math/big: recognize z.Mul(x, x) as squaring of x

math/big: recognize z.Mul(x, x) as squaring of x

updates #13745

Multiprecision squaring can be done in a straightforward manner
with about half the multiplications of a basic multiplication
due to the symmetry of the operands.  This change implements
basic squaring for nat types and uses it for Int multiplication
when the same variable is supplied to both arguments of
z.Mul(x, x). This has some overhead to allocate a temporary
variable to hold the cross products, shift them to double and
add them to the diagonal terms.  There is a speed benefit in
the intermediate range when the overhead is neglible and the
asymptotic performance of karatsuba multiplication has not been
reached.

basicSqrThreshold = 20
karatsubaSqrThreshold = 400

Were set by running calibrate_test.go to measure timing differences
between the algorithms.  Benchmarks for squaring:

name           old time/op  new time/op  delta
IntSqr/1-4     51.5ns ±25%  25.1ns ± 7%  -51.38%  (p=0.008 n=5+5)
IntSqr/2-4     79.1ns ± 4%  72.4ns ± 2%   -8.47%  (p=0.008 n=5+5)
IntSqr/3-4      102ns ± 4%    97ns ± 5%     ~     (p=0.056 n=5+5)
IntSqr/5-4      161ns ± 4%   163ns ± 7%     ~     (p=0.952 n=5+5)
IntSqr/8-4      277ns ± 5%   267ns ± 6%     ~     (p=0.087 n=5+5)
IntSqr/10-4     358ns ± 3%   360ns ± 4%     ~     (p=0.730 n=5+5)
IntSqr/20-4    1.07µs ± 3%  1.01µs ± 6%     ~     (p=0.056 n=5+5)
IntSqr/30-4    2.36µs ± 4%  1.72µs ± 2%  -27.03%  (p=0.008 n=5+5)
IntSqr/50-4    5.19µs ± 3%  3.88µs ± 4%  -25.37%  (p=0.008 n=5+5)
IntSqr/80-4    11.3µs ± 4%   8.6µs ± 3%  -23.78%  (p=0.008 n=5+5)
IntSqr/100-4   16.2µs ± 4%  12.8µs ± 3%  -21.49%  (p=0.008 n=5+5)
IntSqr/200-4   50.1µs ± 5%  44.7µs ± 3%  -10.65%  (p=0.008 n=5+5)
IntSqr/300-4    105µs ±11%    95µs ± 3%   -9.50%  (p=0.008 n=5+5)
IntSqr/500-4    231µs ± 5%   227µs ± 2%     ~     (p=0.310 n=5+5)
IntSqr/800-4    496µs ± 9%   459µs ± 3%   -7.40%  (p=0.016 n=5+5)
IntSqr/1000-4   700µs ± 3%   710µs ± 5%     ~     (p=0.841 n=5+5)

Show a speed up of 10-25% in the range where basicSqr is optimal,
improved single word squaring and no significant difference when
the fallback to standard multiplication is used.

Change-Id: Iae2c82ca91cf890823f91e5c83bbe9a2c534b72b
Reviewed-on: https://go-review.googlesource.com/53638
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>