+/*
+ 0 at threshold, 1 at 0, with 1/x falloff.
+ */
+Real
+peak_around (Real epsilon, Real threshold, Real x)
+{
+ if (x < 0)
+ return 1.0;
+ return max (- epsilon * (x - threshold) / ((x + epsilon) * threshold), 0.0);
+}
+
+/*
+ 0 at 0, 1 at standard_x, and increasing thereafter.
+ */
+Real
+convex_amplifier (Real standard_x, Real increase_factor, Real x)
+{
+ return (exp (increase_factor * x / standard_x) - 1.0) / (exp (increase_factor) - 1.0);
+}
+
+string
+camel_case_to_lisp_identifier (string in)
+{
+ vector<char> out;
+
+ /* don't add '-' before first character */
+ out.push_back (char (tolower (in[0])));
+
+ for (size_t inpos = 1; inpos < in.size (); inpos++)
+ {
+ if (isupper (in[inpos]))
+ out.push_back ('-');
+ out.push_back ( char (tolower (in[inpos])));
+ }
+
+ string result (&out[0], out.size ());
+ replace_all (&result, '_', '-');
+
+ return result;
+}
+
+vsize
+utf8_char_len (char current)
+{
+ vsize char_len = 1;
+
+ // U+10000 - U+10FFFF
+ if ((current & 0xF0) == 0xF0)
+ char_len = 4;
+ // U+0800 - U+FFFF
+ else if ((current & 0xE0) == 0xE0)
+ char_len = 3;
+ // U+0080 - U+07FF
+ else if ((current & 0xC0) == 0xC0)
+ char_len = 2;
+ else if (current & 0x80)
+ programming_error ("invalid UTF-8 string");
+
+ return char_len;
+}