math/big: implement Lehmer's extended GCD algorithm

math/big: implement Lehmer's extended GCD algorithm

Updates #15833

The extended GCD algorithm can be implemented using
Lehmer's algorithm with additional updates for the
cosequences following Algorithm 10.45 from Cohen et al.
"Handbook of Elliptic and Hyperelliptic Curve Cryptography" pp 192.
This brings the speed of the extended GCD calculation within
~2x of the base GCD calculation.  There is a slight degradation in
the non-extended GCD speed for small inputs (1-2 words) due to the
additional code to handle the extended updates.

name                          old time/op    new time/op    delta
GCD10x10/WithoutXY-4             262ns ± 1%     266ns ± 2%     ~     (p=0.333 n=5+5)
GCD10x10/WithXY-4               1.42µs ± 2%    0.74µs ± 3%  -47.90%  (p=0.008 n=5+5)
GCD10x100/WithoutXY-4            520ns ± 2%     539ns ± 1%   +3.81%  (p=0.008 n=5+5)
GCD10x100/WithXY-4              2.32µs ± 1%    1.67µs ± 0%  -27.80%  (p=0.008 n=5+5)
GCD10x1000/WithoutXY-4          1.40µs ± 1%    1.45µs ± 2%   +3.26%  (p=0.016 n=4+5)
GCD10x1000/WithXY-4             4.78µs ± 1%    3.43µs ± 1%  -28.37%  (p=0.008 n=5+5)
GCD10x10000/WithoutXY-4         10.0µs ± 0%    10.2µs ± 3%   +1.80%  (p=0.008 n=5+5)
GCD10x10000/WithXY-4            20.9µs ± 3%    17.9µs ± 1%  -14.20%  (p=0.008 n=5+5)
GCD10x100000/WithoutXY-4        96.8µs ± 0%    96.3µs ± 1%     ~     (p=0.310 n=5+5)
GCD10x100000/WithXY-4            196µs ± 3%     159µs ± 2%  -18.61%  (p=0.008 n=5+5)
GCD100x100/WithoutXY-4          2.53µs ±15%    2.34µs ± 0%   -7.35%  (p=0.008 n=5+5)
GCD100x100/WithXY-4             19.3µs ± 0%     3.9µs ± 1%  -79.58%  (p=0.008 n=5+5)
GCD100x1000/WithoutXY-4         4.23µs ± 0%    4.17µs ± 3%     ~     (p=0.127 n=5+5)
GCD100x1000/WithXY-4            22.8µs ± 1%     7.5µs ±10%  -67.00%  (p=0.008 n=5+5)
GCD100x10000/WithoutXY-4        19.1µs ± 0%    19.0µs ± 0%     ~     (p=0.095 n=5+5)
GCD100x10000/WithXY-4           75.1µs ± 2%    30.5µs ± 2%  -59.38%  (p=0.008 n=5+5)
GCD100x100000/WithoutXY-4        170µs ± 5%     167µs ± 1%     ~     (p=1.000 n=5+5)
GCD100x100000/WithXY-4           542µs ± 2%     267µs ± 2%  -50.79%  (p=0.008 n=5+5)
GCD1000x1000/WithoutXY-4        28.0µs ± 0%    27.1µs ± 0%   -3.29%  (p=0.008 n=5+5)
GCD1000x1000/WithXY-4            329µs ± 0%      42µs ± 1%  -87.12%  (p=0.008 n=5+5)
GCD1000x10000/WithoutXY-4       47.2µs ± 0%    46.4µs ± 0%   -1.65%  (p=0.016 n=5+4)
GCD1000x10000/WithXY-4           607µs ± 9%     123µs ± 1%  -79.70%  (p=0.008 n=5+5)
GCD1000x100000/WithoutXY-4       260µs ±17%     245µs ± 0%     ~     (p=0.056 n=5+5)
GCD1000x100000/WithXY-4         3.64ms ± 1%    0.93ms ± 1%  -74.41%  (p=0.016 n=4+5)
GCD10000x10000/WithoutXY-4       513µs ± 0%     507µs ± 0%   -1.22%  (p=0.008 n=5+5)
GCD10000x10000/WithXY-4         7.44ms ± 1%    1.00ms ± 0%  -86.58%  (p=0.008 n=5+5)
GCD10000x100000/WithoutXY-4     1.23ms ± 0%    1.23ms ± 1%     ~     (p=0.056 n=5+5)
GCD10000x100000/WithXY-4        37.3ms ± 0%     7.3ms ± 1%  -80.45%  (p=0.008 n=5+5)
GCD100000x100000/WithoutXY-4    24.2ms ± 0%    24.2ms ± 0%     ~     (p=0.841 n=5+5)
GCD100000x100000/WithXY-4        505ms ± 1%      56ms ± 1%  -88.92%  (p=0.008 n=5+5)

Change-Id: I25f42ab8c55033acb83cc32bb03c12c1963925e8
Reviewed-on: https://go-review.googlesource.com/78755
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>