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Use a better algorithm for mul64x64_128 #3957

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Apr 3, 2024
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Use a better algorithm for mul64x64_128 #3957

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23 changes: 9 additions & 14 deletions src/lib/utils/mul128.h
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Original file line number Diff line number Diff line change
Expand Up @@ -51,22 +51,17 @@ constexpr inline void mul64x64_128(uint64_t a, uint64_t b, uint64_t* lo, uint64_
const uint32_t b_hi = (b >> HWORD_BITS);
const uint32_t b_lo = (b & HWORD_MASK);

uint64_t x0 = static_cast<uint64_t>(a_hi) * b_hi;
uint64_t x1 = static_cast<uint64_t>(a_lo) * b_hi;
uint64_t x2 = static_cast<uint64_t>(a_hi) * b_lo;
uint64_t x3 = static_cast<uint64_t>(a_lo) * b_lo;
const uint64_t x0 = static_cast<uint64_t>(a_hi) * b_hi;
const uint64_t x1 = static_cast<uint64_t>(a_lo) * b_hi;
const uint64_t x2 = static_cast<uint64_t>(a_hi) * b_lo;
const uint64_t x3 = static_cast<uint64_t>(a_lo) * b_lo;

// this cannot overflow as (2^32-1)^2 + 2^32-1 < 2^64-1
x2 += x3 >> HWORD_BITS;
// this cannot overflow as (2^32-1)^2 + 2^32-1 + 2^32-1 = 2^64-1
const uint64_t middle = x2 + (x3 >> HWORD_BITS) + (x1 & HWORD_MASK);

// this one can overflow
x2 += x1;

// propagate the carry if any
x0 += static_cast<uint64_t>(static_cast<bool>(x2 < x1)) << HWORD_BITS;

*hi = x0 + (x2 >> HWORD_BITS);
*lo = ((x2 & HWORD_MASK) << HWORD_BITS) + (x3 & HWORD_MASK);
// likewise these cannot overflow
*hi = x0 + (middle >> HWORD_BITS) + (x1 >> HWORD_BITS);
*lo = (middle << HWORD_BITS) + (x3 & HWORD_MASK);
#endif
}

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