// MIT License
//
// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com)
// Copyright(c) 2020 Contributors
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files(the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions :
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//
// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'...        ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll
// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'....       ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo
// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd
// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx
// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'...      ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx
// . ....';:cloddddo___________,,,,;;:clooddddoolc:,...      ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd
// .......',;:cccc:|           |,,,;;:cclooddddoll:;'..     ..';cox|  \KKK000|   |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo
// .......'',,,,,''|   ________|',,;;::cclloooooolc:;'......___:ldk|   \KK000|   |XKKK0Okxolc|   |;;::cclodxxkkkkxxdoolllcclllooodddooooo
// ''......''''....|   |  ....'',,,,;;;::cclloooollc:;,''.'|   |oxk|    \OOO0|   |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo
// ;;,''.......... |   |_____',,;;;____:___cllo________.___|   |___|     \xkk|   |KK_______ool___:::;________;;;_______...'',;;:ccclllloo
// c:;,''......... |         |:::/     '   |lo/        |           |      \dx|   |0/       \d|   |cc/        |'/       \......',,;;:ccllo
// ol:;,'..........|    _____|ll/    __    |o/   ______|____    ___|   |   \o|   |/   ___   \|   |o/   ______|/   ___   \ .......'',;:clo
// dlc;,...........|   |::clooo|    /  |   |x\___   \KXKKK0|   |dol|   |\   \|   |   |   |   |   |d\___   \..|   |  /   /       ....',:cl
// xoc;'...  .....'|   |llodddd|    \__|   |_____\   \KKK0O|   |lc:|   |'\       |   |___|   |   |_____\   \.|   |_/___/...      ...',;:c
// dlc;'... ....',;|   |oddddddo\          |          |Okkx|   |::;|   |..\      |\         /|   |          | \         |...    ....',;:c
// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc
// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll
// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo
// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd
// .    .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk
//       ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000
//       ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX
//
// VERSION: 1.0.1
// https://github.com/Auburn/FastNoise

// In *one* C or C++ file, use #define FNL_IMPL to generate implementation

#ifndef FASTNOISELITE_H
#define FASTNOISELITE_H

// Switch between using floats or doubles for input position
typedef float FNLfloat;
//typedef double FNLfloat;

#if defined(__cplusplus)
extern "C"
{
#endif

#include <math.h>
#include <stdint.h>
#include <stdbool.h>
#include <float.h>

  // Enums
  typedef enum
  {
    FNL_NOISE_OPENSIMPLEX2,
    FNL_NOISE_OPENSIMPLEX2S,
    FNL_NOISE_CELLULAR,
    FNL_NOISE_PERLIN,
    FNL_NOISE_VALUE_CUBIC,
    FNL_NOISE_VALUE
  } fnl_noise_type;

  typedef enum
  {
    FNL_ROTATION_NONE,
    FNL_ROTATION_IMPROVE_XY_PLANES,
    FNL_ROTATION_IMPROVE_XZ_PLANES
  } fnl_rotation_type_3d;

  typedef enum
  {
    FNL_FRACTAL_NONE,
    FNL_FRACTAL_FBM,
    FNL_FRACTAL_RIDGED,
    FNL_FRACTAL_PINGPONG,
    FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE,
    FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT
  } fnl_fractal_type;

  typedef enum
  {
    FNL_CELLULAR_DISTANCE_EUCLIDEAN,
    FNL_CELLULAR_DISTANCE_EUCLIDEANSQ,
    FNL_CELLULAR_DISTANCE_MANHATTAN,
    FNL_CELLULAR_DISTANCE_HYBRID
  } fnl_cellular_distance_func;

  typedef enum
  {
    FNL_CELLULAR_RETURN_VALUE_CELLVALUE,
    FNL_CELLULAR_RETURN_VALUE_DISTANCE,
    FNL_CELLULAR_RETURN_VALUE_DISTANCE2,
    FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD,
    FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB,
    FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL,
    FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV,
  } fnl_cellular_return_type;

  typedef enum
  {
    FNL_DOMAIN_WARP_OPENSIMPLEX2,
    FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED,
    FNL_DOMAIN_WARP_BASICGRID
  } fnl_domain_warp_type;

  /**
 * Structure containing entire noise system state.
 * @note Must only be created using fnlCreateState(optional: seed). To ensure defaults are set.
 */
  typedef struct fnl_state
  {
    /**
     * Seed used for all noise types.
     * @remark Default: 1337
     */
    int seed;

    /**
     * The frequency for all noise types.
     * @remark Default: 0.01
     */
    float frequency;

    /**
     * The noise algorithm to be used by GetNoise(...).
     * @remark Default: FNL_NOISE_OPENSIMPLEX2
     */
    fnl_noise_type noise_type;

    /**
     * Sets noise rotation type for 3D.
     * @remark Default: FNL_ROTATION_NONE
     */
    fnl_rotation_type_3d rotation_type_3d;

    /**
     * The method used for combining octaves for all fractal noise types.
     * @remark Default: None
     * @remark FNL_FRACTAL_DOMAIN_WARP_... only effects fnlDomainWarp...
     */
    fnl_fractal_type fractal_type;

    /**
     * The octave count for all fractal noise types.
     * @remark Default: 3
     */
    int octaves;

    /**
     * The octave lacunarity for all fractal noise types.
     * @remark Default: 2.0
     */
    float lacunarity;

    /**
     * The octave gain for all fractal noise types.
     * @remark Default: 0.5
     */
    float gain;

    /**
     * The octave weighting for all none Domaain Warp fractal types.
     * @remark Default: 0.0
     * @remark 
     */
    float weighted_strength;

    /**
     * The strength of the fractal ping pong effect.
     * @remark Default: 2.0
     */
    float ping_pong_strength;

    /**
     * The distance function used in cellular noise calculations.
     * @remark Default: FNL_CELLULAR_FUNC_DISTANCE
     */
    fnl_cellular_distance_func cellular_distance_func;

    /**
     * The cellular return type from cellular noise calculations.
     * @remark Default: FNL_CELLULAR_RETURN_VALUE_EUCLIEANSQ
     */
    fnl_cellular_return_type cellular_return_type;

    /**
     * The maximum distance a cellular point can move from it's grid position.
     * @remark Default: 1.0
     * @note Setting this higher than 1 will cause artifacts.
     */
    float cellular_jitter_mod;

    /**
     * The warp algorithm when using fnlDomainWarp...
     * @remark Default: OpenSimplex2
     */
    fnl_domain_warp_type domain_warp_type;

    /**
     * The maximum warp distance from original position when using fnlDomainWarp...
     * @remark Default: 1.0
     */
    float domain_warp_amp;
  } fnl_state;

  /**
 * Creates a noise state with default values.
 * @param seed Optionally set the state seed.
 */
  fnl_state fnlCreateState();

  /**
 * 2D noise at given position using the state settings
 * @returns Noise output bounded between -1 and 1.
 */
  float fnlGetNoise2D(fnl_state *state, FNLfloat x, FNLfloat y);

  /**
 * 3D noise at given position using the state settings
 * @returns Noise output bounded between -1 and 1.
 */
  float fnlGetNoise3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z);

  /**
 * 2D warps the input position using current domain warp settings.
 * 
 * Example usage with fnlGetNoise2D:
 * ```
 * fnlDomainWarp2D(&state, &x, &y);
 * noise = fnlGetNoise2D(&state, x, y);
 * ```
 */
  void fnlDomainWarp2D(fnl_state *state, FNLfloat *x, FNLfloat *y);

  /**
 * 3D warps the input position using current domain warp settings.
 * 
 * Example usage with fnlGetNoise3D:
 * ```
 * fnlDomainWarp3D(&state, &x, &y, &z);
 * noise = fnlGetNoise3D(&state, x, y, z);
 * ```
 */
  void fnlDomainWarp3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z);

  // ====================
  // Below this line is the implementation
  // ====================

#if defined(FNL_IMPL)

  // Constants

  static const float GRADIENTS_2D[] =
      {
          0.130526192220052f,
          0.99144486137381f,
          0.38268343236509f,
          0.923879532511287f,
          0.608761429008721f,
          0.793353340291235f,
          0.793353340291235f,
          0.608761429008721f,
          0.923879532511287f,
          0.38268343236509f,
          0.99144486137381f,
          0.130526192220051f,
          0.99144486137381f,
          -0.130526192220051f,
          0.923879532511287f,
          -0.38268343236509f,
          0.793353340291235f,
          -0.60876142900872f,
          0.608761429008721f,
          -0.793353340291235f,
          0.38268343236509f,
          -0.923879532511287f,
          0.130526192220052f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          -0.38268343236509f,
          -0.923879532511287f,
          -0.608761429008721f,
          -0.793353340291235f,
          -0.793353340291235f,
          -0.608761429008721f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          0.130526192220051f,
          -0.923879532511287f,
          0.38268343236509f,
          -0.793353340291235f,
          0.608761429008721f,
          -0.608761429008721f,
          0.793353340291235f,
          -0.38268343236509f,
          0.923879532511287f,
          -0.130526192220052f,
          0.99144486137381f,
          0.130526192220052f,
          0.99144486137381f,
          0.38268343236509f,
          0.923879532511287f,
          0.608761429008721f,
          0.793353340291235f,
          0.793353340291235f,
          0.608761429008721f,
          0.923879532511287f,
          0.38268343236509f,
          0.99144486137381f,
          0.130526192220051f,
          0.99144486137381f,
          -0.130526192220051f,
          0.923879532511287f,
          -0.38268343236509f,
          0.793353340291235f,
          -0.60876142900872f,
          0.608761429008721f,
          -0.793353340291235f,
          0.38268343236509f,
          -0.923879532511287f,
          0.130526192220052f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          -0.38268343236509f,
          -0.923879532511287f,
          -0.608761429008721f,
          -0.793353340291235f,
          -0.793353340291235f,
          -0.608761429008721f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          0.130526192220051f,
          -0.923879532511287f,
          0.38268343236509f,
          -0.793353340291235f,
          0.608761429008721f,
          -0.608761429008721f,
          0.793353340291235f,
          -0.38268343236509f,
          0.923879532511287f,
          -0.130526192220052f,
          0.99144486137381f,
          0.130526192220052f,
          0.99144486137381f,
          0.38268343236509f,
          0.923879532511287f,
          0.608761429008721f,
          0.793353340291235f,
          0.793353340291235f,
          0.608761429008721f,
          0.923879532511287f,
          0.38268343236509f,
          0.99144486137381f,
          0.130526192220051f,
          0.99144486137381f,
          -0.130526192220051f,
          0.923879532511287f,
          -0.38268343236509f,
          0.793353340291235f,
          -0.60876142900872f,
          0.608761429008721f,
          -0.793353340291235f,
          0.38268343236509f,
          -0.923879532511287f,
          0.130526192220052f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          -0.38268343236509f,
          -0.923879532511287f,
          -0.608761429008721f,
          -0.793353340291235f,
          -0.793353340291235f,
          -0.608761429008721f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          0.130526192220051f,
          -0.923879532511287f,
          0.38268343236509f,
          -0.793353340291235f,
          0.608761429008721f,
          -0.608761429008721f,
          0.793353340291235f,
          -0.38268343236509f,
          0.923879532511287f,
          -0.130526192220052f,
          0.99144486137381f,
          0.130526192220052f,
          0.99144486137381f,
          0.38268343236509f,
          0.923879532511287f,
          0.608761429008721f,
          0.793353340291235f,
          0.793353340291235f,
          0.608761429008721f,
          0.923879532511287f,
          0.38268343236509f,
          0.99144486137381f,
          0.130526192220051f,
          0.99144486137381f,
          -0.130526192220051f,
          0.923879532511287f,
          -0.38268343236509f,
          0.793353340291235f,
          -0.60876142900872f,
          0.608761429008721f,
          -0.793353340291235f,
          0.38268343236509f,
          -0.923879532511287f,
          0.130526192220052f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          -0.38268343236509f,
          -0.923879532511287f,
          -0.608761429008721f,
          -0.793353340291235f,
          -0.793353340291235f,
          -0.608761429008721f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          0.130526192220051f,
          -0.923879532511287f,
          0.38268343236509f,
          -0.793353340291235f,
          0.608761429008721f,
          -0.608761429008721f,
          0.793353340291235f,
          -0.38268343236509f,
          0.923879532511287f,
          -0.130526192220052f,
          0.99144486137381f,
          0.130526192220052f,
          0.99144486137381f,
          0.38268343236509f,
          0.923879532511287f,
          0.608761429008721f,
          0.793353340291235f,
          0.793353340291235f,
          0.608761429008721f,
          0.923879532511287f,
          0.38268343236509f,
          0.99144486137381f,
          0.130526192220051f,
          0.99144486137381f,
          -0.130526192220051f,
          0.923879532511287f,
          -0.38268343236509f,
          0.793353340291235f,
          -0.60876142900872f,
          0.608761429008721f,
          -0.793353340291235f,
          0.38268343236509f,
          -0.923879532511287f,
          0.130526192220052f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          -0.38268343236509f,
          -0.923879532511287f,
          -0.608761429008721f,
          -0.793353340291235f,
          -0.793353340291235f,
          -0.608761429008721f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.99144486137381f,
          -0.130526192220052f,
          -0.99144486137381f,
          0.130526192220051f,
          -0.923879532511287f,
          0.38268343236509f,
          -0.793353340291235f,
          0.608761429008721f,
          -0.608761429008721f,
          0.793353340291235f,
          -0.38268343236509f,
          0.923879532511287f,
          -0.130526192220052f,
          0.99144486137381f,
          0.38268343236509f,
          0.923879532511287f,
          0.923879532511287f,
          0.38268343236509f,
          0.923879532511287f,
          -0.38268343236509f,
          0.38268343236509f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.923879532511287f,
          -0.923879532511287f,
          -0.38268343236509f,
          -0.923879532511287f,
          0.38268343236509f,
          -0.38268343236509f,
          0.923879532511287f,
  };

  static const float RAND_VECS_2D[] =
      {
          -0.2700222198f,
          -0.9628540911f,
          0.3863092627f,
          -0.9223693152f,
          0.04444859006f,
          -0.999011673f,
          -0.5992523158f,
          -0.8005602176f,
          -0.7819280288f,
          0.6233687174f,
          0.9464672271f,
          0.3227999196f,
          -0.6514146797f,
          -0.7587218957f,
          0.9378472289f,
          0.347048376f,
          -0.8497875957f,
          -0.5271252623f,
          -0.879042592f,
          0.4767432447f,
          -0.892300288f,
          -0.4514423508f,
          -0.379844434f,
          -0.9250503802f,
          -0.9951650832f,
          0.0982163789f,
          0.7724397808f,
          -0.6350880136f,
          0.7573283322f,
          -0.6530343002f,
          -0.9928004525f,
          -0.119780055f,
          -0.0532665713f,
          0.9985803285f,
          0.9754253726f,
          -0.2203300762f,
          -0.7665018163f,
          0.6422421394f,
          0.991636706f,
          0.1290606184f,
          -0.994696838f,
          0.1028503788f,
          -0.5379205513f,
          -0.84299554f,
          0.5022815471f,
          -0.8647041387f,
          0.4559821461f,
          -0.8899889226f,
          -0.8659131224f,
          -0.5001944266f,
          0.0879458407f,
          -0.9961252577f,
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  };

  static const float GRADIENTS_3D[] =
      {
          0, 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0,
          1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0,
          1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0,
          0, 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0,
          1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0,
          1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0,
          0, 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0,
          1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0,
          1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0,
          0, 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0,
          1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0,
          1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0,
          0, 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0,
          1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0,
          1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0,
          1, 1, 0, 0, 0, -1, 1, 0, -1, 1, 0, 0, 0, -1, -1, 0};

  static const float RAND_VECS_3D[] =
      {
          -0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, -0.2739291014f, 0, 0.7217578935f, 0.6226212466f, -0.3023380997f, 0, 0.565683137f, -0.8208298145f, -0.0790000257f, 0, 0.760049034f, -0.5555979497f, -0.3370999617f, 0, 0.3713945616f, 0.5011264475f, 0.7816254623f, 0, -0.1277062463f, -0.4254438999f, -0.8959289049f, 0, -0.2881560924f, -0.5815838982f, 0.7607405838f, 0,
          0.5849561111f, -0.662820239f, -0.4674352136f, 0, 0.3307171178f, 0.0391653737f, 0.94291689f, 0, 0.8712121778f, -0.4113374369f, -0.2679381538f, 0, 0.580981015f, 0.7021915846f, 0.4115677815f, 0, 0.503756873f, 0.6330056931f, -0.5878203852f, 0, 0.4493712205f, 0.601390195f, 0.6606022552f, 0, -0.6878403724f, 0.09018890807f, -0.7202371714f, 0, -0.5958956522f, -0.6469350577f, 0.475797649f, 0,
          -0.5127052122f, 0.1946921978f, -0.8361987284f, 0, -0.9911507142f, -0.05410276466f, -0.1212153153f, 0, -0.2149721042f, 0.9720882117f, -0.09397607749f, 0, -0.7518650936f, -0.5428057603f, 0.3742469607f, 0, 0.5237068895f, 0.8516377189f, -0.02107817834f, 0, 0.6333504779f, 0.1926167129f, -0.7495104896f, 0, -0.06788241606f, 0.3998305789f, 0.9140719259f, 0, -0.5538628599f, -0.4729896695f, -0.6852128902f, 0,
          -0.7261455366f, -0.5911990757f, 0.3509933228f, 0, -0.9229274737f, -0.1782808786f, 0.3412049336f, 0, -0.6968815002f, 0.6511274338f, 0.3006480328f, 0, 0.9608044783f, -0.2098363234f, -0.1811724921f, 0, 0.06817146062f, -0.9743405129f, 0.2145069156f, 0, -0.3577285196f, -0.6697087264f, -0.6507845481f, 0, -0.1868621131f, 0.7648617052f, -0.6164974636f, 0, -0.6541697588f, 0.3967914832f, 0.6439087246f, 0,
          0.6993340405f, -0.6164538506f, 0.3618239211f, 0, -0.1546665739f, 0.6291283928f, 0.7617583057f, 0, -0.6841612949f, -0.2580482182f, -0.6821542638f, 0, 0.5383980957f, 0.4258654885f, 0.7271630328f, 0, -0.5026987823f, -0.7939832935f, -0.3418836993f, 0, 0.3202971715f, 0.2834415347f, 0.9039195862f, 0, 0.8683227101f, -0.0003762656404f, -0.4959995258f, 0, 0.791120031f, -0.08511045745f, 0.6057105799f, 0,
          -0.04011016052f, -0.4397248749f, 0.8972364289f, 0, 0.9145119872f, 0.3579346169f, -0.1885487608f, 0, -0.9612039066f, -0.2756484276f, 0.01024666929f, 0, 0.6510361721f, -0.2877799159f, -0.7023778346f, 0, -0.2041786351f, 0.7365237271f, 0.644859585f, 0, -0.7718263711f, 0.3790626912f, 0.5104855816f, 0, -0.3060082741f, -0.7692987727f, 0.5608371729f, 0, 0.454007341f, -0.5024843065f, 0.7357899537f, 0,
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  // Utilities

  static inline float _fnlFastMin(float x, float y) { return x < y ? x : y; }

  static inline float _fnlFastMax(float x, float y) { return x > y ? x : y; }

  static inline float _fnlFastAbs(float f) { return f < 0 ? -f : f; }

  static inline float _fnlCasti32Tof32(int i)
  {
    union
    {
      float f;
      int32_t i;
    } u;
    u.i = i;
    return u.f;
  }

  static inline int _fnlCastf32Toi32(float f)
  {
    union
    {
      float f;
      int32_t i;
    } u;
    u.f = f;
    return u.i;
  }

  static inline float _fnlInvSqrt(float a)
  {
    float xhalf = 0.5f * a;
    a = _fnlCasti32Tof32(0x5f3759df - (_fnlCastf32Toi32(a) >> 1));
    a = a * (1.5f - xhalf * a * a);
    return a;
  }

  // NOTE: If your language does not support this method (seen above), then simply use the native sqrt function.
  static inline float _fnlFastSqrt(float a) { return a * _fnlInvSqrt(a); }

  static inline int _fnlFastFloor(FNLfloat f) { return (f >= 0 ? (int)f : (int)f - 1); }

  static inline int _fnlFastRound(FNLfloat f) { return (f >= 0) ? (int)(f + 0.5f) : (int)(f - 0.5f); }

  static inline float _fnlLerp(float a, float b, float t) { return a + t * (b - a); }

  static inline float _fnlInterpHermite(float t) { return t * t * (3 - 2 * t); }

  static inline float _fnlInterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); }

  static inline float _fnlCubicLerp(float a, float b, float c, float d, float t)
  {
    float p = (d - c) - (a - b);
    return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b;
  }

  static inline float _fnlPingPong(float t)
  {
    t -= (int)(t * 0.5f) * 2;
    return t < 1 ? t : 2 - t;
  }

  static float _fnlCalculateFractalBounding(fnl_state *state)
  {
    float gain = _fnlFastAbs(state->gain);
    float amp = gain;
    float ampFractal = 1.0f;
    for (int i = 1; i < state->octaves; i++)
    {
      ampFractal += amp;
      amp *= gain;
    }
    return 1.0f / ampFractal;
  }

  // Hashing

  static const int PRIME_X = 501125321;
  static const int PRIME_Y = 1136930381;
  static const int PRIME_Z = 1720413743;

  static inline int _fnlHash2D(int seed, int xPrimed, int yPrimed)
  {
    int hash = seed ^ xPrimed ^ yPrimed;

    hash *= 0x27d4eb2d;
    return hash;
  }

  static inline int _fnlHash3D(int seed, int xPrimed, int yPrimed, int zPrimed)
  {
    int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed;

    hash *= 0x27d4eb2d;
    return hash;
  }

  static inline float _fnlValCoord2D(int seed, int xPrimed, int yPrimed)
  {
    int hash = _fnlHash2D(seed, xPrimed, yPrimed);
    hash *= hash;
    hash ^= hash << 19;
    return hash * (1 / 2147483648.0f);
  }

  static inline float _fnlValCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed)
  {
    int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
    hash *= hash;
    hash ^= hash << 19;
    return hash * (1 / 2147483648.0f);
  }

  static inline float _fnlGradCoord2D(int seed, int xPrimed, int yPrimed, float xd, float yd)
  {
    int hash = _fnlHash2D(seed, xPrimed, yPrimed);
    hash ^= hash >> 15;
    hash &= 127 << 1;
    return xd * GRADIENTS_2D[hash] + yd * GRADIENTS_2D[hash | 1];
  }

  static inline float _fnlGradCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd)
  {
    int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
    hash ^= hash >> 15;
    hash &= 63 << 2;
    return xd * GRADIENTS_3D[hash] + yd * GRADIENTS_3D[hash | 1] + zd * GRADIENTS_3D[hash | 2];
  }

  static inline void _fnlGradCoordOut2D(int seed, int xPrimed, int yPrimed, float *xo, float *yo)
  {
    int hash = _fnlHash2D(seed, xPrimed, yPrimed) & (255 << 1);

    *xo = RAND_VECS_2D[hash];
    *yo = RAND_VECS_2D[hash | 1];
  }

  static inline void _fnlGradCoordOut3D(int seed, int xPrimed, int yPrimed, int zPrimed, float *xo, float *yo, float *zo)
  {
    int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed) & (255 << 2);

    *xo = RAND_VECS_3D[hash];
    *yo = RAND_VECS_3D[hash | 1];
    *zo = RAND_VECS_3D[hash | 2];
  }

  static inline void _fnlGradCoordDual2D(int seed, int xPrimed, int yPrimed, float xd, float yd, float *xo, float *yo)
  {
    int hash = _fnlHash2D(seed, xPrimed, yPrimed);
    int index1 = hash & (127 << 1);
    int index2 = (hash >> 7) & (255 << 1);

    float xg = GRADIENTS_2D[index1];
    float yg = GRADIENTS_2D[index1 | 1];
    float value = xd * xg + yd * yg;

    float xgo = RAND_VECS_2D[index2];
    float ygo = RAND_VECS_2D[index2 | 1];

    *xo = value * xgo;
    *yo = value * ygo;
  }

  static inline void _fnlGradCoordDual3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, float *xo, float *yo, float *zo)
  {
    int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
    int index1 = hash & (63 << 2);
    int index2 = (hash >> 6) & (255 << 2);

    float xg = GRADIENTS_3D[index1];
    float yg = GRADIENTS_3D[index1 | 1];
    float zg = GRADIENTS_3D[index1 | 2];
    float value = xd * xg + yd * yg + zd * zg;

    float xgo = RAND_VECS_3D[index2];
    float ygo = RAND_VECS_3D[index2 | 1];
    float zgo = RAND_VECS_3D[index2 | 2];

    *xo = value * xgo;
    *yo = value * ygo;
    *zo = value * zgo;
  }

  // Generic Noise Gen

  static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y);
  static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
  static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y);
  static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
  static float _fnlSingleCellular2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y);
  static float _fnlSingleCellular3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z);
  static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y);
  static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
  static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y);
  static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
  static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y);
  static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);

  static float _fnlGenNoiseSingle2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y)
  {
    switch (state->noise_type)
    {
    case FNL_NOISE_OPENSIMPLEX2:
      return _fnlSingleSimplex2D(seed, x, y);
    case FNL_NOISE_OPENSIMPLEX2S:
      return _fnlSingleOpenSimplex2S2D(seed, x, y);
    case FNL_NOISE_CELLULAR:
      return _fnlSingleCellular2D(state, seed, x, y);
    case FNL_NOISE_PERLIN:
      return _fnlSinglePerlin2D(seed, x, y);
    case FNL_NOISE_VALUE_CUBIC:
      return _fnlSingleValueCubic2D(seed, x, y);
    case FNL_NOISE_VALUE:
      return _fnlSingleValue2D(seed, x, y);
    default:
      return 0;
    }
  }

  static float _fnlGenNoiseSingle3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    switch (state->noise_type)
    {
    case FNL_NOISE_OPENSIMPLEX2:
      return _fnlSingleOpenSimplex23D(seed, x, y, z);
    case FNL_NOISE_OPENSIMPLEX2S:
      return _fnlSingleOpenSimplex2S3D(seed, x, y, z);
    case FNL_NOISE_CELLULAR:
      return _fnlSingleCellular3D(state, seed, x, y, z);
    case FNL_NOISE_PERLIN:
      return _fnlSinglePerlin3D(seed, x, y, z);
    case FNL_NOISE_VALUE_CUBIC:
      return _fnlSingleValueCubic3D(seed, x, y, z);
    case FNL_NOISE_VALUE:
      return _fnlSingleValue3D(seed, x, y, z);
    default:
      return 0;
    }
  }

  // Noise Coordinate Transforms (frequency, and possible skew or rotation)

  static void _fnlTransformNoiseCoordinate2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
  {
    *x *= state->frequency;
    *y *= state->frequency;

    switch (state->noise_type)
    {
    case FNL_NOISE_OPENSIMPLEX2:
    case FNL_NOISE_OPENSIMPLEX2S:
    {
      const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059;
      const FNLfloat F2 = 0.5f * (SQRT3 - 1);
      FNLfloat t = (*x + *y) * F2;
      *x += t;
      *y += t;
    }
    break;
    default:
      break;
    }
  }

  static void _fnlTransformNoiseCoordinate3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
  {
    *x *= state->frequency;
    *y *= state->frequency;
    *z *= state->frequency;

    switch (state->rotation_type_3d)
    {
    case FNL_ROTATION_IMPROVE_XY_PLANES:
    {
      FNLfloat xy = *x + *y;
      FNLfloat s2 = xy * -(FNLfloat)0.211324865405187;
      *z *= (FNLfloat)0.577350269189626;
      *x += s2 - *z;
      *y = *y + s2 - *z;
      *z += xy * (FNLfloat)0.577350269189626;
    }
    break;
    case FNL_ROTATION_IMPROVE_XZ_PLANES:
    {
      FNLfloat xz = *x + *z;
      FNLfloat s2 = xz * -(FNLfloat)0.211324865405187;
      *y *= (FNLfloat)0.577350269189626;
      *x += s2 - *y;
      *z += s2 - *y;
      *y += xz * (FNLfloat)0.577350269189626;
    }
    break;
    default:
      switch (state->noise_type)
      {
      case FNL_NOISE_OPENSIMPLEX2:
      case FNL_NOISE_OPENSIMPLEX2S:
      {
        const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
        FNLfloat r = (*x + *y + *z) * R3; // Rotation, not skew
        *x = r - *x;
        *y = r - *y;
        *z = r - *z;
      }
      break;
      default:
        break;
      }
    }
  }

  // Domain Warp Coordinate Transforms

  static void _fnlTransformDomainWarpCoordinate2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
  {
    switch (state->domain_warp_type)
    {
    case FNL_DOMAIN_WARP_OPENSIMPLEX2:
    case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED:
    {
      const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059;
      const FNLfloat F2 = 0.5f * (SQRT3 - 1);
      FNLfloat t = (*x + *y) * F2;
      *x += t;
      *y += t;
    }
    break;
    default:
      break;
    }
  }

  static void _fnlTransformDomainWarpCoordinate3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
  {
    switch (state->rotation_type_3d)
    {
    case FNL_ROTATION_IMPROVE_XY_PLANES:
    {
      FNLfloat xy = *x + *y;
      FNLfloat s2 = xy * -(FNLfloat)0.211324865405187;
      *z *= (FNLfloat)0.577350269189626;
      *x += s2 - *z;
      *y = *y + s2 - *z;
      *z += xy * (FNLfloat)0.577350269189626;
    }
    break;
    case FNL_ROTATION_IMPROVE_XZ_PLANES:
    {
      FNLfloat xz = *x + *z;
      FNLfloat s2 = xz * -(FNLfloat)0.211324865405187;
      *y *= (FNLfloat)0.577350269189626;
      *x += s2 - *y;
      *z += s2 - *y;
      *y += xz * (FNLfloat)0.577350269189626;
    }
    break;
    default:
      switch (state->domain_warp_type)
      {
      case FNL_DOMAIN_WARP_OPENSIMPLEX2:
      case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED:
      {
        const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
        FNLfloat r = (*x + *y + *z) * R3; // Rotation, not skew
        *x = r - *x;
        *y = r - *y;
        *z = r - *z;
      }
      break;
      default:
        break;
      }
    }
  }

  // Fractal FBm
  static float _fnlGenFractalFBM2D(fnl_state *state, FNLfloat x, FNLfloat y)
  {
    int seed = state->seed;
    float sum = 0;
    float amp = _fnlCalculateFractalBounding(state);

    for (int i = 0; i < state->octaves; i++)
    {
      float noise = _fnlGenNoiseSingle2D(state, seed++, x, y);
      sum += noise * amp;
      amp *= _fnlLerp(1.0f, _fnlFastMin(noise + 1, 2) * 0.5f, state->weighted_strength);

      x *= state->lacunarity;
      y *= state->lacunarity;
      amp *= state->gain;
    }

    return sum;
  }

  static float _fnlGenFractalFBM3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int seed = state->seed;
    float sum = 0;
    float amp = _fnlCalculateFractalBounding(state);

    for (int i = 0; i < state->octaves; i++)
    {
      float noise = _fnlGenNoiseSingle3D(state, seed++, x, y, z);
      sum += noise * amp;
      amp *= _fnlLerp(1.0f, (noise + 1) * 0.5f, state->weighted_strength);

      x *= state->lacunarity;
      y *= state->lacunarity;
      z *= state->lacunarity;
      amp *= state->gain;
    }

    return sum;
  }

  // Fractal Ridged

  static float _fnlGenFractalRidged2D(fnl_state *state, FNLfloat x, FNLfloat y)
  {
    int seed = state->seed;
    float sum = 0;
    float amp = _fnlCalculateFractalBounding(state);

    for (int i = 0; i < state->octaves; i++)
    {
      float noise = _fnlFastAbs(_fnlGenNoiseSingle2D(state, seed++, x, y));
      sum += (noise * -2 + 1) * amp;
      amp *= _fnlLerp(1.0f, 1 - noise, state->weighted_strength);

      x *= state->lacunarity;
      y *= state->lacunarity;
      amp *= state->gain;
    }

    return sum;
  }

  static float _fnlGenFractalRidged3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int seed = state->seed;
    float sum = 0;
    float amp = _fnlCalculateFractalBounding(state);

    for (int i = 0; i < state->octaves; i++)
    {
      float noise = _fnlFastAbs(_fnlGenNoiseSingle3D(state, seed++, x, y, z));
      sum += (noise * -2 + 1) * amp;
      amp *= _fnlLerp(1.0f, 1 - noise, state->weighted_strength);

      x *= state->lacunarity;
      y *= state->lacunarity;
      z *= state->lacunarity;
      amp *= state->gain;
    }

    return sum;
  }

  // Fractal PingPong

  static float _fnlGenFractalPingPong2D(fnl_state *state, FNLfloat x, FNLfloat y)
  {
    int seed = state->seed;
    float sum = 0;
    float amp = _fnlCalculateFractalBounding(state);

    for (int i = 0; i < state->octaves; i++)
    {
      float noise = _fnlPingPong((_fnlGenNoiseSingle2D(state, seed++, x, y) + 1) * state->ping_pong_strength);
      sum += (noise - 0.5f) * 2 * amp;
      amp *= _fnlLerp(1.0f, noise, state->weighted_strength);

      x *= state->lacunarity;
      y *= state->lacunarity;
      amp *= state->gain;
    }

    return sum;
  }

  static float _fnlGenFractalPingPong3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int seed = state->seed;
    float sum = 0;
    float amp = _fnlCalculateFractalBounding(state);

    for (int i = 0; i < state->octaves; i++)
    {
      float noise = _fnlPingPong((_fnlGenNoiseSingle3D(state, seed++, x, y, z) + 1) * state->ping_pong_strength);
      sum += (noise - 0.5f) * 2 * amp;
      amp *= _fnlLerp(1.0f, noise, state->weighted_strength);

      x *= state->lacunarity;
      y *= state->lacunarity;
      z *= state->lacunarity;
      amp *= state->gain;
    }

    return sum;
  }

  // Simplex/OpenSimplex2 Noise

  static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y)
  {
    // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex.

    const float SQRT3 = 1.7320508075688772935274463415059f;
    const float G2 = (3 - SQRT3) / 6;

    /*
     * --- Skew moved to TransformNoiseCoordinate method ---
     * const FNLfloat F2 = 0.5f * (SQRT3 - 1);
     * FNLfloat s = (x + y) * F2;
     * x += s; y += s;
     */

    int i = _fnlFastFloor(x);
    int j = _fnlFastFloor(y);
    float xi = (float)(x - i);
    float yi = (float)(y - j);

    float t = (xi + yi) * G2;
    float x0 = (float)(xi - t);
    float y0 = (float)(yi - t);

    i *= PRIME_X;
    j *= PRIME_Y;

    float n0, n1, n2;

    float a = 0.5f - x0 * x0 - y0 * y0;
    if (a <= 0)
      n0 = 0;
    else
    {
      n0 = (a * a) * (a * a) * _fnlGradCoord2D(seed, i, j, x0, y0);
    }

    float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a);
    if (c <= 0)
      n2 = 0;
    else
    {
      float x2 = x0 + (2 * (float)G2 - 1);
      float y2 = y0 + (2 * (float)G2 - 1);
      n2 = (c * c) * (c * c) * _fnlGradCoord2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2);
    }

    if (y0 > x0)
    {
      float x1 = x0 + (float)G2;
      float y1 = y0 + ((float)G2 - 1);
      float b = 0.5f - x1 * x1 - y1 * y1;
      if (b <= 0)
        n1 = 0;
      else
      {
        n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x1, y1);
      }
    }
    else
    {
      float x1 = x0 + ((float)G2 - 1);
      float y1 = y0 + (float)G2;
      float b = 0.5f - x1 * x1 - y1 * y1;
      if (b <= 0)
        n1 = 0;
      else
      {
        n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i + PRIME_X, j, x1, y1);
      }
    }

    return (n0 + n1 + n2) * 99.83685446303647f;
  }

  static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    // 3D OpenSimplex2 case uses two offset rotated cube grids.

    /*
     * --- Rotation moved to TransformNoiseCoordinate method ---
     * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
     * FNLfloat r = (x + y + z) * R3; // Rotation, not skew
     * x = r - x; y = r - y; z = r - z;
     */

    int i = _fnlFastRound(x);
    int j = _fnlFastRound(y);
    int k = _fnlFastRound(z);
    float x0 = (float)(x - i);
    float y0 = (float)(y - j);
    float z0 = (float)(z - k);

    int xNSign = (int)(-1.0f - x0) | 1;
    int yNSign = (int)(-1.0f - y0) | 1;
    int zNSign = (int)(-1.0f - z0) | 1;

    float ax0 = xNSign * -x0;
    float ay0 = yNSign * -y0;
    float az0 = zNSign * -z0;

    i *= PRIME_X;
    j *= PRIME_Y;
    k *= PRIME_Z;

    float value = 0;
    float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0);

    for (int l = 0;; l++)
    {
      if (a > 0)
      {
        value += (a * a) * (a * a) * _fnlGradCoord3D(seed, i, j, k, x0, y0, z0);
      }

      float b = a + 1;
      int i1 = i;
      int j1 = j;
      int k1 = k;
      float x1 = x0;
      float y1 = y0;
      float z1 = z0;
      if (ax0 >= ay0 && ax0 >= az0)
      {
        x1 += xNSign;
        b -= xNSign * 2 * x1;
        i1 -= xNSign * PRIME_X;
      }
      else if (ay0 > ax0 && ay0 >= az0)
      {
        y1 += yNSign;
        b -= yNSign * 2 * y1;
        j1 -= yNSign * PRIME_Y;
      }
      else
      {
        z1 += zNSign;
        b -= zNSign * 2 * z1;
        k1 -= zNSign * PRIME_Z;
      }

      if (b > 0)
      {
        value += (b * b) * (b * b) * _fnlGradCoord3D(seed, i1, j1, k1, x1, y1, z1);
      }

      if (l == 1)
        break;

      ax0 = 0.5f - ax0;
      ay0 = 0.5f - ay0;
      az0 = 0.5f - az0;

      x0 = xNSign * ax0;
      y0 = yNSign * ay0;
      z0 = zNSign * az0;

      a += (0.75f - ax0) - (ay0 + az0);

      i += (xNSign >> 1) & PRIME_X;
      j += (yNSign >> 1) & PRIME_Y;
      k += (zNSign >> 1) & PRIME_Z;

      xNSign = -xNSign;
      yNSign = -yNSign;
      zNSign = -zNSign;

      seed = ~seed;
    }

    return value * 32.69428253173828125f;
  }

  // OpenSimplex2S Noise

  static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y)
  {
    // 2D OpenSimplex2S case is a modified 2D simplex noise.

    const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059;
    const FNLfloat G2 = (3 - SQRT3) / 6;

    /*
     * --- Skew moved to TransformNoiseCoordinate method ---
     * const FNLfloat F2 = 0.5f * (SQRT3 - 1);
     * FNLfloat s = (x + y) * F2;
     * x += s; y += s;
    */

    int i = _fnlFastFloor(x);
    int j = _fnlFastFloor(y);
    float xi = (float)(x - i);
    float yi = (float)(y - j);

    i *= PRIME_X;
    j *= PRIME_Y;
    int i1 = i + PRIME_X;
    int j1 = j + PRIME_Y;

    float t = (xi + yi) * (float)G2;
    float x0 = xi - t;
    float y0 = yi - t;

    float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0;
    float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord2D(seed, i, j, x0, y0);

    float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0);
    float x1 = x0 - (float)(1 - 2 * G2);
    float y1 = y0 - (float)(1 - 2 * G2);
    value += (a1 * a1) * (a1 * a1) * _fnlGradCoord2D(seed, i1, j1, x1, y1);

    // Nested conditionals were faster than compact bit logic/arithmetic.
    float xmyi = xi - yi;
    if (t > G2)
    {
      if (xi + xmyi > 1)
      {
        float x2 = x0 + (float)(3 * G2 - 2);
        float y2 = y0 + (float)(3 * G2 - 1);
        float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;
        if (a2 > 0)
        {
          value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i + (PRIME_X << 1), j + PRIME_Y, x2, y2);
        }
      }
      else
      {
        float x2 = x0 + (float)G2;
        float y2 = y0 + (float)(G2 - 1);
        float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;
        if (a2 > 0)
        {
          value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x2, y2);
        }
      }

      if (yi - xmyi > 1)
      {
        float x3 = x0 + (float)(3 * G2 - 1);
        float y3 = y0 + (float)(3 * G2 - 2);
        float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3;
        if (a3 > 0)
        {
          value += (a3 * a3) * (a3 * a3) * _fnlGradCoord2D(seed, i + PRIME_X, j + (PRIME_Y << 1), x3, y3);
        }
      }
      else
      {
        float x3 = x0 + (float)(G2 - 1);
        float y3 = y0 + (float)G2;
        float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3;
        if (a3 > 0)
        {
          value += (a3 * a3) * (a3 * a3) * _fnlGradCoord2D(seed, i + PRIME_X, j, x3, y3);
        }
      }
    }
    else
    {
      if (xi + xmyi < 0)
      {
        float x2 = x0 + (float)(1 - G2);
        float y2 = y0 - (float)G2;
        float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;
        if (a2 > 0)
        {
          value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i - PRIME_X, j, x2, y2);
        }
      }
      else
      {
        float x2 = x0 + (float)(G2 - 1);
        float y2 = y0 + (float)G2;
        float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;
        if (a2 > 0)
        {
          value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i + PRIME_X, j, x2, y2);
        }
      }

      if (yi < xmyi)
      {
        float x2 = x0 - (float)G2;
        float y2 = y0 - (float)(G2 - 1);
        float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;
        if (a2 > 0)
        {
          value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i, j - PRIME_Y, x2, y2);
        }
      }
      else
      {
        float x2 = x0 + (float)G2;
        float y2 = y0 + (float)(G2 - 1);
        float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;
        if (a2 > 0)
        {
          value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x2, y2);
        }
      }
    }

    return value * 18.24196194486065f;
  }

  static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    // 3D OpenSimplex2S case uses two offset rotated cube grids.

    /*
     * --- Rotation moved to TransformNoiseCoordinate method ---
     * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
     * FNLfloat r = (x + y + z) * R3; // Rotation, not skew
     * x = r - x; y = r - y; z = r - z;
     */

    int i = _fnlFastFloor(x);
    int j = _fnlFastFloor(y);
    int k = _fnlFastFloor(z);
    float xi = (float)(x - i);
    float yi = (float)(y - j);
    float zi = (float)(z - k);

    i *= PRIME_X;
    j *= PRIME_Y;
    k *= PRIME_Z;
    int seed2 = seed + 1293373;

    int xNMask = (int)(-0.5f - xi);
    int yNMask = (int)(-0.5f - yi);
    int zNMask = (int)(-0.5f - zi);

    float x0 = xi + xNMask;
    float y0 = yi + yNMask;
    float z0 = zi + zNMask;
    float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0;
    float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord3D(seed, i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x0, y0, z0);

    float x1 = xi - 0.5f;
    float y1 = yi - 0.5f;
    float z1 = zi - 0.5f;
    float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1;
    value += (a1 * a1) * (a1 * a1) * _fnlGradCoord3D(seed2, i + PRIME_X, j + PRIME_Y, k + PRIME_Z, x1, y1, z1);

    float xAFlipMask0 = ((xNMask | 1) << 1) * x1;
    float yAFlipMask0 = ((yNMask | 1) << 1) * y1;
    float zAFlipMask0 = ((zNMask | 1) << 1) * z1;
    float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f;
    float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f;
    float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f;

    bool skip5 = false;
    float a2 = xAFlipMask0 + a0;
    if (a2 > 0)
    {
      float x2 = x0 - (xNMask | 1);
      float y2 = y0;
      float z2 = z0;
      value += (a2 * a2) * (a2 * a2) * _fnlGradCoord3D(seed, i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x2, y2, z2);
    }
    else
    {
      float a3 = yAFlipMask0 + zAFlipMask0 + a0;
      if (a3 > 0)
      {
        float x3 = x0;
        float y3 = y0 - (yNMask | 1);
        float z3 = z0 - (zNMask | 1);
        value += (a3 * a3) * (a3 * a3) * _fnlGradCoord3D(seed, i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x3, y3, z3);
      }

      float a4 = xAFlipMask1 + a1;
      if (a4 > 0)
      {
        float x4 = (xNMask | 1) + x1;
        float y4 = y1;
        float z4 = z1;
        value += (a4 * a4) * (a4 * a4) * _fnlGradCoord3D(seed2, i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + PRIME_Z, x4, y4, z4);
        skip5 = true;
      }
    }

    bool skip9 = false;
    float a6 = yAFlipMask0 + a0;
    if (a6 > 0)
    {
      float x6 = x0;
      float y6 = y0 - (yNMask | 1);
      float z6 = z0;
      value += (a6 * a6) * (a6 * a6) * _fnlGradCoord3D(seed, i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x6, y6, z6);
    }
    else
    {
      float a7 = xAFlipMask0 + zAFlipMask0 + a0;
      if (a7 > 0)
      {
        float x7 = x0 - (xNMask | 1);
        float y7 = y0;
        float z7 = z0 - (zNMask | 1);
        value += (a7 * a7) * (a7 * a7) * _fnlGradCoord3D(seed, i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x7, y7, z7);
      }

      float a8 = yAFlipMask1 + a1;
      if (a8 > 0)
      {
        float x8 = x1;
        float y8 = (yNMask | 1) + y1;
        float z8 = z1;
        value += (a8 * a8) * (a8 * a8) * _fnlGradCoord3D(seed2, i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, x8, y8, z8);
        skip9 = true;
      }
    }

    bool skipD = false;
    float aA = zAFlipMask0 + a0;
    if (aA > 0)
    {
      float xA = x0;
      float yA = y0;
      float zA = z0 - (zNMask | 1);
      value += (aA * aA) * (aA * aA) * _fnlGradCoord3D(seed, i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), xA, yA, zA);
    }
    else
    {
      float aB = xAFlipMask0 + yAFlipMask0 + a0;
      if (aB > 0)
      {
        float xB = x0 - (xNMask | 1);
        float yB = y0 - (yNMask | 1);
        float zB = z0;
        value += (aB * aB) * (aB * aB) * _fnlGradCoord3D(seed, i + (~xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), xB, yB, zB);
      }

      float aC = zAFlipMask1 + a1;
      if (aC > 0)
      {
        float xC = x1;
        float yC = y1;
        float zC = (zNMask | 1) + z1;
        value += (aC * aC) * (aC * aC) * _fnlGradCoord3D(seed2, i + PRIME_X, j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), xC, yC, zC);
        skipD = true;
      }
    }

    if (!skip5)
    {
      float a5 = yAFlipMask1 + zAFlipMask1 + a1;
      if (a5 > 0)
      {
        float x5 = x1;
        float y5 = (yNMask | 1) + y1;
        float z5 = (zNMask | 1) + z1;
        value += (a5 * a5) * (a5 * a5) * _fnlGradCoord3D(seed2, i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + (zNMask & (PRIME_Z << 1)), x5, y5, z5);
      }
    }

    if (!skip9)
    {
      float a9 = xAFlipMask1 + zAFlipMask1 + a1;
      if (a9 > 0)
      {
        float x9 = (xNMask | 1) + x1;
        float y9 = y1;
        float z9 = (zNMask | 1) + z1;
        value += (a9 * a9) * (a9 * a9) * _fnlGradCoord3D(seed2, i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), x9, y9, z9);
      }
    }

    if (!skipD)
    {
      float aD = xAFlipMask1 + yAFlipMask1 + a1;
      if (aD > 0)
      {
        float xD = (xNMask | 1) + x1;
        float yD = (yNMask | 1) + y1;
        float zD = z1;
        value += (aD * aD) * (aD * aD) * _fnlGradCoord3D(seed2, i + (xNMask & (PRIME_X << 1)), j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, xD, yD, zD);
      }
    }

    return value * 9.046026385208288f;
  }

  // Cellular Noise

  static float _fnlSingleCellular2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y)
  {
    int xr = _fnlFastRound(x);
    int yr = _fnlFastRound(y);

    float distance0 = FLT_MAX;
    float distance1 = FLT_MAX;
    int closestHash = 0;

    float cellularJitter = 0.5f * state->cellular_jitter_mod;

    int xPrimed = (xr - 1) * PRIME_X;
    int yPrimedBase = (yr - 1) * PRIME_Y;

    switch (state->cellular_distance_func)
    {
    default:
    case FNL_CELLULAR_DISTANCE_EUCLIDEAN:
    case FNL_CELLULAR_DISTANCE_EUCLIDEANSQ:
      for (int xi = xr - 1; xi <= xr + 1; xi++)
      {
        int yPrimed = yPrimedBase;

        for (int yi = yr - 1; yi <= yr + 1; yi++)
        {
          int hash = _fnlHash2D(seed, xPrimed, yPrimed);
          int idx = hash & (255 << 1);

          float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter;
          float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter;

          float newDistance = vecX * vecX + vecY * vecY;

          distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0);
          if (newDistance < distance0)
          {
            distance0 = newDistance;
            closestHash = hash;
          }
          yPrimed += PRIME_Y;
        }
        xPrimed += PRIME_X;
      }
      break;
    case FNL_CELLULAR_DISTANCE_MANHATTAN:
      for (int xi = xr - 1; xi <= xr + 1; xi++)
      {
        int yPrimed = yPrimedBase;

        for (int yi = yr - 1; yi <= yr + 1; yi++)
        {
          int hash = _fnlHash2D(seed, xPrimed, yPrimed);
          int idx = hash & (255 << 1);

          float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter;
          float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter;

          float newDistance = _fnlFastAbs(vecX) + _fnlFastAbs(vecY);

          distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0);
          if (newDistance < distance0)
          {
            distance0 = newDistance;
            closestHash = hash;
          }
          yPrimed += PRIME_Y;
        }
        xPrimed += PRIME_X;
      }
      break;
    case FNL_CELLULAR_DISTANCE_HYBRID:
      for (int xi = xr - 1; xi <= xr + 1; xi++)
      {
        int yPrimed = yPrimedBase;
        for (int yi = yr - 1; yi <= yr + 1; yi++)
        {
          int hash = _fnlHash2D(seed, xPrimed, yPrimed);
          int idx = hash & (255 << 1);

          float vecX = (float)(xi - x) + RAND_VECS_2D[idx] * cellularJitter;
          float vecY = (float)(yi - y) + RAND_VECS_2D[idx | 1] * cellularJitter;

          float newDistance = (_fnlFastAbs(vecX) + _fnlFastAbs(vecY)) + (vecX * vecX + vecY * vecY);

          distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0);
          if (newDistance < distance0)
          {
            distance0 = newDistance;
            closestHash = hash;
          }
          yPrimed += PRIME_Y;
        }
        xPrimed += PRIME_X;
      }
      break;
    }

    if (state->cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN && state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE)
    {
      distance0 = _fnlFastSqrt(distance0);
      if (state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE2)
        distance1 = _fnlFastSqrt(distance1);
    }

    switch (state->cellular_return_type)
    {
    case FNL_CELLULAR_RETURN_VALUE_CELLVALUE:
      return closestHash * (1 / 2147483648.0f);
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE:
      return distance0 - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2:
      return distance1 - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD:
      return (distance1 + distance0) * 0.5f - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB:
      return distance1 - distance0 - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL:
      return distance1 * distance0 * 0.5f - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV:
      return distance0 / distance1 - 1;
    default:
      return 0;
    }
  }

  static float _fnlSingleCellular3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int xr = _fnlFastRound(x);
    int yr = _fnlFastRound(y);
    int zr = _fnlFastRound(z);

    float distance0 = FLT_MAX;
    float distance1 = FLT_MAX;
    int closestHash = 0;

    float cellularJitter = 0.39614353f * state->cellular_jitter_mod;

    int xPrimed = (xr - 1) * PRIME_X;
    int yPrimedBase = (yr - 1) * PRIME_Y;
    int zPrimedBase = (zr - 1) * PRIME_Z;

    switch (state->cellular_distance_func)
    {
    default:
    case FNL_CELLULAR_DISTANCE_EUCLIDEAN:
    case FNL_CELLULAR_DISTANCE_EUCLIDEANSQ:
      for (int xi = xr - 1; xi <= xr + 1; xi++)
      {
        int yPrimed = yPrimedBase;

        for (int yi = yr - 1; yi <= yr + 1; yi++)
        {
          int zPrimed = zPrimedBase;

          for (int zi = zr - 1; zi <= zr + 1; zi++)
          {
            int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
            int idx = hash & (255 << 2);

            float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter;
            float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter;
            float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter;

            float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ;

            distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0);
            if (newDistance < distance0)
            {
              distance0 = newDistance;
              closestHash = hash;
            }
            zPrimed += PRIME_Z;
          }
          yPrimed += PRIME_Y;
        }
        xPrimed += PRIME_X;
      }
      break;
    case FNL_CELLULAR_DISTANCE_MANHATTAN:
      for (int xi = xr - 1; xi <= xr + 1; xi++)
      {
        int yPrimed = yPrimedBase;

        for (int yi = yr - 1; yi <= yr + 1; yi++)
        {
          int zPrimed = zPrimedBase;

          for (int zi = zr - 1; zi <= zr + 1; zi++)
          {
            int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
            int idx = hash & (255 << 2);

            float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter;
            float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter;
            float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter;

            float newDistance = _fnlFastAbs(vecX) + _fnlFastAbs(vecY) + _fnlFastAbs(vecZ);

            distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0);
            if (newDistance < distance0)
            {
              distance0 = newDistance;
              closestHash = hash;
            }
            zPrimed += PRIME_Z;
          }
          yPrimed += PRIME_Y;
        }
        xPrimed += PRIME_X;
      }
      break;
    case FNL_CELLULAR_DISTANCE_HYBRID:
      for (int xi = xr - 1; xi <= xr + 1; xi++)
      {
        int yPrimed = yPrimedBase;

        for (int yi = yr - 1; yi <= yr + 1; yi++)
        {
          int zPrimed = zPrimedBase;

          for (int zi = zr - 1; zi <= zr + 1; zi++)
          {
            int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
            int idx = hash & (255 << 2);

            float vecX = (float)(xi - x) + RAND_VECS_3D[idx] * cellularJitter;
            float vecY = (float)(yi - y) + RAND_VECS_3D[idx | 1] * cellularJitter;
            float vecZ = (float)(zi - z) + RAND_VECS_3D[idx | 2] * cellularJitter;

            float newDistance = (_fnlFastAbs(vecX) + _fnlFastAbs(vecY) + _fnlFastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ);

            distance1 = _fnlFastMax(_fnlFastMin(distance1, newDistance), distance0);
            if (newDistance < distance0)
            {
              distance0 = newDistance;
              closestHash = hash;
            }
            zPrimed += PRIME_Z;
          }
          yPrimed += PRIME_Y;
        }
        xPrimed += PRIME_X;
      }
      break;
    }

    if (state->cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN && state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE)
    {
      distance0 = _fnlFastSqrt(distance0);
      if (state->cellular_return_type >= FNL_CELLULAR_RETURN_VALUE_DISTANCE2)
        distance1 = _fnlFastSqrt(distance1);
    }

    switch (state->cellular_return_type)
    {
    case FNL_CELLULAR_RETURN_VALUE_CELLVALUE:
      return closestHash * (1 / 2147483648.0f);
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE:
      return distance0 - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2:
      return distance1 - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD:
      return (distance1 + distance0) * 0.5f - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB:
      return distance1 - distance0 - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL:
      return distance1 * distance0 * 0.5f - 1;
    case FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV:
      return distance0 / distance1 - 1;
    default:
      return 0;
    }
  }

  // Perlin Noise

  static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y)
  {
    int x0 = _fnlFastFloor(x);
    int y0 = _fnlFastFloor(y);

    float xd0 = (float)(x - x0);
    float yd0 = (float)(y - y0);
    float xd1 = xd0 - 1;
    float yd1 = yd0 - 1;

    float xs = _fnlInterpQuintic(xd0);
    float ys = _fnlInterpQuintic(yd0);

    x0 *= PRIME_X;
    y0 *= PRIME_Y;
    int x1 = x0 + PRIME_X;
    int y1 = y0 + PRIME_Y;

    float xf0 = _fnlLerp(_fnlGradCoord2D(seed, x0, y0, xd0, yd0), _fnlGradCoord2D(seed, x1, y0, xd1, yd0), xs);
    float xf1 = _fnlLerp(_fnlGradCoord2D(seed, x0, y1, xd0, yd1), _fnlGradCoord2D(seed, x1, y1, xd1, yd1), xs);

    return _fnlLerp(xf0, xf1, ys) * 1.4247691104677813f;
  }

  static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int x0 = _fnlFastFloor(x);
    int y0 = _fnlFastFloor(y);
    int z0 = _fnlFastFloor(z);

    float xd0 = (float)(x - x0);
    float yd0 = (float)(y - y0);
    float zd0 = (float)(z - z0);
    float xd1 = xd0 - 1;
    float yd1 = yd0 - 1;
    float zd1 = zd0 - 1;

    float xs = _fnlInterpQuintic(xd0);
    float ys = _fnlInterpQuintic(yd0);
    float zs = _fnlInterpQuintic(zd0);

    x0 *= PRIME_X;
    y0 *= PRIME_Y;
    z0 *= PRIME_Z;
    int x1 = x0 + PRIME_X;
    int y1 = y0 + PRIME_Y;
    int z1 = z0 + PRIME_Z;

    float xf00 = _fnlLerp(_fnlGradCoord3D(seed, x0, y0, z0, xd0, yd0, zd0), _fnlGradCoord3D(seed, x1, y0, z0, xd1, yd0, zd0), xs);
    float xf10 = _fnlLerp(_fnlGradCoord3D(seed, x0, y1, z0, xd0, yd1, zd0), _fnlGradCoord3D(seed, x1, y1, z0, xd1, yd1, zd0), xs);
    float xf01 = _fnlLerp(_fnlGradCoord3D(seed, x0, y0, z1, xd0, yd0, zd1), _fnlGradCoord3D(seed, x1, y0, z1, xd1, yd0, zd1), xs);
    float xf11 = _fnlLerp(_fnlGradCoord3D(seed, x0, y1, z1, xd0, yd1, zd1), _fnlGradCoord3D(seed, x1, y1, z1, xd1, yd1, zd1), xs);

    float yf0 = _fnlLerp(xf00, xf10, ys);
    float yf1 = _fnlLerp(xf01, xf11, ys);

    return _fnlLerp(yf0, yf1, zs) * 0.964921414852142333984375f;
  }

  // Value Cubic

  static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y)
  {
    int x1 = _fnlFastFloor(x);
    int y1 = _fnlFastFloor(y);

    float xs = x - (float)x1;
    float ys = y - (float)y1;

    x1 *= PRIME_X;
    y1 *= PRIME_Y;

    int x0 = x1 - PRIME_X;
    int y0 = y1 - PRIME_Y;
    int x2 = x1 + PRIME_X;
    int y2 = y1 + PRIME_Y;
    int x3 = x1 + (int)((long)PRIME_X << 1);
    int y3 = y1 + (int)((long)PRIME_Y << 1);

    return _fnlCubicLerp(
               _fnlCubicLerp(_fnlValCoord2D(seed, x0, y0), _fnlValCoord2D(seed, x1, y0), _fnlValCoord2D(seed, x2, y0), _fnlValCoord2D(seed, x3, y0),
                             xs),
               _fnlCubicLerp(_fnlValCoord2D(seed, x0, y1), _fnlValCoord2D(seed, x1, y1), _fnlValCoord2D(seed, x2, y1), _fnlValCoord2D(seed, x3, y1),
                             xs),
               _fnlCubicLerp(_fnlValCoord2D(seed, x0, y2), _fnlValCoord2D(seed, x1, y2), _fnlValCoord2D(seed, x2, y2), _fnlValCoord2D(seed, x3, y2),
                             xs),
               _fnlCubicLerp(_fnlValCoord2D(seed, x0, y3), _fnlValCoord2D(seed, x1, y3), _fnlValCoord2D(seed, x2, y3), _fnlValCoord2D(seed, x3, y3),
                             xs),
               ys) *
           (1 / (1.5f * 1.5f));
  }

  static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int x1 = _fnlFastFloor(x);
    int y1 = _fnlFastFloor(y);
    int z1 = _fnlFastFloor(z);

    float xs = x - (float)x1;
    float ys = y - (float)y1;
    float zs = z - (float)z1;

    x1 *= PRIME_X;
    y1 *= PRIME_Y;
    z1 *= PRIME_Z;

    int x0 = x1 - PRIME_X;
    int y0 = y1 - PRIME_Y;
    int z0 = z1 - PRIME_Z;
    int x2 = x1 + PRIME_X;
    int y2 = y1 + PRIME_Y;
    int z2 = z1 + PRIME_Z;
    int x3 = x1 + (int)((long)PRIME_X << 1);
    int y3 = y1 + (int)((long)PRIME_Y << 1);
    int z3 = z1 + (int)((long)PRIME_Z << 1);

    return _fnlCubicLerp(
               _fnlCubicLerp(
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z0), _fnlValCoord3D(seed, x1, y0, z0), _fnlValCoord3D(seed, x2, y0, z0), _fnlValCoord3D(seed, x3, y0, z0), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z0), _fnlValCoord3D(seed, x1, y1, z0), _fnlValCoord3D(seed, x2, y1, z0), _fnlValCoord3D(seed, x3, y1, z0), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z0), _fnlValCoord3D(seed, x1, y2, z0), _fnlValCoord3D(seed, x2, y2, z0), _fnlValCoord3D(seed, x3, y2, z0), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z0), _fnlValCoord3D(seed, x1, y3, z0), _fnlValCoord3D(seed, x2, y3, z0), _fnlValCoord3D(seed, x3, y3, z0), xs),
                   ys),
               _fnlCubicLerp(
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z1), _fnlValCoord3D(seed, x1, y0, z1), _fnlValCoord3D(seed, x2, y0, z1), _fnlValCoord3D(seed, x3, y0, z1), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z1), _fnlValCoord3D(seed, x1, y1, z1), _fnlValCoord3D(seed, x2, y1, z1), _fnlValCoord3D(seed, x3, y1, z1), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z1), _fnlValCoord3D(seed, x1, y2, z1), _fnlValCoord3D(seed, x2, y2, z1), _fnlValCoord3D(seed, x3, y2, z1), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z1), _fnlValCoord3D(seed, x1, y3, z1), _fnlValCoord3D(seed, x2, y3, z1), _fnlValCoord3D(seed, x3, y3, z1), xs),
                   ys),
               _fnlCubicLerp(
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z2), _fnlValCoord3D(seed, x1, y0, z2), _fnlValCoord3D(seed, x2, y0, z2), _fnlValCoord3D(seed, x3, y0, z2), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z2), _fnlValCoord3D(seed, x1, y1, z2), _fnlValCoord3D(seed, x2, y1, z2), _fnlValCoord3D(seed, x3, y1, z2), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z2), _fnlValCoord3D(seed, x1, y2, z2), _fnlValCoord3D(seed, x2, y2, z2), _fnlValCoord3D(seed, x3, y2, z2), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z2), _fnlValCoord3D(seed, x1, y3, z2), _fnlValCoord3D(seed, x2, y3, z2), _fnlValCoord3D(seed, x3, y3, z2), xs),
                   ys),
               _fnlCubicLerp(
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y0, z3), _fnlValCoord3D(seed, x1, y0, z3), _fnlValCoord3D(seed, x2, y0, z3), _fnlValCoord3D(seed, x3, y0, z3), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y1, z3), _fnlValCoord3D(seed, x1, y1, z3), _fnlValCoord3D(seed, x2, y1, z3), _fnlValCoord3D(seed, x3, y1, z3), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y2, z3), _fnlValCoord3D(seed, x1, y2, z3), _fnlValCoord3D(seed, x2, y2, z3), _fnlValCoord3D(seed, x3, y2, z3), xs),
                   _fnlCubicLerp(_fnlValCoord3D(seed, x0, y3, z3), _fnlValCoord3D(seed, x1, y3, z3), _fnlValCoord3D(seed, x2, y3, z3), _fnlValCoord3D(seed, x3, y3, z3), xs),
                   ys),
               zs) *
           (1 / 1.5f * 1.5f * 1.5f);
  }

  // Value noise

  static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y)
  {
    int x0 = _fnlFastFloor(x);
    int y0 = _fnlFastFloor(y);

    float xs = _fnlInterpHermite((float)(x - x0));
    float ys = _fnlInterpHermite((float)(y - y0));

    x0 *= PRIME_X;
    y0 *= PRIME_Y;
    int x1 = x0 + PRIME_X;
    int y1 = y0 + PRIME_Y;

    float xf0 = _fnlLerp(_fnlValCoord2D(seed, x0, y0), _fnlValCoord2D(seed, x1, y0), xs);
    float xf1 = _fnlLerp(_fnlValCoord2D(seed, x0, y1), _fnlValCoord2D(seed, x1, y1), xs);

    return _fnlLerp(xf0, xf1, ys);
  }

  static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    int x0 = _fnlFastFloor(x);
    int y0 = _fnlFastFloor(y);
    int z0 = _fnlFastFloor(z);

    float xs = _fnlInterpHermite((float)(x - x0));
    float ys = _fnlInterpHermite((float)(y - y0));
    float zs = _fnlInterpHermite((float)(z - z0));

    x0 *= PRIME_X;
    y0 *= PRIME_Y;
    z0 *= PRIME_Z;
    int x1 = x0 + PRIME_X;
    int y1 = y0 + PRIME_Y;
    int z1 = z0 + PRIME_Z;

    float xf00 = _fnlLerp(_fnlValCoord3D(seed, x0, y0, z0), _fnlValCoord3D(seed, x1, y0, z0), xs);
    float xf10 = _fnlLerp(_fnlValCoord3D(seed, x0, y1, z0), _fnlValCoord3D(seed, x1, y1, z0), xs);
    float xf01 = _fnlLerp(_fnlValCoord3D(seed, x0, y0, z1), _fnlValCoord3D(seed, x1, y0, z1), xs);
    float xf11 = _fnlLerp(_fnlValCoord3D(seed, x0, y1, z1), _fnlValCoord3D(seed, x1, y1, z1), xs);

    float yf0 = _fnlLerp(xf00, xf10, ys);
    float yf1 = _fnlLerp(xf01, xf11, ys);

    return _fnlLerp(yf0, yf1, zs);
  }

  // Domain Warp

  // Forward declare
  static void _fnlSingleDomainWarpBasicGrid2D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xp, FNLfloat *yp);
  static void _fnlSingleDomainWarpBasicGrid3D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xp, FNLfloat *yp, FNLfloat *zp);
  static void _fnlSingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xr, FNLfloat *yr, bool outGradOnly);
  static void _fnlSingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xr, FNLfloat *yr, FNLfloat *zr, bool outGradOnly);

  static inline void _fnlDoSingleDomainWarp2D(fnl_state *state, int seed, float amp, float freq, FNLfloat x, FNLfloat y, FNLfloat *xp, FNLfloat *yp)
  {
    switch (state->domain_warp_type)
    {
    case FNL_DOMAIN_WARP_OPENSIMPLEX2:
      _fnlSingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, xp, yp, false);
      break;
    case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED:
      _fnlSingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, xp, yp, true);
      break;
    case FNL_DOMAIN_WARP_BASICGRID:
      _fnlSingleDomainWarpBasicGrid2D(seed, amp, freq, x, y, xp, yp);
      break;
    }
  }

  static inline void _fnlDoSingleDomainWarp3D(fnl_state *state, int seed, float amp, float freq, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xp, FNLfloat *yp, FNLfloat *zp)
  {
    switch (state->domain_warp_type)
    {
    case FNL_DOMAIN_WARP_OPENSIMPLEX2:
      _fnlSingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, xp, yp, zp, false);
      break;
    case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED:
      _fnlSingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, xp, yp, zp, true);
      break;
    case FNL_DOMAIN_WARP_BASICGRID:
      _fnlSingleDomainWarpBasicGrid3D(seed, amp, freq, x, y, z, xp, yp, zp);
      break;
    }
  }

  // Domain Warp Single Wrapper

  static void _fnlDomainWarpSingle2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
  {
    int seed = state->seed;
    float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state);
    float freq = state->frequency;

    FNLfloat xs = *x;
    FNLfloat ys = *y;
    _fnlTransformDomainWarpCoordinate2D(state, &xs, &ys);

    _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y);
  }

  static void _fnlDomainWarpSingle3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
  {
    int seed = state->seed;
    float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state);
    float freq = state->frequency;

    FNLfloat xs = *x;
    FNLfloat ys = *y;
    FNLfloat zs = *z;
    _fnlTransformDomainWarpCoordinate3D(state, &xs, &ys, &zs);

    _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z);
  }

  // Domain Warp Fractal Progressive

  static void _fnlDomainWarpFractalProgressive2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
  {
    int seed = state->seed;
    float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state);
    float freq = state->frequency;

    for (int i = 0; i < state->octaves; i++)
    {
      FNLfloat xs = *x;
      FNLfloat ys = *y;
      _fnlTransformDomainWarpCoordinate2D(state, &xs, &ys);

      _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y);

      seed++;
      amp *= state->gain;
      freq *= state->lacunarity;
    }
  }

  static void _fnlDomainWarpFractalProgressive3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
  {
    int seed = state->seed;
    float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state);
    float freq = state->frequency;

    for (int i = 0; i < state->octaves; i++)
    {
      FNLfloat xs = *x;
      FNLfloat ys = *y;
      FNLfloat zs = *z;
      _fnlTransformDomainWarpCoordinate3D(state, &xs, &ys, &zs);

      _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z);

      seed++;
      amp *= state->gain;
      freq *= state->lacunarity;
    }
  }

  // Domain Warp Fractal Independent

  static void _fnlDomainWarpFractalIndependent2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
  {
    FNLfloat xs = *x;
    FNLfloat ys = *y;
    _fnlTransformDomainWarpCoordinate2D(state, &xs, &ys);

    int seed = state->seed;
    float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state);
    float freq = state->frequency;

    for (int i = 0; i < state->octaves; i++)
    {
      _fnlDoSingleDomainWarp2D(state, seed, amp, freq, xs, ys, x, y);

      seed++;
      amp *= state->gain;
      freq *= state->lacunarity;
    }
  }

  static void _fnlDomainWarpFractalIndependent3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
  {
    FNLfloat xs = *x;
    FNLfloat ys = *y;
    FNLfloat zs = *z;
    _fnlTransformDomainWarpCoordinate3D(state, &xs, &ys, &zs);

    int seed = state->seed;
    float amp = state->domain_warp_amp * _fnlCalculateFractalBounding(state);
    float freq = state->frequency;

    for (int i = 0; i < state->octaves; i++)
    {
      _fnlDoSingleDomainWarp3D(state, seed, amp, freq, xs, ys, zs, x, y, z);

      seed++;
      amp *= state->gain;
      freq *= state->lacunarity;
    }
  }

  // Domain Warp Basic Grid

  static void _fnlSingleDomainWarpBasicGrid2D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xp, FNLfloat *yp)
  {
    FNLfloat xf = x * frequency;
    FNLfloat yf = y * frequency;

    int x0 = _fnlFastFloor(xf);
    int y0 = _fnlFastFloor(yf);

    float xs = _fnlInterpHermite((float)(xf - x0));
    float ys = _fnlInterpHermite((float)(yf - y0));

    x0 *= PRIME_X;
    y0 *= PRIME_Y;
    int x1 = x0 + PRIME_X;
    int y1 = y0 + PRIME_Y;

    int idx0 = _fnlHash2D(seed, x0, y0) & (255 << 1);
    int idx1 = _fnlHash2D(seed, x1, y0) & (255 << 1);

    float lx0x = _fnlLerp(RAND_VECS_2D[idx0], RAND_VECS_2D[idx1], xs);
    float ly0x = _fnlLerp(RAND_VECS_2D[idx0 | 1], RAND_VECS_2D[idx1 | 1], xs);

    idx0 = _fnlHash2D(seed, x0, y1) & (255 << 1);
    idx1 = _fnlHash2D(seed, x1, y1) & (255 << 1);

    float lx1x = _fnlLerp(RAND_VECS_2D[idx0], RAND_VECS_2D[idx1], xs);
    float ly1x = _fnlLerp(RAND_VECS_2D[idx0 | 1], RAND_VECS_2D[idx1 | 1], xs);

    *xp += _fnlLerp(lx0x, lx1x, ys) * warpAmp;
    *yp += _fnlLerp(ly0x, ly1x, ys) * warpAmp;
  }

  static void _fnlSingleDomainWarpBasicGrid3D(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xp, FNLfloat *yp, FNLfloat *zp)
  {
    FNLfloat xf = x * frequency;
    FNLfloat yf = y * frequency;
    FNLfloat zf = z * frequency;

    int x0 = _fnlFastFloor(xf);
    int y0 = _fnlFastFloor(yf);
    int z0 = _fnlFastFloor(zf);

    float xs = _fnlInterpHermite((float)(xf - x0));
    float ys = _fnlInterpHermite((float)(yf - y0));
    float zs = _fnlInterpHermite((float)(zf - z0));

    x0 *= PRIME_X;
    y0 *= PRIME_Y;
    z0 *= PRIME_Z;
    int x1 = x0 + PRIME_X;
    int y1 = y0 + PRIME_Y;
    int z1 = z0 + PRIME_Z;

    int idx0 = _fnlHash3D(seed, x0, y0, z0) & (255 << 2);
    int idx1 = _fnlHash3D(seed, x1, y0, z0) & (255 << 2);

    float lx0x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs);
    float ly0x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs);
    float lz0x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs);

    idx0 = _fnlHash3D(seed, x0, y1, z0) & (255 << 2);
    idx1 = _fnlHash3D(seed, x1, y1, z0) & (255 << 2);

    float lx1x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs);
    float ly1x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs);
    float lz1x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs);

    float lx0y = _fnlLerp(lx0x, lx1x, ys);
    float ly0y = _fnlLerp(ly0x, ly1x, ys);
    float lz0y = _fnlLerp(lz0x, lz1x, ys);

    idx0 = _fnlHash3D(seed, x0, y0, z1) & (255 << 2);
    idx1 = _fnlHash3D(seed, x1, y0, z1) & (255 << 2);

    lx0x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs);
    ly0x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs);
    lz0x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs);

    idx0 = _fnlHash3D(seed, x0, y1, z1) & (255 << 2);
    idx1 = _fnlHash3D(seed, x1, y1, z1) & (255 << 2);

    lx1x = _fnlLerp(RAND_VECS_3D[idx0], RAND_VECS_3D[idx1], xs);
    ly1x = _fnlLerp(RAND_VECS_3D[idx0 | 1], RAND_VECS_3D[idx1 | 1], xs);
    lz1x = _fnlLerp(RAND_VECS_3D[idx0 | 2], RAND_VECS_3D[idx1 | 2], xs);

    *xp += _fnlLerp(lx0y, _fnlLerp(lx0x, lx1x, ys), zs) * warpAmp;
    *yp += _fnlLerp(ly0y, _fnlLerp(ly0x, ly1x, ys), zs) * warpAmp;
    *zp += _fnlLerp(lz0y, _fnlLerp(lz0x, lz1x, ys), zs) * warpAmp;
  }

  // Domain Warp Simplex/OpenSimplex2

  static void _fnlSingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat *xr, FNLfloat *yr, bool outGradOnly)
  {
    const float SQRT3 = 1.7320508075688772935274463415059f;
    const float G2 = (3 - SQRT3) / 6;

    x *= frequency;
    y *= frequency;

    /*
     * --- Skew moved to TransformNoiseCoordinate method ---
     * const FNLfloat F2 = 0.5f * (SQRT3 - 1);
     * FNLfloat s = (x + y) * F2;
     * x += s; y += s;
     */

    int i = _fnlFastFloor(x);
    int j = _fnlFastFloor(y);
    float xi = (float)(x - i);
    float yi = (float)(y - j);

    float t = (xi + yi) * G2;
    float x0 = (float)(xi - t);
    float y0 = (float)(yi - t);

    i *= PRIME_X;
    j *= PRIME_Y;

    float vx, vy;
    vx = vy = 0;

    float a = 0.5f - x0 * x0 - y0 * y0;
    if (a > 0)
    {
      float aaaa = (a * a) * (a * a);
      float xo, yo;
      if (outGradOnly)
        _fnlGradCoordOut2D(seed, i, j, &xo, &yo);
      else
        _fnlGradCoordDual2D(seed, i, j, x0, y0, &xo, &yo);
      vx += aaaa * xo;
      vy += aaaa * yo;
    }

    float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a);
    if (c > 0)
    {
      float x2 = x0 + (2 * (float)G2 - 1);
      float y2 = y0 + (2 * (float)G2 - 1);
      float cccc = (c * c) * (c * c);
      float xo, yo;
      if (outGradOnly)
        _fnlGradCoordOut2D(seed, i + PRIME_X, j + PRIME_Y, &xo, &yo);
      else
        _fnlGradCoordDual2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2, &xo, &yo);
      vx += cccc * xo;
      vy += cccc * yo;
    }

    if (y0 > x0)
    {
      float x1 = x0 + (float)G2;
      float y1 = y0 + ((float)G2 - 1);
      float b = 0.5f - x1 * x1 - y1 * y1;
      if (b > 0)
      {
        float bbbb = (b * b) * (b * b);
        float xo, yo;
        if (outGradOnly)
          _fnlGradCoordOut2D(seed, i, j + PRIME_Y, &xo, &yo);
        else
          _fnlGradCoordDual2D(seed, i, j + PRIME_Y, x1, y1, &xo, &yo);
        vx += bbbb * xo;
        vy += bbbb * yo;
      }
    }
    else
    {
      float x1 = x0 + ((float)G2 - 1);
      float y1 = y0 + (float)G2;
      float b = 0.5f - x1 * x1 - y1 * y1;
      if (b > 0)
      {
        float bbbb = (b * b) * (b * b);
        float xo, yo;
        if (outGradOnly)
          _fnlGradCoordOut2D(seed, i + PRIME_X, j, &xo, &yo);
        else
          _fnlGradCoordDual2D(seed, i + PRIME_X, j, x1, y1, &xo, &yo);
        vx += bbbb * xo;
        vy += bbbb * yo;
      }
    }

    *xr += vx * warpAmp;
    *yr += vy * warpAmp;
  }

  static void _fnlSingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNLfloat x, FNLfloat y, FNLfloat z, FNLfloat *xr, FNLfloat *yr, FNLfloat *zr, bool outGradOnly)
  {
    x *= frequency;
    y *= frequency;
    z *= frequency;

    /*
     * --- Rotation moved to TransformDomainWarpCoordinate method ---
     * const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
     * FNLfloat r = (x + y + z) * R3; // Rotation, not skew
     * x = r - x; y = r - y; z = r - z;
     */

    int i = _fnlFastRound(x);
    int j = _fnlFastRound(y);
    int k = _fnlFastRound(z);
    float x0 = (float)x - i;
    float y0 = (float)y - j;
    float z0 = (float)z - k;

    int xNSign = (int)(-x0 - 1.0f) | 1;
    int yNSign = (int)(-y0 - 1.0f) | 1;
    int zNSign = (int)(-z0 - 1.0f) | 1;

    float ax0 = xNSign * -x0;
    float ay0 = yNSign * -y0;
    float az0 = zNSign * -z0;

    i *= PRIME_X;
    j *= PRIME_Y;
    k *= PRIME_Z;

    float vx, vy, vz;
    vx = vy = vz = 0;

    float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0);
    for (int l = 0; l < 2; l++)
    {
      if (a > 0)
      {
        float aaaa = (a * a) * (a * a);
        float xo, yo, zo;
        if (outGradOnly)
          _fnlGradCoordOut3D(seed, i, j, k, &xo, &yo, &zo);
        else
          _fnlGradCoordDual3D(seed, i, j, k, x0, y0, z0, &xo, &yo, &zo);
        vx += aaaa * xo;
        vy += aaaa * yo;
        vz += aaaa * zo;
      }

      float b = a + 1;
      int i1 = i;
      int j1 = j;
      int k1 = k;
      float x1 = x0;
      float y1 = y0;
      float z1 = z0;
      if (ax0 >= ay0 && ax0 >= az0)
      {
        x1 += xNSign;
        b -= xNSign * 2 * x1;
        i1 -= xNSign * PRIME_X;
      }
      else if (ay0 > ax0 && ay0 >= az0)
      {
        y1 += yNSign;
        b -= yNSign * 2 * y1;
        j1 -= yNSign * PRIME_Y;
      }
      else
      {
        z1 += zNSign;
        b -= zNSign * 2 * z1;
        k1 -= zNSign * PRIME_Z;
      }

      if (b > 0)
      {
        float bbbb = (b * b) * (b * b);
        float xo, yo, zo;
        if (outGradOnly)
          _fnlGradCoordOut3D(seed, i1, j1, k1, &xo, &yo, &zo);
        else
          _fnlGradCoordDual3D(seed, i1, j1, k1, x1, y1, z1, &xo, &yo, &zo);
        vx += bbbb * xo;
        vy += bbbb * yo;
        vz += bbbb * zo;
      }

      if (l == 1)
        break;

      ax0 = 0.5f - ax0;
      ay0 = 0.5f - ay0;
      az0 = 0.5f - az0;

      x0 = xNSign * ax0;
      y0 = yNSign * ay0;
      z0 = zNSign * az0;

      a += (0.75f - ax0) - (ay0 + az0);

      i += (xNSign >> 1) & PRIME_X;
      j += (yNSign >> 1) & PRIME_Y;
      k += (zNSign >> 1) & PRIME_Z;

      xNSign = -xNSign;
      yNSign = -yNSign;
      zNSign = -zNSign;

      seed += 1293373;
    }

    *xr += vx * warpAmp;
    *yr += vy * warpAmp;
    *zr += vz * warpAmp;
  }

  // ====================
  // Public API
  // ====================

  fnl_state fnlCreateState()
  {
    fnl_state newState;
    newState.seed = 0;
    newState.frequency = 0.01f;
    newState.noise_type = FNL_NOISE_OPENSIMPLEX2;
    newState.rotation_type_3d = FNL_ROTATION_NONE;
    newState.fractal_type = FNL_FRACTAL_NONE;
    newState.octaves = 3;
    newState.lacunarity = 2.0f;
    newState.gain = 0.5f;
    newState.weighted_strength = 0.0f;
    newState.ping_pong_strength = 2.0f;
    newState.cellular_distance_func = FNL_CELLULAR_DISTANCE_EUCLIDEANSQ;
    newState.cellular_return_type = FNL_CELLULAR_RETURN_VALUE_DISTANCE;
    newState.cellular_jitter_mod = 1.0f;
    newState.domain_warp_amp = 30.0f;
    newState.domain_warp_type = FNL_DOMAIN_WARP_OPENSIMPLEX2;
    return newState;
  }

  float fnlGetNoise2D(fnl_state *state, FNLfloat x, FNLfloat y)
  {
    _fnlTransformNoiseCoordinate2D(state, &x, &y);

    switch (state->fractal_type)
    {
    default:
      return _fnlGenNoiseSingle2D(state, state->seed, x, y);
    case FNL_FRACTAL_FBM:
      return _fnlGenFractalFBM2D(state, x, y);
    case FNL_FRACTAL_RIDGED:
      return _fnlGenFractalRidged2D(state, x, y);
    case FNL_FRACTAL_PINGPONG:
      return _fnlGenFractalPingPong2D(state, x, y);
    }
  }

  float fnlGetNoise3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
  {
    _fnlTransformNoiseCoordinate3D(state, &x, &y, &z);

    // Select a noise type
    switch (state->fractal_type)
    {
    default:
      return _fnlGenNoiseSingle3D(state, state->seed, x, y, z);
    case FNL_FRACTAL_FBM:
      return _fnlGenFractalFBM3D(state, x, y, z);
    case FNL_FRACTAL_RIDGED:
      return _fnlGenFractalRidged3D(state, x, y, z);
    case FNL_FRACTAL_PINGPONG:
      return _fnlGenFractalPingPong3D(state, x, y, z);
    }
  }

  void fnlDomainWarp2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
  {
    switch (state->fractal_type)
    {
    default:
      _fnlDomainWarpSingle2D(state, x, y);
      break;
    case FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE:
      _fnlDomainWarpFractalProgressive2D(state, x, y);
      break;
    case FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT:
      _fnlDomainWarpFractalIndependent2D(state, x, y);
      break;
    }
  }

  void fnlDomainWarp3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
  {
    switch (state->fractal_type)
    {
    default:
      _fnlDomainWarpSingle3D(state, x, y, z);
      break;
    case FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE:
      _fnlDomainWarpFractalProgressive3D(state, x, y, z);
      break;
    case FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT:
      _fnlDomainWarpFractalIndependent3D(state, x, y, z);
      break;
    }
  }

#endif // FNL_IMPL

#if defined(__cplusplus)
}
#endif

#endif // FASTNOISELITE_H