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s_cexpl.c revision 1.1 
      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 #ifdef __i386__
     35 #include <ieeefp.h>
     36 #endif
     37 
     38 #include "fpmath.h"
     39 #include "math.h"
     40 #include "math_private.h"
     41 #include "k_expl.h"
     42 
     43 long double complex
     44 cexpl (long double complex z)
     45 {
     46 	long double c, exp_x, s, x, y;
     47 	uint64_t lx, ly;
     48 	uint16_t hx, hy;
     49 
     50 	ENTERI();
     51 
     52 	x = creall(z);
     53 	y = cimagl(z);
     54 
     55 	EXTRACT_LDBL80_WORDS(hy, ly, y);
     56 	hy &= 0x7fff;
     57 
     58 	/* cexp(x + I 0) = exp(x) + I 0 */
     59 	if ((hy | ly) == 0)
     60 		RETURNI(CMPLXL(expl(x), y));
     61 	EXTRACT_LDBL80_WORDS(hx, lx, x);
     62 	/* cexp(0 + I y) = cos(y) + I sin(y) */
     63 	if (((hx & 0x7fff) | lx) == 0) {
     64 		sincosl(y, &s, &c);
     65 		RETURNI(CMPLXL(c, s));
     66 	}
     67 
     68 	if (hy >= 0x7fff) {
     69 		if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
     70 		    (lx & 0x7fffffffffffffffULL) != 0)) {
     71 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
     72 			RETURNI(CMPLXL(y - y, y - y));
     73 		} else if (hx & 0x8000) {
     74 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
     75 			RETURNI(CMPLXL(0.0, 0.0));
     76 		} else {
     77 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
     78 			RETURNI(CMPLXL(x, y - y));
     79 		}
     80 	}
     81 
     82 	/*
     83 	 *  exp_ovfl = 11356.5234062941439497
     84 	 * cexp_ovfl = 22755.3287906024445633
     85 	 */
     86 	if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
     87 	    (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
     88 		/*
     89 		 * x is between exp_ovfl and cexp_ovfl, so we must scale to
     90 		 * avoid overflow in exp(x).
     91 		 */
     92 		RETURNI(__ldexp_cexpl(z, 0));
     93 	} else {
     94 		/*
     95 		 * Cases covered here:
     96 		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
     97 		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
     98 		 *  -  x = +-Inf (generated by exp())
     99 		 *  -  x = NaN (spurious inexact exception from y)
    100 		 */
    101 		exp_x = expl(x);
    102 		sincosl(y, &s, &c);
    103 		RETURNI(CMPLXL(exp_x * c, exp_x * s));
    104 	}
    105 }
    106