/*
* 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 __csqrt = csqrt
/* INDENT OFF */
/*
* dcomplex csqrt(dcomplex z);
*
* 2 2 2
* Let w=r+i*s = sqrt(x+iy). Then (r + i s) = r - s + i 2sr = x + i y.
*
* Hence x = r*r-s*s, y = 2sr.
*
* Note that x*x+y*y = (s*s+r*r)**2. Thus, we have
* ________
* 2 2 / 2 2
* (1) r + s = \/ x + y ,
*
* 2 2
* (2) r - s = x
*
* (3) 2sr = y.
*
* Perform (1)-(2) and (1)+(2), we obtain
*
* 2
* (4) 2 r = hypot(x,y)+x,
*
* 2
* (5) 2*s = hypot(x,y)-x
* ________
* / 2 2
* where hypot(x,y) = \/ x + y .
*
* In order to avoid numerical cancellation, we use formula (4) for
* positive x, and (5) for negative x. The other component is then
* computed by formula (3).
*
*
* ALGORITHM
* ------------------
*
* (assume x and y are of medium size, i.e., no over/underflow in squaring)
*
* If x >=0 then
* ________
* / 2 2
* 2 \/ x + y + x y
* r = ---------------------, s = -------; (6)
* 2 2 r
*
* (note that we choose sign(s) = sign(y) to force r >=0).
* Otherwise,
* ________
* / 2 2
* 2 \/ x + y - x y
* s = ---------------------, r = -------; (7)
* 2 2 s
*
* EXCEPTION:
*
* One may use the polar coordinate of a complex number to justify the
* following exception cases:
*
* EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)):
* csqrt(+-0+ i 0 ) = 0 + i 0
* csqrt( x + i inf ) = inf + i inf for all x (including NaN)
* csqrt( x + i NaN ) = NaN + i NaN with invalid for finite x
* csqrt(-inf+ iy ) = 0 + i inf for finite positive-signed y
* csqrt(+inf+ iy ) = inf + i 0 for finite positive-signed y
* csqrt(-inf+ i NaN) = NaN +-i inf
* csqrt(+inf+ i NaN) = inf + i NaN
* csqrt(NaN + i y ) = NaN + i NaN for finite y
* csqrt(NaN + i NaN) = NaN + i NaN
*/
/* INDENT ON */
#include "libm.h" /* fabs/sqrt */
#include "complex_wrapper.h"
/* INDENT OFF */
static const double
two300 = 2.03703597633448608627e+90,
twom300 = 4.90909346529772655310e-91,
two599 = 2.07475778444049647926e+180,
twom601 = 1.20495993255144205887e-181,
two = 2.0,
zero = 0.0,
half = 0.5;
/* INDENT ON */
dcomplex
csqrt(dcomplex z) {
dcomplex ans;
double x, y, t, ax, ay;
int n, ix, iy, hx, hy, lx, ly;
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;
ay = fabs(y);
ax = fabs(x);
if (ix >= 0x7ff00000 || iy >= 0x7ff00000) {
/* x or y is Inf or NaN */
if (ISINF(iy, ly))
D_IM(ans) = D_RE(ans) = ay;
else if (ISINF(ix, lx)) {
if (hx > 0) {
D_RE(ans) = ax;
D_IM(ans) = ay * zero;
} else {
D_RE(ans) = ay * zero;
D_IM(ans) = ax;
}
} else
D_IM(ans) = D_RE(ans) = ax + ay;
} else if ((iy | ly) == 0) { /* y = 0 */
if (hx >= 0) {
D_RE(ans) = sqrt(ax);
D_IM(ans) = zero;
} else {
D_IM(ans) = sqrt(ax);
D_RE(ans) = zero;
}
} else if (ix >= iy) {
n = (ix - iy) >> 20;
if (n >= 30) { /* x >> y or y=0 */
t = sqrt(ax);
} else if (ix >= 0x5f300000) { /* x > 2**500 */
ax *= twom601;
y *= twom601;
t = two300 * sqrt(ax + sqrt(ax * ax + y * y));
} else if (iy < 0x20b00000) { /* y < 2**-500 */
ax *= two599;
y *= two599;
t = twom300 * sqrt(ax + sqrt(ax * ax + y * y));
} else
t = sqrt(half * (ax + sqrt(ax * ax + ay * ay)));
if (hx >= 0) {
D_RE(ans) = t;
D_IM(ans) = ay / (t + t);
} else {
D_IM(ans) = t;
D_RE(ans) = ay / (t + t);
}
} else {
n = (iy - ix) >> 20;
if (n >= 30) { /* y >> x */
if (n >= 60)
t = sqrt(half * ay);
else if (iy >= 0x7fe00000)
t = sqrt(half * ay + half * ax);
else if (ix <= 0x00100000)
t = half * sqrt(two * (ay + ax));
else
t = sqrt(half * (ay + ax));
} else if (iy >= 0x5f300000) { /* y > 2**500 */
ax *= twom601;
y *= twom601;
t = two300 * sqrt(ax + sqrt(ax * ax + y * y));
} else if (ix < 0x20b00000) { /* x < 2**-500 */
ax *= two599;
y *= two599;
t = twom300 * sqrt(ax + sqrt(ax * ax + y * y));
} else
t = sqrt(half * (ax + sqrt(ax * ax + ay * ay)));
if (hx >= 0) {
D_RE(ans) = t;
D_IM(ans) = ay / (t + t);
} else {
D_IM(ans) = t;
D_RE(ans) = ay / (t + t);
}
}
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}