number

A number represents a numeric scalar value. Numbers support arithmetic, comparison, and conversion operations. Mech distinguishes numeric kinds by precision and representation, but they share common semantics. Numbers are divided into several categories: integers (signed and unsigned), floating-point, rational, and complex. Each type has its own range and precision characteristics, and are supported by various built-in operations and functions.

Numbers in Mech can be classified into the following categories:

Integers - Whole numbers, which can be positive, negative, or zero

Signed - Can represent both negative and positive values

i8 - 8-bit signed integer
i16 - 16-bit signed integer
i32 - 32-bit signed integer
i64 - 64-bit signed integer
i128 - 128-bit signed integer

Unsigned - Can only represent zero and positive values

u8 - 8-bit unsigned integer
u16 - 16-bit unsigned integer
u32 - 32-bit unsigned integer
u64 - 64-bit unsigned integer
u128 - 128-bit unsigned integer

Float - Decimal numbers with fractional components

f32 - 32-bit floating-point number
f64 - 64-bit floating-point number

Rational - Numbers represented as fractions of integers

r64 - 64-bit rational number

Complex - Numbers with real and imaginary components

c64 - 64-bit complex number

Numeric Types

Integer Numbers

Both signed and unsigned integers from 8 to 128 bits are supported in Mech. Signed integers can represent negative values, while unsigned integers can only represent zero and positive values.

Signed Integers

Type	Description	Minimum Value	Maximum Value
`i8`	`8-bit` signed integer	`-128`	`127`
`i16`	`16-bit` signed integer	`-32,768`	`32,767`
`i32`	`32-bit` signed integer	`-2e9`	`2e9 - 1`
`i64`	`64-bit` signed integer	`-9e18`	`9e18 - 1`
`i128`	`128-bit` signed integer	`-1.7e38`	`1.7e38 - 1`

Unsigned Integers

Type	Description	Minimum Value	Maximum Value
`u8`	`8-bit` unsigned integer	`0`	`255`
`u16`	`16-bit` unsigned integer	`0`	`65535`
`u32`	`32-bit` unsigned integer	`0`	`4e9 - 1`
`u64`	`64-bit` unsigned integer	`0`	`18e18 - 1`
`u128`	`128-bit` unsigned integer	`0`	`3.4e38 - 1`

For more, see integer.

Float Numbers

Float numbers in Mech are represented using standard floating-point types. Mech supports both f32 and f64 types, which correspond to 32-bit and 64-bit IEEE 754 floating-point numbers, respectively.

Type	Description	Precision	Range
`f32`	32-bit floating-point number	7 decimal digits	`±1.5e-45` to `±3.4e38`
`f64`	64-bit floating-point number	15 decimal digits	`±5e-324` to `±1.7e308`

For more, see float.

Rational Numbers

Rational numbers in Mech are represented using the r64 type, which allows for exact representation of fractions as ratios of two integers.

Type	Description	Examples
`r64`	64-bit rational number	3/4, -5/2, 7/1

For more, see rational.

Complex Numbers

Complex numbers in Mech are represented using the c64 type, which consists of a real and an imaginary component, both represented as f64 floating-point numbers.

Type	Description	Examples
`c64`	64-bit complex number	3+4i, 1+-2i, 0+1i

For more, see complex.

Syntax

Numeric literals can be expressed in various formats:

Floating-point numbers, expressed in standard decimal notation and scientific notation
Integers, expressed in decimal (base 10), hexadecimal (base 16), octal (base 8), and binary (base 2)
Rational numbers, expressed as fractions a/b, where a is the numerator and b is the denominator
Complex numbers, expressed in the form a + bi or a + bj, where a is the real part and b is the imaginary part

Floating-Point Literals

Floating-point literals are used to represent decimal numbers with fractional components. They are flexible in that they can represent both very large and very small numbers, and also can represent integer values between -1.7e308 and 1.7e308 for f64, and between -3.4e38 and 3.4e38 for f32.

Floating-point literals are expressed in standard decimal notation or scientific notation:

42-- inferred as f643.14-0.0012.5e+3.-1.2e-2.

Each value is inferred as f64 unless otherwise specified. To specify a specific type, floating-point literals can also be suffixed with a specific kind:

42<f32>3.14<f32>-0.001<f64>2.5e+3.<f32>-1.2e-2.<f64>

Integer Literals

Integer literals can be written in the following formats:

0d42-- decimal0x2ABC-- hexadecimal0o654-- octal0b101010-- binary

Decimals without a prefix are inferred as floating-point numbers (f64), while those with the 0d prefix are inferred as signed integers (i64). Each of the other formats are also inferred as i64 unless otherwise specified. Any integer literal can be suffixed with a specific kind to indicate its type:

42u8-- unsigned 8-bit integer

Decimal literals can be signed or unsigned. Signed literal types include i8, i16, i32, i64, and i128. Unsigned literal types include u8, u16, u32, u64, and u128.

Rational Literals

Rational numbers are used to represent fractions exactly as ratios of two integers. They are expressed in the form a/b, where a is the numerator and b is the denominator.

Rational numbers are written as follows:

3/4-5/27/7-- A whole number represented as a rational

Two rational literals can represent the same numeric value but have different representations:

ex 2.3.2

x:=1/2--

Represents 0.5

y:=2/4--

Also represents 0.5

x⩵y--

Evaluates to true

Complex Literals

Complex numbers are used to represent numbers with both real and imaginary components. They are expressed in the form a + bi or a + bj, where a is the real part and b is the imaginary part.

Complex numbers are written as follows:

3+4i1+-2i0+1i

The imaginary unit can be represented by either i or j. Both representations are equivalent and can be used interchangeably.