Numbers and Units

A face draws bars, gauges, and graphs, and shows readings in the wearer's own units. The framework gives it the maths behind those: how full a goal bar is, how many cells of a battery gauge to light, which row a reading sits on in a graph, a walked distance in kilometres or miles to a tenth, and a wind speed in km/h, mph, knots, or m/s. None of it uses floating point. Float maths pulls library code into the app, and the watch's snprintf cannot print a float anyway (see Fitting Text), so every sum here multiplies before it divides and stays in whole numbers.

The maths lives in src/c/core/math/, in pct.h, scale.h, and series.h, and the conversions in src/c/core/units/, in distance.h and wind.h. They are in c/core (see Where the Code Lives), so they take plain numbers and give plain numbers back, never a GRect or a reading from the watch.

How Far to a Goal

pct_of(value, goal) gives a goal's progress from 0 to 100:

if (goal <= 0 || value <= 0)
{
    return 0;
}

int pct = (value * 100) / goal;
return pct > 100 ? 100 : pct;

Capped at 100. Walking twice the step goal is an ordinary day, and a bar drawn from 200 would run past its own outline.

Rounded Down. 9,999 steps of a 10,000 goal reads 99, so a bar is only full once the goal is really met.

No Goal, No Reading. A goal of 0 reads 0 rather than dividing by it. So does a negative value, which is how the readouts mark "no reading yet". That makes no data look the same as none of the goal done, so a face that shows dashes for no data checks before it asks.

Lighting Cells

segments_filled(level, segments) says how many cells of a gauge a level from 0 to 100 lights. It rounds up, so any charge at all lights a cell:

level = clamp_int(level, 0, 100);
int filled = (level * segments + 99) / 100;

On a five cell battery gauge, 1% and 20% each light one cell, 21% lights two, and only 100% lights all five. Rounding down would show an empty gauge on a battery with 19% left. A level outside 0 to 100 is pinned first, so a stray reading cannot light a sixth cell.

The rest of scale.h and series.h covers the other sums a chart needs, such as pinning a value to a range, splitting a strip into cells, placing a reading on a graph's rows, and the lowest, highest, and latest real reading in a history with gaps.

Distance in Kilometres or Miles

The health store reports the distance walked in metres. distance_format_value turns that into kilometres or miles to one decimal place, and distance_format adds the unit, as in 3.1 MI or 5.0 KM.

It counts in tenths of the unit, in whole numbers. A tenth of a kilometre is 100 metres. A tenth of a mile is 160.9344 metres, so the tenths are the metres times 10000 / 1609344, which is 625 / 100584 once both are divided by 16:

int tenths = miles ? (meters * 625 + 50292) / 100584 : (meters + 50) / 100;
snprintf(buffer, size, "%d.%d", tenths / 10, tenths % 10);

Adding half the divisor before dividing rounds to the nearest tenth rather than down. For 5,000 metres:

miles: (5000 × 625 + 50292) / 100584 = 3175292 / 100584 = 31   reads 3.1
km:    (5000 + 50) / 100             = 5050 / 100       = 50   reads 5.0

The rounding carries across the point, so 4,960 metres reads 5.0 km rather than 4.9. A negative distance reads 0.0.

How Far It Reaches. The miles sum multiplies before it divides, and the product stays inside a 32-bit int up to about 3,400 km. Reducing the fraction is what makes that room. Multiplying by the unreduced 10000 would overflow past about 215 km.

Wind Speed

The weather store keeps the wind in km/h whichever provider it came from, rounded to a whole number on the phone. wind_from_kmh(kmh, unit) converts it on the watch, and wind_unit_label gives the label to show beside it, KM/H, MPH, KTS, or M/S:

case WIND_UNIT_MPH: return (kmh * 621) / 1000;
case WIND_UNIT_KTS: return (kmh * 540) / 1000;
case WIND_UNIT_MS:  return (kmh * 278) / 1000;

The factors are the real ones to three places, and the result is cut to a whole number rather than rounded. 30 km/h is 18.6 mph and reads 18, 16.2 knots and reads 16, and 8.3 m/s and reads 8. So a converted speed can read one below the nearest whole number, which is small next to how much the wind gusts.

No Reading First. The store's marker for no wind reading is -1, and -1 km/h converts to 0 mph, since the division rounds toward zero. A face checks for no reading before it converts, or a missing wind shows as calm.

The Setting Is the Face's. The framework has no wind unit setting of its own. The units are numbered 0 for km/h, 1 for mph, 2 for knots, and 3 for m/s, so a face adds a four way select to its page with those values and passes the stored byte straight in. A number outside that range reads as km/h.