693 Opensource replacement of sunwlibm

Reviewed by: Igor Kozhukhov ikozhukhov@gmail.com
Reviewed by: Keith M Wesolowski <keith.wesolowski@joyent.com>
Reviewed by: Richard Lowe <richlowe@richlowe.net>
Approved by: Dan McDonald <danmcd@omniti.com>

1 files changed, 232 insertions, 0 deletions

diff --git a/usr/src/lib/libm/common/complex/casinl.c b/usr/src/lib/libm/common/complex/casinl.c
new file mode 100644
index 0000000000..8fe5e6c959
--- /dev/null
+++ b/usr/src/lib/libm/common/complex/casinl.c
@@ -0,0 +1,232 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak casinl = __casinl
+
+#include "libm.h"		/* asinl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
+#include "complex_wrapper.h"
+#include "longdouble.h"
+
+/* INDENT OFF */
+static const long double
+zero = 0.0L,
+one = 1.0L,
+Acrossover = 1.5L,
+Bcrossover = 0.6417L,
+half = 0.5L,
+ln2 = 6.931471805599453094172321214581765680755e-0001L,
+Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L,	/* 2**-8189 */
+#if defined(__x86)
+E = 5.4210108624275221700372640043497085571289e-20L,	/* 2**-64 */
+pi_4 = 0.7853981633974483095739921312272713294078130L,
+pi_4_l = 4.1668714592604391641479322342670193036704898e-20L,
+pi_2 = 1.5707963267948966191479842624545426588156260L,
+pi_2_l = 8.3337429185208783282958644685340386073409796e-20L;
+
+#else
+E = 9.6296497219361792652798897129246365926905e-35L,	/* 2**-113 */
+pi_4 = 0.7853981633974483096156608458198756993697670L,
+pi_4_l = 2.1679525325309452561992610065108379921905808e-35L,
+pi_2 = 1.5707963267948966192313216916397513987395340L,
+pi_2_l = 4.3359050650618905123985220130216759843811616e-35L;
+
+#endif
+/* INDENT ON */
+
+#if defined(__x86)
+static const int ip1 = 0x40400000;	/* 2**65 */
+#else
+static const int ip1 = 0x40710000;	/* 2**114 */
+#endif
+
+ldcomplex
+casinl(ldcomplex z) {
+	long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
+	int ix, iy, hx, hy;
+	ldcomplex ans;
+
+	x = LD_RE(z);
+	y = LD_IM(z);
+	hx = HI_XWORD(x);
+	hy = HI_XWORD(y);
+	ix = hx & 0x7fffffff;
+	iy = hy & 0x7fffffff;
+	x = fabsl(x);
+	y = fabsl(y);
+
+	/* special cases */
+
+	/* x is inf or NaN */
+	if (ix >= 0x7fff0000) {	/* x is inf or NaN */
+		if (isinfl(x)) {	/* x is INF */
+			LD_IM(ans) = x;
+			if (iy >= 0x7fff0000) {
+				if (isinfl(y))
+					/* casin(inf + i inf) = pi/4 + i inf */
+					LD_RE(ans) = pi_4 + pi_4_l;
+				else	/* casin(inf + i NaN) = NaN + i inf */
+					LD_RE(ans) = y + y;
+			} else	/* casin(inf + iy) = pi/2 + i inf */
+				LD_RE(ans) = pi_2 + pi_2_l;
+		} else {		/* x is NaN */
+			if (iy >= 0x7fff0000) {
+				/* INDENT OFF */
+				/*
+				 * casin(NaN + i inf) = NaN  + i inf
+				 * casin(NaN + i NaN) = NaN  + i NaN
+				 */
+				/* INDENT ON */
+				LD_IM(ans) = y + y;
+				LD_RE(ans) = x + x;
+			} else {
+				/* INDENT OFF */
+				/* casin(NaN + i y ) = NaN  + i NaN */
+				/* INDENT ON */
+				LD_IM(ans) = LD_RE(ans) = x + y;
+			}
+		}
+		if (hx < 0)
+			LD_RE(ans) = -LD_RE(ans);
+		if (hy < 0)
+			LD_IM(ans) = -LD_IM(ans);
+		return (ans);
+	}
+
+	/* casin(+0 + i 0) = 0 + i 0. */
+	if (x == zero && y == zero)
+		return (z);
+
+	if (iy >= 0x7fff0000) {	/* y is inf or NaN */
+		if (isinfl(y)) {	/* casin(x + i inf) = 0 + i inf */
+			LD_IM(ans) = y;
+			LD_RE(ans) = zero;
+		} else {		/* casin(x + i NaN) = NaN + i NaN */
+			LD_IM(ans) = x + y;
+			if (x == zero)
+				LD_RE(ans) = x;
+			else
+				LD_RE(ans) = y;
+		}
+		if (hx < 0)
+			LD_RE(ans) = -LD_RE(ans);
+		if (hy < 0)
+			LD_IM(ans) = -LD_IM(ans);
+		return (ans);
+	}
+
+	if (y == zero) {	/* region 1: y=0 */
+		if (ix < 0x3fff0000) {	/* |x| < 1 */
+			LD_RE(ans) = asinl(x);
+			LD_IM(ans) = zero;
+		} else {
+			LD_RE(ans) = pi_2 + pi_2_l;
+			if (ix >= ip1)	/* |x| >= i386 ? 2**65 : 2**114 */
+				LD_IM(ans) = ln2 + logl(x);
+			else if (ix >= 0x3fff8000)	/* x > Acrossover */
+				LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
+					one)));
+			else {
+				xm1 = x - one;
+				LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
+					one)));
+			}
+		}
+	} else if (y <= E * fabsl(x - one)) {	/* region 2: y < tiny*|x-1| */
+		if (ix < 0x3fff0000) {	/* x < 1 */
+			LD_RE(ans) = asinl(x);
+			LD_IM(ans) = y / sqrtl((one + x) * (one - x));
+		} else {
+			LD_RE(ans) = pi_2 + pi_2_l;
+			if (ix >= ip1)	/* i386 ? 2**65 : 2**114 */
+				LD_IM(ans) = ln2 + logl(x);
+			else if (ix >= 0x3fff8000)	/* x > Acrossover */
+				LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
+					one)));
+			else
+				LD_IM(ans) = log1pl((x - one) + sqrtl((x -
+					one) * (x + one)));
+		}
+	} else if (y < Foursqrtu) {	/* region 3 */
+		t = sqrtl(y);
+		LD_RE(ans) = pi_2 - (t - pi_2_l);
+		LD_IM(ans) = t;
+	} else if (E * y - one >= x) {	/* region 4 */
+		LD_RE(ans) = x / y;	/* need to fix underflow cases */
+		LD_IM(ans) = ln2 + logl(y);
+	} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
+		/* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
+		t = x / y;
+		LD_RE(ans) = atanl(t);
+		LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
+	} else if (x < Foursqrtu) {
+		/* region 6: x is very small, < 4sqrt(min) */
+		A = sqrtl(one + y * y);
+		LD_RE(ans) = x / A;	/* may underflow */
+		if (iy >= 0x3fff8000)	/* if y > Acrossover */
+			LD_IM(ans) = logl(y + A);
+		else
+			LD_IM(ans) = half * log1pl((y + y) * (y + A));
+	} else {	/* safe region */
+		y2 = y * y;
+		xp1 = x + one;
+		xm1 = x - one;
+		R = sqrtl(xp1 * xp1 + y2);
+		S = sqrtl(xm1 * xm1 + y2);
+		A = half * (R + S);
+		B = x / A;
+		if (B <= Bcrossover)
+			LD_RE(ans) = asinl(B);
+		else {		/* use atan and an accurate approx to a-x */
+			Apx = A + x;
+			if (x <= one)
+				LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 /
+					(R + xp1) + (S - xm1))));
+			else
+				LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx /
+					(R + xp1) + Apx / (S + xm1)))));
+		}
+		if (A <= Acrossover) {
+			/* use log1p and an accurate approx to A-1 */
+			if (x < one)
+				Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
+			else
+				Am1 = half * (y2 / (R + xp1) + (S + xm1));
+			LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
+		} else {
+			LD_IM(ans) = logl(A + sqrtl(A * A - one));
+		}
+	}
+
+	if (hx < 0)
+		LD_RE(ans) = -LD_RE(ans);
+	if (hy < 0)
+		LD_IM(ans) = -LD_IM(ans);
+
+	return (ans);
+}