[WIP] ext/bcmath: optimized bcsqrt()

[SakiTakamachi]

Benchmark

The smaller the number of digits handled, the greater the performance improvement.

Small size value (fast path)

Code:

for ($i = 0; $i < 1000000; $i++) {
    bcsqrt(20, 6);
}

Result:

Benchmark 1: /php-dev2/sapi/cli/php /mount/bc/sqrt/0.php
  Time (mean ± σ):      87.5 ms ±   1.0 ms    [User: 81.6 ms, System: 3.5 ms]
  Range (min … max):    86.4 ms …  91.5 ms    33 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/0.php
  Time (mean ± σ):     748.1 ms ±   6.3 ms    [User: 741.6 ms, System: 3.9 ms]
  Range (min … max):   741.1 ms … 758.4 ms    10 runs
 
Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/0.php' ran
    8.55 ± 0.12 times faster than '/master/sapi/cli/php /mount/bc/sqrt/0.php'

Middle size value (standard path)

Code:

for ($i = 0; $i < 500000; $i++) {
    bcsqrt('15151324141414.412312232141241', 0);
}

Result:

Benchmark 1: /php-dev2/sapi/cli/php /mount/bc/sqrt/1.php
  Time (mean ± σ):     136.2 ms ±   0.5 ms    [User: 129.9 ms, System: 3.9 ms]
  Range (min … max):   135.5 ms … 137.2 ms    22 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/1.php
  Time (mean ± σ):     795.9 ms ±  29.1 ms    [User: 789.5 ms, System: 4.0 ms]
  Range (min … max):   782.8 ms … 878.1 ms    10 runs

Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/1.php' ran
    5.85 ± 0.21 times faster than '/master/sapi/cli/php /mount/bc/sqrt/1.php'

Big size value (standard path)

Code:

for ($i = 0; $i < 100; $i++) {
    bcsqrt('15151324141414.412312232141241', 3000);
}

Result:

Benchmark 1: /php-dev2/sapi/cli/php /mount/bc/sqrt/2.php
  Time (mean ± σ):     250.2 ms ±   1.4 ms    [User: 244.2 ms, System: 3.5 ms]
  Range (min … max):   248.5 ms … 253.7 ms    12 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/2.php
  Time (mean ± σ):     276.8 ms ±   1.0 ms    [User: 270.8 ms, System: 3.5 ms]
  Range (min … max):   274.9 ms … 278.5 ms    10 runs
 
Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/2.php' ran
    1.11 ± 0.01 times faster than '/master/sapi/cli/php /mount/bc/sqrt/2.php'