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reciprocal multiplication

How compilers divide by a fixed number without a divide instruction - multiply by a carefully chosen big number and keep the top bits.

For a constant divisor d, x / d is computed as the high half of x * M followed by a shift, with M about 2^(n+s) / d chosen so the result is exact for every n-bit x; signed division adds a correction for negative x.

Examples

  • Clang divides an unsigned 32-bit x by 10 by multiplying by 0xCCCCCCCD and shifting the 64-bit product right by 35.

See also

strength reduction zeroing idiom
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