Write a calculator that reads mathematical terms containing floating point numbers, +, -, * and / as well as parenthesis.

Calculate the result by applying the "usual" mathematical rules:

• operators are used in infix notation: 2 + 3
• multiply/div have higher precedence then add/sub
• parenthesis have higher precedence then operators
• numbers can contain a mix of integers and floating point numbers
• calculation should follow mathematical rules, i.e. 2 / 0 is an error and not something like NaN or -Inf

The calculator should

• calculate the result of a single mathematical expression (no matter how long)
• print the result in a human readable style
• report any error and refuse the calculation (error reporting style doesn't matter)
• handle arbitrary long terms (i.e. tens of megabytes of input) well (i.e. in terms of memory usage as well as running time)

The calculator processes input that is read as UTF-8 encoded characters. A formal specification of the input language is defined by the following EBNF:

(* An expression defines the start of the production. *)
expr = number (* A bare number is a valid expression*)
     | ( expr, S, operator, S, number ) (* left-recursive operator chained expression *)
     | ( "(" S, expr, S, ")" ); (* parenthesis surround an expression *)

(* The list of available operators. *)
operator = "+" | "-" | "*" | "/";

(* Definition of a number - either 0.xyz or abc.xyz *)
number = zero_fraction 
       | non_zero_fraction;

non_zero_fraction = non_zero_digit { digit } { "." digit { digit } };

zero_fraction = "0" { "." digit { digit } };

non_zero_digit = "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9";

digit = "0" | non_zero_digit;

(* Any whitespace used as a separator including none. *)
S = "" | { " " | "\n" | "\t" | "\r" | "\f" | "\b" } ;

Note that expressions in parenthesis can also contain parenthesis.

The following lines are all valid input sequences:

0
0.123
807.1328
17 * 19
(21 - 3) * 8

• Only use the standard library for the production code; do not rely on external libraries (except for testing/benchmarking)
• Apply an appropriate structure (i.e. packages, types, ...)
• Write idiomatic code
• Write unit tests to

A couple of test files with increasing sizes are provided in testdata. The file names roughly tell the file's sizes. You can use them for functional as well as for benchmark tests.

The results are

• testdata/1k -> 248253190541.03891
• testdata/10k -> 214512826488689376
• testdata/100k -> 481585283158357967896576
• testdata/1m -> 830415166156152287340265472
• testdata/10m -> 6780466519056739908798922614519103488