The Challenge

We'll use some fancy math to get the precise angle that the magnetic field forms with the X and Y axes of the magnetometer. This will allow us to figure out which LED is pointing north.

We'll use the atan2 function. This function returns an angle in the -PI to PI range. The graphic below shows how this angle is measured:

atan2

Although not explicitly shown, in this graph the X axis points to the right and the Y axis points up. Note that our coordinate system is rotated 180° from this.

Here's the starter code (in templates/compass.rs). theta, in radians, has already been computed. You need to pick which LED to turn on based on the value of theta.

#![deny(unsafe_code)]
#![no_main]
#![no_std]

use cortex_m_rt::entry;
use embedded_hal::delay::DelayNs;
use panic_rtt_target as _;
use rtt_target::rtt_init_print;

// You'll find these useful ;-).
use core::f32::consts::PI;
use libm::{atan2f, floorf};

use microbit::{
    display::blocking::Display,
    hal::{Timer, twim},
    pac::twim0::frequency::FREQUENCY_A,
};

use lsm303agr::{Lsm303agr, MagMode, MagOutputDataRate};

#[entry]
fn main() -> ! {
    rtt_init_print!();
    let board = microbit::Board::take().unwrap();

    let i2c = { twim::Twim::new(board.TWIM0, board.i2c_internal.into(), FREQUENCY_A::K100) };

    let mut timer0 = Timer::new(board.TIMER0);
    let mut display = Display::new(board.display_pins);

    let mut sensor = Lsm303agr::new_with_i2c(i2c);
    sensor.init().unwrap();
    sensor.set_mag_mode_and_odr(
        &mut timer0,
        MagMode::HighResolution,
        MagOutputDataRate::Hz10,
    ).unwrap();
    let mut sensor = sensor.into_mag_continuous().ok().unwrap();

    let mut leds = [[0u8; 5]; 5];

    // Indexes of the 16 LEDs to be used in the display, and their
    // compass directions.
    #[rustfmt::skip]
    let indices = [
        (2, 0) /* W */, (3, 0) /* W-SW */, (3, 1) /* SW */, (4, 1) /* S-SW */,
        (4, 2) /* S */, (4, 3) /* S-SE */, (3, 3) /* SE */, (3, 4) /* E-SE */,
        (2, 4) /* E */, (1, 4) /* E-NE */, (1, 3) /* NE */, (0, 3) /* N-NE */,
        (0, 2) /* N */, (0, 1) /* N-NW */, (1, 1) /* NW */, (1, 0) /* W-NW */,
    ];

    loop {
        // Measure the magnetic field.
        let (x, y) = todo!();

        // Get an angle between -180° and 180° from the x axis.
        let theta = atan2f(y as f32, x as f32);

        // Figure out what LED index to blink.
        let index = todo!();

        // Blink the given LED.
        let (r, c) = indices[index];
        leds[r][c] = 255u8;
        display.show(&mut timer0, leds, 50);
        leds[r][c] = 0u8;
        display.show(&mut timer0, leds, 50);
    }
}

Suggestions/tips:

A whole circle rotation equals 360 degrees.
PI radians is equivalent to 180 degrees.
If theta is zero, which direction are you pointing at?
If theta is instead very close to zero, which direction are you pointing at?
If theta keeps increasing, at what value should you change the direction

Discovery

The Challenge