1 /* origin: OpenBSD /usr/src/lib/libm/src/s_catanf.c */
3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5 * Permission to use, copy, modify, and distribute this software for any
6 * purpose with or without fee is hereby granted, provided that the above
7 * copyright notice and this permission notice appear in all copies.
9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
18 * Complex circular arc tangent
23 * float complex catanf();
36 * Re w = - arctan(-----------) + k PI
42 * Im w = - log(------------)
46 * Where k is an arbitrary integer.
52 * arithmetic domain # trials peak rms
53 * IEEE -10,+10 30000 2.3e-6 5.2e-8
56 #include "complex_impl.h"
58 #define MAXNUMF 1.0e38F
60 static const double DP1
= 3.140625;
61 static const double DP2
= 9.67502593994140625E-4;
62 static const double DP3
= 1.509957990978376432E-7;
64 static float _redupif(float xx
)
76 i
= t
; /* the multiple */
78 t
= ((x
- t
* DP1
) - t
* DP2
) - t
* DP3
;
82 float complex catanf(float complex z
)
90 if ((x
== 0.0f
) && (y
> 1.0f
))
94 a
= 1.0f
- x2
- (y
* y
);
98 t
= 0.5f
* atan2f(2.0f
* x
, a
);
107 a
= (x2
+ (t
* t
))/a
;
108 w
= w
+ (0.25f
* logf (a
)) * I
;
113 w
= MAXNUMF
+ MAXNUMF
* I
;