package SimplexNoise;
# see __END__ for credits
use strict;
use warnings;

my @grad3 = (
[1, 1, 0], [-1, 1, 0], [1, -1, 0], [-1, -1, 0], 
[1, 0, 1], [-1, 0, 1], [1, 0, -1], [-1, 0, -1], 
[0, 1, 1], [0, -1, 1], [0, 1, -1], [0, -1, -1], 
);

my @grad4 = (
[0, 1, 1, 1],  [0, 1, 1, -1],  [0, 1, -1, 1],  [0, 1, -1, -1], 
[0, -1, 1, 1], [0, -1, 1, -1], [0, -1, -1, 1], [0, -1, -1, -1], 
[1, 0, 1, 1],  [1, 0, 1, -1],  [1, 0, -1, 1],  [1, 0, -1, -1], 
[-1, 0, 1, 1], [-1, 0, 1, -1], [-1, 0, -1, 1], [-1, 0, -1, -1], 
[1, 1, 0, 1],  [1, 1, 0, -1],  [1, -1, 0, 1],  [1, -1, 0, -1], 
[-1, 1, 0, 1], [-1, 1, 0, -1], [-1, -1, 0, 1], [-1, -1, 0, -1], 
[1, 1, 1, 0],  [1, 1, -1, 0],  [1, -1, 1, 0],  [1, -1, -1, 0], 
[-1, 1, 1, 0], [-1, 1, -1, 0], [-1, -1, 1, 0], [-1, -1, -1, 0], 
);

use constant p => qw(151 160 137 91 90 15 131 13 201 95 96 53 194 233 7 225
140 36 103 30 69 142 8 99 37 240 21 10 23 190 6 148 247 120 234 75 0 26 197 62
94 252 219 203 117 35 11 32 57 177 33 88 237 149 56 87 174 20 125 136 171 168
68 175 74 165 71 134 139 48 27 166 77 146 158 231 83 111 229 122 60 211 133 230
220 105 92 41 55 46 245 40 244 102 143 54 65 25 63 161 1 216 80 73 209 76 132
187 208 89 18 169 200 196 135 130 116 188 159 86 164 100 109 198 173 186 3 64
52 217 226 250 124 123 5 202 38 147 118 126 255 82 85 212 207 206 59 227 47 16
58 17 182 189 28 42 223 183 170 213 119 248 152 2 44 154 163 70 221 153 101 155
167 43 172 9 129 22 39 253 19 98 108 110 79 113 224 232 178 185 112 104 218 246
97 228 251 34 242 193 238 210 144 12 191 179 162 241 81 51 145 235 249 14 239
107 49 192 214 31 181 199 106 157 184 84 204 176 115 121 50 45 127 4 150 254
138 236 205 93 222 114 67 29 24 72 243 141 128 195 78 66 215 61 156 180);

use constant perm => (p, p);
use constant permMod12 => map { $_ % 12 } perm;

# Skewing and unskewing factors for 2, 3, and 4 dimensions
use constant {
    F2 => 0.5 * (sqrt(3.0) - 1.0),
    G2 => (3.0 - sqrt(3.0)) / 6.0,
    F3 => 1.0 / 3.0,
    G3 => 1.0 / 6.0,
    F4 => (sqrt(5.0) - 1.0) / 4.0,
    G4 => (5.0 - sqrt(5.0)) / 20.0,
};

sub floor {
    my $x = shift;
    my $xi = int($x);
    return $x < $xi ? $xi - 1 : $xi;
}

sub dot {
    my @grad = @{shift()};
    my $sum = 0;
    $sum += $_ * shift @grad for @_;
    $sum;
}

sub noise {
    if (@_ == 2) {
	# 2D noise
	my ($n0, $n1, $n2);
	my ($xin, $yin) = @_;
	my $s = ($xin + $yin) * F2;
	my ($i, $j) = map { floor($_) } $xin + $s, $yin + $s;
	my $t = ($i + $j) * G2;
	my ($X0, $Y0) = ($i - $t, $j - $t);
	my ($x0, $y0) = ($xin - $X0, $yin - $Y0);
	my ($i1, $j1) = $x0 > $y0 ? (1, 0) : (0, 1);
	my ($x1, $y1) = ($x0 - $i1 + G2, $y0 - $j1 + G2);
	my ($x2, $y2) = ($x0 - 1 + 2 * G2, $y0 - 1 + 2 * G2);
	my ($ii, $jj) = ($i & 255, $j & 255);
	my ($gi0, $gi1, $gi2) = (permMod12)[
	$ii + (perm)[$jj],
	$ii + $i1 + (perm)[$jj + $j1],
	$ii + 1 + (perm)[$jj + 1]
	];
	my $t0 = 0.5 - $x0 * $x0 - $y0 * $y0;
	if ($t0 < 0) { $n0 = 0 }
	else {
	    $t0 *= $t0;
	    $n0 = $t0 * $t0 * dot($grad3[$gi0], $x0, $y0);
	}
	my $t1 = 0.5 - $x1 * $x1 - $y1 * $y1;
	if ($t1 < 0) { $n1 = 0 }
	else {
	    $t1 *= $t1;
	    $n1 = $t1 * $t1 * dot($grad3[$gi1], $x1, $y1);
	}
	my $t2 = 0.5 - $x2 * $x2 - $y2 * $y2;
	if ($t2 < 0) { $n2 = 0 }
	else {
	    $t2 *= $t2;
	    $n2 = $t2 * $t2 * dot($grad3[$gi2], $x2, $y2);
	}
	return 70 * ($n0 + $n1 + $n2);
    } elsif (@_ == 3) {
	# 3D noise
	...
    } elsif (@_ == 4) {
	# 4D noise
	...
    } else {...}
}

my $N = 256;

print "P2\n";
print "$N $N\n";
print "255\n";
for my $i (1 .. $N) {
    my $x = $i / 10;
    for my $j (1 .. $N) {
	my $y = $j / 10;
	my $noise =  noise $x, $y;
	print int(($noise + 1) / 2 * 256);
	print $j == $N ? "\n" : ' ';
    }
}

__END__

=pod
=begin java
    /*
     * A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
     *
     * Based on example code by Stefan Gustavson (stegu@itn.liu.se).
     * Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
     * Better rank ordering method by Stefan Gustavson in 2012.
     *
     * This could be speeded up even further, but it's useful as it is.
     *
     * Version 2012-03-09
     *
     * This code was placed in the public domain by its original author,
     * Stefan Gustavson. You may use it as you see fit, but
     * attribution is appreciated.
     *
     */

    public class SimplexNoise {  // Simplex noise in 2D, 3D and 4D
      private static Grad grad3[] = {new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
				     new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1),
				     new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)};

      private static Grad grad4[]= {new Grad(0,1,1,1),new Grad(0,1,1,-1),new Grad(0,1,-1,1),new Grad(0,1,-1,-1),
		       new Grad(0,-1,1,1),new Grad(0,-1,1,-1),new Grad(0,-1,-1,1),new Grad(0,-1,-1,-1),
		       new Grad(1,0,1,1),new Grad(1,0,1,-1),new Grad(1,0,-1,1),new Grad(1,0,-1,-1),
		       new Grad(-1,0,1,1),new Grad(-1,0,1,-1),new Grad(-1,0,-1,1),new Grad(-1,0,-1,-1),
		       new Grad(1,1,0,1),new Grad(1,1,0,-1),new Grad(1,-1,0,1),new Grad(1,-1,0,-1),
		       new Grad(-1,1,0,1),new Grad(-1,1,0,-1),new Grad(-1,-1,0,1),new Grad(-1,-1,0,-1),
		       new Grad(1,1,1,0),new Grad(1,1,-1,0),new Grad(1,-1,1,0),new Grad(1,-1,-1,0),
		       new Grad(-1,1,1,0),new Grad(-1,1,-1,0),new Grad(-1,-1,1,0),new Grad(-1,-1,-1,0)};

      private static short p[] = {151,160,137,91,90,15,
      131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
      190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
      88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
      77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
      102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
      135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
      5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
      223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
      129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
      251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
      49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
      138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180};
      // To remove the need for index wrapping, double the permutation table length
      private static short perm[] = new short[512];
      private static short permMod12[] = new short[512];
      static {
	for(int i=0; i<512; i++)
	{
	  perm[i]=p[i & 255];
	  permMod12[i] = (short)(perm[i] % 12);
	}
      }

      // Skewing and unskewing factors for 2, 3, and 4 dimensions
      private static final double F2 = 0.5*(Math.sqrt(3.0)-1.0);
      private static final double G2 = (3.0-Math.sqrt(3.0))/6.0;
      private static final double F3 = 1.0/3.0;
      private static final double G3 = 1.0/6.0;
      private static final double F4 = (Math.sqrt(5.0)-1.0)/4.0;
      private static final double G4 = (5.0-Math.sqrt(5.0))/20.0;

      // This method is a *lot* faster than using (int)Math.floor(x)
      private static int fastfloor(double x) {
	int xi = (int)x;
	return x<xi ? xi-1 : xi;
      }

      private static double dot(Grad g, double x, double y) {
	return g.x*x + g.y*y; }

      private static double dot(Grad g, double x, double y, double z) {
	return g.x*x + g.y*y + g.z*z; }

      private static double dot(Grad g, double x, double y, double z, double w) {
	return g.x*x + g.y*y + g.z*z + g.w*w; }


      // 2D simplex noise
      public static double noise(double xin, double yin) {
	double n0, n1, n2; // Noise contributions from the three corners
	// Skew the input space to determine which simplex cell we're in
	double s = (xin+yin)*F2; // Hairy factor for 2D
	int i = fastfloor(xin+s);
	int j = fastfloor(yin+s);
	double t = (i+j)*G2;
	double X0 = i-t; // Unskew the cell origin back to (x,y) space
	double Y0 = j-t;
	double x0 = xin-X0; // The x,y distances from the cell origin
	double y0 = yin-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
	double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
	double y1 = y0 - j1 + G2;
	double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
	double y2 = y0 - 1.0 + 2.0 * G2;
	// Work out the hashed gradient indices of the three simplex corners
	int ii = i & 255;
	int jj = j & 255;
	int gi0 = permMod12[ii+perm[jj]];
	int gi1 = permMod12[ii+i1+perm[jj+j1]];
	int gi2 = permMod12[ii+1+perm[jj+1]];
	// Calculate the contribution from the three corners
	double t0 = 0.5 - x0*x0-y0*y0;
	if(t0<0) n0 = 0.0;
	else {
	  t0 *= t0;
	  n0 = t0 * t0 * dot(grad3[gi0], x0, y0);  // (x,y) of grad3 used for 2D gradient
	}
	double t1 = 0.5 - x1*x1-y1*y1;
	if(t1<0) n1 = 0.0;
	else {
	  t1 *= t1;
	  n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
	}
	double t2 = 0.5 - x2*x2-y2*y2;
	if(t2<0) n2 = 0.0;
	else {
	  t2 *= t2;
	  n2 = t2 * t2 * dot(grad3[gi2], 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 70.0 * (n0 + n1 + n2);
      }


      // 3D simplex noise
      public static double noise(double xin, double yin, double zin) {
	double n0, n1, n2, n3; // Noise contributions from the four corners
	// Skew the input space to determine which simplex cell we're in
	double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
	int i = fastfloor(xin+s);
	int j = fastfloor(yin+s);
	int k = fastfloor(zin+s);
	double t = (i+j+k)*G3;
	double X0 = i-t; // Unskew the cell origin back to (x,y,z) space
	double Y0 = j-t;
	double Z0 = k-t;
	double x0 = xin-X0; // The x,y,z distances from the cell origin
	double y0 = yin-Y0;
	double z0 = zin-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
	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.
	double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
	double y1 = y0 - j1 + G3;
	double z1 = z0 - k1 + G3;
	double x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords
	double y2 = y0 - j2 + 2.0*G3;
	double z2 = z0 - k2 + 2.0*G3;
	double x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords
	double y3 = y0 - 1.0 + 3.0*G3;
	double z3 = z0 - 1.0 + 3.0*G3;
	// Work out the hashed gradient indices of the four simplex corners
	int ii = i & 255;
	int jj = j & 255;
	int kk = k & 255;
	int gi0 = permMod12[ii+perm[jj+perm[kk]]];
	int gi1 = permMod12[ii+i1+perm[jj+j1+perm[kk+k1]]];
	int gi2 = permMod12[ii+i2+perm[jj+j2+perm[kk+k2]]];
	int gi3 = permMod12[ii+1+perm[jj+1+perm[kk+1]]];
	// Calculate the contribution from the four corners
	double t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
	if(t0<0) n0 = 0.0;
	else {
	  t0 *= t0;
	  n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
	}
	double t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
	if(t1<0) n1 = 0.0;
	else {
	  t1 *= t1;
	  n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
	}
	double t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
	if(t2<0) n2 = 0.0;
	else {
	  t2 *= t2;
	  n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
	}
	double t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
	if(t3<0) n3 = 0.0;
	else {
	  t3 *= t3;
	  n3 = t3 * t3 * dot(grad3[gi3], 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 32.0*(n0 + n1 + n2 + n3);
      }


      // 4D simplex noise, better simplex rank ordering method 2012-03-09
      public static double noise(double x, double y, double z, double w) {

	double 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
	double s = (x + y + z + w) * F4; // Factor for 4D skewing
	int i = fastfloor(x + s);
	int j = fastfloor(y + s);
	int k = fastfloor(z + s);
	int l = fastfloor(w + s);
	double t = (i + j + k + l) * G4; // Factor for 4D unskewing
	double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
	double Y0 = j - t;
	double Z0 = k - t;
	double W0 = l - t;
	double x0 = x - X0;  // The x,y,z,w distances from the cell origin
	double y0 = y - Y0;
	double z0 = z - Z0;
	double 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.
	// Six pair-wise comparisons are performed between each possible pair
	// of the four coordinates, and the results are used to rank the numbers.
	int rankx = 0;
	int ranky = 0;
	int rankz = 0;
	int rankw = 0;
	if(x0 > y0) rankx++; else ranky++;
	if(x0 > z0) rankx++; else rankz++;
	if(x0 > w0) rankx++; else rankw++;
	if(y0 > z0) ranky++; else rankz++;
	if(y0 > w0) ranky++; else rankw++;
	if(z0 > w0) rankz++; else rankw++;
	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.
	// Rank 3 denotes the largest coordinate.
	i1 = rankx >= 3 ? 1 : 0;
	j1 = ranky >= 3 ? 1 : 0;
	k1 = rankz >= 3 ? 1 : 0;
	l1 = rankw >= 3 ? 1 : 0;
	// Rank 2 denotes the second largest coordinate.
	i2 = rankx >= 2 ? 1 : 0;
	j2 = ranky >= 2 ? 1 : 0;
	k2 = rankz >= 2 ? 1 : 0;
	l2 = rankw >= 2 ? 1 : 0;
	// Rank 1 denotes the second smallest coordinate.
	i3 = rankx >= 1 ? 1 : 0;
	j3 = ranky >= 1 ? 1 : 0;
	k3 = rankz >= 1 ? 1 : 0;
	l3 = rankw >= 1 ? 1 : 0;
	// The fifth corner has all coordinate offsets = 1, so no need to compute that.
	double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
	double y1 = y0 - j1 + G4;
	double z1 = z0 - k1 + G4;
	double w1 = w0 - l1 + G4;
	double x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
	double y2 = y0 - j2 + 2.0*G4;
	double z2 = z0 - k2 + 2.0*G4;
	double w2 = w0 - l2 + 2.0*G4;
	double x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
	double y3 = y0 - j3 + 3.0*G4;
	double z3 = z0 - k3 + 3.0*G4;
	double w3 = w0 - l3 + 3.0*G4;
	double x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
	double y4 = y0 - 1.0 + 4.0*G4;
	double z4 = z0 - 1.0 + 4.0*G4;
	double w4 = w0 - 1.0 + 4.0*G4;
	// Work out the hashed gradient indices of the five simplex corners
	int ii = i & 255;
	int jj = j & 255;
	int kk = k & 255;
	int ll = l & 255;
	int gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
	int gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
	int gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
	int gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
	int gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32;
	// Calculate the contribution from the five corners
	double t0 = 0.6 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
	if(t0<0) n0 = 0.0;
	else {
	  t0 *= t0;
	  n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
	}
       double t1 = 0.6 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
	if(t1<0) n1 = 0.0;
	else {
	  t1 *= t1;
	  n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
	}
       double t2 = 0.6 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
	if(t2<0) n2 = 0.0;
	else {
	  t2 *= t2;
	  n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
	}
       double t3 = 0.6 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
	if(t3<0) n3 = 0.0;
	else {
	  t3 *= t3;
	  n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
	}
       double t4 = 0.6 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
	if(t4<0) n4 = 0.0;
	else {
	  t4 *= t4;
	  n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
	}
	// Sum up and scale the result to cover the range [-1,1]
	return 27.0 * (n0 + n1 + n2 + n3 + n4);
      }

      // Inner class to speed upp gradient computations
      // (array access is a lot slower than member access)
      private static class Grad
      {
	double x, y, z, w;

	Grad(double x, double y, double z)
	{
	  this.x = x;
	  this.y = y;
	  this.z = z;
	}

	Grad(double x, double y, double z, double w)
	{
	  this.x = x;
	  this.y = y;
	  this.z = z;
	  this.w = w;
	}
      }
    }
=end java

=cut