Source file
src/math/big/nat_test.go
1
2
3
4
5 package big
6
7 import (
8 "fmt"
9 "math"
10 "runtime"
11 "strings"
12 "testing"
13 )
14
15 var cmpTests = []struct {
16 x, y nat
17 r int
18 }{
19 {nil, nil, 0},
20 {nil, nat(nil), 0},
21 {nat(nil), nil, 0},
22 {nat(nil), nat(nil), 0},
23 {nat{0}, nat{0}, 0},
24 {nat{0}, nat{1}, -1},
25 {nat{1}, nat{0}, 1},
26 {nat{1}, nat{1}, 0},
27 {nat{0, _M}, nat{1}, 1},
28 {nat{1}, nat{0, _M}, -1},
29 {nat{1, _M}, nat{0, _M}, 1},
30 {nat{0, _M}, nat{1, _M}, -1},
31 {nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1},
32 {nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1},
33 }
34
35 func TestCmp(t *testing.T) {
36 for i, a := range cmpTests {
37 r := a.x.cmp(a.y)
38 if r != a.r {
39 t.Errorf("#%d got r = %v; want %v", i, r, a.r)
40 }
41 }
42 }
43
44 type funNN func(z, x, y nat) nat
45 type argNN struct {
46 z, x, y nat
47 }
48
49 var sumNN = []argNN{
50 {},
51 {nat{1}, nil, nat{1}},
52 {nat{1111111110}, nat{123456789}, nat{987654321}},
53 {nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}},
54 {nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}},
55 {nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}},
56 }
57
58 var prodNN = []argNN{
59 {},
60 {nil, nil, nil},
61 {nil, nat{991}, nil},
62 {nat{991}, nat{991}, nat{1}},
63 {nat{991 * 991}, nat{991}, nat{991}},
64 {nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}},
65 {nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}},
66 {nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}},
67
68 {
69 natFromString("11790184577738583171520872861412518665678211592275841109096961"),
70 natFromString("515377520732011331036461129765621272702107522001"),
71 natFromString("22876792454961"),
72 },
73
74
75
76 {
77 natFromString(strings.Repeat("1", 70000)),
78 natFromString("1" + strings.Repeat(strings.Repeat("0", 699)+"1", 99)),
79 natFromString(strings.Repeat("1", 700)),
80 },
81
82
83
84 {
85 natFromString(strings.Repeat("1", 20000)),
86 natFromString("1" + strings.Repeat("0", 9999) + "1"),
87 natFromString(strings.Repeat("1", 10000)),
88 },
89 }
90
91 func natFromString(s string) nat {
92 x, _, _, err := nat(nil).scan(strings.NewReader(s), 0, false)
93 if err != nil {
94 panic(err)
95 }
96 return x
97 }
98
99 func TestSet(t *testing.T) {
100 for _, a := range sumNN {
101 z := nat(nil).set(a.z)
102 if z.cmp(a.z) != 0 {
103 t.Errorf("got z = %v; want %v", z, a.z)
104 }
105 }
106 }
107
108 func testFunNN(t *testing.T, msg string, f funNN, a argNN) {
109 z := f(nil, a.x, a.y)
110 if z.cmp(a.z) != 0 {
111 t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z)
112 }
113 }
114
115 func TestFunNN(t *testing.T) {
116 for _, a := range sumNN {
117 arg := a
118 testFunNN(t, "add", nat.add, arg)
119
120 arg = argNN{a.z, a.y, a.x}
121 testFunNN(t, "add symmetric", nat.add, arg)
122
123 arg = argNN{a.x, a.z, a.y}
124 testFunNN(t, "sub", nat.sub, arg)
125
126 arg = argNN{a.y, a.z, a.x}
127 testFunNN(t, "sub symmetric", nat.sub, arg)
128 }
129
130 for _, a := range prodNN {
131 arg := a
132 testFunNN(t, "mul", nat.mul, arg)
133
134 arg = argNN{a.z, a.y, a.x}
135 testFunNN(t, "mul symmetric", nat.mul, arg)
136 }
137 }
138
139 var mulRangesN = []struct {
140 a, b uint64
141 prod string
142 }{
143 {0, 0, "0"},
144 {1, 1, "1"},
145 {1, 2, "2"},
146 {1, 3, "6"},
147 {10, 10, "10"},
148 {0, 100, "0"},
149 {0, 1e9, "0"},
150 {1, 0, "1"},
151 {100, 1, "1"},
152 {1, 10, "3628800"},
153 {1, 20, "2432902008176640000"},
154 {1, 100,
155 "933262154439441526816992388562667004907159682643816214685929" +
156 "638952175999932299156089414639761565182862536979208272237582" +
157 "51185210916864000000000000000000000000",
158 },
159 {math.MaxUint64 - 0, math.MaxUint64, "18446744073709551615"},
160 {math.MaxUint64 - 1, math.MaxUint64, "340282366920938463408034375210639556610"},
161 {math.MaxUint64 - 2, math.MaxUint64, "6277101735386680761794095221682035635525021984684230311930"},
162 {math.MaxUint64 - 3, math.MaxUint64, "115792089237316195360799967654821100226821973275796746098729803619699194331160"},
163 }
164
165 func TestMulRangeN(t *testing.T) {
166 for i, r := range mulRangesN {
167 prod := string(nat(nil).mulRange(r.a, r.b).utoa(10))
168 if prod != r.prod {
169 t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
170 }
171 }
172 }
173
174
175 func allocBytes(f func()) uint64 {
176 var stats runtime.MemStats
177 runtime.ReadMemStats(&stats)
178 t := stats.TotalAlloc
179 f()
180 runtime.ReadMemStats(&stats)
181 return stats.TotalAlloc - t
182 }
183
184
185
186
187 func TestMulUnbalanced(t *testing.T) {
188 defer runtime.GOMAXPROCS(runtime.GOMAXPROCS(1))
189 x := rndNat(50000)
190 y := rndNat(40)
191 allocSize := allocBytes(func() {
192 nat(nil).mul(x, y)
193 })
194 inputSize := uint64(len(x)+len(y)) * _S
195 if ratio := allocSize / uint64(inputSize); ratio > 10 {
196 t.Errorf("multiplication uses too much memory (%d > %d times the size of inputs)", allocSize, ratio)
197 }
198 }
199
200
201
202
203 func rndNat(n int) nat {
204 return nat(rndV(n)).norm()
205 }
206
207
208 func rndNat1(n int) nat {
209 x := nat(rndV(n)).norm()
210 if len(x) == 0 {
211 x.setWord(1)
212 }
213 return x
214 }
215
216 func BenchmarkMul(b *testing.B) {
217 mulx := rndNat(1e4)
218 muly := rndNat(1e4)
219 b.ResetTimer()
220 for i := 0; i < b.N; i++ {
221 var z nat
222 z.mul(mulx, muly)
223 }
224 }
225
226 func benchmarkNatMul(b *testing.B, nwords int) {
227 x := rndNat(nwords)
228 y := rndNat(nwords)
229 var z nat
230 b.ResetTimer()
231 for i := 0; i < b.N; i++ {
232 z.mul(x, y)
233 }
234 }
235
236 var mulBenchSizes = []int{10, 100, 1000, 10000, 100000}
237
238 func BenchmarkNatMul(b *testing.B) {
239 for _, n := range mulBenchSizes {
240 if isRaceBuilder && n > 1e3 {
241 continue
242 }
243 b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
244 benchmarkNatMul(b, n)
245 })
246 }
247 }
248
249 func TestNLZ(t *testing.T) {
250 var x Word = _B >> 1
251 for i := 0; i <= _W; i++ {
252 if int(nlz(x)) != i {
253 t.Errorf("failed at %x: got %d want %d", x, nlz(x), i)
254 }
255 x >>= 1
256 }
257 }
258
259 type shiftTest struct {
260 in nat
261 shift uint
262 out nat
263 }
264
265 var leftShiftTests = []shiftTest{
266 {nil, 0, nil},
267 {nil, 1, nil},
268 {natOne, 0, natOne},
269 {natOne, 1, natTwo},
270 {nat{1 << (_W - 1)}, 1, nat{0}},
271 {nat{1 << (_W - 1), 0}, 1, nat{0, 1}},
272 }
273
274 func TestShiftLeft(t *testing.T) {
275 for i, test := range leftShiftTests {
276 var z nat
277 z = z.shl(test.in, test.shift)
278 for j, d := range test.out {
279 if j >= len(z) || z[j] != d {
280 t.Errorf("#%d: got: %v want: %v", i, z, test.out)
281 break
282 }
283 }
284 }
285 }
286
287 var rightShiftTests = []shiftTest{
288 {nil, 0, nil},
289 {nil, 1, nil},
290 {natOne, 0, natOne},
291 {natOne, 1, nil},
292 {natTwo, 1, natOne},
293 {nat{0, 1}, 1, nat{1 << (_W - 1)}},
294 {nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}},
295 }
296
297 func TestShiftRight(t *testing.T) {
298 for i, test := range rightShiftTests {
299 var z nat
300 z = z.shr(test.in, test.shift)
301 for j, d := range test.out {
302 if j >= len(z) || z[j] != d {
303 t.Errorf("#%d: got: %v want: %v", i, z, test.out)
304 break
305 }
306 }
307 }
308 }
309
310 func BenchmarkZeroShifts(b *testing.B) {
311 x := rndNat(800)
312
313 b.Run("Shl", func(b *testing.B) {
314 for i := 0; i < b.N; i++ {
315 var z nat
316 z.shl(x, 0)
317 }
318 })
319 b.Run("ShlSame", func(b *testing.B) {
320 for i := 0; i < b.N; i++ {
321 x.shl(x, 0)
322 }
323 })
324
325 b.Run("Shr", func(b *testing.B) {
326 for i := 0; i < b.N; i++ {
327 var z nat
328 z.shr(x, 0)
329 }
330 })
331 b.Run("ShrSame", func(b *testing.B) {
332 for i := 0; i < b.N; i++ {
333 x.shr(x, 0)
334 }
335 })
336 }
337
338 type modWTest struct {
339 in string
340 dividend string
341 out string
342 }
343
344 var modWTests32 = []modWTest{
345 {"23492635982634928349238759823742", "252341", "220170"},
346 }
347
348 var modWTests64 = []modWTest{
349 {"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
350 }
351
352 func runModWTests(t *testing.T, tests []modWTest) {
353 for i, test := range tests {
354 in, _ := new(Int).SetString(test.in, 10)
355 d, _ := new(Int).SetString(test.dividend, 10)
356 out, _ := new(Int).SetString(test.out, 10)
357
358 r := in.abs.modW(d.abs[0])
359 if r != out.abs[0] {
360 t.Errorf("#%d failed: got %d want %s", i, r, out)
361 }
362 }
363 }
364
365 func TestModW(t *testing.T) {
366 if _W >= 32 {
367 runModWTests(t, modWTests32)
368 }
369 if _W >= 64 {
370 runModWTests(t, modWTests64)
371 }
372 }
373
374 var montgomeryTests = []struct {
375 x, y, m string
376 k0 uint64
377 out32, out64 string
378 }{
379 {
380 "0xffffffffffffffffffffffffffffffffffffffffffffffffe",
381 "0xffffffffffffffffffffffffffffffffffffffffffffffffe",
382 "0xfffffffffffffffffffffffffffffffffffffffffffffffff",
383 1,
384 "0x1000000000000000000000000000000000000000000",
385 "0x10000000000000000000000000000000000",
386 },
387 {
388 "0x000000000ffffff5",
389 "0x000000000ffffff0",
390 "0x0000000010000001",
391 0xff0000000fffffff,
392 "0x000000000bfffff4",
393 "0x0000000003400001",
394 },
395 {
396 "0x0000000080000000",
397 "0x00000000ffffffff",
398 "0x1000000000000001",
399 0xfffffffffffffff,
400 "0x0800000008000001",
401 "0x0800000008000001",
402 },
403 {
404 "0x0000000080000000",
405 "0x0000000080000000",
406 "0xffffffff00000001",
407 0xfffffffeffffffff,
408 "0xbfffffff40000001",
409 "0xbfffffff40000001",
410 },
411 {
412 "0x0000000080000000",
413 "0x0000000080000000",
414 "0x00ffffff00000001",
415 0xfffffeffffffff,
416 "0xbfffff40000001",
417 "0xbfffff40000001",
418 },
419 {
420 "0x0000000080000000",
421 "0x0000000080000000",
422 "0x0000ffff00000001",
423 0xfffeffffffff,
424 "0xbfff40000001",
425 "0xbfff40000001",
426 },
427 {
428 "0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
429 "0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
430 "0x33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
431 0xdecc8f1249812adf,
432 "0x04eb0e11d72329dc0915f86784820fc403275bf2f6620a20e0dd344c5cd0875e50deb5",
433 "0x0d7144739a7d8e11d72329dc0915f86784820fc403275bf2f61ed96f35dd34dbb3d6a0",
434 },
435 {
436 "0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444",
437 "0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc",
438 "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
439 0xdecc8f1249812adf,
440 "0x5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715",
441 "0x92fcad4b5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d799c32fe2f3cc5422f9711078d51a3797eb18e691295293284d8f5e69caf6decddfe1df6",
442 },
443 }
444
445 func TestMontgomery(t *testing.T) {
446 one := NewInt(1)
447 _B := new(Int).Lsh(one, _W)
448 for i, test := range montgomeryTests {
449 x := natFromString(test.x)
450 y := natFromString(test.y)
451 m := natFromString(test.m)
452 for len(x) < len(m) {
453 x = append(x, 0)
454 }
455 for len(y) < len(m) {
456 y = append(y, 0)
457 }
458
459 if x.cmp(m) > 0 {
460 _, r := nat(nil).div(nil, x, m)
461 t.Errorf("#%d: x > m (0x%s > 0x%s; use 0x%s)", i, x.utoa(16), m.utoa(16), r.utoa(16))
462 }
463 if y.cmp(m) > 0 {
464 _, r := nat(nil).div(nil, x, m)
465 t.Errorf("#%d: y > m (0x%s > 0x%s; use 0x%s)", i, y.utoa(16), m.utoa(16), r.utoa(16))
466 }
467
468 var out nat
469 if _W == 32 {
470 out = natFromString(test.out32)
471 } else {
472 out = natFromString(test.out64)
473 }
474
475
476
477
478 xi := &Int{abs: x}
479 yi := &Int{abs: y}
480 mi := &Int{abs: m}
481 p := new(Int).Mod(new(Int).Mul(xi, new(Int).Mul(yi, new(Int).ModInverse(new(Int).Lsh(one, uint(len(m))*_W), mi))), mi)
482 if out.cmp(p.abs.norm()) != 0 {
483 t.Errorf("#%d: out in table=0x%s, computed=0x%s", i, out.utoa(16), p.abs.norm().utoa(16))
484 }
485
486
487 k := new(Int).Mod(&Int{abs: m}, _B)
488 k = new(Int).Sub(_B, k)
489 k = new(Int).Mod(k, _B)
490 k0 := Word(new(Int).ModInverse(k, _B).Uint64())
491 if k0 != Word(test.k0) {
492 t.Errorf("#%d: k0 in table=%#x, computed=%#x\n", i, test.k0, k0)
493 }
494
495
496 z := nat(nil).montgomery(x, y, m, k0, len(m))
497 z = z.norm()
498 if z.cmp(out) != 0 {
499 t.Errorf("#%d: got 0x%s want 0x%s", i, z.utoa(16), out.utoa(16))
500 }
501 }
502 }
503
504 var expNNTests = []struct {
505 x, y, m string
506 out string
507 }{
508 {"0", "0", "0", "1"},
509 {"0", "0", "1", "0"},
510 {"1", "1", "1", "0"},
511 {"2", "1", "1", "0"},
512 {"2", "2", "1", "0"},
513 {"10", "100000000000", "1", "0"},
514 {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
515 {"0x8000000000000000", "2", "6719", "4944"},
516 {"0x8000000000000000", "3", "6719", "5447"},
517 {"0x8000000000000000", "1000", "6719", "1603"},
518 {"0x8000000000000000", "1000000", "6719", "3199"},
519 {
520 "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
521 "298472983472983471903246121093472394872319615612417471234712061",
522 "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
523 "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
524 },
525 {
526 "11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379",
527 "426343618817810911523",
528 "444747819283133684179",
529 "42",
530 },
531 {"375", "249", "388", "175"},
532 {"375", "18446744073709551801", "388", "175"},
533 {"0", "0x40000000000000", "0x200", "0"},
534 {"0xeffffff900002f00", "0x40000000000000", "0x200", "0"},
535 {"5", "1435700818", "72", "49"},
536 {"0xffff", "0x300030003000300030003000300030003000302a3000300030003000300030003000300030003000300030003000300030003030623066307f3030783062303430383064303630343036", "0x300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0xa3f94c08b0b90e87af637cacc9383f7ea032352b8961fc036a52b659b6c9b33491b335ffd74c927f64ddd62cfca0001"},
537 }
538
539 func TestExpNN(t *testing.T) {
540 for i, test := range expNNTests {
541 x := natFromString(test.x)
542 y := natFromString(test.y)
543 out := natFromString(test.out)
544
545 var m nat
546 if len(test.m) > 0 {
547 m = natFromString(test.m)
548 }
549
550 z := nat(nil).expNN(x, y, m, false)
551 if z.cmp(out) != 0 {
552 t.Errorf("#%d got %s want %s", i, z.utoa(10), out.utoa(10))
553 }
554 }
555 }
556
557 func FuzzExpMont(f *testing.F) {
558 f.Fuzz(func(t *testing.T, x1, x2, x3, y1, y2, y3, m1, m2, m3 uint) {
559 if m1 == 0 && m2 == 0 && m3 == 0 {
560 return
561 }
562 x := new(Int).SetBits([]Word{Word(x1), Word(x2), Word(x3)})
563 y := new(Int).SetBits([]Word{Word(y1), Word(y2), Word(y3)})
564 m := new(Int).SetBits([]Word{Word(m1), Word(m2), Word(m3)})
565 out := new(Int).Exp(x, y, m)
566 want := new(Int).expSlow(x, y, m)
567 if out.Cmp(want) != 0 {
568 t.Errorf("x = %#x\ny=%#x\nz=%#x\nout=%#x\nwant=%#x\ndc: 16o 16i %X %X %X |p", x, y, m, out, want, x, y, m)
569 }
570 })
571 }
572
573 func BenchmarkExp3Power(b *testing.B) {
574 const x = 3
575 for _, y := range []Word{
576 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000,
577 } {
578 b.Run(fmt.Sprintf("%#x", y), func(b *testing.B) {
579 var z nat
580 for i := 0; i < b.N; i++ {
581 z.expWW(x, y)
582 }
583 })
584 }
585 }
586
587 func fibo(n int) nat {
588 switch n {
589 case 0:
590 return nil
591 case 1:
592 return nat{1}
593 }
594 f0 := fibo(0)
595 f1 := fibo(1)
596 var f2 nat
597 for i := 1; i < n; i++ {
598 f2 = f2.add(f0, f1)
599 f0, f1, f2 = f1, f2, f0
600 }
601 return f1
602 }
603
604 var fiboNums = []string{
605 "0",
606 "55",
607 "6765",
608 "832040",
609 "102334155",
610 "12586269025",
611 "1548008755920",
612 "190392490709135",
613 "23416728348467685",
614 "2880067194370816120",
615 "354224848179261915075",
616 }
617
618 func TestFibo(t *testing.T) {
619 for i, want := range fiboNums {
620 n := i * 10
621 got := string(fibo(n).utoa(10))
622 if got != want {
623 t.Errorf("fibo(%d) failed: got %s want %s", n, got, want)
624 }
625 }
626 }
627
628 func BenchmarkFibo(b *testing.B) {
629 for i := 0; i < b.N; i++ {
630 fibo(1e0)
631 fibo(1e1)
632 fibo(1e2)
633 fibo(1e3)
634 fibo(1e4)
635 fibo(1e5)
636 }
637 }
638
639 var bitTests = []struct {
640 x string
641 i uint
642 want uint
643 }{
644 {"0", 0, 0},
645 {"0", 1, 0},
646 {"0", 1000, 0},
647
648 {"0x1", 0, 1},
649 {"0x10", 0, 0},
650 {"0x10", 3, 0},
651 {"0x10", 4, 1},
652 {"0x10", 5, 0},
653
654 {"0x8000000000000000", 62, 0},
655 {"0x8000000000000000", 63, 1},
656 {"0x8000000000000000", 64, 0},
657
658 {"0x3" + strings.Repeat("0", 32), 127, 0},
659 {"0x3" + strings.Repeat("0", 32), 128, 1},
660 {"0x3" + strings.Repeat("0", 32), 129, 1},
661 {"0x3" + strings.Repeat("0", 32), 130, 0},
662 }
663
664 func TestBit(t *testing.T) {
665 for i, test := range bitTests {
666 x := natFromString(test.x)
667 if got := x.bit(test.i); got != test.want {
668 t.Errorf("#%d: %s.bit(%d) = %v; want %v", i, test.x, test.i, got, test.want)
669 }
670 }
671 }
672
673 var stickyTests = []struct {
674 x string
675 i uint
676 want uint
677 }{
678 {"0", 0, 0},
679 {"0", 1, 0},
680 {"0", 1000, 0},
681
682 {"0x1", 0, 0},
683 {"0x1", 1, 1},
684
685 {"0x1350", 0, 0},
686 {"0x1350", 4, 0},
687 {"0x1350", 5, 1},
688
689 {"0x8000000000000000", 63, 0},
690 {"0x8000000000000000", 64, 1},
691
692 {"0x1" + strings.Repeat("0", 100), 400, 0},
693 {"0x1" + strings.Repeat("0", 100), 401, 1},
694 }
695
696 func TestSticky(t *testing.T) {
697 for i, test := range stickyTests {
698 x := natFromString(test.x)
699 if got := x.sticky(test.i); got != test.want {
700 t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i, got, test.want)
701 }
702 if test.want == 1 {
703
704 for d := uint(1); d <= 3; d++ {
705 if got := x.sticky(test.i + d); got != 1 {
706 t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i+d, got, 1)
707 }
708 }
709 }
710 }
711 }
712
713 func testSqr(t *testing.T, x nat) {
714 got := make(nat, 2*len(x))
715 want := make(nat, 2*len(x))
716 got = got.sqr(x)
717 want = want.mul(x, x)
718 if got.cmp(want) != 0 {
719 t.Errorf("basicSqr(%v), got %v, want %v", x, got, want)
720 }
721 }
722
723 func TestSqr(t *testing.T) {
724 for _, a := range prodNN {
725 if a.x != nil {
726 testSqr(t, a.x)
727 }
728 if a.y != nil {
729 testSqr(t, a.y)
730 }
731 if a.z != nil {
732 testSqr(t, a.z)
733 }
734 }
735 }
736
737 func benchmarkNatSqr(b *testing.B, nwords int) {
738 x := rndNat(nwords)
739 var z nat
740 b.ResetTimer()
741 for i := 0; i < b.N; i++ {
742 z.sqr(x)
743 }
744 }
745
746 var sqrBenchSizes = []int{
747 1, 2, 3, 5, 8, 10, 20, 30, 50, 80,
748 100, 200, 300, 500, 800,
749 1000, 10000, 100000,
750 }
751
752 func BenchmarkNatSqr(b *testing.B) {
753 for _, n := range sqrBenchSizes {
754 if isRaceBuilder && n > 1e3 {
755 continue
756 }
757 b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
758 benchmarkNatSqr(b, n)
759 })
760 }
761 }
762
763 var subMod2NTests = []struct {
764 x string
765 y string
766 n uint
767 z string
768 }{
769 {"1", "2", 0, "0"},
770 {"1", "0", 1, "1"},
771 {"0", "1", 1, "1"},
772 {"3", "5", 3, "6"},
773 {"5", "3", 3, "2"},
774
775 {"36893488147419103232", "73786976294838206463", 67, "110680464442257309697"},
776
777 {"73786976294838206463", "36893488147419103232", 67, "36893488147419103231"},
778 }
779
780 func TestNatSubMod2N(t *testing.T) {
781 for _, mode := range []string{"noalias", "aliasX", "aliasY"} {
782 t.Run(mode, func(t *testing.T) {
783 for _, tt := range subMod2NTests {
784 x0 := natFromString(tt.x)
785 y0 := natFromString(tt.y)
786 want := natFromString(tt.z)
787 x := nat(nil).set(x0)
788 y := nat(nil).set(y0)
789 var z nat
790 switch mode {
791 case "aliasX":
792 z = x
793 case "aliasY":
794 z = y
795 }
796 z = z.subMod2N(x, y, tt.n)
797 if z.cmp(want) != 0 {
798 t.Fatalf("subMod2N(%d, %d, %d) = %d, want %d", x0, y0, tt.n, z, want)
799 }
800 if mode != "aliasX" && x.cmp(x0) != 0 {
801 t.Fatalf("subMod2N(%d, %d, %d) modified x", x0, y0, tt.n)
802 }
803 if mode != "aliasY" && y.cmp(y0) != 0 {
804 t.Fatalf("subMod2N(%d, %d, %d) modified y", x0, y0, tt.n)
805 }
806 }
807 })
808 }
809 }
810
811 func BenchmarkNatSetBytes(b *testing.B) {
812 const maxLength = 128
813 lengths := []int{
814
815 8, 24, maxLength,
816
817 7, 23, maxLength - 1,
818 }
819 n := make(nat, maxLength/_W)
820 buf := make([]byte, maxLength)
821 for _, l := range lengths {
822 b.Run(fmt.Sprint(l), func(b *testing.B) {
823 for i := 0; i < b.N; i++ {
824 n.setBytes(buf[:l])
825 }
826 })
827 }
828 }
829
830 func TestNatDiv(t *testing.T) {
831 sizes := []int{
832 1, 2, 5, 8, 15, 25, 40, 65, 100,
833 200, 500, 800, 1500, 2500, 4000, 6500, 10000,
834 }
835 for _, i := range sizes {
836 for _, j := range sizes {
837 a := rndNat1(i)
838 b := rndNat1(j)
839
840 if len(b) == 1 && b[0] == 1 {
841 b[0] = 2
842 }
843
844 c := rndNat1(len(b))
845 if len(c) == len(b) && c[len(c)-1] >= b[len(b)-1] {
846 c[len(c)-1] = 0
847 c = c.norm()
848 }
849
850 x := nat(nil).mul(a, b)
851 x = x.add(x, c)
852
853 var q, r nat
854 q, r = q.div(r, x, b)
855 if q.cmp(a) != 0 {
856 t.Fatalf("wrong quotient: got %s; want %s for %s/%s", q.utoa(10), a.utoa(10), x.utoa(10), b.utoa(10))
857 }
858 if r.cmp(c) != 0 {
859 t.Fatalf("wrong remainder: got %s; want %s for %s/%s", r.utoa(10), c.utoa(10), x.utoa(10), b.utoa(10))
860 }
861 }
862 }
863 }
864
865
866
867
868 func TestIssue37499(t *testing.T) {
869
870
871
872 u := natFromString("0x2b6c385a05be027f5c22005b63c42a1165b79ff510e1706b39f8489c1d28e57bb5ba4ef9fd9387a3e344402c0a453381")
873 v := natFromString("0x2b6c385a05be027f5c22005b63c42a1165b79ff510e1706c")
874
875 q := nat(nil).make(8)
876 q.divBasic(u, v)
877 q = q.norm()
878 if s := string(q.utoa(16)); s != "fffffffffffffffffffffffffffffffffffffffffffffffb" {
879 t.Fatalf("incorrect quotient: %s", s)
880 }
881 }
882
883
884
885
886 func TestIssue42552(t *testing.T) {
887 u := natFromString("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")
888 v := natFromString("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")
889 q := nat(nil).make(16)
890 q.div(q, u, v)
891 }
892
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