import (
"fmt"
+ "io"
"os"
"rand"
"strings"
}
-// Scan is a support routine for fmt.Scanner. It accepts the formats
-// 'b' (binary), 'o' (octal), 'd' (decimal), 'x' (lowercase hexadecimal),
-// and 'X' (uppercase hexadecimal).
-func (x *Int) Scan(s fmt.ScanState, ch int) os.Error {
- var base int
+// scan sets z to the integer value corresponding to the longest possible prefix
+// read from r representing a signed integer number in a given conversion base.
+// It returns z, the actual conversion base used, and an error, if any. In the
+// error case, the value of z is undefined. The syntax follows the syntax of
+// integer literals in Go.
+//
+// The base argument must be 0 or a value from 2 through MaxBase. If the base
+// is 0, the string prefix determines the actual conversion base. A prefix of
+// ``0x'' or ``0X'' selects base 16; the ``0'' prefix selects base 8, and a
+// ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
+//
+func (z *Int) scan(r io.RuneScanner, base int) (*Int, int, os.Error) {
+ // determine sign
+ ch, _, err := r.ReadRune()
+ if err != nil {
+ return z, 0, err
+ }
+ neg := false
+ switch ch {
+ case '-':
+ neg = true
+ case '+': // nothing to do
+ default:
+ r.UnreadRune()
+ }
+
+ // determine mantissa
+ z.abs, base, err = z.abs.scan(r, base)
+ if err != nil {
+ return z, base, err
+ }
+ z.neg = len(z.abs) > 0 && neg // 0 has no sign
+
+ return z, base, nil
+}
+
+
+// Scan is a support routine for fmt.Scanner; it sets z to the value of
+// the scanned number. It accepts the formats 'b' (binary), 'o' (octal),
+// 'd' (decimal), 'x' (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
+func (z *Int) Scan(s fmt.ScanState, ch int) os.Error {
+ base := 0
switch ch {
case 'b':
base = 2
default:
return os.ErrorString("Int.Scan: invalid verb")
}
-
- ch, _, err := s.ReadRune()
- if err != nil {
- return err
- }
- neg := false
- switch ch {
- case '-':
- neg = true
- case '+': // nothing to do
- default:
- s.UnreadRune()
- }
-
- x.abs, _, err = x.abs.scan(s, base)
- if err != nil {
- return err
- }
- x.neg = len(x.abs) > 0 && neg // 0 has no sign
-
- return nil
+ _, _, err := z.scan(s, base)
+ return err
}
-// Int64 returns the int64 representation of z.
-// If z cannot be represented in an int64, the result is undefined.
+// Int64 returns the int64 representation of x.
+// If x cannot be represented in an int64, the result is undefined.
func (x *Int) Int64() int64 {
if len(x.abs) == 0 {
return 0
// and returns z and a boolean indicating success. If SetString fails,
// the value of z is undefined.
//
-// If the base argument is 0, the string prefix determines the actual
-// conversion base. A prefix of ``0x'' or ``0X'' selects base 16; the
-// ``0'' prefix selects base 8, and a ``0b'' or ``0B'' prefix selects
-// base 2. Otherwise the selected base is 10.
+// The base argument must be 0 or a value from 2 through MaxBase. If the base
+// is 0, the string prefix determines the actual conversion base. A prefix of
+// ``0x'' or ``0X'' selects base 16; the ``0'' prefix selects base 8, and a
+// ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
//
func (z *Int) SetString(s string, base int) (*Int, bool) {
- neg := false
- if len(s) > 0 {
- switch s[0] {
- case '-':
- neg = true
- fallthrough
- case '+':
- s = s[1:]
- }
- }
-
r := strings.NewReader(s)
- abs, _, err := z.abs.scan(r, base)
+ _, _, err := z.scan(r, base)
if err != nil {
return z, false
}
_, _, err = r.ReadRune()
-
- z.abs = abs
- z.neg = len(abs) > 0 && neg // 0 has no sign
- return z, err == os.EOF // err == os.EOF => scan consumed all of s
+ return z, err == os.EOF // err == os.EOF => scan consumed all of s
}
}
-func hexValue(ch int) int {
- var d int
+// MaxBase is the largest number base accepted for string conversions.
+const MaxBase = 'z' - 'a' + 10 + 1 // = hexValue('z') + 1
+
+func hexValue(ch int) Word {
+ d := MaxBase + 1 // illegal base
switch {
case '0' <= ch && ch <= '9':
d = ch - '0'
d = ch - 'a' + 10
case 'A' <= ch && ch <= 'Z':
d = ch - 'A' + 10
- default:
- return -1
}
- return d
+ return Word(d)
}
-// scan returns the natural number corresponding to the longest
-// possible prefix read from r representing a natural number in a
-// given conversion base, the actual conversion base used, and an
-// error, if any. The syntax of natural numbers follows the syntax of
+// scan sets z to the natural number corresponding to the longest possible prefix
+// read from r representing an unsigned integer in a given conversion base.
+// It returns z, the actual conversion base used, and an error, if any. In the
+// error case, the value of z is undefined. The syntax follows the syntax of
// unsigned integer literals in Go.
//
-// If the base argument is 0, the string prefix determines the actual
-// conversion base. A prefix of ``0x'' or ``0X'' selects base 16; the
-// ``0'' prefix selects base 8, and a ``0b'' or ``0B'' prefix selects
-// base 2. Otherwise the selected base is 10.
+// The base argument must be 0 or a value from 2 through MaxBase. If the base
+// is 0, the string prefix determines the actual conversion base. A prefix of
+// ``0x'' or ``0X'' selects base 16; the ``0'' prefix selects base 8, and a
+// ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
//
func (z nat) scan(r io.RuneScanner, base int) (nat, int, os.Error) {
- n := 0
+ // reject illegal bases
+ if base < 0 || base == 1 || MaxBase < base {
+ return z, 0, os.ErrorString("illegal number base")
+ }
+
+ // one char look-ahead
ch, _, err := r.ReadRune()
if err != nil {
return z, 0, err
}
+
// determine base if necessary
+ b := Word(base)
if base == 0 {
- base = 10
+ b = 10
if ch == '0' {
- n++
switch ch, _, err = r.ReadRune(); err {
case nil:
- base = 8
+ b = 8
switch ch {
case 'x', 'X':
- base = 16
+ b = 16
case 'b', 'B':
- base = 2
+ b = 2
}
- if base == 2 || base == 16 {
- n--
+ if b == 2 || b == 16 {
if ch, _, err = r.ReadRune(); err != nil {
- return z, 0, os.ErrorString("syntax error scanning binary or hexadecimal number")
+ return z, 0, err
}
}
case os.EOF:
return z, 10, nil
default:
- return z, 0, err
+ return z, 10, err
}
}
}
- // reject illegal bases
- if base < 2 || 'z'-'a'+10 < base {
- return z, 0, os.ErrorString("illegal number base")
- }
-
// convert string
+ // - group as many digits d as possible together into a "super-digit" dd with "super-base" bb
+ // - only when bb does not fit into a word anymore, do a full number mulAddWW using bb and dd
z = z.make(0)
+ bb := Word(1)
+ dd := Word(0)
for {
d := hexValue(ch)
- if 0 <= d && d < base {
- z = z.mulAddWW(z, Word(base), Word(d))
+ if d >= b {
+ r.UnreadRune() // ch does not belong to number anymore
+ break
+ }
+
+ if tmp := bb * b; tmp < bb {
+ // overflow
+ z = z.mulAddWW(z, bb, dd)
+ bb = b
+ dd = d
} else {
- r.UnreadRune()
- if n > 0 {
- break
- }
- return z, 0, os.ErrorString("syntax error scanning number")
+ bb = tmp
+ dd = dd*b + d
}
- n++
+
if ch, _, err = r.ReadRune(); err != nil {
- if err == os.EOF {
- break
+ if err != os.EOF {
+ return z, int(b), err
}
- return z, 0, err
+ break
}
}
- return z.norm(), base, nil
+ switch {
+ case bb > 1:
+ // there was at least one mantissa digit
+ z = z.mulAddWW(z, bb, dd)
+ case base == 0 && b == 8:
+ // there was only the octal prefix 0 (possibly followed by digits > 7);
+ // return base 10, not 8
+ return z, 10, nil
+ case base != 0 || b != 8:
+ // there was neither a mantissa digit nor the octal prefix 0
+ return z, int(b), os.ErrorString("syntax error scanning number")
+ }
+
+ return z.norm(), int(b), nil
}
package big
import (
+ "os"
"strings"
"testing"
)
var natScanTests = []struct {
s string // string to be scanned
+ base int // input base
x nat // expected nat
- base int // expected base
+ b int // expected base
ok bool // expected success
+ next int // next character (or 0, if at EOF)
}{
- {s: ""},
- {"0", nil, 10, true},
- {"0 ", nil, 8, true},
+ // error: illegal base
+ {base: -1},
+ {base: 1},
+ {base: 37},
+
+ // error: no mantissa
+ {},
+ {s: "?"},
+ {base: 10},
+ {base: 36},
+ {s: "?", base: 10},
{s: "0x"},
- {"08", nil, 8, true},
- {"0b1", nat{1}, 2, true},
- {"0b11000101", nat{0xc5}, 2, true},
- {"03271", nat{03271}, 8, true},
- {"10ab", nat{10}, 10, true},
- {"1234567890", nat{1234567890}, 10, true},
- {"0xdeadbeef", nat{0xdeadbeef}, 16, true},
- {"0XDEADBEEF", nat{0xdeadbeef}, 16, true},
+ {s: "345", base: 2},
+
+ // no errors
+ {"0", 0, nil, 10, true, 0},
+ {"0", 10, nil, 10, true, 0},
+ {"0", 36, nil, 36, true, 0},
+ {"1", 0, nat{1}, 10, true, 0},
+ {"1", 10, nat{1}, 10, true, 0},
+ {"0 ", 0, nil, 10, true, ' '},
+ {"08", 0, nil, 10, true, '8'},
+ {"018", 0, nat{1}, 8, true, '8'},
+ {"0b1", 0, nat{1}, 2, true, 0},
+ {"0b11000101", 0, nat{0xc5}, 2, true, 0},
+ {"03271", 0, nat{03271}, 8, true, 0},
+ {"10ab", 0, nat{10}, 10, true, 'a'},
+ {"1234567890", 0, nat{1234567890}, 10, true, 0},
+ {"xyz", 36, nat{(33*36+34)*36 + 35}, 36, true, 0},
+ {"xyz?", 36, nat{(33*36+34)*36 + 35}, 36, true, '?'},
+ {"0x", 16, nil, 16, true, 'x'},
+ {"0xdeadbeef", 0, nat{0xdeadbeef}, 16, true, 0},
+ {"0XDEADBEEF", 0, nat{0xdeadbeef}, 16, true, 0},
+ {"0xfedcba9876543213fedcba9876543212fedcba9876543211fedcba9876543210",
+ 0,
+ nat{0xfedcba9876543210, 0xfedcba9876543211, 0xfedcba9876543212, 0xfedcba9876543213},
+ 16,
+ true,
+ 0},
}
-func TestScanBase0(t *testing.T) {
+func TestScanBase(t *testing.T) {
for _, a := range natScanTests {
- x, b, err := nat(nil).scan(strings.NewReader(a.s), 0)
+ r := strings.NewReader(a.s)
+ x, b, err := nat(nil).scan(r, a.base)
if err == nil && !a.ok {
t.Errorf("scan%+v\n\texpected error", a)
}
if x.cmp(a.x) != 0 {
t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
}
- if b != a.base {
+ if b != a.b {
t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.base)
}
+ next, _, err := r.ReadRune()
+ if err == os.EOF {
+ next = 0
+ err = nil
+ }
+ if err == nil && next != a.next {
+ t.Errorf("scan%+v\n\tgot next = %q; want %q", a, next, a.next)
+ }
+ }
+}
+
+
+var pi = "3" +
+ "14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651" +
+ "32823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461" +
+ "28475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920" +
+ "96282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179" +
+ "31051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798" +
+ "60943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901" +
+ "22495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837" +
+ "29780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083" +
+ "81420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909" +
+ "21642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151" +
+ "55748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035" +
+ "63707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104" +
+ "75216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992" +
+ "45863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818" +
+ "34797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548" +
+ "16136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179" +
+ "04946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886" +
+ "26945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645" +
+ "99581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745" +
+ "53050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382" +
+ "68683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244" +
+ "13654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767" +
+ "88952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288" +
+ "79710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821" +
+ "68299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610" +
+ "21359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435" +
+ "06430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675" +
+ "14269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672" +
+ "21825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539" +
+ "05796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007" +
+ "23055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816" +
+ "90915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398" +
+ "31501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064" +
+ "20467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325" +
+ "97463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100" +
+ "44929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915" +
+ "44110104468232527162010526522721116603966655730925471105578537634668206531098965269186205647693125705863566201" +
+ "85581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318" +
+ "58676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797" +
+ "27082668306343285878569830523580893306575740679545716377525420211495576158140025012622859413021647155097925923" +
+ "09907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111" +
+ "79042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043" +
+ "06332175182979866223717215916077166925474873898665494945011465406284336639379003976926567214638530673609657120" +
+ "91807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862" +
+ "94726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939" +
+ "78054193414473774418426312986080998886874132604721569516239658645730216315981931951673538129741677294786724229" +
+ "24654366800980676928238280689964004824354037014163149658979409243237896907069779422362508221688957383798623001" +
+ "59377647165122893578601588161755782973523344604281512627203734314653197777416031990665541876397929334419521541" +
+ "34189948544473456738316249934191318148092777710386387734317720754565453220777092120190516609628049092636019759" +
+ "88281613323166636528619326686336062735676303544776280350450777235547105859548702790814356240145171806246436267" +
+ "94561275318134078330336254232783944975382437205835311477119926063813346776879695970309833913077109870408591337"
+
+
+// Test case for BenchmarkScanPi.
+func TestScanPi(t *testing.T) {
+ var x nat
+ z, _, err := x.scan(strings.NewReader(pi), 10)
+ if err != nil {
+ t.Errorf("scanning pi: %s", err)
+ }
+ if s := z.decimalString(); s != pi {
+ t.Errorf("scanning pi: got %s", s)
+ }
+}
+
+
+func BenchmarkScanPi(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ var x nat
+ x.scan(strings.NewReader(pi), 10)
}
}