// 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
{"0x8000000000000000", "1000", "6719", "1603"},
{"0x8000000000000000", "1000000", "6719", "3199"},
{"0x8000000000000000", "-1000000", "6719", "1"},
+
+ {"0xffffffffffffffffffffffffffffffff", "0x12345678123456781234567812345678123456789", "0x01112222333344445555666677778889", "0x36168FA1DB3AAE6C8CE647E137F97A"},
+
{
"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
"298472983472983471903246121093472394872319615612417471234712061",
"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
},
// test case for issue 8822
+ {
+ "11001289118363089646017359372117963499250546375269047542777928006103246876688756735760905680604646624353196869572752623285140408755420374049317646428185270079555372763503115646054602867593662923894140940837479507194934267532831694565516466765025434902348314525627418515646588160955862839022051353653052947073136084780742729727874803457643848197499548297570026926927502505634297079527299004267769780768565695459945235586892627059178884998772989397505061206395455591503771677500931269477503508150175717121828518985901959919560700853226255420793148986854391552859459511723547532575574664944815966793196961286234040892865",
+ "0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
+ "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
+ "21484252197776302499639938883777710321993113097987201050501182909581359357618579566746556372589385361683610524730509041328855066514963385522570894839035884713051640171474186548713546686476761306436434146475140156284389181808675016576845833340494848283681088886584219750554408060556769486628029028720727393293111678826356480455433909233520504112074401376133077150471237549474149190242010469539006449596611576612573955754349042329130631128234637924786466585703488460540228477440853493392086251021228087076124706778899179648655221663765993962724699135217212118535057766739392069738618682722216712319320435674779146070442",
+ },
{
"-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
"0xB08FFB20760FFED58FADA86DFEF71AD72AA0FA763219618FE022C197E54708BB1191C66470250FCE8879487507CEE41381CA4D932F81C2B3F1AB20B539D50DCD",
"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
"21484252197776302499639938883777710321993113097987201050501182909581359357618579566746556372589385361683610524730509041328855066514963385522570894839035884713051640171474186548713546686476761306436434146475140156284389181808675016576845833340494848283681088886584219750554408060556769486628029028720727393293111678826356480455433909233520504112074401376133077150471237549474149190242010469539006449596611576612573955754349042329130631128234637924786466585703488460540228477440853493392086251021228087076124706778899179648655221663765993962724699135217212118535057766739392069738618682722216712319320435674779146070442",
},
+
+ // 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) {
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 {
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)
}
}
}
t.Errorf("#%d: failed (sqrt(e) = %s)", i, &sqrt)
}
}
+
+ if testing.Short() && i > 2 {
+ break
+ }
+ }
+
+ if testing.Short() {
+ return
}
// exhaustive test for small values
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
// 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
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)
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
}
// 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()
}
"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
},
+ {
+ "11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379",
+ "426343618817810911523",
+ "444747819283133684179",
+ "42",
+ },
}
func TestExpNN(t *testing.T) {