[newlib-cygwin] Importing csqrtl.c from NetBSD.

[newlib-cygwin] Importing csqrtl.c from NetBSD.

[Corinna Vinschen]

https://sourceware.org/git/gitweb.cgi?p=newlib-cygwin.git;h=436bf2929c579c70a981b7153d2fd269bcf3d86a

commit 436bf2929c579c70a981b7153d2fd269bcf3d86a
Author: Aditya Upadhyay <aadit0402@gmail.com>
Date:   Thu Jun 29 01:28:51 2017 +0530

    Importing csqrtl.c from NetBSD.

Diff:
---
 newlib/libm/complex/Makefile.am |   2 +-
 newlib/libm/complex/csqrtl.c    | 112 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 113 insertions(+), 1 deletion(-)

diff --git a/newlib/libm/complex/Makefile.am b/newlib/libm/complex/Makefile.am
index ad5d9a9..c70726e 100644
--- a/newlib/libm/complex/Makefile.am
+++ b/newlib/libm/complex/Makefile.am
@@ -11,7 +11,7 @@ src = cabs.c cacos.c cacosh.c carg.c casin.c casinh.c \
       csin.c csinh.c csqrt.c ctan.c ctanh.c
 
 lsrc = cabsl.c creall.c cimagl.c ccoshl.c cacoshl.c \
-       clogl.c
+       clogl.c csqrtl.c
 
 fsrc =	cabsf.c casinf.c ccosf.c cimagf.c cprojf.c  \
         csqrtf.c cacosf.c casinhf.c ccoshf.c clogf.c clog10f.c \
diff --git a/newlib/libm/complex/csqrtl.c b/newlib/libm/complex/csqrtl.c
new file mode 100755
index 0000000..c10a126
--- /dev/null
+++ b/newlib/libm/complex/csqrtl.c
@@ -0,0 +1,112 @@
+/*-
+ * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include <sys/cdefs.h>
+#if 0
+__FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $");
+#else
+__RCSID("$NetBSD: csqrtl.c,v 1.2 2014/10/11 00:43:51 christos Exp $");
+#endif
+
+#include <complex.h>
+#include <float.h>
+#include <math.h>
+#include <stdbool.h>
+/*
+ * gcc doesn't implement complex multiplication or division correctly,
+ * so we need to handle infinities specially. We turn on this pragma to
+ * notify conforming c99 compilers that the fast-but-incorrect code that
+ * gcc generates is acceptable, since the special cases have already been
+ * handled.
+ */
+// #pragma	STDC CX_LIMITED_RANGE	ON
+
+/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
+#define	THRESH	(LDBL_MAX / 2.414213562373095048801688724209698L)
+
+#define cpackl(r, i) ((r) + (i) * I)
+
+long double complex
+csqrtl(long double complex z)
+{
+	long double complex result;
+	long double a, b;
+	long double t;
+	bool scale;
+
+	a = creall(z);
+	b = cimagl(z);
+
+	/* Handle special cases. */
+	if (z == 0.0L)
+		return (cpackl(0.0L, b));
+	if (isinf(b))
+		return (cpackl(INFINITY, b));
+	if (isnan(a)) {
+		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
+		return (cpackl(a, t));	/* return NaN + NaN i */
+	}
+	if (isinf(a)) {
+		/*
+		 * csqrt(inf + NaN i)  = inf +  NaN i
+		 * csqrt(inf + y i)    = inf +  0 i
+		 * csqrt(-inf + NaN i) = NaN +- inf i
+		 * csqrt(-inf + y i)   = 0   +  inf i
+		 */
+		if (signbit(a))
+			return (cpackl(fabsl(b - b), copysignl(a, b)));
+		else
+			return (cpackl(a, copysignl(b - b, b)));
+	}
+	/*
+	 * The remaining special case (b is NaN) is handled just fine by
+	 * the normal code path below.
+	 */
+
+	/* Scale to avoid overflow. */
+	if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
+		a *= 0.25L;
+		b *= 0.25L;
+		scale = true;
+	} else {
+		scale = false;
+	}
+
+	/* Algorithm 312, CACM vol 10, Oct 1967. */
+	if (a >= 0L) {
+		t = sqrtl((a + hypotl(a, b)) * 0.5L);
+		result = cpackl(t, b / (2.0L * t));
+	} else {
+		t = sqrtl((-a + hypotl(a, b)) * 0.5L);
+		result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
+	}
+
+	/* Rescale. */
+	if (scale)
+		return (result * 2.0L);
+	else
+		return (result);
+}