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x87 Floating-Point Optimizations
Chapter 10
25112
Rev. 3.06
September 2005
Software Optimization Guide for AMD64 Processors
10.1
Using Multiplication Rather Than Division
Optimization
If accuracy requirements allow, convert floating-point division by a constant to multiplication by the 
reciprocal. 
Application
This optimization applies to:
32-bit software
64-bit software
Rationale
Divisors that are powers of two—and their reciprocals—are exactly representable, and therefore do 
not cause an accuracy issue, except for the rare case in which the reciprocal overflows or underflows. 
Unless such an overflow or underflow occurs, always convert a division by a power of two for 
multiplication. Although the AMD Athlon 64 and AMD Opteron processors have high-performance 
division, multiplication is significantly faster than division.