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# Source file src/math/big/nat_test.go

## Documentation: math/big

```     1  // Copyright 2009 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  package big
6
7  import (
8  	"fmt"
9  	"runtime"
10  	"strings"
11  	"testing"
12  )
13
14  var cmpTests = []struct {
15  	x, y nat
16  	r    int
17  }{
18  	{nil, nil, 0},
19  	{nil, nat(nil), 0},
20  	{nat(nil), nil, 0},
21  	{nat(nil), nat(nil), 0},
22  	{nat{0}, nat{0}, 0},
23  	{nat{0}, nat{1}, -1},
24  	{nat{1}, nat{0}, 1},
25  	{nat{1}, nat{1}, 0},
26  	{nat{0, _M}, nat{1}, 1},
27  	{nat{1}, nat{0, _M}, -1},
28  	{nat{1, _M}, nat{0, _M}, 1},
29  	{nat{0, _M}, nat{1, _M}, -1},
30  	{nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1},
31  	{nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1},
32  }
33
34  func TestCmp(t *testing.T) {
35  	for i, a := range cmpTests {
36  		r := a.x.cmp(a.y)
37  		if r != a.r {
38  			t.Errorf("#%d got r = %v; want %v", i, r, a.r)
39  		}
40  	}
41  }
42
43  type funNN func(z, x, y nat) nat
44  type argNN struct {
45  	z, x, y nat
46  }
47
48  var sumNN = []argNN{
49  	{},
50  	{nat{1}, nil, nat{1}},
51  	{nat{1111111110}, nat{123456789}, nat{987654321}},
52  	{nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}},
53  	{nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}},
54  	{nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}},
55  }
56
57  var prodNN = []argNN{
58  	{},
59  	{nil, nil, nil},
60  	{nil, nat{991}, nil},
61  	{nat{991}, nat{991}, nat{1}},
62  	{nat{991 * 991}, nat{991}, nat{991}},
63  	{nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}},
64  	{nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}},
65  	{nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}},
66  	// 3^100 * 3^28 = 3^128
67  	{
68  		natFromString("11790184577738583171520872861412518665678211592275841109096961"),
69  		natFromString("515377520732011331036461129765621272702107522001"),
70  		natFromString("22876792454961"),
71  	},
72  	// z = 111....1 (70000 digits)
73  	// x = 10^(99*700) + ... + 10^1400 + 10^700 + 1
74  	// y = 111....1 (700 digits, larger than Karatsuba threshold on 32-bit and 64-bit)
75  	{
76  		natFromString(strings.Repeat("1", 70000)),
77  		natFromString("1" + strings.Repeat(strings.Repeat("0", 699)+"1", 99)),
78  		natFromString(strings.Repeat("1", 700)),
79  	},
80  	// z = 111....1 (20000 digits)
81  	// x = 10^10000 + 1
82  	// y = 111....1 (10000 digits)
83  	{
84  		natFromString(strings.Repeat("1", 20000)),
85  		natFromString("1" + strings.Repeat("0", 9999) + "1"),
86  		natFromString(strings.Repeat("1", 10000)),
87  	},
88  }
89
90  func natFromString(s string) nat {
91  	x, _, _, err := nat(nil).scan(strings.NewReader(s), 0, false)
92  	if err != nil {
93  		panic(err)
94  	}
95  	return x
96  }
97
98  func TestSet(t *testing.T) {
99  	for _, a := range sumNN {
100  		z := nat(nil).set(a.z)
101  		if z.cmp(a.z) != 0 {
102  			t.Errorf("got z = %v; want %v", z, a.z)
103  		}
104  	}
105  }
106
107  func testFunNN(t *testing.T, msg string, f funNN, a argNN) {
108  	z := f(nil, a.x, a.y)
109  	if z.cmp(a.z) != 0 {
110  		t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z)
111  	}
112  }
113
114  func TestFunNN(t *testing.T) {
115  	for _, a := range sumNN {
116  		arg := a
118
119  		arg = argNN{a.z, a.y, a.x}
121
122  		arg = argNN{a.x, a.z, a.y}
123  		testFunNN(t, "sub", nat.sub, arg)
124
125  		arg = argNN{a.y, a.z, a.x}
126  		testFunNN(t, "sub symmetric", nat.sub, arg)
127  	}
128
129  	for _, a := range prodNN {
130  		arg := a
131  		testFunNN(t, "mul", nat.mul, arg)
132
133  		arg = argNN{a.z, a.y, a.x}
134  		testFunNN(t, "mul symmetric", nat.mul, arg)
135  	}
136  }
137
138  var mulRangesN = []struct {
139  	a, b uint64
140  	prod string
141  }{
142  	{0, 0, "0"},
143  	{1, 1, "1"},
144  	{1, 2, "2"},
145  	{1, 3, "6"},
146  	{10, 10, "10"},
147  	{0, 100, "0"},
148  	{0, 1e9, "0"},
149  	{1, 0, "1"},                    // empty range
150  	{100, 1, "1"},                  // empty range
151  	{1, 10, "3628800"},             // 10!
152  	{1, 20, "2432902008176640000"}, // 20!
153  	{1, 100,
154  		"933262154439441526816992388562667004907159682643816214685929" +
155  			"638952175999932299156089414639761565182862536979208272237582" +
156  			"51185210916864000000000000000000000000", // 100!
157  	},
158  }
159
160  func TestMulRangeN(t *testing.T) {
161  	for i, r := range mulRangesN {
162  		prod := string(nat(nil).mulRange(r.a, r.b).utoa(10))
163  		if prod != r.prod {
164  			t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
165  		}
166  	}
167  }
168
169  // allocBytes returns the number of bytes allocated by invoking f.
170  func allocBytes(f func()) uint64 {
171  	var stats runtime.MemStats
173  	t := stats.TotalAlloc
174  	f()
176  	return stats.TotalAlloc - t
177  }
178
179  // TestMulUnbalanced tests that multiplying numbers of different lengths
180  // does not cause deep recursion and in turn allocate too much memory.
181  // Test case for issue 3807.
182  func TestMulUnbalanced(t *testing.T) {
183  	defer runtime.GOMAXPROCS(runtime.GOMAXPROCS(1))
184  	x := rndNat(50000)
185  	y := rndNat(40)
186  	allocSize := allocBytes(func() {
187  		nat(nil).mul(x, y)
188  	})
189  	inputSize := uint64(len(x)+len(y)) * _S
190  	if ratio := allocSize / uint64(inputSize); ratio > 10 {
191  		t.Errorf("multiplication uses too much memory (%d > %d times the size of inputs)", allocSize, ratio)
192  	}
193  }
194
195  func rndNat(n int) nat {
196  	return nat(rndV(n)).norm()
197  }
198
199  func BenchmarkMul(b *testing.B) {
200  	mulx := rndNat(1e4)
201  	muly := rndNat(1e4)
202  	b.ResetTimer()
203  	for i := 0; i < b.N; i++ {
204  		var z nat
205  		z.mul(mulx, muly)
206  	}
207  }
208
209  func TestNLZ(t *testing.T) {
210  	var x Word = _B >> 1
211  	for i := 0; i <= _W; i++ {
212  		if int(nlz(x)) != i {
213  			t.Errorf("failed at %x: got %d want %d", x, nlz(x), i)
214  		}
215  		x >>= 1
216  	}
217  }
218
219  type shiftTest struct {
220  	in    nat
221  	shift uint
222  	out   nat
223  }
224
225  var leftShiftTests = []shiftTest{
226  	{nil, 0, nil},
227  	{nil, 1, nil},
228  	{natOne, 0, natOne},
229  	{natOne, 1, natTwo},
230  	{nat{1 << (_W - 1)}, 1, nat{0}},
231  	{nat{1 << (_W - 1), 0}, 1, nat{0, 1}},
232  }
233
234  func TestShiftLeft(t *testing.T) {
235  	for i, test := range leftShiftTests {
236  		var z nat
237  		z = z.shl(test.in, test.shift)
238  		for j, d := range test.out {
239  			if j >= len(z) || z[j] != d {
240  				t.Errorf("#%d: got: %v want: %v", i, z, test.out)
241  				break
242  			}
243  		}
244  	}
245  }
246
247  var rightShiftTests = []shiftTest{
248  	{nil, 0, nil},
249  	{nil, 1, nil},
250  	{natOne, 0, natOne},
251  	{natOne, 1, nil},
252  	{natTwo, 1, natOne},
253  	{nat{0, 1}, 1, nat{1 << (_W - 1)}},
254  	{nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}},
255  }
256
257  func TestShiftRight(t *testing.T) {
258  	for i, test := range rightShiftTests {
259  		var z nat
260  		z = z.shr(test.in, test.shift)
261  		for j, d := range test.out {
262  			if j >= len(z) || z[j] != d {
263  				t.Errorf("#%d: got: %v want: %v", i, z, test.out)
264  				break
265  			}
266  		}
267  	}
268  }
269
270  func BenchmarkZeroShifts(b *testing.B) {
271  	x := rndNat(800)
272
273  	b.Run("Shl", func(b *testing.B) {
274  		for i := 0; i < b.N; i++ {
275  			var z nat
276  			z.shl(x, 0)
277  		}
278  	})
279  	b.Run("ShlSame", func(b *testing.B) {
280  		for i := 0; i < b.N; i++ {
281  			x.shl(x, 0)
282  		}
283  	})
284
285  	b.Run("Shr", func(b *testing.B) {
286  		for i := 0; i < b.N; i++ {
287  			var z nat
288  			z.shr(x, 0)
289  		}
290  	})
291  	b.Run("ShrSame", func(b *testing.B) {
292  		for i := 0; i < b.N; i++ {
293  			x.shr(x, 0)
294  		}
295  	})
296  }
297
298  type modWTest struct {
299  	in       string
300  	dividend string
301  	out      string
302  }
303
304  var modWTests32 = []modWTest{
305  	{"23492635982634928349238759823742", "252341", "220170"},
306  }
307
308  var modWTests64 = []modWTest{
309  	{"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
310  }
311
312  func runModWTests(t *testing.T, tests []modWTest) {
313  	for i, test := range tests {
314  		in, _ := new(Int).SetString(test.in, 10)
315  		d, _ := new(Int).SetString(test.dividend, 10)
316  		out, _ := new(Int).SetString(test.out, 10)
317
318  		r := in.abs.modW(d.abs[0])
319  		if r != out.abs[0] {
320  			t.Errorf("#%d failed: got %d want %s", i, r, out)
321  		}
322  	}
323  }
324
325  func TestModW(t *testing.T) {
326  	if _W >= 32 {
327  		runModWTests(t, modWTests32)
328  	}
329  	if _W >= 64 {
330  		runModWTests(t, modWTests64)
331  	}
332  }
333
334  var montgomeryTests = []struct {
335  	x, y, m      string
336  	k0           uint64
337  	out32, out64 string
338  }{
339  	{
340  		"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
341  		"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
342  		"0xfffffffffffffffffffffffffffffffffffffffffffffffff",
343  		1,
344  		"0x1000000000000000000000000000000000000000000",
345  		"0x10000000000000000000000000000000000",
346  	},
347  	{
348  		"0x000000000ffffff5",
349  		"0x000000000ffffff0",
350  		"0x0000000010000001",
351  		0xff0000000fffffff,
352  		"0x000000000bfffff4",
353  		"0x0000000003400001",
354  	},
355  	{
356  		"0x0000000080000000",
357  		"0x00000000ffffffff",
358  		"0x1000000000000001",
359  		0xfffffffffffffff,
360  		"0x0800000008000001",
361  		"0x0800000008000001",
362  	},
363  	{
364  		"0x0000000080000000",
365  		"0x0000000080000000",
366  		"0xffffffff00000001",
367  		0xfffffffeffffffff,
368  		"0xbfffffff40000001",
369  		"0xbfffffff40000001",
370  	},
371  	{
372  		"0x0000000080000000",
373  		"0x0000000080000000",
374  		"0x00ffffff00000001",
375  		0xfffffeffffffff,
376  		"0xbfffff40000001",
377  		"0xbfffff40000001",
378  	},
379  	{
380  		"0x0000000080000000",
381  		"0x0000000080000000",
382  		"0x0000ffff00000001",
383  		0xfffeffffffff,
384  		"0xbfff40000001",
385  		"0xbfff40000001",
386  	},
387  	{
388  		"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
389  		"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
390  		"0x33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
392  		"0x04eb0e11d72329dc0915f86784820fc403275bf2f6620a20e0dd344c5cd0875e50deb5",
393  		"0x0d7144739a7d8e11d72329dc0915f86784820fc403275bf2f61ed96f35dd34dbb3d6a0",
394  	},
395  	{
396  		"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444",
397  		"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc",
398  		"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
400  		"0x5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715",
402  	},
403  }
404
405  func TestMontgomery(t *testing.T) {
406  	one := NewInt(1)
407  	_B := new(Int).Lsh(one, _W)
408  	for i, test := range montgomeryTests {
409  		x := natFromString(test.x)
410  		y := natFromString(test.y)
411  		m := natFromString(test.m)
412  		for len(x) < len(m) {
413  			x = append(x, 0)
414  		}
415  		for len(y) < len(m) {
416  			y = append(y, 0)
417  		}
418
419  		if x.cmp(m) > 0 {
420  			_, r := nat(nil).div(nil, x, m)
421  			t.Errorf("#%d: x > m (0x%s > 0x%s; use 0x%s)", i, x.utoa(16), m.utoa(16), r.utoa(16))
422  		}
423  		if y.cmp(m) > 0 {
424  			_, r := nat(nil).div(nil, x, m)
425  			t.Errorf("#%d: y > m (0x%s > 0x%s; use 0x%s)", i, y.utoa(16), m.utoa(16), r.utoa(16))
426  		}
427
428  		var out nat
429  		if _W == 32 {
430  			out = natFromString(test.out32)
431  		} else {
432  			out = natFromString(test.out64)
433  		}
434
435  		// t.Logf("#%d: len=%d\n", i, len(m))
436
437  		// check output in table
438  		xi := &Int{abs: x}
439  		yi := &Int{abs: y}
440  		mi := &Int{abs: m}
441  		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)
442  		if out.cmp(p.abs.norm()) != 0 {
443  			t.Errorf("#%d: out in table=0x%s, computed=0x%s", i, out.utoa(16), p.abs.norm().utoa(16))
444  		}
445
446  		// check k0 in table
447  		k := new(Int).Mod(&Int{abs: m}, _B)
448  		k = new(Int).Sub(_B, k)
449  		k = new(Int).Mod(k, _B)
450  		k0 := Word(new(Int).ModInverse(k, _B).Uint64())
451  		if k0 != Word(test.k0) {
452  			t.Errorf("#%d: k0 in table=%#x, computed=%#x\n", i, test.k0, k0)
453  		}
454
455  		// check montgomery with correct k0 produces correct output
456  		z := nat(nil).montgomery(x, y, m, k0, len(m))
457  		z = z.norm()
458  		if z.cmp(out) != 0 {
459  			t.Errorf("#%d: got 0x%s want 0x%s", i, z.utoa(16), out.utoa(16))
460  		}
461  	}
462  }
463
464  var expNNTests = []struct {
465  	x, y, m string
466  	out     string
467  }{
468  	{"0", "0", "0", "1"},
469  	{"0", "0", "1", "0"},
470  	{"1", "1", "1", "0"},
471  	{"2", "1", "1", "0"},
472  	{"2", "2", "1", "0"},
473  	{"10", "100000000000", "1", "0"},
474  	{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
475  	{"0x8000000000000000", "2", "6719", "4944"},
476  	{"0x8000000000000000", "3", "6719", "5447"},
477  	{"0x8000000000000000", "1000", "6719", "1603"},
478  	{"0x8000000000000000", "1000000", "6719", "3199"},
479  	{
480  		"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
481  		"298472983472983471903246121093472394872319615612417471234712061",
482  		"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
483  		"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
484  	},
485  	{
486  		"11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379",
487  		"426343618817810911523",
488  		"444747819283133684179",
489  		"42",
490  	},
491  }
492
493  func TestExpNN(t *testing.T) {
494  	for i, test := range expNNTests {
495  		x := natFromString(test.x)
496  		y := natFromString(test.y)
497  		out := natFromString(test.out)
498
499  		var m nat
500  		if len(test.m) > 0 {
501  			m = natFromString(test.m)
502  		}
503
504  		z := nat(nil).expNN(x, y, m)
505  		if z.cmp(out) != 0 {
506  			t.Errorf("#%d got %s want %s", i, z.utoa(10), out.utoa(10))
507  		}
508  	}
509  }
510
511  func BenchmarkExp3Power(b *testing.B) {
512  	const x = 3
513  	for _, y := range []Word{
514  		0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000,
515  	} {
516  		b.Run(fmt.Sprintf("%#x", y), func(b *testing.B) {
517  			var z nat
518  			for i := 0; i < b.N; i++ {
519  				z.expWW(x, y)
520  			}
521  		})
522  	}
523  }
524
525  func fibo(n int) nat {
526  	switch n {
527  	case 0:
528  		return nil
529  	case 1:
530  		return nat{1}
531  	}
532  	f0 := fibo(0)
533  	f1 := fibo(1)
534  	var f2 nat
535  	for i := 1; i < n; i++ {
537  		f0, f1, f2 = f1, f2, f0
538  	}
539  	return f1
540  }
541
542  var fiboNums = []string{
543  	"0",
544  	"55",
545  	"6765",
546  	"832040",
547  	"102334155",
548  	"12586269025",
549  	"1548008755920",
550  	"190392490709135",
551  	"23416728348467685",
552  	"2880067194370816120",
553  	"354224848179261915075",
554  }
555
556  func TestFibo(t *testing.T) {
557  	for i, want := range fiboNums {
558  		n := i * 10
559  		got := string(fibo(n).utoa(10))
560  		if got != want {
561  			t.Errorf("fibo(%d) failed: got %s want %s", n, got, want)
562  		}
563  	}
564  }
565
566  func BenchmarkFibo(b *testing.B) {
567  	for i := 0; i < b.N; i++ {
568  		fibo(1e0)
569  		fibo(1e1)
570  		fibo(1e2)
571  		fibo(1e3)
572  		fibo(1e4)
573  		fibo(1e5)
574  	}
575  }
576
577  var bitTests = []struct {
578  	x    string
579  	i    uint
580  	want uint
581  }{
582  	{"0", 0, 0},
583  	{"0", 1, 0},
584  	{"0", 1000, 0},
585
586  	{"0x1", 0, 1},
587  	{"0x10", 0, 0},
588  	{"0x10", 3, 0},
589  	{"0x10", 4, 1},
590  	{"0x10", 5, 0},
591
592  	{"0x8000000000000000", 62, 0},
593  	{"0x8000000000000000", 63, 1},
594  	{"0x8000000000000000", 64, 0},
595
596  	{"0x3" + strings.Repeat("0", 32), 127, 0},
597  	{"0x3" + strings.Repeat("0", 32), 128, 1},
598  	{"0x3" + strings.Repeat("0", 32), 129, 1},
599  	{"0x3" + strings.Repeat("0", 32), 130, 0},
600  }
601
602  func TestBit(t *testing.T) {
603  	for i, test := range bitTests {
604  		x := natFromString(test.x)
605  		if got := x.bit(test.i); got != test.want {
606  			t.Errorf("#%d: %s.bit(%d) = %v; want %v", i, test.x, test.i, got, test.want)
607  		}
608  	}
609  }
610
611  var stickyTests = []struct {
612  	x    string
613  	i    uint
614  	want uint
615  }{
616  	{"0", 0, 0},
617  	{"0", 1, 0},
618  	{"0", 1000, 0},
619
620  	{"0x1", 0, 0},
621  	{"0x1", 1, 1},
622
623  	{"0x1350", 0, 0},
624  	{"0x1350", 4, 0},
625  	{"0x1350", 5, 1},
626
627  	{"0x8000000000000000", 63, 0},
628  	{"0x8000000000000000", 64, 1},
629
630  	{"0x1" + strings.Repeat("0", 100), 400, 0},
631  	{"0x1" + strings.Repeat("0", 100), 401, 1},
632  }
633
634  func TestSticky(t *testing.T) {
635  	for i, test := range stickyTests {
636  		x := natFromString(test.x)
637  		if got := x.sticky(test.i); got != test.want {
638  			t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i, got, test.want)
639  		}
640  		if test.want == 1 {
641  			// all subsequent i's should also return 1
642  			for d := uint(1); d <= 3; d++ {
643  				if got := x.sticky(test.i + d); got != 1 {
644  					t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i+d, got, 1)
645  				}
646  			}
647  		}
648  	}
649  }
650
651  func testSqr(t *testing.T, x nat) {
652  	got := make(nat, 2*len(x))
653  	want := make(nat, 2*len(x))
654  	got = got.sqr(x)
655  	want = want.mul(x, x)
656  	if got.cmp(want) != 0 {
657  		t.Errorf("basicSqr(%v), got %v, want %v", x, got, want)
658  	}
659  }
660
661  func TestSqr(t *testing.T) {
662  	for _, a := range prodNN {
663  		if a.x != nil {
664  			testSqr(t, a.x)
665  		}
666  		if a.y != nil {
667  			testSqr(t, a.y)
668  		}
669  		if a.z != nil {
670  			testSqr(t, a.z)
671  		}
672  	}
673  }
674
675  func benchmarkNatSqr(b *testing.B, nwords int) {
676  	x := rndNat(nwords)
677  	var z nat
678  	b.ResetTimer()
679  	for i := 0; i < b.N; i++ {
680  		z.sqr(x)
681  	}
682  }
683
684  var sqrBenchSizes = []int{1, 2, 3, 5, 8, 10, 20, 30, 50, 80, 100, 200, 300, 500, 800, 1000}
685
686  func BenchmarkNatSqr(b *testing.B) {
687  	for _, n := range sqrBenchSizes {
688  		if isRaceBuilder && n > 1e3 {
689  			continue
690  		}
691  		b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
692  			benchmarkNatSqr(b, n)
693  		})
694  	}
695  }
696
697  func BenchmarkNatSetBytes(b *testing.B) {
698  	const maxLength = 128
699  	lengths := []int{
700  		// No remainder:
701  		8, 24, maxLength,
702  		// With remainder:
703  		7, 23, maxLength - 1,
704  	}
705  	n := make(nat, maxLength/_W) // ensure n doesn't need to grow during the test
706  	buf := make([]byte, maxLength)
707  	for _, l := range lengths {
708  		b.Run(fmt.Sprint(l), func(b *testing.B) {
709  			for i := 0; i < b.N; i++ {
710  				n.setBytes(buf[:l])
711  			}
712  		})
713  	}
714  }
715
```

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