machine/rescap.h: Implemented audio potentiometer law. (#13588)

* machine/rescap.h: Implemented audio potentiometer law.
Used it in oberheim/dmx.cpp and linn/linndrum.cpp.

* machine/rescap.h: Function should not be a constexpr.
Also avoiding pow in constexpr constants.

src/devices/machine/rescap.h

@@ -26,6 +26,24 @@ constexpr double RES_VOLTAGE_DIVIDER(double r1, double r2) { return r2 / (r1 + r
 
 #define RES_2_SERIAL(r1,r2)             ((r1)+(r2))
 
+// Audio taper (aka "logarithmic") potentiometer law.
+// `x` should be in the range 0-1, and so is the return value.
+inline double RES_AUDIO_POT_LAW(double x)
+{
+	// The implementation is that of an ideal log potentiometer, based on:
+	// https://electronics.stackexchange.com/questions/304692/formula-for-logarithmic-audio-taper-pot
+
+	// Note that most audio potentiometers are not ideal, but they try to
+	// approximate this curve.
+
+	// The 10% midpoint ("A2" potentiometer curve) is typical for audio
+	// applications. See any datasheet for a log potentiometer.
+	constexpr const double MIDPOINT = 0.1;
+	constexpr const double B = (1.0 / MIDPOINT - 1.0) * (1.0 / MIDPOINT - 1.0);  // pow(1.0 / MIDPOINT - 1.0, 2);
+	constexpr const double A = 1.0 / (B - 1.0);
+	return A * pow(B, x) - A;
+}
+
 // macro for the RC time constant on a 74LS123 with C > 1000pF
 // R is in ohms, C is in farads
 constexpr double TIME_OF_74LS123(double r, double c) { return 0.45 * r * c; }

src/mame/linn/linndrum.cpp

@@ -65,7 +65,6 @@ Reasons for MACHINE_IMPERFECT_SOUND:
 * Missing snare / sidestick volume envelope.
 * Missing tom / conga LPF and filter envelope.
 * Inaccurate filter for "click".
-* Linear, instead of audio-taper volume sliders and master volume knob.
 * Linear, instead of tanh response for hi-hat VCA.
 
 PCBoards:
@@ -856,7 +855,7 @@ void linndrum_audio_device::update_volume_and_pan(int channel)
 	static constexpr const float C_VOICE = CAP_U(10);
 
 	const s32 volume = m_volume[channel]->read();
-	const float r_vol_bottom = volume * R_VOL_MAX / 100.0F;
+	const float r_vol_bottom = R_VOL_MAX * RES_AUDIO_POT_LAW(volume / 100.0F);
 	const float r_vol_top = R_VOL_MAX - r_vol_bottom;
 	const float r_pan_left = m_pan[channel]->read() * R_PAN_MAX / 100.0F;
 	const float r_pan_right = R_PAN_MAX - r_pan_left;
@@ -903,7 +902,7 @@ void linndrum_audio_device::update_master_volume()
 {
 	static constexpr const float R_MASTER_VOLUME_MAX = RES_K(10);
 
-	const float r_pot_bottom = m_master_volume->read() * R_MASTER_VOLUME_MAX / 100.0F;
+	const float r_pot_bottom = R_MASTER_VOLUME_MAX * RES_AUDIO_POT_LAW(m_master_volume->read() / 100.0F);
 	const float r_pot_top = R_MASTER_VOLUME_MAX - r_pot_bottom;
 	const float v_input = RES_VOLTAGE_DIVIDER(r_pot_top, RES_2_PARALLEL(r_pot_bottom, OUTPUT_R_INPUT));
 

src/mame/oberheim/dmx.cpp

@@ -46,7 +46,6 @@ PCBoards:
 Possible audio inaccuracies:
 - Some uncertainty on component values for HIHAT and PERC2 (see comments in
   HIHAT_CONFIG and PERC_CONFIG).
-- Linear- instead of audio-taper faders.
 - Envelope decay ignores diodes in capacitor discharge path. Given the quick
   decay, and that the error is larger at low volumes, this might not be
   noticeable.
@@ -1206,7 +1205,7 @@ void dmx_state::update_mix_level(int voice)
 	static constexpr const float R_FEEDBACK_RIGHT = RES_K(27);  // R29.
 
 	const s32 pot_percent = m_faders[VOICE_TO_FADER_MAP[voice]]->read();
-	const float r_pot_bottom = P_MAX * pot_percent / 100.0F;
+	const float r_pot_bottom = P_MAX * RES_AUDIO_POT_LAW(pot_percent / 100.0F);
 	const float r_pot_top = P_MAX - r_pot_bottom;
 	const float r_mix_left = std::get<0>(MIX_RESISTORS[voice]);
 	const float r_mix_right = std::get<1>(MIX_RESISTORS[voice]);
@@ -1237,7 +1236,7 @@ void dmx_state::update_master_volume()
 	static constexpr const float VOLTAGE_TO_SOUND_SCALER = 0.04F;
 
 	const s32 volume_value = m_master_volume->read();
-	const float gain = VOLTAGE_TO_SOUND_SCALER * volume_value / 100.0F;
+	const float gain = VOLTAGE_TO_SOUND_SCALER * RES_AUDIO_POT_LAW(volume_value / 100.0F);
 	m_left_mixer->set_output_gain(0, gain);
 	m_right_mixer->set_output_gain(0, gain);
 	LOGMASKED(LOG_FADERS, "Master volume changed: %d - %f\n", volume_value, gain);