{
  "instrawave": 1,
  "name": "dulcimer",
  "description": "One plucked string over a rigid box with a sound hole, radiating along its line and driving a bridge patch above the plate.",
  "params": [
    {
      "key": "nx",
      "label": "air cells along x",
      "unit": "1",
      "value": 96,
      "min": 32,
      "max": 256,
      "class": "accuracy",
      "hint": "The air grid; ny = nz = nx/2. The simulation is honest to about c/(8h). Must be even.",
      "step": 2
    },
    {
      "key": "Lx",
      "label": "domain length",
      "unit": "m",
      "value": 1,
      "min": 0.6,
      "max": 2,
      "class": "geometry",
      "hint": "The air box around the instrument, twice as long in x as in y and z."
    },
    {
      "key": "ir_seconds",
      "label": "room response length",
      "unit": "s",
      "value": 0.5,
      "min": 0.1,
      "max": 2,
      "class": "accuracy",
      "hint": "How long the recorded room responses run; a room still ringing past this is truncated."
    },
    {
      "key": "L1",
      "label": "speaking length",
      "unit": "m",
      "value": 0.6,
      "min": 0.3,
      "max": 0.9,
      "class": "geometry"
    },
    {
      "key": "oy",
      "label": "across",
      "unit": "m",
      "value": 0,
      "min": -0.15,
      "max": 0.15,
      "class": "geometry"
    },
    {
      "key": "oz",
      "label": "height",
      "unit": "m",
      "value": 0.02,
      "min": 0.005,
      "max": 0.15,
      "class": "geometry",
      "hint": "Height of the string above z = 0."
    },
    {
      "key": "boxl",
      "label": "box length",
      "unit": "m",
      "value": 0.66,
      "min": 0.3,
      "max": 0.9,
      "class": "geometry"
    },
    {
      "key": "boxw",
      "label": "box width",
      "unit": "m",
      "value": 0.16,
      "min": 0.08,
      "max": 0.4,
      "class": "geometry"
    },
    {
      "key": "boxd",
      "label": "box depth",
      "unit": "m",
      "value": 0.08,
      "min": 0.03,
      "max": 0.25,
      "class": "geometry",
      "hint": "How far the box hangs below its top plate at z = 0."
    },
    {
      "key": "thick",
      "label": "wall thickness",
      "unit": "m",
      "value": 0.016,
      "min": 0.008,
      "max": 0.05,
      "class": "geometry"
    },
    {
      "key": "holer",
      "label": "sound hole radius",
      "unit": "m",
      "value": 0.035,
      "min": 0,
      "max": 0.12,
      "class": "geometry",
      "hint": "0 seals the box; the hole is what lets the cavity speak."
    },
    {
      "key": "holex",
      "label": "sound hole x",
      "unit": "m",
      "value": -0.05,
      "min": -0.3,
      "max": 0.3,
      "class": "geometry"
    },
    {
      "key": "absorb",
      "label": "surface absorption",
      "unit": "1/s",
      "value": 800,
      "min": 0,
      "max": 4000,
      "class": "geometry"
    },
    {
      "key": "mic_x",
      "label": "microphone x",
      "unit": "m",
      "value": 0.12,
      "min": -0.45,
      "max": 0.45,
      "class": "geometry"
    },
    {
      "key": "mic_y",
      "label": "microphone y",
      "unit": "m",
      "value": 0.08,
      "min": -0.2,
      "max": 0.2,
      "class": "geometry"
    },
    {
      "key": "mic_z",
      "label": "microphone z",
      "unit": "m",
      "value": 0.1,
      "min": -0.2,
      "max": 0.2,
      "class": "geometry"
    },
    {
      "key": "f0",
      "label": "pitch",
      "unit": "Hz",
      "value": 294,
      "min": 80,
      "max": 880,
      "class": "tuning",
      "hint": "The fundamental; the wave speed follows, cs = 2 L f0."
    },
    {
      "key": "B",
      "label": "inharmonicity",
      "unit": "1",
      "value": 0.0001,
      "min": 0,
      "max": 0.002,
      "class": "tuning",
      "hint": "Bending stiffness as the inharmonicity coefficient."
    },
    {
      "key": "t60",
      "label": "decay t60",
      "unit": "s",
      "value": 4,
      "min": 0.2,
      "max": 8,
      "class": "tuning"
    },
    {
      "key": "sig1",
      "label": "brightness decay",
      "unit": "m^2/s",
      "value": 0.005,
      "min": 0,
      "max": 0.05,
      "class": "tuning"
    },
    {
      "key": "pluckpos",
      "label": "pluck position",
      "unit": "1",
      "value": 0.22,
      "min": 0.08,
      "max": 0.92,
      "class": "tuning"
    },
    {
      "key": "amp",
      "label": "pluck height",
      "unit": "m",
      "value": 0.002,
      "min": 0.0002,
      "max": 0.005,
      "class": "tuning"
    },
    {
      "key": "gair",
      "label": "line radiation gain",
      "unit": "1",
      "value": 0.3,
      "min": 0,
      "max": 2,
      "class": "tuning"
    },
    {
      "key": "gbridge",
      "label": "bridge drive gain",
      "unit": "1",
      "value": 1,
      "min": 0,
      "max": 2,
      "class": "tuning",
      "hint": "The pull at the far end driving a patch above the plate."
    }
  ],
  "derived": {
    "c0": "343",
    "cfl": "0.5",
    "ny": "nx / 2",
    "nz": "nx / 2",
    "npts": "nx * ny * nz",
    "h": "Lx / nx",
    "Ly": "ny * h",
    "Lz": "nz * h",
    "dt": "cfl * h / (sqrt(3) * c0)",
    "ir_steps": "max(1, round(ir_seconds / dt))",
    "mic_index": "clamp(round((mic_x + Lx/2) / h - 0.5), 0, nx - 1) + nx * (clamp(round((mic_y + Ly/2) / h - 0.5), 0, ny - 1) + ny * clamp(round((mic_z + Lz/2) / h - 0.5), 0, nz - 1))",
    "cs_worst": "2 * L1 * f0__max",
    "kap2_worst": "B__max * (cs_worst * cs_worst * L1 * L1) / (pi * pi)",
    "a_worst": "cs_worst*cs_worst*dt*dt + 4*sig1__max*dt",
    "h_min": "sqrt((a_worst + sqrt(a_worst*a_worst + 16*kap2_worst*dt*dt)) / 2) / 0.95",
    "n1": "max(5, min(1024, floor(L1 / h_min) + 1))",
    "h1": "L1 / (n1 - 1)",
    "mx": "n1 - 2",
    "n_rows": "mx + 1"
  },
  "shaders": {
    "medium": {
      "code": "// The medium: the body's rigid mask, the absorption, and where the object\n// couples into the air. One thread per air cell.\nconst PI = 3.14159265358979;\noverride npts: u32;\noverride nx: u32;\noverride ny: u32;\noverride h: f32;\noverride Lx: f32;\noverride Ly: f32;\noverride Lz: f32;\noverride boxl: f32;\noverride boxw: f32;\noverride boxd: f32;\noverride thick: f32;\noverride holer: f32;\noverride holex: f32;\noverride absorb: f32;\noverride oy: f32;\noverride oz: f32;\noverride L1: f32;\n@group(0) @binding(0) var<storage, read_write> wall: array<f32>;\n@group(0) @binding(1) var<storage, read_write> sig: array<f32>;\n@group(0) @binding(2) var<storage, read_write> prof: array<f32>;\n@group(0) @binding(3) var<storage, read_write> bprof: array<f32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= npts) { return; }\n  let ix = i % nx;\n  let iy = (i / nx) % ny;\n  let iz = i / (nx * ny);\n  let x = -Lx/2.0 + (f32(ix) + 0.5) * h;\n  let y = -Ly/2.0 + (f32(iy) + 0.5) * h;\n  let z = -Lz/2.0 + (f32(iz) + 0.5) * h;\n  let sw = 0.45 * h;\n  // The box: the outer solid minus its cavity, top plate at z = 0, with a\n  // round sound hole cut out of the top plate only.\n  let box_ox = 0.5 * (1.0 - tanh((abs(x) - boxl/2.0) / sw));\n  let box_oy = 0.5 * (1.0 - tanh((abs(y) - boxw/2.0) / sw));\n  let box_oz = 0.5 * (1.0 - tanh((abs(z + boxd/2.0) - boxd/2.0) / sw));\n  let box_ix = 0.5 * (1.0 - tanh((abs(x) - (boxl/2.0 - thick)) / sw));\n  let box_iy = 0.5 * (1.0 - tanh((abs(y) - (boxw/2.0 - thick)) / sw));\n  let box_iz = 0.5 * (1.0 - tanh((abs(z + boxd/2.0) - (boxd/2.0 - thick)) / sw));\n  var shell = max(0.0, box_ox * box_oy * box_oz - box_ix * box_iy * box_iz);\n  let hole_r = sqrt((x - holex)*(x - holex) + y*y);\n  let hole = 0.5 * (1.0 - tanh((hole_r - holer) / sw));\n  let top = 0.5 * (1.0 - tanh((abs(z + thick/2.0) - thick/2.0) / sw));\n  shell = max(0.0, shell - hole * top);\n  let w = 1.0 - shell;\n  wall[i] = w;\n  // Open boundary at the domain edge (a quadratic absorbing ramp over the\n  // outer 0.15 Ly of each face), plus the body's lossy surface skin.\n  let spw = 0.15 * Ly;\n  let dx = max(0.0, spw - (Lx/2.0 - abs(x))) / spw;\n  let dy = max(0.0, spw - (Ly/2.0 - abs(y))) / spw;\n  let dz = max(0.0, spw - (Lz/2.0 - abs(z))) / spw;\n  let d = max(max(dx, dy), dz);\n  sig[i] = 9000.0 * d * d + absorb * (4.0 * shell * (1.0 - shell));\n  // The object radiates from its line: a tube two cells wide around\n  // (y = oy, z = oz), fading at its ends, cross-section normalized to one.\n  let aw = 2.0 * h;\n  let tube = exp(-((y - oy)*(y - oy) + (z - oz)*(z - oz)) / (aw*aw)) / (PI * aw * aw);\n  let span = 0.5 * (1.0 + tanh((L1/2.0 - abs(x)) / (1.5*h)));\n  prof[i] = tube * span * w;\n  // ...and its bridge force drives a patch of air just above the plate,\n  // around the x = +L/2 end (a stand-in for a moving top plate).\n  let pw = 1.5 * h;\n  let pr = exp(-((x - L1/2.0)*(x - L1/2.0) + (y - oy)*(y - oy)) / (0.04*0.04)) / (PI * 0.04 * 0.04);\n  let skin = exp(-(z - pw)*(z - pw) / (pw*pw)) / (sqrt(PI) * pw);\n  bprof[i] = pr * skin * w;\n}\n",
      "constants": [
        "npts",
        "nx",
        "ny",
        "h",
        "Lx",
        "Ly",
        "Lz",
        "boxl",
        "boxw",
        "boxd",
        "thick",
        "holer",
        "holex",
        "absorb",
        "oy",
        "oz",
        "L1"
      ]
    },
    "sines_x": {
      "code": "// Sine mode m of the object grid, interpolated to air\n// x centers: sx[(mode-1) * nx + ix]. One thread per table entry.\nconst PI = 3.14159265358979;\noverride n1: u32;\noverride mx: u32;\noverride nx: u32;\noverride L1: f32;\noverride h1: f32;\noverride Lx: f32;\noverride h: f32;\n@group(0) @binding(0) var<storage, read_write> table: array<f32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= mx * nx) { return; }\n  let mi = i % mx;\n  let ia = i / mx;\n  let xw = -Lx/2.0 + (f32(ia) + 0.5) * h;\n  let u = (xw + L1/2.0) / h1;\n  let j = i32(floor(u));\n  var v = 0.0;\n  if (j >= 0 && j < i32(n1) - 1) {\n    let f = u - f32(j);\n    let mm = f32(mi + 1u);\n    let s0 = sin(mm * PI * f32(j) / f32(n1 - 1u));\n    let s1 = sin(mm * PI * f32(j + 1) / f32(n1 - 1u));\n    v = (1.0 - f) * s0 + f * s1;\n  }\n  table[mi * nx + ia] = v;\n}\n",
      "constants": [
        "n1",
        "mx",
        "nx",
        "L1",
        "h1",
        "Lx",
        "h"
      ]
    },
    "impulse": {
      "code": "// The reciprocal kick: one unit impulse at the microphone cell, entering\n// the way a source enters the first step. One thread.\noverride mic_index: u32;\noverride dt: f32;\n@group(0) @binding(0) var<storage, read_write> p: array<f32>;\n@group(0) @binding(1) var<storage, read> wall: array<f32>;\n@group(0) @binding(2) var<storage, read> sig: array<f32>;\n@compute @workgroup_size(1)\nfn main() {\n  p[mic_index] = dt * dt * wall[mic_index] / (1.0 + sig[mic_index] * dt);\n}\n",
      "constants": [
        "mic_index",
        "dt"
      ]
    },
    "step": {
      "code": "// One leapfrog step of the air: the wall-masked Laplacian (each stencil\n// face scaled by the mask at the neighbour it reads, the rigid condition in\n// divergence form) fused with the update. One thread per air cell.\noverride npts: u32;\noverride nx: u32;\noverride ny: u32;\noverride nz: u32;\noverride h: f32;\noverride dt: f32;\noverride c0: f32;\n@group(0) @binding(0) var<storage, read> p: array<f32>;\n@group(0) @binding(1) var<storage, read> pm: array<f32>;\n@group(0) @binding(2) var<storage, read_write> pn: array<f32>;\n@group(0) @binding(3) var<storage, read> wall: array<f32>;\n@group(0) @binding(4) var<storage, read> sig: array<f32>;\nfn face(ix: i32, iy: i32, iz: i32, pc: f32) -> f32 {\n  if (ix < 0 || ix >= i32(nx) || iy < 0 || iy >= i32(ny) || iz < 0 || iz >= i32(nz)) {\n    return -pc; // outside the domain: p = 0, open\n  }\n  let k = u32(ix) + nx * (u32(iy) + ny * u32(iz));\n  return wall[k] * (p[k] - pc);\n}\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= npts) { return; }\n  let ix = i32(i % nx);\n  let iy = i32((i / nx) % ny);\n  let iz = i32(i / (nx * ny));\n  let pc = p[i];\n  let s = face(ix - 1, iy, iz, pc) + face(ix + 1, iy, iz, pc)\n        + face(ix, iy - 1, iz, pc) + face(ix, iy + 1, iz, pc)\n        + face(ix, iy, iz - 1, pc) + face(ix, iy, iz + 1, pc);\n  let lp = wall[i] * s / (h * h);\n  let sd = sig[i] * dt;\n  pn[i] = wall[i] * ((2.0 * pc - (1.0 - sd) * pm[i] + (c0 * dt) * (c0 * dt) * lp) / (1.0 + sd));\n}\n",
      "constants": [
        "npts",
        "nx",
        "ny",
        "nz",
        "h",
        "dt",
        "c0"
      ]
    },
    "plane": {
      "code": "// Contract the field against the radiation profile over z:\n// one thread per air column.\noverride nx: u32;\noverride ny: u32;\noverride nz: u32;\n@group(0) @binding(0) var<storage, read_write> plane: array<f32>;\n@group(0) @binding(1) var<storage, read> p: array<f32>;\n@group(0) @binding(2) var<storage, read> prof: array<f32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= nx * ny) { return; }\n  var s = 0.0;\n  for (var iz = 0u; iz < nz; iz++) {\n    let k = i + nx * ny * iz;\n    s += prof[k] * p[k];\n  }\n  plane[i] = s;\n}\n",
      "constants": [
        "nx",
        "ny",
        "nz"
      ]
    },
    "xc": {
      "code": "// Contract the plane against every x sine row: tmp[m + mx * iy].\noverride nx: u32;\noverride ny: u32;\noverride mx: u32;\n@group(0) @binding(0) var<storage, read_write> tmp: array<f32>;\n@group(0) @binding(1) var<storage, read> plane: array<f32>;\n@group(0) @binding(2) var<storage, read> sx: array<f32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= mx * ny) { return; }\n  let m = i % mx;\n  let iy = i / mx;\n  var s = 0.0;\n  for (var ix = 0u; ix < nx; ix++) {\n    s += sx[m * nx + ix] * plane[ix + nx * iy];\n  }\n  tmp[i] = s;\n}\n",
      "constants": [
        "nx",
        "ny",
        "mx"
      ]
    },
    "proj": {
      "code": "// A line object's y factor is one everywhere: finish by summing tmp over\n// iy and write this step's sample of every kernel row.\noverride ny: u32;\noverride mx: u32;\noverride ir_steps: u32;\n@group(0) @binding(0) var<storage, read_write> kernels: array<f32>;\n@group(0) @binding(1) var<storage, read> tmp: array<f32>;\n@group(0) @binding(2) var<storage, read> tick: array<u32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= mx) { return; }\n  var s = 0.0;\n  for (var iy = 0u; iy < ny; iy++) {\n    s += tmp[i + mx * iy];\n  }\n  let t = tick[0];\n  if (t < ir_steps) {\n    kernels[i * ir_steps + t] = s;\n  }\n}\n",
      "constants": [
        "ny",
        "mx",
        "ir_steps"
      ]
    },
    "excite_x": {
      "code": "// Project this axis's excitation profile onto each recorded sine mode:\n// bx[e * mx + (mode-1)]. One thread per (event, mode).\nconst PI = 3.14159265358979;\noverride n1: u32;\noverride mx: u32;\noverride ev_stride: u32;\noverride h1: f32;\noverride L1: f32;\n@group(0) @binding(0) var<storage, read_write> bout: array<f32>;\n@group(0) @binding(1) var<storage, read> ev: array<f32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= mx * arrayLength(&ev) / ev_stride) { return; }\n  let mi = i % mx;\n  let e = i / mx;\n  let base = e * ev_stride;\n  let pluckpos = ev[base + 5u];\n  let amp = ev[base + 6u];\n  let mm = f32(mi + 1u);\n  var s = 0.0;\n  for (var k = 1u; k < n1 - 1u; k++) {\n    let xi = f32(k) * h1;\n    let ta = xi / (pluckpos * L1);\n    let tb = (L1 - xi) / (L1 - pluckpos * L1);\n    let u0 = amp * 0.5 * (ta + tb - abs(ta - tb));\n    s += sin(mm * PI * f32(k) / f32(n1 - 1u)) * u0;\n  }\n  bout[i] = s;\n}\n",
      "constants": [
        "n1",
        "mx",
        "ev_stride",
        "h1",
        "L1"
      ]
    },
    "slots": {
      "code": "// One thread per (event, mode) of the string: the stiff damped string's\n// roots, its radiation slots, and the bridge slots its arriving slope\n// drives (the last kernel row, row mx).\nconst PI = 3.14159265358979;\noverride mx: u32;\noverride n1: u32;\noverride ev_stride: u32;\noverride h1: f32;\noverride L1: f32;\noverride dt: f32;\n@group(0) @binding(0) var<storage, read_write> slots: array<f32>;\n@group(0) @binding(1) var<storage, read> ev: array<f32>;\n@group(0) @binding(2) var<storage, read> bx: array<f32>;\n\nfn cmul(ar: f32, ai: f32, br: f32, bi: f32) -> vec2f {\n  return vec2f(ar * br - ai * bi, ar * bi + ai * br);\n}\n// c = a * gain * (z - 2 + 1/z) = a * gain * (z-1)^2 / z, the acceleration\n// series, with z-1 supplied stably (the naive z - 1 cancels).\nfn acc_scale(p: vec4f, zm1Re: f32, gain: f32) -> vec4f {\n  let m2 = p.z * p.z + p.w * p.w;\n  if (m2 == 0.0) { return vec4f(0.0); }\n  let sq = cmul(zm1Re, p.w, zm1Re, p.w);\n  let num = cmul(sq.x, sq.y, p.z, -p.w);\n  let c = cmul(p.x, p.y, gain * num.x / m2, gain * num.y / m2);\n  return vec4f(c.x, c.y, p.z, p.w);\n}\n// c = a * gain * z, the next-displacement series (what a string's bridge\n// slope is read from).\nfn next_scale(p: vec4f, gain: f32) -> vec4f {\n  let c = cmul(p.x, p.y, gain * p.z, gain * p.w);\n  return vec4f(c.x, c.y, p.z, p.w);\n}\n\n\nfn write_slot(idx: u32, p: vec4f, row: f32, start: f32) {\n  slots[idx * 6u] = p.x;\n  slots[idx * 6u + 1u] = p.y;\n  slots[idx * 6u + 2u] = p.z;\n  slots[idx * 6u + 3u] = p.w;\n  slots[idx * 6u + 4u] = row;\n  slots[idx * 6u + 5u] = start;\n}\n\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  let n_events = arrayLength(&ev) / ev_stride;\n  if (i >= n_events * mx) { return; }\n  let e = i / mx;\n  let mi = i % mx;\n  let base = e * ev_stride;\n  let start = ev[base];\n  let f0 = ev[base + 1u];\n  let B = ev[base + 2u];\n  let t60 = ev[base + 3u];\n  let sig1 = ev[base + 4u];\n  let gair = ev[base + 7u];\n  let gbridge = ev[base + 8u];\n  let m = f32(mi + 1u);\n  let b = bx[i] * 2.0 / f32(n1 - 1u);\n  let s1 = sin(m * PI / (2.0 * f32(n1 - 1u)));\n  let lam = (4.0 / (h1 * h1)) * s1 * s1;\n  let cs = 2.0 * L1 * f0;\n  let kap2 = B * (cs * L1 / PI) * (cs * L1 / PI);\n  let w2 = cs * cs * lam + kap2 * lam * lam;\n\n  let d = (6.91 / t60) * dt;\n  let opd = 1.0 + d;\n  let g = d + 2.0 * sig1 * dt * lam;\n  let x = dt * dt * w2 + 2.0 * sig1 * dt * lam;\n  let zRe = (1.0 - 0.5 * x) / opd;\n  let zm1Re = -(0.5 * x + d) / opd;\n  let nn = dt * dt * w2 - g * d - 0.25 * x * x;\n  var p0 = vec4f(0.0);\n  var p1 = vec4f(0.0);\n  var zm10 = 0.0;\n  var zm11 = 0.0;\n  if (nn > 0.0) {\n    let zIm = sqrt(nn) / opd;\n    let mag2 = (1.0 - g) / opd;\n    let aRe = b;\n    let aIm = b * ((0.5 * x - g) / opd) / zIm;\n    p0 = vec4f(aRe, aIm, zRe, zIm);\n    zm10 = zm1Re;\n  } else {\n    let sq = sqrt(-nn) / opd;\n    let r1 = zRe + sq;\n    let r2 = zRe - sq;\n    if (r1 != r2 && r1 != 0.0 && r2 != 0.0) {\n      let det = 1.0 / r1 - 1.0 / r2;\n      let a1 = (b - b / r2) / det;\n      let a2 = b - a1;\n      p0 = vec4f(a1, 0.0, r1, 0.0);\n      p1 = vec4f(a2, 0.0, r2, 0.0);\n      zm10 = zm1Re + sq;\n      zm11 = zm1Re - sq;\n    }\n  }\n  let ga = gair / (dt * dt);\n  write_slot(i * 4u, acc_scale(p0, zm10, ga), f32(mi), start);\n  write_slot(i * 4u + 1u, acc_scale(p1, zm11, ga), f32(mi), start);\n  // The bridge: the far end is pinned, so the arriving slope is\n  // -u[n-2]/h1, and the generated step's term is\n  // -(gbridge cs^2 / L) bprof fb; together, +gbridge cs^2/(L h1) times\n  // sin(m pi (n1-2)/(n1-1)) times the next-displacement series.\n  let gb = (gbridge * cs * cs / (L1 * h1)) * sin(m * PI * f32(n1 - 2u) / f32(n1 - 1u));\n  write_slot(i * 4u + 2u, next_scale(p0, gb), f32(mx), start);\n  write_slot(i * 4u + 3u, next_scale(p1, gb), f32(mx), start);\n}\n",
      "constants": [
        "mx",
        "n1",
        "ev_stride",
        "h1",
        "L1",
        "dt"
      ]
    },
    "synth": {
      "code": "// One thread per slot: a complex one-pole over this tile of samples, the\n// kernel row as input while it lasts and silence after (the closed-form\n// tail). State persists across tiles.\noverride tile: u32;\noverride total_steps: u32;\noverride ir_steps: u32;\noverride n_slots: u32;\n@group(0) @binding(0) var<storage, read> slots: array<f32>;\n@group(0) @binding(1) var<storage, read_write> state: array<f32>;\n@group(0) @binding(2) var<storage, read> kernels: array<f32>;\n@group(0) @binding(3) var<storage, read_write> partial: array<f32>;\n@group(0) @binding(4) var<storage, read> tick: array<u32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= n_slots) { return; }\n  let cRe = slots[i * 6u];\n  let cIm = slots[i * 6u + 1u];\n  let zRe = slots[i * 6u + 2u];\n  let zIm = slots[i * 6u + 3u];\n  let row = u32(slots[i * 6u + 4u]);\n  let start = u32(slots[i * 6u + 5u]);\n  var wRe = state[i * 2u];\n  var wIm = state[i * 2u + 1u];\n  let t0 = tick[0] * tile;\n  for (var s = 0u; s < tile; s++) {\n    let t = t0 + s;\n    if (t >= total_steps) { break; }\n    var hv = 0.0;\n    if (t >= start && t - start < ir_steps) {\n      hv = kernels[row * ir_steps + (t - start)];\n    }\n    let nRe = zRe * wRe - zIm * wIm + hv;\n    let nIm = zRe * wIm + zIm * wRe;\n    wRe = nRe;\n    wIm = nIm;\n    partial[i * tile + s] = cRe * wRe - cIm * wIm;\n  }\n  state[i * 2u] = wRe;\n  state[i * 2u + 1u] = wIm;\n}\n",
      "constants": [
        "tile",
        "total_steps",
        "ir_steps",
        "n_slots"
      ]
    },
    "reduce": {
      "code": "// One thread per sample of the tile: sum every slot's contribution.\noverride tile: u32;\noverride total_steps: u32;\noverride n_slots: u32;\n@group(0) @binding(0) var<storage, read> partial: array<f32>;\n@group(0) @binding(1) var<storage, read_write> trace: array<f32>;\n@group(0) @binding(2) var<storage, read> tick: array<u32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= tile) { return; }\n  let t = tick[0] * tile + i;\n  if (t >= total_steps) { return; }\n  var s = 0.0;\n  for (var q = 0u; q < n_slots; q++) {\n    s += partial[q * tile + i];\n  }\n  trace[t] = s;\n}\n",
      "constants": [
        "tile",
        "total_steps",
        "n_slots"
      ]
    },
    "bplane": {
      "code": "// Contract the field against the bridge patch profile over z:\n// one thread per air column.\noverride nx: u32;\noverride ny: u32;\noverride nz: u32;\n@group(0) @binding(0) var<storage, read_write> bplane: array<f32>;\n@group(0) @binding(1) var<storage, read> p: array<f32>;\n@group(0) @binding(2) var<storage, read> bprof: array<f32>;\n@compute @workgroup_size(64)\nfn main(@builtin(global_invocation_id) gid: vec3<u32>) {\n  let i = gid.x + gid.y * 4194240u;\n  if (i >= nx * ny) { return; }\n  var s = 0.0;\n  for (var iz = 0u; iz < nz; iz++) {\n    let k = i + nx * ny * iz;\n    s += bprof[k] * p[k];\n  }\n  bplane[i] = s;\n}\n",
      "constants": [
        "nx",
        "ny",
        "nz"
      ]
    },
    "bridge_proj": {
      "code": "// The bridge patch is a single fixed pattern: sum its plane and write the\n// sample into the last kernel row (row mx). One thread.\noverride nx: u32;\noverride ny: u32;\noverride mx: u32;\noverride ir_steps: u32;\n@group(0) @binding(0) var<storage, read_write> kernels: array<f32>;\n@group(0) @binding(1) var<storage, read> bplane: array<f32>;\n@group(0) @binding(2) var<storage, read> tick: array<u32>;\n@compute @workgroup_size(1)\nfn main() {\n  var s = 0.0;\n  for (var k = 0u; k < nx * ny; k++) {\n    s += bplane[k];\n  }\n  let t = tick[0];\n  if (t < ir_steps) {\n    kernels[mx * ir_steps + t] = s;\n  }\n}\n",
      "constants": [
        "nx",
        "ny",
        "mx",
        "ir_steps"
      ]
    }
  },
  "precompute": {
    "buffers": [
      {
        "name": "wall",
        "count": "npts"
      },
      {
        "name": "sig",
        "count": "npts"
      },
      {
        "name": "prof",
        "count": "npts"
      },
      {
        "name": "bprof",
        "count": "npts"
      },
      {
        "name": "sx",
        "count": "mx * nx"
      },
      {
        "name": "p",
        "count": "npts"
      },
      {
        "name": "pm",
        "count": "npts"
      },
      {
        "name": "pn",
        "count": "npts"
      },
      {
        "name": "plane",
        "count": "nx * ny"
      },
      {
        "name": "bplane",
        "count": "nx * ny"
      },
      {
        "name": "tmp",
        "count": "mx * ny"
      },
      {
        "name": "kernels",
        "count": "n_rows * ir_steps"
      }
    ],
    "setup": [
      {
        "shader": "medium",
        "buffers": [
          "wall",
          "sig",
          "prof",
          "bprof"
        ],
        "dispatch": "npts"
      },
      {
        "shader": "sines_x",
        "buffers": [
          "sx"
        ],
        "dispatch": "mx * nx"
      },
      {
        "shader": "impulse",
        "buffers": [
          "p",
          "wall",
          "sig"
        ],
        "dispatch": "1"
      }
    ],
    "loop": {
      "count": "ir_steps",
      "batch": 512,
      "rotate": [
        [
          "p",
          "pm",
          "pn"
        ]
      ],
      "body": [
        {
          "shader": "plane",
          "buffers": [
            "plane",
            "p",
            "prof"
          ],
          "dispatch": "nx * ny"
        },
        {
          "shader": "xc",
          "buffers": [
            "tmp",
            "plane",
            "sx"
          ],
          "dispatch": "mx * ny"
        },
        {
          "shader": "proj",
          "buffers": [
            "kernels",
            "tmp",
            "__tick"
          ],
          "dispatch": "mx"
        },
        {
          "shader": "bplane",
          "buffers": [
            "bplane",
            "p",
            "bprof"
          ],
          "dispatch": "nx * ny"
        },
        {
          "shader": "bridge_proj",
          "buffers": [
            "kernels",
            "bplane",
            "__tick"
          ],
          "dispatch": "1"
        },
        {
          "shader": "step",
          "buffers": [
            "p",
            "pm",
            "pn",
            "wall",
            "sig"
          ],
          "dispatch": "npts"
        }
      ]
    },
    "outputs": [
      "kernels"
    ]
  },
  "render": {
    "buffers": [
      {
        "name": "kernels",
        "count": "n_rows * ir_steps"
      },
      {
        "name": "bx",
        "count": "n_events * mx"
      },
      {
        "name": "slots",
        "count": "n_slots * 6"
      },
      {
        "name": "state",
        "count": "n_slots * 2"
      },
      {
        "name": "partial",
        "count": "n_slots * tile"
      },
      {
        "name": "trace",
        "count": "total_steps"
      }
    ],
    "inputs": [
      "kernels"
    ],
    "eventParams": [
      "f0",
      "B",
      "t60",
      "sig1",
      "pluckpos",
      "amp",
      "gair",
      "gbridge"
    ],
    "derived": {
      "ev_stride": "9",
      "n_slots": "n_events * mx * 4"
    },
    "setup": [
      {
        "shader": "excite_x",
        "buffers": [
          "bx",
          "__events"
        ],
        "dispatch": "n_events * mx"
      },
      {
        "shader": "slots",
        "buffers": [
          "slots",
          "__events",
          "bx"
        ],
        "dispatch": "n_events * mx"
      }
    ],
    "loop": {
      "count": "n_tiles",
      "batch": 8,
      "body": [
        {
          "shader": "synth",
          "buffers": [
            "slots",
            "state",
            "kernels",
            "partial",
            "__tick"
          ],
          "dispatch": "n_slots"
        },
        {
          "shader": "reduce",
          "buffers": [
            "partial",
            "trace",
            "__tick"
          ],
          "dispatch": "tile"
        }
      ]
    },
    "trace": "trace"
  },
  "visual": {
    "dims": [
      "nx",
      "ny",
      "nz"
    ],
    "extents": [
      "Lx",
      "Ly",
      "Lz"
    ],
    "buffers": [
      {
        "name": "wall",
        "count": "npts"
      },
      {
        "name": "sig",
        "count": "npts"
      },
      {
        "name": "prof",
        "count": "npts"
      },
      {
        "name": "bprof",
        "count": "npts"
      }
    ],
    "setup": [
      {
        "shader": "medium",
        "buffers": [
          "wall",
          "sig",
          "prof",
          "bprof"
        ],
        "dispatch": "npts"
      }
    ],
    "volumes": [
      {
        "buffer": "wall",
        "style": "solid",
        "invert": true,
        "color": [
          0.62,
          0.48,
          0.34
        ]
      },
      {
        "buffer": "prof",
        "style": "cloud",
        "color": [
          1,
          0.45,
          0.2
        ]
      },
      {
        "buffer": "bprof",
        "style": "cloud",
        "color": [
          0.35,
          0.65,
          1
        ]
      }
    ],
    "markers": [
      {
        "kind": "line",
        "from": [
          "-L1/2",
          "oy",
          "oz"
        ],
        "to": [
          "L1/2",
          "oy",
          "oz"
        ],
        "color": [
          1,
          0.85,
          0.3
        ],
        "label": "string"
      },
      {
        "kind": "point",
        "at": [
          "mic_x",
          "mic_y",
          "mic_z"
        ],
        "color": [
          0.3,
          0.85,
          1
        ],
        "label": "mic"
      }
    ],
    "partials": {
      "buffer": "slots",
      "stride": 6,
      "zRe": 2,
      "zIm": 3
    }
  }
}