public StaticModInt <T>[][] Strassen(StaticModInt <T>[][] mat1, StaticModInt <T>[][] mat2)
{
Contract.Assert(default(T).Mod % 2 == 1);
Contract.Assert(mat1.Length <= S);
Contract.Assert(mat2.Length <= S);
Contract.Assert(mat1[0].Length <= S);
Contract.Assert(mat2[0].Length <= S);
var a = ToVectorize(mat1);
var b = ToVectorize(mat2);
var c = new VectorizedStaticModInt <T> [S8 * S];
var s = new VectorizedStaticModInt <T> [S8 * S * 3 / 2];
var t = new VectorizedStaticModInt <T> [S8 * S * 3 / 2];
var u = new VectorizedStaticModInt <T> [S8 * S * 3 / 2];
PlaceS(S, 0, 0, s.AsSpan(), a);
PlaceT(S, 0, 0, t.AsSpan(), b);
for (int i = 0; i < S * S8; i++)
{
s[i] = s[i].Itom();
}
for (int i = 0; i < S * S8; i++)
{
t[i] = t[i].Itom();
}
StrassenImpl(S, s, t, u.AsSpan());
for (int i = 0; i < S * S8; i++)
{
u[i] = u[i].Mtoi();
}
PlaceRev(S, 0, 0, u.AsSpan(), c);
return(ToMatrix(c, mat1.Length, mat2[0].Length));
}
private static void MulSimd(Span <VectorizedStaticModInt <T> > s, Span <VectorizedStaticModInt <T> > t, Span <VectorizedStaticModInt <T> > u)
{
for (int i = 0; i < B * B8; i++)
{
var cmpS = Avx2.CompareGreaterThan(s[i].Value.AsInt32(), VectorizedStaticModInt <T> .M1.AsInt32()).AsUInt32();
var cmpT = Avx2.CompareGreaterThan(t[i].Value.AsInt32(), VectorizedStaticModInt <T> .M1.AsInt32()).AsUInt32();
var difS = Avx2.And(cmpS, VectorizedStaticModInt <T> .M1);
var difT = Avx2.And(cmpT, VectorizedStaticModInt <T> .M1);
s[i] = Avx2.Subtract(s[i].Value, difS);
t[i] = Avx2.Subtract(t[i].Value, difT);
}
var m1v = VectorizedStaticModInt <T> .M1.GetElement(0);
var m2v = VectorizedStaticModInt <T> .M2.GetElement(0);
var zero = new VectorizedStaticModInt <T>().Value;
var th1 = new VectorizedStaticModInt <T>(0, m1v, 0, m1v, 0, m1v, 0, m1v).Value.AsInt64();
var th2 = new VectorizedStaticModInt <T>(0, m2v, 0, m2v, 0, m2v, 0, m2v).Value.AsInt64();
for (int i = 0; i < B; i += 8)
{
for (int j = 0; j < B8; j += 1)
{
Vector256 <ulong> prod0200 = default; Vector256 <ulong> prod1300 = default;
Vector256 <ulong> prod0210 = default; Vector256 <ulong> prod1310 = default;
Vector256 <ulong> prod0220 = default; Vector256 <ulong> prod1320 = default;
Vector256 <ulong> prod0230 = default; Vector256 <ulong> prod1330 = default;
Vector256 <ulong> prod0240 = default; Vector256 <ulong> prod1340 = default;
Vector256 <ulong> prod0250 = default; Vector256 <ulong> prod1350 = default;
Vector256 <ulong> prod0260 = default; Vector256 <ulong> prod1360 = default;
Vector256 <ulong> prod0270 = default; Vector256 <ulong> prod1370 = default;
for (int k = 0; k < B; k += 8)
{
for (int l = 0; l < 8; l++)
{
Vector256 <uint> T0 = t[j * B + k + l].Value; var T130 = Avx2.Shuffle(T0, 0xF5);
var S00 = Vector256.Create(s[(i + 0) * B8 + k / 8].Value.GetElement(l));
var ST0200 = Avx2.Multiply(S00, T0);
var ST1300 = Avx2.Multiply(S00, T130);
prod0200 = Avx2.Add(prod0200, ST0200);
prod1300 = Avx2.Add(prod1300, ST1300);
var S10 = Vector256.Create(s[(i + 1) * B8 + k / 8].Value.GetElement(l));
var ST0210 = Avx2.Multiply(S10, T0);
var ST1310 = Avx2.Multiply(S10, T130);
prod0210 = Avx2.Add(prod0210, ST0210);
prod1310 = Avx2.Add(prod1310, ST1310);
var S20 = Vector256.Create(s[(i + 2) * B8 + k / 8].Value.GetElement(l));
var ST0220 = Avx2.Multiply(S20, T0);
var ST1320 = Avx2.Multiply(S20, T130);
prod0220 = Avx2.Add(prod0220, ST0220);
prod1320 = Avx2.Add(prod1320, ST1320);
var S30 = Vector256.Create(s[(i + 3) * B8 + k / 8].Value.GetElement(l));
var ST0230 = Avx2.Multiply(S30, T0);
var ST1330 = Avx2.Multiply(S30, T130);
prod0230 = Avx2.Add(prod0230, ST0230);
prod1330 = Avx2.Add(prod1330, ST1330);
var S40 = Vector256.Create(s[(i + 4) * B8 + k / 8].Value.GetElement(l));
var ST0240 = Avx2.Multiply(S40, T0);
var ST1340 = Avx2.Multiply(S40, T130);
prod0240 = Avx2.Add(prod0240, ST0240);
prod1340 = Avx2.Add(prod1340, ST1340);
var S50 = Vector256.Create(s[(i + 5) * B8 + k / 8].Value.GetElement(l));
var ST0250 = Avx2.Multiply(S50, T0);
var ST1350 = Avx2.Multiply(S50, T130);
prod0250 = Avx2.Add(prod0250, ST0250);
prod1350 = Avx2.Add(prod1350, ST1350);
var S60 = Vector256.Create(s[(i + 6) * B8 + k / 8].Value.GetElement(l));
var ST0260 = Avx2.Multiply(S60, T0);
var ST1360 = Avx2.Multiply(S60, T130);
prod0260 = Avx2.Add(prod0260, ST0260);
prod1360 = Avx2.Add(prod1360, ST1360);
var S70 = Vector256.Create(s[(i + 7) * B8 + k / 8].Value.GetElement(l));
var ST0270 = Avx2.Multiply(S70, T0);
var ST1370 = Avx2.Multiply(S70, T130);
prod0270 = Avx2.Add(prod0270, ST0270);
prod1370 = Avx2.Add(prod1370, ST1370);
}
var cmp0200 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0200.AsInt64());
var cmp1300 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1300.AsInt64());
var dif0200 = Avx2.And(cmp0200, th2);
var dif1300 = Avx2.And(cmp1300, th2);
prod0200 = Avx2.Subtract(prod0200, dif0200.AsUInt64());
prod1300 = Avx2.Subtract(prod1300, dif1300.AsUInt64());
var cmp0210 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0210.AsInt64());
var cmp1310 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1310.AsInt64());
var dif0210 = Avx2.And(cmp0210, th2);
var dif1310 = Avx2.And(cmp1310, th2);
prod0210 = Avx2.Subtract(prod0210, dif0210.AsUInt64());
prod1310 = Avx2.Subtract(prod1310, dif1310.AsUInt64());
var cmp0220 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0220.AsInt64());
var cmp1320 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1320.AsInt64());
var dif0220 = Avx2.And(cmp0220, th2);
var dif1320 = Avx2.And(cmp1320, th2);
prod0220 = Avx2.Subtract(prod0220, dif0220.AsUInt64());
prod1320 = Avx2.Subtract(prod1320, dif1320.AsUInt64());
var cmp0230 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0230.AsInt64());
var cmp1330 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1330.AsInt64());
var dif0230 = Avx2.And(cmp0230, th2);
var dif1330 = Avx2.And(cmp1330, th2);
prod0230 = Avx2.Subtract(prod0230, dif0230.AsUInt64());
prod1330 = Avx2.Subtract(prod1330, dif1330.AsUInt64());
var cmp0240 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0240.AsInt64());
var cmp1340 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1340.AsInt64());
var dif0240 = Avx2.And(cmp0240, th2);
var dif1340 = Avx2.And(cmp1340, th2);
prod0240 = Avx2.Subtract(prod0240, dif0240.AsUInt64());
prod1340 = Avx2.Subtract(prod1340, dif1340.AsUInt64());
var cmp0250 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0250.AsInt64());
var cmp1350 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1350.AsInt64());
var dif0250 = Avx2.And(cmp0250, th2);
var dif1350 = Avx2.And(cmp1350, th2);
prod0250 = Avx2.Subtract(prod0250, dif0250.AsUInt64());
prod1350 = Avx2.Subtract(prod1350, dif1350.AsUInt64());
var cmp0260 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0260.AsInt64());
var cmp1360 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1360.AsInt64());
var dif0260 = Avx2.And(cmp0260, th2);
var dif1360 = Avx2.And(cmp1360, th2);
prod0260 = Avx2.Subtract(prod0260, dif0260.AsUInt64());
prod1360 = Avx2.Subtract(prod1360, dif1360.AsUInt64());
var cmp0270 = Avx2.CompareGreaterThan(zero.AsInt64(), prod0270.AsInt64());
var cmp1370 = Avx2.CompareGreaterThan(zero.AsInt64(), prod1370.AsInt64());
var dif0270 = Avx2.And(cmp0270, th2);
var dif1370 = Avx2.And(cmp1370, th2);
prod0270 = Avx2.Subtract(prod0270, dif0270.AsUInt64());
prod1370 = Avx2.Subtract(prod1370, dif1370.AsUInt64());
}
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0200.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1300.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0200 = Avx2.Subtract(prod0200, dif02.AsUInt64());
prod1300 = Avx2.Subtract(prod1300, dif13.AsUInt64());
}
u[(i + 0) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0200.AsUInt32(), prod1300.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0210.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1310.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0210 = Avx2.Subtract(prod0210, dif02.AsUInt64());
prod1310 = Avx2.Subtract(prod1310, dif13.AsUInt64());
}
u[(i + 1) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0210.AsUInt32(), prod1310.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0220.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1320.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0220 = Avx2.Subtract(prod0220, dif02.AsUInt64());
prod1320 = Avx2.Subtract(prod1320, dif13.AsUInt64());
}
u[(i + 2) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0220.AsUInt32(), prod1320.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0230.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1330.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0230 = Avx2.Subtract(prod0230, dif02.AsUInt64());
prod1330 = Avx2.Subtract(prod1330, dif13.AsUInt64());
}
u[(i + 3) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0230.AsUInt32(), prod1330.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0240.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1340.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0240 = Avx2.Subtract(prod0240, dif02.AsUInt64());
prod1340 = Avx2.Subtract(prod1340, dif13.AsUInt64());
}
u[(i + 4) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0240.AsUInt32(), prod1340.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0250.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1350.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0250 = Avx2.Subtract(prod0250, dif02.AsUInt64());
prod1350 = Avx2.Subtract(prod1350, dif13.AsUInt64());
}
u[(i + 5) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0250.AsUInt32(), prod1350.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0260.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1360.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0260 = Avx2.Subtract(prod0260, dif02.AsUInt64());
prod1360 = Avx2.Subtract(prod1360, dif13.AsUInt64());
}
u[(i + 6) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0260.AsUInt32(), prod1360.AsUInt32());
for (int _ = 0; _ < 2; _++)
{
var cmp02 = Avx2.CompareGreaterThan(prod0270.AsInt64(), th1);
var cmp13 = Avx2.CompareGreaterThan(prod1370.AsInt64(), th1);
var dif02 = Avx2.And(cmp02, th1);
var dif13 = Avx2.And(cmp13, th1);
prod0270 = Avx2.Subtract(prod0270, dif02.AsUInt64());
prod1370 = Avx2.Subtract(prod1370, dif13.AsUInt64());
}
u[(i + 7) * B8 + j + 0] = VectorizedStaticModInt <T> .Reduce(prod0270.AsUInt32(), prod1370.AsUInt32());
}
}
}
