/* SimplexNoise1234, Simplex noise with true analytic
 * derivative in 1D to 4D.
 *
 * Author: Stefan Gustavson, 2003-2005
 * Contact: stefan.gustavson@liu.se
 *
 * This code was GPL licensed until February 2011.
 * As the original author of this code, I hereby
 * release it into the public domain.
 * Please feel free to use it for whatever you want.
 * Credit is appreciated where appropriate, and I also
 * appreciate being told where this code finds any use,
 * but you may do as you like.
 */

/*
 * This implementation is "Simplex Noise" as presented by
 * Ken Perlin at a relatively obscure and not often cited course
 * session "Real-Time Shading" at Siggraph 2001 (before real
 * time shading actually took off), under the title "hardware noise".
 * The 3D function is numerically equivalent to his Java reference
 * code available in the PDF course notes, although I re-implemented
 * it from scratch to get more readable code. The 1D, 2D and 4D cases
 * were implemented from scratch by me from Ken Perlin's text.
 *
 * This file has no dependencies on any other file, not even its own
 * header file. The header file is made for use by external code only.
 */

// We don't really need to include this, but play nice and do it anyway.
#include	"simplexnoise1234.h"
#include	"perm.h"

#define FASTFLOOR(x) ( ((int)(x)<=(x)) ? ((int)x) : (((int)x)-1) )

//---------------------------------------------------------------------
// Static data

//---------------------------------------------------------------------

  // A lookup table to traverse the simplex around a given point in 4D.
  // Details can be found where this table is used, in the 4D noise method.
  /* TODO: This should not be required, backport it from Bill's GLSL code! */
  static unsigned char simplex[64][4] = {
    {0,1,2,3},{0,1,3,2},{0,0,0,0},{0,2,3,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,2,3,0},
    {0,2,1,3},{0,0,0,0},{0,3,1,2},{0,3,2,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,3,2,0},
    {0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},
    {1,2,0,3},{0,0,0,0},{1,3,0,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,3,0,1},{2,3,1,0},
    {1,0,2,3},{1,0,3,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,0,3,1},{0,0,0,0},{2,1,3,0},
    {0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},
    {2,0,1,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,0,1,2},{3,0,2,1},{0,0,0,0},{3,1,2,0},
    {2,1,0,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,1,0,2},{0,0,0,0},{3,2,0,1},{3,2,1,0}};

// 1D simplex noise
float snoise1(float x) {

  int i0 = FASTFLOOR(x);
  int i1 = i0 + 1;
  float x0 = x - i0;
  float x1 = x0 - 1.0f;

  float n0, n1;

  float t0 = 1.0f - x0*x0;
//  if(t0 < 0.0f) t0 = 0.0f; // this never happens for the 1D case
  t0 *= t0;
  n0 = t0 * t0 * grad1(perm[i0 & 0xff], x0);

  float t1 = 1.0f - x1*x1;
//  if(t1 < 0.0f) t1 = 0.0f; // this never happens for the 1D case
  t1 *= t1;
  n1 = t1 * t1 * grad1(perm[i1 & 0xff], x1);
  // The maximum value of this noise is 8*(3/4)^4 = 2.53125
  // A factor of 0.395 would scale to fit exactly within [-1,1], but
  // we want to match PRMan's 1D noise, so we scale it down some more.
  return 0.25f * (n0 + n1);

}

// 2D simplex noise
float snoise2(float x, float y) {

#define F2 0.366025403 // F2 = 0.5*(sqrt(3.0)-1.0)
#define G2 0.211324865 // G2 = (3.0-Math.sqrt(3.0))/6.0

    float n0, n1, n2; // Noise contributions from the three corners

    // Skew the input space to determine which simplex cell we're in
    float s = (x+y)*F2; // Hairy factor for 2D
    float xs = x + s;
    float ys = y + s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);

    float t = (float)(i+j)*G2;
    float X0 = i-t; // Unskew the cell origin back to (x,y) space
    float Y0 = j-t;
    float x0 = x-X0; // The x,y distances from the cell origin
    float y0 = y-Y0;

    // For the 2D case, the simplex shape is an equilateral triangle.
    // Determine which simplex we are in.
    int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
    if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
    else {i1=0; j1=1;}      // upper triangle, YX order: (0,0)->(0,1)->(1,1)

    // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
    // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
    // c = (3-sqrt(3))/6

    float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
    float y1 = y0 - j1 + G2;
    float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
    float y2 = y0 - 1.0f + 2.0f * G2;

    // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
    int ii = i & 0xff;
    int jj = j & 0xff;

    // Calculate the contribution from the three corners
    float t0 = 0.5f - x0*x0-y0*y0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad2(perm[ii+perm[jj]], x0, y0); 
    }

    float t1 = 0.5f - x1*x1-y1*y1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad2(perm[ii+i1+perm[jj+j1]], x1, y1);
    }

    float t2 = 0.5f - x2*x2-y2*y2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad2(perm[ii+1+perm[jj+1]], x2, y2);
    }

    // Add contributions from each corner to get the final noise value.
    // The result is scaled to return values in the interval [-1,1].
    return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
  }

// 3D simplex noise
float snoise3(float x, float y, float z) {

// Simple skewing factors for the 3D case
#define F3 0.333333333
#define G3 0.166666667

    float n0, n1, n2, n3; // Noise contributions from the four corners

    // Skew the input space to determine which simplex cell we're in
    float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
    float xs = x+s;
    float ys = y+s;
    float zs = z+s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);
    int k = FASTFLOOR(zs);

    float t = (float)(i+j+k)*G3; 
    float X0 = i-t; // Unskew the cell origin back to (x,y,z) space
    float Y0 = j-t;
    float Z0 = k-t;
    float x0 = x-X0; // The x,y,z distances from the cell origin
    float y0 = y-Y0;
    float z0 = z-Z0;

    // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
    // Determine which simplex we are in.
    int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
    int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords

/* This code would benefit from a backport from the GLSL version! */
    if(x0>=y0) {
      if(y0>=z0)
        { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order
        else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order
        else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order
      }
    else { // x0<y0
      if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order
      else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order
      else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order
    }

    // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
    // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
    // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
    // c = 1/6.

    float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
    float y1 = y0 - j1 + G3;
    float z1 = z0 - k1 + G3;
    float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords
    float y2 = y0 - j2 + 2.0f*G3;
    float z2 = z0 - k2 + 2.0f*G3;
    float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords
    float y3 = y0 - 1.0f + 3.0f*G3;
    float z3 = z0 - 1.0f + 3.0f*G3;

    // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
    int ii = i & 0xff;
    int jj = j & 0xff;
    int kk = k & 0xff;

    // Calculate the contribution from the four corners
    float t0 = 0.5f - x0*x0 - y0*y0 - z0*z0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad3(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
    }

    float t1 = 0.5f - x1*x1 - y1*y1 - z1*z1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad3(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
    }

    float t2 = 0.5f - x2*x2 - y2*y2 - z2*z2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad3(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
    }

    float t3 = 0.5f - x3*x3 - y3*y3 - z3*z3;
    if(t3<0.0f) n3 = 0.0f;
    else {
      t3 *= t3;
      n3 = t3 * t3 * grad3(perm[ii+1+perm[jj+1+perm[kk+1]]], x3, y3, z3);
    }

    // Add contributions from each corner to get the final noise value.
    // The result is scaled to stay just inside [-1,1]
    return 72.0f * (n0 + n1 + n2 + n3);
  }


// 4D simplex noise
float snoise4(float x, float y, float z, float w) {
  
  // The skewing and unskewing factors are hairy again for the 4D case
#define F4 0.309016994 // F4 = (Math.sqrt(5.0)-1.0)/4.0
#define G4 0.138196601 // G4 = (5.0-Math.sqrt(5.0))/20.0

    float n0, n1, n2, n3, n4; // Noise contributions from the five corners

    // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
    float s = (x + y + z + w) * F4; // Factor for 4D skewing
    float xs = x + s;
    float ys = y + s;
    float zs = z + s;
    float ws = w + s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);
    int k = FASTFLOOR(zs);
    int l = FASTFLOOR(ws);

    float t = (i + j + k + l) * G4; // Factor for 4D unskewing
    float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
    float Y0 = j - t;
    float Z0 = k - t;
    float W0 = l - t;

    float x0 = x - X0;  // The x,y,z,w distances from the cell origin
    float y0 = y - Y0;
    float z0 = z - Z0;
    float w0 = w - W0;

    // For the 4D case, the simplex is a 4D shape I won't even try to describe.
    // To find out which of the 24 possible simplices we're in, we need to
    // determine the magnitude ordering of x0, y0, z0 and w0.
    // The method below is a good way of finding the ordering of x,y,z,w and
    // then find the correct traversal order for the simplex were in.
    // First, six pair-wise comparisons are performed between each possible pair
    // of the four coordinates, and the results are used to add up binary bits
    // for an integer index.
    int c1 = (x0 > y0) ? 32 : 0;
    int c2 = (x0 > z0) ? 16 : 0;
    int c3 = (y0 > z0) ? 8 : 0;
    int c4 = (x0 > w0) ? 4 : 0;
    int c5 = (y0 > w0) ? 2 : 0;
    int c6 = (z0 > w0) ? 1 : 0;
    int c = c1 + c2 + c3 + c4 + c5 + c6;

    int i1, j1, k1, l1; // The integer offsets for the second simplex corner
    int i2, j2, k2, l2; // The integer offsets for the third simplex corner
    int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner

    // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
    // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
    // impossible. Only the 24 indices which have non-zero entries make any sense.
    // We use a thresholding to set the coordinates in turn from the largest magnitude.
    // The number 3 in the "simplex" array is at the position of the largest coordinate.
    i1 = simplex[c][0]>=3 ? 1 : 0;
    j1 = simplex[c][1]>=3 ? 1 : 0;
    k1 = simplex[c][2]>=3 ? 1 : 0;
    l1 = simplex[c][3]>=3 ? 1 : 0;
    // The number 2 in the "simplex" array is at the second largest coordinate.
    i2 = simplex[c][0]>=2 ? 1 : 0;
    j2 = simplex[c][1]>=2 ? 1 : 0;
    k2 = simplex[c][2]>=2 ? 1 : 0;
    l2 = simplex[c][3]>=2 ? 1 : 0;
    // The number 1 in the "simplex" array is at the second smallest coordinate.
    i3 = simplex[c][0]>=1 ? 1 : 0;
    j3 = simplex[c][1]>=1 ? 1 : 0;
    k3 = simplex[c][2]>=1 ? 1 : 0;
    l3 = simplex[c][3]>=1 ? 1 : 0;
    // The fifth corner has all coordinate offsets = 1, so no need to look that up.

    float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
    float y1 = y0 - j1 + G4;
    float z1 = z0 - k1 + G4;
    float w1 = w0 - l1 + G4;
    float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords
    float y2 = y0 - j2 + 2.0f*G4;
    float z2 = z0 - k2 + 2.0f*G4;
    float w2 = w0 - l2 + 2.0f*G4;
    float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords
    float y3 = y0 - j3 + 3.0f*G4;
    float z3 = z0 - k3 + 3.0f*G4;
    float w3 = w0 - l3 + 3.0f*G4;
    float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords
    float y4 = y0 - 1.0f + 4.0f*G4;
    float z4 = z0 - 1.0f + 4.0f*G4;
    float w4 = w0 - 1.0f + 4.0f*G4;

    // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
    int ii = i & 0xff;
    int jj = j & 0xff;
    int kk = k & 0xff;
    int ll = l & 0xff;

    // Calculate the contribution from the five corners
    float t0 = 0.5f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
    }

   float t1 = 0.5f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
    }

   float t2 = 0.5f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
    }

   float t3 = 0.5f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
    if(t3 < 0.0f) n3 = 0.0f;
    else {
      t3 *= t3;
      n3 = t3 * t3 * grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
    }

   float t4 = 0.5f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
    if(t4 < 0.0f) n4 = 0.0f;
    else {
      t4 *= t4;
      n4 = t4 * t4 * grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4);
    }

    // Sum up and scale the result to cover the range [-1,1]
    return 62.0f * (n0 + n1 + n2 + n3 + n4);
  }
//---------------------------------------------------------------------
