author | Shawn Walker-Salas <shawn.walker@oracle.com> |
Thu, 21 Jan 2016 09:20:59 -0800 | |
changeset 5331 | 9c955076ffe3 |
permissions | -rw-r--r-- |
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From b2cf5e7aa096fabd624440fbb94b93a692c13024 Mon Sep 17 00:00:00 2001 |
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From: Russ Cox <[email protected]> |
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Date: Mon, 11 Jan 2016 09:52:56 -0500 |
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Subject: [PATCH 70/73] [release-branch.go1.5] math/big: fix Exp(x, x, x) for |
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certain large x |
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Fixes #13907. |
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Change-Id: Ieaa5183f399b12a9177372212adf481c8f0b4a0d |
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Reviewed-on: https://go-review.googlesource.com/18491 |
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Reviewed-by: Robert Griesemer <[email protected]> |
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Reviewed-by: Vlad Krasnov <[email protected]> |
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Reviewed-by: Adam Langley <[email protected]> |
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Reviewed-on: https://go-review.googlesource.com/18586 |
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Reviewed-by: Chris Broadfoot <[email protected]> |
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--- |
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src/math/big/int_test.go | 10 ++++++++-- |
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src/math/big/nat.go | 17 +++++++++++++++++ |
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2 files changed, 25 insertions(+), 2 deletions(-) |
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diff --git a/src/math/big/int_test.go b/src/math/big/int_test.go |
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index 88c8c2b..f3def5a 100644 |
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--- a/src/math/big/int_test.go |
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+++ b/src/math/big/int_test.go |
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@@ -555,6 +555,12 @@ var expTests = []struct { |
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"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|
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"21484252197776302499639938883777710321993113097987201050501182909581359357618579566746556372589385361683610524730509041328855066514963385522570894839035884713051640171474186548713546686476761306436434146475140156284389181808675016576845833340494848283681088886584219750554408060556769486628029028720727393293111678826356480455433909233520504112074401376133077150471237549474149190242010469539006449596611576612573955754349042329130631128234637924786466585703488460540228477440853493392086251021228087076124706778899179648655221663765993962724699135217212118535057766739392069738618682722216712319320435674779146070442", |
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}, |
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+ |
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+ // test cases for issue 13907 |
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+ {"0xffffffff00000001", "0xffffffff00000001", "0xffffffff00000001", "0"}, |
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+ {"0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0xffffffffffffffff00000001", "0"}, |
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+ {"0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffff00000001", "0"}, |
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+ {"0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0xffffffffffffffffffffffffffffffff00000001", "0"}, |
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} |
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func TestExp(t *testing.T) { |
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@@ -582,7 +588,7 @@ func TestExp(t *testing.T) { |
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t.Errorf("#%d: %v is not normalized", i, *z1) |
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} |
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if z1.Cmp(out) != 0 { |
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- t.Errorf("#%d: got %s want %s", i, z1, out) |
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+ t.Errorf("#%d: got %x want %x", i, z1, out) |
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} |
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if m == nil { |
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@@ -591,7 +597,7 @@ func TestExp(t *testing.T) { |
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m = &Int{abs: nat{}} // m != nil && len(m.abs) == 0 |
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z2 := new(Int).Exp(x, y, m) |
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if z2.Cmp(z1) != 0 { |
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- t.Errorf("#%d: got %s want %s", i, z2, z1) |
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+ t.Errorf("#%d: got %x want %x", i, z2, z1) |
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} |
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} |
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} |
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diff --git a/src/math/big/nat.go b/src/math/big/nat.go |
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index c7362e6..6c242c8 100644 |
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--- a/src/math/big/nat.go |
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+++ b/src/math/big/nat.go |
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@@ -1151,6 +1151,23 @@ func (z nat) expNNMontgomery(x, y, m nat) nat { |
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} |
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// convert to regular number |
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zz = zz.montgomery(z, one, m, k0, numWords) |
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+ |
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+ // One last reduction, just in case. |
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+ // See golang.org/issue/13907. |
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+ if zz.cmp(m) >= 0 { |
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+ // Common case is m has high bit set; in that case, |
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+ // since zz is the same length as m, there can be just |
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+ // one multiple of m to remove. Just subtract. |
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+ // We think that the subtract should be sufficient in general, |
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+ // so do that unconditionally, but double-check, |
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+ // in case our beliefs are wrong. |
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+ // The div is not expected to be reached. |
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+ zz = zz.sub(zz, m) |
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+ if zz.cmp(m) >= 0 { |
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+ _, zz = nat(nil).div(nil, zz, m) |
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+ } |
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+ } |
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+ |
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return zz.norm() |
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} |
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-- |
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2.6.1 |
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