Add truncate(x,n) presto function

[gosharz]

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Context: of https://github.com/facebookincubator/velox/issues/2262

Presto supports two versions of truncate: truncate(x) and truncate(x,n). The former one has been added per https://github.com/facebookincubator/velox/pull/2862. This issue add adding implementation for the second overload.

Here is the java reference implementation which must be mimicked: https://github.com/prestodb/presto/blob/ff412ef4b745eb31549cc0abe25e885a63875f58/presto-main/src/main/java/com/facebook/presto/operator/scalar/MathFunctions.java#L365

[pedroerp]

@gosharz are you going to be working on this Issue as well?

[gosharz]

@pedroerp giving it a quick shot here: https://github.com/facebookincubator/velox/pull/2892

[gosharz]

Catching up with @mbasmanova: it looks we need to have a closer look at the ways to properly mimick the Java implementation. Main reasons:

1. Java implementation relies heavily on BigDecimal support. We need to research c++ alternatives for BigDecimal.
2. Naive implementation with using std::pow and std::trunc most probably will introduce a lot of mismatches due to rounding errors and double time limits

Adding references we've collected so far on the 1st point:

1. BigDecimal alternative in C++ - https://stackoverflow.com/questions/4798777/is-there-a-c-equivalent-to-javas-bigdecimal
2. The GNU Multiple Precision Arithmetic Library - https://gmplib.org/
3. The GNU MPFR Library - https://www.mpfr.org/
4. Boost.multiprecision- https://www.boost.org/doc/libs/1_72_0/libs/multiprecision/doc/html/index.html
5. double-conversion - https://github.com/google/double-conversion
6. Postrgres sql trunc implementation - https://github.com/postgres/postgres/blob/40c7fcbbed5d922e905f8032c5035826d0406980/src/backend/utils/adt/numeric.c#L11068
7. mysql - https://github.com/mysql/mysql-server/blob/a246bad76b9271cb4333634e954040a970222e0a/sql/item_func.cc#L3469

[gosharz]

From https://prestodb.io/docs/current/language/types.html#decimal:

Fixed-Precision[#](https://prestodb.io/docs/current/language/types.html#fixed-precision)
DECIMAL[#](https://prestodb.io/docs/current/language/types.html#decimal)
A fixed precision decimal number. Precision up to 38 digits is supported but performance is best up to 18 digits.

The decimal type takes two literal parameters:

precision - total number of digits

scale - number of digits in fractional part. Scale is optional and defaults to 0.

Example type definitions: DECIMAL(10,3), DECIMAL(20)

Example literals: DECIMAL '10.3', DECIMAL '1234567890', 1.1

Note

For compatibility reasons decimal literals without explicit type specifier (e.g. 1.2) are treated as values of the DOUBLE type by default up to version 0.198. After 0.198 they are parsed as DECIMAL.

System wide property: parse-decimal-literals-as-double

Session wide property: parse_decimal_literals_as_double

Wondering if using one of the above libraries with maximal precision to match type boundaries will guarantee full parity.

[gosharz]

From https://en.wikipedia.org/wiki/Floating-point_arithmetic:

Type	Sign	Exponent	Significand field	Total bits		Exponent bias	Bits precision	Number of decimal digits
Half (IEEE 754-2008)	1	5	10	16		15	11	~3.3
Single	1	8	23	32		127	24	~7.2
Double	1	11	52	64		1023	53	~15.9
x86 extended precision	1	15	64	80		16383	64	~19.2
Quad	1	15	112	128		16383	113	~34.0

Type Sign Exponent Significand field Total bits Exponent bias Bits precision Number of decimal digits Half (IEEE 754-2008) 1 5 10 16 15 11 ~3.3 Single 1 8 23 32 127 24 ~7.2 Double 1 11 52 64 1023 53 ~15.9 x86 extended precision 1 15 64 80 16383 64 ~19.2 Quad 1 15 112 128 16383 113 ~34.0

[gosharz]

Per https://github.com/facebookincubator/velox/pull/2892