feat(02-02): stereo mixer utilities with constant-power pan law

- PanGains uses cos/sin constant-power pan law (D-11)
- StereoFramesToInt16Bytes converts stereo frames to interleaved LE int16 bytes
- clamp prevents int16 overflow for values outside [-1.0, 1.0]
- All 7 mixer tests pass (pan law, byte conversion, clamping)

synth/mixer.go

@@ -0,0 +1,40 @@
+package synth
+
+import (
+	"encoding/binary"
+	"math"
+)
+
+// PanGains returns left and right channel gains for a pan position p in [-1, 1].
+// Uses constant-power (equal-power) pan law: cos/sin mapping.
+// Per D-11: bass frequencies center, mid spread L/R, higher frequencies wider.
+// At p=-1.0: gainL=1.0, gainR=0.0; at p=0.0: gainL=gainR=sqrt(2)/2; at p=1.0: gainL=0.0, gainR=1.0.
+func PanGains(p float64) (gainL, gainR float64) {
+	angle := (p + 1.0) / 2.0 * math.Pi / 2.0
+	return math.Cos(angle), math.Sin(angle)
+}
+
+// StereoFramesToInt16Bytes converts [][2]float64 stereo frames to interleaved
+// little-endian int16 bytes suitable for go-lame's Write method.
+// Clamps values to [-1.0, 1.0] before conversion.
+// Output format: [L0_lo, L0_hi, R0_lo, R0_hi, L1_lo, L1_hi, R1_lo, R1_hi, ...]
+func StereoFramesToInt16Bytes(frames [][2]float64) []byte {
+	buf := make([]byte, len(frames)*4) // 2 channels * 2 bytes per sample
+	for i, frame := range frames {
+		l := clamp(frame[0])
+		r := clamp(frame[1])
+		binary.LittleEndian.PutUint16(buf[i*4:], uint16(int16(l*32767)))
+		binary.LittleEndian.PutUint16(buf[i*4+2:], uint16(int16(r*32767)))
+	}
+	return buf
+}
+
+func clamp(v float64) float64 {
+	if v > 1.0 {
+		return 1.0
+	}
+	if v < -1.0 {
+		return -1.0
+	}
+	return v
+}

synth/mixer_test.go

@@ -0,0 +1,96 @@
+package synth
+
+import (
+	"math"
+	"testing"
+)
+
+func TestPanGainsCenter(t *testing.T) {
+	gainL, gainR := PanGains(0.0)
+	expected := math.Sqrt2 / 2 // cos(pi/4) = sin(pi/4) = 0.707...
+	if math.Abs(gainL-expected) > 1e-9 {
+		t.Errorf("PanGains(0.0) gainL = %v, want ~%v", gainL, expected)
+	}
+	if math.Abs(gainR-expected) > 1e-9 {
+		t.Errorf("PanGains(0.0) gainR = %v, want ~%v", gainR, expected)
+	}
+}
+
+func TestPanGainsFullLeft(t *testing.T) {
+	gainL, gainR := PanGains(-1.0)
+	if math.Abs(gainL-1.0) > 1e-9 {
+		t.Errorf("PanGains(-1.0) gainL = %v, want ~1.0", gainL)
+	}
+	if math.Abs(gainR-0.0) > 1e-9 {
+		t.Errorf("PanGains(-1.0) gainR = %v, want ~0.0", gainR)
+	}
+}
+
+func TestPanGainsFullRight(t *testing.T) {
+	gainL, gainR := PanGains(1.0)
+	if math.Abs(gainL-0.0) > 1e-9 {
+		t.Errorf("PanGains(1.0) gainL = %v, want ~0.0", gainL)
+	}
+	if math.Abs(gainR-1.0) > 1e-9 {
+		t.Errorf("PanGains(1.0) gainR = %v, want ~1.0", gainR)
+	}
+}
+
+func TestPanGainsPowerPreserved(t *testing.T) {
+	pans := []float64{-1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0}
+	for _, p := range pans {
+		gainL, gainR := PanGains(p)
+		power := gainL*gainL + gainR*gainR
+		if math.Abs(power-1.0) > 1e-9 {
+			t.Errorf("PanGains(%v) power = %v, want 1.0 (constant power law)", p, power)
+		}
+	}
+}
+
+func TestStereoFramesToInt16Bytes(t *testing.T) {
+	frames := [][2]float64{{1.0, -1.0}}
+	buf := StereoFramesToInt16Bytes(frames)
+	if len(buf) != 4 {
+		t.Fatalf("expected 4 bytes, got %d", len(buf))
+	}
+	// int16(32767) in little-endian = [0xFF, 0x7F]
+	// int16(-32767) in little-endian = [0x01, 0x80]
+	expectedL := int16(32767)
+	expectedR := int16(-32767)
+	gotL := int16(uint16(buf[0]) | uint16(buf[1])<<8)
+	gotR := int16(uint16(buf[2]) | uint16(buf[3])<<8)
+	if gotL != expectedL {
+		t.Errorf("left channel = %d, want %d", gotL, expectedL)
+	}
+	if gotR != expectedR {
+		t.Errorf("right channel = %d, want %d", gotR, expectedR)
+	}
+}
+
+func TestStereoFramesToInt16BytesZero(t *testing.T) {
+	frames := [][2]float64{{0.0, 0.0}}
+	buf := StereoFramesToInt16Bytes(frames)
+	if len(buf) != 4 {
+		t.Fatalf("expected 4 bytes, got %d", len(buf))
+	}
+	for i, b := range buf {
+		if b != 0 {
+			t.Errorf("byte[%d] = %d, want 0", i, b)
+		}
+	}
+}
+
+func TestClampPreventsOverflow(t *testing.T) {
+	// Values > 1.0 should be clamped to 1.0 before int16 conversion
+	frames := [][2]float64{{2.0, -2.0}}
+	buf := StereoFramesToInt16Bytes(frames)
+	gotL := int16(uint16(buf[0]) | uint16(buf[1])<<8)
+	gotR := int16(uint16(buf[2]) | uint16(buf[3])<<8)
+	// Should be clamped to max int16 positive / negative
+	if gotL != int16(32767) {
+		t.Errorf("clamped left = %d, want 32767", gotL)
+	}
+	if gotR != int16(-32767) {
+		t.Errorf("clamped right = %d, want -32767", gotR)
+	}
+}