ext/bcmath: Performance improvement bcsqrt()

[SakiTakamachi]

Test

Approximately 40 million calculations were performed using values of various magnitudes and scales, and all results matched those from the previous implementation.

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):      66.9 ms ±   1.5 ms    [User: 61.2 ms, System: 3.3 ms]
  Range (min … max):    64.8 ms …  73.2 ms    45 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/0.php
  Time (mean ± σ):     748.0 ms ±   7.9 ms    [User: 742.1 ms, System: 3.5 ms]
  Range (min … max):   741.6 ms … 764.9 ms    10 runs
 
Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/0.php' ran
   11.18 ± 0.27 times faster than '/master/sapi/cli/php /mount/bc/sqrt/0.php'

Middle size value (< 1) (standard path)

Code:

for ($i = 0; $i < 500000; $i++) {
    bcsqrt('0.000045689101', 20);
}

Result:

Benchmark 1: /php-dev2/sapi/cli/php /mount/bc/sqrt/1.php
  Time (mean ± σ):     109.6 ms ±   0.6 ms    [User: 103.9 ms, System: 3.4 ms]
  Range (min … max):   108.5 ms … 110.8 ms    27 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/1.php
  Time (mean ± σ):      1.082 s ±  0.003 s    [User: 1.075 s, System: 0.005 s]
  Range (min … max):    1.077 s …  1.087 s    10 runs
 
Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/1.php' ran
    9.88 ± 0.06 times faster than '/master/sapi/cli/php /mount/bc/sqrt/1.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/2.php
  Time (mean ± σ):     115.7 ms ±   0.6 ms    [User: 110.6 ms, System: 2.8 ms]
  Range (min … max):   114.0 ms … 116.5 ms    25 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/2.php
  Time (mean ± σ):     786.6 ms ±   1.3 ms    [User: 780.2 ms, System: 4.0 ms]
  Range (min … max):   784.6 ms … 788.0 ms    10 runs
 
Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/2.php' ran
    6.80 ± 0.04 times faster than '/master/sapi/cli/php /mount/bc/sqrt/2.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/3.php
  Time (mean ± σ):     195.0 ms ±   0.7 ms    [User: 189.3 ms, System: 3.3 ms]
  Range (min … max):   194.0 ms … 196.6 ms    15 runs
 
Benchmark 2: /master/sapi/cli/php /mount/bc/sqrt/3.php
  Time (mean ± σ):     277.1 ms ±   0.8 ms    [User: 270.1 ms, System: 4.5 ms]
  Range (min … max):   275.9 ms … 278.5 ms    10 runs
 
Summary
  '/php-dev2/sapi/cli/php /mount/bc/sqrt/3.php' ran
    1.42 ± 0.01 times faster than '/master/sapi/cli/php /mount/bc/sqrt/3.php'

[SakiTakamachi]

Sorry, it was still incomplete.