examples: improve the pendulum simulation, with several modes and diagrams (#13446)

examples/pendulum-simulation/modules/sim/anim/app.v

@@ -0,0 +1,64 @@
+module anim
+
+import gg
+import gx
+import sim
+import sim.args as simargs
+
+const bg_color = gx.white
+
+struct Pixel {
+	x     f32
+	y     f32
+	color gx.Color
+}
+
+struct App {
+pub:
+	args         simargs.ParallelArgs
+	request_chan chan &sim.SimRequest
+	result_chan  chan &sim.SimResult
+pub mut:
+	gg     &gg.Context = 0
+	iidx   int
+	pixels []u32
+}
+
+pub fn new_app(args simargs.ParallelArgs) &App {
+	total_pixels := args.grid.height * args.grid.width
+
+	mut app := &App{
+		args: args
+		pixels: []u32{len: total_pixels}
+		request_chan: chan &sim.SimRequest{cap: args.grid.width}
+	}
+	app.gg = gg.new_context(
+		width: args.grid.width
+		height: args.grid.height
+		create_window: true
+		window_title: 'V Pendulum Simulation'
+		user_data: app
+		bg_color: anim.bg_color
+		frame_fn: frame
+		init_fn: init
+	)
+	return app
+}
+
+fn init(mut app App) {
+	app.iidx = app.gg.new_streaming_image(app.args.grid.width, app.args.grid.height, 4,
+		pixel_format: .rgba8)
+	go pixels_worker(mut app)
+}
+
+fn frame(mut app App) {
+	app.gg.begin()
+	app.draw()
+	app.gg.end()
+}
+
+fn (mut app App) draw() {
+	mut istream_image := app.gg.get_cached_image_by_idx(app.iidx)
+	istream_image.update_pixel_data(&app.pixels[0])
+	app.gg.draw_image(0, 0, app.args.grid.width, app.args.grid.height, istream_image)
+}

examples/pendulum-simulation/modules/sim/anim/worker.v

@@ -0,0 +1,19 @@
+module anim
+
+import benchmark
+import sim
+import sim.img
+
+fn pixels_worker(mut app App) {
+	mut bmark := benchmark.new_benchmark()
+	for {
+		result := <-app.result_chan or { break }
+		bmark.step()
+		// find the closest magnet
+		pixel_color := img.compute_pixel(result)
+		app.pixels[result.id] = u32(pixel_color.abgr8())
+		bmark.ok()
+	}
+	bmark.stop()
+	println(bmark.total_message(@FN))
+}

examples/pendulum-simulation/modules/sim/args/parser.v

@@ -0,0 +1,158 @@
+module args
+
+import flag
+import os
+import runtime
+import sim
+import math
+
+// customisable through setting VJOBS
+const max_parallel_workers = runtime.nr_jobs()
+
+[params]
+pub struct ParserSettings {
+	sequential    bool
+	img           bool
+	extra_workers int
+}
+
+pub struct SequentialArgs {
+pub:
+	params   sim.SimParams
+	grid     sim.GridSettings
+	filename string
+}
+
+pub struct ParallelArgs {
+	SequentialArgs
+pub:
+	workers int = args.max_parallel_workers
+}
+
+pub type SimArgs = ParallelArgs | SequentialArgs
+
+pub fn parse_args(config ParserSettings) ?SimArgs {
+	if config.sequential {
+		args := parse_sequential_args() ?
+		return SimArgs(args)
+	} else {
+		args := parse_parallel_args(config.extra_workers) ?
+		return SimArgs(args)
+	}
+}
+
+fn parse_sequential_args() ?SequentialArgs {
+	mut fp := flag.new_flag_parser(os.args)
+	fp.application('vps')
+	fp.version('v0.1.0')
+	fp.limit_free_args(0, 0) ?
+	fp.description('This is a pendulum simulation written in pure V')
+	fp.skip_executable()
+
+	// output parameters
+	width := fp.int('width', `w`, sim.default_width, 'width of the image output. Defaults to $sim.default_width')
+	height := fp.int('height', `h`, sim.default_height, 'height of the image output. Defaults to $sim.default_height')
+	filename := fp.string('output', `o`, 'out.ppm', 'name of the image output. Defaults to out.ppm')
+
+	// simulation parameters
+	rope_length := fp.float('rope-length', 0, sim.default_rope_length, 'rope length to use on simulation. Defaults to $sim.default_rope_length')
+	bearing_mass := fp.float('bearing-mass', 0, sim.default_bearing_mass, 'bearing mass to use on simulation. Defaults to $sim.default_bearing_mass')
+	magnet_spacing := fp.float('magnet-spacing', 0, sim.default_magnet_spacing, 'magnet spacing to use on simulation. Defaults to $sim.default_magnet_spacing')
+	magnet_height := fp.float('magnet-height', 0, sim.default_magnet_height, 'magnet height to use on simulation. Defaults to $sim.default_magnet_height')
+	magnet_strength := fp.float('magnet-strength', 0, sim.default_magnet_strength, 'magnet strength to use on simulation. Defaults to $sim.default_magnet_strength')
+	gravity := fp.float('gravity', 0, sim.default_gravity, 'gravity to use on simulation. Defaults to $sim.default_gravity')
+
+	fp.finalize() or {
+		println(fp.usage())
+		return none
+	}
+
+	params := sim.sim_params(
+		rope_length: rope_length
+		bearing_mass: bearing_mass
+		magnet_spacing: magnet_spacing
+		magnet_height: magnet_height
+		magnet_strength: magnet_strength
+		gravity: gravity
+	)
+
+	grid := sim.new_grid_settings(
+		width: width
+		height: height
+	)
+
+	args := SequentialArgs{
+		params: params
+		filename: filename
+		grid: grid
+	}
+
+	sim.log('$args')
+
+	return args
+}
+
+fn parse_parallel_args(extra_workers int) ?ParallelArgs {
+	mut fp := flag.new_flag_parser(os.args)
+	fp.application('vps')
+	fp.version('v0.1.0')
+	fp.limit_free_args(0, 0) ?
+	fp.description('This is a pendulum simulation written in pure V')
+	fp.skip_executable()
+
+	workers := fp.int('workers', 0, args.max_parallel_workers, 'amount of workers to use on simulation. Defaults to $args.max_parallel_workers')
+
+	// output parameters
+	width := fp.int('width', `w`, sim.default_width, 'width of the image output. Defaults to $sim.default_width')
+	height := fp.int('height', `h`, sim.default_height, 'height of the image output. Defaults to $sim.default_height')
+	filename := fp.string('output', `o`, 'out.ppm', 'name of the image output. Defaults to out.ppm')
+
+	// simulation parameters
+	rope_length := fp.float('rope-length', 0, sim.default_rope_length, 'rope length to use on simulation. Defaults to $sim.default_rope_length')
+	bearing_mass := fp.float('bearing-mass', 0, sim.default_bearing_mass, 'bearing mass to use on simulation. Defaults to $sim.default_bearing_mass')
+	magnet_spacing := fp.float('magnet-spacing', 0, sim.default_magnet_spacing, 'magnet spacing to use on simulation. Defaults to $sim.default_magnet_spacing')
+	magnet_height := fp.float('magnet-height', 0, sim.default_magnet_height, 'magnet height to use on simulation. Defaults to $sim.default_magnet_height')
+	magnet_strength := fp.float('magnet-strength', 0, sim.default_magnet_strength, 'magnet strength to use on simulation. Defaults to $sim.default_magnet_strength')
+	gravity := fp.float('gravity', 0, sim.default_gravity, 'gravity to use on simulation. Defaults to $sim.default_gravity')
+
+	fp.finalize() or {
+		println(fp.usage())
+		return none
+	}
+
+	params := sim.sim_params(
+		rope_length: rope_length
+		bearing_mass: bearing_mass
+		magnet_spacing: magnet_spacing
+		magnet_height: magnet_height
+		magnet_strength: magnet_strength
+		gravity: gravity
+	)
+
+	grid := sim.new_grid_settings(
+		width: width
+		height: height
+	)
+
+	args := ParallelArgs{
+		params: params
+		filename: filename
+		grid: grid
+		workers: get_workers(workers, extra_workers)
+	}
+
+	sim.log('$args')
+
+	return args
+}
+
+[inline]
+fn get_workers(workers int, extra_workers int) int {
+	result := if workers + extra_workers <= args.max_parallel_workers {
+		workers
+	} else {
+		args.max_parallel_workers - extra_workers
+	}
+
+	return math.max(1, result)
+}

examples/pendulum-simulation/modules/sim/img/ppm.v

@@ -0,0 +1,74 @@
+module img
+
+import gx
+import os
+import sim
+
+[params]
+pub struct ImageSettings {
+pub:
+	width      int = sim.default_width
+	height     int = sim.default_height
+	cache_size int = 200
+}
+
+pub fn new_image_settings(settings ImageSettings) ImageSettings {
+	return ImageSettings{
+		...settings
+	}
+}
+
+pub fn image_settings_from_grid(grid sim.GridSettings) ImageSettings {
+	return ImageSettings{
+		width: grid.width
+		height: grid.height
+	}
+}
+
+pub fn (s ImageSettings) to_grid_settings() sim.GridSettings {
+	return sim.GridSettings{
+		width: s.width
+		height: s.height
+	}
+}
+
+pub struct PPMWriter {
+mut:
+	file       os.File
+	cache      []byte
+	cache_size int
+}
+
+pub fn ppm_writer_for_fname(fname string, settings ImageSettings) ?&PPMWriter {
+	mut writer := &PPMWriter{
+		cache_size: settings.cache_size
+		cache: []byte{cap: settings.cache_size}
+	}
+	writer.start_for_file(fname, settings) ?
+	return writer
+}
+
+pub fn (mut writer PPMWriter) start_for_file(fname string, settings ImageSettings) ? {
+	writer.file = os.create(fname) ?
+	writer.file.writeln('P6 $settings.width $settings.height 255') ?
+}
+
+pub fn (mut writer PPMWriter) handle_pixel(p gx.Color) ? {
+	if writer.cache.len >= writer.cache_size {
+		writer.write() ?
+		writer.flush() ?
+	}
+	writer.cache << [p.r, p.g, p.b]
+}
+
+pub fn (mut writer PPMWriter) flush() ? {
+	writer.cache.clear()
+}
+
+pub fn (mut writer PPMWriter) write() ? {
+	writer.file.write(writer.cache) ?
+}
+
+pub fn (mut writer PPMWriter) close() {
+	writer.file.close()
+}

examples/pendulum-simulation/modules/sim/img/worker.v

@@ -0,0 +1,40 @@
+module img
+
+import benchmark
+import sim
+
+pub fn image_worker(mut writer PPMWriter, result_chan chan &sim.SimResult, settings ImageSettings) {
+	width := settings.width
+	height := settings.height
+	total_pixels := width * height
+
+	// as new pixels come in, write them to the image file
+	mut current_index := u64(0)
+	mut pixel_buf := []ValidColor{len: total_pixels, init: ValidColor{
+		valid: false
+	}}
+
+	mut bmark := benchmark.new_benchmark()
+	for {
+		result := <-result_chan or { break }
+
+		// find the closest magnet
+		pixel_buf[result.id].Color = compute_pixel(result)
+		pixel_buf[result.id].valid = true
+
+		for current_index < total_pixels && pixel_buf[current_index].valid {
+			bmark.step()
+			writer.handle_pixel(pixel_buf[current_index].Color) or {
+				bmark.fail()
+				sim.log(@MOD + '.' + @FN + ': pixel handler failed. Error $err')
+				break
+			}
+			bmark.ok()
+			current_index++
+		}
+	}
+	bmark.stop()
+	println(bmark.total_message(@FN))
+
+	writer.write() or { panic('Could not write image') }
+}

examples/pendulum-simulation/modules/sim/img/writer.v

@@ -0,0 +1,68 @@
+module img
+
+import gx
+import sim
+
+pub struct ValidColor {
+	gx.Color
+pub mut:
+	valid bool
+}
+
+pub struct ImageWritter {
+	settings ImageSettings
+pub mut:
+	writer        PPMWriter
+	current_index int
+	buffer        []ValidColor
+}
+
+pub fn new_image_writer(mut writer PPMWriter, settings ImageSettings) &ImageWritter {
+	total_pixels := settings.width * settings.height
+	mut buffer := []ValidColor{len: total_pixels, init: ValidColor{
+		valid: false
+	}}
+	return &ImageWritter{
+		writer: writer
+		settings: settings
+		buffer: buffer
+	}
+}
+
+pub fn (mut iw ImageWritter) handle(result sim.SimResult) ?int {
+	total_pixels := iw.settings.width * iw.settings.height
+
+	// find the closest magnet
+	iw.buffer[result.id].Color = compute_pixel(result)
+	iw.buffer[result.id].valid = true
+
+	for iw.current_index < total_pixels && iw.buffer[iw.current_index].valid {
+		iw.writer.handle_pixel(iw.buffer[iw.current_index].Color) or {
+			sim.log(@MOD + '.' + @FN + ': pixel handler failed. Error $err')
+			break
+		}
+		iw.current_index++
+	}
+
+	if iw.current_index == total_pixels {
+		iw.writer.write() or { panic('Could not write image') }
+		return none
+	}
+
+	return iw.current_index
+}
+
+pub fn compute_pixel(result sim.SimResult) gx.Color {
+	closest_to_m1 := result.magnet1_distance < result.magnet2_distance
+		&& result.magnet1_distance < result.magnet3_distance
+	closest_to_m2 := result.magnet2_distance < result.magnet1_distance
+		&& result.magnet2_distance < result.magnet3_distance
+
+	if closest_to_m1 {
+		return gx.red
+	} else if closest_to_m2 {
+		return gx.green
+	} else {
+		return gx.blue
+	}
+}

examples/pendulum-simulation/modules/sim/log.v

@@ -0,0 +1,9 @@
+module sim
+
+// log is a helper function to print debug info
+[inline]
+pub fn log(info string) {
+	$if verbose ? {
+		println(info)
+	}
+}

examples/pendulum-simulation/modules/sim/params.v

@@ -0,0 +1,96 @@
+module sim
+
+import math
+
+pub const (
+	default_rope_length     = 0.25
+	default_bearing_mass    = 0.03
+	default_magnet_spacing  = 0.05
+	default_magnet_height   = 0.03
+	default_magnet_strength = 10.0
+	default_gravity         = 4.9
+)
+
+[params]
+pub struct SimParams {
+	rope_length     f64 = sim.default_rope_length
+	bearing_mass    f64 = sim.default_bearing_mass
+	magnet_spacing  f64 = sim.default_magnet_spacing
+	magnet_height   f64 = sim.default_magnet_height
+	magnet_strength f64 = sim.default_magnet_strength
+	gravity         f64 = sim.default_gravity
+}
+
+pub fn sim_params(params SimParams) SimParams {
+	return SimParams{
+		...params
+	}
+}
+
+pub fn (params SimParams) get_rope_vector(state SimState) Vector3D {
+	rope_origin := vector(z: params.rope_length)
+
+	return state.position + rope_origin.scale(-1)
+}
+
+pub fn (params SimParams) get_forces_sum(state SimState) Vector3D {
+	// force due to gravity
+	f_gravity := params.get_grav_force(state)
+
+	// force due to magnets
+	f_magnet1 := params.get_magnet1_force(state)
+	f_magnet2 := params.get_magnet2_force(state)
+	f_magnet3 := params.get_magnet3_force(state)
+
+	mut f_passive := vector(x: 0.0, y: 0.0, z: 0.0)
+	for force in [f_gravity, f_magnet1, f_magnet2, f_magnet3] {
+		f_passive = f_passive + force
+	}
+
+	// force due to tension of the rope
+	f_tension := params.get_tension_force(state, f_passive)
+
+	return f_passive + f_tension
+}
+
+pub fn (params SimParams) get_grav_force(state SimState) Vector3D {
+	return vector(z: -params.bearing_mass * params.gravity)
+}
+
+pub fn (params SimParams) get_magnet_position(theta f64) Vector3D {
+	return vector(
+		x: math.cos(theta) * params.magnet_spacing
+		y: math.sin(theta) * params.magnet_spacing
+		z: -params.magnet_height
+	)
+}
+
+pub fn (params SimParams) get_magnet_force(theta f64, state SimState) Vector3D {
+	magnet_position := params.get_magnet_position(theta)
+	mut diff := magnet_position + state.position.scale(-1)
+	distance_squared := diff.norm_squared()
+	diff = diff.scale(1.0 / math.sqrt(distance_squared))
+	return diff.scale(params.magnet_strength / distance_squared)
+}
+
+pub fn (params SimParams) get_magnet_dist(theta f64, state SimState) f64 {
+	return (params.get_magnet_position(theta) + state.position.scale(-1)).norm()
+}
+
+pub fn (params SimParams) get_magnet1_force(state SimState) Vector3D {
+	return params.get_magnet_force(0.0 * math.pi / 3.0, state)
+}
+
+pub fn (params SimParams) get_magnet2_force(state SimState) Vector3D {
+	return params.get_magnet_force(2.0 * math.pi / 3.0, state)
+}
+
+pub fn (params SimParams) get_magnet3_force(state SimState) Vector3D {
+	return params.get_magnet_force(4.0 * math.pi / 3.0, state)
+}
+
+pub fn (params SimParams) get_tension_force(state SimState, f_passive Vector3D) Vector3D {
+	rope_vector := params.get_rope_vector(state)
+	rope_vector_norm := rope_vector.scale(1.0 / rope_vector.norm())
+	return rope_vector_norm.scale(-1.0 * (rope_vector_norm * f_passive))
+}

examples/pendulum-simulation/modules/sim/params_test.v

@@ -0,0 +1,125 @@
+module sim
+
+import math
+
+const (
+	params_test_mock_params = SimParams{
+		rope_length: 0.25
+		bearing_mass: 0.03
+		magnet_spacing: 0.05
+		magnet_height: 0.03
+		magnet_strength: 10
+		gravity: 4.9
+	}
+	params_test_mock_state = SimState{
+		position: vector(
+			x: -0.016957230930171364
+			y: -0.02937078552673521
+			z: 0.002311063475327252
+		)
+		velocity: vector(
+			x: -7.251158929833104
+			y: -12.559375680227724
+			z: -105.91539687686381
+		)
+		accel: vector(
+			x: -8.337034766251843e-11
+			y: -2.842170943040401e-10
+			z: 1.2126596023639044e-10
+		)
+	}
+	params_test_mock_tetha = 2.0 * math.pi / 3.0
+)
+
+pub fn test_get_rope_vector() {
+	result := sim.params_test_mock_params.get_rope_vector(sim.params_test_mock_state)
+	expected := vector(
+		x: -0.016957230930171364
+		y: -0.02937078552673521
+		z: -0.24768893652467275
+	)
+	assert result == expected
+}
+
+pub fn test_get_forces_sum() {
+	result := sim.params_test_mock_params.get_forces_sum(sim.params_test_mock_state)
+	expected := vector(
+		x: 3.637978807091713e-12
+		y: 5.229594535194337e-12
+		z: 9.094947017729282e-13
+	)
+	assert result == expected
+}
+
+pub fn test_get_grav_force() {
+	result := sim.params_test_mock_params.get_grav_force(sim.params_test_mock_state)
+	expected := vector(
+		z: -0.147
+	)
+	assert result == expected
+}
+
+pub fn test_get_magnet_position() {
+	result := sim.params_test_mock_params.get_magnet_position(sim.params_test_mock_tetha)
+	expected := vector(
+		x: -0.024999999999999988
+		y: 0.043301270189221946
+		z: -0.03
+	)
+	assert result == expected
+}
+
+pub fn test_get_magnet_force() {
+	result := sim.params_test_mock_params.get_magnet_force(sim.params_test_mock_tetha,
+		sim.params_test_mock_state)
+	expected := vector(
+		x: -157.45722976925555
+		y: 1422.736432604726
+		z: -632.5695169850264
+	)
+	assert result == expected
+}
+
+pub fn test_get_magnet_dist() {
+	result := sim.params_test_mock_params.get_magnet_dist(sim.params_test_mock_tetha,
+		sim.params_test_mock_state)
+	expected := 0.07993696666249227
+	assert result == expected
+}
+
+pub fn test_get_magnet1_force() {
+	result := sim.params_test_mock_params.get_magnet1_force(sim.params_test_mock_state)
+	expected := vector(
+		x: 1310.8545084099674
+		y: 575.0062553126633
+		z: -632.5695169850262
+	)
+	assert result == expected
+}
+
+pub fn test_get_magnet2_force() {
+	result := sim.params_test_mock_params.get_magnet2_force(sim.params_test_mock_state)
+	expected := vector(
+		x: -157.45722976925555
+		y: 1422.736432604726
+		z: -632.5695169850264
+	)
+	assert result == expected
+}
+
+pub fn test_get_magnet3_force() {
+	result := sim.params_test_mock_params.get_magnet3_force(sim.params_test_mock_state)
+	expected := vector(
+		x: -1710.46541088048
+		y: -2962.612996234165
+		z: -6871.632889552589
+	)
+	assert result == expected
+}
+
+pub fn test_get_tension_force() {
+	result := sim.params_test_mock_params.get_tension_force(sim.params_test_mock_state,
+		vector(x: 0.0, y: 0.0, z: 0.0))
+	expected := vector(x: 0.0, y: 0.0, z: 0.0)
+	assert result == expected
+}

examples/pendulum-simulation/modules/sim/runner.v

@@ -0,0 +1,96 @@
+module sim
+
+import benchmark
+import term
+
+pub type SimRequestHandler = fn (request &SimRequest) ?
+
+pub type SimStartHandler = fn () ?
+
+pub type SimFinishHandler = fn () ?
+
+pub const (
+	default_width  = 600
+	default_height = 600
+)
+
+[params]
+pub struct GridSettings {
+pub:
+	width  int = sim.default_width
+	height int = sim.default_height
+}
+
+pub fn new_grid_settings(settings GridSettings) GridSettings {
+	return GridSettings{
+		...settings
+	}
+}
+
+[params]
+pub struct RunnerSettings {
+pub:
+	grid       GridSettings
+	on_request SimRequestHandler
+	on_start   SimStartHandler
+	on_finish  SimFinishHandler
+}
+
+pub fn run(params SimParams, settings RunnerSettings) {
+	height := settings.grid.height
+	width := settings.grid.width
+
+	if !isnil(settings.on_start) {
+		settings.on_start() or {
+			log(@MOD + '.' + @FN + ': Simulation start handler failed. Error $err')
+		}
+	}
+
+	mut index := 0
+	log('')
+
+	mut bmark := benchmark.new_benchmark()
+	for y in 0 .. height {
+		$if verbose ? {
+			term.clear_previous_line()
+		}
+		log(@MOD + '.' + @FN + ': y: ${y + 1}')
+		for x in 0 .. width {
+			bmark.step()
+			// setup state conditions
+			position := vector(
+				x: 0.1 * ((f64(x) - 0.5 * f64(width - 1)) / f64(width - 1))
+				y: 0.1 * ((f64(y) - 0.5 * f64(height - 1)) / f64(height - 1))
+				z: 0.0
+			)
+			velocity := vector(x: 0, y: 0, z: 0)
+
+			mut state := new_state(
+				position: position
+				velocity: velocity
+			)
+
+			state.satisfy_rope_constraint(params)
+			request := &SimRequest{
+				id: index
+				state: state
+				params: params
+			}
+			settings.on_request(request) or {
+				log(@MOD + '.' + @FN + ': request handler failed. Error $err')
+				bmark.fail()
+				break
+			}
+			index++
+			bmark.ok()
+		}
+	}
+	bmark.stop()
+	println(bmark.total_message(@FN))
+
+	if !isnil(settings.on_finish) {
+		settings.on_finish() or {
+			log(@MOD + '.' + @FN + ': Simulation stop handler failed. Error $err')
+		}
+	}
+}

examples/pendulum-simulation/modules/sim/sim.v

@@ -0,0 +1,47 @@
+module sim
+
+pub struct SimState {
+mut:
+	position Vector3D
+	velocity Vector3D
+	accel    Vector3D
+}
+
+pub fn new_state(state SimState) SimState {
+	return SimState{
+		...state
+	}
+}
+
+pub fn (mut state SimState) satisfy_rope_constraint(params SimParams) {
+	mut rope_vector := params.get_rope_vector(state)
+	rope_vector = rope_vector.scale(params.rope_length / rope_vector.norm())
+	state.position = vector(z: params.rope_length) + rope_vector
+}
+
+pub fn (mut state SimState) increment(delta_t f64, params SimParams) {
+	// 1. add up all forces
+	// 2. get an accelleration
+	// 3. add to velocity
+	// 4. ensure rope constraint is satisfied
+
+	// sum up all forces
+	forces_sum := params.get_forces_sum(state)
+
+	// get the acceleration
+	accel := forces_sum.scale(1.0 / params.bearing_mass)
+	state.accel = accel
+
+	// update the velocity
+	state.velocity = state.velocity + accel.scale(delta_t)
+
+	// update the position
+	state.position = state.position + state.velocity.scale(delta_t)
+
+	// ensure the position satisfies rope constraint
+	state.satisfy_rope_constraint(params)
+}
+
+pub fn (state SimState) done() bool {
+	return state.velocity.norm() < 0.05 && state.accel.norm() < 0.01
+}

examples/pendulum-simulation/modules/sim/sim_test.v

@@ -0,0 +1,64 @@
+module sim
+
+const (
+	sim_test_mock_params = SimParams{
+		rope_length: 0.25
+		bearing_mass: 0.03
+		magnet_spacing: 0.05
+		magnet_height: 0.03
+		magnet_strength: 10
+		gravity: 4.9
+	}
+	sim_test_mock_state = SimState{
+		position: vector(
+			x: -0.016957230930171364
+			y: -0.02937078552673521
+			z: 0.002311063475327252
+		)
+		velocity: vector(
+			x: -7.251158929833104
+			y: -12.559375680227724
+			z: -105.91539687686381
+		)
+		accel: vector(
+			x: -8.337034766251843e-11
+			y: -2.842170943040401e-10
+			z: 1.2126596023639044e-10
+		)
+	}
+)
+
+pub fn test_satisfy_rope_constraint() {
+	mut state := SimState{
+		...sim.sim_test_mock_state
+	}
+
+	state.satisfy_rope_constraint(sim.sim_test_mock_params)
+	assert state.position.x == -0.016957230930171364
+	assert state.position.y == -0.02937078552673521
+	assert state.position.z == 0.002311063475327252
+	assert state.velocity.x == -7.251158929833104
+	assert state.velocity.y == -12.559375680227724
+	assert state.velocity.z == -105.91539687686381
+	assert state.accel.x == -8.337034766251843e-11
+	assert state.accel.y == -2.842170943040401e-10
+	assert state.accel.z == 1.2126596023639044e-10
+}
+
+pub fn test_increment() {
+	mut state := SimState{
+		...sim.sim_test_mock_state
+	}
+
+	delta_t := 0.0005
+	state.increment(delta_t, sim.sim_test_mock_params)
+	assert state.position.x == -0.016957230930171364
+	assert state.position.y == -0.02937078552673524
+	assert state.position.z == 0.0023110634753272796
+	assert state.velocity.x == -7.251158929833044
+	assert state.velocity.y == -12.559375680227637
+	assert state.velocity.z == -105.9153968768638
+	assert state.accel.x == 1.2126596023639044e-10
+	assert state.accel.y == 1.7431981783981126e-10
+	assert state.accel.z == 3.031649005909761e-11
+}

examples/pendulum-simulation/modules/sim/vec.v

@@ -0,0 +1,50 @@
+module sim
+
+import math
+
+// Vector3D is a 3D vector
+pub struct Vector3D {
+	x f64
+	y f64
+	z f64
+}
+
+// vector creates a Vector3D passing x,y,z as parameteres
+pub fn vector(data Vector3D) Vector3D {
+	return Vector3D{
+		...data
+	}
+}
+
+// addition
+pub fn (v Vector3D) + (v2 Vector3D) Vector3D {
+	return Vector3D{
+		x: v.x + v2.x
+		y: v.y + v2.y
+		z: v.z + v2.z
+	}
+}
+
+// dot product
+pub fn (v Vector3D) * (v2 Vector3D) f64 {
+	return (v.x * v2.x) + (v.y * v2.y) + (v.z * v2.z)
+}
+
+// scale gets a scaled vector
+pub fn (v Vector3D) scale(scalar f64) Vector3D {
+	return Vector3D{
+		x: v.x * scalar
+		y: v.y * scalar
+		z: v.z * scalar
+	}
+}
+
+// norm_squared returns the square of the norm of the vector
+pub fn (v Vector3D) norm_squared() f64 {
+	return v * v
+}
+
+// norm returns the norm of the vector
+pub fn (v Vector3D) norm() f64 {
+	return math.sqrt(v.norm_squared())
+}

examples/pendulum-simulation/modules/sim/vec_test.v

@@ -0,0 +1,64 @@
+module sim
+
+fn test_add() {
+	v := vector(
+		x: -0.016957230930171364
+		y: -0.02937078552673521
+		z: 0.002311063475327252
+	)
+	result := v + v
+	expected := vector(
+		x: -0.03391446186034273
+		y: -0.05874157105347042
+		z: 0.004622126950654504
+	)
+	assert result == expected
+}
+
+fn test_dot() {
+	v := vector(
+		x: -0.016957230930171364
+		y: -0.02937078552673521
+		z: 0.002311063475327252
+	)
+	result := v * v
+	expected := 0.0011555317376636305
+	assert result == expected
+}
+
+fn test_scale() {
+	v := vector(
+		x: -0.016957230930171364
+		y: -0.02937078552673521
+		z: 0.002311063475327252
+	)
+	result := v.scale(2.0)
+	expected := vector(
+		x: -0.03391446186034273
+		y: -0.05874157105347042
+		z: 0.004622126950654504
+	)
+	assert result == expected
+}
+
+fn test_norm_squared() {
+	v := vector(
+		x: -0.016957230930171364
+		y: -0.02937078552673521
+		z: 0.002311063475327252
+	)
+	result := v.norm_squared()
+	expected := 0.0011555317376636305
+	assert result == expected
+}
+
+fn test_norm() {
+	v := vector(
+		x: -0.016957230930171364
+		y: -0.02937078552673521
+		z: 0.002311063475327252
+	)
+	result := v.norm()
+	expected := 0.033993113091678295
+	assert result == expected
+}

examples/pendulum-simulation/modules/sim/worker.v

@@ -0,0 +1,67 @@
+module sim
+
+import math
+import benchmark
+
+const (
+	max_iterations     = 1000
+	simulation_delta_t = 0.0005
+)
+
+pub struct SimRequest {
+	params SimParams
+	state  SimState
+pub:
+	id int
+}
+
+pub struct SimResult {
+	state SimState
+pub:
+	id               int
+	magnet1_distance f64
+	magnet2_distance f64
+	magnet3_distance f64
+}
+
+pub fn sim_worker(id int, request_chan chan &SimRequest, result_channels []chan &SimResult) {
+	mut bmark := benchmark.new_benchmark()
+	for {
+		request := <-request_chan or { break }
+		bmark.step()
+		result := compute_result(request)
+		for ch in result_channels {
+			ch <- result
+		}
+		bmark.ok()
+	}
+	bmark.stop()
+	println(bmark.total_message(@FN + ': worker $id'))
+}
+
+pub fn compute_result(request SimRequest) &SimResult {
+	mut state := request.state
+	params := request.params
+
+	for _ in 0 .. sim.max_iterations {
+		state.increment(sim.simulation_delta_t, params)
+		if state.done() {
+			println('done!')
+			break
+		}
+	}
+
+	m1_dist := params.get_magnet_dist(0, state)
+	m2_dist := params.get_magnet_dist(2.0 * math.pi / 3.0, state)
+	m3_dist := params.get_magnet_dist(4.0 * math.pi / 3.0, state)
+
+	id := request.id
+
+	return &SimResult{
+		id: id
+		state: state
+		magnet1_distance: m1_dist
+		magnet2_distance: m2_dist
+		magnet3_distance: m3_dist
+	}
+}

examples/pendulum-simulation/modules/sim/worker_test.v

@@ -0,0 +1,63 @@
+module sim
+
+const (
+	worker_test_mock_params = SimParams{
+		rope_length: 0.25
+		bearing_mass: 0.03
+		magnet_spacing: 0.05
+		magnet_height: 0.03
+		magnet_strength: 10
+		gravity: 4.9
+	}
+	worker_test_mock_state = SimState{
+		position: vector(
+			x: -0.016957230930171364
+			y: -0.02937078552673521
+			z: 0.002311063475327252
+		)
+		velocity: vector(
+			x: -7.251158929833104
+			y: -12.559375680227724
+			z: -105.91539687686381
+		)
+		accel: vector(
+			x: -8.337034766251843e-11
+			y: -2.842170943040401e-10
+			z: 1.2126596023639044e-10
+		)
+	}
+)
+
+fn test_compute_result() {
+	request := SimRequest{
+		id: 0
+		params: sim.worker_test_mock_params
+		state: sim.worker_test_mock_state
+	}
+	expected_state := SimState{
+		position: vector(
+			x: -0.01695723093017133
+			y: -0.02937078552673517
+			z: 0.002311063475327252
+		)
+		velocity: vector(
+			x: -7.251158929832518
+			y: -12.559375680226692
+			z: -105.91539687685668
+		)
+		accel: vector(
+			x: -3.789561257387201e-12
+			y: 3.410605131648481e-11
+			z: 3.031649005909761e-11
+		)
+	}
+	expected := &SimResult{
+		state: expected_state
+		id: 0
+		magnet1_distance: 0.07993696666249224
+		magnet2_distance: 0.07993696666249223
+		magnet3_distance: 0.03609361938278009
+	}
+	result := compute_result(request)
+	assert result == expected
+}