From b9caa4ac56f306e4195dcbf5db1afd831a6049fa Mon Sep 17 00:00:00 2001 From: Robert Griesemer Date: Mon, 3 May 2010 18:48:05 -0700 Subject: [PATCH] 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 --- src/pkg/big/int.go | 235 ++++++++++++++++++---------- src/pkg/big/int_test.go | 235 +++++++++++++++++++--------- src/pkg/big/nat.go | 8 +- src/pkg/bignum/integer.go | 2 +- src/pkg/crypto/rsa/pkcs1v15.go | 10 +- src/pkg/crypto/rsa/pkcs1v15_test.go | 2 +- src/pkg/crypto/rsa/rsa.go | 8 +- test/bench/pidigits.go | 4 +- 8 files changed, 332 insertions(+), 172 deletions(-) diff --git a/src/pkg/big/int.go b/src/pkg/big/int.go index 4d1be5db697..23829247870 100755 --- a/src/pkg/big/int.go +++ b/src/pkg/big/int.go @@ -14,8 +14,11 @@ type Int struct { } -// New allocates and returns a new Int set to x. -func (z *Int) New(x int64) *Int { +var intOne = &Int{false, natOne} + + +// SetInt64 sets z to x and returns z. +func (z *Int) SetInt64(x int64) *Int { z.neg = false if x < 0 { z.neg = true @@ -27,7 +30,9 @@ func (z *Int) New(x int64) *Int { // NewInt allocates and returns a new Int set to x. -func NewInt(x int64) *Int { return new(Int).New(x) } +func NewInt(x int64) *Int { + return new(Int).SetInt64(x) +} // Set sets z to x. @@ -38,57 +43,51 @@ func (z *Int) Set(x *Int) *Int { } -// Add computes z = x+y. +// Add sets z to the sum x+y and returns z. func (z *Int) Add(x, y *Int) *Int { + neg := x.neg if x.neg == y.neg { // x + y == x + y // (-x) + (-y) == -(x + y) - z.neg = x.neg z.abs = z.abs.add(x.abs, y.abs) } else { // x + (-y) == x - y == -(y - x) // (-x) + y == y - x == -(x - y) if x.abs.cmp(y.abs) >= 0 { - z.neg = x.neg z.abs = z.abs.sub(x.abs, y.abs) } else { - z.neg = !x.neg + neg = !neg z.abs = z.abs.sub(y.abs, x.abs) } } - if len(z.abs) == 0 { - z.neg = false // 0 has no sign - } + z.neg = len(z.abs) > 0 && neg // 0 has no sign return z } -// Sub computes z = x-y. +// Sub sets z to the difference x-y and returns z. func (z *Int) Sub(x, y *Int) *Int { + neg := x.neg if x.neg != y.neg { // x - (-y) == x + y // (-x) - y == -(x + y) - z.neg = x.neg z.abs = z.abs.add(x.abs, y.abs) } else { // x - y == x - y == -(y - x) // (-x) - (-y) == y - x == -(x - y) if x.abs.cmp(y.abs) >= 0 { - z.neg = x.neg z.abs = z.abs.sub(x.abs, y.abs) } else { - z.neg = !x.neg + neg = !neg z.abs = z.abs.sub(y.abs, x.abs) } } - if len(z.abs) == 0 { - z.neg = false // 0 has no sign - } + z.neg = len(z.abs) > 0 && neg // 0 has no sign return z } -// Mul computes z = x*y. +// Mul sets z to the product x*y and returns z. func (z *Int) Mul(x, y *Int) *Int { // x * y == x * y // x * (-y) == -(x * y) @@ -100,38 +99,117 @@ func (z *Int) Mul(x, y *Int) *Int { } -// Div calculates q = (x-r)/y and sets z = q. -func (z *Int) Div(x, y *Int) *Int { - r := new(Int) - div(z, r, x, y) +// Quo sets z to the quotient x/y for y != 0 and returns z. +// If y == 0, a division-by-zero run-time panic occurs. +// See QuoRem for more details. +func (z *Int) Quo(x, y *Int) *Int { + z.abs, _ = z.abs.div(nil, x.abs, y.abs) + z.neg = len(z.abs) > 0 && x.neg != y.neg // 0 has no sign return z } -// Mod calculates q = (x-r)/y and sets z = r. -func (z *Int) Mod(x, y *Int) *Int { - q := new(Int) - div(q, z, x, y) +// Rem sets z to the remainder x%y for y != 0 and returns z. +// If y == 0, a division-by-zero run-time panic occurs. +// See QuoRem for more details. +func (z *Int) Rem(x, y *Int) *Int { + _, z.abs = nat(nil).div(z.abs, x.abs, y.abs) + z.neg = len(z.abs) > 0 && x.neg // 0 has no sign return z } -// DivMod calculates q = (x-r)/y and sets z = q. (It returns z, r.) -func (z *Int) DivMod(x, y, r *Int) (*Int, *Int) { - div(z, r, x, y) +// QuoRem sets z to the quotient x/y and r to the remainder x%y +// and returns the pair (z, r) for y != 0. +// If y == 0, a division-by-zero run-time panic occurs. +// +// QuoRem implements T-division and modulus (like Go): +// +// q = x/y with the result truncated to zero +// r = x - y*q +// +// (See Daan Leijen, ``Division and Modulus for Computer Scientists''.) +// +func (z *Int) QuoRem(x, y, r *Int) (*Int, *Int) { + z.abs, r.abs = z.abs.div(r.abs, x.abs, y.abs) + z.neg, r.neg = len(z.abs) > 0 && x.neg != y.neg, len(r.abs) > 0 && x.neg // 0 has no sign return z, r } -func div(q, r, x, y *Int) { - q.neg = x.neg != y.neg - r.neg = x.neg - q.abs, r.abs = q.abs.div(r.abs, x.abs, y.abs) - return +// Div sets z to the quotient x/y for y != 0 and returns z. +// If y == 0, a division-by-zero run-time panic occurs. +// See DivMod for more details. +func (z *Int) Div(x, y *Int) *Int { + y_neg := y.neg // z may be an alias for y + var r Int + z.QuoRem(x, y, &r) + if r.neg { + if y_neg { + z.Add(z, intOne) + } else { + z.Sub(z, intOne) + } + } + return z } -// Neg computes z = -x. +// Mod sets z to the modulus x%y for y != 0 and returns z. +// If y == 0, a division-by-zero run-time panic occurs. +// See DivMod for more details. +func (z *Int) Mod(x, y *Int) *Int { + y0 := y // save y + if z == y || alias(z.abs, y.abs) { + y0 = new(Int).Set(y) + } + var q Int + q.QuoRem(x, y, z) + if z.neg { + if y0.neg { + z.Sub(z, y0) + } else { + z.Add(z, y0) + } + } + return z +} + + +// DivMod sets z to the quotient x div y and m to the modulus x mod y +// and returns the pair (z, m) for y != 0. +// If y == 0, a division-by-zero run-time panic occurs. +// +// DivMod implements Euclidian division and modulus (unlike Go): +// +// q = x div y such that +// m = x - y*q with 0 <= m < |q| +// +// (See Raymond T. Boute, ``The Euclidian definition of the functions +// div and mod''. ACM Transactions on Programming Languages and +// Systems (TOPLAS), 14(2):127-144, New York, NY, USA, 4/1992. +// ACM press.) +// +func (z *Int) DivMod(x, y, m *Int) (*Int, *Int) { + y0 := y // save y + if z == y || alias(z.abs, y.abs) { + y0 = new(Int).Set(y) + } + z.QuoRem(x, y, m) + if m.neg { + if y0.neg { + z.Add(z, intOne) + m.Sub(m, y0) + } else { + z.Sub(z, intOne) + m.Add(m, y0) + } + } + return z, m +} + + +// Neg computes the negation z = -x. func (z *Int) Neg(x *Int) *Int { z.abs = z.abs.set(x.abs) z.neg = len(z.abs) > 0 && !x.neg // 0 has no sign @@ -139,7 +217,7 @@ func (z *Int) Neg(x *Int) *Int { } -// Cmp compares x and y. The result is +// Cmp compares x and y and returns: // // -1 if x < y // 0 if x == y @@ -205,26 +283,23 @@ func (z *Int) SetString(s string, base int) (*Int, bool) { goto Error } + neg := false if s[0] == '-' { - z.neg = true + neg = true s = s[1:] - } else { - z.neg = false } z.abs, _, scanned = z.abs.scan(s, base) if scanned != len(s) { goto Error } - if len(z.abs) == 0 { - z.neg = false // 0 has no sign - } + z.neg = len(z.abs) > 0 && neg // 0 has no sign return z, true Error: - z.neg = false z.abs = nil + z.neg = false return z, false } @@ -234,7 +309,6 @@ Error: func (z *Int) SetBytes(b []byte) *Int { s := int(_S) z.abs = z.abs.make((len(b) + s - 1) / s) - z.neg = false j := 0 for len(b) >= s { @@ -262,7 +336,7 @@ func (z *Int) SetBytes(b []byte) *Int { } z.abs = z.abs.norm() - + z.neg = false return z } @@ -289,14 +363,10 @@ func (z *Int) Bytes() []byte { } -// Len returns the length of the absolute value of z in bits. Zero is -// considered to have a length of zero. -func (z *Int) Len() int { - if len(z.abs) == 0 { - return 0 - } - - return len(z.abs)*_W - int(leadingZeros(z.abs[len(z.abs)-1])) +// BitLen returns the length of the absolute value of z in bits. +// The bit length of 0 is 0. +func (z *Int) BitLen() int { + return z.abs.bitLen() } @@ -304,7 +374,7 @@ func (z *Int) Len() int { // See Knuth, volume 2, section 4.6.3. func (z *Int) Exp(x, y, m *Int) *Int { if y.neg || len(y.abs) == 0 { - z.New(1) + z.SetInt64(1) z.neg = x.neg return z } @@ -315,7 +385,7 @@ func (z *Int) Exp(x, y, m *Int) *Int { } z.abs = z.abs.expNN(x.abs, y.abs, mWords) - z.neg = x.neg && y.abs[0]&1 == 1 + z.neg = len(z.abs) > 0 && x.neg && y.abs[0]&1 == 1 // 0 has no sign return z } @@ -326,12 +396,12 @@ func (z *Int) Exp(x, y, m *Int) *Int { // If either a or b is not positive, GcdInt sets d = x = y = 0. func GcdInt(d, x, y, a, b *Int) { if a.neg || b.neg { - d.New(0) + d.SetInt64(0) if x != nil { - x.New(0) + x.SetInt64(0) } if y != nil { - y.New(0) + y.SetInt64(0) } return } @@ -340,9 +410,9 @@ func GcdInt(d, x, y, a, b *Int) { B := new(Int).Set(b) X := new(Int) - Y := new(Int).New(1) + Y := new(Int).SetInt64(1) - lastX := new(Int).New(1) + lastX := new(Int).SetInt64(1) lastY := new(Int) q := new(Int) @@ -350,7 +420,7 @@ func GcdInt(d, x, y, a, b *Int) { for len(B.abs) > 0 { r := new(Int) - q, r = q.DivMod(A, B, r) + q, r = q.QuoRem(A, B, r) A, B = B, r @@ -382,13 +452,15 @@ func GcdInt(d, x, y, a, b *Int) { // ProbablyPrime performs n Miller-Rabin tests to check whether z is prime. // If it returns true, z is prime with probability 1 - 1/4^n. // If it returns false, z is not prime. -func ProbablyPrime(z *Int, n int) bool { return !z.neg && z.abs.probablyPrime(n) } +func ProbablyPrime(z *Int, n int) bool { + return !z.neg && z.abs.probablyPrime(n) +} // Lsh sets z = x << n and returns z. func (z *Int) Lsh(x *Int, n uint) *Int { - z.neg = x.neg z.abs = z.abs.shl(x.abs, n) + z.neg = x.neg return z } @@ -397,18 +469,19 @@ func (z *Int) Lsh(x *Int, n uint) *Int { func (z *Int) Rsh(x *Int, n uint) *Int { if x.neg { // (-x) >> s == ^(x-1) >> s == ^((x-1) >> s) == -(((x-1) >> s) + 1) - z.neg = true t := z.abs.sub(x.abs, natOne) // no underflow because |x| > 0 t = t.shr(t, n) z.abs = t.add(t, natOne) + z.neg = true // z cannot be zero if x is negative return z } - z.neg = false z.abs = z.abs.shr(x.abs, n) + z.neg = false return z } + // And sets z = x & y and returns z. func (z *Int) And(x, y *Int) *Int { if x.neg == y.neg { @@ -416,14 +489,14 @@ func (z *Int) And(x, y *Int) *Int { // (-x) & (-y) == ^(x-1) & ^(y-1) == ^((x-1) | (y-1)) == -(((x-1) | (y-1)) + 1) x1 := nat{}.sub(x.abs, natOne) y1 := z.abs.sub(y.abs, natOne) - z.neg = true z.abs = z.abs.add(z.abs.or(x1, y1), natOne) + z.neg = true // z cannot be zero if x and y are negative return z } // x & y == x & y - z.neg = false z.abs = z.abs.and(x.abs, y.abs) + z.neg = false return z } @@ -434,8 +507,8 @@ func (z *Int) And(x, y *Int) *Int { // x & (-y) == x & ^(y-1) == x &^ (y-1) y1 := z.abs.sub(y.abs, natOne) - z.neg = false z.abs = z.abs.andNot(x.abs, y1) + z.neg = false return z } @@ -447,29 +520,29 @@ func (z *Int) AndNot(x, y *Int) *Int { // (-x) &^ (-y) == ^(x-1) &^ ^(y-1) == ^(x-1) & (y-1) == (y-1) &^ (x-1) x1 := nat{}.sub(x.abs, natOne) y1 := z.abs.sub(y.abs, natOne) - z.neg = false z.abs = z.abs.andNot(y1, x1) + z.neg = false return z } // x &^ y == x &^ y - z.neg = false z.abs = z.abs.andNot(x.abs, y.abs) + z.neg = false return z } if x.neg { // (-x) &^ y == ^(x-1) &^ y == ^(x-1) & ^y == ^((x-1) | y) == -(((x-1) | y) + 1) x1 := z.abs.sub(x.abs, natOne) - z.neg = true z.abs = z.abs.add(z.abs.or(x1, y.abs), natOne) + z.neg = true // z cannot be zero if x is negative and y is positive return z } // x &^ (-y) == x &^ ^(y-1) == x & (y-1) y1 := z.abs.add(y.abs, natOne) - z.neg = false z.abs = z.abs.and(x.abs, y1) + z.neg = false return z } @@ -481,14 +554,14 @@ func (z *Int) Or(x, y *Int) *Int { // (-x) | (-y) == ^(x-1) | ^(y-1) == ^((x-1) & (y-1)) == -(((x-1) & (y-1)) + 1) x1 := nat{}.sub(x.abs, natOne) y1 := z.abs.sub(y.abs, natOne) - z.neg = true z.abs = z.abs.add(z.abs.and(x1, y1), natOne) + z.neg = true // z cannot be zero if x and y are negative return z } // x | y == x | y - z.neg = false z.abs = z.abs.or(x.abs, y.abs) + z.neg = false return z } @@ -499,8 +572,8 @@ func (z *Int) Or(x, y *Int) *Int { // x | (-y) == x | ^(y-1) == ^((y-1) &^ x) == -(^((y-1) &^ x) + 1) y1 := z.abs.sub(y.abs, natOne) - z.neg = true z.abs = z.abs.add(z.abs.andNot(y1, x.abs), natOne) + z.neg = true // z cannot be zero if one of x or y is negative return z } @@ -512,26 +585,26 @@ func (z *Int) Xor(x, y *Int) *Int { // (-x) ^ (-y) == ^(x-1) ^ ^(y-1) == (x-1) ^ (y-1) x1 := nat{}.sub(x.abs, natOne) y1 := z.abs.sub(y.abs, natOne) - z.neg = false z.abs = z.abs.xor(x1, y1) + z.neg = false return z } // x ^ y == x ^ y - z.neg = false z.abs = z.abs.xor(x.abs, y.abs) + z.neg = false return z } // x.neg != y.neg if x.neg { - x, y = y, x // | is symmetric + x, y = y, x // ^ is symmetric } // x ^ (-y) == x ^ ^(y-1) == ^(x ^ (y-1)) == -((x ^ (y-1)) + 1) y1 := z.abs.sub(y.abs, natOne) - z.neg = true z.abs = z.abs.add(z.abs.xor(x.abs, y1), natOne) + z.neg = true // z cannot be zero if only one of x or y is negative return z } @@ -540,13 +613,13 @@ func (z *Int) Xor(x, y *Int) *Int { func (z *Int) Not(x *Int) *Int { if x.neg { // ^(-x) == ^(^(x-1)) == x-1 - z.neg = false z.abs = z.abs.sub(x.abs, natOne) + z.neg = false return z } // ^x == -x-1 == -(x+1) - z.neg = true z.abs = z.abs.add(x.abs, natOne) + z.neg = true // z cannot be zero if x is positive return z } diff --git a/src/pkg/big/int_test.go b/src/pkg/big/int_test.go index deacdfac4f2..fe2974308da 100755 --- a/src/pkg/big/int_test.go +++ b/src/pkg/big/int_test.go @@ -11,9 +11,13 @@ import ( "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 @@ type argZZ struct { 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 @@ func TestSetZ(t *testing.T) { 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 TestSetZ(t *testing.T) { 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 @@ func TestSetString(t *testing.T) { 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 @@ func TestSetString(t *testing.T) { 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 @@ func TestSetString(t *testing.T) { } -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 TestBytes(t *testing.T) { } -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 @@ func checkDiv(x, y []byte) bool { } 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 @@ func checkDiv(x, y []byte) bool { } -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 @@ var divTests = []divTest{ } -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 TestDiv(t *testing.T) { } -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 @@ func TestDivStepD6(t *testing.T) { 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 @@ func TestDivStepD6(t *testing.T) { } -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 @@ var expTests = []expTest{ 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 @@ func TestExp(t *testing.T) { } 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 @@ var gcdTests = []gcdTest{ 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 @@ func TestRsh(t *testing.T) { 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 @@ func TestRshSelf(t *testing.T) { 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 @@ func TestLsh(t *testing.T) { 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 @@ func TestLshSelf(t *testing.T) { 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 @@ func TestLshRsh(t *testing.T) { 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 @@ func TestLshRsh(t *testing.T) { 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 @@ var bitwiseTests = []bitwiseTest{ 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"}, diff --git a/src/pkg/big/nat.go b/src/pkg/big/nat.go index fd4c49f5cf5..1cad23777b5 100755 --- a/src/pkg/big/nat.go +++ b/src/pkg/big/nat.go @@ -356,7 +356,7 @@ func karatsuba(z, x, y nat) { // alias returns true if x and y share the same base array. func alias(x, y nat) bool { - return &x[0:cap(x)][cap(x)-1] == &y[0:cap(y)][cap(y)-1] + return cap(x) > 0 && cap(y) > 0 && &x[0:cap(x)][cap(x)-1] == &y[0:cap(y)][cap(y)-1] } @@ -412,7 +412,7 @@ func (z nat) mul(x, y nat) nat { // m >= n > 1 // determine if z can be reused - if len(z) > 0 && (alias(z, x) || alias(z, y)) { + if alias(z, x) || alias(z, y) { z = nil // z is an alias for x or y - cannot reuse } @@ -757,7 +757,7 @@ func (z nat) shl(x nat, s uint) nat { // determine if z can be reused // TODO(gri) change shlVW so we don't need this - if len(z) > 0 && alias(z, x) { + if alias(z, x) { z = nil // z is an alias for x - cannot reuse } @@ -780,7 +780,7 @@ func (z nat) shr(x nat, s uint) nat { // determine if z can be reused // TODO(gri) change shrVW so we don't need this - if len(z) > 0 && alias(z, x) { + if alias(z, x) { z = nil // z is an alias for x - cannot reuse } diff --git a/src/pkg/bignum/integer.go b/src/pkg/bignum/integer.go index 873b2664a7f..a8d26829d18 100644 --- a/src/pkg/bignum/integer.go +++ b/src/pkg/bignum/integer.go @@ -253,7 +253,7 @@ func (x *Integer) QuoRem(y *Integer) (*Integer, *Integer) { // Div and Mod implement Euclidian division and modulus: // // q = x.Div(y) -// r = x.Mod(y) with: 0 <= r < |q| and: y = x*q + r +// r = x.Mod(y) with: 0 <= r < |q| and: x = y*q + r // // (Raymond T. Boute, ``The Euclidian definition of the functions // div and mod''. ACM Transactions on Programming Languages and diff --git a/src/pkg/crypto/rsa/pkcs1v15.go b/src/pkg/crypto/rsa/pkcs1v15.go index cfad9545448..5fd25d58c75 100644 --- a/src/pkg/crypto/rsa/pkcs1v15.go +++ b/src/pkg/crypto/rsa/pkcs1v15.go @@ -18,7 +18,7 @@ import ( // WARNING: use of this function to encrypt plaintexts other than session keys // is dangerous. Use RSA OAEP in new protocols. func EncryptPKCS1v15(rand io.Reader, pub *PublicKey, msg []byte) (out []byte, err os.Error) { - k := (pub.N.Len() + 7) / 8 + k := (pub.N.BitLen() + 7) / 8 if len(msg) > k-11 { err = MessageTooLongError{} return @@ -66,7 +66,7 @@ func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (out [ // Encryption Standard PKCS #1'', Daniel Bleichenbacher, Advances in Cryptology // (Crypto '98), func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []byte, key []byte) (err os.Error) { - k := (priv.N.Len() + 7) / 8 + k := (priv.N.BitLen() + 7) / 8 if k-(len(key)+3+8) < 0 { err = DecryptionError{} return @@ -83,7 +83,7 @@ func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []by } func decryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (valid int, msg []byte, err os.Error) { - k := (priv.N.Len() + 7) / 8 + k := (priv.N.BitLen() + 7) / 8 if k < 11 { err = DecryptionError{} return @@ -179,7 +179,7 @@ func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash PKCS1v15Hash, hashed [] } tLen := len(prefix) + hashLen - k := (priv.N.Len() + 7) / 8 + k := (priv.N.BitLen() + 7) / 8 if k < tLen+11 { return nil, MessageTooLongError{} } @@ -212,7 +212,7 @@ func VerifyPKCS1v15(pub *PublicKey, hash PKCS1v15Hash, hashed []byte, sig []byte } tLen := len(prefix) + hashLen - k := (pub.N.Len() + 7) / 8 + k := (pub.N.BitLen() + 7) / 8 if k < tLen+11 { err = VerificationError{} return diff --git a/src/pkg/crypto/rsa/pkcs1v15_test.go b/src/pkg/crypto/rsa/pkcs1v15_test.go index 69edeaa2eed..bfc12be2850 100644 --- a/src/pkg/crypto/rsa/pkcs1v15_test.go +++ b/src/pkg/crypto/rsa/pkcs1v15_test.go @@ -67,7 +67,7 @@ func TestEncryptPKCS1v15(t *testing.T) { if err != nil { t.Errorf("Failed to open /dev/urandom") } - k := (rsaPrivateKey.N.Len() + 7) / 8 + k := (rsaPrivateKey.N.BitLen() + 7) / 8 tryEncryptDecrypt := func(in []byte, blind bool) bool { if len(in) > k-11 { diff --git a/src/pkg/crypto/rsa/rsa.go b/src/pkg/crypto/rsa/rsa.go index 941b061b5f5..c7a8d2053d8 100644 --- a/src/pkg/crypto/rsa/rsa.go +++ b/src/pkg/crypto/rsa/rsa.go @@ -50,11 +50,11 @@ func randomPrime(rand io.Reader, bits int) (p *big.Int, err os.Error) { // randomNumber returns a uniform random value in [0, max). func randomNumber(rand io.Reader, max *big.Int) (n *big.Int, err os.Error) { - k := (max.Len() + 7) / 8 + k := (max.BitLen() + 7) / 8 // r is the number of bits in the used in the most significant byte of // max. - r := uint(max.Len() % 8) + r := uint(max.BitLen() % 8) if r == 0 { r = 8 } @@ -244,7 +244,7 @@ func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int { // twice the hash length plus 2. func EncryptOAEP(hash hash.Hash, rand io.Reader, pub *PublicKey, msg []byte, label []byte) (out []byte, err os.Error) { hash.Reset() - k := (pub.N.Len() + 7) / 8 + k := (pub.N.BitLen() + 7) / 8 if len(msg) > k-2*hash.Size()-2 { err = MessageTooLongError{} return @@ -365,7 +365,7 @@ func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.E // DecryptOAEP decrypts ciphertext using RSA-OAEP. // If rand != nil, DecryptOAEP uses RSA blinding to avoid timing side-channel attacks. func DecryptOAEP(hash hash.Hash, rand io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) (msg []byte, err os.Error) { - k := (priv.N.Len() + 7) / 8 + k := (priv.N.BitLen() + 7) / 8 if len(ciphertext) > k || k < hash.Size()*2+2 { err = DecryptionError{} diff --git a/test/bench/pidigits.go b/test/bench/pidigits.go index a05515028ae..dcfb502ce2a 100644 --- a/test/bench/pidigits.go +++ b/test/bench/pidigits.go @@ -81,8 +81,8 @@ func extract_digit() int64 { func next_term(k int64) { // TODO(eds) If big.Int ever gets a Scale method, y2 and bigk could be int64 - y2.New(k*2 + 1) - bigk.New(k) + y2.SetInt64(k*2 + 1) + bigk.SetInt64(k) tmp1.Lsh(numer, 1) accum.Add(accum, tmp1)