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[resubmit] Fix bug of FastReducer used in BigInteger.ModPow #55122

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[resubmit] Fix bug of FastReducer used in BigInteger.ModPow #55122

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949fef4
fix formula in comment
key-moon Jun 9, 2021
6d3345a
add test for FastReducer boundary case
key-moon Jun 9, 2021
9c967ba
fix size of buffer used in FastReducer
key-moon Jun 9, 2021
c8d064d
Add testcase to boundary test
key-moon Jun 20, 2021
5626f23
fix assertion error in SubMod function
key-moon Jun 20, 2021
05b78c1
reduce k from k + 1
key-moon Jun 20, 2021
a66b571
Fix function name and description
key-moon Oct 7, 2021
1e07f92
Merge branch 'main' into 'fix-fastreducer'
key-moon Nov 29, 2021
bdc5196
Add assertion for SubMod
key-moon Nov 29, 2021
a53f36e
fix scale of k
key-moon Nov 29, 2021
9b9d398
Merge branch 'main' of github:dotnet/runtime into fix-fastreducer
key-moon Jan 27, 2022
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51 changes: 40 additions & 11 deletions ...libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.FastReducer.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -27,19 +27,19 @@ public FastReducer(uint[] modulus)
{
Debug.Assert(modulus != null);

// Let r = 4^k, with 2^k > m
// Let r = (2^32)^(2k), with (2^32)^k > m
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@tannergooding tannergooding Oct 4, 2021 •
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Could you explain why base is 2^32, which I'm interpreting as 4294967296?

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@key-moon key-moon Oct 7, 2021 •
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The formula in the comment changed because the following formula is not correct. It should be v/2^(k-32) * mu.

runtime/src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.FastReducer.cs

Lines 55 to 57 in b759ac9

// Let q1 = v/2^(k-1) * mu
int l1 = DivMul(value, length, _mu, _muLength,
_q1, _modulus.Length - 1);

Instead of change (k-1) to (k-32), I choose to change base to 2^32 from 2 because the base of the number notation in this code is 2^32. If you write as 2^(k-32), I think it is more harder to understand because the reader doesn't sure where 32 came from.

But I can understand why you prefer base 2. So, what about //Let r = 2^(32*2*k), with 2^(32*2*k) > m instead of 2^(2k) or (2^32)^(2k)?

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I'd prefer to keep this inline with the paper and just use 2^(k-32). We can leave a comment that its 32 because we operate on 32-bits at a time

uint[] r = new uint[modulus.Length * 2 + 1];
r[r.Length - 1] = 1;

// Let mu = 4^k / m
// Let mu = r / m
_mu = Divide(r, modulus);
_modulus = modulus;

// Allocate memory for quotients once
_q1 = new uint[modulus.Length * 2 + 2];
_q2 = new uint[modulus.Length * 2 + 1];

_muLength = ActualLength(_mu);

// Allocate memory for quotients once
_q1 = new uint[_muLength + modulus.Length + 1];
_q2 = new uint[_muLength + modulus.Length];
}

public int Reduce(uint[] value, int length)
Expand All @@ -52,17 +52,18 @@ public int Reduce(uint[] value, int length)
if (length < _modulus.Length)
return length;

// Let q1 = v/2^(k-1) * mu
// Let q1 = v/(2^32)^(k-1) * mu
int l1 = DivMul(value, length, _mu, _muLength,
_q1, _modulus.Length - 1);

// Let q2 = q1/2^(k+1) * m
// Let q2 = q1/(2^32)^(k+1) * m
int l2 = DivMul(_q1, l1, _modulus, _modulus.Length,
_q2, _modulus.Length + 1);

// Let v = (v - q2) % 2^(k+1) - i*m
// Let v = (v - q2) % (2^32)^k
// while m <= v: Let v = v - m
return SubMod(value, length, _q2, l2,
_modulus, _modulus.Length + 1);
_modulus, _modulus.Length);
}

private static unsafe int DivMul(uint[] left, int leftLength,
Expand Down Expand Up @@ -130,7 +131,7 @@ private static unsafe int SubMod(uint[] left, int leftLength,

fixed (uint* l = left, r = right, m = modulus)
{
SubtractSelf(l, leftLength, r, rightLength);
OverflowableSubtractSelf(l, leftLength, r, rightLength);
leftLength = ActualLength(left, leftLength);

while (Compare(l, leftLength, m, modulus.Length) >= 0)
Expand All @@ -144,6 +145,34 @@ private static unsafe int SubMod(uint[] left, int leftLength,

return leftLength;
}

private static unsafe void OverflowableSubtractSelf(uint* left, int leftLength,
uint* right, int rightLength)
{
Debug.Assert(leftLength >= 0);
Debug.Assert(rightLength >= 0);
Debug.Assert(leftLength >= rightLength);

// Executes the "grammar-school" algorithm for computing z = a - b.
// We're writing the result directly to a and
// stop execution, if we're out of b.

int i = 0;
long carry = 0L;

for (; i < rightLength; i++)
{
long digit = (left[i] + carry) - right[i];
left[i] = unchecked((uint)digit);
carry = digit >> 32;
}
for (; carry != 0 && i < leftLength; i++)
{
long digit = left[i] + carry;
left[i] = (uint)digit;
carry = digit >> 32;
}
}
}
}
}
49 changes: 49 additions & 0 deletions src/libraries/System.Runtime.Numerics/tests/BigInteger/modpow.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -286,6 +286,55 @@ public static void ModPowBoundary()
VerifyModPowString(Math.Pow(2, 35) + " " + Math.Pow(2, 33) + " 2 tModPow");
}

[Fact]
[OuterLoop]
public static void ModPowFastReducerBoundary()
{
BigIntTools.Utils.RunWithFakeThreshold("ReducerThreshold", 8, () =>
{
byte[] tempByteArray1 = new byte[40];
byte[] tempByteArray2 = new byte[40];
byte[] tempByteArray3 = new byte[40];
byte[] tempByteArray4 = new byte[40];
byte[] tempByteArray5 = new byte[40];
byte[] tempByteArray6 = new byte[40];

for (int i = 0; i < 32; i++)
{
tempByteArray2[i] = 0xff;
}
tempByteArray3[0] = 1;
for (int i = 0; i < 36; i++)
{
tempByteArray4[i] = 0xff;
}
tempByteArray5[36] = 1;
tempByteArray6[0] = 1;
tempByteArray6[36] = 1;

for (int i = 32; i < 40; i++)
{
for (int j = 0; j < 8; j++)
{
tempByteArray1[i] = (byte)(1 << j);
tempByteArray2[i] |= (byte)(1 << j);
tempByteArray3[i] = (byte)(1 << j);
VerifyModPowString(Print(tempByteArray4) + "2 " + Print(tempByteArray1) + "tModPow");
VerifyModPowString(Print(tempByteArray5) + "2 " + Print(tempByteArray1) + "tModPow");
VerifyModPowString(Print(tempByteArray6) + "2 " + Print(tempByteArray1) + "tModPow");
VerifyModPowString(Print(tempByteArray4) + "2 " + Print(tempByteArray2) + "tModPow");
VerifyModPowString(Print(tempByteArray5) + "2 " + Print(tempByteArray2) + "tModPow");
VerifyModPowString(Print(tempByteArray6) + "2 " + Print(tempByteArray2) + "tModPow");
VerifyModPowString(Print(tempByteArray4) + "2 " + Print(tempByteArray3) + "tModPow");
VerifyModPowString(Print(tempByteArray5) + "2 " + Print(tempByteArray3) + "tModPow");
VerifyModPowString(Print(tempByteArray6) + "2 " + Print(tempByteArray3) + "tModPow");
}
tempByteArray1[i] = 0;
tempByteArray3[i] = 0;
}
});
}

private static void VerifyModPowString(string opstring)
{
StackCalc sc = new StackCalc(opstring);
Expand Down