ext/bcmath: bcpow() performance improvement

[jorgsowa]

This PR improves the performance of the BCMath function bcpow.

We don't need to perform the usual multiplication when we raise a number to a specific set of numbers. I modified the content of bc_mulitply and removed all the redundant operations for the same number.

For small exponents, there is neglectable improvement, but for bigger there is up to 5%. However, I'm not quite happy with this benchmark and I need to use something else.

Benchmark:

<?php

$numbers = ['10', '2.1234567', '2'];
$exponents = [1, 2, 10, 64, 100];

foreach($numbers as $number) {
    foreach($exponents as $exponent) {
        echo "Number: $number, Exponent: $exponent = ";
        $start = microtime(true);
        for ($i = 0; $i < 1000000; $i++) {
            bcpow($number, $exponent, 20);
        }
        echo microtime(true) - $start . PHP_EOL;
    }
}

Number	Exponent	Before	After	Difference
10	1	0.369961977005	0.3674750328064	-0.67 %
10	2	0.39027285575867	0.38206386566162	-2.14 %
10	10	0.73798298835754	0.70764207839966	-4.28 %
10	64	1.6131219863892	1.4904029369354	-8.23 %
10	100	2.5796089172363	2.4571402072906	-4.98 %
2.1234567	1	0.36139988899231	0.36435699462891	+0.82 %
2.1234567	2	0.448086977005	0.44263195991516	-1.23 %
2.1234567	10	1.6505491733551	1.5602447986603	-5.78 %
2.1234567	64	6.6499609947205	6.3584640026093	-4.58 %
2.1234567	100	14.168872833252	13.804186105728	-2.64 %
2	1	0.33516597747803	0.32968902587891	-1.66 %
2	2	0.38029599189758	0.36791205406189	-3.36 %
2	10	0.59442806243896	0.5603358745575	-6.08 %
2	64	0.94932103157043	0.86743497848511	-9.44 %
2	100	1.4967222213745	1.39244389534	-7.48 %

Edit:
Benchmark using hyperfine:
0. Benchmark script

foreach($numbers as $number) {
    foreach($exponents as $exponent) {
        echo "Number: $number, Exponent: $exponent = ";
        $start = microtime(true);
        for ($i = 0; $i < 10000; $i++) {
            bcpow($number, $exponent, 20);
        }
        echo microtime(true) - $start . PHP_EOL;
    }
}

1. Float numbers, small exp

$numbers = ['1.0432151', '2.1234567', '0.798432'];
$exponents = [2, 5, 7, 8, 10];

Benchmark 1: sapi/cli/php test_float_numbers_small_exp.php
Time (mean ± σ): 168.0 ms ± 1.1 ms [User: 164.3 ms, System: 1.8 ms]
Range (min … max): 166.8 ms … 171.4 ms 17 runs

Benchmark 2: sapi/cli/php_bc/bin/php test_float_numbers_small_exp.php
Time (mean ± σ): 160.1 ms ± 1.1 ms [User: 156.1 ms, System: 1.8 ms]
Range (min … max): 158.3 ms … 161.9 ms 18 runs

Summary
sapi/cli/php_bc/bin/php test_float_numbers_small_exp.php ran
1.05 ± 0.01 times faster than sapi/cli/php test_float_numbers_small_exp.php

2. Float numbers, big exp

$numbers = ['1.0432151', '2.1234567', '0.798432'];
$exponents = [32, 64, 67, 100];

Benchmark 1: sapi/cli/php test_float_numbers_big_exp.php
Time (mean ± σ): 943.9 ms ± 5.2 ms [User: 934.5 ms, System: 2.2 ms]
Range (min … max): 936.8 ms … 952.4 ms 10 runs

Benchmark 2: sapi/cli/php_bc/bin/php test_float_numbers_big_exp.php
Time (mean ± σ): 872.4 ms ± 1.7 ms [User: 865.4 ms, System: 2.1 ms]
Range (min … max): 870.8 ms … 876.0 ms 10 runs

Summary
sapi/cli/php_bc/bin/php test_float_numbers_big_exp.php ran
1.08 ± 0.01 times faster than sapi/cli/php test_float_numbers_big_exp.php

3. Int numbers, small exp

$numbers = ['10', '72', '11', '99'];
$exponents = [2, 5, 7, 8, 10];

Benchmark 1: sapi/cli/php test_int_numbers_small_exp.php
Time (mean ± σ): 118.1 ms ± 0.5 ms [User: 114.9 ms, System: 1.7 ms]
Range (min … max): 117.4 ms … 119.5 ms 24 runs

Benchmark 2: sapi/cli/php_bc/bin/php test_int_numbers_small_exp.php
Time (mean ± σ): 112.9 ms ± 0.4 ms [User: 109.9 ms, System: 1.6 ms]
Range (min … max): 112.5 ms … 114.1 ms 26 runs

Summary
sapi/cli/php_bc/bin/php test_int_numbers_small_exp.php ran
1.05 ± 0.01 times faster than sapi/cli/php test_int_numbers_small_exp.php

4. Int numbers, big exp

$numbers = ['10', '72', '11', '99'];
$exponents = [32, 64, 67, 100];

Benchmark 1: sapi/cli/php test_int_numbers_big_exp.php
Time (mean ± σ): 355.1 ms ± 0.8 ms [User: 350.9 ms, System: 1.8 ms]
Range (min … max): 353.7 ms … 356.2 ms 10 runs

Benchmark 2: sapi/cli/php_bc/bin/php test_int_numbers_big_exp.php
Time (mean ± σ): 331.5 ms ± 0.4 ms [User: 327.1 ms, System: 1.8 ms]
Range (min … max): 330.9 ms … 332.1 ms 10 runs

Summary
sapi/cli/php_bc/bin/php test_int_numbers_big_exp.php ran
1.07 ± 0.00 times faster than sapi/cli/php test_int_numbers_big_exp.php

5. Large numbers

$numbers = ['5614987514.43124124321', '21318945190.432132591','954319523410491'];
$exponents = [2, 5, 7, 8, 10];

Benchmark 1: sapi/cli/php test_large_numbers.php
Time (mean ± σ): 303.0 ms ± 1.3 ms [User: 298.8 ms, System: 1.8 ms]
Range (min … max): 300.9 ms … 305.6 ms 10 runs

Benchmark 2: sapi/cli/php_bc/bin/php test_large_numbers.php
Time (mean ± σ): 285.7 ms ± 2.5 ms [User: 281.0 ms, System: 1.9 ms]
Range (min … max): 283.3 ms … 292.0 ms 10 runs

Summary
sapi/cli/php_bc/bin/php test_large_numbers.php ran
1.06 ± 0.01 times faster than sapi/cli/php test_large_numbers.php

[nielsdos]

Thanks for this! It generally looks good and I only have remarks about some details of the code.
Regarding the benchmark: I prefer to use hyperfine. This runs the code multiple times and computes the mean and standard deviation and filters outliers. (Note that you will still need a for loop in the PHP script because otherwise runtime gets dominated by startup and shutdown).
Please also bench with some longer numbers.

[jorgsowa]

Thank you for the review. I changed everything mentioned and tested using hyperfine. The difference depending on the number and exponent shape is between 1.05 and 1.08 faster than the previous solution. I attached the results into the description.

[nielsdos]

LGTM cc @SakiTakamachi Please also check this
Also: Do we need RM approval for optimizations like this?

[SakiTakamachi]

LGTM, thx!

@nielsdos

This shouldn't be required as it doesn't affect userland, but it's better to have RM approval.

I can approve this and merge it into 8.4.

[nielsdos]

Alright thanks! I'll let you merge it then 🙂

[nielsdos]

Seems like this was forgotten, I'll merge it now.

[SakiTakamachi]

ahhh, sorry, thanks