
814		testGcd(t, d, x, nil, a, b)
815		testGcd(t, d, nil, y, a, b)
816		testGcd(t, d, x, y, a, b)
817	}
818
819	if err := quick.Check(checkGcd, nil); err != nil {
820		t.Error(err)
821	}
822
823	if err := quick.Check(checkLehmerGcd, nil); err != nil {
824		t.Error(err)
825	}
826
827	if err := quick.Check(checkLehmerExtGcd, nil); err != nil {
828		t.Error(err)
829	}
830}
831
832type intShiftTest struct {
833	in    string
834	shift uint
835	out   string
836}
837
838var rshTests = []intShiftTest{
839	{"0", 0, "0"},
840	{"-0", 0, "0"},
841	{"0", 1, "0"},
842	{"0", 2, "0"},
843	{"1", 0, "1"},
844	{"1", 1, "0"},
845	{"1", 2, "0"},
846	{"2", 0, "2"},
847	{"2", 1, "1"},
848	{"-1", 0, "-1"},
849	{"-1", 1, "-1"},
850	{"-1", 10, "-1"},
851	{"-100", 2, "-25"},
852	{"-100", 3, "-13"},
853	{"-100", 100, "-1"},
854	{"4294967296", 0, "4294967296"},
855	{"4294967296", 1, "2147483648"},
856	{"4294967296", 2, "1073741824"},
857	{"18446744073709551616", 0, "18446744073709551616"},
858	{"18446744073709551616", 1, "9223372036854775808"},
859	{"18446744073709551616", 2, "4611686018427387904"},
860	{"18446744073709551616", 64, "1"},
861	{"340282366920938463463374607431768211456", 64, "18446744073709551616"},
862	{"340282366920938463463374607431768211456", 128, "1"},
863}
864
865func TestRsh(t *testing.T) {
866	for i, test := range rshTests {
867		in, _ := new(Int).SetString(test.in, 10)
868		expected, _ := new(Int).SetString(test.out, 10)
869		out := new(Int).Rsh(in, test.shift)
870
871		if !isNormalized(out) {
872			t.Errorf("#%d: %v is not normalized", i, *out)
873		}
874		if out.Cmp(expected) != 0 {
875			t.Errorf("#%d: got %s want %s", i, out, expected)
876		}
877	}
878}
879
880func TestRshSelf(t *testing.T) {
881	for i, test := range rshTests {
882		z, _ := new(Int).SetString(test.in, 10)
883		expected, _ := new(Int).SetString(test.out, 10)
884		z.Rsh(z, test.shift)
885
886		if !isNormalized(z) {
887			t.Errorf("#%d: %v is not normalized", i, *z)
888		}
889		if z.Cmp(expected) != 0 {
890			t.Errorf("#%d: got %s want %s", i, z, expected)
891		}
892	}
893}
894
895var lshTests = []intShiftTest{
896	{"0", 0, "0"},
897	{"0", 1, "0"},
898	{"0", 2, "0"},
899	{"1", 0, "1"},
900	{"1", 1, "2"},
901	{"1", 2, "4"},
902	{"2", 0, "2"},
903	{"2", 1, "4"},
904	{"2", 2, "8"},
905	{"-87", 1, "-174"},
906	{"4294967296", 0, "4294967296"},
907	{"4294967296", 1, "8589934592"},
908	{"4294967296", 2, "17179869184"},
909	{"18446744073709551616", 0, "18446744073709551616"},
910	{"9223372036854775808", 1, "18446744073709551616"},
911	{"4611686018427387904", 2, "18446744073709551616"},
912	{"1", 64, "18446744073709551616"},
913	{"18446744073709551616", 64, "340282366920938463463374607431768211456"},
914	{"1", 128, "340282366920938463463374607431768211456"},
915}
916
917func TestLsh(t *testing.T) {
918	for i, test := range lshTests {
919		in, _ := new(Int).SetString(test.in, 10)
920		expected, _ := new(Int).SetString(test.out, 10)
921		out := new(Int).Lsh(in, test.shift)
922
923		if !isNormalized(out) {
924			t.Errorf("#%d: %v is not normalized", i, *out)
925		}
926		if out.Cmp(expected) != 0 {
927			t.Errorf("#%d: got %s want %s", i, out, expected)
928		}
929	}
930}
931
932func TestLshSelf(t *testing.T) {
933	for i, test := range lshTests {
934		z, _ := new(Int).SetString(test.in, 10)
935		expected, _ := new(Int).SetString(test.out, 10)
936		z.Lsh(z, test.shift)
937
938		if !isNormalized(z) {
939			t.Errorf("#%d: %v is not normalized", i, *z)
940		}
941		if z.Cmp(expected) != 0 {
942			t.Errorf("#%d: got %s want %s", i, z, expected)
943		}
944	}
945}
946
947func TestLshRsh(t *testing.T) {
948	for i, test := range rshTests {
949		in, _ := new(Int).SetString(test.in, 10)
950		out := new(Int).Lsh(in, test.shift)
951		out = out.Rsh(out, test.shift)
952
953		if !isNormalized(out) {
954			t.Errorf("#%d: %v is not normalized", i, *out)
955		}
956		if in.Cmp(out) != 0 {
957			t.Errorf("#%d: got %s want %s", i, out, in)
958		}
959	}
960	for i, test := range lshTests {
961		in, _ := new(Int).SetString(test.in, 10)
962		out := new(Int).Lsh(in, test.shift)
963		out.Rsh(out, test.shift)
964
965		if !isNormalized(out) {
966			t.Errorf("#%d: %v is not normalized", i, *out)
967		}
968		if in.Cmp(out) != 0 {
969			t.Errorf("#%d: got %s want %s", i, out, in)
970		}
971	}
972}
973
974// Entries must be sorted by value in ascending order.
975var cmpAbsTests = []string{
976	"0",
977	"1",
978	"2",
979	"10",
980	"10000000",
981	"2783678367462374683678456387645876387564783686583485",
982	"2783678367462374683678456387645876387564783686583486",
983	"32957394867987420967976567076075976570670947609750670956097509670576075067076027578341538",
984}
985
986func TestCmpAbs(t *testing.T) {
987	values := make([]*Int, len(cmpAbsTests))
988	var prev *Int
989	for i, s := range cmpAbsTests {
990		x, ok := new(Int).SetString(s, 0)
991		if !ok {
992			t.Fatalf("SetString(%s, 0) failed", s)
993		}
994		if prev != nil && prev.Cmp(x) >= 0 {
995			t.Fatal("cmpAbsTests entries not sorted in ascending order")
996		}
997		values[i] = x
998		prev = x
999	}
1000
1001	for i, x := range values {
1002		for j, y := range values {
1003			// try all combinations of signs for x, y
1004			for k := 0; k < 4; k++ {
1005				var a, b Int
1006				a.Set(x)
1007				b.Set(y)
1008				if k&1 != 0 {
1009					a.Neg(&a)
1010				}
1011				if k&2 != 0 {
1012					b.Neg(&b)
1013				}
1014
1015				got := a.CmpAbs(&b)
1016				want := 0
1017				switch {
1018				case i > j:
1019					want = 1
1020				case i < j:
1021					want = -1
1022				}
1023				if got != want {
1024					t.Errorf("absCmp |%s|, |%s|: got %d; want %d", &a, &b, got, want)
1025				}
1026			}
1027		}
1028	}
1029}
1030
1031var int64Tests = []string{
1032	// int64
1033	"0",
1034	"1",
1035	"-1",
1036	"4294967295",
1037	"-4294967295",
1038	"4294967296",
1039	"-4294967296",
1040	"9223372036854775807",
1041	"-9223372036854775807",
1042	"-9223372036854775808",
1043
1044	// not int64
1045	"0x8000000000000000",
1046	"-0x8000000000000001",
1047	"38579843757496759476987459679745",
1048	"-38579843757496759476987459679745",
1049}
1050
1051func TestInt64(t *testing.T) {
1052	for _, s := range int64Tests {
1053		var x Int
1054		_, ok := x.SetString(s, 0)
1055		if !ok {
1056			t.Errorf("SetString(%s, 0) failed", s)
1057			continue
1058		}
1059
1060		want, err := strconv.ParseInt(s, 0, 64)
1061		if err != nil {
1062			if err.(*strconv.NumError).Err == strconv.ErrRange {
1063				if x.IsInt64() {
1064					t.Errorf("IsInt64(%s) succeeded unexpectedly", s)
1065				}
1066			} else {
1067				t.Errorf("ParseInt(%s) failed", s)
1068			}
1069			continue
1070		}
1071
1072		if !x.IsInt64() {
1073			t.Errorf("IsInt64(%s) failed unexpectedly", s)
1074		}
1075
1076		got := x.Int64()
1077		if got != want {
1078			t.Errorf("Int64(%s) = %d; want %d", s, got, want)
1079		}
1080	}
1081}
1082
1083var uint64Tests = []string{
1084	// uint64
1085	"0",
1086	"1",
1087	"4294967295",
1088	"4294967296",
1089	"8589934591",
1090	"8589934592",
1091	"9223372036854775807",
1092	"9223372036854775808",
1093	"0x08000000000000000",
1094
1095	// not uint64
1096	"0x10000000000000000",
1097	"-0x08000000000000000",
1098	"-1",
1099}
1100
1101func TestUint64(t *testing.T) {
1102	for _, s := range uint64Tests {
1103		var x Int
1104		_, ok := x.SetString(s, 0)
1105		if !ok {
1106			t.Errorf("SetString(%s, 0) failed", s)
1107			continue
1108		}
1109
1110		want, err := strconv.ParseUint(s, 0, 64)
1111		if err != nil {
1112			// check for sign explicitly (ErrRange doesn't cover signed input)
1113			if s[0] == '-' || err.(*strconv.NumError).Err == strconv.ErrRange {
1114				if x.IsUint64() {
1115					t.Errorf("IsUint64(%s) succeeded unexpectedly", s)
1116				}
1117			} else {
1118				t.Errorf("ParseUint(%s) failed", s)
1119			}
1120			continue
1121		}
1122
1123		if !x.IsUint64() {
1124			t.Errorf("IsUint64(%s) failed unexpectedly", s)
1125		}
1126
1127		got := x.Uint64()
1128		if got != want {
1129			t.Errorf("Uint64(%s) = %d; want %d", s, got, want)
1130		}
1131	}
1132}
1133
1134var bitwiseTests = []struct {
1135	x, y                 string
1136	and, or, xor, andNot string
1137}{
1138	{"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"},
1139	{"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
1140	{"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
1141	{"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
1142	{"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"},
1143	{"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
1144	{"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
1145	{"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
1146	{"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"},
1147	{"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"},
1148	{"0xff", "-0x0a", "0xf6", "-0x01", "-0xf7", "0x09"},
1149	{"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"},
1150	{"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"},
1151	{"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"},
1152	{
1153		"0x1000009dc6e3d9822cba04129bcbe3401",
1154		"0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1155		"0x1000001186210100001000009048c2001",
1156		"0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
1157		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
1158		"0x8c40c2d8822caa04120b8321400",
1159	},
1160	{
1161		"0x1000009dc6e3d9822cba04129bcbe3401",
1162		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1163		"0x8c40c2d8822caa04120b8321401",
1164		"-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd",
1165		"-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe",
1166		"0x1000001186210100001000009048c2000",
1167	},
1168	{
1169		"-0x1000009dc6e3d9822cba04129bcbe3401",
1170		"-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1171		"-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
1172		"-0x1000001186210100001000009048c2001",
1173		"0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
1174		"0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc",
1175	},
1176}
1177
1178type bitFun func(z, x, y *Int) *Int
1179
1180func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
1181	expected := new(Int)
1182	expected.SetString(exp, 0)
1183
1184	out := f(new(Int), x, y)
1185	if out.Cmp(expected) != 0 {
1186		t.Errorf("%s: got %s want %s", msg, out, expected)
1187	}
1188}
1189
1190func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
1191	self := new(Int)
1192	self.Set(x)
1193	expected := new(Int)
1194	expected.SetString(exp, 0)
1195
1196	self = f(self, self, y)
1197	if self.Cmp(expected) != 0 {
1198		t.Errorf("%s: got %s want %s", msg, self, expected)
1199	}
1200}
1201
1202func altBit(x *Int, i int) uint {
1203	z := new(Int).Rsh(x, uint(i))
1204	z = z.And(z, NewInt(1))
1205	if z.Cmp(new(Int)) != 0 {
1206		return 1
1207	}
1208	return 0
1209}
1210
1211func altSetBit(z *Int, x *Int, i int, b uint) *Int {
1212	one := NewInt(1)
1213	m := one.Lsh(one, uint(i))
1214	switch b {
1215	case 1:
1216		return z.Or(x, m)
1217	case 0:
1218		return z.AndNot(x, m)
1219	}
1220	panic("set bit is not 0 or 1")
1221}
1222
1223func testBitset(t *testing.T, x *Int) {
1224	n := x.BitLen()
1225	z := new(Int).Set(x)
1226	z1 := new(Int).Set(x)
1227	for i := 0; i < n+10; i++ {
1228		old := z.Bit(i)
1229		old1 := altBit(z1, i)
1230		if old != old1 {
1231			t.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1, i, old, old1)
1232		}
1233		z := new(Int).SetBit(z, i, 1)
1234		z1 := altSetBit(new(Int), z1, i, 1)
1235		if z.Bit(i) == 0 {
1236			t.Errorf("bitset: bit %d of %s got 0 want 1", i, x)
1237		}
1238		if z.Cmp(z1) != 0 {
1239			t.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z, z1)
1240		}
1241		z.SetBit(z, i, 0)
1242		altSetBit(z1, z1, i, 0)
1243		if z.Bit(i) != 0 {
1244			t.Errorf("bitset: bit %d of %s got 1 want 0", i, x)
1245		}
1246		if z.Cmp(z1) != 0 {
1247			t.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z, z1)
1248		}
1249		altSetBit(z1, z1, i, old)
1250		z.SetBit(z, i, old)
1251		if z.Cmp(z1) != 0 {
1252			t.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z, z1)
1253		}
1254	}
1255	if z.Cmp(x) != 0 {
1256		t.Errorf("bitset: got %s want %s", z, x)
1257	}
1258}
1259
1260var bitsetTests = []struct {
1261	x string
1262	i int
1263	b uint
1264}{
1265	{"0", 0, 0},
1266	{"0", 200, 0},
1267	{"1", 0, 1},
1268	{"1", 1, 0},
1269	{"-1", 0, 1},
1270	{"-1", 200, 1},
1271	{"0x2000000000000000000000000000", 108, 0},
1272	{"0x2000000000000000000000000000", 109, 1},
1273	{"0x2000000000000000000000000000", 110, 0},
1274	{"-0x2000000000000000000000000001", 108, 1},
1275	{"-0x2000000000000000000000000001", 109, 0},
1276	{"-0x2000000000000000000000000001", 110, 1},
1277}
1278
1279func TestBitSet(t *testing.T) {
1280	for _, test := range bitwiseTests {
1281		x := new(Int)
1282		x.SetString(test.x, 0)
1283		testBitset(t, x)
1284		x = new(Int)
1285		x.SetString(test.y, 0)
1286		testBitset(t, x)
1287	}
1288	for i, test := range bitsetTests {
1289		x := new(Int)
1290		x.SetString(test.x, 0)
1291		b := x.Bit(test.i)
1292		if b != test.b {
1293			t.Errorf("#%d got %v want %v", i, b, test.b)
1294		}
1295	}
1296	z := NewInt(1)
1297	z.SetBit(NewInt(0), 2, 1)
1298	if z.Cmp(NewInt(4)) != 0 {
1299		t.Errorf("destination leaked into result; got %s want 4", z)
1300	}
1301}
1302
1303func BenchmarkBitset(b *testing.B) {
1304	z := new(Int)
1305	z.SetBit(z, 512, 1)
1306	b.ResetTimer()
1307	b.StartTimer()
1308	for i := b.N - 1; i >= 0; i-- {
1309		z.SetBit(z, i&512, 1)
1310	}
1311}
1312
1313func BenchmarkBitsetNeg(b *testing.B) {
1314	z := NewInt(-1)
1315	z.SetBit(z, 512, 0)
1316	b.ResetTimer()
1317	b.StartTimer()
1318	for i := b.N - 1; i >= 0; i-- {
1319		z.SetBit(z, i&512, 0)
1320	}
1321}
1322
1323func BenchmarkBitsetOrig(b *testing.B) {
1324	z := new(Int)
1325	altSetBit(z, z, 512, 1)
1326	b.ResetTimer()
1327	b.StartTimer()
1328	for i := b.N - 1; i >= 0; i-- {
1329		altSetBit(z, z, i&512, 1)
1330	}
1331}
1332
1333func BenchmarkBitsetNegOrig(b *testing.B) {
1334	z := NewInt(-1)
1335	altSetBit(z, z, 512, 0)
1336	b.ResetTimer()
1337	b.StartTimer()
1338	for i := b.N - 1; i >= 0; i-- {
1339		altSetBit(z, z, i&512, 0)
1340	}
1341}
1342
1343// tri generates the trinomial 2**(n*2) - 2**n - 1, which is always 3 mod 4 and
1344// 7 mod 8, so that 2 is always a quadratic residue.
1345func tri(n uint) *Int {
1346	x := NewInt(1)
1347	x.Lsh(x, n)
1348	x2 := new(Int).Lsh(x, n)
1349	x2.Sub(x2, x)
1350	x2.Sub(x2, intOne)
1351	return x2
1352}
1353
1354func BenchmarkModSqrt225_Tonelli(b *testing.B) {
1355	p := tri(225)
1356	x := NewInt(2)
1357	for i := 0; i < b.N; i++ {
1358		x.SetUint64(2)
1359		x.modSqrtTonelliShanks(x, p)
1360	}
1361}
1362
1363func BenchmarkModSqrt225_3Mod4(b *testing.B) {
1364	p := tri(225)
1365	x := new(Int).SetUint64(2)
1366	for i := 0; i < b.N; i++ {
1367		x.SetUint64(2)
1368		x.modSqrt3Mod4Prime(x, p)
1369	}
1370}
1371
1372func BenchmarkModSqrt231_Tonelli(b *testing.B) {
1373	p := tri(231)
1374	p.Sub(p, intOne)
1375	p.Sub(p, intOne) // tri(231) - 2 is a prime == 5 mod 8
1376	x := new(Int).SetUint64(7)
1377	for i := 0; i < b.N; i++ {
1378		x.SetUint64(7)
1379		x.modSqrtTonelliShanks(x, p)
1380	}
1381}
1382
1383func BenchmarkModSqrt231_5Mod8(b *testing.B) {
1384	p := tri(231)
1385	p.Sub(p, intOne)
1386	p.Sub(p, intOne) // tri(231) - 2 is a prime == 5 mod 8
1387	x := new(Int).SetUint64(7)
1388	for i := 0; i < b.N; i++ {
1389		x.SetUint64(7)
1390		x.modSqrt5Mod8Prime(x, p)
1391	}
1392}
1393
1394func TestBitwise(t *testing.T) {
1395	x := new(Int)
1396	y := new(Int)
1397	for _, test := range bitwiseTests {
1398		x.SetString(test.x, 0)
1399		y.SetString(test.y, 0)
1400
1401		testBitFun(t, "and", (*Int).And, x, y, test.and)
1402		testBitFunSelf(t, "and", (*Int).And, x, y, test.and)
1403		testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot)
1404		testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot)
1405		testBitFun(t, "or", (*Int).Or, x, y, test.or)
1406		testBitFunSelf(t, "or", (*Int).Or, x, y, test.or)
1407		testBitFun(t, "xor", (*Int).Xor, x, y, test.xor)
1408		testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor)
1409	}
1410}
1411
1412var notTests = []struct {
1413	in  string
1414	out string
1415}{
1416	{"0", "-1"},
1417	{"1", "-2"},
1418	{"7", "-8"},
1419	{"0", "-1"},
1420	{"-81910", "81909"},
1421	{
1422		"298472983472983471903246121093472394872319615612417471234712061",
1423		"-298472983472983471903246121093472394872319615612417471234712062",
1424	},
1425}
1426
1427func TestNot(t *testing.T) {
1428	in := new(Int)
1429	out := new(Int)
1430	expected := new(Int)
1431	for i, test := range notTests {
1432		in.SetString(test.in, 10)
1433		expected.SetString(test.out, 10)
1434		out = out.Not(in)
1435		if out.Cmp(expected) != 0 {
1436			t.Errorf("#%d: got %s want %s", i, out, expected)
1437		}
1438		out = out.Not(out)
1439		if out.Cmp(in) != 0 {
1440			t.Errorf("#%d: got %s want %s", i, out, in)
1441		}
1442	}
1443}
1444
1445var modInverseTests = []struct {
1446	element string
1447	modulus string
1448}{
1449	{"1234567", "458948883992"},
1450	{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
1451	{"-10", "13"}, // issue #16984
1452	{"10", "-13"},
1453	{"-17", "-13"},
1454}
1455
1456func TestModInverse(t *testing.T) {
1457	var element, modulus, gcd, inverse Int
1458	one := NewInt(1)
1459	for _, test := range modInverseTests {
1460		(&element).SetString(test.element, 10)
1461		(&modulus).SetString(test.modulus, 10)
1462		(&inverse).ModInverse(&element, &modulus)
1463		(&inverse).Mul(&inverse, &element)
1464		(&inverse).Mod(&inverse, &modulus)
1465		if (&inverse).Cmp(one) != 0 {
1466			t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
1467		}
1468	}
1469	// exhaustive test for small values
1470	for n := 2; n < 100; n++ {
1471		(&modulus).SetInt64(int64(n))
1472		for x := 1; x < n; x++ {
1473			(&element).SetInt64(int64(x))
1474			(&gcd).GCD(nil, nil, &element, &modulus)
1475			if (&gcd).Cmp(one) != 0 {
1476				continue
1477			}
1478			(&inverse).ModInverse(&element, &modulus)
1479			(&inverse).Mul(&inverse, &element)
1480			(&inverse).Mod(&inverse, &modulus)
1481			if (&inverse).Cmp(one) != 0 {
1482				t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
1483			}
1484		}
1485	}
1486}
1487
1488func BenchmarkModInverse(b *testing.B) {
1489	p := new(Int).SetInt64(1) // Mersenne prime 2**1279 -1
1490	p.abs = p.abs.shl(p.abs, 1279)
1491	p.Sub(p, intOne)
1492	x := new(Int).Sub(p, intOne)
1493	z := new(Int)
1494	for i := 0; i < b.N; i++ {
1495		z.ModInverse(x, p)
1496	}
1497}
1498
1499// testModSqrt is a helper for TestModSqrt,
1500// which checks that ModSqrt can compute a square-root of elt^2.
1501func testModSqrt(t *testing.T, elt, mod, sq, sqrt *Int) bool {
1502	var sqChk, sqrtChk, sqrtsq Int
1503	sq.Mul(elt, elt)
1504	sq.Mod(sq, mod)
1505	z := sqrt.ModSqrt(sq, mod)
1506	if z != sqrt {
1507		t.Errorf("ModSqrt returned wrong value %s", z)
1508	}
1509
1510	// test ModSqrt arguments outside the range [0,mod)
1511	sqChk.Add(sq, mod)
1512	z = sqrtChk.ModSqrt(&sqChk, mod)
1513	if z != &sqrtChk || z.Cmp(sqrt) != 0 {
1514		t.Errorf("ModSqrt returned inconsistent value %s", z)
1515	}
1516	sqChk.Sub(sq, mod)
1517	z = sqrtChk.ModSqrt(&sqChk, mod)
1518	if z != &sqrtChk || z.Cmp(sqrt) != 0 {
1519		t.Errorf("ModSqrt returned inconsistent value %s", z)
1520	}
1521
1522	// test x aliasing z
1523	z = sqrtChk.ModSqrt(sqrtChk.Set(sq), mod)
1524	if z != &sqrtChk || z.Cmp(sqrt) != 0 {
1525		t.Errorf("ModSqrt returned inconsistent value %s", z)
1526	}
1527
1528	// make sure we actually got a square root
1529	if sqrt.Cmp(elt) == 0 {
1530		return true // we found the "desired" square root
1531	}
1532	sqrtsq.Mul(sqrt, sqrt) // make sure we found the "other" one
1533	sqrtsq.Mod(&sqrtsq, mod)
1534	return sq.Cmp(&sqrtsq) == 0
1535}
1536
1537func TestModSqrt(t *testing.T) {
1538	var elt, mod, modx4, sq, sqrt Int
1539	r := rand.New(rand.NewSource(9))
1540	for i, s := range primes[1:] { // skip 2, use only odd primes
1541		mod.SetString(s, 10)
1542		modx4.Lsh(&mod, 2)
1543
1544		// test a few random elements per prime
1545		for x := 1; x < 5; x++ {
1546			elt.Rand(r, &modx4)
1547			elt.Sub(&elt, &mod) // test range [-mod, 3*mod)
1548			if !testModSqrt(t, &elt, &mod, &sq, &sqrt) {
1549				t.Errorf("#%d: failed (sqrt(e) = %s)", i, &sqrt)
1550			}
1551		}
1552
1553		if testing.Short() && i > 2 {
1554			break
1555		}
1556	}
1557
1558	if testing.Short() {
1559		return
1560	}
1561
1562	// exhaustive test for small values
1563	for n := 3; n < 100; n++ {
1564		mod.SetInt64(int64(n))
1565		if !mod.ProbablyPrime(10) {
1566			continue
1567		}
1568		isSquare := make([]bool, n)
1569
1570		// test all the squares
1571		for x := 1; x < n; x++ {
1572			elt.SetInt64(int64(x))
1573			if !testModSqrt(t, &elt, &mod, &sq, &sqrt) {
1574				t.Errorf("#%d: failed (sqrt(%d,%d) = %s)", x, &elt, &mod, &sqrt)
1575			}
1576			isSquare[sq.Uint64()] = true
1577		}
1578
1579		// test all non-squares
1580		for x := 1; x < n; x++ {
1581			sq.SetInt64(int64(x))
1582			z := sqrt.ModSqrt(&sq, &mod)
1583			if !isSquare[x] && z != nil {
1584				t.Errorf("#%d: failed (sqrt(%d,%d) = nil)", x, &sqrt, &mod)
1585			}
1586		}
1587	}
1588}
1589
1590func TestJacobi(t *testing.T) {
1591	testCases := []struct {
1592		x, y   int64
1593		result int
1594	}{
1595		{0, 1, 1},
1596		{0, -1, 1},
1597		{1, 1, 1},
1598		{1, -1, 1},
1599		{0, 5, 0},
1600		{1, 5, 1},
1601		{2, 5, -1},
1602		{-2, 5, -1},
1603		{2, -5, -1},
1604		{-2, -5, 1},
1605		{3, 5, -1},
1606		{5, 5, 0},
1607		{-5, 5, 0},
1608		{6, 5, 1},
1609		{6, -5, 1},
1610		{-6, 5, 1},
1611		{-6, -5, -1},
1612	}
1613
1614	var x, y Int
1615
1616	for i, test := range testCases {
1617		x.SetInt64(test.x)
1618		y.SetInt64(test.y)
1619		expected := test.result
1620		actual := Jacobi(&x, &y)
1621		if actual != expected {
1622			t.Errorf("#%d: Jacobi(%d, %d) = %d, but expected %d", i, test.x, test.y, actual, expected)
1623		}
1624	}
1625}
1626
1627func TestJacobiPanic(t *testing.T) {
1628	const failureMsg = "test failure"
1629	defer func() {
1630		msg := recover()
1631		if msg == nil || msg == failureMsg {
1632			panic(msg)
1633		}
1634		t.Log(msg)
1635	}()
1636	x := NewInt(1)
1637	y := NewInt(2)
1638	// Jacobi should panic when the second argument is even.
1639	Jacobi(x, y)
1640	panic(failureMsg)
1641}
1642
1643func TestIssue2607(t *testing.T) {
1644	// This code sequence used to hang.
1645	n := NewInt(10)
1646	n.Rand(rand.New(rand.NewSource(9)), n)
1647}
1648
1649func TestSqrt(t *testing.T) {
1650	root := 0
1651	r := new(Int)
1652	for i := 0; i < 10000; i++ {
1653		if (root+1)*(root+1) <= i {
1654			root++
1655		}
1656		n := NewInt(int64(i))
1657		r.SetInt64(-2)
1658		r.Sqrt(n)
1659		if r.Cmp(NewInt(int64(root))) != 0 {
1660			t.Errorf("Sqrt(%v) = %v, want %v", n, r, root)
1661		}
1662	}
1663
1664	for i := 0; i < 1000; i += 10 {
1665		n, _ := new(Int).SetString("1"+strings.Repeat("0", i), 10)
1666		r := new(Int).Sqrt(n)
1667		root, _ := new(Int).SetString("1"+strings.Repeat("0", i/2), 10)
1668		if r.Cmp(root) != 0 {
1669			t.Errorf("Sqrt(1e%d) = %v, want 1e%d", i, r, i/2)
1670		}
1671	}
1672
1673	// Test aliasing.
1674	r.SetInt64(100)
1675	r.Sqrt(r)
1676	if r.Int64() != 10 {
1677		t.Errorf("Sqrt(100) = %v, want 10 (aliased output)", r.Int64())
1678	}
1679}
1680
1681// We can't test this together with the other Exp tests above because
1682// it requires a different receiver setup.
1683func TestIssue22830(t *testing.T) {
1684	one := new(Int).SetInt64(1)
1685	base, _ := new(Int).SetString("84555555300000000000", 10)
1686	mod, _ := new(Int).SetString("66666670001111111111", 10)
1687	want, _ := new(Int).SetString("17888885298888888889", 10)
1688
1689	var tests = []int64{
1690		0, 1, -1,
1691	}
1692
1693	for _, n := range tests {
1694		m := NewInt(n)
1695		if got := m.Exp(base, one, mod); got.Cmp(want) != 0 {
1696			t.Errorf("(%v).Exp(%s, 1, %s) = %s, want %s", n, base, mod, got, want)
1697		}
1698	}
1699}
1700
1701func BenchmarkSqrt(b *testing.B) {
1702	n, _ := new(Int).SetString("1"+strings.Repeat("0", 1001), 10)
1703	b.ResetTimer()
1704	t := new(Int)
1705	for i := 0; i < b.N; i++ {
1706		t.Sqrt(n)
1707	}
1708}
1709
1710func benchmarkIntSqr(b *testing.B, nwords int) {
1711	x := new(Int)
1712	x.abs = rndNat(nwords)
1713	t := new(Int)
1714	b.ResetTimer()
1715	for i := 0; i < b.N; i++ {
1716		t.Mul(x, x)
1717	}
1718}
1719
1720func BenchmarkIntSqr(b *testing.B) {
1721	for _, n := range sqrBenchSizes {
1722		if isRaceBuilder && n > 1e3 {
1723			continue
1724		}
1725		b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
1726			benchmarkIntSqr(b, n)
1727		})
1728	}
1729}
1730
1731func benchmarkDiv(b *testing.B, aSize, bSize int) {
1732	var r = rand.New(rand.NewSource(1234))
1733	aa := randInt(r, uint(aSize))
1734	bb := randInt(r, uint(bSize))
1735	if aa.Cmp(bb) < 0 {
1736		aa, bb = bb, aa
1737	}
1738	x := new(Int)
1739	y := new(Int)
1740
1741	b.ResetTimer()
1742	for i := 0; i < b.N; i++ {
1743		x.DivMod(aa, bb, y)
1744	}
1745}
1746
1747func BenchmarkDiv(b *testing.B) {
1748	min, max, step := 10, 100000, 10
1749	for i := min; i <= max; i *= step {
1750		j := 2 * i
1751		b.Run(fmt.Sprintf("%d/%d", j, i), func(b *testing.B) {
1752			benchmarkDiv(b, j, i)
1753		})
1754	}
1755}
1756