console: the thermistor table's geometry is named rather than spelled

Steps, counts per step, the rail clearance, the sensor window, the Kelvin
offset and the quarter-degree scale were literals the reader had to
re-derive (4, 256, 1019, 273.15, the shift by 2). Each is now a constant the
table, the interpolation and the battery share. The table is byte-identical.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/thermistor.hpp

@@ -8,7 +8,7 @@
 // NTC thermistor on a series divider, solved entirely at compile time:
 // the Beta equation (logarithm and all) runs consteval into a libavr
 // flash_table - the firmware never does floating point. Raw 10-bit ADC
-// counts map to quarter- C with linear interpolation between table steps.
+// counts map to quarter-degrees C with linear interpolation between table steps.
 namespace app::thermistor {
 
 // The converter's top count: this board reads the divider at the ADC's
@@ -20,43 +20,58 @@ inline constexpr double nominal_resistance = 9270;
 inline constexpr double beta = 3212;
 inline constexpr double nominal_temperature = 25;
 
+inline constexpr std::uint8_t quarter_bits = 2;
+inline constexpr std::uint8_t quarters_per_degree = 1 << quarter_bits;
+
 namespace detail {
 
+inline constexpr double kelvin_offset = 273.15;
+
+// Signed-promoting, so the interpolation below divides a negative slope as one.
+inline constexpr std::uint8_t counts_per_step = 4;
+inline constexpr std::int32_t steps = (adc_full_scale + 1) / counts_per_step;
+
+// A sane sensor window, in whole degrees.
+inline constexpr std::int32_t coldest = -40;
+inline constexpr std::int32_t hottest = 125;
+
 consteval double temperature_of(double adc)
 {
 	double resistance = series_resistor * adc / (adc_full_scale - adc);
 	// __builtin_log constant-folds on the AVR backend, so the table is
 	// built at compile time with no runtime libm.
-	double steinhart = __builtin_log(resistance / nominal_resistance) / beta + 1.0 / (nominal_temperature + 273.15);
-	return 1.0 / steinhart - 273.15;
+	double steinhart =
+	    __builtin_log(resistance / nominal_resistance) / beta + 1.0 / (nominal_temperature + kelvin_offset);
+	return 1.0 / steinhart - kelvin_offset;
 }
 
-// 256 entries over the 10-bit range (steps of 4 counts), quarter- C,
-// clamped to a sane sensor window; entry 256 mirrors 255 so interpolation
-// at full scale has a right neighbour.
+// One entry per step, in quarter-degrees, with the reading kept a step clear of
+// both rails, where the divider has no solution.
 consteval std::int16_t quarters_entry(std::int32_t index)
 {
-	double adc = index * 4.0;
-	if (adc < 4) {
-		adc = 4;
+	double adc = index * double{counts_per_step};
+	if (adc < counts_per_step) {
+		adc = counts_per_step;
 	}
-	if (adc > 1019) {
-		adc = 1019;
+	if (adc > adc_full_scale - counts_per_step) {
+		adc = adc_full_scale - counts_per_step;
 	}
-	double t = temperature_of(adc) * 4.0;
-	if (t < -40 * 4) {
-		t = -40 * 4;
+	double t = temperature_of(adc) * quarters_per_degree;
+	if (t < coldest * quarters_per_degree) {
+		t = coldest * quarters_per_degree;
 	}
-	if (t > 125 * 4) {
-		t = 125 * 4;
+	if (t > hottest * quarters_per_degree) {
+		t = hottest * quarters_per_degree;
 	}
 	return static_cast<std::int16_t>(t < 0 ? t - 0.5 : t + 0.5);
 }
 
+// One entry past the last step, mirroring it, so interpolation at full scale
+// has a right neighbour.
 inline constexpr avr::flash_table<[] {
-	std::array<std::int16_t, 257> out{};
+	std::array<std::int16_t, steps + 1> out{};
 	for (std::int32_t i = 0; i < static_cast<std::int32_t>(out.size()); ++i) {
-		out[static_cast<std::size_t>(i)] = quarters_entry(i < 256 ? i : 255);
+		out[static_cast<std::size_t>(i)] = quarters_entry(i < steps ? i : steps - 1);
 	}
 	return out;
 }()>
@@ -64,14 +79,14 @@ inline constexpr avr::flash_table<[] {
 
 } // namespace detail
 
-// Temperature in quarter- C from a raw (or averaged) 10-bit sample.
+// Temperature in quarter-degrees C from a raw (or averaged) 10-bit sample.
 inline std::int16_t quarters(std::uint16_t adc)
 {
-	std::uint16_t index = adc >> 2; // the 257th entry backs index+1 at full scale
-	std::uint8_t frac = adc & 3;
+	std::uint16_t index = adc / detail::counts_per_step;
+	std::uint8_t frac = adc % detail::counts_per_step;
 	auto a = detail::table[index];
 	auto b = detail::table[static_cast<std::uint16_t>(index + 1)];
-	return static_cast<std::int16_t>(a + ((b - a) * frac) / 4);
+	return static_cast<std::int16_t>(a + ((b - a) * frac) / detail::counts_per_step);
 }
 
 // Whole degrees from quarter-degrees, rounded to nearest. The shift is the
@@ -79,7 +94,7 @@ inline std::int16_t quarters(std::uint16_t adc)
 // -3.00 C as -2, where an arithmetic shift floors and reads it as -3.
 inline constexpr std::int8_t whole_degrees(std::int16_t quarters)
 {
-	return static_cast<std::int8_t>((quarters + 2) >> 2);
+	return static_cast<std::int8_t>((quarters + quarters_per_degree / 2) >> quarter_bits);
 }
 
 } // namespace app::thermistor

test/consteval.cpp

@@ -43,7 +43,7 @@ static_assert(duty_entry(99) == 100);
 // Monotone across the whole table: a warmer reading never asks for less air.
 consteval bool curve_rises()
 {
-	for (std::int32_t t = 1; t < 100; ++t) {
+	for (std::int32_t t = 1; t < static_cast<std::int32_t>(app::curve::detail::table.size()); ++t) {
 		if (duty_entry(t) < duty_entry(t - 1)) {
 			return false;
 		}
@@ -57,23 +57,25 @@ static_assert(curve_rises());
 // thermistor's nominal resistance at
 // adc = full_scale * nominal / (series + nominal), and the equation's own
 // definition puts that count at the nominal temperature.
+using app::thermistor::detail::counts_per_step;
 using app::thermistor::detail::quarters_entry;
+using app::thermistor::detail::steps;
 
 inline constexpr std::int32_t nominal_count =
     static_cast<std::int32_t>(app::thermistor::adc_full_scale * app::thermistor::nominal_resistance /
                               (app::thermistor::series_resistor + app::thermistor::nominal_resistance));
-static_assert(quarters_entry(nominal_count / 4) >= 100);    // 25.00 C, in quarters
-static_assert(quarters_entry(nominal_count / 4 + 1) < 100); // and the step below it
+static_assert(quarters_entry(nominal_count / counts_per_step) >= 100);    // 25.00 C, in quarters
+static_assert(quarters_entry(nominal_count / counts_per_step + 1) < 100); // and the step below it
 
 // Both clamps, at the ends the divider cannot leave.
 static_assert(quarters_entry(0) == 125 * 4);
-static_assert(quarters_entry(255) == -40 * 4);
+static_assert(quarters_entry(steps - 1) == -40 * 4);
 
 // An NTC on this divider falls with the count: more counts is more resistance
 // is a colder sensor, over every step of the table.
 consteval bool thermistor_falls()
 {
-	for (std::int32_t i = 1; i < 256; ++i) {
+	for (std::int32_t i = 1; i < steps; ++i) {
 		if (quarters_entry(i) > quarters_entry(i - 1)) {
 			return false;
 		}