Friday, July 11, 2014

How much does a square root cost?

An interesting diversion: how much (time) does calling the square root function sqrt() cost, and is it even worth trying alternative less-accurate implementations?

Some Assembly Required provides some answers: 

SQUARE ROOT
Method Total time Time per float Avg Error
Compiler sqrt(x) /
x87 FPU FSQRT
404.029ms 24ns 0.0000%
SSE intrinsic ssqrts 200.395ms 11.9ns 0.0000%
Carmack’s Magic Number rsqrt * x 72.682ms 4.33ns 0.0990%
SSE rsqrtss * x 20.495ms 1.22ns 0.0094%
SSE rsqrtss * x
with one NR step
53.401ms 3.18ns 0.0000%
SSE rsqrtss * x
with one NR step, unrolled by four
48.701ms 2.90ns 0.0000%
RECIPROCAL SQRT
Method Total time Time per float Avg Error
Carmack’s Magic Number rsqrt 59.378ms 3.54ns 0.0990%
SSE rsqrtss 14.202ms 0.85ns 0.0094%
SSE rsqrtss
with one NR step
45.952ms 2.74ns 0.0000%

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