--- /dev/null	Sat May 10 12:09:16 2014
+++ new/usr/src/lib/libm/common/complex/cacos.c	Sat May 10 12:09:16 2014
@@ -0,0 +1,404 @@
+/*
+ * 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 cacos = __cacos
+
+/* INDENT OFF */
+/*
+ * dcomplex cacos(dcomplex z);
+ *
+ * Alogrithm
+ * (based on T.E.Hull, Thomas F. Fairgrieve and Ping Tak Peter Tang's
+ * paper "Implementing the Complex Arcsine and Arccosine Functins Using
+ * Exception Handling", ACM TOMS, Vol 23, pp 299-335)
+ *
+ * The principal value of complex inverse cosine function cacos(z),
+ * where z = x+iy, can be defined by
+ *
+ * 	cacos(z) = acos(B) - i sign(y) log (A + sqrt(A*A-1)),
+ *
+ * where the log function is the natural log, and
+ *             ____________           ____________
+ *       1    /     2    2      1    /     2    2
+ *  A = ---  / (x+1)  + y   +  ---  / (x-1)  + y
+ *       2 \/                   2 \/
+ *             ____________           ____________
+ *       1    /     2    2      1    /     2    2
+ *  B = ---  / (x+1)  + y   -  ---  / (x-1)  + y   .
+ *       2 \/                   2 \/
+ *
+ * The Branch cuts are on the real line from -inf to -1 and from 1 to inf.
+ * The real and imaginary parts are based on Abramowitz and Stegun
+ * [Handbook of Mathematic Functions, 1972].  The sign of the imaginary
+ * part is chosen to be the generally considered the principal value of
+ * this function.
+ *
+ * Notes:1. A is the average of the distances from z to the points (1,0)
+ *          and (-1,0) in the complex z-plane, and in particular A>=1.
+ *       2. B is in [-1,1], and A*B = x
+ *
+ * Basic relations
+ *    cacos(conj(z)) = conj(cacos(z))
+ *    cacos(-z)      = pi   - cacos(z)
+ *    cacos( z)      = pi/2 - casin(z)
+ *
+ * Special cases (conform to ISO/IEC 9899:1999(E)):
+ *    cacos(+-0  + i y  ) = pi/2 - i y for y is +-0, +-inf, NaN
+ *    cacos( x   + i inf) = pi/2 - i inf for all x
+ *    cacos( x   + i NaN) = NaN  + i NaN with invalid for non-zero finite x
+ *    cacos(-inf + i y  ) = pi   - i inf for finite +y
+ *    cacos( inf + i y  ) = 0    - i inf for finite +y
+ *    cacos(-inf + i inf) = 3pi/4- i inf
+ *    cacos( inf + i inf) = pi/4 - i inf
+ *    cacos(+-inf+ i NaN) = NaN  - i inf (sign of imaginary is unspecified)
+ *    cacos(NaN  + i y  ) = NaN  + i NaN with invalid for finite y
+ *    cacos(NaN  + i inf) = NaN  - i inf
+ *    cacos(NaN  + i NaN) = NaN  + i NaN
+ *
+ * Special Regions (better formula for accuracy and for avoiding spurious
+ * overflow or underflow) (all x and y are assumed nonnegative):
+ *  case 1: y = 0
+ *  case 2: tiny y relative to x-1: y <= ulp(0.5)*|x-1|
+ *  case 3: tiny y: y < 4 sqrt(u), where u = minimum normal number
+ *  case 4: huge y relative to x+1: y >= (1+x)/ulp(0.5)
+ *  case 5: huge x and y: x and y >= sqrt(M)/8, where M = maximum normal number
+ *  case 6: tiny x: x < 4 sqrt(u)
+ *  --------
+ *  case	1 & 2. y=0 or y/|x-1| is tiny. We have
+ *             ____________              _____________
+ *            /      2    2             /       y    2
+ *           / (x+-1)  + y   =  |x+-1| / 1 + (------)
+ *         \/                        \/       |x+-1|
+ *
+ *                                            1     y    2
+ *                           ~  |x+-1| ( 1 + --- (------)  )
+ *                                            2   |x+-1|
+ *
+ *                                          2
+ *                                         y
+ *                           = |x+-1| + --------.
+ *                                      2|x+-1|
+ *
+ *	Consequently, it is not difficult to see that
+ *                                 2
+ *                                y
+ *                    [ 1 + ------------ ,     if x < 1,
+ *                    [      2(1+x)(1-x)
+ *                    [
+ *                    [
+ *                    [ x,                     if x = 1 (y = 0),
+ *                    [
+ *		A ~=  [             2
+ *                    [        x * y
+ *                    [ x + ------------ ~ x,  if x > 1
+ *                    [      2(x+1)(x-1)
+ *
+ *	and hence
+ *                      ______                                 2
+ *                     / 2                    y               y
+ *               A + \/ A  - 1  ~  1 + ---------------- + -----------, if x < 1,
+ *                                     sqrt((x+1)(1-x))   2(x+1)(1-x)
+ *
+ *
+ *			        ~  x + sqrt((x-1)*(x+1)),             if x >= 1.
+ *
+ *                                         2
+ *                                        y
+ *                          [ x(1 - -----------) ~ x,  if x < 1,
+ *                          [       2(1+x)(1-x)
+ *		B = x/A  ~  [
+ *                          [ 1,                       if x = 1,
+ *			    [
+ *                          [           2
+ *                          [          y
+ *                          [ 1 - ------------ ,       if x > 1,
+ *                          [      2(x+1)(x-1)
+ *	Thus
+ *                            [ acos(x) - i y/sqrt((x-1)*(x+1)),      if x < 1,
+ *                            [
+ *		cacos(x+i*y)~ [ 0 - i 0,                              if x = 1,
+ *                            [
+ *                            [ y/sqrt(x*x-1) - i log(x+sqrt(x*x-1)), if x > 1.
+ *
+ *      Note: y/sqrt(x*x-1) ~ y/x when x >= 2**26.
+ *  case 3. y < 4 sqrt(u), where u = minimum normal x.
+ *	After case 1 and 2, this will only occurs when x=1. When x=1, we have
+ *	   A = (sqrt(4+y*y)+y)/2 ~ 1 + y/2 + y^2/8 + ...
+ *	and
+ *	   B = 1/A = 1 - y/2 + y^2/8 + ...
+ * 	Since
+ *         cos(sqrt(y)) ~ 1 - y/2 + ...
+ *      we have, for the real part,
+ *         acos(B) ~ acos(1 - y/2) ~ sqrt(y)
+ *	For the imaginary part,
+ *	   log(A+sqrt(A*A-1)) ~ log(1+y/2+sqrt(2*y/2))
+ *	                      = log(1+y/2+sqrt(y))
+ *	                      = (y/2+sqrt(y)) - (y/2+sqrt(y))^2/2 + ...
+ *	                      ~ sqrt(y) - y*(sqrt(y)+y/2)/2
+ *	                      ~ sqrt(y)
+ *
+ *  case 4. y >= (x+1)/ulp(0.5). In this case, A ~ y and B ~ x/y. Thus
+ *	   real part = acos(B) ~ pi/2
+ * 	and
+ *	   imag part = log(y+sqrt(y*y-one))
+ *
+ *  case 5. Both x and y are large: x and y > sqrt(M)/8, where M = maximum x
+ *	In this case,
+ *	   A ~ sqrt(x*x+y*y)
+ *	   B ~ x/sqrt(x*x+y*y).
+ *	Thus
+ *	   real part = acos(B) = atan(y/x),
+ *	   imag part = log(A+sqrt(A*A-1)) ~ log(2A)
+ *	             = log(2) + 0.5*log(x*x+y*y)
+ *	             = log(2) + log(y) + 0.5*log(1+(x/y)^2)
+ *
+ *  case 6. x < 4 sqrt(u). In this case, we have
+ *	    A ~ sqrt(1+y*y), B = x/sqrt(1+y*y).
+ *	Since B is tiny, we have
+ *	    real part = acos(B) ~ pi/2
+ *	    imag part = log(A+sqrt(A*A-1)) = log (A+sqrt(y*y))
+ *	              = log(y+sqrt(1+y*y))
+ *	              = 0.5*log(y^2+2ysqrt(1+y^2)+1+y^2)
+ *	              = 0.5*log(1+2y(y+sqrt(1+y^2)));
+ *	              = 0.5*log1p(2y(y+A));
+ *
+ * 	cacos(z) = acos(B) - i sign(y) log (A + sqrt(A*A-1)),
+ */
+/* INDENT ON */
+
+#include "libm.h"
+#include "complex_wrapper.h"
+
+/* INDENT OFF */
+static const double
+	zero = 0.0,
+	one = 1.0,
+	E = 1.11022302462515654042e-16,			/* 2**-53 */
+	ln2 = 6.93147180559945286227e-01,
+	pi = 3.1415926535897931159979634685,
+	pi_l = 1.224646799147353177e-16,
+	pi_2 = 1.570796326794896558e+00,
+	pi_2_l = 6.123233995736765886e-17,
+	pi_4 = 0.78539816339744827899949,
+	pi_4_l = 3.061616997868382943e-17,
+	pi3_4 = 2.356194490192344836998,
+	pi3_4_l = 9.184850993605148829195e-17,
+	Foursqrtu = 5.96667258496016539463e-154,	/* 2**(-509) */
+	Acrossover = 1.5,
+	Bcrossover = 0.6417,
+	half = 0.5;
+/* INDENT ON */
+
+dcomplex
+cacos(dcomplex z) {
+	double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
+	int ix, iy, hx, hy;
+	unsigned lx, ly;
+	dcomplex ans;
+
+	x = D_RE(z);
+	y = D_IM(z);
+	hx = HI_WORD(x);
+	lx = LO_WORD(x);
+	hy = HI_WORD(y);
+	ly = LO_WORD(y);
+	ix = hx & 0x7fffffff;
+	iy = hy & 0x7fffffff;
+
+	/* x is 0 */
+	if ((ix | lx) == 0) {
+		if (((iy | ly) == 0) || (iy >= 0x7ff00000)) {
+			D_RE(ans) = pi_2;
+			D_IM(ans) = -y;
+			return (ans);
+		}
+	}
+
+	/* |y| is inf or NaN */
+	if (iy >= 0x7ff00000) {
+		if (ISINF(iy, ly)) {	/* cacos( x + i inf ) = pi/2  - i inf */
+			D_IM(ans) = -y;
+			if (ix < 0x7ff00000) {
+				D_RE(ans) = pi_2 + pi_2_l;
+			} else if (ISINF(ix, lx)) {
+				if (hx >= 0)
+					D_RE(ans) = pi_4 + pi_4_l;
+				else
+					D_RE(ans) = pi3_4 + pi3_4_l;
+			} else {
+				D_RE(ans) = x;
+			}
+		} else {		/* cacos( x + i NaN ) = NaN  + i NaN */
+			D_RE(ans) = y + x;
+			if (ISINF(ix, lx))
+				D_IM(ans) = -fabs(x);
+			else
+				D_IM(ans) = y;
+		}
+		return (ans);
+	}
+
+	x = fabs(x);
+	y = fabs(y);
+
+	/* x is inf or NaN */
+	if (ix >= 0x7ff00000) {	/* x is inf or NaN */
+		if (ISINF(ix, lx)) {	/* x is INF */
+			D_IM(ans) = -x;
+			if (iy >= 0x7ff00000) {
+				if (ISINF(iy, ly)) {
+					/* INDENT OFF */
+					/* cacos(inf + i inf) = pi/4 - i inf */
+					/* cacos(-inf+ i inf) =3pi/4 - i inf */
+					/* INDENT ON */
+					if (hx >= 0)
+						D_RE(ans) = pi_4 + pi_4_l;
+					else
+						D_RE(ans) = pi3_4 + pi3_4_l;
+				} else
+					/* INDENT OFF */
+					/* cacos(inf + i NaN) = NaN  - i inf  */
+					/* INDENT ON */
+					D_RE(ans) = y + y;
+			} else
+				/* INDENT OFF */
+				/* cacos( inf + iy  ) = 0  - i inf */
+				/* cacos(-inf+ iy   ) = pi - i inf */
+				/* INDENT ON */
+			if (hx >= 0)
+				D_RE(ans) = zero;
+			else
+				D_RE(ans) = pi + pi_l;
+		} else {		/* x is NaN */
+			/* INDENT OFF */
+			/*
+			 * cacos(NaN + i inf) = NaN  - i inf
+			 * cacos(NaN + i y  ) = NaN  + i NaN
+			 * cacos(NaN + i NaN) = NaN  + i NaN
+			 */
+			/* INDENT ON */
+			D_RE(ans) = x + y;
+			if (iy >= 0x7ff00000) {
+				D_IM(ans) = -y;
+			} else {
+				D_IM(ans) = x;
+			}
+		}
+		if (hy < 0)
+			D_IM(ans) = -D_IM(ans);
+		return (ans);
+	}
+
+	if ((iy | ly) == 0) {	/* region 1: y=0 */
+		if (ix < 0x3ff00000) {	/* |x| < 1 */
+			D_RE(ans) = acos(x);
+			D_IM(ans) = zero;
+		} else {
+			D_RE(ans) = zero;
+			if (ix >= 0x43500000)	/* |x| >= 2**54 */
+				D_IM(ans) = ln2 + log(x);
+			else if (ix >= 0x3ff80000)	/* x > Acrossover */
+				D_IM(ans) = log(x + sqrt((x - one) * (x +
+					one)));
+			else {
+				xm1 = x - one;
+				D_IM(ans) = log1p(xm1 + sqrt(xm1 * (x + one)));
+			}
+		}
+	} else if (y <= E * fabs(x - one)) {	/* region 2: y < tiny*|x-1| */
+		if (ix < 0x3ff00000) {	/* x < 1 */
+			D_RE(ans) = acos(x);
+			D_IM(ans) = y / sqrt((one + x) * (one - x));
+		} else if (ix >= 0x43500000) {	/* |x| >= 2**54 */
+			D_RE(ans) = y / x;
+			D_IM(ans) = ln2 + log(x);
+		} else {
+			t = sqrt((x - one) * (x + one));
+			D_RE(ans) = y / t;
+			if (ix >= 0x3ff80000)	/* x > Acrossover */
+				D_IM(ans) = log(x + t);
+			else
+				D_IM(ans) = log1p((x - one) + t);
+		}
+	} else if (y < Foursqrtu) {	/* region 3 */
+		t = sqrt(y);
+		D_RE(ans) = t;
+		D_IM(ans) = t;
+	} else if (E * y - one >= x) {	/* region 4 */
+		D_RE(ans) = pi_2;
+		D_IM(ans) = ln2 + log(y);
+	} else if (ix >= 0x5fc00000 || iy >= 0x5fc00000) {	/* x,y>2**509 */
+		/* region 5: x+1 or y is very large (>= sqrt(max)/8) */
+		t = x / y;
+		D_RE(ans) = atan(y / x);
+		D_IM(ans) = ln2 + log(y) + half * log1p(t * t);
+	} else if (x < Foursqrtu) {
+		/* region 6: x is very small, < 4sqrt(min) */
+		D_RE(ans) = pi_2;
+		A = sqrt(one + y * y);
+		if (iy >= 0x3ff80000)	/* if y > Acrossover */
+			D_IM(ans) = log(y + A);
+		else
+			D_IM(ans) = half * log1p((y + y) * (y + A));
+	} else {	/* safe region */
+		y2 = y * y;
+		xp1 = x + one;
+		xm1 = x - one;
+		R = sqrt(xp1 * xp1 + y2);
+		S = sqrt(xm1 * xm1 + y2);
+		A = half * (R + S);
+		B = x / A;
+		if (B <= Bcrossover)
+			D_RE(ans) = acos(B);
+		else {		/* use atan and an accurate approx to a-x */
+			Apx = A + x;
+			if (x <= one)
+				D_RE(ans) = atan(sqrt(half * Apx * (y2 / (R +
+					xp1) + (S - xm1))) / x);
+			else
+				D_RE(ans) = atan((y * sqrt(half * (Apx / (R +
+					xp1) + Apx / (S + xm1)))) / x);
+		}
+		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));
+			D_IM(ans) = log1p(Am1 + sqrt(Am1 * (A + one)));
+		} else {
+			D_IM(ans) = log(A + sqrt(A * A - one));
+		}
+	}
+	if (hx < 0)
+		D_RE(ans) = pi - D_RE(ans);
+	if (hy >= 0)
+		D_IM(ans) = -D_IM(ans);
+	return (ans);
+}
