public override unsafe Number Multiply (Number x, Number y)
{
#if false
uint* px = stackalloc uint[6];
uint* py = stackalloc uint[6];
for (int i = 0; i < x.length; i++) px[i] = x.data[i];
for (int i = x.length; i < 6; i++) px[i] = 0;
for (int i = 0; i < y.length; i++) py[i] = y.data[i];
for (int i = y.length; i < 6; i++) py[i] = 0;
#else
uint[] px = x.data, py = y.data;
if (x.data.Length < 6 || y.data.Length < 6) throw new ArgumentException ();
#endif
ulong tmp;
uint* r = stackalloc uint[6];
ulong tmp1, tmp2;
uint r6, r7, z1;
r[0] = (uint)(tmp = px[0] * ((ulong)py[0])); tmp >>= 32;
r[1] = (uint)(tmp += px[1] * ((ulong)py[0])); tmp >>= 32;
r[2] = (uint)(tmp += px[2] * ((ulong)py[0])); tmp >>= 32;
r[3] = (uint)(tmp += px[3] * ((ulong)py[0])); tmp >>= 32;
r[4] = (uint)(tmp += px[4] * ((ulong)py[0])); tmp >>= 32;
r[5] = (uint)(tmp += px[5] * ((ulong)py[0]));
r6 = (uint)(tmp >> 32);
tmp1 = px[5] * ((ulong)py[1]);
r[0] = (uint)(tmp = tmp1 + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += px[0] * ((ulong)py[1]) + ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += tmp1 + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += px[2] * ((ulong)py[1]) + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += px[3] * ((ulong)py[1]) + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += px[4] * ((ulong)py[1]) + ((ulong)r[5]));
z1 = (uint)(tmp >> 32);
tmp1 = px[4] * ((ulong)py[2]);
tmp2 = px[5] * ((ulong)py[2]);
r[0] = (uint)(tmp = tmp1 + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += tmp2 + ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += tmp1 + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += tmp2 + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += px[2] * ((ulong)py[2]) + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += px[3] * ((ulong)py[2]) + ((ulong)r[5])); tmp >>= 32;
r6 = (uint)(tmp += z1 + ((ulong)r6 ));
r7 = (uint)(tmp >> 32);
tmp1 = px[4] * ((ulong)py[3]);
tmp2 = px[5] * ((ulong)py[3]);
r[0] = (uint)(tmp = px[3] * ((ulong)py[3]) + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += tmp1 + ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += tmp2 + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += tmp1 + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += tmp2 + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += px[2] * ((ulong)py[3]) + ((ulong)r[5]));
z1 = (uint)(tmp >> 32);
tmp1 = px[4] * ((ulong)py[4]);
tmp2 = px[5] * ((ulong)py[4]);
r[0] = (uint)(tmp = px[2] * ((ulong)py[4]) + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += px[3] * ((ulong)py[4]) + ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += tmp1 + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += tmp2 + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += tmp1 + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += tmp2 + ((ulong)r[5])); tmp >>= 32;
r6 = (uint)(tmp += z1 + ((ulong)r6 ));
r7 += (uint)(tmp >> 32);
tmp1 = px[5] * ((ulong)py[5]);
tmp2 = px[4] * ((ulong)py[5]);
r[0] = (uint)(tmp = tmp1 + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += px[2] * ((ulong)py[5]) + ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += tmp1 + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += tmp2 + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += tmp1 + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += tmp2 + ((ulong)r[5]));
z1 = (uint)(tmp >> 32);
r[2] = (uint)(tmp = px[1] * ((ulong)py[1]) + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += px[1] * ((ulong)py[2]) + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += px[1] * ((ulong)py[3]) + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += px[1] * ((ulong)py[4]) + ((ulong)r[5])); tmp >>= 32;
r6 = (uint)(tmp += z1 + ((ulong)r6 ));
r7 += (uint)(tmp >> 32);
r[2] = (uint)(tmp = px[0] * ((ulong)py[2]) + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += px[0] * ((ulong)py[3]) + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += px[0] * ((ulong)py[4]) + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += px[0] * ((ulong)py[5]) + ((ulong)r[5]));
z1 = (uint)(tmp >> 32);
r[2] = (uint)(tmp = px[3] * ((ulong)py[3]) + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += px[3] * ((ulong)py[4]) + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += px[3] * ((ulong)py[5]) + ((ulong)r[4]));
tmp2 = tmp >> 32;
tmp1 = px[1] * ((ulong)py[5]);
r[0] = (uint)(tmp = tmp1 + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += px[3] * ((ulong)py[5]) + ((ulong)r[2])); tmp >>= 32;
r[2] = (uint)(tmp1 += ((ulong)r[2])); tmp1 >>= 32;
r[3] = (uint)(tmp1 += tmp + ((ulong)r[3])); tmp1 >>= 32;
r[2] = (uint)(tmp = px[2] * ((ulong)py[4]) + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += px[2] * ((ulong)py[5]) + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += tmp1 + ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += tmp2 + ((ulong)r[5])); tmp >>= 32;
r6 = (uint)(tmp += z1 + ((ulong)r6 ));
r7 += (uint)(tmp >> 32);
while (r6 != 0 || r7 != 0) {
r[0] = (uint)(tmp = r6 + ((ulong)r[0])); tmp >>= 32;
r[1] = (uint)(tmp += r7 + ((ulong)r[1])); tmp >>= 32;
r[2] = (uint)(tmp += r6 + ((ulong)r[2])); tmp >>= 32;
r[3] = (uint)(tmp += r7 + ((ulong)r[3])); tmp >>= 32;
r[4] = (uint)(tmp += ((ulong)r[4])); tmp >>= 32;
r[5] = (uint)(tmp += ((ulong)r[5]));
r6 = (uint)(tmp >> 32);
r7 = 0;
}
Number ret = new Number (new uint[] { r[0], r[1], r[2], r[3], r[4], r[5] });
if (CompareTo (r[0], r[1], r[2], r[3], r[4], r[5]) < 0) {
ret.SubtractInPlace (PRIME);
}
return ret;
}
public override Number Multiply (Number x, Number y)
{
if (x.data.Length < 8 || y.data.Length < 8) throw new ArgumentException ();
uint[] px = x.data, py = y.data;
ulong r0, r1, r2, r3, r4, r5, r6, r7;
uint tmp32;
ulong tmp, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
ulong d1, d2, d3, d4, d5;
ulong triple1, triple2;
const ulong mask = 0xFFFFFFFF;
const ulong carry = 0x100000000UL;
const ulong negative = ulong.MaxValue - (((ulong)uint.MaxValue) * 16) * 8;
tmp = ((ulong)px[0]) * ((ulong)py[0]); r0 = tmp & mask; r1 = tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[0]); r1 += tmp & mask; r2 = tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[0]); r2 += tmp & mask; r3 = tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[0]); r3 += tmp & mask; r4 = tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[0]); r4 += tmp & mask; r5 = tmp >> 32;
tmp = ((ulong)px[5]) * ((ulong)py[0]); r5 += tmp & mask; r6 = tmp >> 32;
tmp = ((ulong)px[6]) * ((ulong)py[0]); r6 += tmp & mask; r7 = tmp >> 32;
tmp = ((ulong)px[7]) * ((ulong)py[0]); r7 += tmp & mask; tmp32 = (uint)(tmp >> 32);
r7 += tmp32;
r6 -= tmp32;
r3 -= tmp32;
r0 += tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[1]); r1 += tmp & mask; r2 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[1]); r2 += tmp & mask; r3 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[1]); r3 += tmp & mask; r4 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[1]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[1]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[5]) * ((ulong)py[1]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[6]) * ((ulong)py[1]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[1]); tmp1 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
r7 += tmp1;
r6 -= tmp1 + tmp32;
r4 -= tmp32;
r3 -= tmp1 + tmp32;
r1 += tmp32;
r0 += tmp1 + tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[2]); r2 += tmp & mask; r3 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[2]); r3 += tmp & mask; r4 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[2]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[2]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[2]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[5]) * ((ulong)py[2]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[2]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[2]); tmp2 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
r7 += tmp1 - tmp32;
r6 -= tmp1 + tmp2;
r5 -= tmp32;
r4 -= tmp2 + tmp32;
r3 -= tmp1 + tmp2;
r2 += tmp32;
r1 += tmp2 + tmp32;
r0 += tmp1 + tmp2;
tmp = ((ulong)px[0]) * ((ulong)py[3]); r3 += tmp & mask; r4 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[3]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[3]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[3]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[3]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[3]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[3]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[3]); tmp3 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = ((ulong)tmp32) << 1;
r7 += tmp1 - tmp3 - tmp32;
r6 -= tmp1 + tmp2;
r5 -= tmp3 + tmp32;
r4 -= tmp2 + tmp3;
r3 -= tmp1 + tmp2 - d1;
r2 += tmp3 + tmp32;
r1 += tmp2 + tmp3;
r0 += tmp1 + tmp2 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[4]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[4]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[4]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[4]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[4]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[4]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[4]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[4]); tmp4 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = ((ulong)tmp32) << 1;
r7 += tmp1 - tmp3 - tmp4 - tmp32;
r6 -= tmp1 + tmp2;
r5 -= tmp3 + tmp4;
r4 -= tmp2 + tmp3 - d2;
r3 -= tmp1 + tmp2 - d1 - d2;
r2 += tmp3 + tmp4;
r1 += tmp2 + tmp3 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[5]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[5]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[5]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[3]) * ((ulong)py[5]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[5]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[5]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[5]); tmp4 += (uint)tmp; tmp5 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[5]); tmp5 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = tmp5 << 1;
d3 = ((ulong)tmp32) << 1;
r7 += tmp1 - tmp3 - tmp4 - tmp5 - tmp32;
r6 -= tmp1 + tmp2 - tmp32;
r5 -= tmp3 + tmp4 - d3;
r4 -= tmp2 + tmp3 - d2 - d3;
r3 -= tmp1 + tmp2 - d1 - d2 - tmp32;
r2 += tmp3 + tmp4 - tmp32;
r1 += tmp2 + tmp3 - tmp5 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp5 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[6]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[6]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[2]) * ((ulong)py[6]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[3]) * ((ulong)py[6]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[6]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[6]); tmp4 += (uint)tmp; tmp5 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[6]); tmp5 += (uint)tmp; tmp6 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[6]); tmp6 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = tmp5 << 1;
d3 = tmp6 << 1;
d4 = ((ulong)tmp32) << 1;
triple1 = d4 + tmp32;
r7 += tmp1 - tmp3 - tmp4 - tmp5 - tmp6;
r6 -= tmp1 + tmp2 - tmp6 - triple1;
r5 -= tmp3 + tmp4 - d3 - d4;
r4 -= tmp2 + tmp3 - d2 - d3 - tmp32;
r3 -= tmp1 + tmp2 - d1 - d2 - tmp6;
r2 += tmp3 + tmp4 - tmp6 - tmp32;
r1 += tmp2 + tmp3 - tmp5 - tmp6 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp5 - tmp6 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[7]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[1]) * ((ulong)py[7]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[2]) * ((ulong)py[7]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[3]) * ((ulong)py[7]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[7]); tmp4 += (uint)tmp; tmp5 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[7]); tmp5 += (uint)tmp; tmp6 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[7]); tmp6 += (uint)tmp; tmp7 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[7]); tmp7 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = tmp5 << 1;
d3 = tmp6 << 1;
d4 = tmp7 << 1;
d5 = ((ulong)tmp32) << 1;
triple1 = d4 + tmp7;
triple2 = d5 + tmp32;
r7 += tmp1 - tmp3 - tmp4 - tmp5 - tmp6 + triple2;
r6 -= tmp1 + tmp2 - tmp6 - triple1 - d5;
r5 -= tmp3 + tmp4 - d3 - d4 - tmp32;
r4 -= tmp2 + tmp3 - d2 - d3 - tmp7;
r3 -= tmp1 + tmp2 - d1 - d2 - tmp6 + tmp32;
r2 += tmp3 + tmp4 - tmp6 - tmp7 - tmp32;
r1 += tmp2 + tmp3 - tmp5 - tmp6 - tmp7 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp5 - tmp6 - tmp7;
// check negative-value
while (r0 >= negative) { r1--; r0 += carry; }
while (r1 >= negative) { r2--; r1 += carry; }
while (r2 >= negative) { r3--; r2 += carry; }
while (r3 >= negative) { r4--; r3 += carry; }
while (r4 >= negative) { r5--; r4 += carry; }
while (r5 >= negative) { r6--; r5 += carry; }
while (r6 >= negative) { r7--; r6 += carry; }
while (r7 >= negative) {
r0 += P1;
r1 += P2;
r2 += P3;
r3 += P4;
r4 += P5;
r5 += P6;
r6 += P7;
r7 += P8;
}
// check carry
while (r0 > mask || r1 > mask || r2 > mask || r3 > mask || r4 > mask || r5 > mask || r6 > mask || r7 > mask) {
if (r7 > mask) {
tmp32 = (uint)(r7 >> 32);
r0 += tmp32;
r3 -= tmp32;
r6 -= tmp32;
r7 = tmp32 + (ulong)((uint)r7);
// check negative-value
while (r3 >= negative) { r4--; r3 += carry; }
while (r4 >= negative) { r5--; r4 += carry; }
while (r5 >= negative) { r6--; r5 += carry; }
while (r6 >= negative) { r7--; r6 += carry; }
}
tmp32 = (uint)(r0 >> 32); r0 = (uint)r0; r1 += tmp32;
tmp32 = (uint)(r1 >> 32); r1 = (uint)r1; r2 += tmp32;
tmp32 = (uint)(r2 >> 32); r2 = (uint)r2; r3 += tmp32;
tmp32 = (uint)(r3 >> 32); r3 = (uint)r3; r4 += tmp32;
tmp32 = (uint)(r4 >> 32); r4 = (uint)r4; r5 += tmp32;
tmp32 = (uint)(r5 >> 32); r5 = (uint)r5; r6 += tmp32;
tmp32 = (uint)(r6 >> 32); r6 = (uint)r6; r7 += tmp32;
}
Number ret = new Number (new uint[] {
(uint)r0, (uint)r1, (uint)r2,
(uint)r3, (uint)r4, (uint)r5,
(uint)r6, (uint)r7
});
while (ret.CompareTo (PRIME) >= 0)
ret.SubtractInPlace (PRIME);
return ret;
}
