big: completed set of Int division routines & cleanups
- renamed Len -> BitLen, simplified implementation
- renamed old Div, Mod, DivMod -> Que, Rem, QuoRem
- implemented Div, Mod, DivMod (Euclidian definition, more
useful in a mathematical context)
- fixed a bug in Exp (-0 was possible)
- added extra tests to check normalized results everywhere
- uniformly set Int.neg flag at the end of computations
- minor cosmetic cleanups
- ran all tests
R=rsc
CC=golang-dev
https://golang.org/cl/1091041
diff --git a/src/pkg/big/int_test.go b/src/pkg/big/int_test.go
index deacdfa..fe29743 100755
--- a/src/pkg/big/int_test.go
+++ b/src/pkg/big/int_test.go
@@ -11,9 +11,13 @@
"testing/quick"
)
-func newZ(x int64) *Int {
- var z Int
- return z.New(x)
+
+func isNormalized(x *Int) bool {
+ if len(x.abs) == 0 {
+ return !x.neg
+ }
+ // len(x.abs) > 0
+ return x.abs[len(x.abs)-1] != 0
}
@@ -24,20 +28,20 @@
var sumZZ = []argZZ{
- argZZ{newZ(0), newZ(0), newZ(0)},
- argZZ{newZ(1), newZ(1), newZ(0)},
- argZZ{newZ(1111111110), newZ(123456789), newZ(987654321)},
- argZZ{newZ(-1), newZ(-1), newZ(0)},
- argZZ{newZ(864197532), newZ(-123456789), newZ(987654321)},
- argZZ{newZ(-1111111110), newZ(-123456789), newZ(-987654321)},
+ argZZ{NewInt(0), NewInt(0), NewInt(0)},
+ argZZ{NewInt(1), NewInt(1), NewInt(0)},
+ argZZ{NewInt(1111111110), NewInt(123456789), NewInt(987654321)},
+ argZZ{NewInt(-1), NewInt(-1), NewInt(0)},
+ argZZ{NewInt(864197532), NewInt(-123456789), NewInt(987654321)},
+ argZZ{NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)},
}
var prodZZ = []argZZ{
- argZZ{newZ(0), newZ(0), newZ(0)},
- argZZ{newZ(0), newZ(1), newZ(0)},
- argZZ{newZ(1), newZ(1), newZ(1)},
- argZZ{newZ(-991 * 991), newZ(991), newZ(-991)},
+ argZZ{NewInt(0), NewInt(0), NewInt(0)},
+ argZZ{NewInt(0), NewInt(1), NewInt(0)},
+ argZZ{NewInt(1), NewInt(1), NewInt(1)},
+ argZZ{NewInt(-991 * 991), NewInt(991), NewInt(-991)},
// TODO(gri) add larger products
}
@@ -46,6 +50,9 @@
for _, a := range sumZZ {
var z Int
z.Set(a.z)
+ if !isNormalized(&z) {
+ t.Errorf("%v is not normalized", z)
+ }
if (&z).Cmp(a.z) != 0 {
t.Errorf("got z = %v; want %v", z, a.z)
}
@@ -56,6 +63,9 @@
func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) {
var z Int
f(&z, a.x, a.y)
+ if !isNormalized(&z) {
+ t.Errorf("msg: %v is not normalized", z, msg)
+ }
if (&z).Cmp(a.z) != 0 {
t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z)
}
@@ -186,7 +196,7 @@
for i, test := range fromStringTests {
n1, ok1 := new(Int).SetString(test.in, test.base)
n2, ok2 := n2.SetString(test.in, test.base)
- expected := new(Int).New(test.out)
+ expected := NewInt(test.out)
if ok1 != test.ok || ok2 != test.ok {
t.Errorf("#%d (input '%s') ok incorrect (should be %t)", i, test.in, test.ok)
continue
@@ -195,6 +205,13 @@
continue
}
+ if ok1 && !isNormalized(n1) {
+ t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n1)
+ }
+ if ok2 && !isNormalized(n2) {
+ t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n2)
+ }
+
if n1.Cmp(expected) != 0 {
t.Errorf("#%d (input '%s') got: %s want: %d\n", i, test.in, n1, test.out)
}
@@ -205,33 +222,77 @@
}
-type divSignsTest struct {
+type divisionSignsTest struct {
x, y int64
- q, r int64
+ q, r int64 // T-division
+ d, m int64 // Euclidian division
}
-// These examples taken from the Go Language Spec, section "Arithmetic operators"
-var divSignsTests = []divSignsTest{
- divSignsTest{5, 3, 1, 2},
- divSignsTest{-5, 3, -1, -2},
- divSignsTest{5, -3, -1, 2},
- divSignsTest{-5, -3, 1, -2},
- divSignsTest{1, 2, 0, 1},
+// Examples from the Go Language Spec, section "Arithmetic operators"
+var divisionSignsTests = []divisionSignsTest{
+ divisionSignsTest{5, 3, 1, 2, 1, 2},
+ divisionSignsTest{-5, 3, -1, -2, -2, 1},
+ divisionSignsTest{5, -3, -1, 2, -1, 2},
+ divisionSignsTest{-5, -3, 1, -2, 2, 1},
+ divisionSignsTest{1, 2, 0, 1, 0, 1},
+ divisionSignsTest{8, 4, 2, 0, 2, 0},
}
-func TestDivSigns(t *testing.T) {
- for i, test := range divSignsTests {
- x := new(Int).New(test.x)
- y := new(Int).New(test.y)
- r := new(Int)
- q, r := new(Int).DivMod(x, y, r)
- expectedQ := new(Int).New(test.q)
- expectedR := new(Int).New(test.r)
+func TestDivisionSigns(t *testing.T) {
+ for i, test := range divisionSignsTests {
+ x := NewInt(test.x)
+ y := NewInt(test.y)
+ q := NewInt(test.q)
+ r := NewInt(test.r)
+ d := NewInt(test.d)
+ m := NewInt(test.m)
- if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
- t.Errorf("#%d: got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
+ q1 := new(Int).Quo(x, y)
+ r1 := new(Int).Rem(x, y)
+ if !isNormalized(q1) {
+ t.Errorf("#%d Quo: %v is not normalized", i, *q1)
+ }
+ if !isNormalized(r1) {
+ t.Errorf("#%d Rem: %v is not normalized", i, *r1)
+ }
+ if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 {
+ t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r)
+ }
+
+ q2, r2 := new(Int).QuoRem(x, y, new(Int))
+ if !isNormalized(q2) {
+ t.Errorf("#%d Quo: %v is not normalized", i, *q2)
+ }
+ if !isNormalized(r2) {
+ t.Errorf("#%d Rem: %v is not normalized", i, *r2)
+ }
+ if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 {
+ t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r)
+ }
+
+ d1 := new(Int).Div(x, y)
+ m1 := new(Int).Mod(x, y)
+ if !isNormalized(d1) {
+ t.Errorf("#%d Div: %v is not normalized", i, *d1)
+ }
+ if !isNormalized(m1) {
+ t.Errorf("#%d Mod: %v is not normalized", i, *m1)
+ }
+ if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 {
+ t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m)
+ }
+
+ d2, m2 := new(Int).DivMod(x, y, new(Int))
+ if !isNormalized(d2) {
+ t.Errorf("#%d Div: %v is not normalized", i, *d2)
+ }
+ if !isNormalized(m2) {
+ t.Errorf("#%d Mod: %v is not normalized", i, *m2)
+ }
+ if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 {
+ t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m)
}
}
}
@@ -273,7 +334,7 @@
}
-func checkDiv(x, y []byte) bool {
+func checkQuo(x, y []byte) bool {
u := new(Int).SetBytes(x)
v := new(Int).SetBytes(y)
@@ -282,7 +343,7 @@
}
r := new(Int)
- q, r := new(Int).DivMod(u, v, r)
+ q, r := new(Int).QuoRem(u, v, r)
if r.Cmp(v) >= 0 {
return false
@@ -296,20 +357,20 @@
}
-type divTest struct {
+type quoTest struct {
x, y string
q, r string
}
-var divTests = []divTest{
- divTest{
+var quoTests = []quoTest{
+ quoTest{
"476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
"9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
"50911",
"1",
},
- divTest{
+ quoTest{
"11510768301994997771168",
"1328165573307167369775",
"8",
@@ -318,19 +379,19 @@
}
-func TestDiv(t *testing.T) {
- if err := quick.Check(checkDiv, nil); err != nil {
+func TestQuo(t *testing.T) {
+ if err := quick.Check(checkQuo, nil); err != nil {
t.Error(err)
}
- for i, test := range divTests {
+ for i, test := range quoTests {
x, _ := new(Int).SetString(test.x, 10)
y, _ := new(Int).SetString(test.y, 10)
expectedQ, _ := new(Int).SetString(test.q, 10)
expectedR, _ := new(Int).SetString(test.r, 10)
r := new(Int)
- q, r := new(Int).DivMod(x, y, r)
+ q, r := new(Int).QuoRem(x, y, r)
if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
@@ -339,7 +400,7 @@
}
-func TestDivStepD6(t *testing.T) {
+func TestQuoStepD6(t *testing.T) {
// See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises
// a code path which only triggers 1 in 10^{-19} cases.
@@ -347,7 +408,7 @@
v := &Int{false, nat{5, 2 + 1<<(_W-1), 1 << (_W - 1)}}
r := new(Int)
- q, r := new(Int).DivMod(u, v, r)
+ q, r := new(Int).QuoRem(u, v, r)
const expectedQ64 = "18446744073709551613"
const expectedR64 = "3138550867693340382088035895064302439801311770021610913807"
const expectedQ32 = "4294967293"
@@ -359,35 +420,38 @@
}
-type lenTest struct {
+type bitLenTest struct {
in string
out int
}
-var lenTests = []lenTest{
- lenTest{"0", 0},
- lenTest{"1", 1},
- lenTest{"2", 2},
- lenTest{"4", 3},
- lenTest{"0x8000", 16},
- lenTest{"0x80000000", 32},
- lenTest{"0x800000000000", 48},
- lenTest{"0x8000000000000000", 64},
- lenTest{"0x80000000000000000000", 80},
+var bitLenTests = []bitLenTest{
+ bitLenTest{"-1", 1},
+ bitLenTest{"0", 0},
+ bitLenTest{"1", 1},
+ bitLenTest{"2", 2},
+ bitLenTest{"4", 3},
+ bitLenTest{"0xabc", 12},
+ bitLenTest{"0x8000", 16},
+ bitLenTest{"0x80000000", 32},
+ bitLenTest{"0x800000000000", 48},
+ bitLenTest{"0x8000000000000000", 64},
+ bitLenTest{"0x80000000000000000000", 80},
+ bitLenTest{"-0x4000000000000000000000", 87},
}
-func TestLen(t *testing.T) {
- for i, test := range lenTests {
- n, ok := new(Int).SetString(test.in, 0)
+func TestBitLen(t *testing.T) {
+ for i, test := range bitLenTests {
+ x, ok := new(Int).SetString(test.in, 0)
if !ok {
t.Errorf("#%d test input invalid: %s", i, test.in)
continue
}
- if n.Len() != test.out {
- t.Errorf("#%d got %d want %d\n", i, n.Len(), test.out)
+ if n := x.BitLen(); n != test.out {
+ t.Errorf("#%d got %d want %d\n", i, n, test.out)
}
}
}
@@ -404,6 +468,7 @@
expTest{"-5", "0", "", "-1"},
expTest{"5", "1", "", "5"},
expTest{"-5", "1", "", "-5"},
+ expTest{"-2", "3", "2", "0"},
expTest{"5", "2", "", "25"},
expTest{"1", "65537", "2", "1"},
expTest{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
@@ -436,13 +501,16 @@
}
if !ok1 || !ok2 || !ok3 || !ok4 {
- t.Errorf("#%d error in input", i)
+ t.Errorf("#%d: error in input", i)
continue
}
z := new(Int).Exp(x, y, m)
+ if !isNormalized(z) {
+ t.Errorf("#%d: %v is not normalized", i, *z)
+ }
if z.Cmp(out) != 0 {
- t.Errorf("#%d got %s want %s", i, z, out)
+ t.Errorf("#%d: got %s want %s", i, z, out)
}
}
}
@@ -478,16 +546,16 @@
func TestGcd(t *testing.T) {
for i, test := range gcdTests {
- a := new(Int).New(test.a)
- b := new(Int).New(test.b)
+ a := NewInt(test.a)
+ b := NewInt(test.b)
x := new(Int)
y := new(Int)
d := new(Int)
- expectedX := new(Int).New(test.x)
- expectedY := new(Int).New(test.y)
- expectedD := new(Int).New(test.d)
+ expectedX := NewInt(test.x)
+ expectedY := NewInt(test.y)
+ expectedD := NewInt(test.d)
GcdInt(d, x, y, a, b)
@@ -594,8 +662,11 @@
expected, _ := new(Int).SetString(test.out, 10)
out := new(Int).Rsh(in, test.shift)
+ if !isNormalized(out) {
+ t.Errorf("#%d: %v is not normalized", i, *out)
+ }
if out.Cmp(expected) != 0 {
- t.Errorf("#%d got %s want %s", i, out, expected)
+ t.Errorf("#%d: got %s want %s", i, out, expected)
}
}
}
@@ -607,8 +678,11 @@
expected, _ := new(Int).SetString(test.out, 10)
z.Rsh(z, test.shift)
+ if !isNormalized(z) {
+ t.Errorf("#%d: %v is not normalized", i, *z)
+ }
if z.Cmp(expected) != 0 {
- t.Errorf("#%d got %s want %s", i, z, expected)
+ t.Errorf("#%d: got %s want %s", i, z, expected)
}
}
}
@@ -643,8 +717,11 @@
expected, _ := new(Int).SetString(test.out, 10)
out := new(Int).Lsh(in, test.shift)
+ if !isNormalized(out) {
+ t.Errorf("#%d: %v is not normalized", i, *out)
+ }
if out.Cmp(expected) != 0 {
- t.Errorf("#%d got %s want %s", i, out, expected)
+ t.Errorf("#%d: got %s want %s", i, out, expected)
}
}
}
@@ -656,8 +733,11 @@
expected, _ := new(Int).SetString(test.out, 10)
z.Lsh(z, test.shift)
+ if !isNormalized(z) {
+ t.Errorf("#%d: %v is not normalized", i, *z)
+ }
if z.Cmp(expected) != 0 {
- t.Errorf("#%d got %s want %s", i, z, expected)
+ t.Errorf("#%d: got %s want %s", i, z, expected)
}
}
}
@@ -669,8 +749,11 @@
out := new(Int).Lsh(in, test.shift)
out = out.Rsh(out, test.shift)
+ if !isNormalized(out) {
+ t.Errorf("#%d: %v is not normalized", i, *out)
+ }
if in.Cmp(out) != 0 {
- t.Errorf("#%d got %s want %s", i, out, in)
+ t.Errorf("#%d: got %s want %s", i, out, in)
}
}
for i, test := range lshTests {
@@ -678,8 +761,11 @@
out := new(Int).Lsh(in, test.shift)
out.Rsh(out, test.shift)
+ if !isNormalized(out) {
+ t.Errorf("#%d: %v is not normalized", i, *out)
+ }
if in.Cmp(out) != 0 {
- t.Errorf("#%d got %s want %s", i, out, in)
+ t.Errorf("#%d: got %s want %s", i, out, in)
}
}
}
@@ -721,6 +807,7 @@
bitwiseTest{"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
bitwiseTest{"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
bitwiseTest{"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
+ bitwiseTest{"-0xAF", "-0x50", "0x00", "-0xFF", "-0x01", "-0x01"},
bitwiseTest{"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
bitwiseTest{"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
bitwiseTest{"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
