fix(comments): soften "bit-exact" to "~1e-15 floating-point rounding" in velocity_curve

src/vst/velocity_curve.cpp

@@ -97,8 +97,8 @@ namespace {
 // The rule: a tangent whose adjacent secants have opposite signs (or either is flat) is a local
 // extremum — pin the tangent to 0 so the curve does not overshoot past the knot. Otherwise use the
 // weighted-harmonic-mean tangent (Fritsch–Carlson eq. 4), which for COLLINEAR knots (dPrev==dNext)
-// reduces EXACTLY to that common secant — so collinear control points reproduce the straight line
-// bit-for-bit (the Option-B / null-response contract that linear() must still satisfy).
+// reduces to that common secant — so collinear control points reproduce the straight line to within
+// floating-point rounding (~1e-15), preserving the Option-B / null-response contract for linear().
 double fritschCarlsonTangent(double dPrev, double dNext, double spanPrev, double spanNext) {
     if (dPrev * dNext <= 0.0) return 0.0;  // sign change or a flat neighbour -> local extremum
     // Weighted harmonic mean of the two secants (weights = the two segment widths). Collinear case:
@@ -131,8 +131,9 @@ double VelocityCurve::eval(double velocity) const {
             // --- Monotone cubic Hermite (Fritsch–Carlson) interpolation on segment [a,b] ---------
             // Curved (spline) response, not straight lines. The interpolant provably stays within
             // [a.amp, b.amp] between the two knots (no bulge below 0 / above 1), and for collinear
-            // control points its tangents reduce to the secant slope — so it IS the straight line,
-            // keeping linear() an EXACT y = velocity/127 (the null-response contract).
+            // control points its tangents reduce to the secant slope — so it reproduces the straight
+            // line to within floating-point rounding (~1e-15), preserving linear()'s null-response
+            // contract (y = velocity/127 to ~1e-15; the test tolerance of 1e-12 is appropriate).
             const double d = (b.amp - a.amp) / span;  // secant of THIS segment
 
             // Tangent at a: 0 if a is the first knot (endpoint), else the FC-limited tangent using
@@ -161,7 +162,8 @@ double VelocityCurve::eval(double velocity) const {
             }
 
             // Cubic Hermite basis on the normalized position t across [a,b]. For collinear knots
-            // mA==mB==d, so h00*a + (h10*span)*d + h01*b + (h11*span)*d collapses to the exact line.
+            // mA==mB==d, so h00*a + (h10*span)*d + h01*b + (h11*span)*d collapses to the straight
+            // line to within floating-point rounding (~1e-15).
             const double t = (v - a.velocity) / span;
             const double t2 = t * t;
             const double t3 = t2 * t;

src/vst/velocity_curve.h

@@ -63,8 +63,9 @@ inline constexpr int kCurveNodeGrabRadius = 6;
 // curved response (Daniel 2026-07-27: "straight lines sound like shit"), not a polyline. Each
 // velocity still maps to exactly one amp: the interpolant is single-valued and provably stays within
 // each segment's amp range, so the curve never overshoots below 0 or above 1. For COLLINEAR knots the
-// Fritsch–Carlson tangents reduce to the secant slope, so the spline IS the straight line — that
-// keeps linear() an EXACT y = velocity/127 (the Option-B / null-response contract). The two endpoints
+// Fritsch–Carlson tangents reduce to the secant slope, so the spline reproduces the straight line to
+// within floating-point rounding (~1e-15) — that preserves linear()'s null-response contract
+// (y = velocity/127 to ~1e-15; the 1e-12 test tolerance is deliberately conservative). The two endpoints
 // (velocity 0 and 127) are load-bearing: they keep eval total and are never deletable.
 class VelocityCurve {
 public:
@@ -90,7 +91,8 @@ public:
     // so an out-of-range note (shouldn't occur) reads the nearest endpoint. Between two adjacent
     // points the amp follows a MONOTONE cubic Hermite spline (Fritsch–Carlson slope limiting) — a
     // true curve that provably stays within the two knots' amp range (no overshoot below 0 / above
-    // 1) and reduces to the exact straight line for collinear knots. Single-valued / monotonic in X.
+    // 1) and reproduces the straight line to within floating-point rounding (~1e-15) for collinear
+    // knots. Single-valued / monotonic in X.
     // Degenerate cases (shouldn't occur post-construction): an EMPTY curve returns kAmpMax (flat
     // unity); a ONE-point curve returns that point's amp.
     double eval(double velocity) const;