/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License, Version 1.0 only
* (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
* 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 2003 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma ident "%Z%%M% %I% %E% SMI"
/*
* _D_cplx_div(z, w) returns z / w with infinities handled according
* to C99.
*
* If z and w are both finite and w is nonzero, _D_cplx_div(z, w)
* delivers the complex quotient q according to the usual formula:
* let a = Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x +
* I * y where x = (a * c + b * d) / r and y = (b * c - a * d) / r
* with r = c * c + d * d. This implementation scales to avoid
* premature underflow or overflow.
*
* If z is neither NaN nor zero and w is zero, or if z is infinite
* and w is finite and nonzero, _D_cplx_div delivers an infinite
* result. If z is finite and w is infinite, _D_cplx_div delivers
* a zero result.
*
* If z and w are both zero or both infinite, or if either z or w is
* a complex NaN, _D_cplx_div delivers NaN + I * NaN. C99 doesn't
* specify these cases.
*
* This implementation can raise spurious underflow, overflow, in-
* valid operation, inexact, and division-by-zero exceptions. C99
* allows this.
*
* Warning: Do not attempt to "optimize" this code by removing multi-
* plications by zero.
*/
#endif
static union {
int i[2];
double d;
} inf = {
0x7ff00000, 0
};
/*
* Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
*/
static int
testinf(double x)
{
union {
int i[2];
double d;
} xx;
xx.d = x;
}
double _Complex
_D_cplx_div(double _Complex z, double _Complex w)
{
double _Complex v;
union {
int i[2];
double d;
double a, b, c, d, r;
/*
* The following is equivalent to
*
* a = creal(z); b = cimag(z);
* c = creal(w); d = cimag(w);
*/
a = ((double *)&z)[0];
b = ((double *)&z)[1];
c = ((double *)&w)[0];
d = ((double *)&w)[1];
/* extract high-order words to estimate |z| and |w| */
aa.d = a;
bb.d = b;
cc.d = c;
dd.d = d;
/* check for special cases */
r = 0.0;
i = testinf(c);
j = testinf(d);
if (i | j) { /* w is infinite */
/*
* "factor out" infinity, being careful to preserve
* signs of finite values
*/
if (hz >= 0x7fe00000) {
/* scale to avoid overflow below */
c *= 0.5;
d *= 0.5;
}
}
((double *)&v)[0] = (a * c + b * d) * r;
((double *)&v)[1] = (b * c - a * d) * r;
return (v);
}
if (hw < 0x00100000) {
/*
* This nonsense is needed to work around some SPARC
* implementations of nonstandard mode; if both parts
* of w are subnormal, multiply them by one to force
* them to be flushed to zero when nonstandard mode
* is enabled. Sheesh.
*/
cc.d = c = c * 1.0;
dd.d = d = d * 1.0;
}
/* w is zero; multiply z by 1/Re(w) - I * Im(w) */
c = 1.0 / c;
i = testinf(a);
j = testinf(b);
if (i | j) { /* z is infinite */
a = i;
b = j;
}
((double *)&v)[0] = a * c + b * d;
((double *)&v)[1] = b * c - a * d;
return (v);
}
r = 1.0;
i = testinf(a);
j = testinf(b);
if (i | j) { /* z is infinite */
a = i;
b = j;
r = inf.d;
}
((double *)&v)[0] = (a * c + b * d) * r;
((double *)&v)[1] = (b * c - a * d) * r;
return (v);
}
/*
* Scale c and d to compute 1/|w|^2 and the real and imaginary
* parts of the quotient.
*
* Note that for any s, if we let c' = sc, d' = sd, c'' = sc',
* and d'' = sd', then
*
* (ac'' + bd'') / (c'^2 + d'^2) = (ac + bd) / (c^2 + d^2)
*
* and similarly for the imaginary part of the quotient. We want
* to choose s such that (i) r := 1/(c'^2 + d'^2) can be computed
* without overflow or harmful underflow, and (ii) (ac'' + bd'')
* and (bc'' - ad'') can be computed without spurious overflow or
* harmful underflow. To avoid unnecessary rounding, we restrict
* s to a power of two.
*
* To satisfy (i), we need to choose s such that max(|c'|,|d'|)
* is not too far from one. To satisfy (ii), we need to choose
* s such that max(|c''|,|d''|) is also not too far from one.
* There is some leeway in our choice, but to keep the logic
* from getting overly complicated, we simply attempt to roughly
* balance these constraints by choosing s so as to make r about
* the same size as max(|c''|,|d''|). This corresponds to choos-
* ing s to be a power of two near |w|^(-3/4).
*
* Regarding overflow, observe that if max(|c''|,|d''|) <= 1/2,
* then the computation of (ac'' + bd'') and (bc'' - ad'') can-
* not overflow; otherwise, the computation of either of these
* values can only incur overflow if the true result would be
* within a factor of two of the overflow threshold. In other
* words, if we bias the choice of s such that at least one of
*
* max(|c''|,|d''|) <= 1/2 or r >= 2
*
* always holds, then no undeserved overflow can occur.
*
* To cope with underflow, note that if r < 2^-53, then any
* intermediate results that underflow are insignificant; either
* they will be added to normal results, rendering the under-
* flow no worse than ordinary roundoff, or they will contribute
* to a final result that is smaller than the smallest subnormal
* number. Therefore, we need only modify the preceding logic
* when z is very small and w is not too far from one. In that
* case, we can reduce the effect of any intermediate underflow
* to no worse than ordinary roundoff error by choosing s so as
* to make max(|c''|,|d''|) large enough that at least one of
* (ac'' + bd'') or (bc'' - ad'') is normal.
*/
+ 0x3ff00000;
}
ss.i[1] = 0;
c *= ss.d;
d *= ss.d;
r = 1.0 / (c * c + d * d);
c *= ss.d;
d *= ss.d;
((double *)&v)[0] = (a * c + b * d) * r;
((double *)&v)[1] = (b * c - a * d) * r;
return (v);
}