Numbers#

Xarpite supports handling numeric values.

Overview#

Numeric Types#

There are two numeric types: 32-bit integers INT and 64-bit floating-point numbers DOUBLE.

Distinction from Strings Representing Numbers#

In Xarpite, numbers and strings representing numbers are strictly distinguished, affecting the behavior of operators and functions.

$ xa '123 + 1'
# 124

$ xa '"123" + 1'
# 1231

To convert a number to a string, use the stringification operator &value.

The reverse is the numeric conversion operator +value.

$ xa '&123 + 1'
# 1231

$ xa '+"123" + 1'
# 124

Numeric Literals#

123: Integer Literal#

A sequence of one or more digits becomes an integer literal.

$ xa '123'
# 123

Even digit sequences starting with 0 are always interpreted as decimal.

$ xa '00123'
# 123

H#123abc: Hexadecimal Integer Literal#

You can write hexadecimal numbers following H#.

The H# part must be uppercase, but the hexadecimal part is case-insensitive.

$ xa 'H#FF'
# 255

1.23: Floating-Point Number Literal#

You can write real numbers in the form “integer part . decimal part”.

Representation and operations with real numbers involve rounding errors.

$ xa '1.5'
# 1.5

Numeric Literal Separators#

All numeric literals can include any number of _ characters at any position except the beginning of the digit sequence.

The _ characters are simply ignored.

This allows large numbers to be written more readably.

$ xa '1_000_000'
# 1000000

$ xa '1__2__3__'
# 123

$ xa 'H#FF_FF'
# 65535

$ xa '1_000.5'
# 1000.5

$ xa '1.5_0_0'
# 1.5

Numeric Conversion#

There are operators and functions to convert values to numbers.

The behavior of numeric conversion varies depending on the type of the value.

+value: Numeric Conversion#

The prefix + operator performs numeric conversion of a value.

The main purpose is to convert numeric data represented as strings into internal numeric values.

$ xa ' "+123"'
# +123

$ xa '+"+123"'
# 123

Numeric conversion references the +_ method of the value.

You can change the numeric conversion process by overriding the +_ method of an object.

$ xa '+{`+_`: this -> this.value * 2}{value: 100}'
# 200

-value: Negative Numeric Conversion#

The prefix - operator is similar to the numeric conversion operator, but negates the value.

This operator simultaneously performs “converting an arbitrary value to a number” and “negating the number”.

$ xa '-"123"'
# -123

$ xa '-(100 + 20 + 3)'
# -123

TO_NUMBER: Numeric Conversion#

TO_NUMBER(value: VALUE): NUMBER

Converts a value to a number.

It behaves the same as the +value operator.

$ xa 'TO_NUMBER("123")'
# 123

$ xa '1, 2, 3 >> TO_NUMBER'
# 6

$ xa 'TO_NUMBER(NULL)'
# 0

Addition/Subtraction Operators#

Addition/subtraction operators consist of operators that perform addition/subtraction-like operations.

Addition/subtraction operators have left-associative binding.

number + number: Addition#

The addition operator adds two values.

$ xa '1 + 2'
# 3

The addition operator behaves differently depending on the type of the left operand.

Overriding Addition Operation#

You can customize the addition operation of an object by implementing the addition method _+_.

$ xa '
  Obj := {
    `_+_`: this, other -> this.value + other.value
  }

  Obj{value: 100} + Obj{value: 23}
'
# 123

number - number: Subtraction#

The subtraction operator subtracts two values.

$ xa '3 - 1'
# 2

Like the addition operator, the subtraction operator can be overridden.

$ xa '
  Obj := {
    `_-_`: this, other -> this.value - other.value
  }

  Obj{value: 123} - Obj{value: 23}
'
# 100

Multiplication/Division Operators#

Multiplication/division operators consist of operators that perform multiplication/division-like operations.

Multiplication/division operators have left-associative binding.

number * number: Multiplication#

The multiplication operator multiplies two values.

$ xa '2 * 3'
# 6

Multiplication of strings repeats that string.

$ xa '"abc" * 3'
# abcabcabc

Multiplication of arrays repeats that array.

$ xa '[1, 2, 3] * 3'
# [1;2;3;1;2;3;1;2;3]

number / number: Division#

The division operator divides two values.

$ xa '6 / 3'
# 2.0

Even division of integers returns the result as a floating-point number.

$ xa '7 / 4'
# 1.75

number % number: Modulo#

The modulo operator divides two values and returns the remainder.

$ xa '7 % 4'
# 3

It can also handle decimals.

$ xa '1.75 % 0.5'
# 0.25

integer %% integer: Divisibility#

Returns whether the left value is divisible by the right value.

$ xa '7 %% 4'
# FALSE

It can also handle decimals.

$ xa '1.5 %% 0.5'
# TRUE

$ xa '1.75 %% 0.5'
# FALSE

integer !%% integer: Non-Divisibility#

Returns whether the left value is not divisible by the right value.

This operator is equivalent to the negation of the divisibility operator !(integer %% integer).

$ xa '7 !%% 4'
# TRUE

Exponentiation Operators#

Exponentiation operators consist only of the exponentiation operator.

Exponentiation operators have right-associative binding.

number ^ number: Exponentiation#

The exponentiation operator raises the left value to the power of the right value.

Even the result of raising an integer to an integer power is returned as a floating-point number.

$ xa '2 ^ 3'
# 8.0

There is also a function POW that can do the same thing.

$ xa 'POW(2; 3)'
# 8.0

Absolute Value#

The length operator $#number returns the absolute value of a number.

$ xa '$#10'
# 10

$ xa '$#-10'
# 10

Built-in Constants#

Numeric built-in constants.

Built-in Functions#

ABS: Get Absolute Value#

ABS(value: NUMBER): NUMBER

Returns the absolute value of the first argument.

$ xa 'ABS(-10)'
# 10

FLOOR: Round Down#

FLOOR(number: NUMBER): INT

Rounds the first argument down to the nearest integer toward negative infinity.

$ xa 'FLOOR(1.5)'
# 1

DIV: Integer Part of Division#

DIV(x: NUMBER; y: NUMBER): NUMBER

Divides x by y and returns the integer part of the result.

$ xa 'DIV(10; 3)'
# 3

SQRT: Get Square Root#

SQRT(number: NUMBER): NUMBER

Returns the positive square root of the first argument.

$ xa '"$%.3f(  SQRT(100.0)  )"'
# 10.000

SIN: Sine#

SIN(number: NUMBER): NUMBER

Interprets the first argument as radians and returns its sine.

$ xa '"$%.3f(  SIN(PI / 2)  )"'
# 1.000

COS: Cosine#

COS(number: NUMBER): NUMBER

Interprets the first argument as radians and returns its cosine.

$ xa '"$%.3f(  COS(0)  )"'
# 1.000

TAN: Tangent#

TAN(number: NUMBER): NUMBER

Interprets the first argument as radians and returns its tangent.

$ xa '"$%.3f(  TAN(PI / 4)  )"'
# 1.000

POW: Power#

POW(base: NUMBER; exponent: NUMBER): NUMBER

Returns the result of raising the first argument to the power of the second argument.

$ xa 'POW(2; 3)'
# 8.0

EXP: Exponential Function#

EXP(number: NUMBER): NUMBER

Returns the exponential function (base e) of the first argument.

$ xa '"$%.3f(  EXP(1)  )"'
# 2.718

$ xa '"$%.3f(  EXP(2)  )"'
# 7.389

LOG: Natural Logarithm#

LOG(number: NUMBER): NUMBER

Returns the natural logarithm (base e) of the first argument.

$ xa '"$%.3f(  LOG(MATH.E)  )"'
# 1.000

RAND: Get Random Number#

RAND(): DOUBLE

RAND([from: NUMBER; ]until: NUMBER): INT

When called with no arguments, returns a decimal number greater than or equal to 0 and less than 1.

When called with one argument, returns an integer greater than or equal to 0 and less than until.

When called with two arguments, returns an integer greater than or equal to from and less than until.