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more efficient uint128 multiplication algorithm (measured 29.23x speedup)

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theoretical 2015-01-07 14:38:28 -05:00
parent 975649ce5d
commit 64c6c01b80
1 changed files with 35 additions and 24 deletions
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51
src/uint128.cpp
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@ -233,29 +233,40 @@ namespace fc
uint128& uint128::operator*=(const uint128 &b) uint128& uint128::operator*=(const uint128 &b)
{ {
// check for multiply by 0 uint64_t a0 = (uint32_t) (this->lo );
// result is always 0 :-P uint64_t a1 = (uint32_t) (this->lo >> 0x20);
if(b == 0) { uint64_t a2 = (uint32_t) (this->hi );
hi = 0; uint64_t a3 = (uint32_t) (this->hi >> 0x20);
lo = 0;
} else if(b != 1) {
// check we aren't multiplying by 1 uint64_t b0 = (uint32_t) (b.lo );
uint64_t b1 = (uint32_t) (b.lo >> 0x20);
uint64_t b2 = (uint32_t) (b.hi );
uint64_t b3 = (uint32_t) (b.hi >> 0x20);
uint128 a(*this); // (a0 + (a1 << 0x20) + (a2 << 0x40) + (a3 << 0x60)) *
uint128 t = b; // (b0 + (b1 << 0x20) + (b2 << 0x40) + (b3 << 0x60)) =
// a0 * b0
//
// (a1 * b0 + a0 * b1) << 0x20
// (a2 * b0 + a1 * b1 + a0 * b2) << 0x40
// (a3 * b0 + a2 * b1 + a1 * b2 + a0 * b3) << 0x60
//
// all other cross terms are << 0x80 or higher, thus do not appear in result
lo = 0; this->hi = 0;
hi = 0; this->lo = a3*b0;
(*this) += a2*b1;
for (unsigned int i = 0; i < 128; ++i) { (*this) += a1*b2;
if((t & 1) != 0) { (*this) += a0*b3;
*this += (a << i); (*this) <<= 0x20;
} (*this) += a2*b0;
(*this) += a1*b1;
t >>= 1; (*this) += a0*b2;
} (*this) <<= 0x20;
} (*this) += a1*b0;
(*this) += a0*b1;
(*this) <<= 0x20;
(*this) += a0*b0;
return *this; return *this;
} }