math/big: improve scan test and benchmark

Add a few more test cases for scanning (integer conversion),
which were helpful in debugging some upcoming changes.

BenchmarkScan currently times converting the value 10**N
represented in base B back into []Word form.
When B = 10, the text is 1 followed by many zeros, which
could hit a "multiply by zero" special case when processing
many digit chunks, misrepresenting the actual time required
depending on whether that case is optimized.

Change the benchmark to use 9**N, which is about as big and
will not cause runs of zeros in any of the tested bases.

The benchmark comparison below is not showing faster code,
since of course the code is not changing at all here. Instead,
it is showing that the new benchmark work is roughly the same
size as the old benchmark work.

goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
                      │     old     │                new                 │
                      │   sec/op    │   sec/op     vs base               │
ScanPi-12               43.35µ ± 1%   43.59µ ± 1%       ~ (p=0.069 n=15)
Scan/10/Base2-12        202.3n ± 2%   193.7n ± 1%  -4.25% (p=0.000 n=15)
Scan/100/Base2-12       1.512µ ± 3%   1.447µ ± 1%  -4.30% (p=0.000 n=15)
Scan/1000/Base2-12      15.06µ ± 2%   14.33µ ± 0%  -4.83% (p=0.000 n=15)
Scan/10000/Base2-12     188.0µ ± 5%   177.3µ ± 1%  -5.65% (p=0.000 n=15)
Scan/100000/Base2-12    5.814m ± 3%   5.382m ± 1%  -7.43% (p=0.000 n=15)
Scan/10/Base8-12        78.57n ± 2%   75.02n ± 1%  -4.52% (p=0.000 n=15)
Scan/100/Base8-12       548.2n ± 2%   526.8n ± 1%  -3.90% (p=0.000 n=15)
Scan/1000/Base8-12      5.674µ ± 2%   5.421µ ± 0%  -4.46% (p=0.000 n=15)
Scan/10000/Base8-12     94.42µ ± 1%   88.61µ ± 1%  -6.15% (p=0.000 n=15)
Scan/100000/Base8-12    4.906m ± 2%   4.498m ± 3%  -8.31% (p=0.000 n=15)
Scan/10/Base10-12       73.42n ± 1%   69.56n ± 0%  -5.26% (p=0.000 n=15)
Scan/100/Base10-12      511.9n ± 1%   488.2n ± 0%  -4.63% (p=0.000 n=15)
Scan/1000/Base10-12     5.254µ ± 2%   5.009µ ± 0%  -4.66% (p=0.000 n=15)
Scan/10000/Base10-12    90.22µ ± 2%   84.52µ ± 0%  -6.32% (p=0.000 n=15)
Scan/100000/Base10-12   4.842m ± 3%   4.471m ± 3%  -7.65% (p=0.000 n=15)
Scan/10/Base16-12       62.28n ± 1%   58.70n ± 1%  -5.75% (p=0.000 n=15)
Scan/100/Base16-12      398.6n ± 0%   377.9n ± 1%  -5.19% (p=0.000 n=15)
Scan/1000/Base16-12     4.108µ ± 1%   3.782µ ± 0%  -7.94% (p=0.000 n=15)
Scan/10000/Base16-12    83.78µ ± 2%   80.51µ ± 1%  -3.90% (p=0.000 n=15)
Scan/100000/Base16-12   5.080m ± 3%   4.698m ± 3%  -7.53% (p=0.000 n=15)
geomean                 12.41µ        11.74µ       -5.36%

Change-Id: If3ce290ecc7f38672f11b42fd811afb53dee665d
Reviewed-on: https://go-review.googlesource.com/c/go/+/650639
Reviewed-by: Alan Donovan <adonovan@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Auto-Submit: Russ Cox <rsc@golang.org>

src/math/big/intconv_test.go

@@ -7,6 +7,7 @@ package big
 import (
 	"bytes"
 	"fmt"
+	"math/rand/v2"
 	"testing"
 )
 
@@ -389,12 +390,14 @@ func TestFormat(t *testing.T) {
 	}
 }
 
-var scanTests = []struct {
+type scanTest struct {
 	input     string
 	format    string
 	output    string
 	remaining int
-}{
+}
+
+var scanTests = []scanTest{
 	{"1010", "%b", "10", 0},
 	{"0b1010", "%v", "10", 0},
 	{"12", "%o", "10", 0},
@@ -410,6 +413,25 @@ var scanTests = []struct {
 	{"0 ", "%v", "0", 1},
 	{"2+3", "%v", "2", 2},
 	{"0XABC 12", "%v", "2748", 3},
+
+	{"10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444", "%x", "72999049881955123498258745691204661198291656115976958889267080286388402675338838184094604981077942396458276955120179409196748346461468914795561487752253275293347599221664790586512596660792869956", 0},
+	{"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1", "%x", "1167984798111281975972139931059274579172666497855631342228273284582214442805421410945513679697247078343332431249286160621687557589604464869034163736183926240549918956767671325412748661204059352801", 0},
+	{"5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715", "%x", "419981998319789881681348172155240145539175961318447822049735313481433836043208347786919222066492311384432264836938599791362288343314139526391998172436831830624710446410781662672086936222288181013", 0},
+	{"92fcad4b5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d799c32fe2f3cc5422f9711078d51a3797eb18e691295293284d8f5e69caf6decddfe1df6", "%x", "670619546945481998414061201992255225716434798957375727890607516800039934374391281275121813279544891602026798031004764406015624866771554937391445093144221697436880587924204655403711377861305572854", 0},
+	{"10000000000000000000000200000000000000000000003000000000000000000000040000000000000000000000500000000000000000000006", "%d", "10000000000000000000000200000000000000000000003000000000000000000000040000000000000000000000500000000000000000000006", 0},
+}
+
+func init() {
+	for i := range 200 {
+		d := make([]byte, i+1)
+		for j := range d {
+			d[j] = '0' + rand.N(byte(10))
+		}
+		if d[0] == '0' {
+			d[0] = '1'
+		}
+		scanTests = append(scanTests, scanTest{input: string(d), format: "%d", output: string(d)})
+	}
 }
 
 func TestScan(t *testing.T) {

src/math/big/natconv_test.go

@@ -353,7 +353,7 @@ func BenchmarkScan(b *testing.B) {
 	stk := getStack()
 	defer stk.free()
 
-	const x = 10
+	const x = 9 // avoid tested bases, in case runs of 0s are handled specially
 	for _, base := range []int{2, 8, 10, 16} {
 		for _, y := range []Word{10, 100, 1000, 10000, 100000} {
 			if isRaceBuilder && y > 1000 {