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[orx-triangulation] Add smoothScatter

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This commit is contained in:
Edwin Jakobs
2022-10-28 08:52:36 +02:00
parent 0a77411406
commit 0a7b4b7add
8 changed files with 283 additions and 112 deletions
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132
orx-triangulation/src/commonMain/kotlin/DoubleDouble.kt
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@@ -17,8 +17,8 @@ import kotlin.math.pow
* See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
*/
internal fun fastTwoDiff(a: Double, b: Double): DoubleArray {
val x = a - b;
val y = (a - x) - b;
val x = a - b
val y = (a - x) - b
return doubleArrayOf(y, x)
}
@@ -60,11 +60,11 @@ internal fun reduceSignificand(
bits: Int
): Double {
val s = 53 - bits;
val f = 2.0.pow(s) + 1;
val s = 53 - bits
val f = 2.0.pow(s) + 1
val c = f * a;
val r = c - (c - a);
val c = f * a
val r = c - (c - a)
return r;
}
@@ -74,7 +74,7 @@ internal fun reduceSignificand(
* === 2^Math.ceil(p/2) + 1 where p is the # of significand bits in a double === 53.
* @internal
*/
private const val f = 134217729; // 2**27 + 1;
private const val f = 134217729 // 2**27 + 1;
/**
@@ -90,9 +90,9 @@ private const val f = 134217729; // 2**27 + 1;
* @param a A double floating point number
*/
private fun split(a: Double): DoubleArray {
val c = f * a;
val a_h = c - (c - a);
val a_l = a - a_h;
val c = f * a
val a_h = c - (c - a)
val a_l = a - a_h
return doubleArrayOf(a_h, a_l)
}
@@ -104,9 +104,9 @@ private fun split(a: Double): DoubleArray {
* @param b subtrahend - a double-double precision floating point number
*/
internal fun twoDiff(a: Double, b: Double): DoubleArray {
val x = a - b;
val bvirt = a - x;
val y = (a - (x + bvirt)) + (bvirt - b);
val x = a - b
val bvirt = a - x
val y = (a - (x + bvirt)) + (bvirt - b)
return doubleArrayOf(y, x)
}
@@ -130,15 +130,15 @@ internal fun twoProduct(a: Double, b: Double): DoubleArray {
val x = a * b;
//const [ah, al] = split(a);
val c = f * a;
val ah = c - (c - a);
val al = a - ah;
val c = f * a
val ah = c - (c - a)
val al = a - ah
//const [bh, bl] = split(b);
val d = f * b;
val bh = d - (d - b);
val bl = b - bh;
val d = f * b
val bh = d - (d - b)
val bl = b - bh
val y = (al * bl) - ((x - (ah * bh)) - (al * bh) - (ah * bl));
val y = (al * bl) - ((x - (ah * bh)) - (al * bh) - (ah * bl))
//const err1 = x - (ah * bh);
//const err2 = err1 - (al * bh);
@@ -149,14 +149,14 @@ internal fun twoProduct(a: Double, b: Double): DoubleArray {
}
internal fun twoSquare(a: Double): DoubleArray {
val x = a * a;
val x = a * a
//const [ah, al] = split(a);
val c = f * a;
val ah = c - (c - a);
val al = a - ah;
val c = f * a
val ah = c - (c - a)
val al = a - ah
val y = (al * al) - ((x - (ah * ah)) - 2 * (ah * al));
val y = (al * al) - ((x - (ah * ah)) - 2 * (ah * al))
return doubleArrayOf(y, x)
}
@@ -174,8 +174,8 @@ internal fun twoSquare(a: Double): DoubleArray {
* See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
*/
internal fun twoSum(a: Double, b: Double): DoubleArray {
val x = a + b;
val bv = x - a;
val x = a + b
val bv = x - a
return doubleArrayOf((a - (x - bv)) + (b - bv), x)
}
@@ -194,21 +194,21 @@ internal fun twoSum(a: Double, b: Double): DoubleArray {
* @param y another double-double precision floating point number
*/
internal fun ddDiffDd(x: DoubleArray, y: DoubleArray): DoubleArray {
val xl = x[0];
val xh = x[1];
val yl = y[0];
val yh = y[1];
val xl = x[0]
val xh = x[1]
val yl = y[0]
val yh = y[1]
//const [sl,sh] = twoSum(xh,yh);
val sh = xh - yh; val _1 = sh - xh; val sl = (xh - (sh - _1)) + (-yh - _1);
val sh = xh - yh; val _1 = sh - xh; val sl = (xh - (sh - _1)) + (-yh - _1)
//const [tl,th] = twoSum(xl,yl);
val th = xl - yl; val _2 = th - xl; val tl = (xl - (th - _2)) + (-yl - _2);
val c = sl + th;
val th = xl - yl; val _2 = th - xl; val tl = (xl - (th - _2)) + (-yl - _2)
val c = sl + th
//const [vl,vh] = fastTwoSum(sh,c)
val vh = sh + c; val vl = c - (vh - sh);
val vh = sh + c; val vl = c - (vh - sh)
val w = tl + vl
//const [zl,zh] = fastTwoSum(vh,w)
val zh = vh + w; val zl = w - (zh - vh);
val zh = vh + w; val zl = w - (zh - vh)
return doubleArrayOf(zl, zh)
}
@@ -229,19 +229,19 @@ internal fun ddMultDd(x: DoubleArray, y: DoubleArray): DoubleArray {
//const xl = x[0];
val xh = x[1];
val xh = x[1]
//const yl = y[0];
val yh = y[1];
val yh = y[1]
//const [cl1,ch] = twoProduct(xh,yh);
val ch = xh*yh;
val c = f * xh; val ah = c - (c - xh); val al = xh - ah;
val d = f * yh; val bh = d - (d - yh); val bl = yh - bh;
val cl1 = (al*bl) - ((ch - (ah*bh)) - (al*bh) - (ah*bl));
val ch = xh*yh
val c = f * xh; val ah = c - (c - xh); val al = xh - ah
val d = f * yh; val bh = d - (d - yh); val bl = yh - bh
val cl1 = (al*bl) - ((ch - (ah*bh)) - (al*bh) - (ah*bl))
//return fastTwoSum(ch,cl1 + (xh*yl + xl*yh));
val b = cl1 + (xh*y[0] + x[0]*yh);
val xx = ch + b;
val b = cl1 + (xh*y[0] + x[0]*yh)
val xx = ch + b
return doubleArrayOf(b - (xx - ch), xx)
}
@@ -261,21 +261,21 @@ internal fun ddMultDd(x: DoubleArray, y: DoubleArray): DoubleArray {
* @param y another double-double precision floating point number
*/
internal fun ddAddDd(x: DoubleArray, y: DoubleArray): DoubleArray {
val xl = x[0];
val xh = x[1];
val yl = y[0];
val yh = y[1];
val xl = x[0]
val xh = x[1]
val yl = y[0]
val yh = y[1]
//const [sl,sh] = twoSum(xh,yh);
val sh = xh + yh; val _1 = sh - xh; val sl = (xh - (sh - _1)) + (yh - _1);
val sh = xh + yh; val _1 = sh - xh; val sl = (xh - (sh - _1)) + (yh - _1)
//val [tl,th] = twoSum(xl,yl);
val th = xl + yl; val _2 = th - xl; val tl = (xl - (th - _2)) + (yl - _2);
val c = sl + th;
val th = xl + yl; val _2 = th - xl; val tl = (xl - (th - _2)) + (yl - _2)
val c = sl + th
//val [vl,vh] = fastTwoSum(sh,c)
val vh = sh + c; val vl = c - (vh - sh);
val vh = sh + c; val vl = c - (vh - sh)
val w = tl + vl
//val [zl,zh] = fastTwoSum(vh,w)
val zh = vh + w; val zl = w - (zh - vh);
val zh = vh + w; val zl = w - (zh - vh)
return doubleArrayOf(zl, zh)
}
@@ -297,24 +297,24 @@ internal fun ddAddDd(x: DoubleArray, y: DoubleArray): DoubleArray {
* @param x a double-double precision floating point number
*/
internal fun ddMultDouble1(y: Double, x: DoubleArray): DoubleArray {
val xl = x[0];
val xh = x[1];
val xl = x[0]
val xh = x[1]
//val [cl1,ch] = twoProduct(xh,y);
val ch = xh*y;
val c = f * xh; val ah = c - (c - xh); val al = xh - ah;
val d = f * y; val bh = d - (d - y); val bl = y - bh;
val cl1 = (al*bl) - ((ch - (ah*bh)) - (al*bh) - (ah*bl));
val ch = xh*y
val c = f * xh; val ah = c - (c - xh); val al = xh - ah
val d = f * y; val bh = d - (d - y); val bl = y - bh
val cl1 = (al*bl) - ((ch - (ah*bh)) - (al*bh) - (ah*bl))
val cl2 = xl*y;
val cl2 = xl*y
//val [tl1,th] = fastTwoSum(ch,cl2);
val th = ch + cl2;
val tl1 = cl2 - (th - ch);
val th = ch + cl2
val tl1 = cl2 - (th - ch)
val tl2 = tl1 + cl1;
val tl2 = tl1 + cl1
//val [zl,zh] = fastTwoSum(th,tl2);
val zh = th + tl2;
val zl = tl2 - (zh - th);
val zh = th + tl2
val zl = tl2 - (zh - th)
return doubleArrayOf(zl,zh);
return doubleArrayOf(zl,zh)
}