xref: /illumos-gate/usr/src/lib/libm/common/complex/casinl.c (revision ddc0e0b5)

/*
 * 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);
}