Examples

Examples¶

Choose an example below and run it from the directory containing pixi.toml. Each is a standalone program in docs/examples/:

pixi run --locked mojo run -I src docs/examples/<name>.mojo

docs-test compiles the examples with --Werror and checks their output against docs/examples.json.

Getting started¶

Example	What it shows	Page
`quickstart.mojo`	Exact integers and fractions, Floats of any precision and Complex numbers	Arbitrary-precision numbers for Mojo: First program
`first_integer.mojo`	The smallest complete program: one exact Integer calculation	Installation and first run: Work from a checkout
`batch_quickstart.mojo`	Elementwise square roots at a chosen precision, followed by a sum	Batches, mapping and reductions
`integer_values.mojo`	Integer arithmetic and the three division conventions	Integer values: Arithmetic and division
`integer_tour.mojo`	A tour of Integer: text, JSON, division conventions, functions and batch updates	apn_mojo.integer: A tour of Integer
`recovery.mojo`	Reading an error's remedy and keeping the destination unchanged	Errors and recovery: Read the remedy
`conversion.mojo`	Decimal text, JSON and conversion limits for Integers	Text and JSON: Keep every digit in storage

Integer functions¶

Example	What it shows	Page
`functions.mojo`	Exact integer functions such as gcd, lcm and isqrt, on scalars and batches	apn_mojo.integer: Functions on batches
`combinatorics.mojo`	Factorials and binomial coefficients without overflow	Exact combinatorics
`number_theory.mojo`	Modular arithmetic, primality tests and prime search	apn_mojo.integer

Rationals¶

Example	What it shows	Page
`rationals.mojo`	Exact fractions: construction, arithmetic and powers	Exact fractions
`rational_input.mojo`	Exact decimal input into Rationals	Exact fractions: Exact decimal input
`rational_batches.mojo`	Batches of fractions and masked selections	Exact fractions: Batches of fractions
`rational_batch_math.mojo`	Exact elementwise batch calculations	Exact fractions: Exact batch calculations
`rational_reductions.mojo`	Exact totals and weighted sums	Exact fractions: Exact totals and weights
`rational_batch_powers.mojo`	Rounding to integers and signed powers on batches	Exact fractions: Rounding and signed powers
`rational_batch_updates.mojo`	Transactional compound updates of exact quantities	Exact fractions: Updating exact quantities
`rational_batch_json.mojo`	Saving and loading exact batches as JSON	Exact fractions: Saving exact batches

Floats¶

Example	What it shows	Page
`float_values.mojo`	Float values, formats and exact conversion	Floats of any precision: Choose a format
`float_formats.mojo`	Formats, rounding modes and traps	apn_mojo.float: Formats, rounding and traps
`float_arithmetic.mojo`	Correctly rounded arithmetic with an explicit context	Floats of any precision: Arithmetic rounds once
`float_functions.mojo`	Square roots, powers and other rounded functions	Floats of any precision: Functions
`float_interchange.mojo`	Float JSON that keeps every bit	apn_mojo.float: Text and JSON
`float_text.mojo`	Decimal and hexadecimal text	Floats of any precision: Text input and formatting
`float_elementary.mojo`	Constants, exponentials, logarithms, and trigonometric functions	Constants and elementary functions
`special_functions.mojo`	Gamma and beta functions, normal quantiles, and upper-tail probabilities	Special functions
`precision.mojo`	Cancellation, exact totals, and certification of 50 decimal digits	Precision and accuracy

Complex numbers¶

Example	What it shows	Page
`complex_values.mojo`	Complex values with independent component formats	Complex numbers: Values and components
`complex_arithmetic.mojo`	Complex arithmetic rounded per component	Complex numbers: Arithmetic
`complex_functions.mojo`	Magnitudes and square roots	Complex numbers: Magnitudes and square roots
`complex_powers.mojo`	Integral powers	Complex numbers: Powers and phase cycling
`complex_interchange.mojo`	Complex text and JSON	apn_mojo.complex: Text and JSON
`complex_elementary.mojo`	Complex exponentials and the principal logarithm	Complex elementary functions
`exact_complex_values.mojo`	Exact complex fractions, square roots, JSON, and conversion	Keep complex fractions exact

Interval bounds¶

Example	What it shows	Page
`ball_values.mojo`	Measurement uncertainty, comparisons, and a certified rounded result	Calculations with guaranteed bounds
`complex_ball_values.mojo`	Complex rectangles, magnitude bounds, and branch cuts	Rectangles in the complex plane

Batches and mapping¶

Example	What it shows	Page
`batches.mojo`	Batch snapshots, selections and updates	Batches and selections: Snapshots and slicing
`batch_functions.mojo`	NumPy-style construction, broadcasting, selection, and elementary functions	NumPy-style functions
`vectorization.mojo`	A custom scalar function mapped, accumulated, and evaluated over all pairs	Vectorization with vmap and lift
`batch_broadcasting.mojo`	Vector shape rules for operators, `batch.*`, `vmap`, and `lift`	Keep the shape rules separate
`batch_native.mojo`	Native lists and fixed-size arrays, shape, complex components, and Ball midpoints	Native values
`batch_threads.mojo`	Thread counts and numerical results with one or two participants	Threads
`ranked_batches.mojo`	Shapes and axis views	apn_mojo.batch: Shapes and axis views
`ranked_arithmetic.mojo`	Arithmetic with broadcasting across ranks	apn_mojo.batch: Higher-rank arithmetic
`vmap.mojo`	Mapping a scalar function over batches	apn_mojo.batch: Mapping functions
`vmap_tensors.mojo`	Mapping over rows and columns, with tensor results	apn_mojo.batch: Rows, columns and tensor results
`vmap_structures.mojo`	Mapped functions that return tuples	apn_mojo.batch: Tuple results
`vmap_composition.mojo`	Composing mapped functions	apn_mojo.batch: Composing mappings
`vmap_parallel.mojo`	Parallel mapping of a long batch	apn_mojo.batch: Parallel mapping
`lift.mojo`	Lifting a binary function into reduce, accumulate and outer	apn_mojo: Lifting binary functions
`lift_inputs.mojo`	Mixed exact inputs and Ball folds	apn_mojo: Lifting binary functions
`float_batches.mojo`	Float batches and their formats	apn_mojo.batch: Float batches
`float_batch_arithmetic.mojo`	Float batch arithmetic	apn_mojo.batch: Float batches
`float_batch_powers.mojo`	Float batch unary operations and powers	apn_mojo.batch: Unary operations and powers
`float_batch_functions.mojo`	Strict Float batch functions and integral conversion	apn_mojo.batch: Strict functions and integral conversion
`float_batch_updates.mojo`	Float compound updates	apn_mojo.batch: Float compound updates
`float_batch_json.mojo`	Float batch JSON	apn_mojo.batch: Float batch JSON
`complex_batches.mojo`	Complex batches and masks	apn_mojo.batch: Complex batches
`complex_batch_arithmetic.mojo`	Complex batch arithmetic	apn_mojo.batch: Complex batches
`complex_batch_functions.mojo`	Complex batch magnitudes and square roots	apn_mojo.batch: Complex batches
`complex_batch_updates.mojo`	Complex compound updates	apn_mojo.batch: Complex compound updates
`complex_batch_json.mojo`	Complex batch JSON	apn_mojo.batch: Complex batch JSON

Reductions¶

Example	What it shows	Page
`totals.mojo`	Counters and weighted totals with sum, dot and axpy	Counters and weighted totals
`float_sum.mojo`	A Float sum rounded once	apn_mojo: Float sum
`float_dot.mojo`	A Float dot product rounded once	apn_mojo: Float dot
`complex_sum.mojo`	A Complex sum rounded once per component	apn_mojo: Complex sum
`complex_dot.mojo`	Complex dot and vdot	apn_mojo: Complex dot products
`ordered_reductions.mojo`	Sequential and tree reductions	apn_mojo: Ordered reductions
`complex_ordered_reductions.mojo`	Ordered Complex reductions	apn_mojo: Ordered reductions