From a4599efcfb1ca5345efbb4c185ac0094b312f472 Mon Sep 17 00:00:00 2001 From: Robert Griesemer Date: Thu, 21 Jan 2016 16:48:14 -0800 Subject: [PATCH] cmd/compile: update vendored copy of math/big - obtained by running sh vendor.bash - contains updated tests and some bug fixes for Montgomery mult. (not used by compiler) - for consistency of math/big versions only Change-Id: Ib47e48d5b7f6d0e05d7837b1bc74bdb03f2b094e Reviewed-on: https://go-review.googlesource.com/18831 Run-TryBot: Robert Griesemer TryBot-Result: Gobot Gobot Reviewed-by: Brad Fitzpatrick --- src/cmd/compile/internal/big/int.go | 2 +- src/cmd/compile/internal/big/int_test.go | 27 ++++++++++- src/cmd/compile/internal/big/nat.go | 58 ++++++++++++++---------- src/cmd/compile/internal/big/nat_test.go | 6 +++ 4 files changed, 67 insertions(+), 26 deletions(-) diff --git a/src/cmd/compile/internal/big/int.go b/src/cmd/compile/internal/big/int.go index 16b7cd131b..67ab7042ff 100644 --- a/src/cmd/compile/internal/big/int.go +++ b/src/cmd/compile/internal/big/int.go @@ -273,7 +273,7 @@ func (z *Int) Mod(x, y *Int) *Int { // DivMod implements Euclidean division and modulus (unlike Go): // // q = x div y such that -// m = x - y*q with 0 <= m < |q| +// m = x - y*q with 0 <= m < |y| // // (See Raymond T. Boute, ``The Euclidean definition of the functions // div and mod''. ACM Transactions on Programming Languages and diff --git a/src/cmd/compile/internal/big/int_test.go b/src/cmd/compile/internal/big/int_test.go index 5d65217c61..45a3765d3e 100644 --- a/src/cmd/compile/internal/big/int_test.go +++ b/src/cmd/compile/internal/big/int_test.go @@ -544,6 +544,9 @@ var expTests = []struct { {"0x8000000000000000", "1000", "6719", "1603"}, {"0x8000000000000000", "1000000", "6719", "3199"}, {"0x8000000000000000", "-1000000", "6719", "1"}, + + {"0xffffffffffffffffffffffffffffffff", "0x12345678123456781234567812345678123456789", "0x01112222333344445555666677778889", "0x36168FA1DB3AAE6C8CE647E137F97A"}, + { "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347", "298472983472983471903246121093472394872319615612417471234712061", @@ -551,12 +554,24 @@ var expTests = []struct { "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291", }, // test case for issue 8822 + { + "11001289118363089646017359372117963499250546375269047542777928006103246876688756735760905680604646624353196869572752623285140408755420374049317646428185270079555372763503115646054602867593662923894140940837479507194934267532831694565516466765025434902348314525627418515646588160955862839022051353653052947073136084780742729727874803457643848197499548297570026926927502505634297079527299004267769780768565695459945235586892627059178884998772989397505061206395455591503771677500931269477503508150175717121828518985901959919560700853226255420793148986854391552859459511723547532575574664944815966793196961286234040892865", + "0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD", + "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}, { "-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xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD", "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}, + + // test cases for issue 13907 + {"0xffffffff00000001", "0xffffffff00000001", "0xffffffff00000001", "0"}, + {"0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0"}, + {"0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0"}, + {"0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0"}, } func TestExp(t *testing.T) { @@ -584,7 +599,7 @@ func TestExp(t *testing.T) { t.Errorf("#%d: %v is not normalized", i, *z1) } if z1.Cmp(out) != 0 { - t.Errorf("#%d: got %s want %s", i, z1, out) + t.Errorf("#%d: got %x want %x", i, z1, out) } if m == nil { @@ -593,7 +608,7 @@ func TestExp(t *testing.T) { m = &Int{abs: nat{}} // m != nil && len(m.abs) == 0 z2 := new(Int).Exp(x, y, m) if z2.Cmp(z1) != 0 { - t.Errorf("#%d: got %s want %s", i, z2, z1) + t.Errorf("#%d: got %x want %x", i, z2, z1) } } } @@ -1369,6 +1384,14 @@ func TestModSqrt(t *testing.T) { t.Errorf("#%d: failed (sqrt(e) = %s)", i, &sqrt) } } + + if testing.Short() && i > 2 { + break + } + } + + if testing.Short() { + return } // exhaustive test for small values diff --git a/src/cmd/compile/internal/big/nat.go b/src/cmd/compile/internal/big/nat.go index e60318dc88..79cf6e07f7 100644 --- a/src/cmd/compile/internal/big/nat.go +++ b/src/cmd/compile/internal/big/nat.go @@ -213,25 +213,25 @@ func (z nat) montgomery(x, y, m nat, k Word, n int) nat { if len(x) != n || len(y) != n || len(m) != n { panic("math/big: mismatched montgomery number lengths") } - var c1, c2, c3 Word z = z.make(n) z.clear() + var c Word for i := 0; i < n; i++ { d := y[i] - c2 = addMulVVW(z, x, d) + c2 := addMulVVW(z, x, d) t := z[0] * k - c3 = addMulVVW(z, m, t) + c3 := addMulVVW(z, m, t) copy(z, z[1:]) - cx := c1 + c2 + cx := c + c2 cy := cx + c3 z[n-1] = cy if cx < c2 || cy < c3 { - c1 = 1 + c = 1 } else { - c1 = 0 + c = 0 } } - if c1 != 0 { + if c != 0 { subVV(z, z, m) } return z @@ -1056,23 +1056,19 @@ func (z nat) expNNWindowed(x, y, m nat) nat { // expNNMontgomery calculates x**y mod m using a fixed, 4-bit window. // Uses Montgomery representation. func (z nat) expNNMontgomery(x, y, m nat) nat { - var zz, one, rr, RR nat - numWords := len(m) // We want the lengths of x and m to be equal. + // It is OK if x >= m as long as len(x) == len(m). if len(x) > numWords { - _, rr = rr.div(rr, x, m) - } else if len(x) < numWords { - rr = rr.make(numWords) - rr.clear() - for i := range x { - rr[i] = x[i] - } - } else { - rr = x + _, x = nat(nil).div(nil, x, m) + // Note: now len(x) <= numWords, not guaranteed ==. + } + if len(x) < numWords { + rr := make(nat, numWords) + copy(rr, x) + x = rr } - x = rr // Ideally the precomputations would be performed outside, and reused // k0 = -m**-1 mod 2**_W. Algorithm from: Dumas, J.G. "On Newton–Raphson @@ -1086,8 +1082,8 @@ func (z nat) expNNMontgomery(x, y, m nat) nat { k0 = -k0 // RR = 2**(2*_W*len(m)) mod m - RR = RR.setWord(1) - zz = zz.shl(RR, uint(2*numWords*_W)) + RR := nat(nil).setWord(1) + zz := nat(nil).shl(RR, uint(2*numWords*_W)) _, RR = RR.div(RR, zz, m) if len(RR) < numWords { zz = zz.make(numWords) @@ -1095,8 +1091,7 @@ func (z nat) expNNMontgomery(x, y, m nat) nat { RR = zz } // one = 1, with equal length to that of m - one = one.make(numWords) - one.clear() + one := make(nat, numWords) one[0] = 1 const n = 4 @@ -1131,6 +1126,23 @@ func (z nat) expNNMontgomery(x, y, m nat) nat { } // convert to regular number zz = zz.montgomery(z, one, m, k0, numWords) + + // One last reduction, just in case. + // See golang.org/issue/13907. + if zz.cmp(m) >= 0 { + // Common case is m has high bit set; in that case, + // since zz is the same length as m, there can be just + // one multiple of m to remove. Just subtract. + // We think that the subtract should be sufficient in general, + // so do that unconditionally, but double-check, + // in case our beliefs are wrong. + // The div is not expected to be reached. + zz = zz.sub(zz, m) + if zz.cmp(m) >= 0 { + _, zz = nat(nil).div(nil, zz, m) + } + } + return zz.norm() } diff --git a/src/cmd/compile/internal/big/nat_test.go b/src/cmd/compile/internal/big/nat_test.go index 56b62d24d6..563ccb3052 100644 --- a/src/cmd/compile/internal/big/nat_test.go +++ b/src/cmd/compile/internal/big/nat_test.go @@ -483,6 +483,12 @@ var expNNTests = []struct { "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464", "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291", }, + { + "11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379", + "426343618817810911523", + "444747819283133684179", + "42", + }, } func TestExpNN(t *testing.T) { -- 2.48.1