add new aversin and acoversin builtin functions.

Added new aversin(x, [,eps]) for inverse versed sine and acoversin(x, [,eps])
for inverse coversed sine.

Improved trig function help files to reference use of complex arguments
that while supported were not documented.

Removed old Makefile testing rules for make dbx and make gdb.

Improved "make run" to execute calccalc using shared libraries
from the local directory, and with reading of the startup scripts
disabled.

Changed "make prep" to perform various tests that are used to
help verify that calc is ready for a release.

Added Makefile testing rule testfuncsort to check for the sort
of the builtin function list.  Changed the order that builtin
functions are listed by "show builtin" and the help/builtin to
match the sorting of "LANG=C LC_ALL=C sort -d -u".

qtrans.c

@@ -421,6 +421,8 @@ qcsc(NUMBER *q, NUMBER *epsilon)
 	qfree(csc);
 	return res;
 }
+
+
 /*
  * Calculate the arcsine function.
  * The result is in the range -pi/2 to pi/2.
@@ -437,14 +439,16 @@ qasin(NUMBER *q, NUMBER *epsilon)
 		math_error("Zero epsilon value for asin");
 		not_reached();
 	}
-	if (qiszero(q))
+	if (qiszero(q)) {
 		return qlink(&_qzero_);
+	}
 	ztmp = q->num;
 	neg = ztmp.sign;
 	ztmp.sign = 0;
 	r = zrel(ztmp, q->den);
-	if (r > 0)
+	if (r > 0) {
 		return NULL;
+	}
 	if (r == 0) {
 		epsilon1 = qscale(epsilon, 1L);
 		qtmp2 = qpi(epsilon1);
@@ -1981,8 +1985,6 @@ qacoth(NUMBER *q, NUMBER *epsilon)
  *
  *	versin(x) = 1 - cos(x)
  *
- * This calls qsincos() and discards the value of sin.
- *
  * given:
  *	q	    real value to pass to the trig function
  *	epsilon	    error tolerance / precision for trig calculation
@@ -1997,31 +1999,147 @@ qversin(NUMBER *q, NUMBER *epsilon)
 	NUMBER *versin;
 	long n;
 
-	if (qiszero(epsilon)) {
-		math_error("Zero epsilon value for %s", __func__);
+	/*
+	 * firewall
+	 */
+	if (q == NULL) {
+		math_error("q is NULL for %s", __func__);
 		not_reached();
 	}
+	if (check_epsilon(epsilon) == false) {
+		math_error("Invalid epsilon arg for %s", __func__);
+		not_reached();
+	}
+
+	/*
+	 * calculate trig function value
+	 */
 	n = -qilog2(epsilon);
-	if (qiszero(q) || n < 0)
-		return qlink(&_qzero_);
 	qsincos(q, n + 2, &sin, &cos);
 	qfree(sin);
 	versin = qsub(&_qone_, cos);
 	qfree(cos);
+
+	/*
+	 * round value to nearest epsilon
+	 */
 	res = qmappr(versin, epsilon, 24);
 	qfree(versin);
+
+	/*
+	 * return 1 - cos(x)
+	 */
 	return res;
 }
 
 
 /*
- * qversin - coversed sine for NUMBER values
+ * qaversin_or_NULL - inverse versed sine for NUMBER values
  *
  * This uses the formula:
  *
- *	coversin(x) = 1 - sin(x)
+ *	aversin(x) = acos(1 - x)
  *
- * This calls qsincos() and discards the value of cos.
+ * given:
+ *	q	    real value to pass to the trig function
+ *	epsilon	    error tolerance / precision for trig calculation
+ *
+ * returns:
+ *	!= NULL ==> real value result of trig function on q with error epsilon,
+ *	NULL    ==> trig function value cannot be expressed as a NUMBER
+ *
+ * NOTE: If this function returns NULL, consider calling the equivalent
+ *	 COMPLEX function from comfunc.c.  See the help file for the
+ *	 related builtin for details.
+ */
+NUMBER *
+qaversin_or_NULL(NUMBER *q, NUMBER *epsilon)
+{
+	NUMBER *res;	/* inverse trig value result */
+	NUMBER *x;	/* argument to inverse trig function */
+
+	/*
+	 * firewall
+	 */
+	if (q == NULL) {
+		math_error("q is NULL for %s", __func__);
+		not_reached();
+	}
+	if (check_epsilon(epsilon) == false) {
+		math_error("Invalid epsilon arg for %s", __func__);
+		not_reached();
+	}
+
+	/*
+	 * calculate inverse trig function value
+	 */
+	x = qsub(&_qone_, q);
+	res = qacos(x, epsilon);
+	qfree(x);
+	if (res == NULL) {
+		return NULL;
+	}
+
+	/*
+	 * return acos(1 - x)
+	 */
+	return res;
+}
+
+
+/*
+ * qaversin - inverse versed sine for NUMBER values
+ *
+ * This uses the formula:
+ *
+ *	aversin(x) = acos(1 - x)
+ *
+ * given:
+ *	q	    real value to pass to the trig function
+ *	epsilon	    error tolerance / precision for trig calculation
+ *
+ * returns:
+ *	real value result of trig function on q with error epsilon
+ */
+NUMBER *
+qaversin(NUMBER *q, NUMBER *epsilon)
+{
+	NUMBER *res;	/* inverse trig value result */
+
+	/*
+	 * firewall
+	 */
+	if (q == NULL) {
+		math_error("q is NULL for %s", __func__);
+		not_reached();
+	}
+	if (check_epsilon(epsilon) == false) {
+		math_error("Invalid epsilon arg for %s", __func__);
+		not_reached();
+	}
+
+	/*
+	 * calculate inverse trig function value
+	 */
+	res = qaversin_or_NULL(q, epsilon);
+	if (res == NULL) {
+		math_error("cannot compute inverse cos for aversin");
+		not_reached();
+	}
+
+	/*
+	 * return acos(1 - x)
+	 */
+	return res;
+}
+
+
+/*
+ * qcoversin - coversed sine for NUMBER values
+ *
+ * This uses the formula:
+ *
+ *	coversin((x) = 1 - sin(x)
  *
  * given:
  *	q	    real value to pass to the trig function
@@ -2037,10 +2155,21 @@ qcoversin(NUMBER *q, NUMBER *epsilon)
 	NUMBER *coversin;
 	long n;
 
-	if (qiszero(epsilon)) {
-		math_error("Zero epsilon value for %s", __func__);
+	/*
+	 * firewall
+	 */
+	if (q == NULL) {
+		math_error("q is NULL for %s", __func__);
 		not_reached();
 	}
+	if (check_epsilon(epsilon) == false) {
+		math_error("Invalid epsilon arg for %s", __func__);
+		not_reached();
+	}
+
+	/*
+	 * calculate trig function value
+	 */
 	n = -qilog2(epsilon);
 	if (qiszero(q) || n < 0)
 		return qlink(&_qzero_);
@@ -2048,7 +2177,119 @@ qcoversin(NUMBER *q, NUMBER *epsilon)
 	qfree(cos);
 	coversin = qsub(&_qone_, sin);
 	qfree(sin);
+
+	/*
+	 * round value to nearest epsilon
+	 */
 	res = qmappr(coversin, epsilon, 24);
 	qfree(coversin);
+
+	/*
+	 * return 1 - sin(x)
+	 */
+	return res;
+}
+
+
+/*
+ * qacoversin_or_NULL - inverse coversed sine for NUMBER values
+ *
+ * This uses the formula:
+ *
+ *	acoversin(x) = asin(1 - x)
+ *
+ * given:
+ *	q	    real value to pass to the trig function
+ *	epsilon	    error tolerance / precision for trig calculation
+ *
+ * returns:
+ *	real value result of trig function on q with error epsilon
+ *
+ * returns:
+ *	!= NULL ==> real value result of trig function on q with error epsilon,
+ *	NULL    ==> trig function value cannot be expressed as a NUMBER
+ *
+ * NOTE: If this function returns NULL, consider calling the equivalent
+ *	 COMPLEX function from comfunc.c.  See the help file for the
+ *	 related builtin for details.
+ */
+NUMBER *
+qacoversin_or_NULL(NUMBER *q, NUMBER *epsilon)
+{
+	NUMBER *res;	/* inverse trig value result */
+	NUMBER *x;	/* argument to inverse trig function */
+
+	/*
+	 * firewall
+	 */
+	if (q == NULL) {
+		math_error("q is NULL for %s", __func__);
+		not_reached();
+	}
+	if (check_epsilon(epsilon) == false) {
+		math_error("Invalid epsilon arg for %s", __func__);
+		not_reached();
+	}
+
+	/*
+	 * calculate inverse trig function value
+	 */
+	x = qsub(&_qone_, q);
+	res = qasin(x, epsilon);
+	qfree(x);
+	if (res == NULL) {
+		return NULL;
+	}
+
+	/*
+	 * return asin(1 - x)
+	 */
+	return res;
+}
+
+
+/*
+ * qacoversin - inverse coversed sine for NUMBER values
+ *
+ * This uses the formula:
+ *
+ *	acoversin(x) = asin(1 - x)
+ *
+ * given:
+ *	q	    real value to pass to the trig function
+ *	epsilon	    error tolerance / precision for trig calculation
+ *
+ * returns:
+ *	real value result of trig function on q with error epsilon
+ */
+NUMBER *
+qacoversin(NUMBER *q, NUMBER *epsilon)
+{
+	NUMBER *res;	/* inverse trig value result */
+
+	/*
+	 * firewall
+	 */
+	if (q == NULL) {
+		math_error("q is NULL for %s", __func__);
+		not_reached();
+	}
+	if (check_epsilon(epsilon) == false) {
+		math_error("Invalid epsilon arg for %s", __func__);
+		not_reached();
+	}
+
+	/*
+	 * calculate inverse trig function value
+	 */
+	res = qacoversin_or_NULL(q, epsilon);
+	if (res == NULL) {
+		math_error("cannot compute inverse sin for acoversin");
+		not_reached();
+	}
+
+	/*
+	 * return asin(1 - x)
+	 */
 	return res;
 }