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Doc: more details on the syntax of the numbers

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Celestino Amoroso
2024-05-15 22:06:26 +02:00
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doc/Expr.adoc
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@@ -22,7 +22,7 @@ Expressions calculator
toc::[]
#TODO: Work in progress (last update on 2024/05/10, 06:52 a.m.)#
#TODO: Work in progress (last update on 2024/05/15, 10:00 p.m.)#
== Expr
_Expr_ is a GO package capable of analysing, interpreting and calculating expressions.
@@ -113,37 +113,84 @@ Here are some examples of execution.
_Expr_ supports numerical, string, relational, boolean expressions, and mixed-type lists.
=== Numbers
Numbers can be integers (GO int64) or float (GO float64). In mixed operations involving integers and floats, integers are automatically promoted to floats.
_Expr_ supports three type of numbers:
. [blue]#Integers#
. [blue]#Floats#
. [blue]#Factions# internally are stored as _pairs of_ Golang _int64_ values.
In mixed operations involving integers, fractions and floats, automatic type promotion to the largest type take place.
==== Integers
__Expr__'s integers are a subset of the integer set. Internally they are stored as Golang _int64_ values.
.Integer literal syntax
====
*_integer_* = [_sign_] _digit-seq_ +
_sign_ = "**+**" | "**-**" +
_digit-seq_ = _dec-seq_ | _bin-seq_ | _oct-seq_ | _hex-seq_ +
_dec-seq_ = {__dec-digit__} +
_dec-digit_ = "**0**"|"**1**"|...|"**9**" +
_bin-seq_ = "**0b**"{__bin-digit__} +
_bin-digit_ = "**0**"|"**1**" +
_oct-seq_ = "**0o**"{__oct-digit__} +
_oct-digit_ = "**0**"|"**1**"|...|"**7**" +
_hex-seq_ = "**0x**"{__hex-digit__} +
_hex-digit_ = "**0**"|"**1**"|...|"**9**"|"**a**"|...|"**z**"|"**A**"|...|"**Z**"
====
Value range: *-9223372036854775808* to *9223372036854775807*
.Arithmetic operators
[cols="^1,^2,6,4"]
|===
| Symbol | Operation | Description | Examples
| [blue]`+` / [blue]`-` | _change sign_ | Change the sign of values | [blue]`-1` _[-1]_ +
[blue]`-(+2)` _[-2]_
| [blue]`+` | _sum_ | Add two values | [blue]`-1 + 2` _[1]_ +
[blue]`4 + 0.5` _[4.5]_
| [blue]`-` | _subtraction_ | Subtract the right value from the left one | [blue]`3 - 1` _[2]_ +
[blue]`4 - 0.5` _[3.5]_
| [blue]`*` | _product_ | Multiply two values | `-1 * 2` _[-2]_ +
[blue]`4 * 0.5` _[2.0]_
| [blue]`/` | _Division_ | Divide the left value by the right one | [blue]`-1 / 2` _[0]_ +
[blue]`1.0 / 2` _[0.5]_
| [blue]`./` | _Float division_ | Force float division | [blue]`-1 ./ 2` _[-0.5]_
| [blue]`%` | _Modulo_ | Remainder of the integer division | [blue]`5 % 2` _[1]_
| [blue]`+` | _sum_ | Add two values | [blue]`-1 + 2` -> 1
| [blue]`-` | _subtraction_ | Subtract the right value from the left one | [blue]`3 - 1` -> 2
| [blue]`*` | _product_ | Multiply two values | [blue]`-1 * 2` -> -2
| [blue]`/` | _Division_ | Divide the left value by the right one^(*)^ | [blue]`-10 / 2` -> 5
| [blue]`%` | _Modulo_ | Remainder of the integer division | [blue]`5 % 2` -> 1
|===
=== Fractions
^(*)^ See also the _float division_ [blue]`./` below.
==== Floats
__Expr__'s floats are a subset of the rational number set. Note that they can't hold the exact value of an unlimited number; floats can only approximate them. Internally floats are stored as Golang's _float64_ values.
.Float literal syntax
====
*_float_* = [_sign_] _dec-seq_ "**.**" [_dec-seq_] [("**e**"|"**E**") [_sign_] _dec-seq_] +
_sign_ = "**+**" | "**-**" +
_dec-seq_ = _see-integer-literal-syntax_
====
.Arithmetic operators
[cols="^1,^2,6,4"]
|===
| Symbol | Operation | Description | Examples
| [blue]`+` | _sum_ | Add two values | [blue]`4 + 0.5` -> 4.5
| [blue]`-` | _subtraction_ | Subtract the right value from the left one | [blue]`4 - 0.5` -> 3.5
| [blue]`*` | _product_ | Multiply two values | [blue]`4 * 0.5` -> 2.0
| [blue]`/` | _Division_ | Divide the left value by the right one | [blue]`1.0 / 2` -> 0.5
| [blue]`./`| _Float division_ | Force float division | [blue]`-1 ./ 2` -> -0.5
|===
==== Fractions
_Expr_ also supports fractions. Fraction literals are made with two integers separated by a vertical bar `|`.
.Fraction literal syntax
====
*_fraction_* = [__sign__] (_num-den-spec_ | _float-spec_) +
_sign_ = "**+**" | "**-**" +
_num-den-spec_ = _digit-seq_ "**|**" _digit-seq_ +
_float-spec_ = _dec-seq_ "**.**" [_dec-seq_] "**(**" _dec-seq_ "**)**" +
_dec-seq_ = _see-integer-literal-syntax_ +
_digit-seq_ = _see-integer-literal-syntax_ +
====
.Examples
// [source,go]
// ----