math/big: slight improvement to algorithm used for internal bitLen function
The bitLen function currently shifts out blocks of 8 bits at a time.
This change replaces this sorta-linear algorithm with a log(N)
one (shift out 16 bits, then 8, then 4, then 2, then 1).
I left the start of it linear at 16 bits at a time so that
the function continues to work with 32 or 64 bit values
without any funkiness.
The algorithm is similar to several of the nlz ("number of
leading zeros") algorithms from "Hacker's Delight" or the
"bit twiddling hacks" pages.
Doesn't make a big difference to the existing benchmarks, but
I'm using the code in a different context that calls bitLen
much more often, so it seemed worthwhile making the existing
codebase faster so that it's a better building block.
Microbenchmark results on a 64-bit Macbook Pro using 6g from weekly.2012-01-20:
benchmark old ns/op new ns/op delta
big.BenchmarkBitLen0 4 6 +50.12%
big.BenchmarkBitLen1 4 6 +33.91%
big.BenchmarkBitLen2 6 6 +3.05%
big.BenchmarkBitLen3 7 6 -19.05%
big.BenchmarkBitLen4 9 6 -30.19%
big.BenchmarkBitLen5 11 6 -42.23%
big.BenchmarkBitLen8 16 6 -61.78%
big.BenchmarkBitLen9 5 6 +18.29%
big.BenchmarkBitLen16 18 7 -60.99%
big.BenchmarkBitLen17 7 6 -4.64%
big.BenchmarkBitLen31 19 7 -62.49%
On an ARM machine (with the previous weekly):
benchmark old ns/op new ns/op delta
big.BenchmarkBitLen0 37 50 +36.56%
big.BenchmarkBitLen1 59 51 -13.69%
big.BenchmarkBitLen2 74 59 -20.40%
big.BenchmarkBitLen3 92 60 -34.89%
big.BenchmarkBitLen4 110 59 -46.09%
big.BenchmarkBitLen5 127 60 -52.68%
big.BenchmarkBitLen8 181 59 -67.24%
big.BenchmarkBitLen9 78 60 -23.05%
big.BenchmarkBitLen16 199 69 -65.13%
big.BenchmarkBitLen17 91 70 -23.17%
big.BenchmarkBitLen31 210 95 -54.43%
R=golang-dev, dave, edsrzf, gri
CC=golang-dev
https://golang.org/cl/
5570044