Re: bin/170206: complex arcsinh, log, etc.

[Stephen Montgomery-Smith]

Here are some diffs to catrig.c so that it completely passes Peter 
Jeremy's program www.rulingia.com/~peter/ctest.c.  That is, it seems to 
get all the infs and nans correct.

--- catrig.c-old1	2012-07-28 15:00:46.000000000 -0500
+++ catrig.c	2012-07-28 16:39:24.000000000 -0500
@@ -89,7 +89,7 @@
 	S = hypot(x,y-1);
 	A = 0.5*(R + S);
 
-	if (A < 10) {
+	if (A < 10 && isfinite(A)) {
 		fp = f(x,1+y,&fpuf);
 		fm = f(x,1-y,&fmuf);
 		if (fpuf == 1 && fmuf == 1) {
@@ -108,9 +108,23 @@
 		} else {
 			*rx = log1p(fp + fm + sqrt((fp+fm)*(A+1)));
 		}
-	} else
+	} else if (isinf(y))
+		*rx = y;
+	else
 		*rx = log(A + sqrt(A*A-1));
 
+	if (!isfinite(y)) {
+		*B_good = 0;
+		if (isfinite(x)) *A2my2 = 0;
+		else if (isnan(x)) *A2my2 = x;
+		else *A2my2 = y;
+		return;
+	} else if (isnan(x) && y == 0) {
+		*B_good = 0;
+		*A2my2 = 1;
+		return;
+	}
+
 	*B = y/A; /* = 0.5*(R - S) */
 	*B_good = 1;
 
@@ -147,7 +161,7 @@
 	x = fabs(x);
 	y = fabs(y);
 
-	if (cabs(z) > 1e20) {
+	if (cabs(z) > 1e20 && isfinite(x) && isfinite(y)) {
 		if (huge+x>one) { /* set inexact flag. */
 			if (sx == 0) return clog(2*z);
 			if (sx == 1) return -clog(-2*z);
@@ -206,7 +220,7 @@
 	x = fabs(x);
 	y = fabs(y);
 
-	if (cabs(z) > 1e20) {
+	if (cabs(z) > 1e20 && isfinite(x) && isfinite(y)) {
 		if (huge+x>one) { /* set inexact flag. */
 			w = clog(2*z);
 			if (signbit(cimag(w)) == 0)
@@ -271,6 +285,36 @@
 		if (huge+x>one) /* set inexact flag. */
 			return z;
 
+	if (isinf(x) && isfinite(y)) {
+		if (!((signbit(x) == 0) ^ (signbit(y) == 0)))
+			return cpack(0,M_PI_2);
+		return cpack(0,-M_PI_2);
+	}
+
+	if (isinf(y)) {
+		rx = copysign(0,x);
+		if (signbit(y) == 0)
+			return cpack(rx,M_PI_2);
+		return cpack(rx,-M_PI_2);
+	}
+
+	if (isinf(x) && isnan(y)) {
+		rx = copysign(0, x);
+		return cpack(rx, y);
+	}
+
+	if (x == 0 && isnan(y))
+		return cpack(x, y);
+
+	if (isinf(y)) {
+		if (signbit(y) == 0)
+			return cpack(0,M_PI_2);
+		return cpack(0,-M_PI_2);
+	}
+
+	if (isnan(x) || isnan(y))
+		return clog(z);
+
 	if (cabs(z) > 1e20)
 		if (huge+x>one) { /* set inexact flag. */
 			if (signbit(x) == 0)
@@ -290,13 +334,17 @@
 
 	if (hp < 0.5 || hm < 0.5)
 		rx = 0.25*(log(hp/hm));
+	else if (x == 0)
+		rx = x;
 	else if (x > 0)
 		rx = 0.25*log1p(4*x/hm);
 	else
 		rx = -0.25*log1p(-4*x/hp);
 
 	if (x==1 || x==-1) {
-		if (signbit(y) == 0)
+		if (y==0)
+			ry = y;
+		else if (signbit(y) == 0)
 			ry = atan2(2, -y)/2;
 		else
 			ry = atan2(-2, y)/2;
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