Bug #133297: cmath.asin is the same as cmath.asinh.

tim_one · tim_one · commit f6161876c82e · 2001-02-21T03:22:39.000Z
The bug report title isn't correct, but was on the right track. Rev 2.13 applied a patch intended to improve asinh and acosh, but the author mistakenly replaced the body of asin with their new code for asinh. See bug report for all the gory details. This patch: (a) puts the "new" (as of 2.13) asinh code into the asinh function; and, (b) repairs asin via what Abramowitz & Stegun say it should be (which is probably the same as what 2.12 did for asin, although I got tired of matching parentheses before being 100% sure of that -- and I don't care! The source of the old code is a mystery, and I *know* why I picked the new code.). git-svn-id: http://svn.python.org/projects/python/trunk@19587 6015fed2-1504-0410-9fe1-9d1591cc4771
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
@@ -67,11 +67,11 @@ static char c_acosh_doc[] =
 static Py_complex
 c_asin(Py_complex x)
 {
-	Py_complex z;
-	z = c_sqrt(c_half);
-	z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)),
-				  c_sqrt(c_diff(x, c_i)))));
-	return c_sum(z, z);
+	/* -i * log[(sqrt(1-x**2) + i*x] */
+	const Py_complex squared = c_prod(x, x);
+	const Py_complex sqrt_1_minus_x_sq = c_sqrt(c_diff(c_one, squared));
+	const Py_complex sum = c_sum(sqrt_1_minus_x_sq, c_prod(c_i, x));
+        return c_neg(c_prodi(c_log(sum)));
 }
 
 static char c_asin_doc[] =
@@ -83,10 +83,11 @@ static char c_asin_doc[] =
 static Py_complex
 c_asinh(Py_complex x)
 {
-	/* Break up long expression for WATCOM */
 	Py_complex z;
-	z = c_sum(c_one, c_prod(x, x));
-	return c_log(c_sum(c_sqrt(z), x));
+	z = c_sqrt(c_half);
+	z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)),
+				  c_sqrt(c_diff(x, c_i)))));
+	return c_sum(z, z);
 }
 
 static char c_asinh_doc[] =
