feat: add C implementation for math/base/special/round

[Pranavchiku]

Resolves #735.

Checklist

• update readme.md
• include.gypi
• binding.gyp
• include/stdlib/math/base/special/
• src
• manifest.json
• lib
• examples
• benchmark
• test

---

@kgryte

[Pranavchiku]

In test.native.js I removed one test t.strictEqual( round( -4.5 ), -4.0, 'equals -4' ); as for

Javascript

Math.round( -4.5 ) = -4

C

round( -4.5 ) = -5

Rest all tests passed and benchmarks cleared, this PR can have a review.

[kgryte]

@Pranavchiku This is an instance where we want to emulate JS behavior in C, I believe. Or maybe instead, we should do whatever IEEE 754-2008 specifies. Would be worth reading the spec and seeing what the default round behavior is specified to be. IIRC correctly, JavaScript is not IEEE 754 compliant, but this should be confirmed.

[Pranavchiku]

Okay, I will have a look at it.

[Shashankss1205]

Accordin to https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/round:
"If the fractional portion is exactly 0.5, the argument is rounded to the next integer in the direction of +∞."

So I am confused if the rounding is to be done, then what rule will it follow?

[kgryte]

@Shashankss1205 What is the confusion? In short, JS behavior is to round ties in a manner similar to ceil. In all other cases, round to the nearest integer. E.g.,

var v = round( 1.2 );
// returns 1.0

v = round( 1.8 );
// returns 2.0

v = round( 1.5 );
// returns 2.0

v = round( -1.2 );
// returns -1.0

v = round( -1.8 );
// returns -2.0

v = round( -1.5 );
// returns 1.0

Notice the behavior of 1.5 and -1.5 above.

[Shashankss1205]

@Shashankss1205 What is the confusion? In short, JS behave is to round ties in a manner similar to ceil. In all other cases, round to the nearest integer. E.g.,

var v = round( 1.2 );
// returns 1.0

v = round( 1.8 );
// returns 2.0

v = round( 1.5 );
// returns 2.0

v = round( -1.2 );
// returns -1.0

v = round( -1.8 );
// returns -2.0

v = round( -1.5 );
// returns -1.0

Notice the behavior of 1.5 and -1.5 above.

Yeah understood, Thanks for confirming!

[Pranavchiku]

IEEE 754-2008

The roundTiesToEven rounding-direction attribute shall be the default rounding-direction attribute for results in binary formats. The default rounding-direction attribute for results in decimal formats is language-defined, but should be roundTiesToEven.

rountTiesToEven

roundTiesToEven, the floating-point number nearest to the infinitely precise result shall be delivered; if the two nearest floating-point numbers bracketing an unrepresentable infinitely precise result are equally near, the one with an even least significant digit shall be delivered

Source: https://iremi.univ-reunion.fr/IMG/pdf/ieee-754-2008.pdf

[Pranavchiku]

We can continue discussion at #1450, pushing implementation from https://tc39.es/ecma262/multipage/numbers-and-dates.html#sec-math.round.

[Planeshifter]

Subsequently merged in #1450.