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      1 /*-
      2  * Copyright (c) 2007 David Schultz <das (at) FreeBSD.ORG>
      3  * All rights reserved.
      4  *
      5  * Redistribution and use in source and binary forms, with or without
      6  * modification, are permitted provided that the following conditions
      7  * are met:
      8  * 1. Redistributions of source code must retain the above copyright
      9  *    notice, this list of conditions and the following disclaimer.
     10  * 2. Redistributions in binary form must reproduce the above copyright
     11  *    notice, this list of conditions and the following disclaimer in the
     12  *    documentation and/or other materials provided with the distribution.
     13  *
     14  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
     15  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     16  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     17  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
     18  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     19  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     20  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     21  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     22  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     23  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     24  * SUCH DAMAGE.
     25  */
     26 
     27 #include <sys/cdefs.h>
     28 __FBSDID("$FreeBSD$");
     29 
     30 #include <complex.h>
     31 #include <math.h>
     32 
     33 #include "math_private.h"
     34 
     35 /*
     36  * gcc doesn't implement complex multiplication or division correctly,
     37  * so we need to handle infinities specially. We turn on this pragma to
     38  * notify conforming c99 compilers that the fast-but-incorrect code that
     39  * gcc generates is acceptable, since the special cases have already been
     40  * handled.
     41  */
     42 #pragma	STDC CX_LIMITED_RANGE	ON
     43 
     44 float complex
     45 csqrtf(float complex z)
     46 {
     47 	float a = crealf(z), b = cimagf(z);
     48 	double t;
     49 
     50 	/* Handle special cases. */
     51 	if (z == 0)
     52 		return (cpackf(0, b));
     53 	if (isinf(b))
     54 		return (cpackf(INFINITY, b));
     55 	if (isnan(a)) {
     56 		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
     57 		return (cpackf(a, t));	/* return NaN + NaN i */
     58 	}
     59 	if (isinf(a)) {
     60 		/*
     61 		 * csqrtf(inf + NaN i)  = inf +  NaN i
     62 		 * csqrtf(inf + y i)    = inf +  0 i
     63 		 * csqrtf(-inf + NaN i) = NaN +- inf i
     64 		 * csqrtf(-inf + y i)   = 0   +  inf i
     65 		 */
     66 		if (signbit(a))
     67 			return (cpackf(fabsf(b - b), copysignf(a, b)));
     68 		else
     69 			return (cpackf(a, copysignf(b - b, b)));
     70 	}
     71 	/*
     72 	 * The remaining special case (b is NaN) is handled just fine by
     73 	 * the normal code path below.
     74 	 */
     75 
     76 	/*
     77 	 * We compute t in double precision to avoid overflow and to
     78 	 * provide correct rounding in nearly all cases.
     79 	 * This is Algorithm 312, CACM vol 10, Oct 1967.
     80 	 */
     81 	if (a >= 0) {
     82 		t = sqrt((a + hypot(a, b)) * 0.5);
     83 		return (cpackf(t, b / (2.0 * t)));
     84 	} else {
     85 		t = sqrt((-a + hypot(a, b)) * 0.5);
     86 		return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
     87 	}
     88 }
     89