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      1 /*-
      2  * SPDX-License-Identifier: BSD-2-Clause
      3  *
      4  * Copyright (c) 2019 Steven G. Kargl <kargl (at) FreeBSD.ORG>
      5  * All rights reserved.
      6  *
      7  * Redistribution and use in source and binary forms, with or without
      8  * modification, are permitted provided that the following conditions
      9  * are met:
     10  * 1. Redistributions of source code must retain the above copyright
     11  *    notice, this list of conditions and the following disclaimer.
     12  * 2. Redistributions in binary form must reproduce the above copyright
     13  *    notice, this list of conditions and the following disclaimer in the
     14  *    documentation and/or other materials provided with the distribution.
     15  *
     16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
     17  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     18  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     19  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
     20  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     21  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     22  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     23  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     24  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     25  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     26  * SUCH DAMAGE.
     27  */
     28 
     29 #include <sys/cdefs.h>
     30 #include <complex.h>
     31 #include <float.h>
     32 #include <math.h>
     33 
     34 #include "math_private.h"
     35 #include "k_expl.h"
     36 
     37 /* XXX cexpl() should be converted to use bits likeo src/s_cexp.c. */
     38 
     39 static const long double
     40 cexp_ovfl = 2.27892930024498818830197576893019292e+04L,
     41 exp_ovfl = 1.13565234062941439494919310779707649e+04L;
     42 
     43 long double complex
     44 cexpl(long double complex z)
     45 {
     46 	long double c, exp_x, s, x, y;
     47 
     48 	x = creall(z);
     49 	y = cimagl(z);
     50 
     51 	/* cexp(x + I 0) = exp(x) + I 0 */
     52 	if (y == 0)
     53 		return (CMPLXL(expl(x), y));
     54 	/* cexp(0 + I y) = cos(y) + I sin(y) */
     55 	if (x == 0) {
     56 		sincosl(y, &s, &c);
     57 		return (CMPLXL(c, s));
     58 	}
     59 
     60 	if (!isfinite(y)) {
     61 		if (isfinite(x) || isnan(x)) {
     62 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
     63 			return (CMPLXL(y - y, y - y));
     64 		} else if (isinf(x) && copysignl(1.L, x) < 0) {
     65 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
     66 			return (CMPLXL(0.0, 0.0));
     67 		} else {
     68 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
     69 			return (CMPLXL(x, y - y));
     70 		}
     71 	}
     72 
     73 	if (x > exp_ovfl && x < cexp_ovfl) {
     74 		/*
     75 		 * x is between exp_ovfl and cexp_ovfl, so we must scale to
     76 		 * avoid overflow in exp(x).
     77 		 */
     78 		return (__ldexp_cexpl(z, 0));
     79 	} else {
     80 		/*
     81 		 * Cases covered here:
     82 		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
     83 		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
     84 		 *  -  x = +-Inf (generated by exp())
     85 		 *  -  x = NaN (spurious inexact exception from y)
     86 		 */
     87 		exp_x = expl(x);
     88 		sincosl(y, &s, &c);
     89 		return (CMPLXL(exp_x * c, exp_x * s));
     90 	}
     91 }
     92