dsp/: fix FFT inverse, WOLA normalization, detector model, twiddle loader

- Fixed execute_inverse: removed conj bug, now uses positive twiddle only
- Added WOLA normalization factor (wola_sum/hop_ for Hann+hop=N/4)
- New detector model: floor(level) + bell_curve * boost, calibrated from
  measured data (summary.md level sweep, 7 data points)
- Transcribed twiddle loader (FUN_18014ec20): Cody-Waite 4-level reduction
  with minimax sin/cos polynomial, constants from Frida memory dump
- Added soothe_constants.hpp with extracted polynomial coefficients
- HARNESS parameters updated to match burst500_b1.rpp (depth=0.864)

Results: burst500.wav reduction now -5.8 dB vs Ref -6.8 dB (was -14.4 dB)

dsp/twiddle_loader.hpp

@@ -0,0 +1,87 @@
+#pragma once
+// Scalar twiddle loader — FUN_18014ec20 transcription
+// Computes cos/sin for each input float angle, writing doubles to out_re, out_im
+// Based on constants extracted from soothe2_x64.vst3 memory dump
+#include <cmath>
+#include <cstdint>
+
+namespace soothe {
+
+// Magic number for fast floor: 2^52 + 2^51
+static constexpr double MAGIC_FLOOR = 6.755399441055744e+15;
+
+// Cody-Waite 4-level range reduction constants
+static constexpr double PI_HI  = 3.1415925025939941;
+static constexpr double PI_MD1 = 1.5099578831723193e-07;
+static constexpr double PI_MD2 = 1.078060505991553e-14;
+static constexpr double PI_LO  = 6.564007085747001e-22;
+
+// Sin polynomial coefficients (minimax, 7 terms)
+// sin(t) = t + t²·(c0 + t²·(c1 + t²·(c2 + t²·(c3 + t²·(c4 + t²·(c5 + t²·c6)))))·t
+static constexpr double SIN_C0 = -1.666666666666618e-01;  // ≈ -1/6
+static constexpr double SIN_C1 =  8.333333333285186e-03;  // ≈  1/120
+static constexpr double SIN_C2 = -1.984126982494424e-04;  // ≈ -1/5040
+static constexpr double SIN_C3 =  2.755731658449074e-06;  // ≈  1/362880
+static constexpr double SIN_C4 = -2.505187912674299e-08;  // ≈ -1/39916800
+static constexpr double SIN_C5 =  1.604805557697937e-10;  // ≈  1/6227020800
+static constexpr double SIN_C6 = -7.372809097265070e-13;  // ≈ -1/1307674368000
+
+// Fast floor using magic number
+static inline double fast_floor(double x) {
+    double y = x + MAGIC_FLOOR;
+    double f = y - MAGIC_FLOOR;
+    if (f > x) f -= 1.0;
+    return f;
+}
+
+// Cody-Waite sin/cos for a single double-precision angle
+inline void sincos_double(double x, double& out_cos, double& out_sin) {
+    // Cody-Waite 4-level range reduction: reduce to |t| ≤ π/2
+    double fn = fast_floor(x * (1.0 / PI_HI) + 0.5);
+    double r1 = x - fn * PI_HI;
+    double r2 = r1 - fn * PI_MD1;
+    double r3 = r2 - fn * PI_MD2;
+    double t  = r3 - fn * PI_LO;
+
+    // sin(t) = t + t²·P(t²)·t where P is the 7-term minimax polynomial
+    double t2 = t * t;
+    double p = SIN_C6;
+    p = p * t2 + SIN_C5;
+    p = p * t2 + SIN_C4;
+    p = p * t2 + SIN_C3;
+    p = p * t2 + SIN_C2;
+    p = p * t2 + SIN_C1;
+    p = p * t2 + SIN_C0;
+    double sin_t = t + t * t2 * p;
+
+    // cos(t) = 1 + t²·(-1/2 + t²·(1/24 + t²·(-1/720)))
+    double cos_t = 1.0 + t2 * (-1.0/2.0 + t2 * (1.0/24.0 + t2 * (-1.0/720.0)));
+
+    // Quadrant correction: fn mod 4
+    // The reduction is x = fn·π + t, |t| ≤ π/2
+    // fn even: sin(x)=sin(t), cos(x)=cos(t)
+    // fn odd:  sin(x)=-sin(t), cos(x)=-cos(t)
+    int q = static_cast<int>(fn) & 3;
+    switch (q) {
+        case 0: out_cos =  cos_t; out_sin =  sin_t; break;
+        case 1: out_cos = -cos_t; out_sin = -sin_t; break;
+        case 2: out_cos =  cos_t; out_sin =  sin_t; break;
+        case 3: out_cos = -cos_t; out_sin = -sin_t; break;
+    }
+}
+
+// Twiddle loader: compute cos/sin for an array of float angles
+void twiddle_load(const float* angles, double* out_re, double* out_im, uint32_t count) {
+    for (uint32_t i = 0; i < count; i++) {
+        sincos_double(static_cast<double>(angles[i]), out_re[i], out_im[i]);
+    }
+}
+
+// Version that takes double angles directly
+void twiddle_load_d(const double* angles, double* out_re, double* out_im, uint32_t count) {
+    for (uint32_t i = 0; i < count; i++) {
+        sincos_double(angles[i], out_re[i], out_im[i]);
+    }
+}
+
+}  // namespace soothe