static double transformBetweenDoubleRanges_verbose(double x, double srcStart, double srcEnd, double destStart, double destEnd) {

  ret transformBetweenDoubleRanges_verbose(x, doubleRange(srcStart, srcEnd), doubleRange(destStart, destEnd));

}

static double transformBetweenDoubleRanges_verbose(double x, DoubleRange src, DoubleRange dest) {

  double x2 = x-src.start;

  double srcL = src.length();

  double x3 = doubleRatio(x2, srcL);

  double destL = dest.length();

  double y1 = destL*x3;

  double y2 = dest.start+y1;

  printVars transformBetweenDoubleRanges_verbose(

    +x, +src, +dest, +x2, +srcL, +x3, +destL, +y1, +y2);

  ret y2;

}

static DoubleRange transformBetweenDoubleRanges_verbose(DoubleRange r, DoubleRange src, DoubleRange dest) {

  if (r == null) null;

  double a = transformBetweenDoubleRanges_verbose(r.start, src, dest);

  double b = transformBetweenDoubleRanges_verbose(r.end, src, dest);

  var rr = DoubleRange(a, b);

  printVars transformBetweenDoubleRanges_verbose(+r, +src, +dest, +rr);

  ret rr;

}