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      1 /* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */
      2 
      3 /*-
      4  * Copyright (c) 2007 The NetBSD Foundation, Inc.
      5  * All rights reserved.
      6  *
      7  * This code is derived from software written by Stephen L. Moshier.
      8  * It is redistributed by the NetBSD Foundation by permission of the author.
      9  *
     10  * Redistribution and use in source and binary forms, with or without
     11  * modification, are permitted provided that the following conditions
     12  * are met:
     13  * 1. Redistributions of source code must retain the above copyright
     14  *    notice, this list of conditions and the following disclaimer.
     15  * 2. Redistributions in binary form must reproduce the above copyright
     16  *    notice, this list of conditions and the following disclaimer in the
     17  *    documentation and/or other materials provided with the distribution.
     18  *
     19  * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
     20  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
     21  * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
     22  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
     23  * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
     24  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
     25  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     26  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     27  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     28  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     29  * POSSIBILITY OF SUCH DAMAGE.
     30  */
     31 
     32 #include "../src/namespace.h"
     33 #include <complex.h>
     34 #include <math.h>
     35 #include "cephes_subr.h"
     36 
     37 /* calculate cosh and sinh */
     38 
     39 void
     40 _cchsh(double x, double *c, double *s)
     41 {
     42 	double e, ei;
     43 
     44 	if (fabs(x) <= 0.5) {
     45 		*c = cosh(x);
     46 		*s = sinh(x);
     47 	} else {
     48 		e = exp(x);
     49 		ei = 0.5 / e;
     50 		e = 0.5 * e;
     51 		*s = e - ei;
     52 		*c = e + ei;
     53 	}
     54 }
     55 
     56 /* Program to subtract nearest integer multiple of PI */
     57 
     58 /* extended precision value of PI: */
     59 static const double DP1 = 3.14159265160560607910E0;
     60 static const double DP2 = 1.98418714791870343106E-9;
     61 static const double DP3 = 1.14423774522196636802E-17;
     62 #define MACHEP 1.1e-16
     63 
     64 double
     65 _redupi(double x)
     66 {
     67 	double t;
     68 	long i;
     69 
     70 	t = x / M_PI;
     71 	if (t >= 0.0)
     72 		t += 0.5;
     73 	else
     74 		t -= 0.5;
     75 
     76 	i = t;	/* the multiple */
     77 	t = i;
     78 	t = ((x - t * DP1) - t * DP2) - t * DP3;
     79 	return t;
     80 }
     81 
     82 /* Taylor series expansion for cosh(2y) - cos(2x) */
     83 
     84 double
     85 _ctans(double complex z)
     86 {
     87 	double f, x, x2, y, y2, rn, t;
     88 	double d;
     89 
     90 	x = fabs(2.0 * creal(z));
     91 	y = fabs(2.0 * cimag(z));
     92 
     93 	x = _redupi(x);
     94 
     95 	x = x * x;
     96 	y = y * y;
     97 	x2 = 1.0;
     98 	y2 = 1.0;
     99 	f = 1.0;
    100 	rn = 0.0;
    101 	d = 0.0;
    102 	do {
    103 		rn += 1.0;
    104 		f *= rn;
    105 		rn += 1.0;
    106 		f *= rn;
    107 		x2 *= x;
    108 		y2 *= y;
    109 		t = y2 + x2;
    110 		t /= f;
    111 		d += t;
    112 
    113 		rn += 1.0;
    114 		f *= rn;
    115 		rn += 1.0;
    116 		f *= rn;
    117 		x2 *= x;
    118 		y2 *= y;
    119 		t = y2 - x2;
    120 		t /= f;
    121 		d += t;
    122 	} while (fabs(t/d) > MACHEP);
    123 	return d;
    124 }
    125