/* 1D Musgrave fBm
 *
 * H: fractal increment parameter
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 *
 * from "Texturing and Modelling: A procedural approach"
 */

void node_tex_musgrave_fBm_1d(vec3 co,
                              float w,
                              float scale,
                              float detail,
                              float dimension,
                              float lac,
                              float offset,
                              float gain,
                              out float fac)
{
  float p = w * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 0.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value += snoise(p) * pwr;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * snoise(p) * pwr;
  }

  fac = value;
}

/* 1D Musgrave Multifractal
 *
 * H: highest fractal dimension
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 */

void node_tex_musgrave_multi_fractal_1d(vec3 co,
                                        float w,
                                        float scale,
                                        float detail,
                                        float dimension,
                                        float lac,
                                        float offset,
                                        float gain,
                                        out float fac)
{
  float p = w * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 1.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value *= (pwr * snoise(p) + 1.0);
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value *= (rmd * pwr * snoise(p) + 1.0); /* correct? */
  }

  fac = value;
}

/* 1D Musgrave Heterogeneous Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hetero_terrain_1d(vec3 co,
                                         float w,
                                         float scale,
                                         float detail,
                                         float dimension,
                                         float lac,
                                         float offset,
                                         float gain,
                                         out float fac)
{
  float p = w * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  /* first unscaled octave of function; later octaves are scaled */
  float value = offset + snoise(p);
  p *= lacunarity;

  for (int i = 1; i < int(octaves); i++) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += increment;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += rmd * increment;
  }

  fac = value;
}

/* 1D Hybrid Additive/Multiplicative Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hybrid_multi_fractal_1d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  float p = w * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float value = snoise(p) + offset;
  float weight = gain * value;
  p *= lacunarity;

  for (int i = 1; (weight > 0.001f) && (i < int(octaves)); i++) {
    if (weight > 1.0) {
      weight = 1.0;
    }

    float signal = (snoise(p) + offset) * pwr;
    pwr *= pwHL;
    value += weight * signal;
    weight *= gain * signal;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * ((snoise(p) + offset) * pwr);
  }

  fac = value;
}

/* 1D Ridged Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_ridged_multi_fractal_1d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  float p = w * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float signal = offset - abs(snoise(p));
  signal *= signal;
  float value = signal;
  float weight = 1.0;

  for (int i = 1; i < int(octaves); i++) {
    p *= lacunarity;
    weight = clamp(signal * gain, 0.0, 1.0);
    signal = offset - abs(snoise(p));
    signal *= signal;
    signal *= weight;
    value += signal * pwr;
    pwr *= pwHL;
  }

  fac = value;
}

/* 2D Musgrave fBm
 *
 * H: fractal increment parameter
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 *
 * from "Texturing and Modelling: A procedural approach"
 */

void node_tex_musgrave_fBm_2d(vec3 co,
                              float w,
                              float scale,
                              float detail,
                              float dimension,
                              float lac,
                              float offset,
                              float gain,
                              out float fac)
{
  vec2 p = co.xy * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 0.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value += snoise(p) * pwr;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * snoise(p) * pwr;
  }

  fac = value;
}

/* 2D Musgrave Multifractal
 *
 * H: highest fractal dimension
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 */

void node_tex_musgrave_multi_fractal_2d(vec3 co,
                                        float w,
                                        float scale,
                                        float detail,
                                        float dimension,
                                        float lac,
                                        float offset,
                                        float gain,
                                        out float fac)
{
  vec2 p = co.xy * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 1.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value *= (pwr * snoise(p) + 1.0);
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value *= (rmd * pwr * snoise(p) + 1.0); /* correct? */
  }

  fac = value;
}

/* 2D Musgrave Heterogeneous Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hetero_terrain_2d(vec3 co,
                                         float w,
                                         float scale,
                                         float detail,
                                         float dimension,
                                         float lac,
                                         float offset,
                                         float gain,
                                         out float fac)
{
  vec2 p = co.xy * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  /* first unscaled octave of function; later octaves are scaled */
  float value = offset + snoise(p);
  p *= lacunarity;

  for (int i = 1; i < int(octaves); i++) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += increment;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += rmd * increment;
  }

  fac = value;
}

/* 2D Hybrid Additive/Multiplicative Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hybrid_multi_fractal_2d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  vec2 p = co.xy * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float value = snoise(p) + offset;
  float weight = gain * value;
  p *= lacunarity;

  for (int i = 1; (weight > 0.001f) && (i < int(octaves)); i++) {
    if (weight > 1.0) {
      weight = 1.0;
    }

    float signal = (snoise(p) + offset) * pwr;
    pwr *= pwHL;
    value += weight * signal;
    weight *= gain * signal;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * ((snoise(p) + offset) * pwr);
  }

  fac = value;
}

/* 2D Ridged Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_ridged_multi_fractal_2d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  vec2 p = co.xy * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float signal = offset - abs(snoise(p));
  signal *= signal;
  float value = signal;
  float weight = 1.0;

  for (int i = 1; i < int(octaves); i++) {
    p *= lacunarity;
    weight = clamp(signal * gain, 0.0, 1.0);
    signal = offset - abs(snoise(p));
    signal *= signal;
    signal *= weight;
    value += signal * pwr;
    pwr *= pwHL;
  }

  fac = value;
}

/* 3D Musgrave fBm
 *
 * H: fractal increment parameter
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 *
 * from "Texturing and Modelling: A procedural approach"
 */

void node_tex_musgrave_fBm_3d(vec3 co,
                              float w,
                              float scale,
                              float detail,
                              float dimension,
                              float lac,
                              float offset,
                              float gain,
                              out float fac)
{
  vec3 p = co * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 0.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value += snoise(p) * pwr;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * snoise(p) * pwr;
  }

  fac = value;
}

/* 3D Musgrave Multifractal
 *
 * H: highest fractal dimension
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 */

void node_tex_musgrave_multi_fractal_3d(vec3 co,
                                        float w,
                                        float scale,
                                        float detail,
                                        float dimension,
                                        float lac,
                                        float offset,
                                        float gain,
                                        out float fac)
{
  vec3 p = co * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 1.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value *= (pwr * snoise(p) + 1.0);
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value *= (rmd * pwr * snoise(p) + 1.0); /* correct? */
  }

  fac = value;
}

/* 3D Musgrave Heterogeneous Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hetero_terrain_3d(vec3 co,
                                         float w,
                                         float scale,
                                         float detail,
                                         float dimension,
                                         float lac,
                                         float offset,
                                         float gain,
                                         out float fac)
{
  vec3 p = co * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  /* first unscaled octave of function; later octaves are scaled */
  float value = offset + snoise(p);
  p *= lacunarity;

  for (int i = 1; i < int(octaves); i++) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += increment;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += rmd * increment;
  }

  fac = value;
}

/* 3D Hybrid Additive/Multiplicative Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hybrid_multi_fractal_3d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  vec3 p = co * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float value = snoise(p) + offset;
  float weight = gain * value;
  p *= lacunarity;

  for (int i = 1; (weight > 0.001f) && (i < int(octaves)); i++) {
    if (weight > 1.0) {
      weight = 1.0;
    }

    float signal = (snoise(p) + offset) * pwr;
    pwr *= pwHL;
    value += weight * signal;
    weight *= gain * signal;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * ((snoise(p) + offset) * pwr);
  }

  fac = value;
}

/* 3D Ridged Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_ridged_multi_fractal_3d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  vec3 p = co * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float signal = offset - abs(snoise(p));
  signal *= signal;
  float value = signal;
  float weight = 1.0;

  for (int i = 1; i < int(octaves); i++) {
    p *= lacunarity;
    weight = clamp(signal * gain, 0.0, 1.0);
    signal = offset - abs(snoise(p));
    signal *= signal;
    signal *= weight;
    value += signal * pwr;
    pwr *= pwHL;
  }

  fac = value;
}

/* 4D Musgrave fBm
 *
 * H: fractal increment parameter
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 *
 * from "Texturing and Modelling: A procedural approach"
 */

void node_tex_musgrave_fBm_4d(vec3 co,
                              float w,
                              float scale,
                              float detail,
                              float dimension,
                              float lac,
                              float offset,
                              float gain,
                              out float fac)
{
  vec4 p = vec4(co, w) * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 0.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value += snoise(p) * pwr;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * snoise(p) * pwr;
  }

  fac = value;
}

/* 4D Musgrave Multifractal
 *
 * H: highest fractal dimension
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 */

void node_tex_musgrave_multi_fractal_4d(vec3 co,
                                        float w,
                                        float scale,
                                        float detail,
                                        float dimension,
                                        float lac,
                                        float offset,
                                        float gain,
                                        out float fac)
{
  vec4 p = vec4(co, w) * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float value = 1.0;
  float pwr = 1.0;
  float pwHL = pow(lacunarity, -H);

  for (int i = 0; i < int(octaves); i++) {
    value *= (pwr * snoise(p) + 1.0);
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value *= (rmd * pwr * snoise(p) + 1.0); /* correct? */
  }

  fac = value;
}

/* 4D Musgrave Heterogeneous Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hetero_terrain_4d(vec3 co,
                                         float w,
                                         float scale,
                                         float detail,
                                         float dimension,
                                         float lac,
                                         float offset,
                                         float gain,
                                         out float fac)
{
  vec4 p = vec4(co, w) * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  /* first unscaled octave of function; later octaves are scaled */
  float value = offset + snoise(p);
  p *= lacunarity;

  for (int i = 1; i < int(octaves); i++) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += increment;
    pwr *= pwHL;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float increment = (snoise(p) + offset) * pwr * value;
    value += rmd * increment;
  }

  fac = value;
}

/* 4D Hybrid Additive/Multiplicative Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_hybrid_multi_fractal_4d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  vec4 p = vec4(co, w) * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float value = snoise(p) + offset;
  float weight = gain * value;
  p *= lacunarity;

  for (int i = 1; (weight > 0.001f) && (i < int(octaves)); i++) {
    if (weight > 1.0) {
      weight = 1.0;
    }

    float signal = (snoise(p) + offset) * pwr;
    pwr *= pwHL;
    value += weight * signal;
    weight *= gain * signal;
    p *= lacunarity;
  }

  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    value += rmd * ((snoise(p) + offset) * pwr);
  }

  fac = value;
}

/* 4D Ridged Multifractal Terrain
 *
 * H: fractal dimension of the roughest area
 * lacunarity: gap between successive frequencies
 * octaves: number of frequencies in the fBm
 * offset: raises the terrain from `sea level'
 */

void node_tex_musgrave_ridged_multi_fractal_4d(vec3 co,
                                               float w,
                                               float scale,
                                               float detail,
                                               float dimension,
                                               float lac,
                                               float offset,
                                               float gain,
                                               out float fac)
{
  vec4 p = vec4(co, w) * scale;
  float H = max(dimension, 1e-5);
  float octaves = clamp(detail, 0.0, 16.0);
  float lacunarity = max(lac, 1e-5);

  float pwHL = pow(lacunarity, -H);
  float pwr = pwHL;

  float signal = offset - abs(snoise(p));
  signal *= signal;
  float value = signal;
  float weight = 1.0;

  for (int i = 1; i < int(octaves); i++) {
    p *= lacunarity;
    weight = clamp(signal * gain, 0.0, 1.0);
    signal = offset - abs(snoise(p));
    signal *= signal;
    signal *= weight;
    value += signal * pwr;
    pwr *= pwHL;
  }

  fac = value;
}