Numerics¶

Li uses Python-like names with compiled fixed-width behavior. This catches common scientific bugs (like adding an int to a float by accident).

Default mappings¶

You write	Machine
`int`	64-bit signed
`float`	64-bit IEEE
`42`	integer literal → `i64`
`3.14`	float literal → `f64`

Full width tables, suffixes, binary, and physics metadata: Scalar precision (canonical).

You choose precision — explicit types (float32), suffixes (3.14f32), optional li.toml [numerics], and physics float_bits are all per-project / per-module choices; the org does not enforce one global width. See You set precision yourself.

Literal suffixes¶

42       # int (i64)
42u      # uint (u64)
42i32    # int32
255u8    # uint8
3.14     # float64
3.14f32  # float32
1.0f16   # float16
0b1011   # binary
2.0 + 1.0i   # complex

Operators (important rules)¶

Expression	Result
`int + int`	`int`
`float + float`	`float`
`int + float`	Error (must cast explicitly)
`int / int`	`float` (Python 3 division)
`int // int`	floor division

Overflow¶

Default integers are checked: overflow must be impossible to prove, or you use an explicit mode:

Mode	Meaning
`checked int`	Default — must prove no overflow
`wrapping i32`	Modular arithmetic with proof
`saturating i32`	Clamped arithmetic with proof

There is no silent unchecked int.

Effects on numeric ops¶

Situation	Effect
Division by zero	`raises DivZero` or compile error if divisor is literal 0
`sqrt` of negative	`raises Float` (by default)

SIMD numerics¶

simd[T, N] supports lane-wise +, *, and intrinsics such as horizontal sum. Element type T is typically f32 or f64.

See SIMD and parallel.

Roadmap (not all shipped yet)¶

Phase	Features
v1	Scalars, complex, SIMD, parallel CPU
v2	`f16`, `bf16`, async generators
v3	`tensor[Shape, T]`, GPU buffers

Full tables: design spec — numeric roadmap.