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      1 /*-
      2  * SPDX-License-Identifier: BSD-2-Clause
      3  *
      4  * Copyright (c) 2011 David Schultz <das (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  * src/s_cexp.c converted to long double complex by Steven G. Kargl
     29  */
     30 
     31 #include <sys/cdefs.h>
     32 #include <complex.h>
     33 #include <float.h>
     34 
     35 #include "fpmath.h"
     36 #include "math.h"
     37 #include "math_private.h"
     38 #include "k_expl.h"
     39 
     40 long double complex
     41 cexpl (long double complex z)
     42 {
     43 	long double c, exp_x, s, x, y;
     44 	uint64_t lx, ly;
     45 	uint16_t hx, hy;
     46 
     47 	ENTERI();
     48 
     49 	x = creall(z);
     50 	y = cimagl(z);
     51 
     52 	EXTRACT_LDBL80_WORDS(hy, ly, y);
     53 	hy &= 0x7fff;
     54 
     55 	/* cexp(x + I 0) = exp(x) + I 0 */
     56 	if ((hy | ly) == 0)
     57 		RETURNI(CMPLXL(expl(x), y));
     58 	EXTRACT_LDBL80_WORDS(hx, lx, x);
     59 	/* cexp(0 + I y) = cos(y) + I sin(y) */
     60 	if (((hx & 0x7fff) | lx) == 0) {
     61 		sincosl(y, &s, &c);
     62 		RETURNI(CMPLXL(c, s));
     63 	}
     64 
     65 	if (hy >= 0x7fff) {
     66 		if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
     67 		    (lx & 0x7fffffffffffffffULL) != 0)) {
     68 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
     69 			RETURNI(CMPLXL(y - y, y - y));
     70 		} else if (hx & 0x8000) {
     71 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
     72 			RETURNI(CMPLXL(0.0, 0.0));
     73 		} else {
     74 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
     75 			RETURNI(CMPLXL(x, y - y));
     76 		}
     77 	}
     78 
     79 	/*
     80 	 *  exp_ovfl = 11356.5234062941439497
     81 	 * cexp_ovfl = 22755.3287906024445633
     82 	 */
     83 	if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
     84 	    (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
     85 		/*
     86 		 * x is between exp_ovfl and cexp_ovfl, so we must scale to
     87 		 * avoid overflow in exp(x).
     88 		 */
     89 		RETURNI(__ldexp_cexpl(z, 0));
     90 	} else {
     91 		/*
     92 		 * Cases covered here:
     93 		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
     94 		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
     95 		 *  -  x = +-Inf (generated by exp())
     96 		 *  -  x = NaN (spurious inexact exception from y)
     97 		 */
     98 		exp_x = expl(x);
     99 		sincosl(y, &s, &c);
    100 		RETURNI(CMPLXL(exp_x * c, exp_x * s));
    101 	}
    102 }
    103